Pietro MeloniPhD

52 ideas · A.2 · 2025 syllabus

IB Physics IA ideas: forces and momentum

Forces and momentum is the largest pool of IA ideas, because friction, drag, buoyancy and collisions can all be measured with school kit. The risk is the opposite: examiners have seen most of them, so the design has to be sharper than average.

By Pietro Meloni, PhD · Updated on 26 September 2026

52 of 52 ideas

A.2 Forces and momentum: 52 ideas

Falling-sphere viscosity of honey across temperature

Research question. How does the dynamic viscosity of honey, found from the terminal speed of a 3 mm steel ball, vary between 20 °C and 60 °C in 5 °C steps?

A.2 Forces and momentum
SL and HL
Needs care
Overdone: on 5 sites

My take. Overdone (listed on 5 sites), and honey or oil with temperature is what examiners expect. Make it your own by verifying Stokes' law assumptions or by fitting an Arrhenius model, not by only plotting a trend.

Method, physics and where marks are lost+

Independent variable: Honey temperature, 20 to 60 °C in 5 °C steps (9 values), with 3 to 5 drops at each.
What you measure: Terminal speed from a video of the ball passing marked lines in a tall measuring cylinder, timed frame by frame. Viscosity calculated from Stokes' law with a buoyancy correction. Temperature read by a digital thermometer at mid-depth.
Controlled variables: Same honey batch and water content. Same ball diameter, checked with a micrometer, and released on the centre line. Cylinder wide enough that wall effects are small, or a wall correction applied. Timing only in the section where the speed is constant, checked from the video.
Physics and graph: Stokes: F = 6πηrv. At terminal speed, 2r²g(ρs − ρl)/(9v) = η. Plot ln η against 1/T, which should be roughly linear, for an Arrhenius-type gradient. A plot of η against T alone is curved, which is a useful point to discuss.
SL and HL: SL students give η against T and explain the falling trend. Higher marks come from testing the Stokes assumptions (terminal speed reached, Reynolds number small, wall correction) and the linearised ln η against 1/T graph with activation energy. HL gives no extra syllabus, but it suits deeper error analysis.
Where marks are lost: Research design: honey not uniform in temperature after heating, or no check that terminal speed is reached. Data analysis: ignoring the uncertainty of the measured speed and ball diameter. Conclusion: claiming a trend without a quantitative fit. Evaluation: not addressing the temperature drift during a drop.
Data: Needs a tall cylinder, a water bath, a phone camera and a micrometer; honey cools quickly and can be non-uniform, which is the main uncertainty.

Acceleration against sin θ on a friction-affected ramp

Research question. How does the acceleration of a dynamics trolley change as a track is tilted from 3° to 20°, and does the intercept on an a against sin θ graph reveal a rolling resistance force?

A.2 Forces and momentum
SL and HL
Easy data
Overdone: on 4 sites

My take. Common, so the version that works is the intercept one. The three variants about a golf ball, a block and friction coefficients are the same physics, and a friction coefficient from the intercept is a good twist.

Method, physics and where marks are lost+

Independent variable: Track angle, 3°, 5°, 8°, 11°, 14°, 17°, 20°, set by measuring height and length, with 5 runs per angle.
What you measure: Acceleration from two light gates, or from the gradient of a speed against time graph from a motion sensor. Sin θ is calculated from height divided by track length.
Controlled variables: Trolley mass fixed, with a check run with added mass. Same start position and the same distance between gates. Same track and wheels, cleaned each session. Angle checked before each release.
Physics and graph: ma = mg sinθ − F_r, so a = g sinθ − F_r/m. Plot a (y) against sinθ (x). The gradient should be g and the negative intercept is F_r/m. Do it for a second mass to test whether F_r changes.
SL and HL: SL students can obtain g and comment on the intercept. Reaching the top band means quantifying the friction force and its uncertainty. HL students can go further by including the rotational inertia of the wheels, which lowers the gradient below g.
Where marks are lost: Research design: angle chosen with a protractor on a steep range only. Data analysis: forcing the line through the origin. Conclusion: failing to explain a gradient below 9.81 m/s². Evaluation: this topic is overdone, so identical evaluation points lose impact.
Data: Uses a track, trolley and light gates or a phone video, and the main uncertainty is the angle from height measurements at shallow slopes.

Cantilever length and end deflection of a metal strip

Research question. How does the free length of a clamped steel strip (0.15 to 0.40 m, 6 lengths) affect its end deflection under a fixed 100 g load, and what Young's modulus follows?

A.2 Forces and momentum
SL and HL
Needs care
Common: on 3 sites

My take. A good choice as the cubic law gives a strong signal. Use several materials (steel, brass, aluminium) for a personal angle.

Method, physics and where marks are lost+

Independent variable: Free length L from 0.15 to 0.40 m in 0.05 m steps, 3 repeats each, on a strip clamped at a bench edge.
What you measure: End deflection measured with a rule against a fixed vertical scale or from a photograph, in mm. Young's modulus calculated from the gradient.
Controlled variables: Same strip, so width and thickness are fixed and measured with a micrometer. Same 100 g load hung at the end. Same clamp tightness. Deflection kept small so the response is elastic.
Physics and graph: For a cantilever δ = 4FL³/(Ewt³). Plot δ against L³; the gradient is 4F/(Ewt³), so E = 4F/(gradient × wt³). Compare with the tabulated value for steel.
SL and HL: SL students can do the cubic linearisation and estimate E. The top band handles the thickness uncertainty, which enters cubed, and the clamp not being perfectly rigid.
Where marks are lost: Research design: taking a beam supported at both ends and guessing the formula. Data analysis: not linearising the cube or ignoring the thickness uncertainty. Evaluation: strip weight adding its own sag.
Data: Needs a metal strip, clamp, micrometer and a way to read small deflection; thickness is the main uncertainty.

Drag on falling paper cones with changing area

Research question. How does the frontal area A of paper cones cut from circles of radius 6 cm to 12 cm, with the same mass, affect terminal speed, and is v proportional to 1/√A?

A.2 Forces and momentum
SL and HL
Needs care
Common: on 3 sites

My take. Worth doing if mass is truly controlled, which most students miss. Stay with paper cones, not footballs, because balls of different sizes differ in mass and surface.

Method, physics and where marks are lost+

Independent variable: Cone base area from 20 cm² to 100 cm², 6 to 8 values, made by cutting different sectors or sizes, with 5 drops each.
What you measure: Terminal speed from a video of the fall against a metre rule, using the linear part of the position time graph. Calculated quantity is 1/√A.
Controlled variables: Mass kept the same by adding small paper or clay ballast, checked on a 0.01 g balance. Same paper. Same drop height of about 2.5 m. Air movement kept low. Cone shape kept consistent.
Physics and graph: mg = ½ρC_D A v², so v = √(2mg/(ρC_D)) × A^−1/2. Plot v (y) against 1/√A (x) to get a straight line through the origin with gradient √(2mg/(ρC_D)).
SL and HL: SL students can show that terminal speed falls as area rises and test the line. Top band means holding mass fixed properly and discussing C_D. HL students can test alternative drag models with a log-log fit.
Where marks are lost: Research design: mass changes when area changes, so two variables move at once. Data analysis: no uncertainty for area. Conclusion: not linking the gradient to C_D. Evaluation: drift and tumbling not analysed.
Data: Needs a phone camera, a balance and paper, and the hardest thing is keeping mass constant across different cone sizes.

Ball spin and sideways drift in flight

Research question. How does the spin rate of a table tennis ball (about 5 to 30 rev/s, 6 values) affect its sideways deflection over a 1.5 m horizontal launch?

A.2 Forces and momentum
SL and HL
Hard data
Common: on 2 sites

My take. Interesting but hard to do cleanly. Do not follow the drop version, as it barely shows Magnus. Only choose it if you can build a repeatable launcher.

Method, physics and where marks are lost+

Independent variable: Spin rate, set with a spinning launcher of two wheels at different speeds, found from slow motion video at 240 fps. 6 settings, 5 launches each.
What you measure: Sideways or vertical deflection at a fixed distance, measured from video against a scale grid. Spin rate from counting marker rotations per second.
Controlled variables: Same ball and same launch speed, checked from video tracking. Room closed to stop draughts. Same launch height and angle. Same distance to the target grid.
Physics and graph: The Magnus force is proportional to spin and speed, so deflection d = ½at² with a = F/m. Plot deflection against spin rate; expect an approximate straight line at low spin.
SL and HL: SL students report deflection against spin and comment on the trend. Top band work estimates the lift coefficient and compares with a model, treating the change in launch speed as the wheels change.
Where marks are lost: Research design: a basketball dropped from height has almost no horizontal velocity, so the Magnus force is negligible. Data analysis: no uncertainty in spin from video. Evaluation: draughts and inconsistent launch speed.
Data: Needs a launcher and slow motion video; hard to hold launch speed constant while varying spin.

Friction of a wooden block as load increases

Research question. How does the normal force on a wooden block (load from 0.2 to 1.2 N in 6 steps by adding masses) affect the maximum static and the kinetic friction on a felt surface?

A.2 Forces and momentum
SL and HL
Easy data
Common: on 2 sites

My take. Simple and overdone, so it needs both static and kinetic values and a proper check of the intercept. Try an unusual surface pair for a personal angle.

Method, physics and where marks are lost+

Independent variable: Normal force, 6 to 8 values from added masses, each run at least 5 times.
What you measure: Force from a force sensor pulling the block steadily by string. Peak of the trace gives maximum static friction and the plateau gives kinetic friction.
Controlled variables: Same surface pair and the same contact area. Pulling speed kept slow and steady by a motor or by careful hand pulling. Same surface cleaned and reset between runs. Laboratory temperature and humidity noted.
Physics and graph: F ≤ μN. Plot both friction values against N; the gradients give μs and μk, and a non-zero intercept shows the model failing. Static should be above kinetic.
SL and HL: SL work compares both gradients and considers the intercept. Top band adds a second material or contact area and asks when friction is not proportional to N.
Where marks are lost: Research design: pulling by hand so speed varies. Data analysis: forcing the line through the origin. Evaluation: surface wear between runs, which changes μ.
Data: A force sensor makes it good; a newton meter works but reading the peak is difficult, and surface wear is the main uncertainty.

Terminal speed of stacked coffee filters against weight

Research question. How does the number of nested coffee filters, from 1 to 8, affect the terminal speed reached when dropped from 2.5 m, and does drag follow v² proportional to weight?

A.2 Forces and momentum
SL and HL
Needs care
Common: on 2 sites

My take. Popular and easy to run, so it needs the v² test to be worthwhile. Skip the toy parachute, balloon and marble variants as separate ideas. The marble in water is a different regime and needs a Stokes' law discussion.

Method, physics and where marks are lost+

Independent variable: Number of identical nested coffee filters, 1 to 8, so mass from about 1 g to 8 g, with 5 drops for each.
What you measure: Terminal speed from the slope of the position against time graph in phone video with a metre rule in view, using the last 1 m of fall. Calculated quantity is v², and weight W = mg from a balance.
Controlled variables: Same brand and shape of filter, nested the same way and held level. Same drop height and start. Windows and fans off, with the drop in a stairwell or a hall. Same camera position and frame rate.
Physics and graph: At terminal speed, mg = ½ρC_D A v², so v² = 2mg/(ρC_D A). Plot v² (y) against m (x). The gradient is 2g/(ρC_D A), giving C_D. A power law fit tests whether the exponent is 2.
SL and HL: SL students can show the linear v² against m trend and estimate C_D. To reach top band, discuss why the shape may change and whether the flow is quadratic drag. HL students can add the Reynolds number and a comparison of models.
Where marks are lost: Research design: dropping over too short a height so the filters never reach terminal speed. Data analysis: reading v from two points, not a fit. Conclusion: claiming a linear v against m trend without testing. Evaluation: not commenting on filters flipping or tumbling.
Data: A phone at 60 to 240 fps and a rule are enough, and the largest uncertainty is a filter that wobbles and drifts out of frame.

Whirled bung: force on the string against angular speed

Research question. How does the angular speed of a 50 g rubber bung on a 0.50 m radius (ω from about 4 to 14 rad/s, 6 values) affect the tension in its string, measured with a force sensor?

A.2 Forces and momentum
SL and HL
Needs care
Common: on 2 sites

My take. A sound choice if you have a proper rig. The twist is repeating with a different radius to test the mass times radius gradient.

Method, physics and where marks are lost+

Independent variable: Angular speed ω, set by timing 20 revolutions with a stopwatch or a phone video; 6 values with 3 repeats.
What you measure: Tension in the string from a force sensor mounted on the rotating arm or a turntable rig, in N. Compare with mω²r calculated from the timings.
Controlled variables: Mass of the bung fixed and weighed. Radius fixed by a marker on the string and checked from video. Circle kept horizontal by using a turntable or rigid arm. Same sensor zeroing before each run.
Physics and graph: F = mω²r. Plot F against ω²; the gradient should equal mr. Compare it with the value from the measured mass and radius.
SL and HL: SL students do the F against ω² graph and check the gradient. Top band work handles the string angle when the bung is swung by hand and treats the fixed uncertainty in period timing.
Where marks are lost: Research design: a hand-whirled bung does not stay horizontal, so the tension is not the centripetal force. Data analysis: plotting F against ω and calling it a curve without linearising. Evaluation: radius changing during the swing.
Data: A rotating rig with a force sensor is best; hand whirling is cheap but the angle and speed are hard to hold constant.

Acceleration of a trolley against net force and drag

Research question. How does the acceleration of a 0.50 kg dynamics trolley on a level track vary with driving force from 0.10 N to 0.60 N, with and without a card sail attached?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Solid and doable, but choose the constant-total-mass method and the drag extension or it is a textbook lab. Personalise it with a sail shape of your own design.

Method, physics and where marks are lost+

Independent variable: Driving force from hanging masses (10 g to 60 g in 10 g steps, weight transferred from trolley to hanger so total mass is constant), with two conditions: no sail and a fixed 10 cm by 10 cm card sail.
What you measure: Acceleration from a motion sensor or light gate velocity readings, or from video analysis in Tracker (m s⁻²), with three runs per value.
Controlled variables: Total system mass kept constant by moving masses between hanger and trolley. Track levelled or friction compensated and checked. Sail area and orientation fixed. Release point and distance the same.
Physics and graph: F = ma for the whole system. Plot a against F: gradient is 1/m. With a sail, the graph curves or has a lower gradient as drag grows with speed, which lets you estimate a drag coefficient from the deficit.
SL and HL: SL: a against F for the no-sail case and comparison of the gradient with 1/m. Top band: model drag as kv² and extract k, discuss friction as an intercept, and check that acceleration is uniform over the measured section.
Where marks are lost: Research design: the original wording of comparing 'types of force' is not measurable; also changing mass and force together. Data analysis: forcing the line through the origin. Conclusion: no comparison of the gradient with 1/m. Evaluation: ignoring pulley friction and string mass.
Data: Needs a dynamics track, trolley and either light gates or video; the main uncertainty is friction and short timing distances.

Apparent weight loss in liquids and Archimedes' principle

Research question. How does the upthrust on a fully submerged 100 g brass cylinder change with liquid density from 800 kg m⁻³ to 1250 kg m⁻³ using five liquids or salt solutions?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Simple but perfectly reasonable if density is measured rather than assumed. Make it personal with a real-world twist such as saltwater versus fresh water flotation, like the Dead Sea.

Method, physics and where marks are lost+

Independent variable: Liquid density: vegetable oil, ethanol solution, tap water, and three salt solutions at about 1050, 1150 and 1250 kg m⁻³, each density measured with a measuring cylinder and balance.
What you measure: Upthrust from the drop in reading on a newton meter or a top-pan balance (N), taken as weight in air minus apparent weight in liquid, with three repeats.
Controlled variables: Object: same cylinder, fully submerged and not touching the container. Depth: fixed with a marked string length. Temperature: same room, measured. Air bubbles: removed by tapping before reading.
Physics and graph: Upthrust = ρVg. Plot upthrust against liquid density: a straight line through the origin with gradient Vg, which gives the object's volume for comparison with the measured value.
SL and HL: SL: line through the origin and volume from the gradient. Top band: use a balance-based method to reduce reading error, discuss the effect of surface tension on the thread, and test partial submersion and depth as controls.
Where marks are lost: Research design: viscous syrup makes readings hard and mixes in a different variable; use densities you can measure. Data analysis: not measuring density directly. Conclusion: no comparison of gradient with Vg. Evaluation: ignoring bubbles and thread effects.
Data: Newton meter or top-pan balance, measuring cylinder and liquids; the main uncertainty is the coarse resolution of a newton meter, so a balance is preferred.

Ball size and momentum change from a fixed-energy launch

Research question. How does the radius of a ball, from 2 cm to 11 cm across at least five ball types, affect the impulse it receives from a spring-loaded striker released from the same compression?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Only worth choosing if you accept that radius is confounded with mass. The twist: make the question about mass and radius separately and pick the better plot.

Method, physics and where marks are lost+

Independent variable: Ball radius, five to six balls (for example ping pong, squash, tennis, softball, size 3 football and size 5 football), measured with vernier callipers.
What you measure: Launch speed from the distance between two light gates or 240 fps video over 0.5 m; impulse calculated as J = mv, with mass on a 0.1 g balance.
Controlled variables: Striker energy, using the same spring compression each release. Ball position on the striker, marked on the surface. Surface friction, using a smooth level track. Ball inflation, checked with a pressure gauge for the air-filled ones.
Physics and graph: Impulse equals change in momentum, J = Δp = mv. Balls differ in mass and elasticity as well as radius, so plot J against radius, then J against mass to see which is the real driver. A person kicking cannot give a fixed force, hence the spring striker.
SL and HL: SL: plot J against r and comment on scatter and other differences between balls. Top band: separate the effects of mass and stiffness with J against m, and test against an energy conservation model with restitution.
Where marks are lost: Research design: radius cannot be varied on its own since mass and material change too; kicking by foot is not repeatable. Conclusion: claiming radius is the cause. Data analysis: no propagation of uncertainty in speed.
Data: Requires a spring launcher, light gates or video, and a balance; the launch repeatability is about ±3%.

Bending of beams made of different materials

Research question. How does the Young modulus, found from the sag of a 50 cm strip clamped at one end, differ between pine, aluminium, steel and acrylic strips of equal width and thickness under loads of 50 g to 300 g?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Good if you restrict it to stiffness and avoid breaking things. Strength to failure is messy and not repeatable, so keep it to elastic behaviour.

Method, physics and where marks are lost+

Independent variable: Load hung at the free end, 6 values from 50 g to 300 g in 50 g steps, for each of 4 materials, with 3 repeats per load.
What you measure: Deflection of the free end, read with a metre rule against a fixed mark or from a photo. Young modulus is calculated from the gradient of load against deflection.
Controlled variables: Strip dimensions: measured with a micrometer and vernier caliper and kept the same. Clamped length: marked and fixed at 40 cm. Load position: hung at the same point each time. Temperature and time under load: read after 30 seconds each.
Physics and graph: For a cantilever, deflection δ = FL³/(3EI) with I = wt³/12. Plot δ against F, gradient L³/(3EI), so E = L³/(3 × gradient × I). Compare with tabulated E. Stay in the elastic range by checking that the strip returns to zero.
SL and HL: SL students can use the simpler tensile stress and strain idea with a wire and keep the beam as a comparison of stiffness. Top band work compares E with data tables, quantifies the uncertainty in the thickness which enters as t³, and checks the elastic limit.
Where marks are lost: Research design: several dimensions change between materials, so the comparison is not fair. Data analysis: thickness uncertainty ignored although cubed. Conclusion: claiming strength when only stiffness in the elastic range was measured. Evaluation: the clamp slips.
Data: Needs strips, a G-clamp, masses and a ruler, and the main uncertainty is the thickness measurement and clamp movement.

Bending stiffness of a plastic ruler at different temperatures

Research question. How does the temperature of a plastic ruler, from 5 °C to 60 °C, affect its Young's modulus as found from the sag under a fixed load?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. A creative idea, but strictly it fits mechanics of materials, which the syllabus only touches lightly. Manageable if you derive the beam formula and keep the temperature under tight control.

Method, physics and where marks are lost+

Independent variable: Temperature of the ruler: about 5, 15, 25, 35, 45, 60 °C (6 values), set using ice water, room air and a warm water bath, with the ruler dried and measured in the same setup within a short time.
What you measure: Deflection at the free end of a cantilever ruler under a fixed mass, read with a set square or from photographs against a scale. Young's modulus E = 4FL³/(w t³ δ) from the deflection, with width w and thickness t measured with a micrometer.
Controlled variables: Same ruler, clamped with the same overhang length. Same load, kept small so that deflection stays in the elastic range. Ruler thickness measured at several places. Time from bath to reading kept the same, as the ruler cools quickly.
Physics and graph: For a cantilever, δ = 4FL³/(E w t³), so E follows from measured deflection. Plot E against temperature, or plot 1/δ against temperature, since 1/δ is proportional to E. Discuss the change near the glass transition of the polymer.
SL and HL: SL: measure deflection at a range of temperatures and show the trend in E. Top band: check the linearity of force against deflection at one temperature first, and estimate the temperature of the ruler at measurement. The beam formula is not in the syllabus so it must be derived or sourced carefully.
Where marks are lost: Research design: the ruler cools or warms between the bath and the reading, so the recorded temperature is wrong. Data analysis: applying the formula without a consistent way of measuring thickness. Conclusion: extending a trend beyond the tested range. Evaluation: ignoring creep of the plastic under a constant load.
Data: Needs a plastic ruler, clamp, masses, a water bath and a thermometer; the main uncertainty is temperature loss and the small deflection.

Blood pressure reading against arm height above the heart

Research question. How does the systolic pressure reading from a digital cuff change when the cuffed wrist is held at heights from 40 cm below to 40 cm above heart level, in 10 cm steps?

A.2 Forces and momentum
SL and HL
Hard data
Rarely listed

My take. Risky but interesting. The result can be noisy, and the human participant needs approval, so I would only pick it with 5+ repeats. Comparing against ρgΔh gives a clear test.

Method, physics and where marks are lost+

Independent variable: Vertical height of the cuff relative to the heart, in 10 cm steps from -40 to +40 cm (9 values), measured with a metre rule against a fixed mark, with 3 readings each.
What you measure: Systolic pressure reading in mmHg from a wrist digital monitor, converted to pascals with 1 mmHg = 133 Pa.
Controlled variables: Participant: one volunteer, seated. Rest: 3 minutes between readings. Time of day: same hour, no caffeine. Cuff position on the wrist and arm support: same, with the arm relaxed.
Physics and graph: Hydrostatic pressure gives Δp = ρgΔh, with blood density about 1060 kg m⁻³. Plot pressure (y) against height (x); predicted gradient is ρg ≈ 7.8 mmHg per 10 cm ≈ 0.78 mmHg per cm. Compare the measured gradient with this.
SL and HL: SL students plot pressure against height and compare with ρg. Top band work discusses why the effect is smaller in living arteries and veins (valves, vessel tone), and treats the light-exercise data as a separate question.
Where marks are lost: Research design: consumer monitors have poor resolution and natural variation is often bigger than the effect. Data analysis: ignoring the spread between repeats. Evaluation: not discussing the ethics of medical measurements.
Data: Needs a wrist blood pressure monitor and a metre rule; readings vary by several mmHg between repeats, which may hide the trend.

Buoyant force on submerged cylinders of different volume

Research question. How does the volume of a fully submerged aluminium cylinder (5 to 40 cm³, 8 values) affect the apparent loss of weight measured on a newton meter in water?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Simple and safe, but it is a textbook check and will look thin unless you add a second fluid or a good uncertainty analysis. Twist: test the gradient against a salt solution of known density that you make yourself.

Method, physics and where marks are lost+

Independent variable: Volume of the submerged object, 5 to 40 cm³ in 8 steps, made by using cylinders of equal material and different lengths, or by stacking identical metal discs. Three repeats per volume.
What you measure: Weight in air and weight when fully submerged, read with a 0 to 5 N newton meter or a force sensor. Buoyant force is the difference. Compare with ρgV calculated from the measured volume.
Controlled variables: Fluid density: same tap water, temperature recorded. Full submersion with no contact with the beaker walls or base. Same suspension thread. Same reading procedure, eye level with the pointer, or a zeroed force sensor.
Physics and graph: Archimedes: F_b = ρ_fluid V g. Plot F_b (y) against V (x). It should be a straight line through the origin, and the gradient equals ρg, which can be compared with 9.81 × 1000 N m⁻³. Volume is best found from a measured displacement in a measuring cylinder as a cross-check.
SL and HL: An SL student can get a good line, a gradient and a percentage difference from ρg. Top band work checks the intercept, treats the thread and pointer uncertainties and repeats with a second liquid such as brine to show the gradient changes with density. Nothing here needs HL content.
Where marks are lost: Research design: small volume range so force differences are lost in the newton meter resolution. Data analysis: uncertainty in volume ignored. Conclusion: claiming Archimedes is confirmed without comparing the gradient to the accepted value. Evaluation: not discussing that the two supplied entries are the same investigation, and that force sensor resolution limits the small volumes.
Data: A newton meter, measuring cylinder and metal cylinders are enough, but a 0.05 N resolution makes small volumes poor, so a force sensor helps.

Cart collisions: mass ratio, restitution and momentum

Research question. How does the mass ratio of a moving cart to a stationary cart (from 0.25 to 4.0, 6 values) affect the coefficient of restitution in a head-on collision on a level track?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Choose it if you commit to one clear question, probably whether e depends on mass ratio, and show momentum as a check. The result that e stays constant is still a valid finding.

Method, physics and where marks are lost+

Independent variable: Mass of the target cart relative to the moving cart, from 0.25 to 4.0, by adding 0.25 to 1.0 kg masses. Each ratio repeated 5 times.
What you measure: Speeds before and after impact from two light gates or from Tracker on a video. Coefficient of restitution e = (relative speed after)/(relative speed before). Total momentum before and after is also calculated.
Controlled variables: Incoming speed: same push from a spring plunger. Track level: checked with a spirit level. Contact surfaces: same bumpers throughout. Mass of moving cart: fixed at 0.500 kg.
Physics and graph: Momentum is conserved: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. Restitution is e = (v₂ − v₁)/(u₁ − u₂). Plot e against mass ratio and see whether it is constant. Plot total momentum after against total momentum before, where the gradient should be 1. Kinetic energy loss can also be found.
SL and HL: SL students can check momentum and compute e. Better work explains why e might depend on mass ratio, if it does, through cart deformation and contact time. HL students may work in the centre of mass frame to analyse the energy loss.
Where marks are lost: Research design: two different questions (e and momentum) with no clear focus. Data analysis: light gates give speeds for the flag length only and the impact speed is ignored. Evaluation: ignores friction on wheels that makes the momentum before and after different.
Data: Needs a dynamics track, two light gates or video tracking; the main uncertainty is friction and speed measurement near the impact.

Comparing density methods for metals and plastics

Research question. How consistent are densities of six solid samples (aluminium, brass, steel, copper, acrylic, PVC) found by direct measurement of volume and by displacement in water, compared with data book values?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Too basic as stated, with little physics beyond a definition. Frame it as a method comparison using apparent weight in water, which links to A.2 buoyancy, or skip it.

Method, physics and where marks are lost+

Independent variable: Material of the sample: 6 different solids, each with 3 samples of different sizes to test that density does not depend on size, with each method repeated 3 times.
What you measure: Mass from a balance to 0.01 g, volume from callipers (regular shapes) and from a measuring cylinder or a eureka can (displacement); density is mass over volume for each method, with percentage difference to the data book.
Controlled variables: Water temperature: recorded and kept near room temperature. Air bubbles: samples tapped to remove them before reading. Reading position: at eye level of the meniscus. Sample surface: dried before weighing.
Physics and graph: ρ = m / V. Plot mass against volume for each material; the gradient is the density and the points should lie on a line through the origin. Alternatively compare the buoyancy method using apparent weight in water, W_app = W minus ρ_w V g.
SL and HL: SL students compare the two methods with uncertainties and a percentage difference. Higher marks come from a buoyancy-based third method and a clear argument about which method has the least uncertainty for small samples.
Where marks are lost: Research design: there is no real question beyond looking up densities. Data analysis: combining uncertainty in volume from three lengths incorrectly. Conclusion: not saying which method is better or by how much.
Data: Balance, vernier callipers, measuring cylinder and samples; the main uncertainty is the small volume for displacement, giving a large percentage error.

Cushion thickness and peak force in a crash

Research question. How does the thickness of a foam cushion (0.5 to 3.0 cm in 6 steps) affect the peak force on a 0.500 kg trolley that hits it at 1.0 m/s?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. A practical idea with a real world link and a clear check against theory. Worth choosing if your school has a fast force sensor.

Method, physics and where marks are lost+

Independent variable: Foam thickness from 0.5 to 3.0 cm, 6 values, made from stacks of equal foam sheets. Each value tested 5 times.
What you measure: Force from a force sensor with a data logger at 1000 Hz or more. Peak force is read from the graph; impulse is the area under the graph, compared with mΔv from the gate speeds.
Controlled variables: Impact speed: same release height on a ramp, checked with a light gate. Trolley mass: fixed at 0.500 kg. Foam type and area: same material cut to the same size. Rebound: check that the trolley does not bounce much.
Physics and graph: Impulse FΔt = Δp, so for the same Δp a longer collision time gives a lower average force. Plot peak force against 1/thickness or against collision time. Compare the impulse area with mΔv to test the method.
SL and HL: SL students can show the trend and compare impulse with change of momentum. Higher marks come from a model of the foam as a spring giving a time of contact and force. HL students can consider the foam as a damped spring.
Where marks are lost: Research design: impact speed is not the same between trials. Data analysis: sampling too slow so the peak is missed. Evaluation: the foam is compressed by earlier trials and changes.
Data: A force sensor with a fast logger is essential; the main uncertainty is sampling rate and foam wear over repeats.

Draining time of a bottle at different water heights

Research question. How does the starting water height h (6.0, 8.0, 10.0, 12.0, 14.0, 16.0 cm ± 0.1 cm) above a 4 mm side hole in a plastic bottle affect the initial volumetric flow rate, in cm³ s⁻¹?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Cheap, clear and testable against theory, which makes it a good choice if you do the Q² linearisation and the discharge coefficient. Make it personal by using a real bottle or a tank you have at home and comparing hole sizes.

Method, physics and where marks are lost+

Independent variable: Height of water above the hole, 6 values from 6.0 to 16.0 cm, each run 3 times, using a ruler taped to the bottle.
What you measure: Volume leaving in a fixed interval, measured with a measuring cylinder under the hole and a stopwatch (or phone video), giving flow rate Q = V/t. Also the range of the jet can be measured to get exit speed.
Controlled variables: Hole diameter: drilled once and checked with a calliper. Water temperature: measured with a thermometer before each run. Bottle shape: same cylindrical bottle, so the surface level drops slowly. Time interval: short (e.g. 5 s) so h barely changes.
Physics and graph: Torricelli's result v = √(2gh) follows from Bernoulli, and Q = Av. Plot Q² against h: a straight line through the origin with gradient 2gA². Compare the gradient with the measured hole area. Fluid dynamics is not formally in the syllabus, so energy conservation for a small parcel of water can be used as the argument.
SL and HL: SL: plot Q against h, find the trend, and test the square root shape. Top band, both levels: linearise, compare the gradient to 2gA², and discuss a discharge coefficient below 1 and the effect of viscosity and surface tension for a small hole.
Where marks are lost: Research design: letting h fall during a long collection so it is not a single height. Data analysis: uncertainty in timing a short interval is large and often ignored. Conclusion: claiming 'proportional' when the data fit √h. Evaluation: not commenting on why the measured gradient is below the theoretical value.
Data: A bottle, measuring cylinder, stopwatch and ruler are enough, but the main uncertainty is timing short collections and the falling water level.

Grease temperature and impact crater depth

Research question. How does the temperature of a tub of petroleum jelly, varied from 10 °C to 50 °C in steps of 10 °C, affect the depth of the crater made by a steel ball dropped from 0.50 m?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Worth choosing if you want something hands on and slightly messy. Make it personal by using a grease or food product you can justify, and be honest that you measure resistance to penetration, not true viscosity.

Method, physics and where marks are lost+

Independent variable: Temperature of the grease or petroleum jelly, 10, 20, 30, 40, 50 °C (5 values), set in a water bath, with 5 drops at each temperature.
What you measure: Crater depth in mm, measured with a depth gauge or a needle and ruler after each drop. Energy lost to the grease is then calculated from the ball's kinetic energy at impact, or the stopping force is estimated from depth.
Controlled variables: Drop height fixed with a clamped release and metre rule. Same ball mass and diameter every time. Grease surface smoothed flat before each drop, and a fresh spot used each time. Temperature checked with a thermometer just before and after each drop, since grease cools quickly.
Physics and graph: Energy conservation, mgh = F·d for an average stopping force, and the link between temperature and viscosity. Plot ln(depth) against 1/T, or depth against temperature, and comment on whether the trend is exponential like viscosity. Gradient links to how strongly resistance changes with temperature.
SL and HL: SL students can plot depth against temperature and estimate average stopping force from work done. Top band work tests a linearised model of viscosity against temperature, compares with a second drop height, and explains why crater depth is not simply proportional to viscosity.
Where marks are lost: Research design: temperature drifting during the trial, and no justification of the drop height. Data analysis: ignoring uncertainty in reading depth from a soft, ragged crater. Conclusion: claiming a viscosity value when only depth was measured. Evaluation: not discussing that grease is non-Newtonian and deforms rather than flows.
Data: Needs a water bath, thermometer and a way to measure depth in soft material; the main uncertainty is a poorly defined crater bottom and temperature loss during the drop.

Inflation pressure and rolling tyre drag on a slope

Research question. How does the inflation pressure of a bicycle tyre, from 100 kPa to 400 kPa in 5 steps, affect the coefficient of friction measured by the tilt angle at which a loaded wheel just starts to slide on a wooden board?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Good if you measure the contact patch with ink, so that the physics is tested and not assumed. Lock the wheel so that you really measure sliding.

Method, physics and where marks are lost+

Independent variable: Tyre gauge pressure, 100, 150, 200, 300, 400 kPa (5 values), set with a pump and gauge, 5 repeats each.
What you measure: Force to pull the tyre at steady speed with a newton meter or force sensor, or the angle at which a locked wheel slides on a tilting board. μ = F/N, or μ = tan θ.
Controlled variables: Load on the tyre (fixed added mass). Surface (same board, cleaned). Pulling speed. Tyre temperature and wear, using one tyre.
Physics and graph: F = μN, with N = mg on a level surface, or μ = tan θ on a slope at the point of sliding. Plot μ against pressure, or against 1/pressure to test whether contact area is involved.
SL and HL: SL: measure μ for each pressure and comment on the trend. Deeper: relate contact area to pressure using A = N/P and discuss why classical friction predicts no dependence.
Where marks are lost: Research design: pressure loss during tests that is not checked. Data analysis: mixing rolling and sliding friction. Conclusion: claiming that contact area matters without measuring it.
Data: Needs a bicycle pump with gauge and a force sensor; the pressure leak and locked wheel technique are the main uncertainty.

Lift on a flat plate against fan speed

Research question. How does air speed, varied from 2 to 10 m/s in six steps, affect the lift force on a flat card wing set at a fixed 15° angle of attack in a small wind tunnel?

A.2 Forces and momentum
SL and HL
Hard data
Rarely listed

My take. Worth it only if your school has a tunnel or you can build a decent one. The twist is to make your own wing and justify how you measured a very small force.

Method, physics and where marks are lost+

Independent variable: Air speed through the working section, 2, 4, 6, 8, 10 and 12 m/s, set by fan voltage and checked with a handheld anemometer. Three repeats at each speed.
What you measure: Lift force, measured with a top-pan balance or a 0 to 1 N force sensor holding the wing on a low-friction pivot arm. Air speed from the anemometer. Lift coefficient calculated from L = 0.5 ρ v² A C.
Controlled variables: Angle of attack: fixed with a protractor jig. Wing area and shape: the same card wing throughout. Air density: room temperature and pressure recorded. Blockage and turbulence: wing kept in the middle of the section, same distance from the fan and flow straightener.
Physics and graph: Lift scales as v² for a fixed wing, from momentum change of deflected air. Plot L against v². A straight line through the origin has gradient 0.5 ρ A C, which gives C. Compare C with published values for flat plates.
SL and HL: SL: measure L against v, test the v² relationship and find C. Top band: check the Reynolds number range, explain deviation at high speed by stall or vibration, and compare with a momentum-flux estimate. HL adds nothing syllabus-wise but the fluid ideas give depth.
Where marks are lost: Research design: air speed that is not uniform across the wing and no anemometer calibration. Data analysis: plotting L against v and calling it linear without testing v². Evaluation: ignoring wall effects and fan pulsing, which dominate the error.
Data: Needs a tunnel or a box fan with a straightening tube, an anemometer and a sensitive force measurement; forces are only a few tenths of a newton and the flow fluctuates.

Lift on a model wing as its tilt changes

Research question. How does the angle of attack of a cardboard or foam aerofoil, varied from 0° to 30° in 5° steps, affect the lift force measured in a fan-driven airflow at a fixed speed of about 5 m s⁻¹?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Fun and visual but hard to get clean data. Worth it if you have some airflow control. Twist: test a 3D printed or cut-out wing based on a bird or paper plane you actually fly.

Method, physics and where marks are lost+

Independent variable: Angle of attack from 0° to 30° in 5° steps (7 values), each with 3 repeats.
What you measure: Lift measured as an apparent mass change on a top-pan balance or with a force sensor (±0.01 N). Lift coefficient can be calculated from the lift, air density, wing area and air speed.
Controlled variables: Air speed, checked with an anemometer at the wing position each run. Wing shape and area, by using one wing. Distance from fan, fixed with a marked stand. Room air movement, minimised by shielding.
Physics and graph: Lift arises from momentum change of deflected air, L = ½ρv²AC_L. Plot lift against angle to show the linear region and the stall point, then plot C_L against angle for the linear part, where the gradient gives the lift slope.
SL and HL: SL students show the trend and locate the stall angle. Top band work compares C_L with published thin aerofoil data and justifies a physical model. Because this uses only A.2 ideas, depth comes from analysis, not HL content.
Where marks are lost: Research design: airflow from a fan is turbulent and non-uniform, and drag on the mount is not separated from lift. Data analysis: plotting raw force without normalising for speed. Conclusion: claiming stall angle with too few points near it. Evaluation: ignoring wall and edge effects and the sensor's drift.
Data: Needs a fan or small wind tunnel, an anemometer and a sensitive balance or force sensor. The main uncertainty is non-uniform airflow and fan speed drift.

Load position along a cantilever and its sag

Research question. How does the distance x of a 200 g load from the clamped end of a 60 cm steel or wooden ruler, from 10 cm to 50 cm in 5 steps, affect the vertical deflection at the free end?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. A good way to test the model, but the equation is not on the syllabus so you must source and justify it. Compare E to a book value for a clear conclusion.

Method, physics and where marks are lost+

Independent variable: Load position along the beam, 10, 20, 30, 40, 50 cm (5 values), measured with a metre rule, 3 repeats each.
What you measure: Deflection at the free end, read against a vertical rule or from a travelling microscope or a phone photo with a scale, in mm.
Controlled variables: Load mass (same hanger and slotted masses). Beam material and cross section (one ruler measured with calipers). Clamped length and clamp tightness. Temperature, and avoiding loading beyond the elastic limit.
Physics and graph: For a point load at x on a cantilever, deflection at the tip goes as δ = Fx²(3L − x)/(6EI). Plot δ against x²(3L − x); the gradient is F/(6EI), which gives Young modulus E.
SL and HL: SL: plot deflection against x and describe the non linear shape. Strong work applies the beam equation, finds E and compares it with a data book, though the equation itself is beyond the syllabus and must be supported by derivation or source.
Where marks are lost: Research design: loading past the elastic limit. Data analysis: an unlinearised plot with no fit. Evaluation: ignoring the sag from the weight of the beam itself.
Data: Needs a ruler, clamp, masses and a scale; the main uncertainty is reading the tip position.

Mass of a block and distance it travels after a pendulum hit

Research question. How does the mass of a wooden block, from 100 g to 500 g in steps of 100 g, affect the distance it slides along a bench after being struck by a pendulum hammer released from a fixed height?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. A good idea if you define the launch as a fixed pendulum release. The twist: use d against 1/m² so the physics decides the graph, not the other way round.

Method, physics and where marks are lost+

Independent variable: Block mass: 100, 200, 300, 400 and 500 g, using stacked identical blocks or added masses, 5 repeats each.
What you measure: Slide distance measured with a metre rule (±1 mm), and speed of the block just after impact from 240 fps video; momentum transferred calculated as mv.
Controlled variables: Hammer mass and release height, fixed with a clamp and a stop. Contact surface, cleaned and using the same face. Point of impact on the block, marked with tape. Bench surface, the same track each time.
Physics and graph: For a fixed impulse J, v = J/m, and the block then decelerates through friction so d = v²/(2μg) = J²/(2μg m²). Plot d against 1/m² and expect a straight line. Friction depends on m as well, which cancels in the expression, so the model is clean only if μ stays constant.
SL and HL: SL: plot d against 1/m² and discuss the fit. Top band: check that the impulse itself stays constant by measuring hammer speed after the collision, and treat the collision as partly elastic.
Where marks are lost: Research design: 'constant external force' cannot be created; a pendulum gives constant energy, not constant force. Data analysis: an unlinearised d against m plot that hides the model. Evaluation: not seeing that the hammer rebounds differently with each mass.
Data: Pendulum hammer, blocks and a rule; the main uncertainty is the collision repeatability, roughly ±5% in distance.

Maximum load of a model boat in salt water of different concentration

Research question. How does the salt concentration of water (0 to 100 g/L in steps of 20 g/L) change the maximum mass a rectangular model boat can carry before it sinks to its marked waterline?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Easy and doable with cheap equipment, and gives a clean straight line. Twist: relate it to the Dead Sea or the Plimsoll line on real ships.

Method, physics and where marks are lost+

Independent variable: Salt concentration, 0, 20, 40, 60, 80, 100 g/L, made in a large tank with a balance and measuring cylinder. Three repeats per value.
What you measure: Mass added to the boat (weights or coins) to reach a fixed waterline mark, read on a balance. Fluid density from a hydrometer or from mass over volume of a sample. Upthrust is total mass times g.
Controlled variables: Boat shape and hull: same boat, waterline marked on the side. Water temperature: measured with a thermometer and kept about the same. Placement of load: centred, to avoid tilting. Water volume in tank: enough so the level does not affect the result.
Physics and graph: Floating equilibrium: upthrust = weight, ρ V_sub g = (m_boat + m_load)g. With V_sub fixed by the waterline, m_load = ρV − m_boat. Plot m_load against ρ; the gradient is the submerged volume V and the intercept is −m_boat.
SL and HL: SL: plot m_load against density and check gradient with the calculated volume. Top band: uncertainty on density and waterline reading, and compare V from the gradient with V from the hull dimensions.
Where marks are lost: Research design: concentration not converted to density, so no linearisation is possible. Data analysis: no uncertainty on waterline. Conclusion: no link between gradient and volume. Evaluation: salt not fully dissolved or stratified in the tank.
Data: Needs a tank, salt, balance and a simple boat from a plastic box; the main uncertainty is the waterline reading and uneven mixing.

Momentum conservation in trolley collisions using light gates

Research question. How does the fractional change in total momentum in collisions between two dynamics trolleys vary with the initial speed of the moving trolley from 0.20 m/s to 1.00 m/s, on a level track?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Well suited to a school lab and easy to get clean data, but commonly done. Make it your own by quantifying the losses and comparing elastic with inelastic ends.

Method, physics and where marks are lost+

Independent variable: Initial speed of the moving trolley, 5 to 6 values from 0.20 to 1.00 m/s, set by the release height on a small ramp or a spring plunger, with 3 repeats; a second series varies the mass of the target trolley from 0.5 to 2.0 kg.
What you measure: Velocities before and after collision from two light gates and cards, or video analysis at 120 frames per second; total momentum before and after, and the percentage change.
Controlled variables: Track level: checked with a spirit level and by a trolley that does not accelerate. Friction: same track and wheels, with compensation by a small tilt. Collision type: Velcro or magnetic ends, stayed the same. Masses: measured on a balance to 1 g.
Physics and graph: Conservation of momentum, p = mv, total p before equals total p after for an isolated system. Plot total momentum after against total momentum before; the gradient should be 1, and kinetic energy checks distinguish elastic from inelastic collisions.
SL and HL: SL students compute momentum before and after with uncertainties and test a gradient of 1. Extra depth: measure kinetic energy lost and link it to collision type, and quantify the loss from friction using a coasting trolley.
Where marks are lost: Research design: two independent variables changed together, and no control over friction. Data analysis: ignoring uncertainties in card length and gate timing. Evaluation: not explaining a momentum shortfall by friction, or claiming conservation without a stated tolerance.
Data: Trolleys, track, two light gates and a data logger, or a phone camera for video analysis; the main uncertainty is friction and card-length timing error.

Number of rotor blades against thrust at fixed speed

Research question. How does the number of identical blades, from 2 to 6, on a motor-driven rotor affect the thrust measured with a top-pan balance at 1500 rpm?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. An easy build with a decent physics idea behind it (blade interference). The twist is to predict the curve before measuring.

Method, physics and where marks are lost+

Independent variable: Number of blades: 1, 2, 3, 4, 5 and 6 on a hub with equally spaced slots, 3 repeats each.
What you measure: Apparent mass loss on a 0.01 g balance (g), converted to thrust in N; rpm found by video frame counting.
Controlled variables: Rotor speed, adjusted with the supply voltage until the video count gives 1500 rpm. Blade size, pitch and material, all from one template. Hub height above the balance, clamp fixed. Balance zeroed with the stopped rotor in place each time.
Physics and graph: If blades act independently, thrust should rise in proportion to the number of blades, F ∝ N. At high N the blades pass through each other's disturbed air and the plot should curve below the straight line. Plot F against N and compare with a line through the origin.
SL and HL: SL: linear plot and simple discussion of the departure. Top band: use the deviation to estimate an interference effect and quantify with residuals; consider tip vortices.
Where marks are lost: Research design: extra blades add load so rpm drops unless it is corrected each time. Conclusion: claiming proportionality without testing the intercept. Evaluation: no discussion of air recirculation.
Data: Keeping rpm constant needs retuning the supply for every N, which is fiddly but doable.

Object mass and buoyant force at fixed volume

Research question. How does the mass of a fully submerged object of fixed volume (50 cm³, from 50 g to 400 g in 6 steps) affect the apparent weight and the water volume displaced?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. A weak choice as it is, because the answer is known. Change the fluid density as the independent variable instead and it becomes a real investigation.

Method, physics and where marks are lost+

Independent variable: Mass of the object, 50 to 400 g, using sealed 50 cm³ containers filled with different amounts of sand or steel shot; six values, 5 repeats each.
What you measure: Volume of water displaced in a measuring cylinder or overflow can (±0.5 cm³), and apparent weight from a force sensor or newton meter; buoyant force calculated.
Controlled variables: Same container volume and shape; water at the same temperature and depth; fully submerged with the same dry container each time; the same overflow can.
Physics and graph: Archimedes: buoyant force = ρVg, which depends on the submerged volume, not mass. Plot displaced volume against mass and expect a horizontal line. Also plot apparent weight against mass, with gradient g and intercept −ρVg.
SL and HL: SL: show displaced volume is constant and buoyant force equals the weight of the displaced water. Top band: use a range of fluid densities such as salt solutions to show that the force depends on ρ.
Where marks are lost: Research design: the hypothesis is trivial, giving a flat line with no new physics. Data analysis: air bubbles and meniscus reading. Evaluation: no comment on the result being expected.
Data: Needs a measuring cylinder, balance and newton meter or sensor; the main uncertainty is reading the meniscus and trapped air bubbles.

Pitch angle of a card rotor and its thrust

Research question. How does the pitch angle of blades on a small motor-driven rotor, from 5° to 45° in steps of 10°, affect the thrust recorded on a top-pan balance at constant motor voltage?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Good if you accept that the result is a curve with a peak, not a clean law. The twist: report thrust per unit rpm² so pitch is separated from speed.

Method, physics and where marks are lost+

Independent variable: Blade pitch angle: 5°, 15°, 25°, 35°, 45°, set with a protractor jig, 3 repeats each.
What you measure: Balance reading loss (g) with the rotor running, converted to thrust in N; rotor rpm from a slow motion video to check the speed stays similar.
Controlled variables: Supply voltage, from a stabilised supply. Blade area and length, cut from one template. Rotor height above the pan, fixed by a clamp. Room draughts, reduced by closing doors and windows.
Physics and graph: Air deflected downward gives a thrust from the momentum change, but pitch also changes the rotor speed because drag torque changes. Plot thrust against sin of pitch angle, or against angle, and look for a peak. Stall at large angles gives a maximum, which is the interesting result.
SL and HL: SL: describe the trend and suggest a reason for the peak. Top band: model thrust with a simple momentum argument and account for rpm changes by plotting thrust against rpm² for each angle.
Where marks are lost: Research design: rpm changes with angle and is not controlled or recorded. Data analysis: forcing a linear fit onto data with a maximum. Evaluation: setting the angle by eye with about ±3° uncertainty and not stating it.
Data: A protractor jig gives about ±2° in pitch, and a motor's rpm drops with more load, so record it every run.

Projectile mass and swing of a ballistic pendulum

Research question. How does the mass of a plasticine or steel projectile, from 5 g to 30 g in 6 steps, affect the maximum rise in height of a 500 g block pendulum after it embeds, with launch speed fixed by a spring gun?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. A classic that works well when you check the launch speed with a light gate, which is the bit many students skip. Use the linear graph to get v.

Method, physics and where marks are lost+

Independent variable: Projectile mass, 6 values, 5 repeats each. Use a spring launcher compressed to a fixed mark, or a ramp roll to keep speed constant.
What you measure: Maximum height of the pendulum from a video frame against a ruler, or from the angle of the string; h = L(1 − cos θ). Launch speed inferred from the height.
Controlled variables: Launch speed (same spring compression, checked with light gates). Pendulum block mass and string length. Method of catching (the same foam target). Alignment at the centre of mass of the block.
Physics and graph: Momentum conservation m v = (m + M)V, then (m + M)gh = ½(m + M)V². So v = ((m + M)/m)√(2gh). Plot h against (m/(m + M))² to get a straight line if v is fixed; the gradient is v²/2g.
SL and HL: SL: measure h for each mass and compare to the momentum prediction. Stronger: derive the linear graph, find v and compare with the light gate value, and calculate the kinetic energy lost.
Where marks are lost: Research design: launch speed not fixed when the mass changes. Data analysis: missing the m/(m + M) relationship. Evaluation: not checking that the block swings in plane, without rotation.
Data: Needs a spring launcher and camera; the launch speed variation with mass is the main uncertainty.

Puck collisions in two dimensions with video

Research question. How does the impact parameter (0 to 4.0 cm in 0.5 cm steps, 9 values) affect the angle between the two pucks after a glancing collision on an air table?

A.2 Forces and momentum
HL topic
Hard data
Rarely listed

My take. Impressive if you have the equipment, but hard to get clean data without an air table. Without one, choose a different collision topic.

Method, physics and where marks are lost+

Independent variable: Impact parameter, set by offsetting the target puck from the line of the moving puck; 0 to 4.0 cm in 9 steps, each repeated 3 to 5 times.
What you measure: Overhead video at 60 fps or more, digitised with Tracker. The angle between the two outgoing paths is measured, and the total momentum x and y components before and after are calculated.
Controlled variables: Launch speed: same launcher and start distance. Surface: air table or glass with dry ice or air puck, kept level. Puck masses: equal pucks checked on a balance. Camera: mounted directly above with a scale in view.
Physics and graph: Vector momentum conservation gives p = p₁' + p₂' in x and y. For equal masses in an elastic collision the outgoing angle is 90°. Plot separation angle against impact parameter and compare with the prediction. Also plot total final momentum against initial momentum, gradient 1.
SL and HL: SL students can do a simple version with pucks of the same mass. HL work resolves components, checks energy loss and uses unequal masses. Top band analysis includes propagation of uncertainty from the tracked points.
Where marks are lost: Research design: the impact parameter is not measured and cannot be controlled by eye. Data analysis: using only speeds and not vectors. Evaluation: ignores that pucks are slowed by friction between frames.
Data: An air table or very smooth surface plus a camera is required; the main uncertainty is friction and the perspective of the video.

Rolling resistance of a cart with added load

Research question. How does the total mass of a dynamics cart, increased from 0.50 kg to 2.00 kg in six steps, affect the coefficient of rolling resistance on a level wooden track?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Practical and clean, and the two-method comparison makes it stand out. Choose it if you like a simple set-up with a real analysis challenge.

Method, physics and where marks are lost+

Independent variable: Total cart mass from 0.50 kg to 2.00 kg using added masses (6 values, 3 repeats each).
What you measure: Force sensor reading while towing the cart at constant speed, or the tilt angle at which it just rolls at steady speed (measured with a protractor and metre rule for height). The coefficient is F/(mg) or tan θ.
Controlled variables: Track surface: the same board, cleaned and levelled between runs. Speed: a constant tow speed checked with video or a motion sensor. Wheels and axles: the same cart, same tyre pressure if applicable. Load position: added masses placed centrally each time.
Physics and graph: Rolling resistance force F_r = C_rr N, with N = mg. Plot F_r against mg; the gradient is C_rr and a non-zero intercept shows a load independent term such as axle friction. Compare with the incline method where C_rr = tan θ.
SL and HL: SL: measure F_r at each mass and find C_rr from the gradient. Top band: test whether C_rr really is constant and compare two independent methods (tow and incline). HL is not required.
Where marks are lost: Research design: pulling at varying speed so the force is not equilibrium. Data analysis: forcing the line through the origin. Conclusion: not separating rolling from axle friction. Evaluation: ignoring track unevenness and its effect on the spread.
Data: A force sensor and a dynamics cart make it easy; small forces of a few tenths of a newton mean zero offset dominates the uncertainty.

Rotor blade area and thrust from a small spinning rotor

Research question. How does the plan area of a two-blade card rotor, varied from 10 cm² to 50 cm² in five steps, affect the thrust measured on a top-pan balance at a fixed motor speed of 1500 rpm?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Workable once you fix the vague 'cross-sectional area' and separate thrust from blade weight. Choose it only if you enjoy building; the twist is to zero the balance with the rotor stopped for each blade set.

Method, physics and where marks are lost+

Independent variable: Plan area of each blade cut from identical card, 10, 20, 30, 40 and 50 cm², with 3 repeats per area (new blades each time).
What you measure: Apparent loss in balance reading (g) while the rotor spins above the pan, converted to thrust in N (F = Δm × g). Rotor speed checked with a phone slow motion video or a stroboscope app.
Controlled variables: Motor speed, held by a stabilised DC supply and checked by video count each run. Blade pitch, set with a card template at 15°. Blade length, cut identically. Distance of rotor from the floor and walls, fixed with a clamp.
Physics and graph: Thrust comes from the rate of change of momentum of the air pushed down, F = Δp/Δt = ρAv². Plot thrust against blade area and test for a straight line through the origin. The gradient links to ρv² for the air. Note that 'cross-sectional' is ambiguous, so define it as plan area.
SL and HL: SL: measure, plot, discuss proportionality and repeat scatter. Top band: estimate the downward air speed from the gradient and check it independently with an anemometer, and discuss why thrust may saturate at large area. HL depth is not required.
Where marks are lost: Research design: area and mass of the blades change together, so balance changes may come from weight of the rotor, not thrust. Data analysis: ignoring uncertainty from a fluctuating balance reading. Evaluation: not addressing air recirculation and ground effect.
Data: Needs a small motor, a supply and a 0.01 g balance; the balance reading fluctuates by about ±0.2 g because of turbulence, so take a mean over 10 s.

Rubber temperature and the friction needed to start sliding

Research question. How does the temperature of a rubber block, from 5°C to 65°C in steps of 10°C, affect the coefficient of static friction on a wooden plank, found from the angle at which the block first slides?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. An unusual and personal idea if you control the cooling problem. The twist: measure the block's surface temperature with an infrared thermometer at the moment of slip.

Method, physics and where marks are lost+

Independent variable: Rubber temperature: 5, 15, 25, 35, 45, 55 and 65°C, achieved with an ice bath, room air and a water bath, with 5 repeats each.
What you measure: Critical angle θ at which the block first slips on a slowly raised plank, measured with a protractor or phone level app (±0.5°); μs = tan θ.
Controlled variables: Rubber sample and the surface, one block, one plank, wiped and dried between runs. Normal force, kept constant with the same block and no added mass. Rate of raising the plank, slow and steady with a screw jack. Time from taking the block out to testing, under 20 s, with a thermometer or an infrared thermometer checking the block temperature at the moment of release.
Physics and graph: At the point of slipping, the friction force equals μs N, giving μs = tan θ for a block on an incline. Plot μs against temperature and look for a trend. Rubber becomes softer when warmer, which increases the true contact area and adhesion.
SL and HL: SL: measure and describe the trend with uncertainties from repeats. Top band: model the cooling of the block during the test, and explain the trend with the ideas of contact area and viscoelasticity.
Where marks are lost: Research design: the sample cools or warms in the air before the test, and water films on the surface change friction. Data analysis: a small range of angles with only ±0.5° resolution. Evaluation: not repeating with a new block to check sample variation.
Data: Needs a thermometer, a water bath and a tilting plank; the largest uncertainty is temperature change of the block between bath and test.

Sag of a ruler bridge with changing width

Research question. How does the width w (1.0, 1.5, 2.0, 2.5, 3.0, 4.0 cm) of a card or plastic strip bridge, supported at two points 30.0 cm apart, affect its central deflection under a 100 g load?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. A sound project if you use the 1/w plot and find E. Personalise by building an actual model bridge and comparing with the beam theory prediction. Without the linearisation it is too descriptive.

Method, physics and where marks are lost+

Independent variable: Width of the strip, 6 values, cut from one sheet of uniform plastic or thin wood so thickness is constant, with 3 repeat strips of each.
What you measure: Central deflection measured with a ruler against a mirrored scale or a dial gauge, and the difference between loaded and unloaded position. Calculated from it is the effective flexural stiffness.
Controlled variables: Span: fixed by two supports at 30.0 cm. Thickness: measured with a micrometer for every strip. Load: same hanging mass, placed at the centre by the same loop. Material: cut from the same sheet, same grain direction.
Physics and graph: For a beam, deflection δ = FL³/(48EI) with I = wt³/12, so δ ∝ 1/w. Plot δ against 1/w: a line through the origin with gradient FL³/(4Et³), and E can be calculated. Beam bending is beyond the syllabus, but Hooke's law and Young modulus at SL and HL give the base, and the formula can be quoted with a source.
SL and HL: SL: show the inverse relation and describe stiffness. Higher: extract Young modulus E from the gradient and compare with a data book value, then discuss the assumption of small deflection and elastic behaviour.
Where marks are lost: Research design: varying width only by cutting different materials, or not repeating. Data analysis: tiny deflections measured with a ruler have large percentage uncertainty. Conclusion: stating 'wider means less sag' without a quantified relation. Evaluation: not checking permanent deformation or support slipping.
Data: Rulers, clamps, slotted masses and a micrometer are enough; a dial gauge helps, but deflection resolution is the main uncertainty.

Siphon tube bore and water flow rate

Research question. How does the internal diameter of a siphon tube (4 to 12 mm, 6 sizes) affect the volume flow rate of water at a fixed height difference of 30 cm?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Simple and practical, but only scores well if you test the power law and explain any deviation. Use a log-log plot as your personal analytical twist.

Method, physics and where marks are lost+

Independent variable: Internal diameter of clear tubing, 6 sizes from 4 mm to 12 mm, measured with a calliper or by a water column of known length. Three runs each.
What you measure: Volume of water collected in a measuring cylinder over a timed interval with a stopwatch; flow rate Q = V / t, in ml per s.
Controlled variables: Height difference between the water levels, held with a marked stand and a large supply tank kept topped up. Tube length, the same 1 m for all, or the effect of length is shown separately. Water temperature, from a thermometer. Tube kept straight with no kinks.
Physics and graph: Bernoulli gives an ideal exit speed v = √(2 g h), so Q = A v = pi d² v / 4. Plot Q against d²; the gradient gives an effective speed to compare with √(2 g h). Narrow tubes will fall below this because of viscosity, so also test the Poiseuille prediction Q proportional to d⁴.
SL and HL: SL: Q against d² with uncertainty and comparison to the ideal speed. Top band: discuss Reynolds number, plot log Q against log d to find the real power and explain which regime applies. Still fine at HL, since the syllabus needed is small.
Where marks are lost: Research design: letting the water level in the tank fall so the height changes. Data analysis: assuming the area law without testing it. Evaluation: not explaining why the measured speed is well below the ideal value.
Data: Standard clear tubing, a bucket and a measuring cylinder are enough; the main uncertainty is the tank level dropping and bubbles in the tube.

Sliding friction of a ball on artificial turf with different water depth

Research question. How does the depth of water sprayed on a turf sample (0 to 5 mL per 100 cm², 6 values) affect the coefficient of kinetic friction of a rolling or sliding football, found from its stopping distance from a fixed launch speed?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Good sporty idea if you clearly say rolling resistance and not sliding friction. Twist: use your own football and a pitch offcut, and relate it to why wet pitches play faster or slower.

Method, physics and where marks are lost+

Independent variable: Volume of water sprayed on a turf strip, 0 to 5 mL per 100 cm² in 6 steps, measured with a syringe. Five repeats each. The original range in millimetres is not realistic for a school lab.
What you measure: Stopping distance of a ball launched down a ramp of fixed height onto the horizontal turf, measured with a metre rule or video. Launch speed v from energy on the ramp, then μ = v²/(2gd) for sliding, or an effective resistance coefficient for rolling.
Controlled variables: Launch speed: same ramp release height each time, checked by light gates or video. Ball: same ball and inflation pressure. Turf: same sample, dried and combed between trials to keep pile orientation the same. Surface levelness: checked with a spirit level.
Physics and graph: Work done by friction: μmg·d = ½mv², so d = v²/(2μg). Plot 1/d against water volume, or μ against water volume, and look for a trend. For rolling balls the loss is rolling resistance, not sliding friction, so state this and treat the coefficient as an effective value.
SL and HL: SL: measure distances, compute μ and describe the trend. Top band: distinguish rolling from sliding using ½mv² + ½Iω² for a hollow sphere, and test whether the results follow a simple law of water volume.
Where marks are lost: Research design: a rolling ball does not have a kinetic friction coefficient, and the student does not notice. Data analysis: μ averaged across rough repeats without spread. Conclusion: overclaim from a small trend. Evaluation: turf drying and pile direction changing during the session.
Data: Needs a ramp, metre rule, spray or syringe and a turf offcut; the main uncertainty is that the wet surface is not uniform and dries in minutes.

Sliding friction of a block on six surface materials

Research question. How does the kinetic friction coefficient of a 500 g wooden block change when it is pulled at constant speed over six different surface materials (sandpaper, cardboard, felt, rubber mat, acrylic sheet, aluminium foil on board), measured with a force sensor from 0.5 N to 5 N of normal load?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. A very common and safe topic, so it will only stand out if you make it rigorous. The twist is to choose surfaces you actually care about, for example different climbing shoe rubbers or skate deck grips, and test proportionality properly rather than one load per material.

Method, physics and where marks are lost+

Independent variable: Normal force on the block, changed by adding masses of 100 g steps from 0 to 500 g (6 values), repeated on each of 3 chosen surface materials. Optionally extend to 6 materials at one fixed load. Each setting repeated 5 times.
What you measure: Pulling force read from a digital force sensor (or a newton meter) while the block moves at steady speed, taken as the mean of the flat part of the trace. Kinetic friction coefficient is the gradient of friction force against normal force, with uncertainty from the best and worst fit lines.
Controlled variables: Pulling speed: motor-driven pulley or a marked timing of about 5 cm/s, checked with a video and ruler. Contact area: same block face used every time. Surface cleanliness: wipe and use a fresh area of material for each run. Pull angle: string kept parallel to the surface using a pulley or a level-set sensor height.
Physics and graph: Kinetic friction F = μk N when acceleration is zero, so pulling force equals friction. Plot friction force (y) against normal force (x). The line should be straight through the origin and the gradient is μk. An intercept that is not zero suggests a systematic error such as sensor offset or adhesion. Compare gradients between materials.
SL and HL: SL: measure, plot, get μk for each material and compare with a sensible uncertainty. Top band: test whether F really is proportional to N by looking at the intercept, check speed independence with a second set of speeds, and comment on stick slip. HL depth can come from an inclined plane comparison method or a model of energy lost to friction, but this is not needed for the syllabus.
Where marks are lost: Research design: too many materials with only one load and no repeats, or failing to hold speed steady so static and kinetic friction get mixed. Data analysis: calculating μ from single readings instead of a gradient, and ignoring the intercept. Conclusion: stating that a material has a coefficient with no comparison to a data book value. Evaluation: not discussing stick slip jerks, surface wear and non-uniform speed.
Data: Needs a force sensor or a 10 N newton meter, wooden block, masses and test surfaces; the main uncertainty is keeping a truly constant speed by hand, so a motor or a sensor trace is better.

Sphere density and settling time in water

Research question. How does the density of a sphere of fixed radius (1000 to 7800 kg m^-3, 6 materials) affect its terminal speed when sinking through glycerol in a 1 m measuring cylinder?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Worth choosing if you switch to a viscous liquid and measure speed rather than a vague equilibrium time. The twist is using your measured viscosity to check the Stokes model and say where it breaks.

Method, physics and where marks are lost+

Independent variable: Density of 12 mm diameter spheres: nylon, glass, aluminium, titanium or ceramic, steel, brass. 6 materials, 5 drops each. Density found from mass and diameter.
What you measure: Time to fall between two marked lines, measured with a phone video at 240 fps or 60 fps and frame-by-frame analysis. Terminal speed = distance / time. Also compare with the Stokes prediction.
Controlled variables: Sphere diameter, checked with a micrometer at several angles. Liquid temperature, measured with a thermometer before each drop. Release point, by dropping from just under the surface. Tube width, one tube for all runs. Note that water is too fast, so use glycerol or a glycerol/water mix.
Physics and graph: At terminal speed, weight = buoyancy + drag, so (ρ_s - ρ_f) g V = 6 pi eta r v for slow flow. Plot v against (ρ_s - ρ_f). It should be a straight line through the origin with gradient 2 g r² / (9 eta), so eta can be extracted and compared with the data book value.
SL and HL: SL: straight-line graph and a viscosity value with uncertainty. Top band: check the Reynolds number, apply the wall correction for the tube radius, and discuss why the line curves for dense spheres at high speed. HL is not required.
Where marks are lost: Research design: using water so the fall is too quick to time, or letting the density change together with size. Data analysis: timing by stopwatch with reaction-time error swamping the data. Evaluation: ignoring that spheres have not reached terminal speed and ignoring wall effects.
Data: Needs glycerol, spheres of different materials and a video for timing; the main uncertainty is whether terminal speed is reached and the temperature-dependent viscosity.

Sphere diameter and fall time with quadratic drag model

Research question. How does the diameter of a spherical projectile (from 2 cm to 20 cm in 2 cm steps) dropped from 50 m affect its fall time in a numerical model with quadratic air drag and a fixed drag coefficient?

A.2 Forces and momentum
SL and HL
Needs care
simulation
Rarely listed

My take. Only worth it if you add real drops to validate the model, otherwise it reads as a coding exercise. Make it personal with balls you can actually drop, such as steel, wooden and foam spheres.

Method, physics and where marks are lost+

Independent variable: Sphere diameter from 2 cm to 20 cm in 10 values in the model, at a fixed density such as iron; repeat with a different density to check.
What you measure: Fall time from the model, found by stepping the equation of motion in a spreadsheet or Python with a time step of 0.001 s, and checked against the analytical solution using a tanh function. A real check can be made by dropping balls of different sizes from a stairwell and timing them with a video.
Controlled variables: Drag coefficient fixed at 0.47; air density 1.2 kg/m³; fall height fixed; time step tested for convergence by halving it.
Physics and graph: m dv/dt = mg − ½ρ_air C_d A v², with m = ρ_s(4/3)πr³ and A = πr², so the terminal speed scales as √(r). Plot fall time against diameter, and terminal speed squared against diameter, whose gradient tests the model. Small spheres are drag-limited and large ones approach free fall.
SL and HL: An SL student can build the step-by-step model and describe the trend. Top band work compares with the analytic solution, validates against real drops, and discusses the change in C_d with Reynolds number.
Where marks are lost: Research design: purely computational work with no validation against real data. Data analysis: uncertainty not treated, since simulation has no random error but has step-size error. Evaluation: constant C_d assumption not challenged.
Data: Needs a spreadsheet or Python; the main uncertainty is numerical step size and the assumed C_d, so test convergence and vary C_d.

Tension in a whirled bung at different radii

Research question. How does the radius r of a rubber bung swung in a horizontal circle (r = 0.30 to 0.90 m in 6 steps) affect the centripetal force needed to keep the period fixed at 1.0 s?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Simple and safe, though standard, so it needs a personal angle: quantify the sag angle and correct for it. Wear eye protection and swing in an empty area.

Method, physics and where marks are lost+

Independent variable: Radius r of the circle, 0.30, 0.40, 0.50, 0.60, 0.75, 0.90 m, with 5 trials at each.
What you measure: Centripetal force from the weight of hanging washers on the string below a glass tube (F = Mg), balanced when the marker on the string stays at the tube. Period from a phone video at 240 fps or by timing 20 revolutions with a stopwatch.
Controlled variables: Period fixed at 1.0 s by timing over many revolutions and adjusting the swing. Mass of the bung: same bung throughout. Circle kept horizontal by checking the angle of the string in video. Hanging mass changed only to find the balance point.
Physics and graph: F = m·4π² r / T². At fixed T, plot F against r; the gradient equals 4π² m / T², so m can be compared with the balance reading. Also possible to vary T at fixed r and plot F against 1/T².
SL and HL: SL students can get a full mark spread with the linear graph and a comparison of the gradient with the mass. Top band work handles the fact that the string is not horizontal, which needs the vertical component of the tension, and shows that the effective radius is measured from the tube to the centre of mass of the bung.
Where marks are lost: Research design: holding speed constant is hard; fixing the period is much easier and should be said clearly. Data analysis: string angle ignored. Evaluation: judging the period by eye instead of timing many revolutions.
Data: Only a bung, string, glass tube, washers and a stopwatch are needed; the main uncertainty is the sag angle of the string and keeping T constant by hand.

Terminal speed of falling balls of different mass in air

Research question. How does the mass of a hollow plastic ball of fixed diameter (2.0, 3.0, 4.0, 5.0, 6.0, 8.0 g) affect its terminal speed and drag coefficient when dropped from 3 m?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Good if you accept that the expected answer is 'C stays constant'. That makes the conclusion honest and interesting. Personalise by dropping from a real stairwell and using coffee filters as an extension.

Method, physics and where marks are lost+

Independent variable: Mass of the ball, 6 values from 2 to 8 g, adjusted by adding modelling clay or beads inside identical hollow balls (e.g. table tennis or foam balls), each dropped 5 times.
What you measure: Position against time from video at 120 fps or more, analysed in Tracker, with terminal speed from the gradient of the final linear section. Drag coefficient is then calculated as C = 2mg / (ρAv²).
Controlled variables: Ball diameter: same shell each time, checked with a calliper. Drop height: fixed, with a stairwell or balcony giving at least 3 m. Air: indoor, no draughts, with temperature recorded for air density. Camera position: fixed and perpendicular, with a metre rule in view for scale.
Physics and graph: At terminal speed mg = ½CρAv². Plot v² against m: a line through the origin with gradient 2g/(CρA), so C follows from the gradient. If C is constant, the graph is linear, and if not it shows dependence on Reynolds number.
SL and HL: SL: find v_t for each mass and show that v² is proportional to m. Top band: compute C with uncertainty, check Reynolds number, and discuss why C is not expected to depend on mass but might change with speed.
Where marks are lost: Research design: the ball may not reach terminal speed within the drop height, and that is not checked. Data analysis: perspective and frame rate errors. Conclusion: stating that mass changes C when the data are within error. Evaluation: ignoring that uneven mass added inside changes spin and path.
Data: Needs a slow motion phone camera and Tracker; the biggest uncertainty is whether terminal speed is really reached.

Terminal speed of paper cones against weight per area

Research question. How does the ratio of mass to frontal area (from 0.5 to 3.0 g per cm², 6 values) affect the terminal speed of cone shaped paper cases falling through air?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. An accessible idea that can still score well if you fit the exponent honestly. Do not choose it only for its simplicity, since many students have already done this.

Method, physics and where marks are lost+

Independent variable: Mass divided by frontal area, changed by stacking 1 to 6 identical coffee filter cups and using a balance to check the mass. Each value repeated 5 times.
What you measure: Fall time over the last 1.0 m of a 3 m drop, using a phone recording at 120 fps beside a metre rule. Terminal speed is the distance divided by time, with the uniform speed section confirmed on the video.
Controlled variables: Shape: same cup type, nested so the outline is unchanged. Release height and orientation: released from a fixed mark, apex down. Air movement: indoor stairwell with doors closed. Air temperature: read from a thermometer.
Physics and graph: At terminal speed weight equals drag, mg = ½CρAv², so v = √(2mg/CρA). Plot ln v against ln(m/A) and find the gradient. Compare it to 0.5 rather than assuming the value. Then plot v² against m/A to get C from the gradient.
SL and HL: SL students can plot v² against m/A and comment on linearity. Top band work fits the exponent with uncertainty and discusses drag at low Reynolds numbers where the power changes. HL depth can come from discussing Reynolds number and the change in drag regime.
Where marks are lost: Research design: cones are dropped before terminal speed is reached. Data analysis: assumes the exponent is 0.5 without fitting. Evaluation: sticks to random errors and ignores drafts and cups deforming when stacked.
Data: Coffee filters, a balance, a phone and a stairwell are enough; the main uncertainty is timing and drafts.

Terminal speed of paper parachutes of varying radius

Research question. How does the radius of a circular paper or plastic parachute (5.0, 7.5, 10.0, 12.5, 15.0, 20.0 cm) with a fixed 20 g load affect its terminal speed when dropped from 2.5 m?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. A common idea in the physics of drag, so it needs a personal angle. Compare a flat with a hemispherical canopy, or vary the load as well. Do the v² against 1/A plot to reach the top band.

Method, physics and where marks are lost+

Independent variable: Canopy radius, 6 values, cut from the same sheet, each dropped 5 times.
What you measure: Terminal speed from a video analysed in Tracker (position against time, gradient of the linear section), or from the time to fall a marked final 1 m section with a stopwatch.
Controlled variables: Load: same plasticine mass, attached with strings of equal length. Canopy material: cut from one sheet, checked for flatness. Drop height and release: from a fixed height, released by hand at rest. Air: indoors with the doors shut, no fans.
Physics and graph: At terminal speed mg = ½CρAv², so v ∝ 1/r if C is constant. Plot v² against 1/r² (or 1/A): a straight line through the origin, and the gradient gives 2mg/(Cρπ). The line shows C and can be compared with a typical value of about 0.75 to 1.4 for a parachute.
SL and HL: SL: measure v_t, plot the linearised graph and calculate C. Top band: check the Reynolds number range, discuss canopy shape changes at larger radius, and the fact that the load's own drag is not negligible for small canopies.
Where marks are lost: Research design: dropping from too low, so terminal speed is not reached. Data analysis: reading speed from a stopwatch over short distances. Conclusion: claiming 'proportional' from only a curve. Evaluation: not commenting on canopy tilting or oscillation.
Data: A stopwatch and ruler work, but a phone video and Tracker reduce timing uncertainty; the canopy swaying is the main problem.

Tilt-angle measurement of static friction for six material pairs

Research question. How does the coefficient of static friction, from the critical tilt angle, differ for a wooden block on six surfaces (wood, glass, aluminium, sandpaper, rubber, felt)?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. Easy and safe, but the question is only a comparison. Add the force meter graph and test the friction law to make it a proper investigation.

Method, physics and where marks are lost+

Independent variable: Surface material of the incline: 6 surfaces, each with 8 trials. A further test varies the normal force by adding masses to the block from 0.2 kg to 1.0 kg.
What you measure: Angle at which the block begins to slide, from a protractor or a phone inclinometer, tilted slowly. Coefficient μ_s = tan(θ).
Controlled variables: Same block with the same contact face and area. Surface cleaned before each trial. Same tilting rate, ideally by a lab jack raising one end. Same mass on the block (or measured across a set of masses). Humidity and temperature noted.
Physics and graph: At the point of slipping, mg sin(θ) = μ_s mg cos(θ), so μ_s = tan(θ). For mass variation, use a horizontal pull with a force meter: plot F_max (y) against normal force N (x), the gradient is μ_s.
SL and HL: SL students compare μ_s among materials with uncertainties. Higher marks come from showing that μ_s does not depend on the normal force or the area, and from analysing the spread from surface wear.
Where marks are lost: Research design: raising the ramp at an uneven speed so that the angle is hard to read. Data analysis: averaging without treating the trial spread as uncertainty. Evaluation: not seeing that the surface changes with repeated sliding.
Data: Needs a board, block, protractor or phone app and surface sheets; main uncertainty is deciding when sliding starts, about 1 to 2 degrees.

Trolley acceleration with fixed total mass

Research question. How does the driving force from a hanging mass (0.02 to 0.12 N in steps of 0.02 N, 6 values) affect the acceleration of a trolley on a level track when the total mass is kept at 0.500 kg?

A.2 Forces and momentum
SL and HL
Easy data
Rarely listed

My take. A fair and reliable choice, but it is a school classic. Its value is in analysing the intercept and pulley mass carefully, not simply confirming F = ma.

Method, physics and where marks are lost+

Independent variable: Hanging weight from 2 g to 12 g, moved one slice at a time from the trolley to the hanger. Each value repeated at least 5 times.
What you measure: Velocity at two light gates on the track, or a motion sensor v–t plot. Acceleration comes from the gradient of the v–t graph or from (v² − u²)/2s.
Controlled variables: Total mass: all slotted masses stay on the system and are checked on a balance. Track level: checked with a spirit level. Friction: same wheels and track, string parallel to track. Start position: fixed mark.
Physics and graph: For the system, mg = (M + m)a with M + m constant, so a is proportional to m. Plot a against the driving force. The gradient is 1/(total mass) and any non-zero intercept shows friction, which can be used to estimate a friction force.
SL and HL: SL students can verify the gradient against the total mass. Higher marks come from using the intercept to quantify friction and from checking string and pulley effects. HL students can consider the rotational inertia of the pulley in the gradient.
Where marks are lost: Research design: the total mass is not really constant since masses are not weighed. Data analysis: only uses a single trial and no error bars. Conclusion: claims F = ma is proved with no comparison of gradient with 1/M.
Data: Uses a track, light gates or a motion sensor and a balance; the main uncertainty is friction and pulley effects.

Upthrust on an aluminium block in water from 5 to 80 °C

Research question. How does the apparent weight of a fully submerged aluminium block change as water temperature rises from 5 °C to 80 °C in steps of about 15 °C, and does the upthrust change by more than measurement uncertainty?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Fine and honest if you check first that your balance can see a 3% change. Twist: make the hot water case a swimming or bath link, and use a larger block to enlarge the signal.

Method, physics and where marks are lost+

Independent variable: Water temperature: 6 values from about 5 °C (ice bath) to 80 °C, measured with a thermometer next to the block. Five repeated weighings per temperature.
What you measure: Apparent weight of the block hung from a top-pan balance or force sensor while submerged. Upthrust is the true weight minus apparent weight, and is compared with ρgV using tabulated water density.
Controlled variables: Block volume: same block throughout, measured with a calliper (thermal expansion is small but can be discussed). Submersion: fully under, not touching walls, at the same depth. Water volume and container: same beaker, stirred so temperature is uniform. Thread: thin thread, same length, kept out of hot water where possible.
Physics and graph: Upthrust F = ρ_fluid V g, with water density falling from 1000 to about 972 kg/m³ over this range. Plot measured upthrust against tabulated density; the gradient should equal Vg. The expected change is about 3%, so precision matters.
SL and HL: SL: measure the trend and compare with the density table. Top band: propagate uncertainty to show whether a 3% effect can be seen at all, and discuss the effect of convection currents and thermal expansion of the block.
Where marks are lost: Research design: balance resolution too coarse to see a 3% change. Data analysis: no uncertainty on upthrust as a difference of two masses. Conclusion: claiming a trend where the error bars overlap. Evaluation: convection currents and surface tension on the thread ignored.
Data: Needs a 0.01 g balance or sensitive force sensor and a large block; the main uncertainty is that the expected effect is only a few percent.

Warming a lubricant to change sliding friction

Research question. How does the temperature of vegetable oil, varied from 20 °C to 60 °C in 10 °C steps, affect the coefficient of kinetic friction of a wooden block pulled at constant speed across a glass plate?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Worth doing only if you accept that lubricated friction may not follow F = μR. Measure viscosity separately with a falling ball and you have a strong personal twist.

Method, physics and where marks are lost+

Independent variable: Oil temperature, 20, 30, 40, 50, 60 °C (5 values), each with 5 repeat pulls. Oil film heated in a water bath before being spread.
What you measure: Pulling force read from a force sensor (or a newton meter dragged by a motor) at constant speed; μk = F / (mg) from the mean force. Oil temperature checked with a digital thermometer just before each pull.
Controlled variables: Block mass and contact area (same block, same load). Oil volume and film thickness (measured with a syringe and spread with a fixed template). Pulling speed (motor or timed with video). Surface cleaned and re-oiled between runs.
Physics and graph: F = μk R with R = mg on a horizontal surface. Plot μk against temperature, or ln μk against 1/T if testing an Arrhenius type viscosity trend. Gradient shows how sensitive friction is to viscosity change.
SL and HL: SL: measure, plot, describe the trend and discuss uncertainty. Stronger work links μk to viscosity, separates boundary from fluid lubrication, and justifies a model, rather than only reporting a trend.
Where marks are lost: Research design: oil cools during the run, so temperature is not really controlled. Data analysis: pulling force is jerky and the mean is taken without checking for stick slip. Evaluation: not asking whether μk is a valid quantity for a fluid film.
Data: Needs a force sensor and a heated bath; the oil cooling between heating and pulling is the main uncertainty in temperature.

Water flow through tubes of different bore

Research question. How does the internal diameter of a horizontal tube, varied from 2 mm to 8 mm using 6 tubes of equal length 30 cm, affect the volume flow rate of water driven by a constant head of 50 cm?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. A good one if you keep the head constant and check laminar flow. Twist: repeat with a glycerol and water mix to bring viscosity into the analysis.

Method, physics and where marks are lost+

Independent variable: Internal tube diameter, 6 values from 2 mm to 8 mm, measured with a vernier caliper or a travelling microscope and repeated 3 times.
What you measure: Volume collected in a measuring cylinder over a set time, timed with a stopwatch, giving flow rate in mL s⁻¹. The flow is also checked by running for at least 30 s.
Controlled variables: Pressure head, kept constant by an overflow bucket or Mariotte bottle. Water temperature, checked with a thermometer since viscosity depends on it. Tube length, cut to the same length. Tube inlet and outlet height, fixed.
Physics and graph: For laminar flow Poiseuille's law gives Q = πΔP r⁴/(8ηL), so Q ∝ d⁴. Plot Q against d⁴, and the gradient gives πΔP/(128ηL), allowing viscosity to be found. Check the Reynolds number, since turbulent flow breaks the relationship.
SL and HL: SL students plot log Q against log d and find the exponent, comparing it to 4. Top band work considers the range of laminar flow and the inlet effects, and finds the viscosity. Poiseuille's law goes beyond the syllabus, so the physics must be explained clearly.
Where marks are lost: Research design: the head falls as the container drains, so pressure is not constant. Data analysis: uncertainty in a small diameter is large and is raised to the fourth power. Conclusion: fitting a power without testing the exponent against the uncertainty. Evaluation: ignoring turbulence at large diameter and entrance effects.
Data: Needs rigid tubes of different bore, a constant head arrangement and a measuring cylinder. The main uncertainty is bore diameter and unsteady head.

Young modulus of copper wire from load extension graph

Research question. What is the Young modulus of a 2.0 m length of copper or constantantan wire, found by adding masses from 0.5 kg to 4.0 kg in 0.5 kg steps and measuring the extension, and how does it compare with the accepted value?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Solid classic that works well if you use a long, thin wire. It is well known, so a twist helps: compare a wire before and after annealing with a hot flame, or across three different metals.

Method, physics and where marks are lost+

Independent variable: Load applied to the wire, from 0.5 kg to 4.0 kg in 8 steps, loading and then unloading to check for elastic behaviour.
What you measure: Extension measured with a vernier scale, a travelling microscope or a ruler with a pointer (±0.1 mm). Wire diameter measured with a micrometer at several points. Young modulus from the gradient of stress against strain.
Controlled variables: Original wire length, measured from clamp to marker. Wire material and diameter, using one wire from the same reel. Temperature, kept at room level. Kinks removed by preloading with a small mass before starting.
Physics and graph: E = stress/strain = (F/A)/(ΔL/L). Plot force against extension, so the gradient equals EA/L, and E = gradient × L/(πd²/4). Stay within the linear elastic region.
SL and HL: SL students get E from a straight line gradient and compare it. Top band work propagates the diameter uncertainty (squared in the area), identifies the limit of proportionality, and repeats with another wire. There is no HL syllabus need.
Where marks are lost: Research design: the stated variables are muddled, with force as independent but a stated aim to find E, and a short wire that gives tiny extensions. Data analysis: using a single diameter reading, which dominates the uncertainty. Conclusion: not checking elastic limit. Evaluation: ignoring the wire's slippage in the clamp and kinks.
Data: Needs a long thin wire, a strong clamp, a micrometer and a precise extension scale. The main uncertainty is diameter and small extensions.

Young modulus of wires and rubber from load-extension data

Research question. How does the Young modulus of copper, steel and nylon wires of equal diameter, found from load-extension gradients for loads of 0.5 N to 5.0 N in 0.5 N steps, compare with database values?

A.2 Forces and momentum
SL and HL
Needs care
Rarely listed

My take. Worth choosing if you have a long wire and a good way to read tiny extensions. Make it personal by testing something unusual such as fishing line or guitar strings from your own instrument, and avoid the vague 'compare materials' framing.

Method, physics and where marks are lost+

Independent variable: Wire material (copper, steel, nylon, three to four samples), and load added in 8 to 10 steps from 0.5 N to 5 N, each loaded and unloaded three times.
What you measure: Extension measured with a travelling microscope or a ruler against a fixed marker (mm); diameter measured with a micrometer at five points. Stress = F/A and strain = extension/original length are calculated.
Controlled variables: Original length: fixed clamp to marker distance measured with a metre rule. Diameter: micrometer check at several points. Temperature: same room, short runs. Load: kept under the elastic limit by checking the wire returns to zero extension.
Physics and graph: Stress = F/A, strain = x/L, E = stress/strain. Plot stress against strain: the gradient in the linear region is the Young modulus. Rubber gives a curve with hysteresis, which is a useful contrast but cannot give a single E.
SL and HL: SL: get E for two or three wires and compare with tabulated values. Top band: propagate the diameter uncertainty (it enters squared), locate the limit of proportionality objectively, and discuss hysteresis and work done from the area under a force-extension graph.
Where marks are lost: Research design: overloading past the elastic limit, or a vague RQ about 'differences'. Data analysis: ignoring diameter uncertainty, which dominates. Conclusion: no comparison with an accepted value. Evaluation: not mentioning slipping at the clamp or the kinks in the wire.
Data: Long thin wires, a clamp, slotted masses and a travelling microscope are needed; the main uncertainty is the small extension (under 2 mm) and the wire diameter.

Ideas were collected from public lists and published IA titles, merged when they are the same investigation, and rewritten from scratch. “On N sites” counts how many public lists carry the same investigation. How this list was made.

Frequently asked questions

What are good IB Physics IA ideas on forces and momentum?

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Good starting points with easy data that few sites list are apparent weight loss in liquids and archimedes' principle, buoyant force on submerged cylinders of different volume and comparing density methods for metals and plastics. Each one gives a straight-line graph from school equipment, which is what the Data analysis and Conclusion criteria need.

Which forces and momentum IA ideas are overdone?

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falling-sphere viscosity of honey across temperature, acceleration against sin θ on a friction-affected ramp, cantilever length and end deflection of a metal strip and drag on falling paper cones with changing area appear on three or more public lists. They still work, but they need a twist that shows your own thinking.

Can I do a forces and momentum IA at SL?

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51 of the 52 ideas use SL physics. The others rely on HL-only content and are marked as HL topics.

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