75 IB Physics IA Ideas: Scientific Investigation Starters for SL and HL

1. Free fall and the constant-acceleration model

Physics focus: Kinematics, uniform acceleration and the onset of air resistance (SL/HL core).

Investigation starter: Rather than simply determining g, investigate how release height affects the experimentally determined value of g for a dense sphere falling through air — and whether any systematic drift with height is resolvable within uncertainty.

Possible measurement: An electromagnetic or mechanical release with light gates, or high-frame-rate video analysis, across a useful range of heights. Determine g from a linearised model such as s against t², and inspect the residuals for systematic structure.

Variants and extensions: Compare two sphere diameters or densities to identify where drag becomes non-negligible; compare light-gate timing against video analysis of the same drop to quantify method-dependent uncertainty, which converts the investigation into a method-validation study.

2. Projectile range and launch angle

Physics focus: Two-dimensional kinematics and the independence of horizontal and vertical motion (SL/HL core).

Investigation starter: Investigate how launch angle affects horizontal range for a projectile launched at approximately constant speed, testing the full projectile model rather than only locating the angle of maximum range.

Possible measurement: Calibrate the launch speed independently first — this is the step most students skip and the one that determines whether the analysis works. Then launch at several angles with controlled launch and landing geometry, recording range and, where possible, the full trajectory by video analysis.

Variants and extensions: Investigate unequal launch and landing heights, which shifts the optimum angle below 45° and gives you a genuine prediction to test; use maximum height or time of flight as the dependent variable instead; compare two ball sizes to probe drag.

3. Projectile motion with air resistance from video trajectories

Physics focus: Drag forces, model comparison and numerical modelling (HL-level extension).

Investigation starter: Investigate how projectile cross-sectional area affects the departure of a measured trajectory from the no-drag model.

Possible measurement: Launch lightweight objects with controlled initial conditions and obtain x(t) and y(t) from calibrated video analysis. Fit the no-drag model first, then quantify the systematic residuals, or compare against a numerical drag model built in a spreadsheet.

Variants and extensions: Compare spheres of similar mass but different diameter; compare paper projectiles of different shapes; estimate an effective drag coefficient from the trajectory. This is strongest when the modelling is transparent — assumptions stated, models compared quantitatively, no black-box software output.

4. Acceleration on an inclined plane

Physics focus: Resolution of forces, Newton’s second law and rolling resistance (SL/HL core).

Investigation starter: Investigate how ramp angle affects the acceleration of a dynamics cart when rolling resistance is small but not zero — and whether an intercept or modified model is justified by the data.

Possible measurement: A motion sensor, light gates or video analysis at several angles. Plot a against sin θ and interpret both the gradient and the intercept.

Variants and extensions: Compare two surface materials; compare wheel or bearing conditions; use a friction-compensated air track as a control. Angle uncertainty dominates at small slopes and deserves explicit propagation — a point almost no student makes and every examiner notices.

5. Terminal velocity and mass-to-area ratio

Physics focus: Drag models, terminal velocity and power-law relationships (SL/HL core).

Investigation starter: Investigate how mass-to-area ratio affects terminal velocity for nested coffee filters or geometrically similar paper cones.

Possible measurement: Release from sufficient height to establish a clear constant-velocity region, then measure terminal speed by video analysis or multiple light gates for several masses at controlled projected area.

Variants and extensions: Change projected area at approximately constant mass; compare quadratic-drag and linear-drag models over different speed ranges. Test the power-law relationship by fitting an exponent rather than assuming one — the fitted exponent, with its uncertainty, is the result.

6. Viscosity from Stokes drag

Physics focus: Viscous drag, terminal velocity and fluid properties (SL/HL core).

Investigation starter: Investigate how liquid temperature affects the dynamic viscosity determined from the terminal speed of a falling sphere.

Possible measurement: Drop small spheres through a tall transparent column, measuring velocity only in a central region well below the entry point and well above the base. Apply Stokes’ law with an explicit wall-correction discussion if the tube is not wide compared with the sphere.

Variants and extensions: Vary sphere radius at fixed temperature to test the r² dependence; compare two liquids of substantially different viscosity. Check the Reynolds-number assumption explicitly — Stokes’ law requires low Reynolds number, and stating that you have verified it is worth real marks.

7. Newton’s second law with a trolley or air track

Physics focus: Newton’s second law applied to a connected system (SL/HL core).

Investigation starter: Investigate how net driving force affects the acceleration of a trolley system whose total mass is held constant.

Possible measurement: Transfer mass from the trolley to the hanging mass so that the total system mass stays nearly constant while the driving force changes — this is the design detail that separates a real investigation from the standard practical. Measure acceleration with a motion sensor or light gates.

Variants and extensions: Hold force constant and vary total mass; repeat on an air track to quantify the influence of friction. Model the whole system rather than applying F = ma to one object; the intercept of F against a then carries physical meaning.

8. One-dimensional collisions: momentum and restitution

Physics focus: Conservation of momentum, elastic and inelastic collisions (SL/HL core).

Investigation starter: Investigate how mass ratio affects the coefficient of restitution and the momentum transfer in a one-dimensional collision.

Possible measurement: Low-friction carts with magnets, springs or hook-and-loop fastening, recording velocities immediately before and after impact with motion sensors or video analysis. Change the mass ratio while keeping the collision interface identical.

Variants and extensions: Compare elastic-like and inelastic attachments; investigate whether approach speed changes restitution. Treat momentum conservation and energy loss as two separate questions — conflating them is the standard error here.

9. Two-dimensional collisions from overhead video

Physics focus: Vector momentum conservation in two dimensions (HL-level extension).

Investigation starter: Investigate how impact parameter affects the distribution of momentum between two pucks in a two-dimensional collision.

Possible measurement: An air table or very low-friction surface with an overhead camera. Track both objects before and after the collision by video analysis and resolve momentum into perpendicular components.

Variants and extensions: Use equal and unequal masses; compare magnetic repulsion with direct mechanical contact. A component-wise vector uncertainty treatment is essential, and quantifying the fractional momentum discrepancy is far stronger than presenting a vector diagram that “looks about right”.

Where this goes wrong: without a genuinely low-friction surface, the pucks decelerate measurably between frames and the “before” and “after” momenta are measured at different effective times. If your school has no air table, choose entry 8 instead.

10. Coefficient of restitution of a bouncing ball

Physics focus: Energy transfer, deformation and restitution (SL/HL core).

Investigation starter: Investigate how surface material, impact speed, temperature or inflation pressure affects the coefficient of restitution of a ball.

Possible measurement: Drop from controlled heights and determine rebound speed using video analysis, light gates or acoustic timing of successive impacts.

Variants and extensions: Ball temperature is an excellent independent variable if you can control and measure it — it produces a large, clean effect. Using velocities immediately before and after impact is considerably stronger than using peak heights, because it removes the assumption that no energy is lost in flight.

11. Impulse and cushioning

Physics focus: Impulse, the force–time integral and momentum change (SL/HL core).

Investigation starter: Investigate how cushioning thickness affects peak collision force for approximately the same change in momentum.

Possible measurement: Drive a cart into cushioning mounted on a force sensor, recording force–time curves and cart velocities so that the impulse ∫F dt can be compared directly with Δp.

Variants and extensions: Compare material type at equal thickness; compare layered structures of equal total thickness. Analyse both impulse and peak force, and separate genuine changes in collision duration from the sampling limitations of your force sensor — collisions can be shorter than the sensor’s response time.

12. Static and kinetic friction

Physics focus: Frictional forces and the friction model (SL/HL core).

Investigation starter: Investigate how normal force affects the maximum static friction and the kinetic friction for a selected material pair.

Possible measurement: Pull a block using a force sensor while varying added mass, with a consistent surface preparation and a slow, repeatable pulling protocol.

Variants and extensions: Turn the same block onto faces of different contact area to test the area-independence claim directly — a genuine test of a model students are usually told to accept. Fit friction force against normal force and interpret any non-zero intercept rather than forcing the line through the origin.

13. Centripetal force in uniform circular motion

Physics focus: Circular motion and centripetal force (SL/HL core).

Investigation starter: Investigate how angular speed affects the centripetal force required for a fixed rotating mass and radius.

Possible measurement: A rotating platform, purpose-built centripetal-force apparatus, or a carefully controlled whirling-bung system with a force sensor for direct comparison against F = mω²r. Measure radius and period precisely.

Variants and extensions: Vary radius at fixed angular speed; vary rotating mass at fixed radius and speed. Linearise deliberately — plot F against ω² — and propagate uncertainty carefully, since ω is squared and period uncertainty is therefore doubled in fractional terms.

14. Mechanical energy losses on a ramp

Physics focus: Energy conservation, dissipation and rotational kinetic energy (SL/HL core).

Investigation starter: Investigate how surface material affects the fraction of mechanical energy dissipated by a cart travelling down a fixed ramp.

Possible measurement: Measure height loss and speed at a defined position using video analysis or light gates, then compare the change in gravitational potential energy with the kinetic energy gained.

Variants and extensions: Investigate ramp angle at fixed vertical drop; compare rolling objects of different rotational inertia. Account for rotational kinetic energy if anything rolls — for a rolling cylinder this is a third of the total, so ignoring it produces an “energy loss” that is really an arithmetic omission.

15. Efficiency of a small electric motor

Physics focus: Electrical and mechanical power, energy transfer and efficiency (SL/HL core).

Investigation starter: Investigate how mechanical load affects the efficiency of a DC motor lifting a mass.

Possible measurement: Electrical input power from voltage and current, useful mechanical output from mgh/t, across several loads within the motor’s safe operating range. Allow cooling between trials — motor resistance rises with temperature and will drift your results otherwise.

Variants and extensions: Investigate supply voltage at fixed load; compare gear ratios using the same motor. Efficiency typically rises then falls with load, and explaining that shape physically — rather than just plotting it — is where the conclusion marks are.

16. Elastic energy and the limit of Hooke’s law

Physics focus: Elasticity, elastic potential energy and model validity (SL/HL core).

Investigation starter: Investigate how extension affects the validity of Hooke’s law and the elastic energy stored in a spring or elastic cord.

Possible measurement: Record force–extension data over a safe range, including loading and unloading. Integrate the area under the F–x curve numerically rather than assuming E = ½kx² once the response becomes non-linear.

Variants and extensions: Compare two spring constructions; investigate hysteresis in an elastic cord, where the area between loading and unloading curves gives the energy dissipated per cycle. This becomes IA-worthy when the limit of proportionality is identified quantitatively and the linear and non-linear models are compared, not merely mentioned.

17. Young’s modulus from cantilever deflection

Physics focus: Elastic behaviour of materials, stress and strain (SL/HL core, with extension scope).

Investigation starter: Investigate how the free length of a clamped cantilever affects its end deflection under a fixed load, and determine Young’s modulus for the beam material.

Possible measurement: Clamp a metre rule, hacksaw blade or metal strip horizontally, hang known masses at the free end, and measure deflection with a travelling microscope, dial gauge or fixed-camera image analysis. The deflection depends on L³, giving a strong, easily resolved signal.

Variants and extensions: Vary load at fixed length; compare two materials or two beam thicknesses. The beam thickness enters as a cube, so thickness measurement will dominate your uncertainty budget — measure it repeatedly along the beam and say so. An alternative route is direct wire extension using a Searle’s apparatus if your school has one.

18. Rolling resistance and energy dissipation

Physics focus: Rolling resistance as distinct from sliding friction (SL/HL core).

Investigation starter: Investigate how normal load affects the rolling resistance coefficient of a wheeled cart on a fixed surface.

Possible measurement: Use a very small adjustable incline and find the angle at which the cart travels at approximately constant speed, or pull at steady speed with a force sensor. Vary total mass without changing wheels or bearings.

Variants and extensions: Compare hard and soft wheel materials; compare smooth and textured surfaces. Define your rolling-resistance model explicitly and distinguish it from sliding friction; measuring the very small angles involved is the central experimental difficulty and deserves proper treatment.

19. Moment of inertia from torque and angular acceleration

Physics focus: Rigid-body dynamics, torque and moment of inertia (HL).

Investigation starter: Investigate how radial mass distribution affects the moment of inertia of a rotating system at constant total mass.

Possible measurement: Apply a known torque with a hanging mass and pulley, measure angular acceleration with a rotary sensor or video analysis, and infer I from τ = Iα. Move equal masses to different radii while keeping total mass fixed.

Variants and extensions: Compare a disc and a ring; test the predicted r² dependence for point masses by plotting inferred I against r² and comparing the gradient with the theoretical mass contribution. Include pulley inertia and axle friction — both are systematic and both are quantifiable.

20. Conservation of angular momentum

Physics focus: Angular momentum conservation under minimal external torque (HL).

Investigation starter: Investigate how the radial position of added masses affects angular speed when external torque is minimised.

Possible measurement: A low-friction turntable with movable masses, measuring angular velocity before and after the radius change using video markers or a rotary sensor.

Variants and extensions: Use two different total added masses; quantify bearing friction independently by measuring free spin-down, then correct for it. Model the full moment of inertia including the turntable itself — treating the system as point masses on a massless platform is the standard error and it shows up immediately as a systematic discrepancy.

21. Rolling acceleration and the moment-of-inertia factor

Physics focus: Rolling without slipping, combined translational and rotational energy (HL).

Investigation starter: Investigate how the dimensionless moment-of-inertia factor affects the acceleration of objects rolling without slipping down the same incline.

Possible measurement: Roll a solid cylinder, hollow cylinder and sphere down a ramp, obtaining acceleration by video analysis, and compare against a = g sin θ / (1 + I/mR²).

Variants and extensions: Keep outer radius similar while changing internal mass distribution — purpose-built objects give you a continuous variable rather than three categories; investigate the onset of slipping by changing surface material. Verify the no-slip condition is actually satisfied rather than assuming it.

22. Compound pendulum and pivot position

Physics focus: Physical pendulum, moment of inertia and the parallel-axis theorem (HL).

Investigation starter: Investigate how the pivot distance from the centre of mass affects the period of a physical pendulum.

Possible measurement: A metre rule or rigid bar with several drilled pivot positions, timing multiple oscillations at small amplitude, then fitting the physical-pendulum model T = 2π√(I/mgd).

Variants and extensions: Add a movable mass to change both centre of mass and I; determine g from the best-fit model and compare with a local accepted value. This is far stronger as a model-fitting investigation — the period passes through a minimum, which is a genuine prediction to test — than as a one-point determination of g.

23. Specific heat capacity by electrical heating

Physics focus: Thermal energy transfer, specific heat capacity and systematic error (SL/HL core).

Investigation starter: Investigate how insulation thickness around a metal block affects the apparent specific heat capacity obtained by electrical heating — turning the dominant systematic error into the independent variable.

Possible measurement: Supply measured electrical power to a block of known mass and record temperature against time over a controlled interval. Estimate heat loss from the cooling curve after the heater is switched off rather than assuming it away.

Variants and extensions: Compare two block materials with the same heater; vary heating power and extrapolate towards the zero-heat-loss limit. The IA value is entirely in the loss modelling — a single application of Q = mcΔT with a percentage error is not an investigation.

24. Latent heat of fusion of ice by energy balance

Physics focus: Phase change, latent heat and calorimetry (SL/HL core).

Investigation starter: Investigate how initial water temperature affects the experimentally determined specific latent heat of fusion of ice.

Possible measurement: Add dry, melting-point ice to a known mass of warm water in an insulated calorimeter, measuring masses and equilibrium temperature precisely and including the calorimeter’s heat capacity where significant.

Variants and extensions: Compare insulated container designs; use electrical melting as an independent second method. Correct for surface water on the ice and address whether the ice began below 0 °C — starting temperature is the hidden variable that makes results drift systematically high.

25. Latent heat of vaporisation from steady mass-loss rate

Physics focus: Phase change, power and energy accounting (SL/HL core).

Investigation starter: Investigate how heater power affects the latent heat of vaporisation inferred from the steady boiling mass-loss rate of water.

Possible measurement: Once boiling is steady, measure mass loss over time at several electrical powers using a balance and data logger.

Variants and extensions: Compare insulated and uninsulated vessels. The elegant feature here is the analysis: plotting power against mass-loss rate gives latent heat from the gradient while the intercept represents the approximately constant environmental heat loss, which a single-power calculation can never separate. This is one of the cleanest examples on the page of a design that isolates a systematic error rather than apologising for it.

26. Newton’s law of cooling and the exponential model

Physics focus: Heat transfer, exponential decay and model validity (SL/HL core).

Investigation starter: Investigate how exposed surface area affects the cooling constant of water under otherwise identical conditions.

Possible measurement: A temperature probe logging at short regular intervals, analysed as ln(T − T_env) against time over the region where Newton’s cooling is a reasonable model. Record the ambient temperature independently — it is not constant in a laboratory with thirty people in it.

Variants and extensions: Compare insulation thickness; compare covered and uncovered containers to isolate evaporation; compare natural and fan-assisted convection. Inspect the residuals and resist claiming a single exponential holds across the whole range — at high temperatures radiation and evaporation both intrude, and demonstrating where the model breaks is a stronger conclusion than pretending it does not.

27. Thermal conductivity of an insulating layer

Physics focus: Conduction, steady-state heat flow and thermal resistance (SL/HL core).

Investigation starter: Investigate how thickness affects the steady-state rate of heat transfer through a chosen insulating material.

Possible measurement: Establish a repeatable temperature difference across slabs of known area and measure the electrical input required to maintain steady state, or use calibrated heat-flow apparatus.

Variants and extensions: Compare materials at equal thickness; investigate stacked layers and the contact resistance between them, which is a genuinely interesting effect and produces a non-zero intercept when total thermal resistance is plotted against thickness. Edge losses are the main threat to the one-dimensional assumption.

28. Linear thermal expansion of a metal

Physics focus: Thermal expansion and precision displacement measurement (SL/HL core).

Investigation starter: Investigate how temperature change affects the extension of a metal rod over a controlled range.

Possible measurement: Heat a long rod uniformly with steam or a controlled heater and measure the extension with a dial gauge, optical lever or displacement sensor. Measure the rod temperature rather than assuming it equals the heater temperature.

Variants and extensions: Compare two metals; use a bimetallic strip and measure curvature if suitable apparatus exists. Because the displacement is of order tens of micrometres per metre per kelvin, calibration and zero drift are the whole experiment. Fit ΔL against L₀ΔT and quote the expansion coefficient with a properly propagated uncertainty.

Where this goes wrong: if your only length-measuring instrument is a millimetre rule, the expected extension is smaller than your resolution and there is no investigation. Confirm you have a dial gauge or displacement sensor before committing.

29. Albedo and equilibrium temperature

Physics focus: Radiative heating, absorptivity and thermal equilibrium (SL/HL core).

Investigation starter: Investigate how surface reflectivity affects the equilibrium temperature reached under a fixed radiant source.

Possible measurement: Expose matched surfaces to the same lamp at fixed distance and orientation, recording temperature–time curves to near steady state, and quantify reflectivity independently with a light sensor rather than describing the surfaces by colour.

Variants and extensions: Compare matte and glossy finishes of similar colour, which decouples reflectivity from colour; investigate angle of incidence. Equilibrium temperature, initial heating rate and thermal time constant are three different dependent variables — choose one as primary and report the others as supporting evidence.

30. Surface emissivity from cooling curves

Physics focus: Thermal radiation, emissivity and the competing convection channel (SL/HL core).

Investigation starter: Investigate how surface finish affects the radiative cooling rate of objects of identical geometry.

Possible measurement: Identical cans or metal plates with different finishes, cooling through the same temperature interval, using contact probes for true temperature. If you use an infrared camera, calibrate its emissivity setting deliberately — an IR camera reading a polished surface is measuring the reflected room, not the object.

Variants and extensions: Compare matt black paint, polished metal and foil; compare still air with reduced-convection shielding. At modest temperatures convection is comparable to or larger than radiation, so the honest evaluation addresses how far the design isolates emissivity at all.

31. Boyle’s law and syringe dead volume

Physics focus: Ideal gas behaviour and isothermal compression (SL/HL core).

Investigation starter: Investigate how gas volume affects pressure for a trapped gas held as close to isothermal as possible, and estimate the apparatus dead volume from the fit.

Possible measurement: A sealed syringe with a pressure sensor, changing volume slowly and allowing thermal re-equilibration at each setting. Record absolute pressure. Do not use mercury-plug methods — a sealed sensor–syringe system is safer and gives better data.

Variants and extensions: Compare slow and rapid compression to reveal thermal effects. Plot P against 1/V, or fit P(V) = nRT/(V + V₀) where the dead volume matters. Extracting V₀ as a fitted parameter lifts this well clear of the standard practical.

32. Gas thermometry and extrapolation to absolute zero

Physics focus: Absolute temperature scale and the ideal gas law (SL/HL core).

Investigation starter: Investigate how linearly gas pressure at fixed volume varies with temperature across an accessible range, and what that implies for the absolute zero of temperature.

Possible measurement: A small sealed gas volume connected to a pressure sensor, with the reservoir immersed in controlled water baths and time allowed for full thermal equilibrium at each point.

Variants and extensions: Use volume at constant pressure with a gas syringe instead; compare two initial pressures. Fit pressure against Celsius temperature and extrapolate to zero pressure, while being explicit that extrapolating roughly 300 K beyond a 70 K measured range carries an uncertainty most students dramatically understate.

33. Isothermal versus near-adiabatic compression

Physics focus: Polytropic processes, heat-transfer timescales and thermodynamics (HL).

Investigation starter: Investigate how compression time affects the pressure–volume path of a fixed gas sample, and fit the effective polytropic exponent.

Possible measurement: Compress a gas syringe slowly and then rapidly while logging pressure at a high sample rate alongside volume, then compare PV and PV^γ behaviour for the two limits.

Variants and extensions: Investigate expansion as well as compression; fit n in PVⁿ = constant as a continuous function of compression time. The strong version fits the exponent and discusses heat-transfer timescales, sensor response time and leakage, rather than labelling two runs “adiabatic” and “isothermal” by assertion.

Where this goes wrong: obtaining volume simultaneously with a fast pressure trace is the practical difficulty. Film the syringe plunger against a scale in the same frame as a clock, or accept that only the end points are well characterised and design the research question around those.

34. Current–voltage characteristics of non-ohmic devices

Physics focus: Ohmic and non-ohmic conduction, dynamic resistance (SL/HL core).

Investigation starter: Investigate how device temperature or illumination affects the current–voltage characteristic of a filament lamp, diode, thermistor or light-dependent resistor.

Possible measurement: Measure V and I across a safe operating range, changing one physical condition between runs rather than reproducing a single textbook curve.

Variants and extensions: Filament lamp — extract cold and hot resistance and infer filament temperature from the resistance–temperature relation of tungsten; diode — compare characteristics at two temperatures; LDR — vary illuminance at fixed geometry. Use differential resistance dV/dI where the curve is non-linear, and explain the physical origin of the shape.

35. Resistivity and temperature coefficient of a wire

Physics focus: Resistivity, conduction in metals and precision measurement (SL/HL core).

Investigation starter: Investigate how temperature affects the resistivity of a metal wire over a controlled range, and determine the temperature coefficient.

Possible measurement: A four-wire measurement if available, otherwise keep lead and contact resistance small and consistent. Place the wire in a controlled bath and measure resistance only after thermal equilibrium.

Variants and extensions: At fixed temperature, vary length to obtain resistivity from the gradient; compare two alloys of similar diameter. Diameter measurement usually dominates the uncertainty because area depends on diameter squared — take repeated readings at several points along the wire and quote the spread, not the instrument resolution.

36. Thermistor resistance–temperature modelling

Physics focus: Semiconductor conduction and exponential models (SL/HL core).

Investigation starter: Investigate how well a selected NTC thermistor follows an exponential or Beta-parameter model across a chosen temperature range.

Possible measurement: Well-stirred water baths, full equilibration, and a low measuring current to avoid self-heating — a thermistor dissipating even a few milliwatts reads its own heat, not the bath’s.

Variants and extensions: Compare heating and cooling runs to expose thermal lag; estimate the Beta constant from a linearised plot of ln R against 1/T. State the range over which the model holds and check the residuals rather than quoting a correlation coefficient.

37. EMF and internal resistance of a cell

Physics focus: EMF, internal resistance and terminal potential difference (SL/HL core).

Investigation starter: Investigate how cell temperature or state of discharge affects internal resistance.

Possible measurement: Several known load resistances with terminal voltage and current recorded quickly enough to limit state-of-charge drift, then obtain EMF and internal resistance from V = ε − Ir.

Variants and extensions: Track internal resistance as a cell discharges under a controlled protocol — this gives a genuine time series rather than a single fit; compare chemistries only where ratings match and handling is safe. Treat the cell as a system that is changing while you measure it, and use fitted gradient and intercept uncertainties.

38. RC charging and discharging

Physics focus: Capacitance, time constants and exponential decay (HL).

Investigation starter: Investigate how resistance affects the measured time constant of an RC circuit for a fixed capacitor.

Possible measurement: Log capacitor voltage during charge or discharge for several resistances using a data logger or oscilloscope, then fit the exponential directly.

Variants and extensions: Vary capacitance instead; investigate how the voltmeter’s own input resistance distorts the result at large R, which is a real and quantifiable systematic effect and an unusually good evaluation topic. Compare fitted τ with the nominal RC using component tolerances — direct exponential fitting generally preserves the uncertainty structure better than taking logarithms of noisy late-time data.

39. Solar cell characteristics and irradiance

Physics focus: Photovoltaic conversion, maximum power point and efficiency (SL/HL core, extension scope).

Investigation starter: Investigate how incident irradiance affects the maximum power output, open-circuit voltage and short-circuit current of a small photovoltaic cell.

Possible measurement: Vary lamp distance or use calibrated neutral-density filters, measuring irradiance with a light sensor rather than assuming an inverse-square fall-off. Sweep a variable load resistance to trace the full I–V curve at each irradiance and locate the maximum power point.

Variants and extensions: Investigate angle of incidence; investigate cell temperature, which lowers open-circuit voltage measurably and is a genuinely interesting competing effect when using an incandescent lamp. Short-circuit current is close to linear in irradiance while open-circuit voltage is roughly logarithmic — testing both against those predictions is a strong analysis.

40. Transformer turns ratio and efficiency

Physics focus: Electromagnetic induction, mutual inductance and power transfer (HL).

Investigation starter: Investigate how the secondary-to-primary turns ratio affects output voltage and power-transfer efficiency for a demountable transformer under a fixed load.

Possible measurement: A demountable transformer kit with interchangeable coils, measuring primary and secondary RMS voltage and current with a suitable meter or oscilloscope, at low voltage only and under teacher supervision.

Variants and extensions: Investigate load resistance at a fixed turns ratio; compare a closed magnetic core with a deliberately introduced air gap to quantify flux leakage. The ideal-transformer relation fails progressively as losses grow, and characterising how it fails is more interesting than confirming it holds approximately.

41. Comparing measurement methods for one electrical quantity

Physics focus: Measurement uncertainty, systematic bias and method validation (SL/HL core).

Investigation starter: Measure one quantity — resistance, capacitance, a time constant or a power output — by two independent methods, and investigate how their agreement depends on the value being measured.

Possible measurement: For example, resistance from a voltmeter–ammeter method versus a direct multimeter reading, across a range spanning ohms to megohms, where meter loading changes which method is more trustworthy.

Variants and extensions: Frame the research question around accuracy, precision or systematic bias rather than around the quantity itself. This is the Physics counterpart of a method-validation study, and it is consistently under-used: it gives you real data on both sides of a disagreement and a physical explanation for it, which is exactly the territory the evaluation criterion rewards.

42. Mass–spring SHM and the effective mass of the spring

Physics focus: Simple harmonic motion and the limits of an idealised model (SL/HL core).

Investigation starter: Investigate how attached mass affects the period of a vertical spring–mass oscillator when the spring’s own mass is not negligible.

Possible measurement: Time many complete cycles for several added masses at small amplitude, then plot T² against added mass and examine the intercept, which carries the spring’s effective mass contribution — theoretically one third of the spring mass.

Variants and extensions: Compare two springs of markedly different mass and test whether the fitted effective-mass fraction is consistent between them; use a motion sensor to fit the sinusoid directly. The intercept is the whole investigation — it is a specific, testable prediction that the standard practical throws away.

43. Pendulum period beyond the small-angle approximation

Physics focus: SHM, the small-angle approximation and model validity (SL/HL core).

Investigation starter: Investigate how initial angular amplitude affects the period of a simple pendulum, and identify the amplitude at which the small-angle approximation ceases to agree with measurement within uncertainty.

Possible measurement: Fixed length, amplitudes from small to moderately large, timing over many cycles with an optical gate or video analysis to remove reaction-time bias. The correction is roughly 1.7% at 30°, so your timing precision must be better than that — time at least twenty cycles.

Variants and extensions: Compare the measured period against the first-order correction term and against a numerical solution of the full pendulum equation; at small amplitude, vary length to determine g as a supporting result. A “period is independent of amplitude” demonstration is too weak; the point is to find where that stops being true.

44. Damped oscillations and the decay constant

Physics focus: Damping, exponential envelopes and energy dissipation (SL/HL core).

Investigation starter: Investigate how damping strength affects the exponential decay constant of an oscillator.

Possible measurement: A mass–spring system or pendulum with an adjustable vane in air or a viscous medium, tracking successive peak amplitudes by video analysis or motion sensor and fitting A = A₀e^−bt.

Variants and extensions: Vary vane area; vary fluid viscosity; investigate how damping shifts the measured period, which is a small but real effect. Fit the envelope across many peaks and report the parameter uncertainty, and check that changing the damping has not also changed the restoring force.

45. Torsional pendulum: period and moment of inertia

Physics focus: Rotational oscillation and torsion constant (HL).

Investigation starter: Investigate how the radial position of added masses affects the period of a torsional pendulum.

Possible measurement: Suspend a rigid platform from a torsion wire, place equal masses symmetrically at several radii, and test T = 2π√(I/κ) by linearising T² against r².

Variants and extensions: Determine the torsion constant κ independently using an object of calculable moment of inertia; investigate damping at different amplitudes while staying within the linear regime. Account for the platform’s own inertia, which appears as the intercept.

46. Driven resonance and quality factor

Physics focus: Forced oscillation, resonance and damping (HL).

Investigation starter: Investigate how damping affects the resonant frequency and the quality factor of a driven oscillator.

Possible measurement: Drive a spring–mass or pendulum system at controlled frequencies, waiting for transients to decay before recording steady-state amplitude, and repeat for at least two damping conditions.

Variants and extensions: Use the phase difference between driver and oscillator as a second dependent variable, which is more diagnostic than amplitude near resonance; compare mechanical resonance with an electrical RLC resonance if the equipment exists. Collect enough points around the peak to fit a response curve — Q comes from the bandwidth, not from the height of the tallest bar.

47. Wave speed on a string from standing waves

Physics focus: Standing waves, tension and linear density (SL/HL core).

Investigation starter: Investigate how string tension affects wave speed for a string of fixed linear density, testing v = √(T/μ).

Possible measurement: A vibration generator and signal generator, identifying resonant frequencies for known lengths and modes, with μ measured independently by weighing a known length.

Variants and extensions: Vary linear density using several strings and test the μ^−1/2 dependence; hold frequency fixed and vary tension to maintain a chosen mode. Do not assume the hanging weight equals the tension exactly if pulley friction is appreciable — this is a real systematic offset that shows up in the intercept.

48. Air-column resonance and end correction

Physics focus: Standing waves in pipes and the effective length of an open end (SL/HL core).

Investigation starter: Investigate how tube radius affects the end correction for an open pipe — making the correction term itself the object of study rather than a nuisance to be subtracted.

Possible measurement: Measure several resonant frequencies or resonant lengths for tubes of different internal radius, using multiple harmonics to infer effective length and hence end correction. A tone generator and phone microphone with spectrum software works well.

Variants and extensions: Compare one-end-open with both-ends-open tubes; investigate the end correction with and without a flange. A multi-harmonic fit is far stronger than a single tuning fork: plot mode number against resonant length and extract the correction from the intercept. Theory predicts roughly 0.6r, which gives you a specific value to test.

49. Speed of sound in air and its temperature dependence

Physics focus: Sound propagation and the kinetic origin of wave speed (SL/HL core).

Investigation starter: Investigate how air temperature affects the measured speed of sound, and compare the gradient with the prediction from the ideal-gas expression.

Possible measurement: Two microphones with a time-of-flight measurement, or a resonance tube at known frequencies, at several controlled temperatures. Measure the air temperature along the sound path, not at the wall of the room.

Variants and extensions: Compare open-pipe and closed-pipe resonance methods against the time-of-flight method as a three-way method comparison; investigate humidity only with a reliable sensor and a sufficient range. The speed changes by only about 0.6 m s⁻¹ per kelvin, so establish that your method can resolve that before committing.

50. Doppler shift of sound from a moving source

Physics focus: The Doppler effect for a mechanical wave (SL/HL core).

Investigation starter: Investigate how source speed affects the observed frequency shift for a moving sound source.

Possible measurement: Mount a stable tone source on a cart moving at measured speed past a fixed microphone, extracting frequency from short audio windows before and after closest approach using spectrum-analysis software.

Variants and extensions: Compare the exact Doppler expression with the low-speed approximation across your speed range; investigate observer motion instead of source motion, which has a subtly different expression and makes a genuinely interesting comparison. Do not swing a phone on a string — the speed is poorly controlled, the safety case is weak, and the geometry ruins the analysis.

51. Refractive index, Snell’s law and dispersion

Physics focus: Refraction, Snell’s law and wavelength dependence of refractive index (SL/HL core).

Investigation starter: Investigate how wavelength affects the refractive index of a glass or acrylic prism, testing a dispersion model rather than confirming Snell’s law at one wavelength.

Possible measurement: Measure the angle of minimum deviation for several laser wavelengths or for well-separated lines from a discharge lamp, using a spectrometer table or a carefully constructed protractor arrangement with a long optical lever.

Variants and extensions: Fit a two-term Cauchy relation, n = A + B/λ², and report A and B with uncertainties; investigate total internal reflection and determine the critical angle as an independent route to n, then compare the two values. Comparing two independent determinations of the same quantity is consistently one of the strongest analytical moves available.

52. Refractive index and solution concentration

Physics focus: Refraction as a quantitative analytical measurement (SL/HL core).

Investigation starter: Investigate how the concentration of a dissolved solute affects the refractive index of an aqueous solution, and evaluate the method as a concentration-measuring technique.

Possible measurement: A hollow semicircular prism or a rectangular tank with a laser and long screen distance, measuring the deviation angle across a concentration series. Temperature must be controlled — refractive index has a measurable temperature coefficient that will otherwise appear as scatter.

Variants and extensions: Determine an unknown concentration from your calibration and assess its uncertainty; compare two solutes at matched concentration. Frame the research question around the sensitivity and linear range of the method, which converts a calibration exercise into an investigation.

53. Young’s double-slit interference

Physics focus: Two-source interference and path difference (SL/HL core).

Investigation starter: Investigate how slit separation affects fringe spacing for monochromatic light at fixed screen distance.

Possible measurement: Record the pattern with a camera on a fixed mount and extract fringe positions from an intensity profile, or measure across many fringes with a travelling microscope. Measuring across ten or twenty fringe spacings reduces fractional uncertainty proportionally.

Variants and extensions: Compare laser wavelengths where these are known; investigate how finite slit width modulates fringe visibility, which brings in the single-slit envelope and is a genuine extension. State the small-angle approximation used in x = λD/a explicitly and check it is justified at your geometry.

54. Single-slit diffraction

Physics focus: Diffraction and the intensity distribution of a single slit (HL).

Investigation starter: Investigate how slit width affects the angular width of the central diffraction maximum.

Possible measurement: Adjustable or calibrated slits imaged at a fixed distance, determining minima positions from an intensity profile rather than by eye.

Variants and extensions: Vary wavelength at fixed slit width; fit the full sinc-squared intensity profile as an advanced extension, which uses the whole pattern rather than two positions. Slit-width calibration usually dominates the uncertainty — if you are using pre-made slits, measure them under a microscope rather than trusting the printed label.

55. Diffraction grating and spectral resolving power

Physics focus: Diffraction gratings, orders and resolution (HL).

Investigation starter: Investigate how grating line density affects the precision with which a spectral wavelength can be measured.

Possible measurement: Measure first- and higher-order diffraction angles for known spectral lines using two or more gratings, then compare the resulting wavelength uncertainties.

Variants and extensions: Use a discharge lamp and resolve several lines; investigate the ability to separate a close doublet as a direct test of resolving power. This is stronger than “measure the wavelength of a laser” precisely because the research question is about measurement quality, which can be quantified and evaluated rather than merely reported.

56. Polarisation and Malus’s law

Physics focus: Polarisation of light and intensity transmission (SL/HL core).

Investigation starter: Investigate how analyser angle affects transmitted intensity through two linear polarisers, and test Malus’s law across a full rotation.

Possible measurement: A stable light source and a photodiode or lux sensor, rotating the analyser in small angular steps with background intensity subtracted. Fit I = I₀cos²(θ − θ₀) + I_bg, keeping the phase offset and background as free parameters rather than assuming perfect alignment.

Variants and extensions: Insert a third polariser between crossed polarisers and vary its angle, which produces the cos²sin² result and is a much more interesting prediction to test; compare polariser performance at two wavelengths. Watch for sensor saturation and stray room light — both are specific, controllable limitations.

57. Thin-film interference with a wedge or Newton’s rings

Physics focus: Interference in thin films and path difference including phase change on reflection (HL).

Investigation starter: Investigate how wedge angle affects fringe spacing in an air wedge, or how ring radius varies with ring number in a Newton’s rings arrangement.

Possible measurement: An air wedge formed between glass slides separated by a thin spacer of known thickness, viewed under a travelling microscope with monochromatic illumination. A wedge with defined geometry is far easier to quantify than a freely draining soap bubble.

Variants and extensions: Determine the wavelength from known geometry, or the spacer thickness from known wavelength; with Newton’s rings, plot r² against ring number and extract the lens radius of curvature from the gradient.

Where this goes wrong: this entry is the most equipment-sensitive on the page. Without a travelling microscope and a monochromatic source you will not resolve the fringes reliably, and a soap-film version gives colours you cannot convert into thickness. Confirm the apparatus exists before choosing it.

58. Magnetic field around a straight current-carrying wire

Physics focus: Magnetic fields due to currents and the inverse relationship with distance (SL/HL core).

Investigation starter: Investigate how radial distance from a long straight wire affects magnetic flux density at fixed current.

Possible measurement: A Hall probe on a rigid position scale, with the background field zeroed and measurements repeated with the current reversed so that ambient offsets subtract out.

Variants and extensions: Vary current at fixed distance to test the linear dependence separately; compare against B = μ₀I/(2πr) and extract μ₀ from the gradient of B against 1/r. Probe positioning and the finite length of the conductor dominate the error budget; avoid distances comparable to the probe’s own dimensions.

59. Bar-magnet field and the dipole model

Physics focus: Magnetic dipole fields and near-field versus far-field regimes (SL/HL core).

Investigation starter: Investigate how axial distance affects the magnetic field strength of a bar magnet, and identify where the far-field r⁻³ dipole model becomes a good description.

Possible measurement: A Hall probe along the magnet axis with fixed orientation and background subtraction. A smartphone magnetometer can work, but only if you first locate the sensor within the phone, establish its orientation, and check its saturation limit — otherwise you are fitting a curve to a clipped signal.

Variants and extensions: Compare one magnet with two identical magnets stacked; fit a free exponent in B ∝ r⁻ⁿ and watch n approach 3 as distance grows. Fitting the exponent rather than assuming it is the analytical move that makes this an investigation.

60. Field inside a solenoid or Helmholtz pair

Physics focus: Magnetic fields of coils, superposition and field uniformity (SL/HL core).

Investigation starter: Investigate how coil separation affects the uniformity of the magnetic field between a pair of coaxial coils, or how turn density affects the axial field of a solenoid.

Possible measurement: A Hall probe traversed along the axis on a rigid scale, mapping B against position for several coil separations at fixed current.

Variants and extensions: Test the Helmholtz condition — that separation equal to the radius maximises uniformity — by quantifying uniformity as the percentage variation across a defined central region; investigate end effects in a solenoid, where the field falls to half its central value at the ends. Defining a numerical measure of “uniformity” is itself a good design decision to justify.

61. Force on a current-carrying conductor

Physics focus: The motor effect and F = BIL sin θ (SL/HL core).

Investigation starter: Investigate how current, active length or orientation angle affects the magnetic force on a conductor in an approximately uniform field.

Possible measurement: A current-carrying wire in the gap of a magnet assembly, with the force inferred from a top-pan balance reading or a force sensor. Reverse the current between readings to eliminate zero offsets.

Variants and extensions: Vary angle to test the sin θ factor, which is a far better model test than the linear current dependence; vary active length. Map or justify the field uniformity across the active length — assuming uniformity in a short magnet gap is the usual unstated error. A torsion-balance version measuring torque on a coil is possible but needs apparatus most schools lack.

62. Faraday’s law: induced EMF and rate of flux change

Physics focus: Electromagnetic induction and flux linkage (HL).

Investigation starter: Investigate how magnet speed through a coil affects the peak induced EMF and the integrated flux-change signal.

Possible measurement: Drop or drive the same magnet through a coil while measuring its speed independently, recording the EMF–time trace with a data logger or oscilloscope.

Variants and extensions: Vary the number of turns; use a rotating coil as a generator variant; use paired coils for transformer-style induction. Peak EMF depends on geometry and on sampling rate, so the time integral ∫ε dt — which should equal the total flux change regardless of speed — is a valuable complementary quantity and a strong test. Do not infer coil-crossing speed from drop height without measuring it.

63. Eddy-current damping and magnetic braking

Physics focus: Induced currents, Lenz’s law and dissipation (HL).

Investigation starter: Investigate how conductor thickness or conductivity affects the magnetic braking of a moving magnet.

Possible measurement: Time a strong magnet falling through non-magnetic conducting tubes of different wall thickness, or measure the damping of a pendulum swinging between conducting plates. Always include a non-conducting control of identical geometry.

Variants and extensions: Compare aluminium with copper at matched geometry, using the conductivity ratio as a quantitative prediction; compare slotted with unslotted plates to show that interrupting the eddy-current path removes the braking. Interpret results through induced currents and Lenz’s law rather than fitting a universal force law the data cannot support.

64. Electric field mapping and electrode geometry

Physics focus: Electric potential, field as a potential gradient and field mapping (SL/HL core).

Investigation starter: Investigate how electrode geometry affects the spatial variation of electric field magnitude in a two-dimensional conducting-paper model.

Possible measurement: Map potential on a defined grid for a chosen electrode arrangement, then compute field components numerically from the potential gradient. Use a repeatable coordinate system and sample densely in the region of interest.

Variants and extensions: Compare parallel plates with point-like electrodes; investigate how field uniformity between plates degrades as separation increases relative to plate width. Go beyond drawing equipotentials — computing E = −dV/dx numerically, with a discussion of spatial resolution and probe disturbance, is what makes this quantitative.

Where this goes wrong: conducting paper has become scarce in school laboratories, and a shallow electrolytic tank substitute introduces its own difficulties. Check availability first; if neither exists, this is a good candidate for a simulation-based treatment under entry 74.

65. Planck’s constant from LED threshold voltage

Physics focus: Photon energy, semiconductor band gap and the quantum relation E = hf (HL).

Investigation starter: Investigate how LED photon frequency relates to the forward voltage at a consistently defined low-current threshold, and how the threshold definition itself changes the value of h obtained.

Possible measurement: Measure the emission wavelength with a spectrometer where possible rather than trusting the nominal colour, and apply a single, explicitly stated electrical threshold criterion across several LED colours.

Variants and extensions: Compare two or three threshold definitions and quantify how much the estimated h shifts — this turns a systematic bias into the result and is a much better investigation than reporting one number against the accepted value. Use spectral peak energy rather than nominal colour.

Where this goes wrong: this is an approximate band-gap experiment, not the photoelectric effect, and it does not measure Planck’s constant cleanly. Contact potentials, recombination physics and the arbitrary threshold all bias the result, typically low. Say so; a student who explains why eV ≈ hf is an approximation scores better than one who reports 8% error and blames the equipment.

66. Photoelectric stopping potential and frequency

Physics focus: The photoelectric effect, work function and the photon model (HL).

Investigation starter: Investigate how incident light frequency affects the stopping potential for a fixed photocathode material.

Possible measurement: A school photoelectric apparatus with several known frequencies, measuring stopping potential carefully at low photocurrent, then fitting V_s = (h/e)f − φ/e.

Variants and extensions: Investigate intensity at fixed frequency to demonstrate that it changes current but not stopping potential — the observation that actually distinguishes the photon model from the wave model; compare two photocathode materials if the apparatus allows. Obtain both h/e and the work function from the regression, with uncertainties from the fit, and explain precisely how you identified the stopping potential from the current–voltage curve.

67. Hydrogen Balmer spectrum and the Rydberg constant

Physics focus: Atomic energy levels, emission spectra and spectral calibration (HL).

Investigation starter: Investigate how consistently the measured Balmer wavelengths determine the Rydberg constant across several visible hydrogen lines.

Possible measurement: Calibrate the spectrometer with known reference lines from a mercury or sodium lamp first, then measure the hydrogen emission wavelengths and compute R from the Balmer relation.

Variants and extensions: Compare first- and second-order grating measurements as an internal consistency check; investigate how grating line density changes the wavelength uncertainty. Calibration uncertainty is the central issue: use several lines and report the spread and fit uncertainty rather than a single-line value quoted to five figures.

68. Radioactive half-life and counting statistics

Physics focus: Radioactive decay, exponential models and Poisson statistics (SL/HL core).

Investigation starter: Investigate how the counting interval affects the precision of a fitted decay constant — an unusual and genuinely statistical research question that works equally well with primary or secondary data.

Possible measurement: A school-approved short-half-life source and detector under teacher supervision, or an authentic published decay dataset. Measure background separately and fit an exponential to background-corrected count rate.

Variants and extensions: Use repeated fixed-interval counts to test whether the variance really equals the mean, as Poisson statistics predict; compare direct exponential fitting with a log-linear method. Count data are stochastic, so Poisson uncertainties — √N — are the correct treatment, and using them is a distinguishing feature of a strong nuclear IA. Where sources are not permitted, use authentic secondary data rather than a simulation with artificially perfect numbers.

69. Radiation attenuation and the inverse-square law

Physics focus: Attenuation, absorption coefficients and geometric spreading (SL/HL core).

Investigation starter: Investigate how absorber thickness affects transmitted count rate for a selected radiation type and material, or how source–detector distance affects background-corrected gamma count rate.

Possible measurement: A school-approved sealed source with fixed geometry, counting for equal time intervals at several thicknesses or distances, with background determined independently. All work under teacher supervision and school radiation-safety procedures.

Variants and extensions: Compare two absorbers on a mass-thickness basis, which collapses different materials onto a more universal comparison; determine the half-value thickness; investigate where the inverse-square law breaks down at short distances because the detector is no longer small compared with the separation. Recognise that scattering and mixed photon energies make a single exponential imperfect, and treat that as physics rather than as error.

70. Exoplanet properties from transit light curves

Physics focus: Orbital mechanics, gravitation and photometric measurement (SL/HL core, with HL extension scope).

Investigation starter: Investigate how the transit depth and duration in published light curves constrain the planetary radius and orbital parameters for a selected set of exoplanets, and how well those derived values agree with catalogue values.

Possible measurement: Download light curves from a public mission archive and measure fractional flux drop, transit duration and period directly from the data. Planetary radius follows from the depth as (R_p/R_*)², with the stellar radius taken from the catalogue and its uncertainty propagated.

Variants and extensions: Investigate how the scatter in the out-of-transit baseline limits the smallest detectable planet radius — a genuine detection-limit question; compare derived orbital separations against Kepler’s third law across several systems; investigate how the number of stacked transits affects the precision of the fitted depth.

71. Hubble’s law from galaxy redshift catalogues

Physics focus: Cosmological redshift, distance measurement and linear regression with real scatter (HL-level extension).

Investigation starter: Investigate how recession velocity varies with distance for a selected sample of galaxies, and determine the Hubble constant with a properly estimated uncertainty.

Possible measurement: Extract redshift and independently determined distance for a defined galaxy sample from a public survey or catalogue, convert redshift to recession velocity, and fit velocity against distance.

Variants and extensions: Investigate how the fitted Hubble constant changes when nearby galaxies with large peculiar velocities are included or excluded — this is a real astrophysical effect and makes an excellent, self-contained research question; compare results from two distance-determination methods and explain why they disagree. The scatter here is physical, not experimental error, and saying so clearly is worth more than an apology about data quality.

72. Stellar spectra: temperature or radial velocity from archival data

Physics focus: Blackbody radiation, spectral lines and the Doppler effect for light (SL/HL core, with HL extension scope).

Investigation starter: Investigate either how consistently a star’s effective temperature can be inferred from its spectrum, or how measured spectral-line shifts vary with the radial velocity of a selected set of stars. Choose one — not both.

Possible measurement: An authentic calibrated spectrum from a public observatory archive. For temperature, fit a blackbody continuum or apply Wien’s displacement law and compare with the catalogue effective temperature. For radial velocity, identify several lines of known rest wavelength and compute the shift for each.

Variants and extensions: For radial velocity, compare several lines from the same star and use their spread as an empirical uncertainty — a far better uncertainty estimate than the instrument resolution alone; investigate how instrument resolution limits the smallest detectable shift. Planetary and atmospheric spectra from public datasets support a parallel investigation of infrared absorption bands in carbon dioxide, methane or water vapour over a defined wavelength interval.

Where this goes wrong: the failure mode is scope. Attempting composition, temperature and redshift in one report guarantees that none of them is done properly within 3,000 words. Pick a single quantity and go deep. Note also that Wien’s law applied to a filament lamp in the laboratory does not work as a school experiment — a tungsten filament peaks well beyond 1,000 nm, outside the range of essentially every school spectrometer, so the peak you appear to measure is an artefact of the instrument’s response.

73. Testing the inverse-square gravitational model with orbital data

Physics focus: Newtonian gravitation, circular orbits and Kepler’s third law (SL/HL core).

Investigation starter: Investigate how well satellite or planetary orbital data support the inverse-square gravitational model around a single central body, and determine GM for that body.

Possible measurement: Authentic orbital radius and period data for several satellites or moons of one central body. Fit T² against r³ and extract GM from the gradient with its uncertainty.

Variants and extensions: Compare low-Earth and geostationary satellites; fit a free exponent in T ∝ rⁿ and test whether the result is consistent with 3/2, which converts confirmation into a genuine test; compare the derived central mass with the accepted value. Use orbital radius measured from the centre of the body, not altitude above the surface — this is the mistake that quietly wrecks more submissions in this topic than anything else. Discuss orbital eccentricity as a limitation of the circular assumption.

74. Muon flux and relativistic time dilation from authentic data

Physics focus: Special relativity, time dilation and particle decay (HL).

Investigation starter: Investigate the extent to which relativistic time dilation accounts for the observed survival of atmospheric muons between two altitudes.

Possible measurement: An authentic muon-flux or muon-lifetime dataset with documented detector conditions. Compare the observed survival fraction against a classical decay prediction and against a relativistic prediction using the Lorentz factor. If your school has a cosmic-ray detector, this becomes a primary-data investigation.

Variants and extensions: Compare altitude bands; investigate the sensitivity of the conclusion to the assumed mean muon energy, which is the dominant source of uncertainty and makes a good focus in its own right. Treat detector acceptance and selection effects explicitly — and avoid the version of this investigation that uses a simulation generating perfect synthetic data, which tests nothing.

75. Numerical modelling and simulation-based investigations

Physics focus: Computational modelling, numerical methods and model validity (SL/HL core through HL, depending on the system).

Investigation starter: Build a transparent numerical model of a physical system in a spreadsheet or with simple code, and investigate how a physical parameter — or a numerical parameter such as the time step — affects the model’s predictions and their reliability.

Possible measurement: Step-by-step numerical integration of the equations of motion, with the model’s outputs treated as data. Strong systems include projectile motion with quadratic drag, orbital motion under an inverse-square force, damped and driven oscillators, Coulomb scattering to test the Rutherford relationship, and Monte Carlo neutron multiplication for a fission chain reaction.

Variants and extensions: The most rigorous version investigates the numerical method itself — how the time step affects energy conservation in an orbital simulation, for example, which is a real, quantifiable and physically meaningful result. Where a stochastic model is used, run many trials per parameter value and analyse the distribution of outcomes rather than a single run. Validate against an analytic solution in a limiting case, or against your own experimental data, which is the single strongest thing you can do with a model.

Where this goes wrong: running a ready-made simulation and reporting what it shows is the weakest submission type on this entire page. If you cannot state the equations the model is solving, the assumptions it makes, and a way of testing whether its output is trustworthy, choose a different investigation. Using a simulation as one arm of a comparison — model against experiment — is almost always stronger than using it alone.