Topic 24 · Course Skills

Primary Data Investigations

One authoritative practical record for the primary-data investigations in the 2025 Leaving Certificate Physics specification.

PD-1.1 — Investigate constant and varying linear motion

Use primary measurements to describe constant motion and changing motion, and determine velocity and acceleration from measured data.

Dynamics trolley and runway, two light gates (or motion sensor), timer/data logger, metre rule.

Set the light gates a measured distance apart and record the separation s.
Pass the trolley through the gates. For approximately constant motion, use a level track or compensate gently for friction.
Record the time information needed to determine the trolley speed at each gate.
Repeat for several runs and calculate velocity.
For varying motion, incline the track slightly or use a constant pulling force. Record velocities at two known times/positions.
Calculate acceleration from the change in velocity divided by the corresponding time interval.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

Constant motion gives approximately constant velocity. Varying motion gives a change in velocity with time.

What relationship does your data support? Refer to your measurements or graph.

Measure the gate separation from the same reference points each time.
Keep the track straight and minimise friction.
Repeat measurements and average where appropriate.
For acceleration, use data from a region where the acceleration is approximately constant.

PD-1.2 — Verify the law of addition of vectors in one and two dimensions

Show that vectors add according to their directions as well as their magnitudes.

Force table or smooth board, ring, pulleys, strings, mass hangers/Newton weights, protractor.

Attach three strings to a small ring at the centre of the force table.
Pass each string over a pulley and attach known masses.
Choose two forces and their directions.
Adjust the third force until the ring remains centred and in equilibrium.
Record the magnitudes and angles of the forces.
Resolve the chosen forces into x- and y-components and compare their vector sum with the balancing force.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

The calculated resultant of the chosen vectors is equal and opposite to the balancing force, within experimental uncertainty.

What relationship does your data support? Refer to your measurements or graph.

Ensure pulleys turn freely.
Keep the strings tangent to the pulley wheels and in the same horizontal plane.
Use sufficient masses to reduce percentage uncertainty.
Read angles without parallax.

PD-1.3 — Verify Newton’s Second Law of Motion

Investigate how acceleration depends on resultant force for a system of constant mass.

Trolley, runway, pulley, string, hanging mass, slotted masses, light gates/data logger, balance.

Set up the trolley connected by string over a pulley to a hanging mass.
Measure the total moving mass of the system.
Arrange the masses so the total mass stays constant while the pulling force is changed by transferring masses from the trolley to the hanger.
Release the trolley from the same position and measure its acceleration.
Repeat for at least five different resultant forces.
Plot acceleration a against force F.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

A graph of a against F is approximately a straight line through the origin when total mass is constant.

What relationship does your data support? Refer to your measurements or graph.

Keep the total mass constant when changing the force.
Ensure the string is parallel to the track.
Minimise friction; if appropriate, adjust the track to compensate for it.
Release the trolley without an extra push.

PD-1.4 — Investigate density using primary measurements

Determine the density of a regular solid and/or an irregular solid from measured mass and volume.

Electronic balance, ruler/vernier calipers, regular solid; measuring cylinder, water and irregular solid.

Measure the mass m of the object using an electronic balance.
For a regular solid, measure the required dimensions and calculate its volume.
For an irregular solid, record the initial water volume in a measuring cylinder.
Fully immerse the solid and record the final volume. The volume of the solid is the increase in water volume.
Calculate density from mass divided by volume.
Repeat dimension/volume readings where possible.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

The density is obtained from ρ = m/V and can be compared with an accepted value if the material is known.

What relationship does your data support? Refer to your measurements or graph.

Zero the balance before measuring.
Read the bottom of the meniscus at eye level.
Remove trapped air bubbles from an immersed object.
For a regular solid, take repeated dimension measurements at different positions if the object is not perfectly uniform.

PD-1.5 — Investigate conservation of momentum

Compare total momentum before and after a collision using measured masses and velocities.

Two dynamics trolleys, runway, balance, light gates/data logger or motion sensors, collision attachments.

Measure the masses m1 and m2 of the trolleys.
Place the trolleys on a level or friction-compensated track.
Measure the velocities immediately before the collision.
Allow the trolleys to collide and measure their velocities immediately after the collision.
Choose one direction as positive and give all velocities the correct sign.
Calculate total momentum before and total momentum after.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

Total momentum before and after the collision should agree within experimental uncertainty if external forces are negligible.

What relationship does your data support? Refer to your measurements or graph.

Use velocities measured as close to the collision as possible.
Minimise friction and ensure the track is level.
Use signed velocities consistently.
Repeat collisions and compare the percentage difference between total momentum before and after.

PD-1.6 — Investigate the force needed to compress or stretch an object

Measure how the force required changes as an elastic object is compressed or stretched.

Spring or elastic sample, clamp stand, force sensor/Newton meter, ruler, masses if required.

Measure the original length or reference position of the elastic object.
Apply a small force and record the extension or compression.
Increase the force in steps, recording force and deformation each time.
If safe, unload in steps and compare loading and unloading values.
Do not exceed the safe elastic range of the apparatus.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

Within an elastic region, the required force usually increases as the deformation increases.

What relationship does your data support? Refer to your measurements or graph.

Read the ruler at eye level.
Apply the force along the axis of the object.
Allow oscillations to die away before taking each reading.
Do not exceed the elastic limit unless that behaviour is specifically being investigated.

PD-1.7 — Verify Hooke’s Law for an elastic object

Test whether force is directly proportional to extension within the elastic limit.

Spring, clamp stand, mass hanger and slotted masses, metre rule, pointer.

Measure the spring length with no added load.
Add a known mass and allow the spring to come to rest.
Record the new length and calculate the extension.
Repeat for several increasing forces without exceeding the elastic limit.
Plot force F against extension x.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

Within the elastic limit, F is proportional to x and a graph of F against x is a straight line through the origin.

What relationship does your data support? Refer to your measurements or graph.

Measure from the same reference point each time.
Avoid parallax by using a pointer close to the ruler.
Wait until oscillations stop before reading.
Use enough readings to identify where proportional behaviour ends.

PD-1.8 — Investigate conservation of energy with a trolley and falling mass

Compare gravitational potential energy lost by a falling mass with kinetic energy gained by the moving system.

Trolley, track, pulley, string, hanging mass, balance, metre rule, light gate/data logger.

Measure the masses of the trolley and hanging mass.
Measure the vertical distance h through which the hanging mass will fall.
Release the system from rest.
Measure the speed v of the trolley near the end of the fall.
Calculate the gravitational potential energy lost and the kinetic energy gained by the moving masses.
Repeat and compare the energies.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

The kinetic energy gained is close to the gravitational potential energy lost, with differences due mainly to friction and rotational/other energy transfers.

What relationship does your data support? Refer to your measurements or graph.

Minimise friction in the trolley and pulley.
Measure h vertically and from consistent points.
Ensure the string is light, taut and does not slip.
Take the speed measurement as close as possible to the end of the measured fall.

PD-1.9 — Determine g using a simple pendulum

Use primary data for pendulum length and period to determine the acceleration due to gravity.

Pendulum bob, light string, clamp stand, metre rule, stopwatch.

Set up a pendulum and measure its length l from the point of suspension to the centre of the bob.
Displace the bob through a small angle and release without pushing.
Time a fixed number N of complete oscillations and calculate the period T = t/N.
Repeat for at least five different lengths.
Calculate T² and plot T² against l.
Use the slope of the graph to determine g.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

A graph of T² against l should be a straight line through the origin. Its slope is 4π²/g.

What relationship does your data support? Refer to your measurements or graph.

Use a small amplitude.
Measure l to the centre of the bob.
Time many oscillations to reduce reaction-time percentage uncertainty.
Keep the motion in one vertical plane.

PD-2.1 — Analyse the suitability of materials for use as thermometers

Collect primary data for a thermometric property and assess whether it changes in a useful, repeatable way with temperature.

Reference thermometer, thermistor or other sensor/material, water bath, heater, multimeter/ohmmeter, stirrer.

Place the reference thermometer and test sensor in good thermal contact with the same water bath.
Record the bath temperature and the corresponding thermometric property (for example thermistor resistance).
Increase the temperature in small steps, stirring and allowing the system to reach equilibrium before each reading.
Collect at least 8-10 pairs of readings over a useful temperature range.
Plot the thermometric property against temperature and assess sensitivity, range, linearity and repeatability.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

A useful thermometer material has a measurable, repeatable thermometric property that changes predictably with temperature over the intended range.

What relationship does your data support? Refer to your measurements or graph.

Stir the bath to keep its temperature uniform.
Read the reference thermometer and sensor at the same time.
Allow time for thermal equilibrium.
Avoid parallax on analogue scales.

PD-2.2 — Determine specific heat capacity using primary data

Determine the specific heat capacity of a liquid or solid by measuring electrical energy supplied and temperature rise.

Insulated calorimeter or metal block, heater, thermometer, balance, low-voltage DC supply, ammeter, voltmeter, switch and stopwatch (or joulemeter).

Measure the mass m of the substance being heated.
Insert the heater and thermometer and insulate the system well.
Record the initial temperature θ1.
Switch on the heater and start the timer together. Measure the current I and the potential difference V across the heater.
Heat for a measured time t, stirring a liquid where appropriate. Switch off and record the highest/final temperature θ2.
Calculate the temperature rise and the electrical energy supplied, then calculate c.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

The calculated value of c can be compared with a reference value; heat losses usually make the experimental result less accurate.

What relationship does your data support? Refer to your measurements or graph.

Insulate well and heat reasonably quickly to reduce heat loss.
Place the voltmeter in parallel with the heater and ammeter in series.
Stir liquids before reading temperature.
Allow heat in the heater to spread through the substance before taking the final temperature.

PD-2.3 — Determine specific latent heat using primary data

Determine the specific latent heat of fusion of ice from primary measurements of mass and temperature.

Crushed ice at 0 °C, warm water, insulated calorimeter or polystyrene cup, thermometer, electronic balance, tissue/kitchen paper, stirrer.

Place ice in an ice-water mixture so that it is at approximately 0 °C, then dry the pieces thoroughly before use.
Measure the mass of the empty calorimeter/cup and then the mass with warm water.
Record the initial temperature of the warm water.
Add small pieces of dry crushed ice, stir gently and allow all the ice to melt.
Record the lowest/final equilibrium temperature.
Reweigh the calorimeter/cup to find the mass of ice that melted.
Use an energy balance to calculate the specific latent heat of fusion of ice.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

The calculated value should be of the same order as the accepted value. Agreement depends strongly on heat exchange with the surroundings and on ensuring the added ice is dry and at 0 °C.

What relationship does your data support? Refer to your measurements or graph.

Dry the ice before adding it; surface water would otherwise be counted as melted ice.
Use good insulation and work promptly to reduce heat exchange with the surroundings.
Stir gently and record the true equilibrium temperature.
Use enough ice and water to give measurable temperature and mass changes.

PD-2.4 — Verify a model for refraction using primary data

Collect primary measurements of incidence and refraction and test the refraction model for a transparent block.

Ray box or narrow light source, rectangular glass/acrylic block, white paper, ruler, protractor, pencil.

Place the block on paper and trace its outline.
Draw a normal at the point where the incident ray will enter the block.
Shine a narrow ray into the block at a chosen angle of incidence i and mark the incident and refracted paths.
Remove the block, draw the ray paths accurately and measure i and r with a protractor.
Repeat for several different values of i, keeping the same two media.
Calculate sin i and sin r for each reading and compare the ratio sin i / sin r.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

For the same pair of media, sin i / sin r should be approximately constant. This constant is the refractive index of the second medium relative to the first.

What relationship does your data support? Refer to your measurements or graph.

Use a narrow, well-defined ray and mark points far enough apart to reduce angular uncertainty.
Draw a precise normal and measure all angles from the normal, not the surface.
Avoid moving the block while marking the ray path.
Repeat readings and use several incidence angles.

PD-2.5 — Verify the model for a converging lens

Measure object distance and image distance for a converging lens and test the lens equation.

Illuminated object, converging lens and holder, screen, optical bench/metre rule.

Arrange the object, lens and screen in a straight line at the same height.
Adjust the screen until a sharp real image is formed.
Measure object distance u and image distance v from the optical centre of the lens.
Repeat for several different object positions outside the focal length.
Calculate 1/u and 1/v and test whether their sum is approximately constant.
Use the constant value to determine the focal length f.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

For a thin converging lens, 1/u + 1/v is approximately constant and equal to 1/f.

What relationship does your data support? Refer to your measurements or graph.

Measure distances from the optical centre of the lens.
Keep object, lens and screen aligned.
Use a sharply focused image.
Repeat measurements over a wide range of u values.

PD-2.6 — Verify the model for standing waves on a stretched string

Use standing waves on a stretched string to test the relationship between frequency, length, tension and linear density.

Signal generator/vibration generator, string, pulley, mass hanger and masses, metre rule, balance.

Set up the stretched string with one end driven by the vibration generator and the other passing over a pulley to a known hanging mass.
Choose a frequency and adjust the vibrating length until a clear standing-wave pattern is formed.
Record the length l, frequency f, number of loops and tension T = mg.
Determine the string linear density μ from its mass per unit length if required.
Repeat while varying one quantity at a time.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

For the fundamental, frequency varies as predicted by f = (1/2l)√(T/μ).

What relationship does your data support? Refer to your measurements or graph.

Keep the string tension steady.
Measure the vibrating length between the effective fixed points.
Use a clear resonance/standing-wave pattern before taking a reading.
Use the same string so μ remains constant unless μ is the variable being investigated.

PD-2.7 — Investigate the wave nature of light and determine its wavelength

Observe diffraction/interference from a diffraction grating and use primary measurements to determine the wavelength of monochromatic light.

Low-power laser, diffraction grating of known line spacing d, screen, metre rule/tape measure, clamp/holders. Follow school laser-safety procedures.

Align the laser so that it strikes the diffraction grating normally and the pattern falls on a distant screen.
Measure the grating-to-screen distance L.
Mark the central maximum and corresponding first-order maxima on both sides.
Measure the distance x from the central maximum to each first-order maximum and average the left/right values.
Calculate the diffraction angle using tan(theta) = x/L.
Use n lambda = d sin(theta) with the known grating spacing d to calculate the wavelength lambda.
Repeat the measurement or use another diffraction order if the pattern is clear and safe to do so.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

A diffraction pattern is evidence of the wave nature of light. The calculated wavelength should be consistent across usable readings and plausible for the colour of the laser.

What relationship does your data support? Refer to your measurements or graph.

Never look into the laser beam or direct it toward anyone.
Measure L from the grating plane to the screen and x from the central maximum.
Use symmetric maxima on both sides and average their positions to reduce alignment error.
A larger L improves the precision of x provided the pattern remains clear.

PD-3.1 — Model the I-V relationship of a semiconductor diode

Measure current and potential difference for forward and reverse bias and plot the diode I-V characteristic.

Diode, variable low-voltage DC supply, protective resistor/rheostat, ammeter, voltmeter, switch, leads.

Connect the ammeter in series with the diode and protective resistor. Connect the voltmeter across the diode.
For forward bias, increase the supply in small steps and record diode voltage V and current I.
Do not exceed the safe current rating of the diode.
Reverse the diode connections for reverse bias and repeat using an appropriate meter range.
Plot I against V, showing both forward and reverse regions.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

Forward current rises strongly after the characteristic turn-on region; reverse current is very small under ordinary reverse-bias conditions.

What relationship does your data support? Refer to your measurements or graph.

Use a current-limiting resistor.
Check diode polarity before each set of readings.
Use small voltage steps near the turn-on region.
Avoid heating the diode significantly during measurements.

PD-3.2 — Verify the relationship between current and voltage across an ohmic conductor

Test whether current is directly proportional to potential difference for a conductor at approximately constant temperature.

Fixed resistor, variable DC supply, ammeter, voltmeter, rheostat/variable supply, switch.

Connect the ammeter in series with the resistor and the voltmeter in parallel across it.
Set a small potential difference and record V and I.
Increase V in steps, taking several pairs of readings.
Keep the current low enough to minimise heating of the resistor.
Plot V against I (or I against V, but label the axes clearly).

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

For an ohmic conductor at constant temperature, V is proportional to I and V/I is approximately constant.

What relationship does your data support? Refer to your measurements or graph.

Keep the resistor temperature as constant as possible.
Check that the voltmeter is in parallel and the ammeter is in series.
Use a suitable meter range.
Take readings promptly to reduce heating.

PD-3.3 — Investigate the I-V relationship of a non-ohmic conductor

Measure and plot the I-V characteristic of a filament lamp (or another non-ohmic conductor).

Filament lamp, variable DC supply, ammeter, voltmeter, switch and leads.

Connect the ammeter in series with the lamp and the voltmeter across the lamp.
Increase the supply voltage in steps and record V and I.
If appropriate, reverse the supply and collect data for negative V and I as well.
Plot I against V or V against I.
Describe how the slope changes and relate this to changing resistance.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

The graph is curved rather than a straight line through the origin because the filament temperature and resistance increase as current increases.

What relationship does your data support? Refer to your measurements or graph.

Allow the lamp to reach a steady condition before each reading.
Do not exceed the lamp rating.
Use enough readings to show the curvature clearly.
Keep meter connections correct throughout.

PD-3.4 — Investigate the effect of temperature on the resistance of a conductor

Measure how the resistance of a conductor or thermistor changes with temperature.

Thermistor or suitable conductor, water bath, thermometer, heater, ohmmeter/multimeter, stirrer.

Place the test component and thermometer in the same water bath.
Record the initial temperature and resistance.
Heat the bath slowly, stirring continuously.
At regular temperature intervals, allow the reading to stabilise and record temperature and resistance.
Plot resistance R against temperature θ.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

The form of the R-temperature graph depends on the material. An NTC thermistor shows decreasing resistance as temperature increases.

What relationship does your data support? Refer to your measurements or graph.

Stir the water to keep temperature uniform.
Allow the component to reach the bath temperature before recording.
Take temperature and resistance readings at the same time.
Keep electrical measuring current small enough to avoid self-heating.

PD-3.5 — Model resistances in series and parallel

Measure individual and combined resistances and compare with the series and parallel resistance models.

Two or more resistors, digital multimeter/ohmmeter, breadboard or leads.

Measure the resistance of each resistor individually.
Connect the same resistors in series and measure the total resistance.
Connect them in parallel and measure the total resistance.
Calculate the predicted totals using the series and parallel models.
Compare measured and calculated values, allowing for resistor tolerances.

Record the key calculation, graph plan, slope calculation or comparison required for this investigation.

Series resistance is the sum of the component resistances. The parallel equivalent is less than either individual branch resistance.

What relationship does your data support? Refer to your measurements or graph.

Disconnect power before using an ohmmeter.
Ensure good electrical contacts.
Account for component tolerance and meter uncertainty.
Do not touch resistor leads unnecessarily during precision resistance measurements.