CP9 – Force and Change of Momentum | Edexcel A Level Physics

Theory — Force and Change of Momentum

Newton's second law in its impulse-momentum form: FΔt = Δp

Objectives

Use a trolley on a tilted runway with a hanging mass to apply a known force
Transfer 10 g masses from the trolley to the hanger to increase force while keeping total mass constant
Use two light gates to measure velocity before and after the trolley passes through
Verify the impulse-momentum theorem: FΔt = MΔv = Δp
Plot FΔt against MΔv — gradient ≈ 1 confirms Newton's second law

The Impulse-Momentum Theorem

Newton's second law states F = ma = m(Δv/Δt). Rearranging:

FΔt = mΔv = Δp Impulse = Change in momentum

F = net force (N) · Δt = time for which force acts (s) · m = mass of trolley system (kg)
Δv = change in velocity (m/s) · Δp = change in momentum (kg m/s)

The Experimental Setup

Key principle — constant total mass: The total mass of the system (trolley + all 5 masses) stays constant throughout. Masses are transferred one at a time from the trolley to the hanger. This means:

F = mg (weight of hanging masses) M = M_trolley + m_remaining (total trolley mass, decreasing) Δp = MΔv (momentum change of trolley)

By keeping total mass constant, we ensure any change in the trolley's acceleration is due only to the changing force F, not a change in the total mass being accelerated.

The ramp is tilted slightly to compensate for friction — the tilt is adjusted until the trolley moves at constant velocity when given a gentle push (no hanging mass). This way the net force equals only the tension from the hanging mass.

Light Gates

Two light gates are placed at either end of the runway. A card of known width w is attached to the trolley. As the card passes through each gate, the gate records the time t for the card to pass. The velocity at each gate is:

v = w / t

v₁ = velocity at gate 1 (entry) · v₂ = velocity at gate 2 (exit) · Δv = v₂ − v₁

The time Δt between gates is also recorded by the software. The impulse FΔt is calculated from the hanging mass force and this time interval.

The Graph

Plot FΔt (y-axis) against MΔv (x-axis). If Newton's second law holds, FΔt = MΔv, so the graph is a straight line through the origin with gradient = 1.

Any deviation of the gradient from 1 indicates systematic error — typically from friction not being fully compensated by the ramp tilt, or from the hanging mass assumption (the hanging mass itself accelerates, so the true force on the trolley is slightly less than mg).

Procedure

Transfer 10 g masses one at a time from the trolley to the hanger, keeping total mass constant.

Equipment

Dynamics trolley · Runway (tilted) · Bench pulley · String · Mass hanger · Five 10 g masses · Electronic balance · Two light gates + data logger · Card (width w, attached to trolley) · Metre rule

1

Measure total mass M

Weigh the trolley together with all five 10 g masses on a balance. Record M. This total mass remains constant throughout the entire experiment.

💡 Include the mass of the card attached to the trolley. M stays constant because you only transfer masses — never add or remove them from the system.

2

Set up the tilted runway

Secure the bench pulley at one end. Tilt the ramp slightly. Test by giving the trolley a gentle push — if it travels at constant velocity (equal spacing on ticker tape, or constant light gate readings), the tilt correctly compensates for friction.

💡 If the trolley accelerates without any hanging mass, the tilt is too steep. If it decelerates, increase the tilt slightly.

3

Place light gates and set starting position

Place the two light gates at either end of the runway. Connect to timing software. Place all five 10 g masses on the trolley. Connect the string over the pulley to the empty mass hanger (hanger rests on floor, string taut).

💡 The hanger should touch the floor before the trolley reaches the bottom gate — the trolley then coasts through gate 2 at constant velocity after the string goes slack.

4

First run: 1 mass on hanger (m = 10 g)

Move one 10 g mass from the trolley to the hanger. Record m = 10 g in the table. Release the trolley. Record v₁ (velocity at gate 1), v₂ (velocity at gate 2) and Δt (time between gates).

💡 Release the trolley from the same position each time for consistency. The timing software records v₁, v₂ and Δt automatically.

5

Repeat and take the mean

Reset and repeat the run 3 times. Calculate the mean v₁, v₂ and Δt for this value of m. Calculate Δv = v₂ − v₁, then MΔv (change in momentum) and FΔt (impulse, where F = mg).

💡 Repeat runs reduce random error from timing uncertainty and any variation in release position.

6

Transfer another mass and repeat

Move another 10 g mass from the trolley to the hanger. Now m = 20 g on the hanger, 30 g remaining on trolley. Repeat steps 4–5 for m = 20, 30, 40, 50 g.

💡 The last reading has all five masses on the hanger (m = 50 g, trolley mass only remaining on trolley). You will have 5 sets of readings in total.

7

Plot FΔt against MΔv

Plot impulse FΔt (y-axis) against change in momentum MΔv (x-axis). The gradient should be 1 and the line should pass through the origin.

💡 If gradient ≠ 1, check: Is friction properly compensated? Is the hanging mass assumption valid (the hanger itself has mass and accelerates too)?

Fixed: Total System Mass

Trolley mass500 g

5 × 10 g masses50 g

Total M550 g = 0.550 kg

Card width w50 mm

Transfer Masses (Trolley → Hanger)

Display Mode

Light Gate Readings

Status

Ready to run

v₁ (gate 1)

—

v₂ (gate 2)

—

Δv = v₂−v₁

—

Δt (between gates)

—

F = mg

—

MΔv

—

FΔt

—

FΔt / MΔv

—

Readings recorded: 0/5

Press ▶ Release Trolley to run the experiment

Results Data Table

Total system mass M = 0.550 kg (constant). F = mg where m = hanging mass. Δv = v₂ − v₁.

#	m (hanger) / g	F = mg / N	v₁ / m s⁻¹	v₂ / m s⁻¹	Δv / m s⁻¹	Δt / s	MΔv / N s	FΔt / N s	FΔt/MΔv
No data yet.

Graph & Analysis — FΔt vs MΔv

Impulse (y-axis) against change in momentum (x-axis). Gradient = 1 confirms FΔt = MΔv (Newton's second law).

Gradient of best-fit line

—Expected: 1.00 (FΔt = MΔv)

Graph parameters

Gradient—

y-intercept—

R²—

% error from 1.00—

Interpretation

Record all 5 readings to see analysis.

Discussion Questions

Write your answers and reveal model answers when ready.

Q1

Explain why it is important to keep the total mass of the system constant throughout this experiment, and how this is achieved.

Newton's second law states F = ma, where a = Δv/Δt. Rearranged: FΔt = mΔv. If the total mass m changes between readings, then any change in MΔv could be due to either a change in F or a change in m — we could not attribute it solely to the changing force. By transferring masses from the trolley to the hanger (rather than adding new masses), the total mass of the system remains constant at M = trolley mass + all five 10 g masses. This ensures that any change in MΔv is due only to the change in F = mg, allowing a clean test of the relationship FΔt = MΔv.

Q2

Explain why the runway is tilted, and describe how you would find the correct angle of tilt.

The runway is tilted to compensate for friction between the trolley wheels and the track. Without compensation, friction would oppose the motion and the net force would be less than mg — making FΔt > MΔv and the gradient less than 1. The correct tilt angle is found by trial: attach no masses to the hanger, give the trolley a gentle push, and observe the motion. If the trolley decelerates, increase the tilt. If it accelerates, decrease the tilt. At the correct angle, the trolley moves at constant velocity after being given a push — meaning the component of gravity along the ramp exactly balances the frictional force, leaving the net force equal to the tension from the hanging mass alone.

Q3

The gradient of the FΔt vs MΔv graph is found to be 0.92 rather than 1.00. Suggest two reasons for this systematic error.

1. Friction not fully compensated — if the ramp tilt is slightly too small, friction partially opposes the motion. The measured velocity v₂ is lower than it should be, so MΔv is underestimated. FΔt is calculated from F = mg and Δt, which are measured correctly — so FΔt > MΔv, giving a gradient less than 1. 2. The hanging mass assumption — we assume F = mg where m is the mass of the hanger. But the hanger itself accelerates downward during the run. The true net force on the trolley is the tension in the string, which equals m(g−a) rather than mg (by Newton's second law applied to the hanging mass). So F = mg overestimates the actual tension, making FΔt too large and the gradient greater than 1. This effect tends to make the gradient greater than 1 — opposite to friction — so the two effects partially cancel, which is why the gradient is close to 1 even when neither is perfectly corrected.

Q4

Explain how the light gates measure the velocity of the trolley, and why two gates are needed rather than one.

Each light gate consists of an infrared beam and a detector. When the card of known width w (attached to the trolley) passes through the gate, it interrupts the beam for a time t. The velocity at that gate is v = w/t. One gate gives the velocity at a single point on the track — either the initial or final velocity. Two gates are needed to measure both v₁ (entry velocity at gate 1) and v₂ (exit velocity at gate 2), so the change in velocity Δv = v₂ − v₁ can be calculated. The data logger also records the time Δt between the two gate triggers, which is used to calculate the impulse FΔt. Without two gates, neither Δv nor Δt can be measured directly.

Q5

State one advantage of plotting FΔt against MΔv rather than plotting F against MΔv/Δt (i.e. F against ma).

Plotting FΔt against MΔv does not require dividing by Δt to get acceleration a. Dividing by a small, uncertain time interval amplifies the percentage uncertainty — if Δt has an uncertainty of 5%, then a = Δv/Δt has an uncertainty that includes that 5% from Δt plus the uncertainty in Δv. The impulse-momentum plot uses only the directly measured quantities FΔt and MΔv, each of which has its own moderate uncertainty without the amplification caused by division by a small time. This generally gives a cleaner linear graph with smaller scatter, making the gradient more reliable.