IGCSE CP1 – Motion | Edexcel International GCSE Physics

Theory — Motion on a Ramp

A trolley released from rest on a ramp accelerates uniformly down the slope under gravity.

The Setup

The ramp is a fixed length L (e.g. 80 cm — the physical board never changes). To change the acceleration, you raise the high end to different heights h. This automatically changes the angle θ:

sin θ = h / L

h = height of raised end (m) · L = fixed ramp length (m) · θ = ramp angle

The component of gravitational acceleration along the ramp is:

a = g sin θ = g × (h / L)

g = 9.81 m/s² · This is what accelerates the trolley down the ramp.

Investigation 1 — Vary Height (fixed ramp length, light gate at bottom)

Raise the ramp to different heights h. Each time, release the trolley from the top and measure its speed v at the bottom using a light gate. Since u = 0 and s = L (full ramp length):

v² = 2aL = 2g(h/L)L = 2gh → Plot v² (y-axis) against h (x-axis)

Straight line through origin. Gradient = 2g. So g = gradient / 2.

Investigation 2 — Vary Distance (fixed height, light gate moved)

Fix the ramp at one height. Move the light gate to different positions s along the ramp. Release from rest each time and measure speed v at each position. Since u = 0:

v² = 2as = 2g(h/L) × s → Plot v² (y-axis) against s (x-axis)

Straight line through origin. Gradient = 2a = 2g(h/L). So a = gradient/2.

The Light Gate

A card of known width w is fixed to the trolley. When the trolley passes through the light gate, the beam is blocked for time t. The speed at that point is:

v = w / t

w = card width (m) · t = time beam blocked (s). The stopwatch measures total travel time; the light gate measures instantaneous speed.

Procedure

Equipment

Dynamics trolley with card (width w) · Ramp board (fixed length L = 80 cm) · Blocks of different heights · Light gate + datalogger · Metre ruler · Safety barrier at base

1

Measure the ramp length L

Measure and record the full length of the ramp board L. This stays fixed throughout the experiment — you never change the board itself.

💡 Measure along the ramp surface, not horizontally. L is the distance the trolley actually travels.

2

Place light gate at the bottom

Fix the light gate at the very bottom of the ramp. It stays here for all readings in Investigation 1 — only the height changes.

3

Raise ramp to first height and measure h

Place one block under the high end. Measure the height h of the raised end above the bench. Release the trolley from the top. Record v from the light gate.

💡 Measure h vertically — from the bench surface to the underside of the raised end of the ramp. This is the vertical height, not along the ramp.

4

Repeat for 6 different heights

Add blocks to increase h in steps. Take at least 6 readings across a range of heights. Calculate v² for each. Plot v² against h — the gradient = 2g.

💡 Repeat each release 3 times and take the mean v. Always release from rest — any initial push will give too high a speed.

      🚗 Choose an investigation, set the variable, then press ▶ Release Trolley.
    

Investigation

Height of Raised End

Height h 8 cm

4 cm20 cm

Ramp length L80 cm

Height h8 cm

sin θ = h/L0.100

Angle θ5.7°

a = g·h/L1.23 m/s²

Stopwatch

0.000

seconds

— waiting —

Light Gate

Card width w5.0 cm

Beam blocked t—

Speed v = w/t—

v²—

Readings: 0 / 6 target

Data Table

No readings yet.

Graph & Analysis

g from graph

—m/s² — gradient / 2

Results

Gradient (= 2g)—

g calculated—

R²—

Expected g9.81 m/s²

% error—

Interpretation

Record 5+ heights to see analysis.

Acceleration from graph

—m/s² — gradient / 2

Results

Gradient (= 2a)—

a calculated—

R²—

Expected a—

% error—

Interpretation

Record 5+ distances to see analysis.

Questions

Question 1

A ramp of length 80 cm is raised to a height of 12 cm at one end. A trolley is released from the top. A card of width 5 cm passes through a light gate at the bottom in 0.085 s. Calculate: (a) the speed of the trolley at the bottom, (b) the acceleration of the trolley, (c) the value of g from these results.

(a) v = w/t = 0.05/0.085 = 0.588 m/s. (b) Using v² = 2aL: a = v²/(2L) = (0.588)²/(2×0.80) = 0.346/1.60 = 0.216 m/s². (c) Since a = g×h/L: g = a×L/h = 0.216×0.80/0.12 = 1.44 m/s². This is very different from 9.81 — suggesting significant friction, or the timing has errors. A better approach is to use the gradient of the v² vs h graph over many readings rather than a single run.

Question 2

In Investigation 1 (vary height), explain why the graph of v² against h should be a straight line through the origin. What does the gradient represent?

From v² = 2aL and a = g(h/L): substituting gives v² = 2g(h/L)L = 2gh. This is of the form y = mx where y = v², x = h, and gradient m = 2g. Since g and L are both constants, the gradient is constant — giving a straight line. It passes through the origin because when h = 0 (flat ramp), there is no acceleration and v = 0 at the bottom. The gradient = 2g, so g = gradient/2. This is a method of measuring g experimentally.

Question 3

A student raises one end of an 80 cm ramp by 10 cm. They move a light gate to different positions and record the speed at each. Their v² vs s graph has a gradient of 2.45 m/s² per metre. What is the acceleration? Calculate g from this result. What are two sources of error in this experiment?

Gradient = 2a, so a = gradient/2 = 2.45/2 = 1.225 m/s². Since a = g×h/L: g = a×L/h = 1.225×0.80/0.10 = 9.80 m/s². This is very close to 9.81 m/s² (only 0.1% error — excellent). Two sources of error: (1) Friction between the trolley wheels and the ramp surface — this acts against the motion and reduces the acceleration below g sinθ, so v is lower than expected and g appears smaller than 9.81. (2) The light gate measures average speed across the card width, not instantaneous speed — if the card is wide relative to the gate position, this introduces a small systematic error, particularly at short distances where the card width is a significant fraction of the distance travelled.