Required Practical: Acceleration

This lesson covers the required practical investigation into the effect of force and mass on the acceleration of an object, as required by the AQA GCSE Physics specification (4.5.6). This practical tests Newton's second law (F = m x a) and is one of the key required practicals for GCSE Physics. You must know the method, equipment, variables, results analysis, and safety precautions.

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The Theory: Newton's Second Law

Newton's second law states:

The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.

The equation is:

F = m x a

Where:

• F = resultant force (N)
• m = mass (kg)
• a = acceleration (m/s^2)

Rearranging:

• a = F / m (acceleration = force / mass)
• m = F / a (mass = force / acceleration)

This means:

• Increasing the force increases the acceleration (if mass is constant).
• Increasing the mass decreases the acceleration (if force is constant).

Exam Tip: The equation F = m x a is on the AQA equation sheet, but you MUST be able to rearrange it. In the exam, always write the equation, substitute values with units, and show your working. Check your answer makes sense — a small force on a large mass should give a small acceleration.

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Equipment List

You will need the following equipment:

• Dynamics trolley (the object to be accelerated)
• Ramp or track (smooth, low-friction surface)
• Pulley (attached to the end of the track)
• String (to connect the trolley to the hanging masses)
• Hanging masses (to provide the accelerating force)
• Light gates and data logger (to measure acceleration), OR a ticker tape timer and ticker tape
• Balance (to measure the mass of the trolley and masses)
• Ruler (to measure distances if needed)
• Card (attached to the top of the trolley to interrupt the light gates)

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Method: Investigating the Effect of Force on Acceleration

Investigation 1: Changing the Force (Constant Mass)

1. Set up the equipment. Place the trolley on the smooth track. Attach a string to the trolley, pass it over the pulley at the end of the track, and hang a mass holder on the other end.

2. Compensate for friction. Tilt the ramp very slightly until the trolley moves at constant speed when given a gentle push (no hanging mass). This ensures that the component of gravity along the slope exactly compensates for friction, so the only unbalanced force is from the hanging masses.

3. Attach a known mass to the string (e.g. 0.1 kg, providing a force of approximately 1.0 N).

4. Release the trolley and use the light gates and data logger (or ticker tape) to measure the acceleration.

5. Record the force and the acceleration in a results table.

6. Increase the hanging mass in equal steps (e.g. 0.1 kg increments) and repeat, keeping the total mass of the system constant.

7. Keep the total mass constant by transferring masses from the trolley to the hanging mass. This is crucial — as you add mass to the hanging string, remove the same mass from the trolley so the total mass being accelerated remains the same.

8. Repeat each measurement at least 3 times and calculate a mean acceleration.

9. Plot a graph of acceleration (y-axis) against force (x-axis).

graph LR
    T["Trolley (on track)"] -->|"String over pulley"| M["Hanging masses"]
    LG["Light gates"] -.->|"Measure acceleration"| T
    DL["Data logger"] -.-> LG

    style T fill:#2c3e50,color:#fff
    style M fill:#e74c3c,color:#fff
    style LG fill:#27ae60,color:#fff
    style DL fill:#2980b9,color:#fff

Exam Tip: The most commonly forgotten step is compensating for friction by tilting the ramp slightly. If asked "how do you reduce the effect of friction?" in the exam, state that the ramp should be tilted slightly until the trolley moves at constant speed when given a gentle push with no accelerating force attached.

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Investigation 2: Changing the Mass (Constant Force)

1. Set up the equipment as above with a fixed hanging mass (e.g. 0.2 kg providing approximately 2.0 N force).

2. Compensate for friction as before.

3. Measure the acceleration of the trolley using light gates.

4. Add extra mass to the trolley (e.g. 100 g at a time) and repeat the measurement, keeping the hanging mass (and therefore the force) constant.

5. Record the total mass (trolley + added mass + hanging mass) and the acceleration.

6. Repeat each measurement at least 3 times and calculate a mean.

7. Plot a graph of acceleration (y-axis) against 1/mass (x-axis). This should give a straight line through the origin.

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Variables

Investigation 1: Changing the Force

Variable Type	Variable	Details
Independent variable	Force (N)	Changed by altering the hanging mass
Dependent variable	Acceleration (m/s^2)	Measured using light gates or ticker tape
Control variables	Total mass of system, track surface, tilt of ramp	Must remain constant

Investigation 2: Changing the Mass

Variable Type	Variable	Details
Independent variable	Mass of trolley (kg)	Changed by adding masses to the trolley
Dependent variable	Acceleration (m/s^2)	Measured using light gates or ticker tape
Control variables	Force (hanging mass), track surface, tilt of ramp	Must remain constant

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Recording Results

Example Results Table (Investigation 1: Changing Force)

Hanging Mass (kg)	Force (N)	Acceleration Trial 1 (m/s^2)	Acceleration Trial 2 (m/s^2)	Acceleration Trial 3 (m/s^2)	Mean Acceleration (m/s^2)
0.10	1.0	0.48	0.52	0.50	0.50
0.20	2.0	1.02	0.98	1.00	1.00
0.30	3.0	1.48	1.52	1.50	1.50
0.40	4.0	2.02	1.98	2.00	2.00
0.50	5.0	2.48	2.50	2.52	2.50

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Analysing the Results

Graph 1: Acceleration vs Force (Constant Mass)

• The graph should be a straight line through the origin.
• This shows that acceleration is directly proportional to force (when mass is constant).
• The gradient of the line = 1/m (one divided by the total mass of the system).

Graph 2: Acceleration vs Mass (Constant Force)

• A graph of acceleration against mass gives a curve (not a straight line).
• A graph of acceleration against 1/mass gives a straight line through the origin.
• This shows that acceleration is inversely proportional to mass (when force is constant).

graph LR
    subgraph "a vs F (constant m)"
        A1["Origin"] -->|"Straight line"| A2["Gradient = 1/m"]
    end
    subgraph "a vs 1/m (constant F)"
        B1["Origin"] -->|"Straight line"| B2["Gradient = F"]
    end

    style A2 fill:#27ae60,color:#fff
    style B2 fill:#2980b9,color:#fff

Exam Tip: When plotting the graph for Investigation 2, remember to plot acceleration against 1/mass (not mass). If you plot acceleration against mass, you will get a curve, which is harder to analyse. A straight line through the origin confirms the inverse proportionality relationship.

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Using Ticker Tape (Alternative Method)

If light gates are not available, ticker tape can be used: