Required Practical: Acceleration (Force and Mass)

This lesson covers the Required Practical to investigate the effect of varying force and mass on the acceleration of an object, as specified by AQA GCSE Combined Science Trilogy (8464), section 6.5.3 (Required Practical Activity 19). This practical directly tests Newton's second law ($F = ma$F=ma) and is a common source of exam questions.

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Aim

To investigate the relationship between:

1. Force and acceleration (keeping mass constant).
2. Mass and acceleration (keeping force constant).

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Equipment

Item	Purpose
Dynamics trolley	The object being accelerated
Runway (ramp/track)	Smooth surface for the trolley to travel along
Light gates and data logger (or ticker tape and timer)	To measure speed and calculate acceleration
Pulley and string	To connect hanging masses to the trolley
Masses and mass hanger	To provide the accelerating force (weight of hanging masses)
Balance	To measure the mass of the trolley and added masses

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Method

Investigating Force and Acceleration (mass constant)

1. Set up the trolley on a slightly tilted runway. Tilt the runway just enough to compensate for friction — the trolley should move at constant speed when given a gentle push (no acceleration or deceleration).
2. Attach a string from the trolley, over a pulley at the end of the runway, to a mass hanger.
3. Place masses on the hanger — the weight of the hanging masses provides the accelerating force.
4. Release the trolley and use light gates (or ticker tape) to measure the acceleration.
5. Repeat with increasing force (add more mass to the hanger) while keeping the total mass of the system constant (transfer masses from the trolley to the hanger so the total system mass does not change).
6. Record force and acceleration. Repeat each reading at least three times and calculate a mean.

Investigating Mass and Acceleration (force constant)

1. Keep the same force (same hanging mass) throughout.
2. Add extra masses to the trolley to increase the total mass of the system.
3. Measure the acceleration for each total mass.
4. Record mass and acceleration. Repeat and calculate means.

flowchart LR
    A["Trolley on runway"] --> B["String over pulley"]
    B --> C["Hanging masses provide force (F = mg)"]
    C --> D["Light gates measure speed"]
    D --> E["Data logger calculates acceleration"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#e74c3c,color:#fff
    style D fill:#f39c12,color:#fff
    style E fill:#27ae60,color:#fff

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Key Variables

Variable type	When investigating force	When investigating mass
Independent (changed)	Force (weight of hanging masses)	Mass (of trolley + added masses)
Dependent (measured)	Acceleration	Acceleration
Control (kept same)	Total system mass	Applied force

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Expected Results

Force vs Acceleration (constant mass)

As force increases, acceleration increases proportionally (straight-line graph through the origin).

$a = \frac{F}{m}$a=mF​

This confirms Newton's second law: $F = ma$F=ma.

Mass vs Acceleration (constant force)

As mass increases, acceleration decreases. The relationship is inversely proportional: $a \propto \frac{1}{m}$a∝m1​.

A graph of acceleration against $1/m$1/m should be a straight line through the origin.

graph LR
    subgraph "Force vs Acceleration"
        FA["Straight line through origin"]
        FA2["Gradient = 1/m"]
    end
    subgraph "Acceleration vs 1/Mass"
        MA["Straight line through origin"]
        MA2["Gradient = F"]
    end

    style FA fill:#2980b9,color:#fff
    style MA fill:#27ae60,color:#fff

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Worked Example — Calculating Acceleration from Results

A trolley of mass 0.8 kg is accelerated by a force of 2.4 N. Calculate the expected acceleration.

Solution:

$a = \frac{F}{m} = \frac{2.4}{0.8} = 3.0$a=mF​=0.82.4​=3.0 m/s²

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Sources of Error and Improvements

Source of error	How to reduce it
Friction on the runway	Tilt the runway slightly to compensate
Inaccurate timing	Use light gates and a data logger instead of manual timing
Masses not transferred correctly	Ensure total system mass remains constant by transferring masses between trolley and hanger
Parallax error when reading scales	Read the balance at eye level
Air resistance on the trolley	Difficult to eliminate; keep speeds low to minimise the effect

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Why We Tilt the Runway

Tilting the runway compensates for friction. The component of gravity acting down the slope provides a small force that exactly balances the friction force. This means any acceleration measured is due only to the applied force from the hanging masses.

To check: give the trolley a gentle push with no hanging mass. If it travels at constant speed (no acceleration or deceleration), friction has been correctly compensated.

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Calculating Force from Hanging Masses

The accelerating force equals the weight of the hanging masses:

$F = m_{\text{hanger}} \times g$F=mhanger​×g

Using $g = 9.8$g=9.8 N/kg (or 10 N/kg if stated):

• 100 g (0.1 kg) hanging mass → $F = 0.1 \times 9.8 = 0.98$F=0.1×9.8=0.98 N ≈ 1 N
• 200 g (0.2 kg) hanging mass → $F = 0.2 \times 9.8 = 1.96$F=0.2×9.8=1.96 N ≈ 2 N

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Common Mistakes

• Forgetting to compensate for friction by tilting the runway.
• Not keeping the total system mass constant when investigating force vs acceleration (you must transfer masses, not just add to the hanger).
• Confusing the mass on the hanger with the total system mass — the total system mass includes both the trolley and the hanging masses.
• Using only one reading per data point — always take at least three repeats and calculate a mean.
• Forgetting to convert grams to kilograms before calculating.

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Summary

• This practical investigates $F = ma$F=ma by varying force (constant mass) and varying mass (constant force).
• Force and acceleration are directly proportional ($a \propto F$a∝F) when mass is constant.
• Acceleration and mass are inversely proportional ($a \propto 1/m$a∝1/m) when force is constant.
• Tilt the runway to compensate for friction.
• Keep the total system mass constant when changing the force.
• Use light gates and a data logger for accurate timing.
• Repeat measurements and calculate means.