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Physics · Forces

Newton's Second Law

Use \(F = ma\), investigate how force and mass affect acceleration (Required Practical 7), and explain inertial mass (Higher tier).

6 key terms
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Warm-up

Answer each one, then check.

1

What is a resultant force?

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The single force with the same effect as all the forces
2

What is acceleration?

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Rate of change of velocity
3

What is the unit of force?

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Newton
4

What is proportional?

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Doubling one doubles the other
5

What does inversely proportional mean?

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Doubling one halves the other

Learning Objectives

1State Newton's Second Law.
2Recall and apply \(F = ma\).
3Describe how to investigate the effect of force and mass on acceleration (Required Practical 7).
4Explain inertial mass (Higher tier).

NEWTON'S SECOND LAW

resultant force \(=\) mass \(\times\) acceleration \(F = ma\)

The acceleration of an object is proportional to the resultant force and inversely proportional to its mass: \(a \propto F\) and \(a \propto \tfrac{1}{m}\).

Required Practical 7: Force, Mass and Acceleration

A trolley pulled along a runway by a falling mass, with light gates measuring its speed to find acceleration.

Required Practical 7: Method

Two investigations.

1 Force varied
Keep the total mass constant by moving masses from the trolley to the hanger; the force is the weight of the hanging masses.
2 Measure acceleration
From the light gates: a = (v − u) ÷ t.
3 Plot
Acceleration against force: a straight line through the origin.
4 Mass varied
Keep the force constant and add masses to the trolley.
5 Plot
Acceleration against mass (a curve) or against 1/mass (a straight line).
6 Repeat
Take repeat readings and compensate for friction by slightly tilting the runway.

Finding Acceleration

A car of mass 1200 kg has a resultant force of 3000 N. Calculate its acceleration.

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1 Rearrange \(a = F \div m\)
2 Substitute \(a = 3000 \div 1200\)
3 Answer \(a = 2.5\) m/s²

Answer2.5 m/s²

Finding the Force

A 0.50 kg trolley accelerates at 4.0 m/s². Calculate the resultant force.

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1 Write the equation \(F = ma\)
2 Substitute \(F = 0.50 \times 4.0\)
3 Answer \(F = 2.0\) N

Answer2.0 N

Using a Graph

A graph of acceleration against force for a trolley is a straight line through (2.0 N, 1.0 m/s²). Find the mass.

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1 Gradient \(a \div F = 1.0 \div 2.0 = 0.50\) kg⁻¹
2 Since a = F ÷ m Gradient = 1 ÷ m
3 Mass \(m = 1 \div 0.50 = 2.0\) kg

Answer2.0 kg

Inertial Mass (Higher)

Explain what is meant by inertial mass.

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1 Definition The ratio of force to acceleration
2 Meaning A measure of how difficult it is to change the velocity of an object

AnswerInertial mass = force ÷ acceleration: how hard it is to change an object's velocity.

Estimating

Use sensible values.

Everyday values
A car accelerating from 0 to 27 m/s (60 mph) in 10 s has a ≈ 2.7 m/s².
Force
For a 1000 kg car: F = 1000 × 2.7 ≈ 2700 N.
Symbol ~
Means approximately.
Units
Mass in kg, a in m/s², F in N.

Predict the Acceleration

A trolley has a mass of 1.0 kg and accelerates at 2.0 m/s² under a resultant force. What acceleration would the same force give a 2.0 kg trolley? What force is needed for 2.0 kg to accelerate at 2.0 m/s²?

1. Use F = ma.

2. Compare the masses.

A good answer shows: Half the acceleration: 1.0 m/s². Force = 2.0 × 2.0 = 4.0 N.

Can I...?

1State Newton's second law.
2Recall F = ma.
3Rearrange for a or m.
4Describe Required Practical 7.
5Interpret a force–acceleration graph.
6Explain inertial mass.
7Estimate forces on a car.
8Use units.

Summary & Exam Focus

\(F = ma\).
Acceleration ∝ force; ∝ 1/mass.
Inertial mass = force ÷ acceleration.
Use light gates to measure acceleration.

Exam focus

A 1200 kg car has a resultant force of 3000 N. Calculate its acceleration. (2 marks) (2 marks)

a = F ÷ m.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Resultant force: The net force acting on an object.
Acceleration: Rate of change of velocity.
Inertial mass: Force divided by acceleration.
Proportional: Increasing by the same factor.
Inversely proportional: One quantity halves as the other doubles.
Light gate: A sensor that times how long a card takes to pass.

Practice questions

Have a go at each one before you open its answer.

Question 1 Calculate 2 marks

A car has a mass of 1200 kg. The resultant force on the car is 3000 N. Calculate the acceleration of the car. Use the equation: resultant force = mass × acceleration
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Model answer

\(a = 3000 \div 1200 = 2.5\) m/s²

Mark scheme
- Rearranges to a = F ÷ m — 1 mark
- 2.5 m/s² — 1 mark
Question 2 Calculate 2 marks

A trolley of mass 0.50 kg accelerates at 4.0 m/s². Calculate the resultant force on the trolley.
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Model answer

\(F = 0.50 \times 4.0 = 2.0\) N

Mark scheme
- Correct substitution — 1 mark
- 2.0 N — 1 mark
Question 3 Use the graph 4 marks

A student investigates how the acceleration of a trolley depends on the resultant force. The graph shows the results. (a) Describe the relationship. (b) Use the graph to calculate the mass of the trolley.
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Model answer

(a) Acceleration is directly proportional to the resultant force (a straight line through the origin). (b) Gradient \(= 2.5 \div 5.0 = 0.50\); \(m = 1 \div 0.50 = 2.0\) kg

Mark scheme
- Straight line through the origin / directly proportional — 1 mark
- Uses the gradient — 1 mark
- Gradient = 1/m — 1 mark
- 2.0 kg — 1 mark
Question 4 Describe 6 marks

Describe an investigation to show how the acceleration of a trolley depends on the resultant force acting on it. Your answer should include the apparatus, the measurements and how you would use the results.
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Model answer

See levels-of-response scheme.

Mark scheme
- Level 3 (5 to 6 marks): a complete method (trolley, runway, pulley, hanging masses, light gates or ticker timer), keeping total mass constant, measuring acceleration for several forces, plotting acceleration against force and describing the expected straight line, with a precaution or repeat — 5 to 6 marks
- Level 2 (3 to 4 marks): a method with most apparatus and measurements but with gaps — 3 to 4 marks
- Level 1 (1 to 2 marks): simple statements about pulling a trolley — 1 to 2 marks
Question 5 Explain 2 marks

Explain what is meant by the inertial mass of an object.
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Model answer

Inertial mass is a measure of how difficult it is to change the velocity of an object; it is the ratio of force to acceleration.

Mark scheme
- How difficult it is to change velocity — 1 mark
- Force divided by acceleration — 1 mark

Quick check

Newton's second law is...
1. A\(F = m + a\)
2. B\(F = m \div a\)
3. C\(F = a \div m\)
4. D\(F = ma\)
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D: \(F = ma\)

Force is mass times acceleration.
A 2 kg mass with a 10 N resultant force has an acceleration of...
1. A5 m/s²
2. B20 m/s²
3. C0.2 m/s²
4. D12 m/s²
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A: 5 m/s²

10 ÷ 2.
Doubling the force on an object doubles its...
1. Amass
2. Bacceleration
3. Cweight
4. Dinertia
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B: acceleration

a ∝ F.
Doubling the mass for the same force makes the acceleration...
1. Adouble
2. Bthe same
3. Chalf
4. Dzero
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C: half

a ∝ 1/m.
Inertial mass is...
1. Aforce × acceleration
2. Bweight ÷ time
3. Cspeed ÷ distance
4. Dforce ÷ acceleration
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D: force ÷ acceleration

It measures resistance to change in velocity.

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