Viewing as
Teacher view: planning notes, the answers to every question, and the teacher copies of the files.
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).
Teacher resources
The teacher copies: slides with the questions built in, the answers, and anything else attached to this lesson for whoever is teaching it.
- Newtons Second Law - Teacher Slides.pptx Teacher The lesson slides with the teacher's notes on each slide, and every question and mark scheme built in. Built from the lesson script on 1 October 2026. View
- Newtons Second Law - Teacher Notes.docx Teacher The complete notes with the teacher's notes and every model answer in full. Built from the lesson script on 1 October 2026. View
Student handouts
The same files the students see, to print or hand out.
- Newtons Second Law.pptx Built from the lesson script on 1 October 2026. View
- Newtons Second Law - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 1 October 2026. View
- Newtons Second Law - Exam Questions.docx Built from the lesson script on 1 October 2026. View
Warm-up
Answer each one, then check.
-
1
What is a resultant force?
Show answerHide answer
The single force with the same effect as all the forces
-
2
What is acceleration?
Show answerHide answer
Rate of change of velocity
-
3
What is the unit of force?
Show answerHide answer
Newton
-
4
What is proportional?
Show answerHide answer
Doubling one doubles the other
-
5
What does inversely proportional mean?
Show answerHide answer
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
The weight of the hanging masses provides the force.
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.
Show the solutionHide the solution
- 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.
Show the solutionHide the solution
- 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.
Show the solutionHide the solution
- 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.
Show the solutionHide the solution
- 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.
Required Practical 7: Variables
Know which is which for each investigation.
-
Effect of force
Independent: Force (weight on the hanger). Dependent: Acceleration. Control: Total mass of trolley and hanger
-
Effect of mass
Independent: Mass of the trolley. Dependent: Acceleration. Control: The accelerating force
Errors and Improvements
Where the practical goes wrong and how to fix it.
-
Friction
Friction reduces the resultant force. Tilting the runway slightly until the trolley rolls at a steady speed compensates for it.
-
Timing
Stopwatches add human reaction time. Light gates and a data logger measure times far more precisely.
-
Keeping mass constant
When varying force, take masses off the trolley and put them on the hanger, so the total mass being accelerated stays the same.
Inertia and Inertial Mass
Mass resists changes in motion.
-
Inertia
The tendency of any object to stay at rest or keep moving at a constant velocity.
-
Inertial mass
Defined as force ÷ acceleration: the bigger it is, the harder it is to change the object's velocity.
-
Example
A loaded lorry needs a much larger force than a car to reach the same acceleration, because its inertial mass is larger.
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.
- Compensate for friction by tilting the runway.
Exam focus
A 1200 kg car has a resultant force of 3000 N. Calculate its acceleration. (2 marks) (2 marks)
Rearrange F = ma to a = F ÷ m, substitute 3000 ÷ 1200 and give 2.5 m/s². Use the resultant force, not just the driving force.
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.
- Independent variable
- The variable you change in an experiment.
- Dependent variable
- The variable you measure in an experiment.
Questions and answers
13 questions set on this lesson, with the mark schemes and model answers open.
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
Mark scheme — 2 marks available
- Rearranges to a = F ÷ m — 1 mark
- 2.5 m/s² — 1 mark
Model answer
\(a = 3000 \div 1200 = 2.5\) m/s²
A trolley of mass 0.50 kg accelerates at 4.0 m/s². Calculate the resultant force on the trolley.
Mark scheme — 2 marks available
- Correct substitution — 1 mark
- 2.0 N — 1 mark
Model answer
\(F = 0.50 \times 4.0 = 2.0\) N
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.
Mark scheme — 4 marks available
- Straight line through the origin / directly proportional — 1 mark
- Uses the gradient — 1 mark
- Gradient = 1/m — 1 mark
- 2.0 kg — 1 mark
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
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.
Mark scheme — 6 marks available
- 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
Model answer
See levels-of-response scheme.
Explain what is meant by the inertial mass of an object.
Mark scheme — 2 marks available
- How difficult it is to change velocity — 1 mark
- Force divided by acceleration — 1 mark
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.
A 1500 kg car accelerates at 2 m/s². What is the resultant force?
Why: F = ma = 1500 × 2 = 3000 N.
In Required Practical 7, why are masses moved from the trolley to the hanger?
Why: This changes the force while keeping the total mass constant, so it is a fair test.
A graph of acceleration against 1/mass for a constant force is...
Why: a = F × (1/m), so a against 1/m is a straight line through the origin.
Newton's second law is...
Why: Force is mass times acceleration.
A 2 kg mass with a 10 N resultant force has an acceleration of...
Why: 10 ÷ 2.
Doubling the force on an object doubles its...
Why: a ∝ F.
Doubling the mass for the same force makes the acceleration...
Why: a ∝ 1/m.
Inertial mass is...
Why: It measures resistance to change in velocity.