IGCSEPhysicsCambridge (CIE)Revision Notes1. Motion, Forces & EnergyEffects of ForcesNewton's Second Law

Newton's Second Law (Cambridge (CIE) IGCSE Physics)

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Leander Oates

Written by: Leander Oates

Reviewed by: Caroline Carroll

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Newton's second law

  • Newton's second law of motion states:

The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to the object's mass

  • Newton's second law of motion explains what happens when a non-zero resultant force acts on an object

  • A resultant force occurs when the forces acting on an object are not balanced

  • A resultant force acting on an object will cause a change in the object's motion

  • This change in motion is an acceleration:

    • Speeding up

    • Slowing down

    • Changing direction

  • If the resultant force on an object is not zero, the object will accelerate in the direction of the resultant force

  • The bigger this resultant force, the larger the acceleration

  • For a given force, the greater the object's mass, the smaller the acceleration experienced

Examples of Newton's second law

Newton second law in action, downloadable IGCSE & GCSE Physics revision notes

Objects like baseballs and lawnmowers accelerate when a resultant force is applied on them. The size of the acceleration is proportional to the size of the resultant force

Calculations using Newton's second law

Extended tier only

  • Newton's second law can be expressed as an equation:

F space equals space m a

  • Where:

    • F = resultant force on the object, measured in newtons (N)

    • m = mass of the object, measured in kilograms (kg)

    • a = acceleration of the object, measured in metres per second squared (m/s2)

  • The acceleration occurs in the same direction as the resultant force

Formula triangle for acceleration, mass and resultant force

Fma Formula Triangle, downloadable IGCSE & GCSE Physics revision notes

To use a formula triangle, simply cover up the quantity you wish calculate and the structure of the equation is revealed

  • A more detailed explanation of how to use formula triangles is covered in the revision note Speed and velocity

Worked Example

A car salesman says that their best car has a mass of 900 kg and can accelerate from 0 to 27 m/s in 3 seconds.

Calculate:

a) the acceleration of the car in the first 3 seconds.

b) the force required to produce this acceleration.

Answer:

Part (a)

Step 1: List the known quantities

  • Initial velocity, v space equals space 0 space straight m divided by straight s 

  • Final velocity, u space equals space 27 space straight m divided by straight s 

  • Time, t space equals space 3 space straight s

Step 2: State the equation for acceleration, in terms of change in velocity

a space equals space fraction numerator v space minus space u over denominator t end fraction

a space equals space fraction numerator 27 space minus space 0 over denominator 3 end fraction

a space equals space 9 space straight m divided by straight s squared

Part (b)

Step 1: List the known quantities

  • Mass of the car, m space equals space 900 space kg 

  • Acceleration, a space equals space 9 space straight m divided by straight s squared 

Step 2: Identify which law of motion to apply

  • The question involves quantities of force, mass and acceleration, so Newton's second law is required:

F space equals space m a

Step 3: Calculate the force required to accelerate the car

F space equals space 900 space cross times space 9

F space equals space 8100 space straight N

Worked Example

Three shopping trolleys, A, B and C, are being pushed using the same force. This force causes each trolley to accelerate.

WE Newton second law, downloadable IGCSE & GCSE Physics revision notes

State which trolley would have the smallest acceleration. Explain your answer.

Answer: C

Step 1: Identify which law of motion to apply

  • The question involves quantities of force and acceleration, and the image shows trolleys of different masses, so Newton's second law is required:

F space equals space m a

Step 2: Re-arrange the equation to make acceleration the subject

a space equals fraction numerator space F over denominator m end fraction

Step 3: Explain the inverse proportionality between acceleration and mass  

  • Acceleration is inversely proportional to mass

  • This means that for the same amount of force, a large mass will experience a small acceleration

  • Therefore, trolley C will have the smallest acceleration because it has the largest mass

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    Leander Oates

    Author: Leander Oates

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.