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Newton's Second Law (Oxford AQA IGCSE Physics)

Revision Note

Leander Oates

Expertise

Physics

Newton's Second Law

What is Newton's second law of motion?

  • 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

Examples of Newton's second law

A man striking a baseball with a bat with a vector showing the acceleration, a man pushing a lawnmower with a vector showing the resultant force
Objects like baseballs and lawnmowers accelerate when a resultant force is applied to them. The size of the acceleration is proportional to the size of the resultant force

  • Newton's second law of motion states:

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

F space equals space m space cross times space a

  • Where:

    • F = resultant force measured in newtons (N)

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

    • a = acceleration measured in metres per second squared ( m/s2)

  • The bigger this resultant force, the larger the acceleration

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

Worked Example

A car salesperson 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 = 0 m/s

  • Final velocity = 27 m/s

  • Time, t = 3 s

Step 2: Calculate the change in velocity

increment v space equals space v subscript f space minus space v subscript i

increment v space equals space 27 space minus space 0

increment v space equals space 27 space straight m divided by straight s

Step 3: State the equation for acceleration

a space equals space fraction numerator increment v over denominator t end fraction

Step 4: Calculate the acceleration

a space equals space 27 over 3 space

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 = 900 kg

  • Acceleration, a = 9 m/s2

Step 2: State the equation for Newton's second law

F space equals space m space cross times space 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.

Three shopping trollies. Trolly A is empty, trolly B has three items inside, trolley C is full of shopping

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

Answer:

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 space F over m

Step 3: Explain the inverse proportionality between acceleration and mass  

  • Acceleration is inversely proportional to mass

  • This means 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

    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.