Newton's Second Law (Oxford AQA IGCSE Physics)

Revision Note

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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