Newton's Second Law

Extended tier only

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

Examiner Tip

The CIE IGCSE Co-ordinated Sciences specification does not require you to know that a resultant force may change the velocity of an object by changing its direction of motion or its speed, but it is helpful to understand this for harder calculations.

Calculations using Newton's second law

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

$F = m a$

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, $v = 0 m / s$
Final velocity, $u = 27 m / s$
Time, $t = 3 s$

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

$a = \frac{v - u}{t}$

$a = \frac{27 - 0}{3}$

$a = 9 m / s^{2}$

Part (b)

Step 1: List the known quantities

Mass of the car, $m = 900 kg$
Acceleration, $a = 9 m / s^{2}$

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:

$F = m a$

Step 3: Calculate the force required to accelerate the car

$F = 900 \times 9$

$F = 8100 N$

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:

$F = m a$

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

$a = \frac{F}{m}$

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

Newton's Second Law (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Revision Note