Newton's Second Law

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

Newton's second law explains the following important principles:
- An object will accelerate (change its velocity) in response to a resultant force or unbalanced 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

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

Calculating with Newton's Second Law

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

F = ma

Where:
- F = resultant force on the object in Newtons (N)
- m = mass of the object in kilograms (kg)
- a = acceleration of the object in metres per second squared (m/s²)

Worked example

A car salesman says that his 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

change in velocity = Δv = final velocity − initial velocity

Δv = 27 − 0 = 27 m/s

Step 3: State the equation for acceleration

$a = \frac{∆ v}{t}$

Step 4: Calculate the acceleration

$a = \frac{27}{3} =$ 9 m/s²

Part (b)

Step 1: List the known quantities

- Mass of the car, m = 900 kg
- Acceleration, a = 9 m/s²

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 = ma

Step 3: Calculate the force required to accelerate the car

F = 900 × 9 = 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

Which trolley will 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 = ma

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 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

Exam Tip

Higher-tier students must memorise the equation and be able to rearrange it for Newton's second law calculation. Other students will be given the equation when it is needed in the question.

This equation can be rearranged with the help of a formula triangle:

Formula Triangle for Newton's Second Law

Fma Formula Triangle, downloadable IGCSE & GCSE Physics revision notes

Unbalanced force, mass and acceleration formula triangle

Newton's Second Law (WJEC GCSE Physics: Combined Science)

Revision Note