Newton's Second Law (Cambridge International IGCSE Science)

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:

  • Acceleration if the object speeds up
  • Deceleration if the object slows down

• 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

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

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

$F=ma$

• 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

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

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

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

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

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

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

Part (b)

Step 1: List the known quantities

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

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:

$F=ma$

Step 3: Calculate the force required to accelerate the car

$F=900\times9$

$F=8100N$

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

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:

$F=ma$

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 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