Unbalanced Forces

When multiple forces act on a single object, the forces can be added together to produce a resultant force

When the forces acting on an object completely cancel out
- the forces are balanced
- the resultant force is zero
When the forces acting on an object do not completely cancel out
- the forces are unbalanced
- there is a resultant force

Balanced forces

Balanced forces mean that the forces have combined in such a way that they cancel each other out and no resultant force acts on the body
- For example, the weight of a book on a desk is balanced by the normal force of the desk
- As a result, no resultant force is experienced by the book, the book and the table are equal and balanced

Balanced Forces, downloadable IGCSE & GCSE Physics revision notes

A book resting on a table is an example of balanced forces

Unbalanced forces

Unbalanced forces mean that the forces have combined in such a way that they do not cancel out completely and there is a resultant force on the object
- For example, imagine two people playing a game of tug-of-war, working against each other on opposite sides of the rope
- If person A pulls with 80 N to the left and person B pulls with 100 N to the right, these forces do not cancel each other out completely
- Since person B pulled with more force than person A the forces will be unbalanced and the rope will experience a resultant force of 20 N to the right

Tug O War, downloadable IGCSE & GCSE Physics revision notes

A tug-of-war is an example of when forces can become unbalanced

Unbalanced Forces, Mass & Acceleration

When forces combine on an object in such a way that they do not cancel out, there is a resultant force on the object
This resultant force causes the object to accelerate (i.e. change its velocity)
- The object might speed up
- The object might slow down
- The object might change direction

The relationship between resultant force, mass and acceleration is given by the equation:

F = m × a

Where:
- F = resultant force, measured in newtons (N)
- m = mass, measured in kilograms (kg)
- a = acceleration, measured in metres per second squared (m/s²)
This equation is also known as Newton's second law of motion

Worked example

A car salesperson claims 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: State the equation for acceleration

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

Step 3: Calculate the acceleration

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

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

Part (b)

Step 1: List the known quantities

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

$F = m a$

Step 3: Calculate the force required to accelerate the car

$F = 900 \times 9$

$F = 8100 N$

Worked example

A passenger of mass 70 kg travels in a car at a speed of 20 m/s. The vehicle is involved in a collision, which brings the car (and the passenger) to a halt in 0.1 seconds.

Calculate:

a) The deceleration of the car (and the passenger).

b) The decelerating force on the passenger.

Answer:

Part (a)

Step 1: List the known quantities

Initial velocity, u = 20 m/s
Final velocity, v = 0 m/s
Time, t = 0.1 s

Step 2: Write out the equation for acceleration

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

Step 3: Calculate the deceleration of the car (and the passenger):

$a = \frac{(0 - 20)}{0.1}$

$a = \frac{- 20}{0.1}$

$a = - 200 m / s^{2}$

Part (b)

Step 1: List the known quantities

Mass of the passenger, m = 70 kg
Acceleration (deceleration, in this case), a = −200 m/s²

Step 2: State the relationship between resultant force, mass and acceleration

This question involves quantities of force, mass and acceleration, so the appropriate equation for this case is:

$F = m a$

Step 3: Calculate the decelerating force

$F = 70 \times (- 200)$

$F = - 14 000 N$

Examiner Tip

Remember that the resultant force is a vector quantity. Examiners may ask you to comment on why its value is negative - this happens when the resultant force acts in the opposite direction to the object's motion. In the worked example above, the resultant force opposes the passenger's motion, slowing them down (decelerating them) to a halt, this is why it has a minus symbol.

Unbalanced Forces (Edexcel IGCSE Physics: Double Science)

Revision Note

Unbalanced forces

Balanced forces

Unbalanced forces

Unbalanced Forces, Mass & Acceleration

Worked example

Worked example

Examiner Tip

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Author: Ashika