# 5.1.6 Resultant Forces

### Resultant Force

• A resultant force is a single force that describes all of the forces operating on a body
• When many forces are applied to an object they can be combined (added) to produce one final force which describes the combined action of all of the forces
• This single resultant force determines:
• The direction in which the object will move as a result of all of the forces
• The magnitude of the final force experienced by the object
• The resultant force is sometimes called the net force
• Forces can combine to produce
• Balanced forces
• Unbalanced 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

A book resting on a table is an example of balanced 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

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

### Calculating Resultant Force

• Resultant forces can be calculated by adding or subtracting all of the forces acting on the object
• Forces working in opposite directions are subtracted from each other
• Forces working in the same direction are added together
• If the forces acting in opposite directions are equal in size, then there will be no resultant force – the forces are said to be balanced

Diagram showing the resultant forces on three different objects

• Imagine the forces on the boxes as two people pushing on either side
• In the first scenario, the two people are evenly matched – the box doesn’t move
• In the second scenario, the two people are pushing on the same side of the box, it moves to the right with their combined strength
• In the third scenario, the two people are pushing against each other and are not evenly matched, so there is a resultant force to the left

#### Worked Example

Calculate the magnitude and direction of the resultant force in the diagram below.

Step 1: Add up all of the forces directed to the right

4 N + 8 N = 12 N

Step 2: Subtract the forces on the right from the forces on the left

14 N – 12 N = 2 N

Step 3: Evaluate the direction of the resultant force

• The force to the left is greater than the force to the right therefore the resultant force is directed to the left

Step 4: State the magnitude and direction of the resultant force

• The resultant force is 2 N to the left

#### Exam Tip

Remember to always provide units for your answer and to state whether the force is to the left, to the right, or maybe up or down

Always provide your final answer as a description of the magnitude and the direction, for example:

• Resultant Force = 4 N to the right

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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