Resultant Forces (AQA GCSE Physics: Combined Science)

• 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

• 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

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