Force diagrams and resultant forces

In a nutshell

A force diagram is a useful way to visualise the different forces acting on an object. Many different forces can act on a single object at the same time, the directions and sizes of these forces determine the movement of the object.

Forces in two-dimensions

If two or more forces are acting in the same direction, then you can add the sizes of the forces together to give you the overall force in that direction. This overall force is called the resultant force in that direction.

Balanced forces

If there is a force acting in the opposite direction to another force, these forces are still acting along the same line and you can subtract the forces to find the resultant force. When the opposite forces are equal in size, these forces are said to balance each other out.

Unbalanced forces

In the case where the opposite forces acting along the same line have different sizes, the forces are said to be unbalanced.

Resultant force

When the forces along the same line balance each other out, the resultant force along that line is zero. Because the overall force along the line is zero, there is no change to the motion of the object along that direction.

If the object was stationary, then the object would remain stationary after the balanced forces were applied. If the object was moving at a constant speed, it would continue to move at that speed in the same direction once the balanced forces were applied.

When the forces are unbalanced, the resultant force along the line is not zero. This means that motion of the object will change once the unbalanced forces are applied. The object will accelerate in the direction of the force with a greater size. In other words, the object will accelerate in the direction of the resultant force.

Example

What is the resultant force acting on the ball shown below and what motion do you expect due to this resultant force?

Science; Forces and motion; KS3 Year 7; Force diagrams and resultant forces

The ball has a force of $30 \,N$ acting upwards and $20 \,N$ acting downwards, so these forces are acting in opposite directions. This means that you subtract one force from the other:

$30 - 20 = 10 \space N$

As this resultant force is not zero, this means that the object is going to accelerate in the upwards direction.