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# Forces and free-body diagrams

## Resultant force

The sum of all the forces acting on a body is the resultant force or net force on the body.

A body is often subject to multiple forces pointing in different directions.

These forces, like all vectors, can be combined by adding them up to give the resultant force.

Remember because they are vectors, the direction of the forces needs to be taken into account when they are added.

The resultant force is a single force that has the same effect on the body as all of the individual forces acting together.

In the two diagrams below, different forces $A$, $B$ and $C$ act on a body. They can be added together to give the resultant force $R.$

Taking the vector sum of forces A, B and C gives the resultant force R.

## Balanced and unbalanced forces

When the resultant (net) force on a body is zero, the forces on the body are said to be balanced.

There is no acceleration when the forces on a body are balanced. If the body is at rest it remains at rest. If the body is moving it will move with constant velocity.

A stationary trolley that is pushed by two people with the same force in opposite directions will not move as the forces are balanced.

When the net force on a body is non-zero, the forces on the body are said to be unbalanced.

There will be acceleration in the direction of the resultant force.

A plane that is pushed north by its engines and east by the wind will move northeast.

Balanced forces (left) and unbalanced forces (right) acting on two objects.

## Free-body diagrams

A free-body diagram is a diagram showing all of the forces acting on a single object.

Free-body diagrams are useful in determining if the forces on an object are balanced.

The object is drawn as a rectangle and each force is represented by an arrow in the direction of the force.

Each arrow must be labelled with the symbol of the force (e.g. $F_{1}$, $N$, $W$).

The magnitude of each force can be indicated by the length of the arrow. However, this is only true if stated in the description of the diagram.

A free-body diagram of an object sliding down a slope.