# Forces: Resultant Forces and Work Done

## Resultant Forces

### Basic Understanding

• A force is a push or pull and can change an object’s motion or state of rest.

• Forces are vector quantities, meaning they have both a magnitude (size) and a direction.

• A single force acting alone is often balanced by other forces, preventing a change in the state of motion of the object.

### Resultant Forces

• The resultant force is the overall force acting on an object when all the individual forces are added together.

• If the resultant force is zero, the object will remain stationary or continue to move at a constant speed in the same direction.

• If there is a non-zero resultant force, the object will accelerate in the direction of the force. This acceleration can cause a change in speed, direction or both.

• Resultant forces can be calculated using diagrams such as force arrows, or vector addition for multiple forces acting at angles to each other.

## Work Done

### Understanding Work

• Work done is a measure of energy transferred. If a force moves an object, energy is transferred and work is done.

• Work done is measured in joules (J) which is the same unit as energy.

### Calculating Work Done

• Work done by a force (joules) can be calculated as: Work done = force (N) x distance (m).

• Note that in this equation the distance is the distance moved in the direction of the force.

• No work is done if the force and the movement are perpendicular to each other, e.g. if you push against a wall and it doesn’t move, despite the effort exerted.

• If a force acts at an angle, only the component of the force in the direction of the motion does work, the rest is ‘wasted’ as it doesn’t contribute to moving the object.

• The work done on an object is equal to the energy transferred to that object. If you do 10 joules of work lifting a book, you’ve given the book 10 joules of potential energy.