Work Done

Definition of Work Done

Work done occurs when a force causes an object to move in the direction of the force applied. It measures how much energy is transferred by the force to move the object.

The amount of work done depends on two key factors:

• The force applied to the object (measured in newtons, N)
• The distance the object moves in the direction of the force (measured in metres, m)

The formula for work done is:

$$\text{Work done} = \text{Force} \times \text{Distance}$$

In symbols, this is written as:

$$W = F \times d$$

where:

• $W$ = work done (in joules, J)
• $F$ = force applied (in newtons, N)
• $d$ = distance moved in the direction of the force (in metres, m)

Note that if the force is not in the exact direction of the movement, only the component of the force in the direction of the movement does work.

Calculating Work Done

Work done is measured in joules (J). One joule is the work done when a force of one newton moves an object one metre in the direction of the force.

To calculate work done, multiply the force applied by the distance moved in the direction of the force.

For example, if a force of 5 N is used to push a box 2 m along the floor, the work done is:

$$W = 5 \text{ N} \times 2 \text{ m} = 10 \text{ J}$$

For example, if a force of 10 N is used to push a box 3 m along the floor, the work done is:

$$W = 10 \text{ N} \times 3 \text{ m} = 30 \text{ J}$$

This means 30 joules of work has been done on the box.

Work Done and Energy Transfer

When work is done, energy is transferred from one object or system to another. For example, when you push a shopping trolley, work done by your muscles transfers energy to the trolley, causing it to move.

The amount of work done equals the amount of energy transferred. This means:

$$\text{Work done} = \text{Energy transferred}$$

For instance, if 100 J of work is done pushing a box, 100 J of energy is transferred to the box, increasing its kinetic energy or overcoming friction.

Energy transferred can increase the object's kinetic energy or be converted into other forms such as heat or sound.

Forces that cause motion do work by transferring energy to the moving object. If the force is in the same direction as the motion, positive work is done, increasing the object's energy.

For example, if a cyclist pedals harder, they do more work on the bike, transferring more energy to increase its speed.

Work Done Against Friction

Friction is a force that opposes motion between two surfaces in contact. When work is done against friction, energy is transferred but not all of it is useful for moving the object.

Instead, some energy is converted into heat due to friction, which can cause surfaces to warm up.

This means that work done against friction reduces the efficiency of machines or moving objects because some energy is wasted as heat.

For example, when you rub your hands together, you do work against friction, and your hands get warm because energy is transferred to thermal energy.