How to Calculate Work Done by a Force

If you finish this lesson, you'll be able to calculate the work done when a force moves an object in a straight line. This is a key skill in physics, especially in mechanics.

What is Work in Physics?

Work is done when a force causes an object to move in the direction of the force. The formula is:

$$W = F \times d$$

where:

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

Important: The force and the movement must be in the same direction for this formula to apply.

Step-by-Step: Calculating Work

Let's break down the process:

1. Identify the Force and Direction

Check that you know the size of the force and the distance moved, and that both are in the same direction.

2. Make Sure Units Match

Force should be in newtons (N) and distance in metres (m). Convert if needed.

3. Use the Formula

Multiply the force by the distance to get the work done.

Worked Example

A student pushes a box with a force of 20 N for 3 m along a flat floor. How much work is done?

• Force, $F = 20\ \text{N}$
• Distance, $d = 3\ \text{m}$

Plug into the formula:

$$W = F \times d = 20\ \text{N} \times 3\ \text{m} = 60\ \text{J}$$

So, the work done is 60 joules.

Where This Shows Up in Real Life

Whenever you lift a bag, push a cart, or pull a sled, you're doing work in the physics sense. Calculating work helps engineers design machines, and helps athletes understand their energy use.

Common Mistakes and How to Avoid Them

• Forgetting to check the direction: If the force and movement are not in the same direction, use $W = F \times d \times \cos(\theta)$, where $\theta$ is the angle between force and movement.
• Wrong units: Always use newtons for force and metres for distance.
• Forgetting the force must cause the movement: If the object doesn't move, no work is done, even if a force is applied!

Try It Yourself

A child pulls a sled with a force of 50 N for 2 m along the snow. How much work is done?

Takeaway

If you know the force (in newtons) and the distance moved (in metres), and both are in the same direction, multiply them to find the work done in joules.