How do you calculate work done by a force?

Work done by a force is calculated by multiplying the force by the distance moved in the direction of the force.

To understand this better, let's break it down. The formula for work done (W) is:

\[ W = F \times d \times \cos(\theta) \]

Here, \( W \) is the work done, \( F \) is the magnitude of the force applied, \( d \) is the distance over which the force is applied, and \( \theta \) is the angle between the force and the direction of movement.

In simpler terms, if you push an object with a certain force and it moves a certain distance in the direction of the force, you can calculate the work done by multiplying the force by the distance. For example, if you push a box with a force of 10 newtons (N) and it moves 5 metres (m) in the direction of the push, the work done is:

\[ W = 10 \, \text{N} \times 5 \, \text{m} = 50 \, \text{J} \]

The unit of work is the joule (J), where 1 joule is equal to 1 newton-metre (N·m).

If the force is not applied in the exact direction of the movement, you need to consider the angle \( \theta \). For instance, if the force is applied at an angle, only the component of the force in the direction of the movement does the work. This is where the \( \cos(\theta) \) part of the formula comes in. For example, if the force is applied at a 30-degree angle to the direction of movement, you would use:

\[ W = F \times d \times \cos(30^\circ) \]

Understanding this concept is crucial in physics as it helps you analyse how energy is transferred in different situations, such as lifting objects, pushing carts, or even in more complex systems like engines and machinery.