What is the definition of work done by a force?

Work done by a force is the energy transferred when a force moves an object over a distance.

In physics, work is a measure of energy transfer that occurs when an object is moved by a force. The amount of work done depends on three key factors: the magnitude of the force, the distance over which the force is applied, and the direction of the force relative to the direction of movement. Mathematically, work done (W) is calculated using the formula:

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

where \( F \) is the force applied, \( d \) is the distance moved by the object, and \( \theta \) is the angle between the force and the direction of movement. If the force is applied in the same direction as the movement, \( \theta \) is 0 degrees, and \( \cos(0) = 1 \), simplifying the formula to \( W = F \times d \).

For example, if you push a box with a force of 10 newtons over a distance of 5 metres in the same direction as the force, the work done is:

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

Here, the unit of work is the joule (J), which is equivalent to one newton-metre (N·m).

It's important to note that if the force is perpendicular to the direction of movement, no work is done because \( \cos(90^\circ) = 0 \). For instance, if you carry a heavy bag while walking horizontally, the force you exert vertically to hold the bag does no work in the horizontal direction.

Understanding work done by a force helps us analyse various physical situations, such as lifting objects, moving vehicles, and even the functioning of machines. It is a fundamental concept that links force, energy, and motion, providing a clearer picture of how energy is transferred and utilised in different scenarios.