Question

A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10N is acting on it in a direction making an angle \[{60^0}\] with the axis and displacing it along the x-axis by 4 meters. Then find the work done by the force.

Answer 1

Hint:Before we start proceeding with this problem let us understand the term displacement and work done. When a force is applied, the object changes its position which is known as displacement. Since it is a vector quantity it has both direction and magnitude. Work is nothing but a force needed to move an object from one place to another.

Formula Used:
The formula to find the work done is,
\[W = \overrightarrow F \cdot \overrightarrow S \]
Where, \[\overrightarrow F \] is force applied and \[\overrightarrow S \] is displacement.

Complete step by step solution:
Consider a body of mass 5 kg is placed at the origin and it can move only on the x-axis. Say a force of 10N is acting on it in a direction making an angle \[{60^0}\] with the x-axis and displacing it by 4 meters. We have to find the work done by the force. By the formula of work done, we know that,
\[W = \overrightarrow F \cdot \overrightarrow S \]
\[\Rightarrow W = F \cdot S\cos \theta \]
\[\Rightarrow W = 10 \times 4 \times \cos {60^0}\]
\[\Rightarrow W = 10 \times 4 \times \dfrac{1}{2}\]
\[\therefore W = 20J\]

Therefore, when the work done by the force is 20J.

Note:Work done can be positive, negative, or zero depending on the angle between the force applied and the displacement. Since the work done of an object is directly proportional to the force applied and the displacement. A fixed change in either the force or displacement will lead to an equivalent change in work done.