Question

If the work done is negative, find the angle between the force and displacement of the body.
A) 0°
B) 45°
C) 90°
D) 180°

Answer 1

Work done on a body refers to the force acting on the body and the associated displacement it causes. Work done is defined as the scalar product or the dot product of the force acting on the body and the displacement of the body.

Formula Used: The work done by the force $F$ is given by, $W = F \cdot d$ where $d$ is the displacement of the body on which the force acts.

Complete step by step answer:
Step 1: List the points of importance mentioned in the question.
Here, it is given that the work done by the force acting on a body is negative.
This implies that the force acting on the body and the resulting displacement of the body are in opposite directions.
Step 2: Find the angle between the force and displacement.
The work done by the force $F$ is given by, $W = F \cdot d$ where $d$ is the displacement of the body on which the force acts.
The force $F$ and displacement $d$ are vector quantities i.e., they have both direction and magnitude.
The scalar product of two vectors is given by, $A \cdot B = AB\cos \theta$ where $\theta$ is the angle between the two vectors $A$ and $B$ .
Let $\theta$ be the angle between the force and displacement.
Then we have the work done on the body $W = F \cdot d = Fd\cos \theta$
Given work is negative, i.e., $W = - Fd$ . This implies that $\theta = 180^\circ$ since $\cos 180^\circ = - 1$ .
$\therefore$ The angle between force and displacement is $\theta = 180^\circ$ . Hence the correct option is (D).

Note:
If the force is parallel to the direction of the displacement of the body i.e., $\theta = 0^\circ$ the work done will be positive. If the force is anti-parallel to the direction of displacement of the body i.e., $\theta = 180^\circ$ the work done will be negative. The work done can be negative for values of $\theta$ ranging from $90^\circ$ to $180^\circ$ since $\cos \theta$ is negative for those values of $\theta$ .