Question

A stone is tied to a string and displaced from A to B by application of constant force F in three different ways as shown in the diagram below. Arrange the three cases in ascending order of the work done by the force.

(Given: AJB is a semi-circle, θ < 90° and AB = 20 m)

Answer 1

Given: AJB is a semicircle

θ < 90°

AB = 20 m

Work done by a force is given by

W = Force × Displacement × cos θ

Where θ is the angle between force and displacement.

In Case 1, the stone moves along a semicircular path, so the force is always perpendicular to the direction of displacement, which makes θ = 90°. Hence, work done is zero.

In Case 2, the force acts along the direction of displacement from A to B, so θ = 0°. Hence, the work done is maximum.

In Case 3, the force acts at an angle θ < 90° to the displacement, so only the component Fcos θ does work. Hence, the work done is less than Case 2 but more than Case 1.

Therefore, the ascending order of work done is Case 1 < Case 3 < Case 2.