Question

A particle moves around a semicircle of radius R, from one end A of a diameter to the other B. It is attracted to its starting point A by a force proportional to its distance from A. When the particle is at B, the force towards A is F0. Calculate the work done against this force when the particle moves around the semicircle from A to B.

Answer 1

work = 2 F₀ R

Explanation:

As the particle moves along the circumference of semicircle . It reaches from A to B . The force at B is F₀.  The displacement from A to B is 2 R .

Because the displacement is defined as the shortest path between two points . Here it is 2 R .

The work done can be defined as the product of force and displacement .

Thus the work done in moving from A to B  =  F₀ x 2 R  = 2 F₀ R