Question

A body is moved along a closed loop. Is the work done in moving the body necessarily zero? If not, state the condition under which work done over a closed path is always zero.

Answer 1

Hint: Work done by conservative force in a closed loop is zero while work done by non-conservative force on a moving body along a closed loop will be non-zero.

Complete step by step answer:
Case (i)
The work done by the celestial body moon revolving around the earth in a closed circular orbit under the influence of the earth’s gravity is zero. This is because the force of gravity is a conservative and it does not depend upon the path along which work is done.
Case (ii)
The work done by a body to move along a closed loop can be non-zero if the force involved is conservative like-friction, viscous force etc.
Suppose an object is moving uniformly along a rough circular track. The frictional force exists between the contact surface of the object and the surface of the track. After completion of one revolution along the track the work done by the friction will be non-zero as it again reaches at its initial position.
Reason:- Friction is a non-conservative force and it does not depend upon the path along which the work is to be done. The work done by the friction during motion of the object will get converted into heat.

Where, f = frictional force.
and v = speed of the object.

Note: Students should understand the difference between conservative and non-conservative forces.
Conservative force:
Work done by conservative force is path independent.
Work done in a closed path is zero.
The word potential energy is defined for conservative forces.
Examples :- Gravitational force, Electrostatic force, spring force, etc.
Conservative force:
Work done by non-conservative force is path dependent.
Work done in a closed path is non-zero.
The word potential energy is not defined for non-conservative forces.
Examples :- Frictional force, Viscous force, etc.