Question

A man applying a force on a stretched spring is stationary in a compartment moving with the constant speed $v$. If the compartment covers a distance $L$ in some time $t$, then

A) The man acting with force F on spring does the work $(w) = FL$.
B) The total work performed by the man on the compartment with respect to the ground is zero.
C) The work done by friction acting on the man with respect to the ground is, $(w) = FL$.
D) The total work done by the man with respect to the ground is, $(w) = FL$.

Answer 1

It is said that a force is being applied. Force basically is a push, pull, twist or stretch that can change the shape or position of a body. Also, recall the concept of work done. Work is said to be done when a force is applied on the body to displace it from its position.

Complete step by step answer:
Step I:
It is given that the compartment is moving with constant speed v. Therefore its acceleration will be zero. The formula for the force applied is
$F = m.a$
Where m is the mass and a is the acceleration
$F = m.0$
$\Rightarrow F = 0$
Hence, force applied on the man will also be zero.
Step II:
Again if the force applied is zero, hence work done is also zero. The formula for work done is
$Work = Force \times Displacement$
$\Rightarrow Work = 0 \times displacement$
$\Rightarrow Work = 0$
Step III:
It is clear that the work is done by man only. Since man is applying force F and L is the distance covered therefore work done by the man with respect to the ground is given by
$\Rightarrow W = F.L$
Where F is the force applied
L is the distance covered.
Step IV:
Also, frictional force does the same work but in an opposite direction.
$\Rightarrow W = FL$

Hence Option A, C and D are correct.

Note:
It is to be noted that the frictional force is the force that tends to slow down or oppose the motion of a body. But the frictional force not always opposes the motion. It also sometimes helps in moving an object. In this case, the tyres of the compartment are in contact with each other. The compartment is moving by applying a force on the surface of the ground. The surface of the ground also exerts an equal and opposite force on the compartment and it moves.