A body is being raised to a height $h$ from the surface of earth. What is the sign of work done by
(a) applied force and
(b) gravitational force?
(a) Force is applied on the body to lift it in upward direction and displacement of the body is also in upward direction, therefore, angle between the applied force and displacement is $$\theta=0^{\circ}$$
$$\therefore$$ Work done by the applied force
$$W=F s \cos \theta=F s \cos 0^{\circ}=F s \left(\because \cos 0^{\circ}=1\right)$$
i.e., $$\qquad W=$$ Positive
(b) The gravitational force acts in downward direction and displacement in upward direction, therefore, angle between them is $$\theta=180^{\circ}$$.
$$\therefore$$ Work done by the gravitational force
$$W=F s \cos 180^{\circ}=-F s \quad\left(\because \cos 180^{\circ}=1\right)$$
Calculate the work done by a car against gravity in moving along a straight horizontal road. The mass of the car is 400 kg and the distance moved is 2 m.
Force of gravity acts on the car vertically downward while car is moving along horizontal road, i.e., angle between them is $$90^{\circ}$$.
Work done by the car against gravity
$$W=F s \cos 90^{\circ}=0 \quad\left(\because \cos 90^{\circ}=0\right)$$
A body falls towards earth in air. Will its total mechanical energy be conserved during the fall? Justify.
No, total mechanical energy of the body falling freely under gravity is not conserved, because a small part of its energy is utilised against resistive force of air, which is non-conservative force. In this condition, gain in $$\mathrm{KE}<$$ loss in PE.
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.
No, work done in moving along a closed loop is not necessarily zero. It is zero only when all the forces are conservative forces.
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact)?
(a) Kinetic energy.
(b) Total linear momentum.
Give reason for your answer in each case.
Total linear momentum of the system of two balls is always conserved. While balls are in contact, there may be deformation which means elastic PE which came from part of KE Therefore, KE may not be conserved.