Question 1

When you lift a box from the floor and put it on an almirah the potential energy of the box increases, but there is no change in its kinetic energy. Is it a violation of conservation of energy?

Accepted Answer

No.Work done in lifting the box increases the potential energy of the box. During lifting at every point, the force applied by us on the box in the upward direction is equal to the gravitational force acting on the box in the downward direction. Therefore, there is no change in the velocity of the box. As a result, the kinetic energy of the box will not change.

Question 2

A particle is released from the top of an incline of height h. Does the kinetic energy of the particle at the bottom of the incline depend on the angle of incline? Do you need any more information to answer this question in Yes or No?

Accepted Answer

No, the kinetic energy of the particle at the bottom of the inclined plane does not depend on the angle of inclination. When the particle reaches the ground, all its potential energy, while at the top of the inclined plane, is converted into kinetic energy. As we know that potential energy depends only on the height of the particle, it will be the same for different angles of inclination.No, we do not need any other information to answer this question.

Question 3

Can the work by kinetic friction on an object be positive? Zero?

Accepted Answer

Yes. Let us consider a block A which is resting on another block B. Block B is resting on a smooth horizontal surface. Let the coefficient of friction between the blocks be  μ .When a force F is applied on block B in the forward direction as shown in the above figure, block A moves with block B in the direction of the applied force. The frictional force on block A and the displacement will be in the forward direction. Therefore, work done by the frictional force is positive.  If we consider the reference frame of block B, then displacement of block A will be zero. Therefore, work done by the frictional force is zero.

Question 4

Can static friction do nonzero work on an object? If yes, give an example. If no, give reason.

Accepted Answer

Yes. Let us consider a block A which is resting on another block B. Block B is resting on a smooth horizontal surface. Let the coefficient of kinetic friction between the blocks be μk​ .When a force F is applied on block B in the forward direction as shown in the above figure, block A moves with block B in the direction of the applied force. The friction force on block A and the displacement will be in the forward direction. Therefore, work done by the friction force is positive. In this case, block A will remain in contact with block B. This shows that static friction is doing a nonzero work on an object.

Question 5

Can normal force do nonzero work on an object? If yes, give an example. If no, give reason.

Accepted Answer

Yes. Let us consider an elevator accelerating upward with a body placed in it. In this case, the normal reaction offered by the floor of the elevator on the body is greater than the weight of the body acting in the downward direction. If a person is observing this from the ground, then, for him, the normal reaction is doing a positive work, as the elevator is moving upward.

Question 6

Can kinetic energy of a system be increased without applying any external force on the system?

Accepted Answer

Yes. Let us consider an isolated system of two particles falling towards each other under their mutual gravitational force of attraction. Here, the net force on the system is zero, but the velocities of the particles keep on increasing. Also, the kinetic energy of the system is increased without applying any external force on it.

Question 7

Is work-energy theorem valid in non-inertial frames?

Accepted Answer

In an non-inertial frame, pseudo force also comes into account. As we know that pseudo force does not exist, work-energy theorem is not valid in non-inertial frames.

Question 8

A heavy box is kept on a smooth inclined plane and is pushed up by a force F acting parallel to the plane. Does the work done by the force F as the box goes from A to B depend on how fast the box was moving at A and B? Does the work by the force of gravity depend on this?

Accepted Answer

(i) No. As the surface is smooth and the friction is zero, work done by the force will only depend on the force and the displacement.(ii) No, because gravitational force is a conservative force and work done by a conservative force will depend only on the force and the displacement

Question 9

One person says that the potential energy of a particular book kept in an almirah is 20 J and the other says it is 30 J. One of them necessarily wrong?

Accepted Answer

No, both are correct. We measure potential energy from a reference level chosen by the observer. Therefore, in this case, both observers are measuring the potential energy from different reference levels.

Question 10

A book is lifted from the floor and is kept in an almirah. One person says that the potential energy of the book is increased by 20 J and the other says it is increased by 30 J. Is one of them necessarily wrong?

Accepted Answer

Yes, one of them is necessarily wrong. We measure potential energy from a reference level chosen by the observer. However, the change in potential energy of a body does not depend on the level of reference.

Question 11

In one of the exercises to strengthen the wrist and fingers, a person squeezes and releases a soft rubber ball. Is the work done on the ball positive, negative or zero during compression? During expansion?

Accepted Answer

(i) During compression, the work done on the ball is positive as the direction of the force applied by the fingers is along the compression of the ball.(ii) During expansion, the work done is negative as expansion takes place against the force applied by the fingers on the ball.

Question 12

In tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. List which of the following works are positive, which are negative and which are zero?(a) work by the winning team on the losing team(b) work by the losing team on the winning team(c) work by the ground on the winning team(d) work by the ground on the losing team(e) total external work on the two teams.

Accepted Answer

(a) Work by the winning team on the losing team is positive, as the displacement of the losing team is along the force applied by the winning team.(b) Work by the losing team on the winning team is negative, as the displacement of the winning team is opposite to the force applied by losing team.(c) Work by the ground on the winning team is positive.(d) Work by the ground on the losing team is negative.(e) Total external work on the two teams is positive.

Question 13

When an apple falls from a tree what happens to its gravitational potential energy just as it reaches the ground? After it strikes the ground?

Accepted Answer

When an apple falls from a tree, its gravitational potential energy decreases as it reaches the ground. After it strikes the ground, its potential energy will remain unchanged.

Question 14

When you push your bicycle up on an inclined plane, the potential energy of the bicycle and yourself increases. Where does this energy come from?

Accepted Answer

When a person pushes his bicycle up on an inclined plane, the potential energies of the bicycle and the person increase because moving up on the inclined plane the kinetic energy decreases. and as mechanical energy is sum of kinetic energy and potential energy, and remains constant for a conservative system. Therefore, potential energy must increase in this case.

Question 15

The magnetic force on a charged particle is always perpendicular to its velocity. Can the magnetic force change the velocity of the particles? Speed of the particle?

Accepted Answer

The magnetic force on a charged particle is always perpendicular to its velocity. Therefore, the work done by the magnetic force on the charged particle is zero. Here, the kinetic energy and speed of the particle remain unaffected, while the velocity changes due to the change in direction of its motion.

Question 16

A ball is given a speed v on a rough horizontal surface. The ball travels through a distance l on the surface and stops.(a) what are the initial and final kinetic energies of the ball?  (b) What is the work done by the kinetic friction?

Accepted Answer

(a) Initial kinetic energy of the ball,Ki​=21​m v2Here, m is the mass of the ball.The final kinetic of the ball is zero. (b) Work done by the kinetic friction is equal to the change in kinetic energy of the ball.∴ Work done by the kinetic friction = Kf​−Ki​=0−21​ mv 2 =−21​ mv 2

Question 17

Consider the situation of the previous question from a frame moving with a speed v0 parallel to the initial velocity of the block. (a) What are the initial and final kinetic energies? (b) What is the work done by the kinetic friction?

Accepted Answer

The relative velocity of the ball w.r.t. the moving frame is given by vr​=v−v0​(a) Initial kinetic energy of the ball =21​mvr​2=21​m(v−v0​)2Also, final kinetic energy of the ball =21​m(0−v0​)2=21​mv0​2(b) Work done by the kinetic friction = final kinetic energy -  initial kinetic energy                                                           =21​m(v0​)2−21​m(v−v0​)2                                                        = −21​mv2+mv v0​

Question 18

A heavy stone is thrown from a cliff of height h with a speed v. The stone will hit the ground with maximum speed if it is thrown

Accepted Answer

the speed does not depend on the initial direction.As the stone falls under the gravitational force, which is a conservative force, the total energy of the stone remains the same at every point during its motion.From the conservation of energy, we have:Initial energy of the stone = final energy of the stonei.e.,(K.E.)i​+(P.E.)i​=(K.E.)f​+(P.E.)f​⇒21​mv2+mgh=21​m(vmax​)2$$From the above expression, we can say that the maximum speed with which stone hits the ground does not depend on the initial direction.

Question 19

Two springs A and B(kA​  = 2kB​ ) are stretched by applying forces of equal magnitudes a the four ends. If the energy stored in A is E, that in B is A

Accepted Answer

2ELet xA​  and xB​  be the extensions produced in springs A and B, respectively.Restoring force on spring A, F=kA​xA​   ...(i)Restoring force on spring B, F=kB​xB​     ...(ii)From (i) and (ii), we get:kA​xA​=kB​xB​It is given that kA = 2kB ∴xB​=2xA​Energy stored in spring A : E=21​kA​xA​2   ...(iii)Energy stored in spring B : E′=21​kB​xB​2=21​(2kA​​)(2xA​)2∴E′=2×(21​kA​xA​2)=2E[ From (iii)]

Question 20

Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is

Accepted Answer

The work done by the spring on both the masses is equal to the negative of the increase in the elastic potential energy of the spring.The elastic potential energy of the spring is given by Ep​=21​kx2 .Work done by the spring on both the masses =−21​kx2∴ Work done by the spring on each mass = 21​(−21​kx2)=−41​kx2

Chapter 8 : Work and Energy