# Work Energy

## NCERT Solution II

Question 10. An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.

Answer: Given; m = 40 kg, h = 5 m

Potential Energy = mgh
= 40 kg xx 9.8 ms^-2 xx 5 m = 1960 J

At halfway down, i.e. at the height of 2.5 m, the potential energy = 1960 J/2 = 980 J

At halfway down, kinetic energy = potential energy because of the law of conservation of energy.

Hence, kinetic energy at halfway down = 980 J

Question 11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.

Answer: The direction of force of gravity and direction of displacement of satellite are perpendicular to each other. Hence, work done is zero in this case.

Question 12. Can there be displacement of an object in the absence of any force acting on it? Think. Discuss this question with your friends and teacher.

Answer: When an object is in uniform motion, no external force is acting on the object. In this situation, displacement is non-zero even in the absence of a force.

Question 13. A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer.

Answer: While holding a bundle over his head, the person does not cause displacement in the bundle. Hence, work done is zero.

Question 14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?

Answer: Given; P = 1500 W and t = 10 h
Energy consumed = P xx t
= 1500 W xx 10 h = 15000 Wh = 15 kW\h

Question 15. Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy?

Answer: Law of Conservation of Energy: Energy cannot be created and cannot be destroyed. We can only change one form of energy into another form.

Let us take the case of a simple pendulum. Its mean position is O and extreme positions are A and B.

When the pendulum moves to point A, it reaches the maximum height. At this stage, the potential energy of the bob is maximum and kinetic energy is zero.

When the pendulum moves to point O, it reaches its mean position. At this stage, the kinetic energy of the bob is maximum and potential energy is zero.

In both the cases, the sum of kinetic energy and potential energy remains constant. Thus, the pendulum obeys the law of conservation of energy.

But the pendulum does not keep on oscillating forever. It eventually comes to rest. This happens because of air resistance. Some of the energy of the bob is utilized in overcoming the air resistance. This energy is taken up by the surrounding. In this case also, the total energy of the system remains constant. Hence, it does not violate the law of conservation of energy.

Question 16. An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest?

Answer: Given; mass = m and velocity = v
Hence, kinetic energy = ½ mv^2

Work that needs to be done to bring the object to rest = kinetic energy = ½ mv^2

Question 17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?

Answer: Given; m = 1500 kg and v = 60 km/h = 16.67 m/s
Kinetic energy = ½ mv^2
= ½ 1500 xx 16.67^2
= 208333.33 J = 20.8 xx 10^4 J

Work that needs to be done to bring the car to rest = 20.8 xx 10^4 J

Question 18. In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero.

Answer: In the first figure; direction of force is perpendicular to direction of displacement. Hence, work done is zero.

In the second figure, direction of force is same as direction of displacement. Hence, work done is positive.

In the third figure, direction of force is opposite to direction of displacement. Hence, work done is negative.

Question 19. Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why?

Answer: When all the forces acting on an object cancel out each other; the net force becomes zero. In this situation, acceleration in the object will be zero.

Question 20. Find the energy in kW h consumed in 10 hours by four devices of power 500 W each.

Answer: Given; P = 500 W, t = 10 h and number of devices = 4
Energy consumed = text(Number of devices) xx P xx t
= 4 xx 500 W xx 10 h = 20000 Wh = 20 kW\h

Question 21. A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?

Answer: When a free falling object hits the ground, its potential energy becomes zero and its kinetic energy becomes maximum. The kinetic energy changes into heat and sound energy while the object comes to rest.