## WORK AND ENERGY notes

**WORK AND ENERGY**

**1. Work :**Work is said to be done, when a force causes displacement in its own direction.

**2.**No work is done, if the displacement is not in the direction of applied force or its rectangular component.

**3. Factors which determine work :**

(i) Work done is directly proportional to the magnitude of applied force.

(ii) Work done is directly proportional to the displacement in the direction of applied force.

**4. Mathematical expression for work :**

If

*F*is the force, which causes a displacement*S*, in its own direction, such that*W*is the work done, then*W*=

*F*×

*S*

**5. SI unit of work :**SI unit of work is Joule (J).

**6. Bigger units of work :**

(a) kilojoule = 103 J = 1000 J

(b) Megajoule = 106 J = 1000,000 J

(c) Gigajoule = 109 J = 1000,000,000 J

**7. Definition of Joule :**When a force of 1 N, causes a displacement of 1 m in its own direction, the work done is said to be one joule. So, 1 J = 1 N × 1 m = 1 kgms–2 × 1 m = 1 kgm2s–2.

**8. Energy :**Capacity of doing work is called energy.

**9. Units of energy :**Same as units of work, i.e., Joule.

**10. Potential energy :**The energy possessed by a body on account of its position or configuration is called potential energy.

**11. Mathematical expression for potential energy :**P.E. =

*mgh*

where ‘

*m*’ is the mass, ‘*g*’ is the acceleration ue to gravity and ‘*h*’ is the height.

**12. Characteristics of potential energy :**

(a) Potential energy of a body at the surface of earth is taken as zero.

(b) When a body is raised above the ground level, its potential energy increases.

(c) When a body is brought from a height towards the ground, its potential energy decreases. (d) At any point above the surface of the earth, potential energy is numerically equal to the work done in raising the body.

**13. Kinetic energy :**The energy possessed by a body by virtue of its motion is called kinetic energy.

**14. Mathematical expression for kinetic energy :**Κ.Ε. = 1/2(

*mv*2)

where ‘

*m*’ is the mass of the body and ‘*v*’ is the uniform velocity.

**15. Power :**Rate of doing work is called power.

**16. SI unit of power :**SI unit of power is watt (

*W*), where 1 W = 1 Js–1

**17. Mathematical expression for power :**

*P*=

*W/t*

where ‘

*P*’ is the power, ‘*W*’ is the work done (or energy used) and*t*is the time in seconds.

**18. Bigger units of power :**

(a) kilowatt (kW) = 103 W = 1000 W

(b) Megawatt (MW) = 106 W = 1000,000 W

(c) Gigawatt (GW) = 109 W = 1000,000,000 W

**19. Definition of watt :**When a work of 1 J is done in 1 s, then the power is said to be 1 watt.

Assignments

**1.**Seema tried to push a heavy rock of 100 kg for 200s but could not move it. Find the work done by Seema at the end of 200 s.

**2.**At what speed a body of mass 1 kg will have a kinetic energy of 1 J?

**3.**Define 1 Joule of work.

**4.**Identify the energy possessed by a rolling stone.

**5.**Identify the kind of energy possessed by a running athlete.

**6.**What would be the amount of work done on an object by a force, if the displacement of the object is zero?

**7.**How much work is done by a weight lifter when he holds a weight of 80 kgs on his shoulders for two minutes?

**8.**A car and a truck are moving with the same velocity of 60 km/hr. Which one has more kinetic energy? (Mass of truck > Mass of car).

**9.**A body is thrown vertically upwards. Its velocity goes on decreasing. Write the change in kinetic energy when its velocity becomes zero.

**10.**A force of 10 N moves a body with a constant speed of 2 m/s. Calculate the power of the body.

**11.**What will be the kinetic energy of a body when its mass is made four times and the velocity is doubled?

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

**13.**State the energy conversions in a dry cell.

**14.**What is the work done by the Earth in moving around the Sun?

**15.**A coolie is walking on a railway platform with load of 30 kg on his head. How much work is done by coolie?

**16.**How many times does the kinetic energy of a body become when its speed is doubled?

**17.**In an oscillating pendulum, at what positions the potential and kinetic energy are maximum?

**18.**Define S.I. unit of work?

**19.**Name the type of energy possessed by a raised hammer?

**20.**What is the form of energy possessed by a running car?

**21.**State the value of commercial unit of electrical energy in joules?

**22.**A 2 m high person is holding a 25 kg trunk on his head and is standing at a roadways bus-terminus. How much work is done by the person?

**23.**A horse of mass 210 kg and a dog of mass 25 kg are running at the same speed. Which of the two possesses more kinetic energy? How?

**24.**If the speed of the body is halved, what is the change in its kinetic energy?

**25.**Moon is experiencing a gravitational force due to Earth and is revolving around the Earth in a circular orbit. How much work is done by moon?

**26.**Give the formula for calculating work done.What is the SI unit of work?

**27.**Define 1 watt of power.

**28.**A man holding a bucket of water on his head stands stationary. Is he doing any work? Give reason.

**29.**Name the type of energy possessed by the following?

(i) Stretched slinky (ii) Speeding car

**30.**Write the formula to measure the work done, if the displacement of the object is at an angle of 90° to the direction of force.

**Assignments for summative Assessment**

**I. Very Short Answer Questions (1 Mark)**

**32.**At what rate is electrical energy consumed by a bulb of 60 watt?

**33.**Give an example of a body having potential energy due to change of shape.

**34.**When is work done by a force zero?

**35.**If the heart works 60 joules in one minute, what is its power?

**36.**Name the term used for the sum of kinetic energy and potential energy of a body.

**37.**Write the observed energy transformation that takes place at thermal power station.

**38.**A 40 kg girl is running along a circular path of radius 1 m with a uniform speed. How much work is done by the girl in completing one circle?

**39.**Calculate the work done when a force of 15 N moves a body by 5 m in its direction.

**40.**Write the S.I. unit of power.

**41.**A student is writing a three hours science paper. How much work is done by student? Give reasons to your answer.

**42.**When displacement is in a direction opposite to the direction of force applied, what is the type of work done?

**43.**What is the work done against gravity when a body is moved horizontally along a friction less surface?

**Other Important Questions**

**1.**When does a force do work? How is this work measured?

**2.**State the mathematical expression for work.

**3.**What are the conditions for doing work?

**4.**Is work a scalar or a vector quantity?

**5.**Give one example of a moving body, where no work is done.

**6.**Explain, why no work is done when a man pushes a wall.

**7.**Define the term ‘power’.

**8.**A boy climbs 100 stairs to reach at the top of a building. What happens to the potential energy of the boy?

**9.**Water flows down the mountains to the plains. What happens to the potential energy of water?

**10.**Give two examples in which a body possesses potential energy.

**11.**What do you understand by the term kinetic energy?

**12.**What determines the kinetic energy of a body of a given mass?

**13.**What is the biggest source of energy?

**14.**How is power related to work and time?

**15.**What do you understand by the term mechanical energy?

**16.**What do you understand by the term potential energy?

**17.**State the law of conservation of energy.

**18.**What do you understand by the term energy transformation?

**19.**What kind of energy transformation takes place when the hands are rubbed?

**II. Short Answer Questions - I (2 Marks)**

**Previous Years’ Questions**

**1.**The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force

on the body.

**3.**(a) Define 1 watt.

b) An electric bulb of 60 W (sixty watt) is used for 6 (six) hours per day. Calculate the units of energy consumed in one day by the bulb.

**4.**(a) Is it possible that a force is acting on a body but still work done is zero? Explain giving one example.

(b) Two bodies of equal masses move with uniform velocities of

*v*and 3*v*respectively. Find the ratio of their kinetic energies.

**1.**A sparrow and a crow are having the same kinetic energy during a flight. Which of the two is moving fast and why?

**2.**Why does a satellite going around the Earth in a circular path does not work?

**3.**A locomotive exerts a force of 7500 N and pulls a train by 1.5 km. How much work is

done by the locomotive in mega joules?

**4.**Why is no work done, when a force acts at right angles to the direction of displacement?

**5.**The energy of a torch cell is converted into two other forms of energy in a flashlight bulb.Name the energy conversions.

**5.**(a) How much work is done when a force of 1 N moves a body through a distance of 1 m in its direction?

(b) Is it possible that a force is acting on a body but still the work done is zero? Explain giving one example.

**6.**(a) What is meant by potential energy? Is potential energy a vector or scalar quantity?

(b) Given one example of a body having potential energy.

**Other Important Questions**

**6.**A man climbs a slope and another walks the same distance on a level road. Which of the two expends more energy and why?

**7.**A nail becomes hot when hammered into a plank. Explain, why?

**8.**If you apply 1 J of energy to lift a book of. 0.5 kg, how high will it rise? [Take g = 10 ms–2]

**9.**What force will cause a displacement of 2 m,

while doing a work of 60 J?

**10.**Calculate the work done by a machine of 50 W power rating in 30 s.

**III. short Answer Questions - ii (3 Marks)**

**5.**(a) Can any object have momentum even if its mechanical energy is zero? Explain why?

(b) A ball is dropped from a height of 10 m. If energy of the ball reduces by 40% after striking the ground, how high can the ball bounce back? (g = 10 m/s2).

**6.**(a) Define potential energy. Write an expression for potential energy of an object of mass m raised through a height

*h*.

(b) Find the energy possessed by an object of mass 10 kg when it is raised to a height of six metre above the ground given g = 9.8 ms–2.

**7.**Define power. A boy of mass 45 kg climbs up 20 steps in 20 sec. If each step is 25 cm high, calculate the power of the boy used in climbing. (Take g = 10 m/s2)

**8.**(a) Write the relation between commercial unit of electricity and the S.I. unit of energy.

(b) A boy of mass 45 kg climbs up 20 steps in 20 second. If each step is 25 cm high,

**1.**A mass of 10 kg is dropped from a height of 50 cm. Find its :

(a) potential energy just before dropping

(b) kinetic energy just on touching the ground

(c) velocity with which it hits the ground [Given g = 10 ms–2]

**2.**(i) Define the term potential energy. Write the S.I. unit of potential energy.

(ii) A body of mass 50 kg is situated at a height of 10 m. What is its potential energy (Given g = 10 ms–2)

**3.**(i) Define power. Mention its S.I. Unit.

(ii) A body of mass 50 kg runs up a staircase of 40 steps in 8 s. If the height of each step is 15 cm, find his power. (Given, g = 10 ms–2)

**. Long Answer Questions (5 Marks)**

**Previous Years’ Questions**

**Other Important Questions**

**1.**Define work, energy and power. Give the SI units for each of the these quantities. A man whose mass is 80 kg climbs up 30 steps of the stairs in 30 s. If each step is 12.5 cm in height, calculate the power used in climbing the stairs, (g = 10 m/s2).

**[2011 (T-II)]**

**2.**Define kinetic energy and potential energy. Write an expression for K.E. of a body of mass

*m*moving with a speed

*v*. Find the kinetic energy of a stone of 10 kg moving with a velocity of 10 m/s.

**[2011 (T-II)]**

**3.**(i) Derive an expression for the kinetic energy of an object. Write the S.I. unit of kinetic energy.

(ii) An object of mass 10 kg is moving with a uniform velocity of 5 ms–1. Calculate the kinetic energy possessed by the object.

**4.**(i) Give the S.I. unit of power.

(ii) What is the commercial unit of energy?

(iii) An electric heater is rated 1500 W. How much energy does it use in 10 hours?

**5.**(i) Define the potential energy.

(ii) Derive the expression for work done by an object with mass

*m*, when it is to be raised to a height*h*, from the ground. If the mass of the truck is 10 times that of the car, calculate the ratio of the kinetic energy of the truck with respect to the car.

**6.**A mass of 10 kg is dropped from a height of 50 cm. Find : (a) kinetic energy and (b) velocity, just as it reaches the ground. Does the velocity depend on the mass of the particle? Explain.

**7.**Write the energy change taking place when the heat of the Sun evaporates water, till it starts raining.

**8.**(i) A man whose mass is 50 kg, climbs up 30 steps of stairs in 30 seconds. If each step is 20 cm high, calculate the power used in climbing the stairs.

(ii) A boy pushes a box through 10 m across a floor, offering 50 N resistance. What is the work done by the resisting force?law of conservation of energy? Why?

(b) An object is dropped from a height

*h*. When is its
(i) potential energy maximum

(ii) kinetic energy maximum

**1.**Derive an expression for kinetic energy of a body moving with a uniform velocity ‘

*v*’ and having a mass ‘

*m*’.

**2.**Two bodies A and B of masses 4 kg and 16 kg respectively have the same kinetic energy. Calculate the ratio of their velocities.

**3.**A boy of mass of 50 kg runs up a flight of 120 stairs, each measuring 25 cm in one minute and 40 seconds. Calculate the power of the boy. [Take g = 10 ms–2]

**Read more topics**

newtons-laws-force-and-motion

motion

force-pressure-and-friction

sound

work-energy-and-power

laws-of-motion-key-points

gravitation-gravitation-is-force-

work-and-energy(notes)

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