**1.** Work will be done if a force acts on an object and displacement occurs in the direction of force. According to this explanation work is done in following activities:

(a) Suma is swimming in a pond.

(b) A donkey is carrying a load on its back.

(c) A wind-mill is lifting water from a well.

(d) An engine is pulling a train.

(e) A sailboat is moving due to wind energy.

**2.** For calculating work done there must be displacement but since in this example vertical displacement is zero(as initial and final points lie on the same horizontal line) so the work done by force of gravity is zero.

**3.** Chemical energy of battery is changed into heat energy and light energy.

**4.** Work done by the force = change in kinetic energy

= ½ × m (v1^{2} – v2^{2})

= ½ × 20 × (5^{2 }– 2^{2})

= 10 × (25 – 4) = 10 × 21 = 210 J

**5.** Since work done on the object by gravitational force depends upon change in the vertical height of the object. Vertical height of the object is not changing as the joining A and B is horizontal at the same height hence the work done is zero.

**6.** It doesn’t violate the law of conservation of energy because the potential energy of a freely falling object decreases progressively since it keeps changing into kinetic energy of the free falling object therefore the total energy to the object remains conserved.

**7.** It is the transformation of our muscular energy into mechanical energy to ride the bicycle.

**8.** While we push a huge rock with all our might(power) but fail to move it no energy transfer occurs as cellular energy simply wastes out in muscle contraction and relaxation even heat generation(sweating).

**9.** Energy consumed by a certain household = 250 kWh

since 1 kWh = 3.6 × 10^{6} J

therefore 250 kWh= 250 × 3.6 × 10^{6} = 9 × 10^{8} J

**10. **Potential energy (P) = m × g × h = 40 × 5 × 10 = 2000 J

When the object is half way down the height of the object is = 2.5 m

initial velocity (u) = 0 (thrown from ground/rest)

since v^{2} = u^{2} + 2gh

= 0 + 2 × 10 × 2.5 = 50

Kinetic energy = ½ × m × v^{2}

= ½ × 40 × 50 = 1000 J

**11. **The satellite is moving on a round path , displacement in the object is perpendicular to the direction of force. θ = 90°.

W= F × s Cos θ

= F × s Cos 90°

= F × 0 = 0

Therefore work done is zero.

**12.** No

**13. ** When a person holds a bundle of hay over his head for 30 minutes and gets tired he applies force in upward direction and displacement of bundle of hay is in forward direction which is perpendicular to the direction of force applied therefore displacement is zero

W = F × s Cos θ

= F × s Cos 90°

= F × 0 = 0

No work done.

**14.** Electric heater’s power (p) = 1500 W = 1.5 kW

Energy = power x time = 1.5 kW x 10h = 15 kWh

**15. ** The bob eventually comes to rest due to the frictional force offered by the air and the rigid support holding the thread.

It is not a violation of the law of conservation of energy since mechanical energy can get converted into another form of energy which cannot be utilised for useful work. This loss of energy is called dissipation of energy.

**16.** In order to bring the object to rest the work done must be equal to the kinetic energy of the moving object = ½ mv^{2}

**17.** Initial velocity of the car (u) = 60 km/h = (60 × 1000)/60 × 60 = 50/3 ms^{-1}

Final velocity (v) = 0 (object has to be stopped)

Initial kinetic energy = ½ × m × v2

= ½ × 1500 × (50/3)^{2} = 208333.30 J

Final kinetic energy = ½ × 1500 × 0 = 0

Therefore, work done = change in kinetic energy = 208333.30 – 0 = 208333.30 J

**18.** (i) Since in this diagram displacement is perpendicular to the direction of force,

so work done is zero.

(ii) Since in this diagram displacement is in the direction of force, so work done is positive.

(iii) Since in this diagram displacement is in the opposite direction of the force applied hence work done is negative.

**19.** Yes we agree with her statement. Because when many balanced forces act on the object its displacement becomes zero.

**20.** Since Energy = power × time

= 4 × 500 × 10 = 20000 Wh = 20 kWh

**21.** A free falling object eventually stops on reaching the ground since on striking the ground its kinetic energy is transmitted to the ground.

**22.** Since Work (W) = Force (F) × displacement (d)

= 7N × 8m = 56 J

**23.** Work is done when a force acts on an object and displacement occurs in the direction of force.

**24.** Work = Force × displacement

W = F × d

**25.** 1J is that work which is done when a force of 1N is applied on an object and it moves a distance of 1m in the direction of force.

**26.** Work done W = F × d

= 140 N × 15 m = 2100 J

**27.** Kinetic energy of an object is a kind of mechanical energy and it is present in that object due to its state of motion(movement).

**28.** Kinetic energy = ½ mv^{2}

where, m = mass of the object, v = velocity of the object(motion)

**29.** K.E. of the object = 1/2 × m × 52

25 = ½ × m × 25

m = (25 × 2)/25 = 2 kg

If velocity is doubled

K.E. = ½ × 2 × 10^{2} = 200/2 = 100 J i.e. K.E. will become four times

If velocity is increased three times

K.E. = ½ × 2 × 15^{2} = 225 J i.e. K.E. will become nine times.

**30.** Power is the rate of work done. It is denoted by P. power = work/time P = W / t

**31.** If an agent works at the rate of 1 J/s then the power of that agent is 1 watt(where watt is the unit of power).

**32.** P = W/t = 1000J/10s = 100 W

**33. ** An agent may not be able to perform same amount of work in a given period of time always. In other words power of that agent may vary with time. Hence we can take average power in such situations. Average power is defined as average amount of work done by a body per unit time(i.e. total energy consumed divided by total time).