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**Page No. 148**

**Ques.1. A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. 11.3). Let us take it that the force acts on the object through the displacement. What is the work done in this case?****Ans. **When a force *F* acts on an object to displace it through a distance *S* in its direction, then the work done *W* on the body by the force is given by:

Work was done = Force Ã— Displacement*W* = *F* Ã— *S*

Where,*F* = 7 N*S* = 8 m

Therefore, work done, *W* = 7 Ã— 8

= 56 Nm

= 56 J**Page No. 149****Ques.1. When do we say that work is done?****Ans. **Work is done whenever the given conditions are satisfied:

(i) A force acts on the body.

(ii) There is a displacement of the body caused by the applied force along the direction of the applied force.**Ques.2****. Write an expression for the work done when a force is acting on an object in the direction of its displacement.****Ans. **When a force *F* displaces a body through a distance *S* in the direction of the applied force, then the work done *W* on the body is given by the expression:

Work was done = Force Ã— Displacement*W* = *F* Ã— *s***Ques.3****. Define 1 J of work.****Ans. **1 J is the amount of work done by a force of 1 N on an object that displaces it through a distance of 1 m in the direction of the applied force.**Ques.4****. A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?****Ans. **Work done by the bullocks is given by the expression:

Work was done = Force Ã— Displacement*W* = *F* Ã— *d*

Where,

Applied force, *F* = 140 N

Displacement, *d* = 15 m*W* = 140 Ã— 15 = 2100 J

Hence, 2100 J of work is done in ploughing the length of the field.**Page No. 152****Ques.1****. What is the kinetic energy of an object?****Ans. **Kinetic energy is the energy possessed by a body by the virtue of its motion. Every moving object possesses kinetic energy. A body uses kinetic energy to do work. Kinetic energy of hammer is used in driving a nail into a log of wood, kinetic energy of air is used to run wind mills, etc.**Ques.2****. Write an expression for the kinetic energy of an object.****Ans. **If a body of mass *m* is moving with a velocity *v*, then its kinetic energy is given by the expression,

Its SI unit is Joule (J).**Ques.3****. The kinetic energy of an object of mass, m moving with a velocity of 5 m s^{âˆ’1} is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?**

Given that kinetic energy,

(i) If the velocity of an object is doubled, then

Therefore, its kinetic energy becomes 4 times its original value, because it is proportional to the square of the velocity. Hence, kinetic energy = 25 Ã— 4 = 100 J.

(ii) If velocity is increased three times, then its kinetic energy becomes 9 times its original value, because it is proportional to the square of the velocity. Hence, kinetic energy = 25 Ã— 9 = 225 J.

It is expressed in watt (W).

Work done = Energy consumed by the lamp = 1000 J

Time = 10 s

= 100 W

**Suma is swimming in a pond.****A donkey is carrying a load on its back.****A wind-mill is lifting water from a well.****A green plant is carrying out photosynthesis.****An engine is pulling a train.****Food grains are getting dried in the sun.****A sailboat is moving due to wind energy**

**Ans.**** (i) Suma is swimming in a pond:** In this case, Suma pushes the water in the backward direction. It is known as action. However, due to reaction, the water pushes the person in the forward direction. In this situation, the force and the displacement are in the same direction. The work is done by Suma and the work done by the force is positive.**(ii) A donkey is carrying a load on its back:** If the displacement of an object is perpendicular to the force acting on it, the work done by the force on the object is zero.

In the given situation, the force of gravity on the load is in the downward direction, whereas the displacement is in the horizontal direction, i.e., the force and the displacement are perpendicular to each other. There is no displacement in the direction of the force of gravity, and therefore, work done is zero.**(iii) A windmill is lifting water from a well:** In this situation, the object (bucket of water from a well) moves upwards. The force exerted by windmill is in the direction of displacement. Therefore, work is done. This work done is positive as the force and the displacement are in same direction.**(iv) A green plant is carrying out photosynthesis:** No work is done in this case.**(v) An engine is pulling a train:** In this situation, an engine is pulling a train parallel to the ground. The force exerted by the engine is in the direction of displacement of the train. Thus, the force and the displacement are in the same direction. Therefore, work is done. This work done is positive.**(vi) Foodgrains are getting dried in the sun:** No work is done in this case.**(vii) A sailboat moving due to wind energy:** The force exerted by wind on the sail move the boat in the directions of force, hence, positive work is done by wind energy.**Ques.2. An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object? Ans. **Work done by the force of gravity on an object depends only on vertical displacement. Vertical displacement is given by the difference in the initial and final positions/heights of the object, which is zero.

Work done by gravity is given by the expression,

Where,

Therefore, the work done by gravity on the given object is zero joule.

Where,

= Kinetic energy of the object moving with a velocity,

(i) Kinetic energy when the object was moving with a velocity 5 m s

Kinetic energy when the object was moving with a velocity 2 m s

Work done by force is equal to the change in kinetic energy.

Therefore, work done by force =

= 40 âˆ’ 250 = âˆ’210 J

The negative sign indicates that the force is acting in the direction opposite to the motion of the object.

Where,

Vertical displacement,

âˆ´

Hence, the work done by gravity on the body is zero.

During the transformation, the total energy remains conserved.

1 unit = 1 kWh

1 kWh = 3.6 Ã— 10

Therefore, 250 units of energy = 250 Ã— 3.6 Ã— 10

Where,

g = Acceleration due to gravity = 9.8 m s

âˆ´

At half-way down, the potential energy of the object will be = 980 J.

At this point, the object has an equal amount of potential and kinetic energy. This is due to the law of conservation of energy. Hence, half-way down, the kinetic energy of the object will be 980 J.

(i) A force acts on the body.

(ii) There is a displacement of the body by the application of force in or opposite to the direction of force.

If the direction of force is perpendicular to displacement, then the work done is zero.

When a satellite moves around the Earth, then the direction of force of gravity on the satellite is perpendicular to its displacement. Hence, the work done on the satellite by the Earth is zero.

Suppose an object is moving with constant velocity. The net force acting on it is zero. But, there is a displacement along the motion of the object. Hence, there can be a displacement without a force.

(i) A force acts on the body.

(ii) There is a displacement of the body by the application of force in or opposite to the direction of force.

When a person holds a bundle of hay over his head, then there is no displacement in the bundle of hay. Although, force of gravity is acting on the bundle, the person is not applying any force on it. Hence, in the absence of force, work done by the person on the bundle is zero.

Where,

Power rating of the heater,

Time for which the heater has operated,

Work done = Energy consumed by the heater

Therefore, energy consumed = Power Ã— Time

= 1.5 Ã— 10 = 15 kWh

Hence, the energy consumed by the heater in 10 h is 15 kWh.

Consider the case of an oscillating pendulum.

To bring the object to rest, amount of work is required to be done on the object.

Where,

Mass of car,

Velocity of car,

Hence, 20.8 Ã— 10^{4} J of work is required to stop the car. **Ques.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.**

(i) A force acts on the body.

(ii) There is a displacement of the body by the application of force in or opposite to the direction of force.

In this case, the direction of force acting on the block is perpendicular to the displacement. Therefore, work done by force on the block will be zero.

In this case, the direction of force acting on the block is in the direction of displacement. Therefore, work done by force on the block will be positive.

In this case, the direction of force acting on the block is opposite to the direction of displacement. Therefore, work done by force on the block will be negative.

Where,

Power rating of the device,

Time for which the device runs,

Work done = Energy consumed by the device

Therefore, energy consumed = Power Ã— Time

= 0.50 Ã— 10 = 5 kWh

Hence, the energy consumed by four equal rating devices in 10 h will be 4 Ã— 5 kWh = 20 kWh = 20 Units.

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