Chapter 11 Work and Energy

Force = 7 N

Displacement = 8 m

Work done = Force × Displacement

W = F × S

W = 7 × 8

= 56 Nm

= 56 J

Therefore, work done is 56 J.

A work is said to be done when a force is applied on a body and makes the body move then we said work is done.

When a force is acting on a body in the direction of the applied force, then the work done on the body is given by the expression:

Work done = Force × Displacement

W = F × s

1 J is defined as the amount of work done when a force of one newton is applied over a displacement of one meter.

Applied force, F = 140 N

Displacement, d = 15 m

Work done = force x displacement

W = 140 × 15 = 2100 J

Work done is 2100 J.

The energy of a body due to its motion is known as kinetic energy. It is a scalar quantity, i.e it does not depend on direction.

Kinetic energy possessed by a body of mass m is moving with a uniform velocity v, is given by the expression,

Its SI unit is Joule (J).

Mass of the object = m

Velocity of the object = v = 5 m/s

Kinetic energy, E_K = 25 J

(i) If the velocity of an object is doubled, then v = 5 × 2 = 10 m/s

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

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

Power is the amount of work done per unit time. It is a scalar quantity.

It is expressed in watt (W).

1 watt of power is defined as the power produced when 1 joule of work is done for 1 second 

Energy consumed by the lamp ( work done ) = 1000 J

Time = 10 s

The average power is defined as the ratio of total work done and the total time taken.

Work is done whenever the given two conditions are satisfied:

(i) Force is applied.

(ii) Displacement takes place.

(iii) The angle between the force and displacement is not 90 degrees .

(a)  When Suma is swimming in a swimming pool, she applies force in forward direction and moves in the forward direction. So, displacement is in the forward direction. Both are in the same direction. Therefore, work is done.

(b)  When a donkey is carrying a load on his back, it is applied a force in the upward direction. But, displacement of the load is in the forward direction. Since, displacement is perpendicular to force, the work done is zero.

(c) When a wind-mill is lifting water from a well, it is applying a force in the upward direction and it is moving water in an upward direction. Hence, work is done by the wind-mill in lifting water from the well.

(d) In this case, there is no force involved when a green plant is carrying photosynthesis.

Therefore, the work done is zero.

(e) When an engine is pulling a train, it is applying a force in the forward direction. This allows the train to move in the forward direction. Hence, there is a displacement in the train in the same direction. Therefore, work is done by the engine on the train.

(f) When food grains are getting dried in the Sun, there is no force involved. Hence, the work done is zero during the process of food grains getting dried in the Sun.

(g) When a sailboat is moving due to wind energy, force is applied by the boat in the forward direction. Therefore, there is a displacement in the boat in the direction of force. Hence, work is done by wind on the boat.

There is no work done because the applied force is in the vertical direction but the displacement of the body is in the horizontal direction. Since the angle between force and displacement is 90 degrees.

When a battery lights a bulb , then the chemical energy of the battery is transferred into electrical energy. When the bulb receives this electrical energy, then it converts it into light and heat energy. Therefore, energy changes are shown as :

Mass of the body = 20 kg

Initial velocity, u = 5 m/s

Final velocity, v = 2 m/s

Kinetic energy is given by the expression,

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

(ii) Kinetic energy when the object was moving with a velocity 2 m/s

Work done = change in kinetic energy. 

Therefore, work done = (E_k)₂ - (E_k)₅

= 40 − 250 = −210 J

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

There is no work done because the force is gravitational force which is in downward direction but the displacement of the body is in horizontal direction. Since the angle between force and displacement is 90 degrees.

No. The process does not violate the law of conservation of energy. This is because when the body falls from a height, then it loses its potential energy. But as it falls, it gains some velocity. Due to increase in velocity, the body gains kinetic energy. During the process, total mechanical energy of the body remains conserved. Hence, the law of conservation of energy is not violated.

While riding a bicycle, we use our muscular energy to make the cycle move and our body also warms up in the process. Therefore, the muscular energy gets converted into kinetic energy and heat energy. The energy transformation can be shown as:

When we push a huge rock, we apply muscular force in order to move it. There is no transfer of muscular energy to the stationary rock. Also, there is no loss of energy because muscular energy is converted into heat energy, which causes our body to feel warm.

1 unit of energy = 1 kilowatt hour (kWh)

1 kWh = 3.6 × 10₆ J

Therefore, 250 units of energy = 250 × 3.6 × 10₆ = 9 × 10₈ J

Vertical displacement = h = 5 m

Mass of the object = m = 40 kg

Acceleration due to gravity = g = 9.8 m/s

Gravitational potential energy is given by the expression,

W = mgh

∴ W = 40 × 9.8 × 5 = 1960 J.

At half-way down, the potential energy of the object will be 1960 / 2 = 980 J.

Work is done whenever the given conditions are satisfied:

(i) Force is applied.

(ii) Displacement takes place.

(iii) The angle between the force and displacement is not 90 degrees.

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

Yes. There can be displacement of an object in the absence of any force acting on it, for a uniformly moving object. Suppose an object is moving with uniform velocity. Force will be zero when acceleration is zero. Hence, there can be a displacement without a force.

Work is done whenever the given conditions are satisfied:

(i) Force is applied.

(ii) Displacement takes place.

(iii) The angle between the force and displacement is not 90 degrees.

When a person holds a bundle of hay over his head, then the bundle of hay remains stationary. 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.

Power of the heater, P = 1500 W = 1.5 kW

Time taken, T = 10 h

Energy consumed by an electric heater can be obtained with the help of the expression,

Power = Energy consumed / time

Therefore, Energy consumed = Power × Time

= 1.5 × 10 = 15 kWh

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

The law of conservation of energy states that energy can neither be created nor be destroyed. It can change from one form to another. Consider the case of an oscillating pendulum.

Mass of the object = m

Velocity = v 

Therefore ,Kinetic energy

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

Mass of car, m = 1500 kg

Velocity of car, v = 60 km/h

Therefore, Kinetic energy

Work is done whenever the given conditions are satisfied:

(i) Force is applied.
(ii) Displacement takes place.
(iii) The angle between the force and displacement is not 90 degrees .

Case I

In this case, the angle between the force and displacement is 90 degrees. Hence, work done by force on the block will be zero.

Case II

In this case, the angle between the force and displacement is 0 degree. Hence, work done by force on the block will be positive.

Case III

In this case, the angle between the force and displacement is 180 degrees. Hence, work done by force on the block will be negative.

Yes, I agree with Soni that acceleration in an object could be zero even when several forces are acting on it. This happens when equal and opposite forces act on an object, they cancel out each other so that the net external force experienced by the object is zero. Therefore, the acceleration of the object is zero. Therefore, Soni is right.

Power of one device, P = 500 W = 500 / 1000 = 0.50 kW

Power of four devices = 500 x 4 = 2000 W = 2000 / 1000 = 2 kW

Time taken, T = 10 h

We know that

Power = energy consumed / time 

Energy consumed = Power × Time

= 2 × 10 = 20 kWh

Therefore, the energy consumed by four equal rating devices in 10 h will be 20 kWh.

When an object falls freely towards the ground, its potential energy decreases and kinetic energy increases. When a free falling object hits the ground, its kinetic energy becomes zero and its potential energy becomes maximum. The kinetic energy changes into heat and sound energy while the object comes to rest.