Chapter - 11 Work and Energy

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 done = Force × Displacement
W = F × S
Where,
F = 7 N
S = 8 m
Therefore, work done, W = 7 × 8
= 56 Nm
= 56 J

Work is done whenever the given conditions are satisfied:

• A force acts on the body.
• There is a displacement of the body caused by the applied force along the direction of the applied force.

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 done = Force × Displacement
W = F × s

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. 80

Work done by the bullocks is given by the expression:
Work done = Force × Displacement
W = F × d
Where,
Applied force, F = 140 N
Displacement, d = 15 m
W = 140 × 15 = 2100 J
Hence, 2100 J of work is done in ploughing the length of the field.

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.

If a body mass m is moving with a velocity v, then its kinetic energy Ek is given by the expression,
Ek= 1⁄2 mv².

Its SI unit is Joule (J).

Expression for kinetic energy
Ek= 1⁄2 mv²
m = Mass of object
v = Velocity of the object in m/s
Given that kinetic energy, Ek=25J

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

Therefore, its kinetic energy becomes 4 times its original value, 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 its original value, because it is proportional to the square of the velocity. Hence, kinetic energy = 25 × 9 = 225 J.80

Power is the rate of doing work or the rate of transfer of energy. If W is the amount of work done in time t, then power is given by the expression,
Power = Work/Time = Energy/Time
P=W/T
It is expressed in watt (W).

A body is said to have power of 1 watt if it does work at the rate of 1 joule in 1 s,

i.e.,  1W=1J/1s

Power is given by the expression,
Power=Work done /Time
Work done = Energy consumed by the lamp = 1000 J
Power=1000 / 10 = 100 Js⁻¹
= 100 W

A body can do different amount of work in different time intervals. Hence, it is better to find average power. Average power is obtained by dividing the total amount of work done in the total time taken to do this work.

Average Power =Total work done / Total time taken

• Suma is swimming in a pond.
  Suma is doing work as she is able to move herself by applying force with the movement of her arms and legs in the water.
• A donkey is carrying a load on its back.
  Donkey is not doing any work (in the sense of physics) as the weight he is carrying (the direction of force) and displacement are perpendicular to each other.
• A wind-mill is lifting water from a well.
  Wind mill is lifting water from a well and doing work against the gravity.
  A green plant is carrying out photosynthesis.
  No force and displacement are present here, so work done is zero.
• An engine is pulling a train.
  During the pulling a train, engine does the work against the friction, present between the railway track and wheels.
• Food grains are getting dried in the sun.
  During the drying the grains, there is no force as well as displacement is present. So, no work is done.
• A sailboat is moving due to wind energy.
  Work is done by the wind as it moves the sailboat towards the direction of
  the force (force of blowing air).

When the object moves upwards, the work done by gravity is negative (as the direction of gravitational force is towards the Earth’s center) and when the object come downwards, there is a positive work done. So, the total work down is zero in throughout the motion.

Battery converts chemical energy into electrical energy. This electrical energy is further converted into light and heat energy.

Mass of the body = 20 kg
Initial velocity = 5 m/s
Final velocity = 2 m/s
We know that,
Work done = change in kinetic energy = $\frac{1}{2}m{u}^2-\frac{1}{2}m{v}^2$

= $\frac{1}{2}m\left(u^2 - v^2\right)$

= $\frac{1}{2}\times 20\times \left(5^2 - 2^2\right)$
= 10(25 − 4)
= 210 J

The work down by the gravitational force acting on the body is zero because the direction of force is vertically downward and the displacement is horizontal i.e. force and displacement are perpendicular to each other.

The potential energy of freely falling object decreases and its kinetic energy increases (as its velocity increases) progressively. So, in this way the total mechanical energy (Kinetic energy + potential energy) remains constant. Thus, the law of conservation of energy is not violated.

The muscular energy of the cyclist is converted into kinetic (rotational) energy of wheels of cycle which is further converted into kinetic energy to run the bicycle.

When we push the rock and fail to move it. Some of our energy is absorbed by the rock in the form of potential energy and the rest of our energy is goes to environment through our muscles and the surface between the rock and out hand.

We know that

1 unit = 3,600,000 J

So,   250 units = 250 × 3,600,000 J
= 900,000,000 J
= 9 × 10⁸J
Hence, the energy consumed = 9 × 10⁸ J

We know that, potential energy = mgh
Where, m = 40 kg
g = 9.8 m/s²
h = 5 m
So, the potential energy = 40 × 9.8 × 5 J = 1960 J

According to law of conservation of energy, the total mechanical energy (Kinetic and potential energy) of an object remains constant.

Therefore, when the object is half-way down, its potential energy become half the original energy and remaining half converted into kinetic energy.

Hence, the kinetic energy = 1⁄2 (1960) J = 980 J

When a satellite moves around the Earth, the displacement in short interval is along the tangential direction and the force (gravitational force) is towards the centre of the Earth. Since, the force and displacement are perpendicular to each other, the work done by gravitational force is zero.

Yes, it is true. There may be displacement in the absence of force.
We know that, F = ma,
In the absence of force, F = 0, then ma = 0

⇒ a = 0 [as m ≠ 0]

If a = 0, the object is either at rest or in a state of uniform motion in a straight line. In case the object is moving in a straight line, there must be displacement. 

So, in the absence of force, there may be displacement in the object.

The person holding a bundle of hay get tired because his muscular energy is converting into thermal energy. There is no displacement at all, so he had no work. As Work done = Force × displacement.

We know that, Energy = Power × time
Here, Power = 1500 W

Time = 10 hours = 10 × 60 × 60 seconds = 36000 seconds

Therefore, The energy used by heater = Power × time

= 1500 × 36000 J
= 54000000 J
= 5.4 × 10⁷ J

The law of conservation of energy states that the total energy of an isolated system remains constant and that energy can neither be created nor destroyed; rather, it can transform from one form to another.

The object is in motion, so its energy = kinetic energy = $\frac{1}{2}m{v}^2$
The kinetic energy of the object, when it comes to rest = 0.
Work done on object = change in kinetic energy

 $$\begin{gathered} \frac{1}{2}m{v}^2 - 0 \\ =\frac{1}{2}m{v}^2 \end{gathered}$$

Mass of the car m = 1500 kg
Velocity of the car v = 60 km/h

$=\frac{60 \times 1000}{60 \times 60} = \frac{50}{3}m/s$

The car is in motion, so its energy = kinetic energy = $\frac{1}{2}m{v}^2$
= $\frac{1}{2}\left(1500\right){\left(\frac{50}{3}\right)}^2$J

= $\frac{1}{2}\left(1500\right)\left(\frac{2500}{9}\right)J$

= 208333.3 J
The kinetic energy of the car, when it comes to rest = 0 J
Work done on object = change in kinetic energy
= 208333.3 − 0 J
= 208333.3 J

Hence, the work required to stop the car is 208333.3 J.

In the first case, the force and displacement are perpendicular to each other, so work done is zero.

In the second case, the force and displacement are in the same direction, so the work done is positive.

In the third case, the force and displacement are in the opposite direction, so the work done is negative.

If the resultant force acting on a body in different directions is zero, then the acceleration will be zero.
We know that, F = ma,
In the net force is zero, F = 0, then ma = 0

⇒ a = 0 [as m ≠ 0]

The power of four devices = 4 × 500 W = 2000 W

Time = 10 hours

Therefore, the energy consumed = power × time

= 2000 × 10 Wh
= 20000 Wh
= 20 kWh
= 20 units [1 unit = 1 kWh]

When a freely falling body eventually stops on reaching the ground, its kinetic energy gets converted into heat energy (as the body and ground become warm due to collision), sound energy and into potential energy (due to change of shape or deformation).