X Physics - Chapter 8 - Work, Energy and Power

Definitions
1. Joule
It is the work done by a force of one Newton when the body is displaced one meter.

2. Erg
It is the work done by a force of one Dyne when the body is displaced one centimeter.

3. Foot Pound (ft-lb)
It is the work done by a force of one pound when the body is displaced one foot.

4. Force
It is an agent that moves or tends to move or stops or tends to stop a body.

5. Watt
Watt is the unit of power that is equal to the quantity of 1 Joule work done in 1 second.




Work
When a force produces displacement in a body, it is said to do work.

Units of Work

S.I System - Joule
C.G.S System - Erg
Explanation

When force is applied in the direction of the displacement we can find the work by using definition

Work = Force * Displacement

W = F*s

W = Fs

Suppose a man is pulling the grass cutting machine then the direction of the foce and displacement is not same. The applied force makes an angle @ with the ground while the motion takes place along the ground.

In this case force is resolved into its components.

Fx = Fcos@

Fy = Fsin@

As the machine moves along the ground, so Fx is doing the work, Hence:

W = Force * Displacement

W = Fcos@*s

W=Fscos@


Energy
Energy is define as the capability to do work. Energy is also measured in Joules.

Some Types of Energy

Potential Energy
Kinetic Energy
Chemical Energy
Heat Energy
Light Energy
Nuclear Energy



Potential Energy
Definition

The energy possessed by a body due to its position is known as the Potential Energy of the body. It is represented by P.E. and is measured in Joules in System International.


Examples

The energy of the following is potential energy:

A brick lying on the roof of a house.
The spring of a watch when wound up.
The compressed spring.
Water stored up in elevated reservoir in water-supply system.

Mathematical Expression

If we lift a body of mass m to a height h, then the force applied on it is the its weight and it will act through a distance h.

So,

Work = Force * Distance

W = W * h

Since W = mg, therefore:

W = mg * h

Since work is equal to energy possessed by a body:

P.E. = mgh




Kinetic Energy
Definition

The energy possessed by a body due to its motion is known as the Kinetic Energy of the body. It is represented by K.E.


Examples

The energy of the following is kinetic energy:

A bullet fired from a gun.
A railway engine moving at high speed.
Motion of a simple pendulum.

Mathematical Expression

Consider a body of mass m at rest (Vi = 0) on a frictionless surface. When a force F is applied, the body covers a distance S and its final velocity becomes Vf.

To calculate the amount of work done, we apply the formula.

W = F * S

According to Newton's Second Law of Motion, the value of force is:

F = ma

The distance that the body traveled is calculated by using third equation of motion:

2as = vf2 - vi2 (Here 2 with Vf and Vi represents square)

We know that Vi = 0, therefore:

2as = v2

s = v2/2a

By substituting the values of F and s, we get:

W = (ma) * (v2/2a)

W = mv2/2

W = 1/2(mv2)

We know that work can be converted into Kinetic Energy, therefore:

K.E = 1/2(mv2)

So, Kinetic Energy of a body is directly proportional to the mass and square of velocity.


Factors on which Kinetic Energy Depends:

It is directly proportional to the mass of the body.
It is directly proportional to the square of the velocity.



Difference Between Kinetic Energy and Potential Energy
Kinetic Energy

1. Energy possessed by a body by virtue of its motion is known as Kinetic Energy.

2. Bodies in motion have Kinetic Energy.

3. It is calculated by K.E = 1/2 (mv2)


Potential Energy

1. Energy possessed by a body by virtue of its position is known as Potential Energy.

2. Bodies at rest have Potential Energy.

3. It is calculated by P.E. = mgh




Law of Conservation of Energy
Statement

Energy can neither be created, nor destroyed, but it can be converted from one form into the other.


Explanation

consider a body of mass mat height h above the ground. Its kinetic energy at that point A is:

K.E = 1/2(mv2)

K.E = 1/2 m * (0)

K.E = 0 ........ (i)

The potential Energy at point A is :

P.E = mgh ............(ii)

So the total energy at point A will be :

T.E = K.E + P.E

E(A) = 0 + mgh

E(A) = mgh

Suppose the body is released from this height and falls through a distance x. Its new height will be (h-x). The velocity with which it reaches point B is calculated by using the third equation of motion:

2gs = Vf2 - Vi2

As we know:

Vi = 0
S = x
Therefore,

2gx = Vf2 - 0

2gx = v2

The kinetic energy at point B is:

K.E. = 1/2 mv2

Substituting the value of v2:

K.E. = 1/2 * m * 2gx

K.E = mgx

The Potential Energy at point B is:

P.E = mgh

The height of the body is (h-x):

P.E. = mg(h-x)

The total energy at point B is :

E(B) = P.E + K.E.

E(B) = mgx + mg(h-x)

E(B) = mgx + mgh - mgx

E(B) = mgh

Hence, the total energy at point A and B are same. It means that the total value of energy remains constant.


Power
Definition

The rate of doing work is called power.


Mathematical Expression

Power = Rate of doing Work

Power = Work/Time

P = W/T


Unit of Power

The unit of Power is Joules per second (J/s) or Watt (W).




Need to Conserve Energy
The fuel that burns in running factories, transport and other activities is mainly obtained from underground deposits in the form of coal, oil, gas and other similar raw forms. These deposits are rapidly decreasing and one day all these resources of energy will be consumed. It is therefore highly important for us to avoid wastage of energy.

the consumption of two much energy is also having adverse effect on our environment. The air in big cities is heavy because of pollution caused by industrial wastes and smoke produced by automobiles. To ensure comfortable living with a neat environment, it is the responsibility of all of us as individuals to conserve energy.