Chapter-08
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
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@
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.
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:
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
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.
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.
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.
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.
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.
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:
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
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
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.
The rate of doing work is called power.
Mathematical Expression
Power = Rate of doing Work
Power = Work/Time
P = W/T
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).
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.
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