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Comprehensive Physics Notes
Class X
Chapter-8 Work Power & Energy
ABDUL RASHEED
Educast
Learning Objectives
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Work
Power
Energy
Kinetic energy
Gravitational potential energy
Elastic potential energy
Law of conservation of energy
Interco version of kinetic energy and potential energy
WORK
PHYSICAL
DEFINITION OF
WORK
"Work is said to be done if a force causes a displacement
in a body in the direction of force".
OR
"The work done by a constant force is defined as the product of
the component of the force and the displacement in the direction of
displacement."
MATHEMATICAL
DEFINITION
"Work is the scalar product of force and displacement".
OR
"Work is the dot product of force and displacement".
Q3. Derive the equation of work done. Also explain maximum and minimum work done?
Ans: DERIVATION FOR WORKDONE:
Consider the following diagram.
In the above figure. Force “F” divided into two components vertical Fy and horizontal Fx. is the
angle between them. So the dot product of Fx and displacement “S” is given by:
W = Fx. S _____________ (i)
We know that, Cos = base / hyp, Cos = Fx / F
Put this Fx = F Cos Cos in equation (i)
W = F Cos S
W = FSCos
The above equation is called work done equation. Where Cos is an angle between F and S.
Work is a scalar quantity.
UNIT OF WORKS
• In S.I system:
Joule (j)
• In C.G.S. system: Erg
• In F.P.S. system: ft X lb
CATEGORIES
OF WORK
(i) POSITIVE WORK:
If force and displacement are in the same direction, work will be positive or if or  <
90°
(ii) ZERO WORK:
If force and displacement are perpendicular to each other, work will be zero. i.e.
since = 90°
Work = 0
as
Work = Fd Cos
Work = Fd Cos 90°
Work = (F)(d)(0)
Work = 0
NEGATIVE WORK:
If force and displacement are in the opposite direction, work will be negative.
since = 180°
Work = - ve
as
Work = Fd Cos
Work = Fd Cos 180°
Work = (F)(d)(-1)
Work = -Fd
ENERGY
ENERGY
"The ability of a body to perform work is called Energy".
A body cannot perform work if it does not posses energy.A body cannot perform work
more than the amount of energy.
It is a scalar quantity.
UNITS OF
ENERGY
(i) Joule
(ii) Calorie
[NOTE: 1 Calorie = 4.2 joule.]
(iii) KWatt-Hour
TYPES OF
ENERGY
There aree numerous types of energy such as:
Heat Energy
Light Energy
Sound Energy
Nuclear Energy
Chemical Energy
Electrical Energy
Solar Energy
Wind Energy
Kinetic Energy
Potential Energy etc. etc.
POWER
"The rate of work done of a body is called Power".
AVERAGE POWER
Average power of a body doing work is numerically equal to the totla work done divided
by the time taken to perform the work.
MATHMATICALLY
Power = Work done/time
Power = Work/t
but [work = Fd]
therefore
Power = Fd/t
UNITS OF POWER
(i) watt
[1 watt = 1joule/sec ]
(ii) Kilo watt
[1Kw = 1000 watt]
(iii) Mega watt (Mw) [1Mw = 106 watt]
(iv) Horse power
[1Hp = 746w]
POTENTIAL ENERGY
INTRODUCTION
Energy stored by a body by any means is called "Potential Energy".
DEFINITION
"The energy stored by a body due to its position in gravitational field is known as
‘Gravitational Potential Energy’".
FORMULA
Consider a body of mass "m" placed at a height of "h" from the surface of earth.
Force = Weight = W
but displacement (d) = h
Work done = Fd
OR
Work done = Wh
[but W = mg]
work done = mgh
We know that the work done in lifting the body is stored in the body in the form of
Potential Energy. Thus
P.E. = mgh
KINETIC ENERGY
KINETIC ENERGY
"Energy posses by a body by virtue of its motion is referred to as ‘Kinetic
Energy’".
FORMULA
K.E. = 1/2 mv2
Kinetic energy depends upon the mass and velocity of body.
If velocity is zero then K.E. of body will also be zero.
Kinetic energy is a scalar quantity like other forms of energies.
DERIVE: K.E = 1/2 mv2
PROOF
Consider a body of mass "m" starts moving from rest. After a time interval "t" its velocity
becomes V.
If initial velocity of the body is Vi = 0 ,final velocity Vf = V and the displacement of body
is "d". Then
First of all we will find the acceleration of body.
Using equation of motion
2aS = Vf2 – Vi2
Putting the above mentioned values
2ad = V2 – 0
a = V2/2d
Now force is given by
F = ma
Putting the value of acceleration
F = m(V2/2d)
As we know that
Work done = Fd
Putting the value of F
Work done = (mv2/2d)(d)
Work done = mV2/2
OR
Work done = ½ mV2
Since the work done is motion is called "Kinetic Energy"
i.e.
K.E. = Work done
OR
K.E. =1/2mV2.
LAW OF CONSERVATION OF ENERGY
LAW OF
CONSERVATION OF
ENERGY
According to the law of conservation of energy :
"Energy can neither be created nor it is destroyed, however
energy can be converted from one form energy to any other form of energy"
INTER CONVERSATION OF ENERGY:
Suppose a body having mass “m” placed at a height of “h” in the position of rest as shown in
figure,
So, its kinetic energy is zero. So its potential energy is. mgh
Total energy = PE + K. E
E = mgh + 0, E = mgh
Suppose the body is released from the height “h”, Now the height of body.
BC = h – x
In this case we use equation of motion to calculate velocity.
AT POSITION “A”
Vi = 0, S = x, Vf = Vi, a = g
Vf2 - Vi2 = 2aS
2gx = V2- 0
V2 = 2g x
AT POSITION “B”
K.E = ½ mv 2 __________ 1
Put the value of V2 in equation 1.
K.E = ½ m 2gx
K.E = mgx
Potential energy at Point “B”
P.E. = mg (h-x)
So total energy at point “B” is,
T.E = K.E + P.E.
T.E = mgx + mg (h-x), T.E = mgx + mgh – mgx
T.E = mgh
SHOW THAT THE MOTION OF A SIMPLE PENDULUM IS ACCORDING TO THE LAW
OF CONSERVATION ENERGY.
OR
PROVE THE LAW OF CONSERVATION WITH THE HELP OF A SUITABLE EXAMPLE.
We know that the motion of the bob of a simple pendulum is simple harmonic motion.
Here we have to prove that the energy is conversed during the motion of pendulum.
Proof: Consider a simple pendulum as shown in the diagram.
Energy Conservation
At Point ‘A’
At point ‘A’ velocity of the bob of simple pendulum is zero. Therefore, K.E. at point ‘A’ =
0. Since the bob is at a height (h), Therefore, P.E. of the bob will be maximum. i.e.
P.E. = mgh.
Energy total = K.E. + P.E
Energy total = 0 + mgh
Energy total = mgh
This shows that at point A total energy is potential energy.
Energy Conservation
At Point ‘M’
If we release the bob of pendulum from point ‘A’, velocity of bob gradually increases, but
the height of bob will decreases from point to the point. At point ‘M’ velocity will become
maximum and the height will be nearly equal to zero.
Thus ,
K.E. = maximum = 1/2mV2 but P.E. = 0.
Energy total = K.E. + P.E
Energy total = 1/2mV2 + 0
Energy total = 1/2mV2
This shows that the P.E. at point is completely converted into K.E. at point ‘M’.
Energy Conservation
At Point ‘B’
At point M the bob of Pendulum will not stop but due to inertia, the bob will moves
toward the point ‘B’. As the bob moves from ‘M’ to ‘B’, its velocity gradually decreases
but the height increases. At point ‘B’ velocity of the bob will become zero.
Thus K.E. at point ‘B’ = 0 but P.E. = max.
P.E. = mgh.
Energy total = K.E. + P.E.
Energy total = 0 + mgh
Energy total = mgh
This shows that at point B total energy is again potential energy.
CONCLUSION
Above analysis indicates that the total energy during the motion does not change. I.e.
the motion of the bob of simple pendulum is according to the law of conservation of
energy.