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Work Power & Energy
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ment". 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 displace.
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:
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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.
• In S.I system:
Joule (j) • In C.G.S.
system: Erg • In F.P.S. system: ft X lb
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(i) POSITIVE WORK:If force and displacement
are in the same direction, work will be
positive or if q = 0 or q < 90°
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If force and displacement are perpendicular to each other, work will
be zero. i.e.
since q = 90°
Work = 0
as
Work = Fd Cos q
Work = Fd Cos 90°
Work = (F)(d)(0)
Work = 0
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If force and displacement are in the opposite direction, work will be negative.
since q = 180°
Work = - ve
as
Work = Fd Cos q
Work = Fd Cos 180°
Work = (F)(d)(-1)
Work = -Fd
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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
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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.
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"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]
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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’".
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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.
"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.
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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
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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.
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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,
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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
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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.
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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’.
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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.