Download WORK POWER ENERGY ENERGY

yWORK
POWER
ENERGY
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WORK - POWER
- ENERGY
work is said to be done by a force
when it moves a body through a certain
distance .
Work done is measured as the
product of component of force along
the direction of displacement and the
displacement Thus
displacement.
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work done =
{ component of force x { displacement }
along
g the
displacement }
F
S
F cos θ
θ
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People pulling a load at an angle with road
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If the application of force displaces the
body at an angle ‘θ’
θ then work is
Work = F cosθ x S = F S cos θ
From this equation
q
we can draw some
results.
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1 If the application of force and
1.
displacement are along same direction
then θ = 0 and cos θ = 1 Hence work
becomes W = F S .
work becomes maximum
maximum.
Ex. A person pushing a load or
pulling
lli a load
l d on a horizontal
h i
t l road
d
makes maximum work.
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A person pulling a body horizontally
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Work is done along the direction of force hence
the body gains the energy
2. If the application of force and displacement
are mutually perpendicular then angle
b t
between
F and
d S becomes
b
90 degree.
d
Thus
Th
θ = 90 and cos θ = 0
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Work done = F S (0) = 0 (zero)
work done is minimum or zero.
Ex. A person carrying a suitcase on his
head and moving horizontally will not
make any work.
F
l d
load
s
F = mg
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3. If the application of force and the
displacement are in opposite direction then
th angle
the
l between
b t
them
th
becomes
b
θ = 180 and cos180 = -1
work becomes
W = - F S negative maximum.
Work is done against the applied force .
Hence the body looses the energy
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When brakes are applied the force is
applied
li d in
i opposite
it direction
di ti to
t
displacement. Thus work becomes
negative.
ti
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Ex. When the brakes are applied to a vehicle
the applied force and displacement are in
opposite
it di
direction.
ti
The same thing happens if a body does
th work
the
k against
i t frictional
f i ti
l force
f
and
d
gravitational force.
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Work done against gravitational force is also
negative as gravitational force acts down
wards and body moves upwards.
upward
motion
Gravitational
force
Displace
p
ment
BALL THROWN UPWARDS DOES NEGATIVE WORK
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Work done is measured in terms of Joule
or Nm
N
Work is a scalar quantity. The total work
i equall to
is
t sum off works
k done
d
.
Ex. If a person pushes a body from one
position to other position
p
p
and brings
g
back to the same position then the
amount of work is sum of works done.
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POWER ;
The rate of doing work is called
power.
power
Power is measured as the ratio of
work done to the time taken to do the
work.
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Power is energy exhausted per second
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If V= S /t is the constant velocity
attained
tt i d in
i the
th body
b d due
d to
t force
f
then
th
Power = F V cosθ
Power is a scalar quantity.
SI unit of power is watt (W) or Js-1
Power is also measured in terms of
horse power (HP).
(HP)
1 HP = 746 Watt
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: ENERGY :
The capacity of doing work by a
body is called the energy of the body. It
is measured by the work it can do.
Energy of a body = work done by
th body
the
b d
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Lets now understand these with an
example.
l
There are two friends called Ramesh
and Mahesh. Let us assign the work of
taking 10 stones each of 2 kg from the
compound to the terrace which is at a
height 5 m , to both of them.
1. Ramesh picks every stone at a time
and climbs the stairs and keeps
p on the
terrace.
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For keeping every stone he takes 2
minutes.
i t
Hence Ramesh totally takes 20
minutes to keep 10 stones on the
terrace.
2. Now Mahesh starts the work .
y time he p
picks 2 stones and
Every
climbs the stairs to keep the stones on
the terrace. He also takes 2 min for
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every two stones keeping.
H
Hence
M
Mahesh
h h totally
ll takes
k 10
minutes to keep 10 stones on the
terrace.
The work done by Ramesh is
Work = F x s = mg x h
=2x9
9.8
8x5
= 98 J
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Now the work done by Mahesh is
Work = F x S = m g h
= 2 x 9.8 x 5
= 98 J
Hence both of them do the same
amount of work.
Si
Since
th
the energy is
i equall to
t the
th
amount of work done , Both spend
same energy.
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Now consider the power they have
Power of Ramesh = work done / time
= 98 / 20
= 4.9 J / min
Power of Mahesh = Work done / time
= 98 / 10
= 9.8 J / min
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This shows that the power of Ramesh is
less than Power of Mahesh
Mahesh.
Hence we can say that a person who
d
does
the
th work
k in
i less
l
time
ti
has
h more
power. Thus coming from home to
college
ll
by
b walk
lk does
d
same work
k as
coming by running. But the difference
i with
is
ith power. Running
R
i
requires
i
more
power than walking.
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y Thus a person who has more power can
do the work in a short time.
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There are different forms of energy.
They are
1. Mechanical energy
2. Electrical energy
3 Heat
3.
H t energy
4. Sound energy
5. Wind energy etc
All forms of energy are inter convertible.
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A generator converts heat energy to
electricity or mechanical energy into
electrical energy
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Wind energy(mechanical energy)
converting to electricity
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Solar panels convert solar energy into
electricity
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A fan converts electrical energy into
mechanical
h i l energy
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Mechanical energy are of two types.
1. Kinetic energy
2. Potential energy
If a body
b d possess both
b th types
t
off
energy then total energy of the body is
s m of kinetic and potential energy.
sum
energ
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KINETIC ENERGY
Kinetic energy
gy is the capacity
p
y of a
body to do work by virtue of its motion.
The faster the object moves
moves, the
greater is the kinetic energy.
When the object is stationary
stationary, its
kinetic energy is zero.
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A girl sliding down will possess P.E.
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If a body of mass ‘m’ moves with a
velocity
l it ‘V’ th
then it will
ill possess kinetic
ki ti
energy
Kinetic energy = Ek =
Examples of kinetic energy :
A bullet fired from a gun , An arrow
fired from bow , A vehicle running , a
person running
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A fastly moving car possess kinetic
energy
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Running girl posses kinetic energy
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POTENTIAL ENERGY
Potential energy (PE) of a body is
gy stored in the body
y by
y virtue
the energy
of its position of configuration in a field.
Potential energy is measured by the
amount of work to be done in taking a
body from a standard position to given
position
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A person at highest point possess P.E.
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Ex : a spring stretched / compressed, A
b
bow
stretched
t t h d , a body
b d raised
i d to
t a
height ,
Gravitational potential energy of a
body is measured as
potential energy = work done in raising
= mgh
m is the mass of the body
g is
i the
th acceleration
l ti due
d to
t gravity
it
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h is the height to which body is
raised
Thus a body
y which is at a larger
g height
g
will have higher potential energy.
Examples of gravitational P.E. :
A stone
t
k
keptt on tterrace , A
An aero plane
l
at a height, water at the top of a fall
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Water in an overhead tank possess P.E.
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The water in a reservoir possess P.E.
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MECHANICAL ENERGY AND ITS
CONSERVATION
The mechanical energy
gy E of a system
y
is the sum of its kinetic energy K and its
potential energy
p
gy U.
Total energy = Kinetic energy +
potential energy
E= K+U
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LAW OF CONSERVATION OF ENERGY
In an isolated system the total
mechanical energy of a body remains
constant.
The kinetic energy
gy of a body
y can be
converted into potential energy and
potential energy
p
gy can be converted into
kinetic energy. In all the total energy
remains constant .
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At highest point the boy possess only P.E.
when he comes down P.E. is converted
into K.E entirely.
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When stretched the bow gets P.E. When
thread is released the P.E. is converted
into K.E of arrow. The arrow moves fast.
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When water is stored in reservoir the
water possess P.E. When gates are
opened the water rushes out and gets
enormous K.E.
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Thus a body
y which is at highest
g
p
point
will have highest P. E. when released it
g kinetic energy
gy .As the
starts attaining
body comes down and down the kinetic
gy g
goes on increasing.
g Just before
energy
reaching ground the body will have only
gy
kinetic energy.
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Consider an example of just leaving a
pen off 10 gm ffrom an h
helicopter
li
t which
hi h
is 800 m high.
P.E = M g h = 10 x 10-3 x 9.8 x 800
= 78. 4 J
When the pen comes to ground entire
energy is converted into kinetic energy
energy.
this energy is sufficient to damage a
car kept in open ground.
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:COLLISION:
A collision is said to occur if the
momentum or the kinetic energy of
colliding bodies change.
1. ELASTIC COLLISION :
Elastic collision is the one in which
both momentum and kinetic energy of a
system remains same (conserved)
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Kinetic energy before = kinetic energy after
collision
collision
momentum before
collision
=
momentum after
collision
Ex. Collisions between atomic
and sub atomic particles
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If you add vectorially total momentum
is conserved
IN ELASTIC COLLISION :
Inelastic collision is the one in which
only momentum is conserved but
kinetic energy is not conserved.
Kinetic energy ≠ kinetic energy after
B f
Before
C
Collision
lli i
collision
lli i
Momentum before = momentum after
Collision
collision
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Ex. Collision between larger bodies like
truck and car
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consider an example of lifting of
water
t from
f
a sump to
t a ttank
k and
d filli
filling
it with 1000 litre which is on the top of
th second
the
d floor
fl
att a height
h i ht off 12 m
from the ground.
The amount of work done = P.E. in the
water
=mgh
The volume of water = 1000 x 1000 cm3
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mass of water = 106 cm3x density
= 106 cm3x 10-3 Kg/cm3
= 1000 kg
work done = m g h = 1000 x 9.8 x 12
= 117.6
117 6 x 10 3
= 1 . 176 x 10 5 J
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2. A cricket ball of mass 0.145 kg moving at
30 m/s has kinetic energy:
K.E = ½ m V2
K E = ½×(0.145
K.E.
½ (0 145 k
kg)×(30
) (30 m/s)
/ )2
= 65.25 kg·m2/s2 ≈ 65 J
3 A mass = 0
3.
0. 5 k
kg fli
flipped
d iinto
t th
the air
i has
h a
speed on reaching your hand of about 5 m/s.
The kinetic energy is:
K.E. = ½×(0. 5 kg)×(5 m/s)2
= 6.25
6 25 J
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4. A 1000 kg car moving at 30 m/s will
h
have
ki
kinetic
ti energy as
K.E. = ½×(1000 kg)×(30 m/s)2
= 450000 kg·m2/s2 = 450 kJ
5. A 1000
kg car moving at 15 m/s will
have kinetic energy as
K.E. = ½×(1000 kg)×( 15 m/s)2
= 112500 kkg·m2/s
/ 2 = 112 kJ
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6. How much gravitational potential
energy does a 70 kg high-diver have on
the 10 meter platform?
P.E=mgh = (70 kg)×(10 m/s2)×(10 m)
= 7,000 kg·m
kg m2/s2 = 7 kJ
7.What is the energy of a book of mass
2 kg
k kept
k t on a shelf
h lf two
t
meters
t
off
ff the
th
floor?
P.E = 2 x 10 x 2 = 40 J
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8. How much p
power does it take to lift
10 kg up 2 m in 2 seconds?
work done = mgh
= (10 kg)×(10 m/s2)×(2 m)
= 200J
power = work done /time
= 200 / 2 = 100 W
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In this session we had learnt about
1. What is work ?
2. What is p
power ?
3. What is energy ?
4 How to measure work , power and
4.
energy ?
5 What
5.
Wh t iis conservation
ti off energy ?
6. How to convert energy from one form
to another form ?
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WORK ENERGY THEOREM
y Work done on a body (work done by a
y) is equal
q
to the change
g in energy
gy
body)
of body.
y Loss in kinetic energy =
y If a bullet fired pierces a wooden plank
and emerges out then loss in K.E. of
bullet is equal to work done in drilling.
drilling
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