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Work
WORK AND ENERGY
Work is said to be done when force produces motion.
Example
An engine pulling bogies of train, horse pulling a cart etc.
The work done by a force on a body depends on two factors: 1. Magnitude of the force
2. Distance through which the body moves
In other words, we can say that work is said to be done when
the point of application of a force moves. Work done in
moving a body is equal to the product of force exerted on the
body in the direction of force.
Work = Force × Distance
Or
W=F×S
(iii) Lift a book through a height. The book rises up. There is a
force applied on the book and the book has moved. The
work is done.
When Work Is Not Said To Be Done?
(i) You are pushing a huge rock and the rock is not at all
moving from its place. As there is no displacement in the
rock even after applying force, work is not done.
(ii) You stand still for a few minutes with a heavy load on
your head. You get tired. No work is done on the load.
Therefore work is not said to be done if there is no
displacement even after the application of the force.
Work Done Against Gravity
Whenever work is done against gravity the amount of work
done is equal to the product of weight of the body and the
vertical distance through which the body is lifted. Work done
by the person against gravity is positive.
Work Done In Lifting A Body Upwards = Weight Of
Body × Vertical Distance
Or
W=m×g×h
When a body of mass m is lifted to a height h above the
ground, work equal to mgh is done on the body.
S. I. Unit Of Work
W=F×S
W = N × m = Nm
Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work
will be Joule.
Work Done When A Body Moves At An Angle To The
Direction Of Force
In such cases, we cannot use the formula W = F × S, because
the distance moved S is not exactly in the direction of force
applied. In such case, the force is applied at certain angle to
the horizontal ground but the body moves horizontally on the
ground.
1 Joule may be defined as, a force of 1N moving a body
through a distance of 1 m in its own direction. In such
case, the work done is known as 1 Joule.
1 Joule = 1Newton × 1metre
1J = 1Nm
S.I. unit of work is joule denoted by J.
Work is a scalar quantity. Note that work is said to be done
only if there is a move in an object through some distance. If
however, the distance moved is zero the work done on the
body of man himself is not zero, because his muscles are
stretched and his blood is displaced.
Examples Of Work Done
(i)
Push a pebble lying on a surface. The pebble moves
through a distance. You exerted the force on the pebble
and the pebble is displaced. In this case the work is done.
(ii) A girl pulls a trolley and the trolley moves through a
distance. The girl has exerted a force and the trolley is
displaced. The work is done.
Calculating The Work Done When A Body Moves
At An Angle To The Direction Of Force
In this case, all force F is not utilized in pulling the body, only
the horizontal component of force F is pulling the body along
the ground. The horizontal component of force F is F Cosθ and
distance moved is S.
Thus,
W = FS Cos θ
Work Done By Force When A Body Moves In A
Direction Different From That Of Force
1. When the displacement is in the direction of force i.e.
when θ = 0°
W=F S Cos θ
W=F S Cos 0° = F S × 1 = F× S
2.
Work done is equal to F×S. It is positive work.
Example
A baby pulling a toy car parallel to the ground.
4.
5.
6.
When the displacement is at right angles to that of force
i.e., when θ = 900
W = F S Cos θ = F S Cos 90° = F × S × 0 = 0
How Does An Object With Energy Do Work?
An object that possesses energy can exert force on another
object. When this happens energy is transferred from one
object to another. The second object may move as it receives
energy and therefore do some work. Thus the first object has
the capacity to do work. This implies that any object that
possesses energy can do work.
No work is done by force. Also we can say that no work
is done when a body is moving along a circular path.
3.
When displacement is in the opposite direction to that of
the force i.e θ =180°
W=F S cos θ = F S cos 180° = F S×-1 = -F× S
It is called negative work.
Work done is negative or work done against the force is
positive.
or
P=
W
T
In other words, we can say that power is work done per unit
time. Power is a scalar quantity.
Units Of Power
Joules
W
J
P=
=
=
= J/s or Js-1
Second
T
s
Joules per second is called watt. The S.I. unit of power is
watt. One watt is the rate of doing work at 1 joule per second.
1 Joule
1 Second
1J
J
1watt =
=
1s
s
1 Watt=
Or
Another unit of power is Horse Power (h.p.)
1Horse Power = 746 Watts
Or
1 h.p. = 746 W
Work
From the formula of power another formula of work done can
be derived that is,
Power =
S.I. unit of energy is Joule (J). Energy is a scalar quantity.
The energy possessed by an object is measured in terms of its
capacity of doing work. Therefore the units of both energy and
work are same.
The energy by which the body can do some mechanical work
is called mechanical energy. Two forms of mechanical energy
are: -
Power is the rate of doing work.
Work Done
Time Taken
Unit Of Energy
Mechanical Energy
POWER
Power =
Light Energy
Nuclear Energy
Heat Or Thermal Energy
Work Done
Time Taken
1. Kinetic Energy
2. Potential Energy
Mechanical energy is equal to sum of kinetic and potential
energy
M.E. = K.E. + P.E.
1. Kinetic Energy
The energy of a body due to its motion is called kinetic
energy. A moving object possesses energy that is why it is
capable of doing work.
Example
A fast moving ball, a stone thrown at a high speed high speed
bullet, flowing wind and flowing water.
Formula For Kinetic Energy
To measure kinetic energy we have to measure the amount of
work done because that is equal to kinetic energy.
Work Done = Kinetic Energy
……………………………(i)
Consider a body of mass m moving against the opposing force
F with velocity v. Before its coming to rest after covering a
certain distance work done by it will be given by
W=F×S
……………………………(ii)
⇒
Work Done = Power × Time
But, because work done is equal to Kinetic Energy from (i) and
(ii), we can say
Or
W=P×t
K.E. = F × S
ENERGY
Energy is the ability or capacity to do work. The amount of
work possessed by a body is equal to the amount of work it
can do when its energy is released. Energy is utilized to do
work.
Forms Of Energy
1. Mechanical Energy
2. Chemical Energy
3. Electrical Energy
Now, assume that
Initial Velocity = 0
Final Velocity = v
Acceleration = a
Distance = S
(v)2 – (0)2 = 2aS
……………………………(i)
From Newton’s second law of motion
F=m×a
∴a=
F
m
……………………………(ii)
By putting the value from (ii) in (i) we get
2FS
v2- 0 =
m
2FS
⇒ v2 =
m
⇒ F×S=
mv
2
2
Now,
F × S = K.E.
1
mv2
⇒ K.E. =
2
Where
m = mass of body
v = velocity of the body
Important Conclusion From The Formula
1
mv2
K.E. =
2
(i)
As K.E. ∝ m, therefore if mass of the body is doubled then
its kinetic energy also gets doubled and if mass of the
body is halved its kinetic energy also gets halved.
(ii) As K.E. ∝ v2, therefore if the velocity of the body is
doubled then its kinetic energy becomes four times and if
the velocity of body is halved, the kinetic energy become
one fourth.
2. Potential Energy
The energy of a body due to its position or change in shape is
known as potential energy. The potential energy exists in two
types: 1. Gravitational Potential Energy
The potential energy of a body due to its position above the
ground is called gravitational potential energy.
Example
(i) Water stored in an overhead tank.
(ii) Coiled spring of a watch/clock.
(iii) Raised hammer etc.
The potential energy may be possessed by a body when it is
not in motion, e.g. a stone lying on the top of the roof.
Formula For Potential Energy
Suppose a body of mass ‘m’ placed at a height ‘h’ above the
ground and ‘g’ is the gravitational pull force acting on the body
is gravitational pull of earth acting in downward direction is
equal to m× g. Therefore,
Force = m × g
Displacement = h
Work Done = Force × Distance
W=m×g×h
This work gets stored up in the body as potential energy. So,
P.E. = m × g × h
S. I. Unit Of Potential Energy
P.E. = m × g × h
P.E. = Kg × m/s2 × m
But,
Kg × m/s2 = N
Therefore,
P.E. = N × m = J
S.I. unit of potential energy is Nm or J.
Can a body possess both kinetic and potential energies
at the same time?
Certain bodies may possess both kinetic and potential energies
at the same time.
Examples
(i) A man climbing a hill.
(ii) An object rolling down a hill.
(iii) A flying aeroplane.
(iv) A flying bird.
Transformation Of Energy
The change of one form of energy into other form of energy is
called transformation of energy.
2. Elastic Potential Energy
The energy of a body due to a change in its shape and size is
called elastic potential energy.
Example
(i) When a body is released from a height then the potential
energy of the body is gradually transformed into kinetic
energy.
(ii) The heat energy converted into K.E by a steam engine.
(iii) The chemical energy of a firework is converted into
thermal energy and light and sound energy when it
explodes.
(iv) A motor converts electrical energy into mechanical
energy.
Transformation In Case Of Mechanical Energy
(i)
When a body falls from a certain height its potential
energy changes into kinetic energy.
(ii) When a body is thrown upwards the kinetic energy of the
body is changed into potential energy.
Solar Energy
The sun is a big store- house of energy. The solar energy gets
changed into many other forms of energy which are very
useful.
(i) Transformation of solar energy into wind energy.
(ii) Transformation of solar energy into electrical energy.
(iii) Transformation of solar energy into food energy.
Law Of Conservation Of Energy
Energy can neither be created nor destroyed; it is only
transformed from one form into other. Whenever energy
changes from one form to another, the total amount of energy
remains constant or conserved. Whenever one form of energy
disappears, an equivalent amount of energy in another form
appears. Or we can say that whenever the energy gets
transformed, the total energy before and after the
transformation remains unchanged.
Proof Of The Law Of Conservation Of Energy
To prove this principle, let us consider kinetic energy, potential
energy and T.E. (total energy) of the body falling freely under
gravity.
Consider an object of mass m, kept at rest at point A, which is
height h, above the ground. We take the potential energy of
the object at the ground to be zero. The potential energy of
the object at A is
U A = mgh
K.E. A = 0
[Q v = 0, it is not moving]
∴ total energy (T.E.) A = U A + K.E. A
= mgh + 0
= mgh
The object is now allowed to fall freely under the action of
gravity. It gains velocity as it comes down and its kinetic
energy increases due to increase in the velocity.
Let us consider a point C at any instant between A
and B such that AC = x and v is the velocity of object at C.
1
Then its kinetic energy will be mv2 and potential energy will
2
be mg (h-x).
Therefore total energy of the body will be
T.E. = K.E. + P.E.
1
T.E. = mv2 + mg (h-x)
2
Using the third equation of motion v2 = u2 + 2gx; v2= 0 + 2gx
v2 = 2gx
⇒
1
∴
T.E. =
m 2gx + mg (h-x)
2
= mgx + mgh – mgx
= mgh
And finally when the object reaches the ground, height from
the ground is zero and therefore the potential energy (U B ) =
0. If the velocity of body on reaching the ground is v, then
1
K.E. = mv2 B
2
Now from the 3 rd equation of motion
v B 2 = u2 – 2 as
v B 2 = (0)2 + 2gh
v B 2 = 2gh
1
∴ at B K.E. =
mv2 B
2
1
=
m (2gh)
2
1
= . 2 mgh
2
∴
T.E. B = v B + K.E. B
= 0 + mgh
= mgh
Therefore the total energy of the object during the free fall
remains constant at all positions. The form of energy however
keeps on changing. At A the energy is entirely potential and at
B it is entirely kinetic. In between A and B the energy is
partiallt potential partially kinetic. But total energy remains
constant throughout.
When the body hits the ground and comes to rest, it looses all
its kinetic energy, the loss of kinetic energy appears as sound,
light and heat. When it hits the ground it produces sound,
sparkling (light) and the point of contact becomes hot(heat).
Example
(i) Conservation of energy during the free fall of a body: As
the ball falls downward its potential energy goes on
decreasing whereas the kinetic energy increases in equal
amount. So, total energy remains conserved.
(ii) Energy of a ball thrown upwards is also conserved.
(iii) A swinging simple pendulum is an example of
conservation of energy.
(iv) If a batsman hits a ball, the ball gets some velocity and at
the same time the batsman looses some energy.
The some total of energy in this universe is a constant
quantity.
Commercial Unit Of Energy
The unit joule is too small and hence it is inconvenient to
express large quantities of energy. A bigger unit of energy can
be used that is kilowatt hour (kW h). The energy used in
households, industries, and commercial establishments are
usually expressed in kilowatt hour. For example electrical
energy used during a month is expressed in terms of ‘units’.
Here one ‘unit ‘ means 1 killowatt hour.
1 kW h is the energy used in one hour at the rate of one
thousand joules per second or 1 kW.
1kW =
=
=
=
1000 W х 1 h
1000 W х 3600 s
3600000 Ws
3600000 J
1kW = 3.6 х 106 J