## LAW OF CONSERVATION OF ENERGY

12/16/2014 CBSE

LAW
OF CONSERVATION OF ENERGY(9th physics)

Energy can neither be created nor
destroyed, but it

is transformed from one form to another. Alternatively,

whenever energy gets transformed, the total energy

remains unchanged.

Proof � Freely falling body

It may be shown that in the absence of external�frictional force the total
mechanical�energy of a body remains constant.

Let a body of mass m falls from a point A,�which is at a height h from the
ground as shown in fig.

At A,

Kinetic energy kE = 0

Potential energy Ep = mgh

Total energy E = Ep + Ek�= mgh + 0= mgh

During the fall, the body is at a
position B. The�body has moved a distance x from A.

At B,

velocity�v2 = u2 + 2as

applying,�v2�=
0 + 2ax = 2ax

Kinetic energy Ek =�1/2 mv2�=
1/2�m x 2gx�= mgx

Potential energy Ep = mg (h � x)

Total energy E = Ep + Ek =�mg (h-x) + mgx�= mgh � mgx + mgx= mgh

If the body reaches the position C.

At C,

Potential energy Ep = 0

Velocity of the body C is

v2 = u2 + 2as

u = 0, a = g, s = h

applying
v2 = 0 + 2gh = 2gh

kinetic energy Ek =1/2�m
v2=1/2�m x 2gh= mgh

Total energy at C

� � � � � � � � � � � E
= Ep + Ek

� � � � � � � � � � �E =
0 + mgh

� � � � � � � � � � �E =
mgh

Thus we have seen that sum of�potential and kinetic energy of
freely�falling body at all points remains same.�Under the force of
gravity, the�mechanical energy of a body remains�constant.

RATE OF DOING WORK (OR) POWER

Power is defined as the rate of doing work or work done per unit time.

Power �=work done/time taken

� � � � P
=�w/t

UNIT OF POWER

The unit of power is J/S
known as�watt, its symbol is W.

1 watt =1 joule/1 second

1 W = 1 J/ S

Commercial unit of energy is kilo
watt�hour

We pay electricity bill in terms of
unit�or kWh. It is a commercial unit of electric�energy consumed by
the user.

Watt hour = power in watt x time in
hour.

Example : How much energy will
be�used when a hundred watt bulb is used�for 10 hour?

Energy = 100 watt x 10 hour�=
1000 w h = 1kw h

I kwh is known as 1 unit.

One kilowatt hour means
thousand�watt of power is consumed in one hour.

1 kWh �= 1 kW x 1 h

� � � � �
� = 1000 W x 60 x 60 s

� � � � �
� = 1000 Js-1 x 3600 s

� � � � �
� = 3.6 x 106 J

1 unit = 1 kilowatt hour = 3.6x106�
J