Page 132 - Understanding NCERT Science 09

Example 10.6 An object of mass 12 kg is 10.2.6 LAW OF CONSERVATION OF ENERGY
at a certain height above the ground.
If the potential energy of the object is
480 J, find the height at which the
object is with respect to the ground.
Given, g = 10 m s .
–2
Solution:
Mass of the object, m = 12 kg,
potential energy, E = 480 J.
p
E = mgh
p
–2
480 J = 12 kg × 10 m s × h
480 J
h = –2 = 4 m.
120 kg m s
The object is at the height of 4 m.
10.2.5 ARE VARIOUS ENERGY FORMS
INTERCONVERTIBLE?
Can we convert energy from one form to
another? We find in nature a number of
instances of conversion of energy from one
form to another.
Activity ___________ 10.13
• Sit in small groups.
• Discuss the various ways of energy
conversion in nature.
• Discuss following questions in your
group:
(a) How do green plants produce food?
(b) Where do they get their energy from? same at all points. That is,
(c) Why does the air move from place
to place?
(d) How are fuels, such as coal and
petroleum formed?
(e) What kinds of energy conversions
sustain the water cycle?
Activity ___________ 10.14
• Many of the human activities and the
gadgets we use involve conversion of
energy from one form to another.
• Make a list of such activities and
gadgets.
• Identify in each activity/gadget the
kind of energy conversion that takes
place.
WORK AND ENERGY
Rationalised 2023-24
In activities 10.13 and 10.14, we learnt that
the form of energy can be changed from one
form to another. What happens to the total
energy of a system during or after the process?
Whenever energy gets transformed, the total
energy remains unchanged. This is the law of
conservation of energy. According to this law,
energy can only be converted from one form
to another; it can neither be created or
destroyed. The total energy before and after
the transformation remains the same. The law
of conservation of energy is valid in
all situations and for all kinds of
transformations.
Consider a simple example. Let an object
of mass, m be made to fall freely from a height,
h. At the start, the potential energy is mgh and
kinetic energy is zero. Why is the kinetic
energy zero? It is zero because its velocity is
zero. The total energy of the object is thus mgh.
As it falls, its potential energy will change into
kinetic energy. If v is the velocity of the object
at a given instant, the kinetic energy would be
2
½mv . As the fall of the object continues, the
potential energy would decrease while the
kinetic energy would increase. When the object
is about to reach the ground, h = 0 and v will
be the highest. Therefore, the kinetic energy
would be the largest and potential energy the
least. However, the sum of the potential energy
and kinetic energy of the object would be the
potential energy + kinetic energy = constant
or
1 2
mgh + 2 mv = constant. (10.7)
The sum of kinetic energy and potential energy
of an object is its total mechanical energy.
We find that during the free fall of the object,
the decrease in potential energy, at any point
in its path, appears as an equal amount of
increase in kinetic energy. (Here the effect of
air resistance on the motion of the object has
been ignored.) There is thus a continual
transformation of gravitational potential
energy into kinetic energy.
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