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10.2.4 POTENTIAL ENERGY OF AN OBJECT The potential energy of an object at
AT A HEIGHT a height depends on the ground level
An object increases its energy when raised or the zero level you choose. An
through a height. This is because work is More to know object in a given position can have a
certain potential energy with respect
done on it against gravity while it is being to one level and a different value of
raised. The energy present in such an object potential energy with respect to
is the gravitational potential energy. another level.
The gravitational potential energy of an
object at a point above the ground is defined
It is useful to note that the work done by
as the work done in raising it from the ground
gravity depends on the difference in vertical
to that point against gravity.
heights of the initial and final positions of
It is easy to arrive at an expression for
the gravitational potential energy of an object the object and not on the path along which
at a height. the object is moved. Fig. 10.8 shows a case
where a block is raised from position A to B
by taking two different paths. Let the height
AB = h. In both the situations the work done
on the object is mgh.
Fig. 10.7
Fig. 10.8
Consider an object of mass, m. Let it be
raised through a height, h from the ground. Example 10.5 Find the energy possessed
A force is required to do this. The minimum by an object of mass 10 kg when it is at
force required to raise the object is equal to a height of 6 m above the ground. Given,
the weight of the object, mg. The object gains –2
g = 9.8 m s .
energy equal to the work done on it. Let the
work done on the object against gravity be Solution:
W. That is,
work done, W = force × displacement Mass of the object, m = 10 kg,
= mg × h displacement (height), h = 6 m, and
–2
acceleration due to gravity, g = 9.8 m s .
= mgh
Since work done on the object is equal to From Eq. (10.6),
Potential energy = mgh
mgh, an energy equal to mgh units is gained
= 10 kg × 9.8 m s × 6 m
–2
by the object. This is the potential energy (E )
P = 588 J.
of the object.
The potential energy is 588 J.
E = mgh (10.6)
p
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