In the figure shown, pulley and spring are ideal. Find the potential energy stored in the spring (m 1 >
m 2 ).

Text Solution
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Given a figure where pulley and spring are ideal. The formula to find potential energy stored in a spring is,

where k is the spring constant and x is the displacement from the mean position.
Let us draw the free body diagram for the problem.

In the figure, F is the restoring force of the spring, T is the tension on the string and g is acceleration due to gravity.
Restoring force is given by the formula,

where
is the spring constant and x is the displacement from the mean position.
From the figure we observe,

Putting the value of F we get,

From the figure we get,

Putting the value of T we get,

Now, putting this value of x in equation (i) we get the potential energy as,

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