A spring is kept compressed by a small trolley of mass $0.5 k g$ lying on a smooth horizontal surface as shown in the adjacent fig. when the trolley is released. it is found to move at a speed $v = 2 m s^{- 1}$ . What potential energy did the spring possess when compressed?

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Solution

Mass of trolley $= 0.5 k g$
Velocity $= 2 m / s$
When the compressed spring is released, its potential energy is converted into kinetic energy completely.
Potential energy of compressed spring = kinetic energy of moving trolley Kinetic energy of trolley $= \frac{1}{2} \times m a s s \times (v e l o c i t y)^{2}$
$= \frac{1}{2} \times 0.5 \times (2)^{2}$
$\frac{1}{2} = \times 0.5 \times 2 \times 2$
Hence, potential energy of compressed spring $= 1.0 J$

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