Question

A block of mass $m$ welded with a light spring of stiffness $k$ is in equilibrium on a smooth inclined plane with an angle of inclination $θ$ . If a variable external force is applied slowly till the spring comes to its relaxed position, find the work done by spring force.

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Accepted Answer

Referring to the FBD as shown in the figure, we have four forces ( $N$ , $m g$ , $F_{spring}$ and $F_{ext}$ ) acting on the particle, here $N$ is the normal force.

Initially, the block is at equilibrium.

$F_{spring} = k x_{i} = m g sinθ$

$\Rightarrow x_{i} = \frac{m g sinθ}{k}$ .

When the block is pulled up by an external force to bring the spring to a relaxed length $x_{f} = 0$ .

Hence, work done by spring force,

$W_{spring} = - \frac{1}{2} k (x_{f}^{2} - x_{i}^{2})$

$= - \frac{1}{2} [0 - {(\frac{m g sinθ}{k})}^{2}] = \frac{1}{2} \frac{(m g sinθ)^{2}}{2 k}$ .

B M Sharma Solutions for Chapter: Work, Energy and Power, Exercise 19: ILLUSTRATION 8.19

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Work, Energy and Power, Exercise 19: ILLUSTRATION 8.19

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