Question

An ideal spring is hung vertically from the ceiling. When a $2.0kg$ block hangs at rest from it the spring is extended $6.0cm$ from its relaxed length. A upward external force is then applied to the block to move it upward a distance of $16cm$. While the block is moving upward the work done by the spring is:

• A. $-0.52J$
• B. $+0.52J$
• C. $-1.67J$
• D. $+1.67J$

Answer 1

The correct option is C $-1.67J$

Initial extension of the spring$=x_o=6cm=0.06m$

Initially the block is in equillibrium

$\Rightarrow mg=k{x}_o$

$\Rightarrow 2\times 10=k\times 0.06$

$\Rightarrow k=\frac{20}{0.06}$ N/m

Distance by which external force moved the spring upward$=x_1=16cm=0.16m$

Net compression of the spring$=x=x_1-x_o=0.16-0.06=0.10m$

Work done by the spring= -Energy stored in the spring$=-0.5\times k{x}^2=-0.5\times \frac{20}{0.06}\times \left({0.1}^2\right)=-1.67J$

Note- Negative sign has appeared as the spring will try to regain its original length and so the force exerted by the spring will be in direction opposite to that of net displacement of the block

Hence, none of the above option is correct.