Question

The spring is compressed by a distance $a$ and released. The block again comes to rest when the spring is elongated by a distance $b$. During this :

• A. Work done by the spring on the block $=\frac{1}{2} k(a+b)^{2}$
• B. Work done by the spring on the block $=\frac{1}{2} k\left(a^{2}-b^{2}\right)$
• C. Coefficient of friction $=\frac{k(a-b)}{2 m g}$
• D. Coefficient of friction $=\frac{k(a+b)}{2 m g}$

Answer 1

Answer: (B), (C)

Work done by spring on block,

$w_{s}=\frac{1}{2} k a^{2}-\frac{1}{2} k b^{2}=\frac{1}{2} k\left(a^{2}-b^{2}\right)$
By work energy theorem,
$K_{i}+w =K_{f} $
$0+\frac{1}{2} k a^{2}-\mu m g(a+b)-\frac{1}{2} k b^{2}=0$
$\mu m g(a+b) =\frac{1}{2} k\left(a^{2}-b^{2}\right)$
$\mu =\frac{k(a-b)}{2 m g}$