Question

A block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $\mu$ and compresses a spring of spring constant $k$ by a distance $x$ before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$.

Then

• A. $h=H-2\mu (d+x)$
• B. $h=H-2\mu (d-x)$
• C. $h=H-2\mu d+k{x}^2/mg$
• D. $h=H-2\mu (d+x)+k{x}^2/2mg$

Answer 1

Answer: (A)

As spring is ideal, it gives energy stored back to the block.
Applying energy conservation, we have
Initial potential energy $=$ Work done against friction $+$ Final potential energy
$\Rightarrow mgH=2\mu mg\left(d+x\right)+mgH$
$\Rightarrow h=H-2\mu \left(d+x\right)$