A block of mass m slides from rest at a height H on a frictionless inclined plane as shown in figure

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5.Work, Energy, Power and Collision

hard

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

$h=H-2 \mu(d+x)+k x^2 / 2 m g$

(KVPY-2013)

Solution

(a)

As spring is ideal, it gives energy stored back to the block.

Applying energy conservation, we have Initial potential energy

$=\text { Work done against friction }$

$\quad+\text { Final potential energy }$

$\Rightarrow \quad m g H=2 \mu m g(d+x)+m g h$

$\Rightarrow \quad h=H-2 \mu(d+x)$

Standard 11

Physics

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