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Question

A block of mass m starts moving  with an initial velocity v0 at a distance L towards a stationary spring of stiffness K attached to the wall as shown in figure.

Find the distance travelled by block before coming to rest.
Given that surface is rough only for distance L and  friction coefficient μ is such that (12mv20>μmgL).


A
v0mK
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B
 12mv0μmLK
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C
 12mv0μmL2K
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D
mv202μmgLK
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Solution

The correct option is D mv202μmgLK
Let block covers distance(L+X0) before coming to rest.
Work done by all forces =ΔKE
(W)friction  + (W)spring=ΔKE 

μmgL12Kx20=12mv20

μmgL+12Kx20=12mv20
12Kx20=12mv20μmgL
x0=mv202μmgLK

Hence option D is the correct answer

Physics

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