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A block rolled on rough surface with velocity of 8m/s comes to rest after travelling 4m. Compute the coefficient of friction (g=10m/s2)

Option: 1

0.8


Option: 2

0.6


Option: 3

0.4


Option: 4

0.5


Answers (1)

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Solution

Given-

Initial velocity of block, u = 8 m/s,

Distance travelled before the block stops, s = 4 m

Let the coefficient of kinetic friction beetween block and surface be \mu_{k}.

F.B.D of the block-

From F.B.D-

\\ N=mg\\ f_{k=}\mu_{k}N\\ \Rightarrow f_{k=}\mu_{k}mg\\

Assuming the acceleration of th block to be 'a'.

\\ N=mg\\ f_{k=}\mu_{k}N\\ \Rightarrow f_{k=}\mu_{k}mg\\ F_{net}=ma\\ -f_{k}=ma\\ \Rightarrow a=-\mu_{k}g\\

The block stops (v=0) after travelling displacement of 4m.

Applying 3rd euation of motion-

\\ v^2=u^2+2as\\ 0=u^2-2\mu_{k}gs\\ \Rightarrow \mu_{k}=\frac{u^2}{2gs}=\frac{8\times8}{2\times10\times4}=0.8

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sudhir.kumar

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