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Question

A block is projected along a rough horizontal road with a speed of 10 m/s. If the coefficient of kinetic friction is 0.10, how far will it travel before coming to rest?

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Solution

Friction force acting on the block will decelerate it.
Let the deceleration be 'a'.

Using free body diagram


R − mg = 0
(where R is the normal reaction force)
⇒ R = mg (1)
Again, ma − μkR = 0
(where μk is the coefficient of kinetic friction)
From Equation (1),
⇒ ma = μkmg
⇒ a = μkg = 0.1 × 10
= 1 m/s2
Given:
initial velocity, u = 10 m/s
final velocity, v = 0 m/s (block comes to rest)
a = −1 m/s2 (deceleration)
Using equation of motion v2 - u2 = 2as
(where s is the distance travelled before coming to rest)
s=v2-u22a
On substituting the respective values, we get
=0-1022 -1 =1002=50 m
Therefore, the block will travel 50 m before coming to rest.

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