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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?
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=(v^2-u^2)/(2a)`
On substituting the respective values, we get
`=0-10^2/2(-1)`
`=100/2=50"m"`
Therefore, the block will travel 50 m before coming to rest.
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