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Question

A body is projected along a rough horizontal surface with a velocity of 6m/s. If the body comes to rest after traveling a distance of 9m, the coefficient of sliding friction is (g=10ms2)


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Solution

Step 1: Given data

A body is projected along a rough horizontal surface with a velocity of 6 m/s. i.e., u=6m/s

The displacement of the body is 9m. i.e., s=9m

Step 2: Formula used

According to third equation of motion ,v2=u2+2as[wherev=finalvelocity,u=initialvelocity,a=acceleration,s=displacement]

Step 3: Calculating acceleration

Due to motion along rough horizontal surfaces, the body comes to rest. Let us assume its final velocity as v. So, v=0m/s

v2=u2+2as02=62+2a(9)0=36+18aa=2m/s2

Negative acceleration means velocity is decreasing and friction is responsible for this decrement.

Step 4: Coefficient of sliding friction
μ=FN[whereμ=coefficientoffriction,F=frictionalforce,N=normalforce]F=μ×N

Due to friction, the body comes to rest.
Appliedforce=frictionforce

m×a=μ×N[AsF=m×a]m×a=μ×mg[AsN=mg]a=μ×gμ=agμ=210μ=0.2


Hence, the coefficient of sliding friction is 0.2.


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