A block is on an incline whose angle can be varied. The angle is gradually increased from 0o. At 34.0o, the block starts to slide down the incline.

Question

It slides 2.9 m down the incline in 1.7 s. Calculate the coefficient of static friction. 

Calculate the kinetic coefficent of friction for the above problem. 

Answer 1

This is a very interesting problem:

the perpendicular surface force (N) equals=mgcos(teta)

and the force dragging the block down the incline is mgsin(teta) when the block starts to move:

μ_smgcos(teta)=mgsin(teta) therefore μ_s=tan(teta) μ_s=tan(34)=0.674

after the block starts to move the kinetic friction coefficient is lower than the static coefficient therefore the motion becomes accelerated as a result:

mgsin(teta)-μ_kmgcos(teta)=ma satisfies however we don't have the value of acceleration (a) to calculate μ_k

Therefore we need to calculate it. remember that for accelerated motion the equation x-x₀=0.5at²+V₀t

satisfies since V₀ is zero therefore having displacement to be 2.9 and t=1.7s we get a=2 m/s²

substituting the value of a in previous equation we can get μ_k=0.428