A 2.00 kg block situated on a rough incline is connected to a spring of negligib

Question

A 2.00 kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100 N/m. Consider the pulley to be massless and frictionless. The block is released from rest when the spring is un-stretched. The block then moves 20.0 cm down the incline before coming to rest.
a. Determine the coefficient of kinetic friction between the block and the incline.
b. Compute the block’s speed at the instant it has moved 10.0 cm down the incline.

NOTE theta =37.0degrees

Explanation / Answer

Here let extension in the spring = x m

Therefore after extension the increase in the potential energy of the spring =0.5*k*x^2

Therefore increase in potential energy of the spring = 0.5*100*x^2=50x^2

 work done by friction = µmgxcos 

Increase in potential energy of spring +  work done by friction = Work dode by gravity

0.5*100*x^2 + µmxgcos = mgxsin

Therefore 50x^2 =  (-µmgcos + mgsin)*x

 

This implies   50x=-µmgcos + mgsin 

Here x=0.20 m  (given)

 

Therefore 10 = -15.65µ + 11.8

 

that gives µ = 0.115

 

 

 

 

 

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