A 1kg block situated on a rough incline is connected to a spring of spring constant `100Nm^(-1)` as shown in figure,. The block is released from rest with the spring in the unstretched position. The block moves 10cm down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has negligible mass and the pulley is frictionless.

Explanation

As is clear from figure,
`R=mgcostheta, F=muR=mu mg costheta`
Net force on the block doen the incline
`=msintheta-F=mg sing theta - mu mg cos theta = mg (sin theta - mu cos theta )`
distance moved, `x=10cm=0.1m. `
In equilibrium, work done `=` P.E. of stretched spring
`mg(sintheta-mu cos theta )x =(1)/(2)Kx^(2)`
`2mg(sintheta-mu cos theta)x=Kx`
`2xx1xx10(sin 37^(@)-mucos 37^(@))=100xx0.1`
`20(0.601-mu.0.798)=10 :. mu=0.126`