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

Explanation

From fig.
R = mg ` cos theta`
`F = mu R = mu mg cos theta`
Net force on the block down the incline
`= mg sin theta - f = mg sin theta - mu mg cos theta `
`= mg ( sin - mu cos theta)`
Distanced moved , x = 10 cm = 0.1 m
In equilibrium work done = P.E of strched spring
`mg (sin theta - mu cos theta) x = (1)/(2) Kx^(2)`
`2 mg (sin theta - mu cos theta) = Kx`
`2 xx 1 xx 10 (sin 37^(@) - mu cos 37^(@)) = 100 xx 0.1 `
`20 (0.601 - mu . 0. 798) = 10 :. mu = 0.126`