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 `K = 100 " N "m^(-1)`
`R = mg cos theta ` , Force of friction `= F muR = mumg cos theta `
Net force on the block down the incline
` = mg sin theta - F `
` = mg sin theta - mu mg cos theta `
` = mg (sin theta - mu cos theta ) `
x = distance moved = 10 cm
0.1 m
At equilibrium
Work done = P.E of streched spring
` mg( sin theta - mu cos theta ) x = 1/2 Kx^(2)`
` 2 mg (sin theta - mu cos theta ) = Kx `
` 2xx1 xx10 ( sin 30^(@) - mu cos 37^(@)) = 100 xx1 `
Solving we get `mu = 0.126 `