Question

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

Answer 1

Given: sin 37° = \(\frac{3}{5}\) and cos 37° = \(\frac{4}{5}\) ; m = 1 kg; K = 100 N.m^-1; x = 10 m = 0.10 m; µ = ?; g = 10ms^-2

When the system is released from rest, then forces acting on the block are shown in figure.

Normal reaction acting on the block, N = mg cos 37°

∴ Force of friction

f = µN = µmg cos 37°

If downwards displacement of the block on incline be x, then potential energy of the spring

Work done against frictional force,

W = fx

Decay in potential energy of the block,

Uh = mgh

∴ From law of conservation of energy,

Uh = US + W

mgh = \(\frac{1}{2}\) .Kx² + fx

From figure,