Find coefficient of kinetic friction?

Question

A 18 kg block is released from point A as shown in the figure. Its path from A to the spring is frictionless except for the portion between B and C. When the block hits the spring, it compresses the spring by 0.3 m from its equilibrium position before coming to rest momentarily. Find the coefficient of kinetic friction between the block and the rough surface loacted between points B and C. Assume the spring constant is 2500 N/m.

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Answer 1 · 2018-06-27T08:09:38

0.394

#mgh=1/2m*u^2 rArr cancel(m)gh=1/2cancel(m)*u^2rArr u^2=2gh#

In B to C,

#u^2 = 2gh#

#a=-gmu_k#

#v^2 = u^2 +2as rArr v^2 = 2gh-2sgmu_krArr v^2 = 2g(h-smu_k)#

Applying conservation of energy from C to rest

#1/2mv^2 = 1/2kx^2 rArr 2mg(h-smu_k)=kx^2#

substituting #m=18kg , g=9.8m*s^(-2), h=3m, s=6m, k=2500 N/m, x=0.3#,

We get #mu_k = 0.394#