Question

Find coefficient of kinetic friction?

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.

Answer 1

0.394

Explanation:

Applying conservation of energy from A to B;

`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`