Two blocks are connected by a light string that passes over a frictionless pulle

Question

Two blocks are connected by a light string that passes over a frictionless pulley as in the %uFB01gure. The block of mass 8.14 kg lies on a horizontal surface and is connected to a spring of force constant 593 N/m. The system is released from rest when the spring is unstretched.

If the hanging 14.2 kg block falls a distance 0.31 m before coming to rest, calculate the coe%uFB03cient of kinetic friction between the block m1 and the surface. The acceleration of gravity is 9.8 m/s^2.

If you could give an in depth explanation. I need to be able to understand and reproduce the work.

Explanation / Answer

When m2 comes to rest then spring is at max compresion and K.E of system=0

So energy conservation gives

m2gh-um1gh=1/2kx^2

Now

h=x=0.31 m2=14.2 m1=8.14 and k=593

So

u=0.592

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