A 10 kg block is released from rest at point A in which is 3 meters above the tr

Question

A 10 kg block is released from rest at point A in which is 3 meters above the track, the track is frictionless except for the portion between points B and C, which has a lenght of 6.00 meters. The block travels down the track, hits a spring of force constant 2000 N/m and compresses the spring 0.300 m from its equilibrium position before coming to rest momentarily.

a. Determine the speed of the block as it reaches point B.

b. Determine the coefficient of kinetic friction between the block and the rough surface between B and C. Recall that the spring has a spring constant of 2000 N/m and its compressed of 0.300 m.

c. After the compressed spring is released, the rebounding block will travel back to the left, across the frictionless surface. Determine the final height of the rebounding block. If you dont have an answer for part b, you may assume the coefficient of kinetic friction is 0.500.

Please show your work clearly and write step by step solution including numeric substitutions and etc. To make it easier, please do this in paper and include the pictures. thanks

Explanation / Answer

part a )

between A and B there is no friction so we can use here energy conservation

mgh = 1/2mv^2

v = sqrt(2gh)

v = sqrt(2*9.8*3) = 7.67 m/s^2

part b )

Between B and C, energy is not conserved due to friction. The change in energy is the work done by friction

1/2mvc^2 - 1/2mvb^2 = f.d

Between C and the final position, energy is conserved and it amounts to

1/2kx^2 = 1/2mvc^2

f.d = 1/2kx^2 - mgh

-mu*m*g*d = 1/2kx^2 - mgh

mu = h/d - kx^2/2mgd

mu = 3/6 - 2000*(0.300)^2/2*10*9.8*6

mu = 0.3469 = 0.35

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