Please include step by step work with the answer! A 4. 05 kg block free to move

Question

Please include step by step work with the answer! A 4. 05 kg block free to move on a horizontal, frictionless surface is attached to one end of a light horizontal spring. The other end of the spring is fixed. The spring is compressed 0. 122 m from equilibrium and is then released. The speed of the block is 1. 11 m/s when it passes the equilibrium position of the spring. The same experiment is now repeated with the frictionless surface replaced by a surface for which muk = 0. 340. Determine the speed of the block at the equilibrium position of the spring.

Explanation / Answer

when experiment is done on rough surface then some energy lost due to friction.

so friction force = u N = umg = 0.340 x 4.05 x 9.81 =13.51 N

work done by friction = F.d = -13.51 x 0.122 = 1.65 J

so 1.65 J enerygy is lost due to friction.

now energy at equilibrium position = (4.05 x 1.11^2 / 2) - 1.65 = 0.845 J

so 0.845 = 4.05 v^2 /2

v = 0.646 m/s

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