Please show each step and include formula with explintion. Thank you! A 2.0kg bl

Question

Please show each step and include formula with explintion. Thank you!

A 2.0kg block slides down a frictionless 30 degree incline from a height of h-2.0m

A) The mass slides on a frictionless horizontal surface and then encounters a spring with a spring constant of 2000 N/m. The spring stops the sliding block. what is the maximum compression of spring?

B) Now suppose that the block and the hill have a coefficient of kinetic friction of 0.25 (the horizontal surface is a still frictionless). Now, what is the maximum compression of spring?

Explanation / Answer

(A) Applying energy conservation,

m g h = k x^2 / 2

(2)(9.8)(2) = 2000 x^2 / 2

x = 0.198 m .......Ans

(B) Now some of energy will be lost against friction work.

f = u N = u m g cos30

f = 0.25 x 2 x 9.8 x cos30 = 4.24 N  

d = h / sin30 = 4 m

W = - fd = - 16.97 J  

So, m g h - 16.97 = k x^2 / 2

(2 x 9.8 x 2) - 16.97 = 2000 x^2 /2

x = 0.149 m  

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