Question

# A man pushes a 4.0 kg block against a horizontal spring, compressing the spring by 20...

A man pushes a 4.0 kg block against a horizontal spring, compressing the spring by 20 cm. Then the man releases the block, and the spring sends it sliding across a tabletop. It stops 90 cm from where you released it. The spring constant is 325 N/m. What is the block–table coefficient of kinetic friction?

 A. 0.47 B. 0.97 C. 0.57 D. 0.37

Using energy conservation:

KEi + PEi + Wf = KEf + PEf

KEi = 0, since initial speed of block is zero

KEf = 0, since finally block stops after traveling 90 cm

PEi = Spring potential energy during compression = (1/2)*k*x^2

PEf = 0, since finally there is no compression in spring

Wf = Work-done by friction force = -Ff*d

Ff = Force of friction = *N = *m*g

So,

0 + (1/2)*k*x^2 - *m*g*d = 0 + 0

(1/2)*k*x^2 = *m*g*d

= Coefficient of kinetic friction = k*x^2/(2*m*g*d)

= 325*0.20^2/(2*4.0*9.81*0.90) = 0.184

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