A 30.0-kg block is resting on a flat horizontal table. On top of this block is r

Question

A 30.0-kg block is resting on a flat horizontal table. On top of this block is resting a 15.0-kg block, to which a horizontal spring is attached, as the drawing illustrates. The spring constant of the spring is 305 N/m. The coefficient of kinetic friction between the lower block and the table is 0.610, and the coefficient of static friction between the two blocks is 0.920. A horizontal force F is applied to the lower block as shown. This force is increasing in such a way as to keep the blocks moving at a constant speed. At the point where the upper block begins to slip on the lower block determine the following. the amount by which the spring is compressed m the magnitude of the force F rightarrow N

Explanation / Answer

Here, constant speed ---> a = 0 . Then:

(a).k x = f m1 g

=> x = f m1 g/k = 0.92*15*9.8/305 = 0.443 m

(b) F - k x - f" (m1+m2)g = 0
F = [f m1 + f"(m1+m2)]g = [0.92*15 + 0.61*45]*9.8 = 404.25 N

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