In the figure, a 1.2-kg block is held at rest against a spring with a force cons

Question

In the figure, a 1.2-kg block is held at rest against a spring with a force constant k = 780 N/m. Initially, the spring is compressed a distance d. When the block is released, it slides across a surface that is frictionless, except for a rough patch of width 5.0 cm that has a coefficient of kinetic friction ?k = 0.44. Find d such that the block's speed after crossing the rough patch is 2.7 m/s.

In the figure, a 1.2-kg block is held at rest against a spring with a force constant k = 780 N/m. Initially, the spring is compressed a distance d. When the block is released, it slides across a surface that is frictionless, except for a rough patch of width 5.0 cm that has a coefficient of kinetic friction ?k = 0.44. Find d such that the block's speed after crossing the rough patch is 2.7 m/s.

Explanation / Answer

Conservation of energy

0.5*780*d^2 - 0.44*1.2*9.8*0.05 = 0.5*1.2*2.7^2

d = 0.10898m = 10.898 cm

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