7. (15 points) A block of mass m 6 kg starts from rest at the top of a frictionl

Question

7. (15 points) A block of mass m 6 kg starts from rest at the top of a frictionless, icy circular quarter-pipe of radius R = 3 m. When let go, it slides down to the bottom of the slope and continues horizontally, until it encounters a rough patch of ice & gravel of length 1.5 m, with a coefficient of kinetic friction between the block and the patch equal to 0.333. It then continues on frictionless ice until it reaches a spring attached to a wall, of spring constant k = 1 10 N/m. As the block compresses the spring, it slowly comes to a rest. How much does the block compress the spring? (Show all your work) (It helps to draw a picture!)

Explanation / Answer

Here we apply work energy theorem i.e

Total work done = Change in kinetic energy

Work done by gravity + work done by friction + work done by spring = KF - Ki

(6 x 9.8 x 3) - (0.333 x 6 x 9.8 x 1.5) - 110 d^2 /2 = 0 - 0

d = 1.63 m

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