To test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindri

Question

To test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindrical mass is dropped onto the mat from a height of 1 m above the mat. During the impact, the cylinder's vertical velocity reaches zero at the instant the mat has compressed to only 4 cm thick.

a. How much kinetic energy does the cylinder have at the instant just before it contacts the mat?

b. How much work does the mat do to stop the fall of the cylinder?

c. What average vertical force does the mat exert on the cylinder during the impact, from contact until the cylinder's vertical velocity is zero?

Explanation / Answer

a)

KE of the cylinder = PE of cylinder when at topmost point = mgh = 20 x 9.8 x 1 = 196 J

b)

work done by the mat = change in KEof cylinder = 0 - 196 = -196 J it is negative since work is done to stop the cylinder

c)

work done by mat is given as

W = F d cos180

-196 = F x (0.04) (-1)

F = 4900 N

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