To test the impact performance of a 15 cm thick gymnastics mat, a 25 kg mass sta
ID: 1458339 • Letter: T
Question
To test the impact performance of a 15 cm thick gymnastics mat, a 25 kg mass starts at rest then is dropped onto the mat from a height of 2 m above the mat. During impact, the mass’s vertical velocity reaches zero and the mat has been compressed to a thickness of 5 cm. Assume complete transfer of energy (no energy is lost to heat). (a) What is the potential and kinetic energy of the mass before it is dropped onto the mat?; (b) What is the mass’s vertical velocity just before it hits the mat?; (c) How much work does the mat do to stop the fall of the mass? (d) What average vertical force does the mat exert on the mass during the impact, from contact until the mass’s vertical velocity reaches zero? (4 pts)
please show all work and use correct significant figures
Explanation / Answer
given,
mass = 25 kg
height = 2 m
mat is compressed by = 15 - 5
mat is compressed by = 10 cm
potential energy just before it dropped into the mat = 0 J
kinetic energy just before it dropped into the mat = mgh J
kinetic energy just before it dropped into the mat = 25 * 9.8 * 2 J
kinetic energy just before it dropped into the mat = 490 J
velocity = sqrt(2gh)
velocity = sqrt(2 * 9.8 * 2)
velocity = 6.261 m/s
v^2 = u^2 + 2as
0 = 6.261^2 - 2 * a * 0.1
a = 196 m/s^2
average force = mass * acceleration
average force = 25 * 196
average force = 4900 N
work done = force * displacement
work done = 4900 * 0.1
work done = 490 J
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