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To test the impact performance of a 15 cm thick gymnastics mat, a 45 kg mass starts at rest then is dropped onto the mat from a height of 2.15 m above the ground (2.0 m above the surface of 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 and what does the sign (i.e. direction) of the work indicate? (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 and what does the sign (i.e. direction) of the force indicate?

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