Question

Mike is a 70 kg pole-vaulter. He falls from a peak height of 5.90 m after pole-vaulting over a crossbar set at that height. He lands on a thick mat. When Mike first makes contact with the mat, his center of gravity is only 1.0 m high. During Mike’s impact with the mat, the mat compresses. At the point of maximum compression, Mike’s vertical velocity reaches zero, and his center of gravity is only 0.5 m high. 1. What is Mike’s potential energy when he is at peak height? 2. What is his kinetic energy just before he makes contact with the mat? 3. What average force did the mat exert on Mike during this impact?

Answer 1

Mike's center of gravity falls 5.90 - 1.0m = 4.9m

Using conversion of energy, PE at max height

PE = 70*9.81*(5.9-0.5)

PE = 3708 J

His speed on impacting the mat is

v = sqrt(2*9.81*4.9) m/s

v = 9.804998 m/s

KE just before impact = ½*70*9.804998²

KE = 3364.8 J

His acceleration after impacting the mat, falling another 1.0 - 0.5m = 0.5m is

a = (-v²)/(2*0.5 m/s²)

a = -96.138 m/s²

So the average force exerted by the mat is

f = ma

f = 70kg * -96.138 m/s²

f = -6729.66 N (-ive means upward direction)