Target: a) 4900 N/m b) -1.85m c) 15.3m Two skate boarders M_1 = 75 kg and M_2 =

Question

Target:

a) 4900 N/m

b) -1.85m

c) 15.3m

Two skate boarders M_1 = 75 kg and M_2 = 50 kg perform a stunt involving a trampoline. The stunt involves them jumping onto the trampoline together from the same height, h = 5m, and at the same time. When the trampoline reaches its lowest point (and momentarily comes to rest), the largest skater gets off the trampoline leaving the smaller one, M_2, there to be flung into the air by herself. During practice the larger skater notices that the trampoline is displaced by 0.15 m while at rest with just himself standing on it. a) Determine the effective spring constant of the trampoline. b) What will the maximum displacement of the trampoline be after both skaters jump onto it? c) What is the maximum height the lighter skater is flung to during the stunt?

Explanation / Answer

a) spring constant is k = F/x = (75*9.8)/0.15 = 4900 N/m

b)

using law of conservation of energy

energy at height h = energy at the maximum displacement

(m1+m2)*g*h = 0.5*k*x^2

(75+50)*9.8*5 = 0.5*4900*x^2

x = -1.58 m

c) 0.5*k*x^2 = m*g*h

0.5*4900*1.58^2 = 50*9.8*h

h = 12.5 m

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