A big person (m = 100 kg) jumps on a trampoline which we model as a linear sprin

Question

A big person (m = 100 kg) jumps on a trampoline which we model as a linear spring with stiffness k. You know that the trampoline deflects d0 = 20 cm under the stationary weight mg of the person (use g = 10 m/s^2). Assume there is no dissipation and the person is jumping repeatedly a height h = 1 m above the unloaded surface of the trampoline. Give all answers with symbols and numbers. What is the stiffness k of the spring (answer in terms of some or all of m, g and d0). What is the maximum deflection of the trampoline during these jumps? What is the peak force of the trampoline on the jumper? (answer in symbols, Newtons, and numbers of body weights).

Explanation / Answer

here,
mass of person, m = 100 kg
deflection, do = 20 cm = 0.2 m

Part A:
From Conservation fo Energy,
PE lost by man = PE gained by spring
mgh = 0.5 * k * d0^2

solving for spring stiffness , k

k = (2*mgh) / (do^2)

k = (2*100*10*1) /(0.2^2)

k = 50000 N/m

Part B:
Maximum Deflection, x = 2 * do = 2 * 0.2 = 0.4 m

Part C:

The Feak spring force, Fs = k*x = 50000 * 0.4 = 20000 N

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