FYKOS Year 32 Series 4 Problem 4 — trampoline · FYKOS 32 #32.4.4

Physics · mechanics

Problem

Two point-like masses were jumping on a trampoline into height

h_0 = 2 \mathrm{m}

. While they both were in the lowest point of the trajectory (corresponding displacement of

y = 160 \mathrm{cm}

), one of them suddenly disappeared. What is the maximum height, which was the other point-like mass bounced into? A round trampoline has circumference of

o = 10 \mathrm{m}

and is held by

N = 42

springs with stiffness

k = 1720 \mathrm{N\cdot m^{-1}}

. Trampoline may be modelled by

N

springs uniformly attached around the circle and connected in the middle. Mass of the disappeared mass is

M = 400 \mathrm{kg}

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