In class, we considered a simple model for jump height, h, resulting in constant

Question

In class, we considered a simple model for jump height, h, resulting in constant scaling as a function of body mass, m. The largest error shows up at the light end, and in this problem we explore why this might be the case.

(a) Determine the power per unit volume, P, required to jump a height, h. You may assume that that an animal squats to zero height and moves with the same constant speed v during the launch time (from the start to the end of a push). (In the future, you should get into the habit of making these assumptions for yourself !)

(b) If there is a maximum power per unit volume that an animal can generate, Pmax, explain the deviation from constant scaling for tiny animals. (Note that click beetles overcome this problem by storing energy in their exoskeleton and jumping only after they have stored sufficient energy!)

Explanation / Answer

a) the power per unit volume, P = F * v

                                                      = mg * v

b) the deviation from constant scaling = (P/Pmax) * h

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