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Science · Biology
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A mouse and an elephant fall from a height of 3 meters. Will they both suffer the same? To answer this question, we will attempt to estimate the stress applied to the bones of the mouse and the elephant in this scenario.

4a) Write down an equation for the energy of an animal of mass m that falls h meters.

4b) Imagine the legs act jointly as a single spring of spring constant k. How far must the bones of the leg compress to dissipate the energy of the fall? (Write this down as an equation that is a function of the mass of the animal, the height of the fall, and other constants.)

4c) Write down an equation for the spring constant of an animal’s legs, as a function of the combined foot area, leg length, and Young’s modulus of bone.

4d) Putting this all together, assume a single elephant foot has an area of .03 m2 , a leg length of 1.5 m, and a mass of 5000 kg. Assume its bone has a Young’s modulus of 14 GPa. Under these assumptions, how much will the bones of the leg buckle after the fall?

4e) Assume a single mouse foot has an area of 4.5*10-5 m2 , a leg length of .025 m, and a mass of .0001 kg. Assume that, like the elephant, it also has bone with a Young’s modulus of 14 GPa. Under these assumptions, how much will the bones of the leg buckle after the fall?

4f) How much stress is applied to the elephant leg bones? How does this compare to the ultimate stress of cortical bone?

4g) How much stress is applied to the mouse leg bones? How does this compare to the ultimate stress of cortical bone?

4h) Who hurts more after the fall – the elephant, or the mouse? Why?

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