The maximum energy a bone can absorb without breaking is surprisingly small. For

Question

The maximum energy a bone can absorb without breaking is surprisingly small. For a healthy human of mass 70KG , experimental data show that the leg bones can absorb about 200J . From what maximum height could a person jump and land rigidly upright on both feet without breaking his legs? Assume that all the energy is absorbed in the leg bones in a rigid landing. From what maximum height could a person jump and land rigidly upright on both feet without breaking his legs? Assume that all the energy is absorbed in the leg bones in a rigid landing.

Explanation / Answer

The easiest way to solve this problem is to recognize that the person's potential energy can be expressed as: U = mgh U = potential energy m = person's mass g = acceleration due to gravity h = height above the ground Since all of the potential energy is converted to kinetic energy as the person falls, and then all of the energy is absorbed by the leg bones, we know that U = 200J, m = 70kg, and g = 9.81 m/s², and we can solve for the height, h, in meters. A few notes: • The problem is poorly worded: can the bones in _each_ leg absorb 200J (in which case the height can be doubled), or 200J in total? • The height will probably be quite a bit less than you'd expect, because most jumps don't end in rigid, feet-first landings. • Probably not a good idea to test your results.....

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