Max Height to Jump Without Breaking Leg Bones

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SUMMARY

The maximum height from which a 75-kg person can jump without breaking their lower leg bones is determined using the principles of physics, specifically conservation of energy and stress calculations. The breaking strength of bone is 170 * 10^6 N/m², and the smallest cross-sectional area of the bone is 2.5 * 10^-4 m². By calculating the force using the formula for stress and applying the work-energy principle, one can derive the maximum jump height. The key equations involve solving for force and height based on the known parameters of mass, gravity, and the distance the center of mass moves during the fall.

PREREQUISITES
  • Understanding of basic physics concepts, particularly conservation of energy
  • Knowledge of stress and strain in materials, specifically in biological contexts
  • Familiarity with the equations for force, mass, and gravity
  • Ability to perform calculations involving area and force
NEXT STEPS
  • Study the principles of conservation of energy in physics
  • Learn about stress and strain calculations in materials science
  • Explore the relationship between force, mass, and acceleration using Newton's laws
  • Practice solving problems involving free fall and impact forces
USEFUL FOR

This discussion is beneficial for physics students, biomechanics researchers, and anyone interested in understanding the mechanics of human movement and injury prevention.

ussjt
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Could someone help me set up this problem and give some helpful hints.

From what maxium height can a 75-kg person jump without breaking the lower leg bone on either leg? Ignore air resistance and assume the CM of the person moves a distance of .60m from standing to the seated position (that is, in breaking the fall). Assume the breaking strenght (force per unit area) of bone is 170 * 10^6 N/m square, and its smallest crosssectional area is 2.5 * 10^-4 m square.
 
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Have you tried it yet?

Conservation of energy.

\int{Fds} = mgh
 
no, because I need help with the set up for each section...I have been out for a couple days so I don't fully understand the problem. If I knew the equations for each step, I could take it from there.
 
I more or less gave it to you already.

You know the breaking stress, and the bone's area. Stress is force divided by area. ->solve for force.

You know the force and the distance that force can act on. You know the mass, you know gravity, solve for height.
 

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