Compression of human bone: forces

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SUMMARY

The discussion focuses on calculating the compressive force on a human leg modeled as a uniform cylinder of bone with a diameter of 2.3 cm, subjected to a fall from a height of 5 m. The maximum compressive strength of human bone is approximately 1.7 × 10^8 N/m². The correct calculation for the force that can compress the leg before breaking is 7.1 × 10^4 N, derived from the area of the circular cross-section using the formula A = π(r²), where r is the radius of the cylinder.

PREREQUISITES
  • Understanding of basic physics concepts, specifically forces and acceleration.
  • Knowledge of the formula for the area of a circle, A = π(r²).
  • Familiarity with unit conversions, particularly between centimeters and meters.
  • Basic comprehension of material properties, specifically the compressive strength of human bone.
NEXT STEPS
  • Study the principles of mechanics related to falling objects and impact forces.
  • Learn about the properties of human bone and its mechanical behavior under stress.
  • Explore advanced calculations involving material strength and failure criteria.
  • Investigate the effects of different fall heights on the forces experienced by the human body.
USEFUL FOR

This discussion is beneficial for physics students, biomechanics researchers, and professionals in fields related to orthopedics and material science, particularly those interested in the mechanical properties of human bones under stress.

maxd23
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Homework Statement



While unrealistic, we will examine the forces on a leg when one falls from a height by approximating the leg as a uniform cylinder of bone with a diameter of 2.3 cm and ignoring any shear forces. Human bone can be compressed with approximately 1.7 × 10^8 N/m2 before breaking. A man with a mass of 80 kg falls from a height of 5 m. Assume his acceleration once he hits the ground is constant. For these calculations, g = 10 m/s2.

With how much force can the "leg" be compressed before breaking?

Homework Equations

The Attempt at a Solution


The correct answer:
I’m confused about how the answer is 7.1E4 N , can you explain how to get this answer from the data given?

wouldn’t it be F = (1.7 × 10^8 N/m2)*(2.3cm(1m/100cm)^2 = 3.9E4 N ?
 
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Looks like you are using the square of the diameter of the cylinder for the area. What is the formula for the area of a circle?
 
A=pi(r^2)
Ahhh I see! lifesaver over here.
 

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