How Much Force Can a Human Femur Withstand Before Fracturing?

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SUMMARY

The maximum force that a human femur can withstand before fracturing is determined using Young's Modulus, which is 1.50 X 1010 N/m2, and the fracture threshold of 1.50 X 108 N/m2. Given a minimum effective diameter of 2.60 cm, the maximum force can be calculated using the formula for tensile stress (F/A). Additionally, the bone's length of 24.0 cm allows for the calculation of how much the bone shortens under this maximum compressive force.

PREREQUISITES
  • Understanding of Young's Modulus in material science
  • Knowledge of tensile stress and strain calculations
  • Familiarity with basic geometry for area calculations
  • Ability to manipulate equations involving force and area
NEXT STEPS
  • Calculate the maximum force on a femur using tensile stress formulas
  • Explore the implications of bone density on fracture resistance
  • Investigate the effects of varying diameters on bone strength
  • Learn about the mechanical properties of different types of biological tissues
USEFUL FOR

Students in biomechanics, orthopedic researchers, and professionals in sports medicine who are interested in understanding the mechanical limits of human bones.

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Homework Statement



Assume that Young's Modulus for bone is 1.50 X 10^10 N/m2 and that the bone will fracture if more than 1.50 X 10^8 N/m2 is exerted.

(a) What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.60 cm?

(b) If a force of this magnitude is applied compressively, by how much does the 24.0 cm long bone shorten?

Homework Equations



Y = tensile stress / tensile strain

tensile stress = F/A
tensile strain = delta L / Initial L

The Attempt at a Solution



I understand the concept, but i can't figure out where to plug the numbers into. Since I don't have any lengths for part a, I guess you wouldn't use the entire young's equation, but what exactly would I use?

Any help would be great! Thanks!
 
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never mind, I figured it out
 

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