Human Falling Determine Force on Achilles

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SUMMARY

The discussion centers on calculating the average force exerted on a woman's feet and Achilles tendon when she jumps from a height of 2.5 meters and lands on a solid floor. The average force required to stop her fall is determined to be 1378 Newtons, based on her mass of 45 kg and an average deceleration of 30.625 m/s². The force experienced by the Achilles tendon is calculated by multiplying the average force by the ratio of the distances from the ball of her foot to the talus and from the talus to the Achilles tendon, resulting in a final force of approximately 5735 Newtons.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Knowledge of kinematic equations, specifically vf² = vi² + 2ad
  • Basic principles of biomechanics related to landing forces
  • Familiarity with the anatomy of the foot, particularly the Achilles tendon
NEXT STEPS
  • Study the biomechanics of landing to understand injury prevention techniques
  • Learn about force distribution in the human body during dynamic movements
  • Explore advanced kinematic analysis using software tools like MATLAB or Python
  • Investigate the effects of different landing techniques on joint forces
USEFUL FOR

Students in physics or biomechanics, physical therapists, sports scientists, and anyone interested in understanding the forces involved in human landing mechanics.

smitty13
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Homework Statement


A 45 kg woman jumps from a height of 2.5 meters to a solid
floor. In an attempt to minimize the likelihood of injury, she lands on the ball
of her feet (the pads just behind her toes) with her knees bent. What
average force is needed on her feet to stop her fall if her center-of-gravity
after touching the floor drops 80 cm before she stops? If the horizontal
distance from the ball of her foot to her talus (where her tibia exerts its
force) is 15 cm, and from talus back to the Achilles tendon is 3.6 cm, what
average force does the Achilles tendon suff er during the stopping time


Homework Equations


F = ma
vf^2 = vi^2 + 2ad


The Attempt at a Solution



I've solved for vf = 7 m/s and the average deceleration of the woman (49/(2*.8m)) = 30.625 and even got to an average force answer of 6028.13 Newtons per second using average deceleration and time but just got stuck from there. Can anybody help me out?
 
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