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Finding out distance before breaking leg using Hooke's Law

  • Thread starter TmrK
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  • #1
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Depending on how you fall, you can break a bone easily. The severity of the break depends on how much energy the bone absorbs in the accident, and to evaluate this let us treat the bone as an ideal spring. The maximum applied force of compression that one man’s thighbone can endure without breaking is 7.0 x104 N. The minimum effective cross-sectional area of the bone is 5 x10-4 m2, its length is 0.57 m, and Young’s modulus is Y=9.4x109 N/m2. The mass of the man is 60 kg. He falls straight down without rotating, strikes the ground stiff-legged on one foot, and comes to a halt without rotating. To see that it is easy to break a thighbone when falling in this fashion, find the maximum distance through which his center of gravity can fall without his breaking a bone.

I assume that somehow the conservation of potential energy comes into play here, as well as Hookes Law.
 

Answers and Replies

  • #2
1,506
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You know the maximum force the bone can withstand. You know Young's modulus and the dimensions of the bone so calculate the compression that this maximum force would produce.
You should then be able to calculate energy stored in the compressed bone and relate (equate) this to the potential energy of the falling man.
 

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