Depending on how you fall, you can break a bone easily. Theseverity of the break

Question

Depending on how you fall, you can break a bone easily. Theseverity of the break depends on how much energy the bone absorbsin the accident, and to evaluate this let us treat the bone as anideal spring. The maximum applied force of compression that oneman’s thighbone can endure without breaking is 7.4x104 N. The minimum effective cross-sectional area ofthe bone is 3 x10-4 m2, its length is 0.53 m,and Young’s modulus is Y=9.4x109N/m2. The mass of the man is 61 kg. He falls straightdown without rotating, strikes the ground stiff-legged on one foot,and comes to a halt without rotating. To see that it is easy tobreak a thighbone when falling in this fashion, find the maximumdistance through which his center of gravity can fall without hisbreaking a bone.

Explanation / Answer

Let x be the distance the bone compresses E = m g h = 1/2 k x2 h = k x2 / (2 m g) h = F x / (2 m g)      since F = kx   the force to compress a spring by x Y = (F / A) / (x / L    and x = F L / (YA) h = F2 L / (2 m g Y A)   substituting for x in the formula for h Substitute and solve h = k x2 / (2 m g) h = F x / (2 m g)      since F = kx   the force to compress a spring by x Y = (F / A) / (x / L    and x = F L / (YA) h = F2 L / (2 m g Y A)   substituting for x in the formula for h Substitute and solve

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