If you jump from a desktop and land stiff-legged on a concrete floor, you run a

Question

If you jump from a desktop and land stiff-legged on a concrete floor, you run a significant risk that you will break a leg. To see how that happens, consider the average force stopping your body when you drop from rest from a height of 1.10 m and stop in a much shorter distance d. Your leg is likely to break at the point where the cross-sectional area of the bone (the tibia) is smallest. This point is just above the ankle, where the cross-sectional area of one bone is about 1.60 cm2. A bone will fracture when the compressive stress on it exceeds about 1.60 108 N/m2. If you land on both legs, the maximum force that your ankles can safely exert on the rest of your body is then about the following.

2(1.60 108 N/m2)(1.60 10-4 m2) = 5.12 104 N

Calculate the minium stopping distance d that will not result in a broken leg if your mass is 65.0 kg. Don't try it! Bend your knees! Answer in m.

Explanation / Answer

velocity at bottom point = sqrt(2 x 9.8 x 1.10) = 4.64 m/s

if he will in d distance den stopping time t :

v^2- u^2 = 2as

0 - 4.64^2 = 2 x a x d

a =10.8/d

so F   = ma

5.12 x 10^4 = 65 x10.8/d

d =0.0136 m    = 1.36 cm

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