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 0.80 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 x i08 N/rn2. 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 x 10^8 N/m^2)(1.60 x 10^-4 m^2) = 5.12 x10^4 N Calculate the minimum stopping distance d that will not result in a broken leg if your mass is 50.0 kg. Don't try it! Bend your knees!

Explanation / Answer

v = 2*9.8*-0.8 = -3.96 m/s

5.12*10^4 - 50*9.8 = 50*a

a = 1014.2 m/s^2

Vf = -3.96^2 - 2*d*1014.2

0 = -3.96^2 + 2*d*1014.2

d = 0.00773 m

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