When pushing off of a pool wall, a swimmer exerts a force parallel to the length

Question

When pushing off of a pool wall, a swimmer exerts a force parallel to the length of her femur, compressing it 4 x 10-5 m. The bone is equivalent to a uniform cylinder 36.0 cm long and 1.75 cm in radius. Young's modulus for bone is 16 x 109 N/m2. (a) Calculate the force exerted (in N). (b) If her mass is 64.0 kg and water resistance is negligible, what is her acceleration (in m/s)? Assume her weight is precisely supported by the water m/s (c) How fast (in m/s) is she going once she exerts this force through a distance of 12.5 cm, starting from rest? m/s

Explanation / Answer

A) Stress = e*E = F/A

Solve for F
F = e*A*E

e = change in length / original length = (4 * 10^-5 m) / (0.360 m) = 11.1 * 10^-5
A = pi*r^2 = pi*(0.0175 m)^2 = 9.62*10^-4 m^2

F = 1.11*10^-4 * 9.62*10^-4 m^2 * 16*10^9 N/m^2 = 1708.5 N

B) a = F/m = 1708.5 N / 64 kg = 26.7 m/s^2

C) v = sqrt (2*a*d) = sqrt (2 * 26.7 m/s^2 * 0.125 m) = 2.58 m/s

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