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 3 105 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 16 109 N/m2.

(a) Calculate the force exerted. __N

(b) If her mass is 72.0 kg and water resistance is negligible, what is her acceleration? Assume her weight is precisely supported by the water. __m/s2

(c) How fast is she going once she exerts this force through a distance of 20.5 cm, starting from rest? __m/s

Explanation / Answer

Given that Compression is e = 3*10^-5 m

Young's modulus is Y = 16*10^9 N/m^2

length of the bone is l = 36 cm = 0.36 m

radius is r = 1.75 cm = 0.0175 m

a) Using Y = stress / strain

Y = (F/A)/(e/l)

F/A = Y*(e/l) = 16*10^9*(3*10^-5/0.36) = 1.34*10^6

Force is F = 1.34*10^6*pi*r^2 = 1.34*10^6*3.142*(0.0175^2)

F = 1289.4 N

b) Fnet = m*a

accelaration is a = Fnet/m = (1289.4)/72 = 17.9 m/s^2

C) distance travelled is d = 20.5 cm = 20.5*10^-2 m

initial speed is Vo = 0 m/sec

a = 17.9 m/s^2

then using v^2 -Vo^2 = 2*a*d

V^2 - 0^2 = 2*17.9*0.205

V = 2.709 m/sec

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