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

ID: 779074 • Letter: W

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 (in N).

(b)

If her mass is 61.0 kg and water resistance is negligible, what is her acceleration (in m/s2)? Assume her weight is precisely supported by the water.

m/s2

(c)

How fast (in m/s) is she going once she exerts this force through a distance of 18.1 cm, starting from rest?

m/s

We know that

Stress = Force/Area = F/A

Strain = Change in length/Original length = dL/L

Young's modulus is given by:

Y = Stress/Strain = (F/A)/(dL/L)

Y = F*L/(A*dL)

F = Y*A*dL/L

A = area = pi*r^2

F = Y*pi*r^2*dL/L

F = 16*10^9*pi*(1.75*10^-2)^2*3*10^-5/(36*10^-2)

F = 1282.82 N

F = m*a

a = F/m = 1282.82/61

a = 21.03 m/sec^2

V^2 = U^2 + 2*a*d

d = 18.1 cm = 0.181 m

U = 0

V = sqrt (0^2 + 2*21.03*0.181)

V = 2.76 m/sec

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