Question

For safety in climbing, a mountaineer uses a nylon rope that is 65 m long and 1.1 cm in diameter. When supporting a(n) 89-kg climber, the rope elongates 1.4 m. Find its Young's modulus. _____ Pa

Answer 1

Young's modulus is given by:

Y = Stress/Strain

Stress = Force/Area = F/A

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

Y = (F/A)/(dL/L) = F*L/(A*dL)

Force = Weight on rope = m*g = 89*9.8

Area = pi*d^2/4

d = diameter = 1.1 cm = 0.011 m

L = length of rope = 65 m

dL = Change in length = 1.4 m

So,

Y = 89*9.8*65/((pi*0.011^2/4)*1.4)

Y = Young's modulus of Nylon rope = 4.26*10^8 Pa

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