Question

(A = 3, B = 9) A steel wire is used to lift heavy object. The cable has a diameter of (5.25 + A) mm and an initial length of (24.5 + B) m. If the cable stretches 2.50 mm, what is the mass of the heavy object? Use 20.0 x 10¹⁰ Pa for Young’s modulus for steel. Give your answer in kg and with 3 significant figures.

Answer 1

We know that Young's modulus is given by:

Y = Stress/Strain

Stress = Force/Area = F/A = F/(pi*d^2/4) = 4*F/(pi*d^2)

Strain = Change in length/original length = dL/L0

So,

Y = 4*F*L0/(pi*d^2*dL)

F = force due to heavy object = Weight of object = m*g

So,

Y = 4*m*g*L0/(pi*d^2*dL)

m = pi*d^2*dL*Y/(4*g*L0)

Using given values:

d = diameter = 5.25 + 3 = 8.25 mm = 8.25*10^-3 m

dL = 2.50*10^-3 m

Y = 20.0*10^10 Pa

L0 = 24.5 + 9 = 33.5 m

So,

m = mass of object = pi*(8.25*10^-3)^2*2.50*10^-3*20.0*10^10/(4*9.81*33.5)

m = 81.33 kg

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