A high-speed lifting mechanism supports a 875-kg object with a steel cable that

Question

A high-speed lifting mechanism supports a 875-kg object with a steel cable that is 33.0 m long and 4.00 cm2 in cross-sectional area.

(a) Determine the elongation of the cable.
_______mm

(b) By what additional amount does the cable increase in length if the object is accelerated upwards at a rate of 3.5 m/s2?
_______mm

(c) What is the greatest mass that can be accelerated upward at 3.5 m/s2 if the stress in the cable is not to exceed the elastic limit of the cable, which is 2.2 ? 108 Pa?
______kg

Explanation / Answer

Part A)

Apply Y = FLo/A(delta L)

Youngs modulus for steel is 20 X 1010 Pa, so...

(20 X 1010) = (875)(9.8)(33)/(4 X 10-4)(delta L)

delta L = 3.54 mm

Part B)

The new force = ma + mg = (875)(9.8 + 3.5) = 11637.5 N

(20 X 1010) = (11637.5)(33)/(4 X 10-4)(Delta L)

Delta L = 4.80 mm

The difference = 4.80 - 3.54 = 1.26 mm

Part C)

F/A = 2.2 X 108

m(9.8 + 3.5)/(4 X 10-4) = 2.2 X 108

m = 6617 kg

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