A high-speed lifting mechanism supports a(n) 700-kg object with a steel cable th

Question

A high-speed lifting mechanism supports a(n) 700-kg object with a steel cable that is 34.0 m long and 4.00 cm2 in cross-sectional area.

(a) Determine the elongation of the cable. (Enter your answer to at least two decimal places.) ___ mm

(b) By what additional amount does the cable increase in length if the object is accelerated upwards at a rate of 3.1 m/s2?
mm

(c) What is the greatest mass that can be accelerated upward at 3.1 m/s2 if the stress in the cable is not to exceed the elastic limit of the cable, which is 2.2 108 Pa?

Explanation / Answer

youngs modulus of steel = 200 * 10^9 N/m^2

youngs modulus = stress / strain

stress = force / area

stress = mg / area

stress = 700 * 9.8 / 0.0004

strain = change in length / original length

strain = change in length / 34

200 * 10^9 = (700 * 9.8 / 0.0004) / (change in length / 34)

elongation of the cable = 0.0029 m or 2.9 mm

if the object is accelerated by 3.1 m/s^2 then

200 * 10^9 = (700 * (9.8 + 3.1) / 0.0004) / (change in length / 34)

if the object is accelerated by 3.1 m/s^2 then elongation = 0.00383 m or 3.83 mm

2.2 * 10^8 = mass * (9.8 + 3.1) / 0.0004

mass = 6821.705 kg

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