AP Physics 1 question

Question

A high-speed lifting mechanism supports an 800-kg object with a steel cable that is 25.0m long and 4.00cm^2 in cross-sectional area

a)Determine the elongation of the cable

b)By what additional amount does the cable increase in length if the object is accelerated upwards at a rate of 3.0m/s^2?

c)What is the greatest mass that can be accelerated upwards at 3.0m/s^2 if the stress in the cable is not to exceed the elastic limit of the cable, which is 2.2x20^8 Pa?

Answer 1

First find the stress which is Force/Area. (800kg)(9.81m/s^2)/(.0004m²) = 19,620,000 N/m² = 19,620,000 Pa

The strain = stress/E. E is 200GPa for steel so 19,600,000 Pa/200GPa = .0000981 m/m

a) elongation is strain x length. .0000981 m/m x 25m = .00245 m or 2.45mm

b) with 3 m/s^2 the additional stress is (800kg)(3)/.0004 = 6,000,000 Pa

the additional elongation is 6000000/200GPa x 25m = .00075 m or .75mm

c) max stress = 2.2x10⁸ Pa = m_max(9.81+3)/.0004. solve, m_max= 6870 kg