A high-speed lifting mechanism supports a 845-kg object with a steel cable that

Question

A high-speed lifting mechanism supports a 845-kg object with a steel cable that is 40.0 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 2.6 m/s2? =___________mm (c) What is the greatest mass that can be accelerated upward at 2.6 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

a)at rest tension in the cable equals the weight of 845kg

F=mg =845*9.8 =8281 N

Y =FLo/AL
the initial elongation of the cable is

L = FLo/AY

L =8281*40/(4*10-4)*(20*1010) =4.14*10-3m =4.14mm

b)from newtons second law

F-mg =may------1

F=m(g+ay) =845(9.8+2.6) =10478N

L = FLo/AY =10478*40/4*10-4*20*1010

L =5.24*103m =5.24mm

thus the increase in elongation has been

increase =5.24-4.14 =1.1mm

c)the maximum tension ,the cable can withstand is

Fmax =A*stressmax =4*10-4*2.2*108 =8.8*104N

from 1

mmax = Fmax/(g+ay) =8.8*104/(9.8+2.6) =7096.8Kg

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