Elastic limits, cable elongation,acceleration, stress!Please be detailed so I can understand :-) Thank you!?

Question

A high-speed lifting mechanism supports a 730 kg object with a steel cable 36.0 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 upward at a rate of 3.4 m/s2?
____________mm
(c) What is the greatest mass that can be accelerated upward at 3.4 m/s2 if the stress in the cable is not to exceed the elastic limit of the cable, 2.2 108 Pa?
_______________ kg

Answer 1

Assume the Young's modulus of steel is 200 Gpa

Using the equation
E=(F/A)/(dL/L0)

dL=L0*F/(A*E)

I will ignore the mass of the steel cable for the first calculation

dL=36*730*9.81/
(200000000000*.0004)

dL=0.322 cm

Adding upward acceleration

dL=36*730*(9.81+3.4)/
(200000000000*.0004)

dL=0.434 cm

the elastic limit
220000000=
m*(9.81+3.4)/.0004

m=6,660 kg

j

Answer 2

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