   Chapter 9, Problem 73P

Chapter
Section
Textbook Problem

A high-speed lifting mechanism supports an 800.-kg object with a steel cable that is 25.0 m long and 4.00 cm2 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 upward at a rate of 3.0 m/s2? (c) What is the greatest mass that can be accelerated upward at 3.0 m/s2 if the stress in the fable is not to exceed the elastic limit of the cable, which is 2.2 × 108 Pa?

(a)

To determine
The elongation of the steel cable.

Explanation
The definition of Young’s modulus is used for the elongation of the steel cable that is Y=(F/A)/(ΔL/L0)ΔL=(mgL0)/(AY) .

Given info: The mass of the object is 800kg , acceleration due to gravity is 9.80m/s2 , cross-sectional area of the steel cable is 4.00cm2 , length of the cable is 25.0m , and the Young’s modulus of the cable is 20.0×1010Pa .

The formula for the elongation of the steel cable is,

ΔL=mgL0AY

• m is mass of the object.
• g is acceleration due to gravity.
• L0 is length of the cable.
• A is area of the steel cable.
• Y is Young’s modulus of the cable.

Substitute 800kg for m , 9

(b)

To determine
The additional the cable increases in length if the object is accelerated upward.

(c)

To determine
The greatest mass that can be accelerated upward if the stress in the cable is not exceeding the classical limit of the cable.

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