A 2.5 m length of aluminum cable is to be used in an attempt to pull a car out of a ditch. The maximum tension that the cable will have to sustain is 1.5 x 104 N, and, to be on the safe side, only 1.0 x 10-3 m of cable stretch will be tolerated. What is the radius of the thinnest cable that should be used?

A 2.5 m length of aluminum cable is to be used in an attempt to pull a car out of a ditch. The maximum tension that the cable will have to sustain is 1.5 x 104 N, and, to be on the safe side, only 1.0 x 10-3 m of cable stretch will be tolerated. What is the radius of the thinnest cable that should be used?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 85PQ

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Concept explainers

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).

Question

A 2.5 m length of aluminum cable is to be used in an attempt to pull a car out of a ditch. The
maximum tension that the cable will have to sustain is 1.5 x 104 N, and, to be on the safe side,
only 1.0 x 10-3 m of cable stretch will be tolerated. What is the radius of the thinnest cable that
should be used?

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