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Physics / University Physics 13 / Chapter 17 / Problem 85P

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

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(a) Equation (17.12) gives the stress required to keep the

Chapter 17, Problem 85P

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QUESTION:

(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount ?L when its temperature changes by ?T, the stress is equal to where F is the tension on the rod, L0 is the original length of the rod, A its cross-sectional area, ? its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends (?Fig. P17.79?). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20o C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140o C? Make any simplifying assumptions you think are justified, but state them.

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QUESTION:

(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount ?L when its temperature changes by ?T, the stress is equal to where F is the tension on the rod, L0 is the original length of the rod, A its cross-sectional area, ? its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends (?Fig. P17.79?). Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20o C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140o C? Make any simplifying assumptions you think are justified, but state them.

ANSWER:

Problem 85P

(a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount when its temperature changes by . The stress is equal to

where F is the tension on the rod, is the original length of the rod, A its cross-sectional area, its coefficient of linear expansion, and Y its Young’s modulus. (b) A heavy brass bar has projections at its ends, as in Fig. P17.85. Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20 degree celsius What is the tensile stress in the steel wires when the temperature of the system is raised to 140 degree celcius Make any simplifying

assumptions you think are justified, but state what they are.

Step by Step Solution

Step 1 of 4

(a)

Given:

Original length of the rod:

Tension in the rod:

Change in temperature:

Coefficient of linear expansion of steel:

Coefficient of linear expansion of brass:

Youngs modulus of steel:

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