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# A steel rod 0.450 m long and an aluminum rod 0.250 m long, ## Problem 88P Chapter 17

University Physics | 13th Edition

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Problem 88P

A steel rod 0.450 m long and an aluminum rod 0.250 m long, both with the same diameter, are placed end to end between rigid supports with no initial stress in the rods. The temperature of the rods is now raised by 60.0 C°. What is the stress in each rod? (Hint: The length of the combined rod remains the same, but the lengths of the individual rods do not. See below.) Problem: (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 ?? ?, the stress is equal to Where ?F is the tension on the rod ?L?0 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 Figure. Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but stale what they are. Figure:

Step-by-Step Solution:

Solution 88P Introduction Since the total length is equal, the change in one rod will be equal to the change in other rod, (one will expand and other will contract). Also, since the rods will be in equilibrium, the stress in both side will be equal. Step 1 The stress on a rod due to temperature change of T and length change L is given by

Step 2 of 2

##### ISBN: 9780321675460

This textbook survival guide was created for the textbook: University Physics, edition: 13. The answer to “A steel rod 0.450 m long and an aluminum rod 0.250 m long, both with the same diameter, are placed end to end between rigid supports with no initial stress in the rods. The temperature of the rods is now raised by 60.0 C°. What is the stress in each rod? (Hint: The length of the combined rod remains the same, but the lengths of the individual rods do not. See below.) Problem: (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 ?? ?, the stress is equal to Where ?F is the tension on the rod ?L?0 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 Figure. Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but stale what they are. Figure:” is broken down into a number of easy to follow steps, and 216 words. University Physics was written by and is associated to the ISBN: 9780321675460. Since the solution to 88P from 17 chapter was answered, more than 264 students have viewed the full step-by-step answer. This full solution covers the following key subjects: rod, its, stress, length, temperature. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The full step-by-step solution to problem: 88P from chapter: 17 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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