Answered: When the pioneers where crossing the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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When the pioneers where crossing the plains in covered wagons, a metal rim could be attached to a wagon wheel by heating the rim to expand it and then placing it over the wheel before it cooled. the shrink-attachment would firmly hold the rim in place and strengthen the wooden wheel. Suppose a certain wooden wagon wheel has an outer circumference of 300.0cm and that its iron rim an inside circumference of 299.5 cm when it is 15 degrees C. To what temperature must the rim be heated so that it will just fit over the wheel?

Expert Solution

Step 1 :Introduction

The change in length due to thermal expansion is calculated by using the formula $L_{f} - L = α L (T_{f} - T_{i})$ , where $L_{f} = 300 c m$ is the final length , $L = 299.5 c m$ is the initial length , $α = 11.8 \times 10^{- 6} / ° C$ is the thermal linear coefficient , $T_{f}$ is the final temperature and $T_{i} = 15 ° C$ is the initial temperature .

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