The strain in a wire can be monitored and computed by measuring the resistance of the wire. Let Li represent the original length of the wire, Ai its original cross-sectional area, Ri = ρLi /Ai the original resistance between its ends, and δ = ΔL/Li = (L - Li )/Li the strain resulting from the application of tension. Assume the resistivity and the volume of the wire do not change as the wire stretches. (a) Show that the resistance between the ends of the wire under strain is given by R = Ri (1 + 2δ + δ2). (b) If the assumptions are precisely true, is this result exact or approximate? Explain your answer.
The strain in a wire can be monitored and computed by measuring the resistance of the wire. Let Li represent the original length of the wire, Ai its original cross-sectional area, Ri = ρLi /Ai the original resistance between its ends, and δ = ΔL/Li = (L - Li )/Li the strain resulting from the application of tension. Assume the resistivity and the volume of the wire do not change as the wire stretches. (a) Show that the resistance between the ends of the wire under strain is given by R = Ri (1 + 2δ + δ2). (b) If the assumptions are precisely true, is this result exact or approximate? Explain your answer.
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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The strain in a wire can be monitored and computed by measuring the resistance of the wire. Let Li represent the original length of the wire, Ai its original cross-sectional area, Ri = ρLi /Ai the original resistance between its ends, and δ = ΔL/Li = (L - Li )/Li the strain resulting from the application of tension. Assume the resistivity and the volume of the wire do not change as the wire stretches. (a) Show that the resistance between the ends of the wire under strain is given by R = Ri (1 + 2δ + δ2). (b) If the assumptions are precisely true, is this result exact or approximate? Explain your answer.
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