Small changes in the length of an object can be measured

Chapter 18, Problem 4SL

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Problem 4SL

Small changes in the length of an object can be measured using a strain gauge sensor, which is a wire that when undeformed has length lo cross-sectional area A0, and resistance R0 This sensor is rigidly affixed to the object’s surface, aligning its length in the direction in which length changes are to be measured. As the object deforms, the length of the wire sensor changes by Δl. and the resulting change Δ R in the sensor’s resistance is measured. Assuming that as the solid wire is deformed to a length l its density and volume remain constant (only approximately valid), show that the strain (=Δl/lo) of the wire sensor, and thus of the object to which it is attached, is approximately Δ R/2R0. [See Sections 18–4 and 9–5.]