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A Capacitive Scale. You and your team are tasked with finding a way to electronically measure weight. You get the idea to measure the capacitance between two circular conducting plates of mass m = 0.112 kg and radius r = 11.5 cm separated by a nonconducting vertical spring of spring constant k = 1.35 x 104 N/m and unstrained length do = 3.55 cm. The idea is that the object whose weight is to be determined is placed on the upper plate, thereby compressing the spring and bringing the two plates closer together. This, in turn, changes the capacitance. An electronic instrument that measures capacitance is interfaced with a computer that records the capacitance of the plates and converts it to weight. (a) Your task is to derive an equation for the weight in terms of the capacitance that the computer will use to convert the measured capacitance to weight (in N). Enter your answer in terms of Wo - the weight of the upper plate, C- the capacitance of the capacitor, the variables given above and the fundamental constants. You can neglect any electrostatic forces between the plates of the capacitor. (b) What is the weight of an object placed on the upper plate that results in a measured capacitance of 16.3 pF? Enter your answer with 3 significant digits.

A Capacitive Scale. You and your team are tasked with finding a way to electronically measure weight. You get the idea to measure the capacitance between two circular conducting plates of mass m = 0.112 kg and radius r = 11.5 cm separated by a nonconducting vertical spring of spring constant k = 1.35 x 104 N/m and unstrained length do = 3.55 cm. The idea is that the object whose weight is to be determined is placed on the upper plate, thereby compressing the spring and bringing the two plates closer together. This, in turn, changes the capacitance. An electronic instrument that measures capacitance is interfaced with a computer that records the capacitance of the plates and converts it to weight. (a) Your task is to derive an equation for the weight in terms of the capacitance that the computer will use to convert the measured capacitance to weight (in N). Enter your answer in terms of Wo - the weight of the upper plate, C- the capacitance of the capacitor, the variables given above and the fundamental constants. You can neglect any electrostatic forces between the plates of the capacitor. (b) What is the weight of an object placed on the upper plate that results in a measured capacitance of 16.3 pF? Enter your answer with 3 significant digits.

College Physics
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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A Capacitive Scale. You and your team are tasked with finding a way to electronically measure weight. You get the idea to measure the capacitance between two circular conducting plates of mass m = 0.112 kg and radius r = 11.5 cm separated by a nonconducting vertical spring of spring constant k = 1.35 × 104 N/m and unstrained length do = 3.55 cm. The idea is that the object whose weight is to be determined is placed on the upper plate, thereby compressing the spring and bringing the two plates closer together. This, in turn, changes the capacitance. An electronic instrument that measures capacitance is interfaced with a computer that records the capacitance of the plates and converts it to weight. (a) Your task is to derive an equation for the weight in terms of the capacitance that the computer will use to convert the measured capacitance to weight (in N). Enter your answer in terms of Wo - the weight of the upper plate, C- the capacitance of the capacitor, the variables given above and the fundamental constants. You can neglect any electrostatic forces between the plates of the capacitor. (b) What is the weight of an object placed on the upper plate that results in a measured capacitance of 16.3 pF? Enter your answer with 3 significant digits. (a) W (b) W N
Transcribed Image Text:A Capacitive Scale. You and your team are tasked with finding a way to electronically measure weight. You get the idea to measure the capacitance between two circular conducting plates of mass m = 0.112 kg and radius r = 11.5 cm separated by a nonconducting vertical spring of spring constant k = 1.35 × 104 N/m and unstrained length do = 3.55 cm. The idea is that the object whose weight is to be determined is placed on the upper plate, thereby compressing the spring and bringing the two plates closer together. This, in turn, changes the capacitance. An electronic instrument that measures capacitance is interfaced with a computer that records the capacitance of the plates and converts it to weight. (a) Your task is to derive an equation for the weight in terms of the capacitance that the computer will use to convert the measured capacitance to weight (in N). Enter your answer in terms of Wo - the weight of the upper plate, C- the capacitance of the capacitor, the variables given above and the fundamental constants. You can neglect any electrostatic forces between the plates of the capacitor. (b) What is the weight of an object placed on the upper plate that results in a measured capacitance of 16.3 pF? Enter your answer with 3 significant digits. (a) W (b) W N
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