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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 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.

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter20: Electric Potential And Capacitance
Section: Chapter Questions
Problem 47P: According to its design specification, the timer circuit delaying the closing of an elevator door is...
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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 då = 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 då = 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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