# Calculate the difference in resistance between the resistance at each length and the resistance before strain is added.

1. Mechanical Sensors Work the problems below. To receive any credit, you must show all work. You may submit your work in a word processing document or in a pdf file. Graphic files are not acceptable submissions. 1. A copper metal wire is used as a strain gauge. The resistivity is 1.68×10-8 Ω.m at 20. The length and cross-sectional area of the wire are 5mm and 4*10-4 m2. The material elongates by an amount of 0.2mm in 0.2mm increments until it reaches 6mm in length. Assuming the volume remains constant, calculate the resistance at each length. You should use the standard equation for the resistance of a metal. What is that equation? Fill in the table below. Show all calculations. Calculate the difference in resistance between the resistance at each length and the resistance before strain is added. Also, calculate the change in resistance using the approximation found in equation 5.12 of your text. How does the change in length change the resistance of the gauge? Is it linear? Why or why not? (You can use Excel to create a plot and paste it in your submission if you want?) How good is the approximation? Length Cross-sectional area Resistance Initial resistance (at 5mm) Change in the resistance Change in resistance using Eq.5.12 5mm 5.2mm 5.4mm 5.6mm 5.8mm 6mm 2. A tensile force of 2150 N is applied to a 12 m steel beam with a cross-sectional area of 5.2 x 10-4 –m2. Find the strain on the beam. 3. A strain gauge has a GF (Gauge factor) = 2.03 and R = 110 ohms and is made from wire with =0.0035/ at 25. The dissipation factor is given as PD = 20mW/. What is the maximum current that can be placed through the strain guage to keep self-heating errors below 1 of strain. 4. The atmospheric pressure is 14.5 psi. If the absolute pressure is 2,865.6 psfa, what is the gauge pressure? 5. What is the gauge pressure in (a) kPa, and (b) N/cm2, at a distance 5.5 ft below the surface of a column of water? 6. What is the flow rate in liters per second through a pipe 32 cm in diameter, if the average velocity is 2.1 m/s? 7. A conveyer belt is traveling at 27 cm/s, and a load cell with a length of 0.72m is reading 5.4 kg. What is the flow rate of the material on the belt?

1. Mechanical Sensors Lab 1. A capacitive displacement sensor is used to measure rotating shaft wobble shown in the figure below. The capacity is 520 pF with no wobble. Find the change in capacity for a +0.035 to -0.035 mm shaft wobble. Show your calculations.

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2. To measure the displacement, assume that the capacitive pickoff in problem 1 is used in an AC bridge constructed of only capacitors. Using 520pF for the bridge capacitors, find the offset bridge voltage for the two extremes of shaft wobble. Assume a sine wave voltage input having an amplitude of 5 Vrms and a frequency of 5 kHz. Rather than using an equation from the book, you are required to derive the offset bridge voltage using circuit analysis principles. Show all your calculations. 3. Using Multisim, construct and simulate the AC bridge of problem 2 for the two extreme conditions. Be sure to provide screenshots. Also, write a brief summary, noting if the results matched expected results.

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