A guitar knob with a half-sphere dome top is going to be coated with a thin...
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A guitar knob with a half-sphere dome top is going to be coated with a thin layer of enamel paint. With the diameter of the dome at 19 mm, the desired thickness of the enamel is 0.05 cm. The picture is provided to help you visualize the knob. The "dome" on the knob in the picture is not a half-sphere, your imagination is required here. What to Do: 1. Use differentials to find the equation for the approximate volume of the enamel needed to cover the dome. 2. Determine the equation for the actual difference in volume between the painted surface and unpainted surface of the dome only. 3. Develop an Excel spreadsheet to determine the percent difference between the approximate change in volume and the actual change in volume based upon the thickness of the enamel, Ar. % difference approximation-actual actual 100% Your spreadsheet columns might look something like the following. thickness of paint layer Ar (in mm) D E F G H dv is % V actual 1 V actual 2 dV actual approxi difference mation difference <1.00% 0.25 1795.682 1941.21 145.528 141.76 2.58601% FALSE 4. Assign Ar increasing values in your spreadsheet. As Ar increases, determine the approximate value of Ar at which the percent difference first exceeds 1.00%. Your answer should be accurate to 2 decimal places. 5. Do all of your values for Ar seem reasonable for a layer of enamel paint in the real world? Explain your reasoning. 6. When would the approximation approach be an acceptable way and/or an easier way to calculate the volume of enamel paint needed? Explain your reasoning. 7. If you need assistance with entering equations for each column, ask your instructor or a person knowledgeable in use of spreadsheeting. A guitar knob with a half-sphere dome top is going to be coated with a thin layer of enamel paint. With the diameter of the dome at 19 mm, the desired thickness of the enamel is 0.05 cm. The picture is provided to help you visualize the knob. The "dome" on the knob in the picture is not a half-sphere, your imagination is required here. What to Do: 1. Use differentials to find the equation for the approximate volume of the enamel needed to cover the dome. 2. Determine the equation for the actual difference in volume between the painted surface and unpainted surface of the dome only. 3. Develop an Excel spreadsheet to determine the percent difference between the approximate change in volume and the actual change in volume based upon the thickness of the enamel, Ar. % difference approximation-actual actual 100% Your spreadsheet columns might look something like the following. thickness of paint layer Ar (in mm) D E F G H dv is % V actual 1 V actual 2 dV actual approxi difference mation difference <1.00% 0.25 1795.682 1941.21 145.528 141.76 2.58601% FALSE 4. Assign Ar increasing values in your spreadsheet. As Ar increases, determine the approximate value of Ar at which the percent difference first exceeds 1.00%. Your answer should be accurate to 2 decimal places. 5. Do all of your values for Ar seem reasonable for a layer of enamel paint in the real world? Explain your reasoning. 6. When would the approximation approach be an acceptable way and/or an easier way to calculate the volume of enamel paint needed? Explain your reasoning. 7. If you need assistance with entering equations for each column, ask your instructor or a person knowledgeable in use of spreadsheeting.
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Related Book For
Fundamentals Of Momentum Heat And Mass Transfer
ISBN: 9781118947463
6th Edition
Authors: James Welty, Gregory L. Rorrer, David G. Foster
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