a, b, and c 2.You are designing a part for a piece of machinery. The part consists of apiece of sheet metal cut as shown below. The shape of the upper edge of the partis given by y, (x), and the shape of the lower edge of the part is given by y2(x).Y1(x) = hy,(x)y2(x) = hb.dmTem,dmdxbYou are going to find the center of mass of the part. To find this, you must usecalculus by breaking the part into small mass elements, dm's, that have a centerof mass located at em dm as indicated in the above diagram. You will then use anintegral to sum up all of these small (differential) mass chunks. We will call themass density per area for the sheet metal o which you can assume is a constant. If you are wondering how o relates to the mass density per volume (this isnormally what you refer to as the density of an object), p, it would be that o =pw, where w is the thickness of the sheet metal.a. For the dm shown, what is the area dA of dm in terms of y1, Y2, dx? Weare essentially asking you for the area of the little rectangle that we arecalling dm. This is a very simple question so don't try to overcomplicate it.b. Because o is the mass per unit area, we can dm = odA. Use your answerfrom the previous part to write dm in terms of o, y,(x),y2(x), dx.c. Find the total mass of the part by adding up (integrating) all of the dm 's. Todo this, put everything in terms of x and compute the integral over x. Don'tforget about limits. You should find the answer to behbm = o=3d. The vector iem,.âm is the position of the center of mass of our dm. Writethis vector in component from in terms of y, and y2.e. We can now find the center of mass of our machine part by using thedefinition of the center of massTem: Fem.dm dmmSubstitute your expressions for Tem.dm and dm in terms of x and calculatethe integral to find the center of mass of the part. You should find theanswer to be9Tem(bî + hŷ)20

2. You are designing a part for a piece of machinery. The part consists of a piece of sheet metal cut as shown below. The shape of the upper edge of the part is given by y, (x), and the shape of the lower edge of the part is given by y2(x). Y:(x) = h{ Y2(x) = h () dm Tem,dm b You are going to find the center of mass of the part. To find this, you must use calculus by breaking the part into small mass elements, dm's, that have a center of mass located at rem dm as indicated in the above diagram. You will then use an integral to sum up all of these small (differential) mass chunks. We will call the mass density per area for the sheet metal o which vou can assume is a constant.

2. You are designing a part for a piece of machinery. The part consists of a piece of sheet metal cut as shown below. The shape of the upper edge of the part is given by y, (x), and the shape of the lower edge of the part is given by y2(x). Y:(x) = h{ Y2(x) = h () dm Tem,dm b You are going to find the center of mass of the part. To find this, you must use calculus by breaking the part into small mass elements, dm's, that have a center of mass located at rem dm as indicated in the above diagram. You will then use an integral to sum up all of these small (differential) mass chunks. We will call the mass density per area for the sheet metal o which vou can assume is a constant.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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