Question

What is the position of the center of mass of the part? 6 point (s) m 2D Moment of Inertia 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 y1(x), and the shape of the lower edge of the part is given by y2(x) You are correct. Your receipt no. is 158-2419 Now you will find the total moment of inertia about the r axis. There are at least two ways to find this. You can try and find it by using an integral with respect to x. This way turns out to by much more difficult than setting up an inte gral expression with respect to y instead y2(r)=h you set up this integral with respect to y, you should no- tice that the expression for the moment of inertia about the x axis is very similar to the expression for the moment of in- ertia about the y axis. If you think about this in the correct way, then you can actually figure this integral out with the work you have already done for Iy and not have to integrate again where h 8.6 m, d = 2.1 m, and the density of the sheet metal o 8.7 kg/m2 Remember that the integration variable is arbitrary for a def inite integral, as it is summed over when calculating the in- tegral. So you are allowed to make the replacement y--x Also, if you make the replacements h--d and d-h, then the expression for , would be exactly the same as that for Iy. So you should be able to make these replacements in your final equation for Iy to give you the final equation for I. У,(к) h dm Enter the numerical value for vour I, below. I = y(x) You are correct. Your receipt no. is 158-5099 Now find the y position of the center of mass. The same procedure used to relate I, to I can be used to relate ycm to rm х dx Yem You are going to calculate the total mass, moment of inertia about the y axis, and center of mass of the part Incorrect. Tries 3/15 Printed from LON-CAPASMSU Licensed under CNU General Publie License To make sure you get started on the right foot, what is dm in terms of , d, h, a,yi(x),y2(x) and dr? Note: This is the only part that is asking for a symbolic, rather than numerical, answer dm = You are correct. Your receipt no. is 158-3614 of the part? What is the total ma m= Incorrect Tries 4/15 What is the moment of inertia of the part about the y axis? Iy

Answer 1

dm = 629 (2) - Y, (x) dx = 6hhe (2 h ( 7 ) &dx 200 - Go24c35" a c3 14 de =ch lice ) (3.dx > m = 6h 14 d - ] =) m = thx d = 8.7x8.6 x x 2.1 = m = 94.3 kg 5x = (szem (21.33"-23"} => y = c [isch is the copy = 6h [id- * d*] = saxlaya =) ly = 8.7X8.6 x 18 x (2.1)3 = 114.2 kg m² Iy = 114.2 kg m² /

Yem = 4 (R) - 4 (4 am (a) - (x) dm Tcm = Ycm S (6) = (*% (%(x) = 4,(x) )dx 2 [{y (0) - 2 (a) 8 de - 1 tuligi yo_ 4 Cafj'az et (5)*+()*2 (33%830 3/2 ] Yem a chan (1 sat as dry Ycm = 2 + ( a -d] = 3.5m Ycm = 3.5m] 2m