Question

4. Two students were asked to find the center of mass of a thin plate of constant density 8 covering the region bounded above by y = x - 22 and below by y = -2. The center of mass of a typical vertical strip is represented by (6,5) (see figure). Both students agree that the mass differential dm = 8 dA = density. length width should be dm = 8. (-)-(-x).da. (a) Student 1 claims that (č, ) is (, ((x – x2] - [ - x)). Student 2 claims that (m, ) is (a, »–7*#1 =). Which student is correct and why? (b) The x-coordinate of the center of mass is 1. Calculate the y-coordinate of the center of mass.

Answer 1

Answer :- o Given, Constant density = 8 y = 1-2 2 the mass differential dm = 8 d A dm = 8. ([r - 72 ] - [+]) , dr. (a) Student2 = (1,9). (*)(11-**]-[-1]) student 2 (x, y) = (x) [x-x²] + [-2] 2451] student 'al is correct becos, mid point of strip fce) +91) +(x) - 3(x) length of the strip, 'y-coordinate of the center of moss. y % [1419)+603) as $64 ) - 914) d. ab Inteosecting Anteo secting points X-X-Y a A x²9x=0 *(x-2)=0 x2 0,2

Area A 2-x² - (-2) dy 2 2 (22-2²) dx . 2. 2 JD 4 - 8 3 3 y 2 3 S (x-7)= x² dx Se (x + x 4 - 2 x 3 x) dx 3 D 2 اكسا 3 25 7 2x 0 3 (95-24 2x (234 32 3 ( 2 oow