Question

Question A thin plate has been bent so as to take the shape of the area pasameleared by R (av) = (2-4 Joos fu? tujt (2-us en (v) & with - 1 4 UK 1 and OSVK 2T Si The density of the plate is proportional to Ho C distance to its left end ; that is, the plane ly= Determine the center of mass of the plate

Answer 1

R(u, v) (2-4) cosv + uſ +(2-42) sau R-12051 and Scary, 2) Ocvs QTI K(4+1) mass - N - SS Schy, z) ds Sol s(Ř (4N)) 11 Rux Rull da S Scary, 2) K (4+1). = K (ute) Rux R = دے -ucas vê + Fucosu t using Jezi usinu Rv |-(2-4 sinu o fwy casu -(2-42) sinvî + 0 +(2-4) cos vr = (2-44) singu? +(2-4²) 11 Řu x Rull = √ (2-42 )(es ut sin v) + I) +(2-6?) siu v R. I for we of budu a sex - 2-42 2 M = QT (42424 - 4 dv ó 1. M = 11 J2 K [v 223 K. at t M(E)= Myz =+ (XS(x, y, z) ds. = [2k ar #5(2-42 ) {c+1) casv dudy Su + w _ 24?) (uti) day du ㅗ = cos v J2k 97 M Tak Spa p cas vodu. constant let P. M [2kp (sinv) 0. =) M MCT) QT = 52k (u²+4) (2-42) du du 211 9TL M(X) = 0 - Macz M M 3 10 o 3 x 17 x 27 22 ME) 2 TL 15 - 17T May √2K 17T 1185 sinu (u +4 - 24² 2 (4+1) du dv. 55 ss sinu (u m an no need to integrate because we kuocs it will be a constant and of Sinudu so (i) = M(X, Y , Z ) (0, 17-21,0) day