Question

I am confused why there are two blocks to fill up. Someone help

A square aluminum plate volume mass ρ-2700 kg/m3 has dimension L 4.1 m and e 02 m A cylinder of radius R-o.5 m and at a distance d 02 m from the center of the plate and at 55 deg with the horizontal, is removed from the plate. Find the centre of mass of this plate from the lower left corner. Note the centre of mass about for the z-axis is neglected in the answer, since it is obviously at e/2. Don't forget to remove the cylinder from the plate 2.0681 m 608 m Submit AnswerIncorrect. Tries 1/99 Previous Tries

Answer 1

Length of the square (l) = 4.1m Density = 2700kg/m^3 width (e) = 0.2m Radius of cylinder (R) = 0.5m Centre of square (2d) = 2 times 1.025 = 2.05m Mass of square aluminum plate M_s = density times volume = 2700 times (l)^3 = 2700 times (4.1)^3 M_s = 186086.7 kg similarly Mass of cylinder = M_c = Density times volume = 2700 times pi r^2 h (because volume of cylinder = pi r^2 h) = 2700 times 3.14 times (0.5)^2 times (0.2) (because h = e) M_c = 423.9kg Area of square A_s = (l)^2 = (4.1)^2 A_s = 16.81m^2 \r\n Area of circle A_c = pi r^2 = 3.14 times (0.5)^2 A_c = 0.785m^2 centre of mass = M_s (2d) - M_c R/M_s - M_c = 180686.7 times 2.05 - 423.9 times 0.5/186086.7 - 423.9 COM = 381477.735 - 211.95/185662.8 = 2.053m also since the mass is proportional to area therefore centre of mass A_s (2d) - A_c (R)/A_s - A_c Here A_s and A_c are area of square and circle respectively. = 16.81 times 2.05 - 0.785 times 0.5/16.81 - 0.785