Question

gether four smaller square plates, each of side a. The weight of each of the four plates is shown in the figure. (2a, 2a) (0,2a) 30 N 30 N 70 N 40 N (0,0) Find the -coordinate of the center of grav (2a, 0) ity (as a multiple of a). Answer in units of a. 010 (part 2 of 2) 10.0 points Find the y-coordinate of the center of gravity (as a multiple of a) Answer in units of a.

Answer 1

Given that w_1 = 30 N, (x_1 y_1) = (a/2, 3a/2) w_2 = 30 N, (x_2 y_2) = (3a/2, 3a/2) w_3 = 70 N, (x_3 y_3) = (a/2, a/2) w_4 = 40 N, (x_4 y_4) = (3a/2, a/2) Now x_cm = w_1 x_1 + w_2 x_2 + w_3 x_3 + w_4 x_4/w_1 + w_2 + w_3 + w_4 = (30 times a/2) + (30 times 3a/2) + (70 times a/2) + (40 times 3a/2)/30 + 30 + 70 + 40 = 0.912 a y_cm = w_1 y_1 + w_2 y_2 + w_3 y_3 + w_4 y_4/w_1 + w_2 + w_3 + w_4 = (30 times 3a/2) + (30 times 3a/2) + (70 times 9/2) +(40 times 9/2)/30 + 30 + 70 + 40 y_cm = 0.853 a