Question

PART ONE

A square plate is produced by welding together four smaller square plates, each of side
a. The weight of each of the four plates is
shown in the figure.
Find the x-coordinate of the center of gravity (as a multiple of a).
Answer in units of a.
(PICTURED)

PART TWO
Find the y-coordinate of the center of gravity
(as a multiple of a).
Answer in units of a

Answer 1

Step-by-step explanation:

Make a table, listing the x and y coordinates of each square's center of gravity and its mass. Multiply the coordinates by the mass, add the results for each x and y, then divide by the total mass.

`\left\begin{array}{ccccc}x&y&m&xm&ym\\(a)/(2) &(a)/(2) &10&5a&5a\\(3a)/(2)&(a)/(2)&70&105a&35a\\(a)/(2)&(3a)/(2)&80&40a&120a\\(3a)/(2)&(3a)/(2)&50&75a&75a\\&\sum&210&225a&235a\\&&Avg&(15a)/(14)&(47a)/(42)\end{array}\right`

The x-coordinate of the center of gravity is 15/14 a.

The y-coordinate of the center of gravity is 47/42 a.