Question

The bricks are homogeneous and have the same mass. Each brick is 5.00 cm

along the short side and 10.00 cm along the long side. The coordinates of the
center of mass of the following bricks is

Answer 1

(5/3,-5/6) or (1.67, -0.83)

Step-by-step explanation:

the center if there are 4 bricks is the point 0,0 or intersection of the two arrow.

if we remove one on the top left, with the center of the mass in (-5,2.5), the the new coordinates of the center of mass can be found like this

x = A1 x1 - A2 x2 / (A1 - A2)

x = new coordinate of the system

A1 is the Area of 4 bricks = 20 x 10 = 200 cm²

A2 is the Area of 1 brick we remove, the top left = 10 x 5 = 50 cm²

x1 = the x coordinate of the center of mass when there are 4 bricks, x = 0

x2 = the x coordinate of the center of mass of the remove brick, x = -5

x = (200 . 0) - (50 . (-5))/(200 - 50)

x = - (-250) / 150

x = 250/150 = 5/3 = 1.67 cm

we can find the value y of the new coordinate, the same way we find x

y = A1 y1 - A2 y2 / (A1 - A2)

y = (200 . 0) - (50 . 2.5) / (200-50)

y = - 125/150

y = -5/6 = -0.83 cm