Question

Four objects are situated along the y axis as follows: a 2.09-kg object is at +2.97 m, a 2.93-kg object is at +2.53 m, a 2.57-kg object is at the origin, and a 3.92-kg object is at -0.496 m. Where is the center of mass of these objects?

Answer 1

x = 0 m

y = 1.02 m

Step-by-step explanation:

M1 = 2.09 kg

y1 = 2.97 m

M2 = 2.93 kg

y2 = 2.53 m

M3 = 2.57 kg

y3 = 0 m

M4 = 3.92 kg

y5 = -0.496 m

since all objects are situated on the Y-axis, this means the x coordinate of the center of mass is 0.

To find the y coordinate of the center of mass, we apply the equation below.

sum of moment of the objects about the origin = moment of the total mass of objects about the center of mass

M1.y1 + M2.y2 + M3.y3 + M4.y4 = Mt.Y

(2.09 x 2.97) + (2.93 x 2.53) + (2.57 x 0) + (3.92 x -0.496) = (2.09 + 2.93 + 2.57 + 3.92) Y

11.68 = 11.51 Y

Y = 11.68 / 11.51 = 1.02 m