Three balls A, B, and C, with masses of 3 kg, 1 kg, and 1 kg, respectively, are connected by massless rods. What are the coordinates of the center of mass?
and your thinking is....?
To find the coordinates of the center of mass for this system of balls, we need to consider both the masses and positions of the balls.
Since the rods connecting the balls are massless, we can treat the system as a point mass located at the center of mass.
The center of mass is the weighted average of the positions of the individual masses, where the weights correspond to their respective masses.
Let's label the coordinates of ball A as (x1, y1), ball B as (x2, y2), and ball C as (x3, y3).
The x-coordinate of the center of mass (CMx) is given by the formula:
CMx = (m1 * x1 + m2 * x2 + m3 * x3) / (m1 + m2 + m3)
where m1, m2, and m3 are the masses of balls A, B, and C, respectively.
Similarly, the y-coordinate of the center of mass (CMy) is given by the formula:
CMy = (m1 * y1 + m2 * y2 + m3 * y3) / (m1 + m2 + m3)
Plugging in the given masses:
m1 = 3 kg, m2 = 1 kg, m3 = 1 kg
We need to know the positions of the individual balls to calculate the center of mass. Please provide the x and y coordinates for each ball.