2 part center of mass problem?
In the figure the red ball has a mass of 5.8 kg and the blue ball of 5.5 kg. To two decimal places what is XCM?
In the previous problem what is YCM?
image link to figure:
In the figure the red ball has a mass of 5.8 kg and the blue ball of 5.5 kg. To two decimal places what is XCM?
In the previous problem what is YCM?
image link to figure:
Comments
x(cm) = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
with respect to point (0,0)
x(cm) = [(1*1) + (2*5.8) + (3*5) + (5*5.5)] / (1 + 5.8 + 5 + 5.5)
x(cm) = 3.185
y(cm) = [(1*1) + (2*5.5) + (3*5.8) + (4*5)] / (1 + 5.5 + 5.8 + 5)
y(cm) = 2.855
To calculate center of mass, what you must do is multiply each individual mass with the position vector to that mass. Then add it up, and divide by total mass.
In this problem, there are four masses. Thus the equations you set up are:
xcm = (m1*x1 + m2*x2 + m3*x3 + m4*x4)/(m1 + m2 + m3 + m4)
ycm = (m1*y1 + m2*y2 + m3*y3 + m4*y4)/(m1 + m2 + m3 + m4)
Data:
Note: du stands for "distance unit". I'm not sure what distance units are intended, so I am keeping it arbitrary.
m1 = 1 kg
x1 = 1 du
y1 = 1 du
m2 = 5.8 kg
x2 = 2 du
y2 = 3 du
m3 = 5 kg
x3 = 3 du
y3 = 4 du
m4 = 5.5 kg
x4 = 5 du
y4 = 2 du
Results:
xcm = 3.18 du
ycm = 2.86 du