How Do You Calculate the Center of Mass for a Three-Mass System?

[gflores]

I'm having a difficult time with this question, and I'm sure it's easy. The question is, find the center of mass of the three-mass system. Specify relative to the left-hand 1.00kg mass.
Mass1 = 1kg Distance = 0m?
Mass2 = 1.5kg Distance = .50m
Mass3 = 1.1kg Distance = .75m

I'm having trouble because when you use the equation
CoM = (m1x1 + m2x2 + m3x3)/(m1+m2+m3), the first m1x1 becomes 0 and I'm sure that's not right.

 

[SpaceTiger]

I'm having trouble because when you use the equation
CoM = (m1x1 + m2x2 + m3x3)/(m1+m2+m3), the first m1x1 becomes 0 and I'm sure that's not right.

No, that's fine. What do you get?

 

[thepatientmental]

The center of mass of a three-mass system can be found by using the equation:

CoM = (m1x1 + m2x2 + m3x3)/(m1+m2+m3)

In this case, the first mass (1kg) is located at a distance of 0m from the left-hand mass. This means that its contribution to the center of mass calculation will be 0. Therefore, the equation becomes:

CoM = (0 + 1.5kg x 0.50m + 1.1kg x 0.75m)/(1kg + 1.5kg + 1.1kg)

= (0 + 0.75kgm + 0.825kgm)/(3.6kg)

= 1.575kgm/3.6kg

= 0.4375m

This means that the center of mass of the three-mass system is located at a distance of 0.4375m from the left-hand 1kg mass. This is the answer to the question "find the center of mass of the three-mass system, specified relative to the left-hand 1.00kg mass."

I understand that the first term in the equation may seem confusing, but it is important to remember that the center of mass is a point where the entire mass of the system can be considered to be concentrated. In this case, since the first mass is located at 0m, it does not contribute to the calculation of the center of mass. I hope this explanation helps you understand the concept better.