Basic Center of mass problem. Need assistance

In summary, the problem is asking for the mass of M3 when the center of mass of all three masses is at x=0. The x-coordinate of the center of mass is found using the equation \sum (mi)(xi)/(mi) with respect to x, but the value of x2 is unknown. By using the initial center of mass for the first two masses, the missing value of x2 can be found and the mass of M3 can be calculated. It is possible that the author meant to write "x-coordinate of the center of mass of the 3 masses is at x=0."
  • #1
blackbyron
48
0

Homework Statement


Two point-like masses have common center of mass located at (xc=2.1cm, yc=4.3cm). Mass M1=49kg is at (x1=65cm, y1). Mass M2=7.5kg is at (x2, y2=(-85)cm). A third mass M3 is placed at (x3=(-15.3)cm, y3=9.4cm). What is the mass of M3 if the x-coordinate of the center of mass of the 3 mass is at x=0?


Homework Equations



[tex]\sum (mi)(xi)/(mi)[/tex] with respect to x.

The Attempt at a Solution


Find out the mass of m3, but what does this mean "x-coordinate of the center of mass of the 3 mass is at x=0?"

I cannot solve for m3 because the x2 is unknown.

Any ideas?

Thanks
 
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  • #2
Find the missing value of x2 using the initial center of mass for the two first masses.

I think that they meant to write, "x-coordinate of the center of mass of the 3 masses is at x=0".
 
  • #3
Thanks for your reply. Yeah I was confused on "3 mass." I thought he meant the 3rd mass. But I just figured out because I admit that I didn't read it carefully though. However, thanks though, I appreciate it.
 

1. What is the definition of center of mass?

The center of mass is a point in an object or system where the entire mass of the object or system can be considered to be concentrated. It is the point at which the object or system will balance and rotate around.

2. How is the center of mass calculated?

The center of mass can be calculated by finding the sum of the products of each particle's mass and its distance from a chosen reference point, divided by the total mass of the object or system.

3. Why is the center of mass important in physics?

The center of mass is important in physics because it allows us to simplify complex systems and analyze the motion of objects. It helps us understand how an object will move and how forces will act on it.

4. What factors affect the location of the center of mass?

The location of the center of mass is affected by the distribution of mass in an object or system. It can also be affected by external forces, such as gravity, acting on the object or system.

5. How can center of mass problems be solved?

Center of mass problems can be solved using the principles of Newton's laws of motion and the concept of torque. By setting up and solving equations based on these principles and the given information, the center of mass can be determined for a given object or system.

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