Calculating Center of Mass: 2 Bodies, Unequal Masses

In summary, the problem involves two masses, m1 and m2, connected by a thread and a spring. When the thread is cut, the spring expands and pushes the masses. The goal is to find the highest height that m1 can reach. By using energy conservation and momentum conservation, it can be determined that the highest height is h_1 = (m_2U)/(gm_1(m_1+m_2)).
  • #1
supercali
53
0
[SOLVED] center of mass

Homework Statement


2 bodies m1 and m2 are hanged from the ceiling with a thread with length L. the bodies are also connected to one another with a thread which length is equal to the length from the masses to the hanging point. around that thread there is a spring contracted and its mass can be neglected. the potential eng. of the spring is U. at a certain moment the thread between the mass m1 and m2 is being torn and the spring pushes the masses. what is the hightest height that m1 can go up to relatively to the first place it was
attched a scheme of the problem

Homework Equations



The Attempt at a Solution


i thought of using the concept to center of mass and say that the center went up...but i don't really know how to implement this...
please help if you can
 

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  • #2
Hint: When the thread is cut and the spring expands, what is conserved? Find the speed/energy of m1 just after the spring expands.
 
  • #3
Doc Al said:
Hint: When the thread is cut and the spring expands, what is conserved? Find the speed/energy of m1 just after the spring expands.

the momntum is being conserved but my problem is kind of how to relate to m2 and its affect in the system
 
  • #4
That's right: The total momentum of m1 and m2 is conserved. What's the total energy of m1 and m2 after the expansion?
 
  • #5
according to the laws of energy the equation should be
[tex]h=\frac{U}{g(m_1+m_2)}[/tex]
i don't think this is the answer though
 
  • #6
It's not. How did you derive this answer?
 
  • #7
I did energy coservation...
again i find it hard with this m2 cause i don't really know what to do with it
with the momentum equation i hve 2 different speeds one of m1 and another of m2
maybe i didnt understand this well
 
  • #8
Show exactly how you did it. To do it correctly, you need both energy conservation and momentum conservation.
 
  • #9
woowowowo
without too many hints i must say you really helped me
the answer is
[tex]h_1=\frac{m_2U}{gm_1(m_1+m_2)}[/tex]

thanks
 

What is the definition of center of mass?

The center of mass is a point in a system where the entire mass of the system can be considered to be concentrated for the purpose of calculations.

How is center of mass calculated for two bodies with unequal masses?

The center of mass for two bodies with unequal masses can be calculated using the formula:
xcm = (m1x1 + m2x2) / (m1 + m2)
ycm = (m1y1 + m2y2) / (m1 + m2)
where m1 and m2 are the masses of the two bodies, and x1, x2, y1, and y2 are the respective coordinates of the bodies.

What is the significance of calculating center of mass?

Calculating the center of mass is important for understanding the overall motion and stability of a system. It can also be used to determine the point where an external force can be applied to cause a body to rotate without causing any translational motion.

Is the center of mass always located within the physical boundaries of the bodies?

No, the center of mass can be located outside the physical boundaries of the bodies, especially in cases where the masses are significantly different or the bodies are irregularly shaped.

How does changing the mass distribution of the bodies affect the center of mass?

Changing the mass distribution of the bodies will change the location of the center of mass. If the mass is distributed more towards one side, the center of mass will shift towards that side. However, the total mass of the system will always remain the same.

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