Center of mass with one object moving

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Homework Help Overview

The problem involves two objects on a stick, where one object is stationary and the other can slide. Both objects have equal mass, and the stick is considered to have negligible mass. The discussion centers around calculating the center of mass (COM) of the system, particularly focusing on the implications of the moving object and its initial position.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula for the center of mass and the need to consider the initial position of the moving mass. There is a focus on the integration of velocity over time and how it affects the calculation of the COM.

Discussion Status

Participants are exploring the implications of their equations and assumptions. There is acknowledgment of the importance of the initial position of the moving mass, and some participants express uncertainty about the conceptual aspects of the problem. Guidance has been offered regarding the integration and initial conditions, but no consensus has been reached.

Contextual Notes

One participant notes that the problem is hypothetical, which may contribute to the uncertainty in the discussion. There is an emphasis on understanding the conceptual framework rather than deriving a definitive solution.

DrummingAtom
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Homework Statement



Two objects are on a stick where one is stuck in place and the other one can slide. Both objects have the same mass and the stick has negligible mass.

Homework Equations



[tex]COM = \frac{m_1 x_1 + m_2x_2}{m_1+m_2}[/tex]
[tex]v_1 = t[/tex]

The Attempt at a Solution



[tex]COM = \frac{m_1 \int v_1 + m_2x_2}{m_1+m_2}[/tex]

Would this be correct assuming that the starting point for measuring x1 and x2 would be the left side? Thanks
 

Attachments

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I would be a little careful here. You need to know the initial position of the moving mass:
[tex]\frac{m_1\left (\int v_1(t) \,dt +x_1(0) \right ) + m_2x_2}{m_1+m_2}[/tex]
where x_1(t) is a function of time and x_1(0) is the constant of integration.
 
Last edited:
RoshanBBQ said:
I would be a little careful here. You need to know the initial position of the moving mass:
[tex]\frac{m_1\left (\int v_1(t) \,dt +x_1(0) \right ) + m_2x_2}{m_1+m_2}[/tex]
where x_1(t) is a function of time and x_1(0) is the constant of integration.

Thanks for responding. Ahh yes good point. Adding your part, would that be correct? I just made up the problem which is why I'm a little unsure of the conceptual part.
 
DrummingAtom said:
Thanks for responding. Ahh yes good point. Adding your part, would that be correct? I just made up the problem which is why I'm a little unsure of the conceptual part.

I believe it is all right. The equation gives the center of mass as a function of time.
 
Ok cool. Thanks for your help. By the way.. Roshan from DotA? :wink:
 
DrummingAtom said:
Ok cool. Thanks for your help. By the way.. Roshan from DotA? :wink:

Yes. DotA 2 now.
 

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