How is the Coordinate of M1 Determined in a Dumbbell System?

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Homework Help Overview

The discussion revolves around determining the coordinate of M1 in a dumbbell system, specifically how it relates to the center of mass (CM) of the system. Participants are examining the equations and relationships that define the positions of the masses in relation to the CM.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the coordinates of the masses and the center of mass, questioning the definitions and formulas presented in the original post. There are discussions about the correct interpretation of the coordinates R1 and R2, and how they relate to the distance R between the spheres.

Discussion Status

The discussion is active, with participants providing insights into the equations for the center of mass and raising questions about the assumptions made regarding the coordinates. Some participants have offered alternative formulations and are clarifying the relationships between the variables involved.

Contextual Notes

There is mention of a specific formula from a book that differs from the one presented by the original poster, indicating a potential misunderstanding or miscommunication regarding the definitions of the variables involved. The discussion also highlights the importance of correctly interpreting the coordinates in relation to the center of mass.

rsaad
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Homework Statement



Attached is the picture of a dumbbell. I do not understand how the coordinate of M1 is
M2 R/ (M1 + M2)

It is not an assignment question but an example from a book.
 

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The origin is at the centre of mass. You certainly know how to determine the position of the CM?

ehild
 
CM= (R1m1+R2M2)/M1+M2
because CM=0, I get M1 R1 = -R2 M2
which further gives me
R1= RM2 / (M2-M1)

=|
 
rsaad said:
CM= (R1m1+R2M2)/M1+M2
because CM=0, I get M1 R1 = -R2 M2
which further gives me
R1= RM2 / (M2-M1)

=|

What do you mean on R1 and R2? If they are coordinates of the spheres with respect to the CM, the formula is correct, but use parentheses. (R1m1+R2M2)/(M1+M2)=0

How are R1 and R2 related to the distance R between the spheres?

ehild
 
R= R_1 + R_2
where R_i is the distance to M_i from CM.
 
In the book R_1 = R M2/ (M1 + M2) but mine is R1= R M2 / (M2-M1)
 
If x1, x2 are coordinates of m1, m2, respectively, the x coordinate of the CM is (x1m1+
x2m2)/(m1+m2).
If they are distances from the CM, the coordinate of m2 is negative: m1R1-M2R2=0

ehild
 
Last edited:

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