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

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SUMMARY

The coordinate of M1 in a dumbbell system is determined using the formula M2 R / (M1 + M2), where R represents the distance between the two masses. The center of mass (CM) is calculated as CM = (R1m1 + R2M2) / (M1 + M2), leading to the relationship M1 R1 = -R2 M2. The distances R1 and R2 are directly related to the total distance R between the spheres, with R = R1 + R2, clarifying the positions of M1 and M2 relative to the CM.

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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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