Velocities seen from the center of mass

[dapias09]

Hello all,

I'm confused with the center of mass concept. Regard the following problem, we have a spring with negligible mass joined to two masses m1 and m2 (m1=m2) on a table without friction force. At t=0 a thrust Vo (initial velocity) is given to m2 with direction perpendicular to the spring direction (see figure adjoint). How are the velocities at t=0 seen from the center of mass?

At t=0 the m1 velocity seen from the laboratory is zero but this particle isn't fixed on the table.

Well, I guess that I should calculate the velocity of the center of mass as:
Vcm = m1V1 + m2V2 / (m1 + m2) = m2V2 / (m1 +m2) = Vo / 2, since m1 and m2 are equals.

So the initial situation is equivalent to give a thrust to the center of mass with velocity Vo/2, but how I know what are the velocities of m1 and m2 seen of the center of mass?

Can anyone help me?

Thanks in advance.

 

[James_Harford]

Hello all,

I'm confused with the center of mass concept. Regard the following problem, we have a spring with negligible mass joined to two masses m1 and m2 (m1=m2) on a table without friction force. At t=0 a thrust Vo (initial velocity) is given to m2 with direction perpendicular to the spring direction (see figure adjoint). How are the velocities at t=0 seen from the center of mass?

At t=0 the m1 velocity seen from the laboratory is zero but this particle isn't fixed on the table.

Well, I guess that I should calculate the velocity of the center of mass as:
Vcm = m1V1 + m2V2 / (m1 + m2) = m2V2 / (m1 +m2) = Vo / 2, since m1 and m2 are equals.

So the initial situation is equivalent to give a thrust to the center of mass with velocity Vo/2, but how I know what are the velocities of m1 and m2 seen of the center of mass?

Can anyone help me?

Thanks in advance.

Ask yourself, instead, what are the velocities of m1 and the center of mass seen from m2. If you can figure that out for m2, use the same method for the center of mass.

 

[dapias09]

Good idea!, James, thank you.

Just to check, isn't it -Vo for m1 and -Vo/2 for the center of mass seen from m2?
In this way, I have another question, do you know what should I do if the masses (m1 and m2) are different.

Greetings.

 

[James_Harford]

Good idea!, James, thank you.

Just to check, isn't it -Vo for m1 and -Vo/2 for the center of mass seen from m2?
In this way, I have another question, do you know what should I do if the masses (m1 and m2) are different.

Greetings.

In regards to your first question, if they are not, what does that say about the principle of (Galilean) relativity?

In regards to your second, clearly, the center of mass speed needs to be recalculated. The rest is the same as before :)