How Does Mass Influence the Velocity of the Center of Mass?

[something_about]

Center of mass and its speed

hi,I'm not shure if this belongs in math section or here

The center of mass is special point in body and is moving as if whole mass was in it.

Velocity of center of mass V(C)= ( m1*v1 + m2*v2... )/(m1 + m2...)

V(c) is in a way an average speed of all the individual speeds bodies in the system have. Value of V(C) depends most on the mass of individual objects in a system. If system contains one very massive body and several others with small mass, then value of V(c) will be very close to the speed of a body with large mass.


It does make some sense,but I'm looking at formula
V(C)= ( m1*v1 + m2*v2... )/(m1 + m2...) and can't figure out how does that work out in this formula. If M1 has very large mass and speed V1 smaller approx. by factor 100 from speeds of other bodies, why would formula for V(C) give result that is closer to V1 than say to V2 and V3 ?

thank you in advance

 

[Tide]

It might help to think about it this way: What happens to the center of mass when the mass of the lighter object goes to zero?

 

[quicknote]

for your answer

The formula for the velocity of the center of mass takes into account the mass of each object in the system. So, even if M1 has a larger mass than M2 and M3, the fact that M2 and M3 have a higher speed will still contribute to the overall velocity of the center of mass. This is because the formula takes into account the mass of each object and calculates the average speed based on that. Therefore, the result may be closer to V1, but it will still be affected by the speeds of M2 and M3. This is because the center of mass is a point that represents the overall motion of the system, not just one individual object.