Calculating Center of Mass Speed in a Colliding System

In summary, the problem involves a collision between a loaded coal car with a mass of 120 metric tons traveling at 2 m/s and an empty, stationary coal car with a mass of 8 metric tons. Using the equation M1r1=M2r2, the speed of the center of mass of the system of two cars can be found by using ordinary geometry. This speed is equal to the final velocity of the two cars, which can also be found using conservation of momentum. Therefore, the speed of the center of mass remains constant throughout the entire process.
  • #1
sealedhuman77
15
0

Homework Statement

[/B]
A loaded coal car with a mass of 120 metric tons traveling at 2 m/s collides and couples with an empty, stationary coal car with a mass of 8 metric tons. (1 metric ton = 103 kg)

(c) What is the speed of the center of mass of the system of two cars throughout the process?

Homework Equations



I am not sure of any relevant equations for part c but I know that M1r1=M2r2 deals with center of mass systems.

The Attempt at a Solution


I already solved parts a and b which are about final speed of two cars, and change in kinetic energy respectively.Thanks for the help
 
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  • #2
The total momentum of the system tends to be the momentum of the center of mass. Using that, just find the velocity of the center of mass. The velocity of the center of mass should technically remain the same throughout the entire process (before and after collision).
 
  • #3
internal forces can't change the velocity or position of center of mass.
 
  • #4
… just use ordinary geometry …

sealedhuman77 said:
(c) What is the speed of the center of mass of the system of two cars throughout the process?

I am not sure of any relevant equations for part c but I know that M1r1=M2r2 deals with center of mass systems.

ok - so you know where the center of mass is (before the collision)!

Just use ordinary geometry to work out how fast it is moving! :smile:
 
  • #5
I still don't understand the problem. I know that the moving coal car is moving at 2m/s and it hits the stationary coal car. But the problem does not specify which direction the moving coal car is coming from or how far it is initially.

I don't know if I could use the final velocity of the two coupled cars or the change in kinetic energy to help find part c.
 
  • #6
You don't know to know which direction the moving coal car is heading; the direction is arbitrary here. You don't need to know how far the coal car moved, either, this is a momentum problem, so use conservation of momentum.
 
  • #7
Ok, I got it now. I realized that the speed of the center of mass was the same as the final velocity of the two cars, which happened to be the same answer to part a. Thanks for the help.
 

What is the speed of center of mass?

The speed of center of mass is a vector quantity that represents the average speed of all the particles in a system. It takes into account both the mass and velocity of each particle in the system.

How is the speed of center of mass calculated?

The speed of center of mass can be calculated by finding the total momentum of all the particles in a system, and dividing it by the total mass of the system. This can also be expressed as the sum of the individual momentums divided by the total mass.

Why is the speed of center of mass important in physics?

The speed of center of mass is important because it helps us understand the overall motion of a system. It can also be used to analyze collisions and other interactions between objects.

Can the speed of center of mass change?

Yes, the speed of center of mass can change if there is an external force acting on the system, or if the mass or velocity of any of the particles in the system changes.

How does the speed of center of mass relate to conservation of momentum?

The speed of center of mass is closely related to the principle of conservation of momentum. In a closed system with no external forces, the total momentum of the system remains constant. This means that the speed of center of mass will also remain constant, unless there is a change in the mass or velocity of the system.

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