Calculating CM Velocity in a Two-Particle System

In summary, the conversation is about a problem involving two masses, one travelling at 4c/5 and the other at rest. The energy and momentum of each particle is calculated, and then the question of the velocity of the center of mass is brought up. There is some debate over the correct value for the velocity, either 2c/5 or c/2. The next step is to solve for the velocities of the particles in the center of mass frame, and the definition of the center of mass for a relativistic system is mentioned. The conversation ends with a hint that the total momentum of the particles in the center of mass frame is zero, and the question of how to solve for the resultant velocities is raised.
  • #1
Tonyt88
62
0
So I have this problem:
A mass m travels to the right at 4c/5, and another mass m is at rest.

They ask fro the energy and momentum of each particle, so I have:

Energy of traveling: 5/3 mc^2

Energy of rest: mc^2

Momentum of traveling: 4mc/3

Momentum of rest: 0

Then they ask for the velocity of the CM of the system:

Which I have 2c/5, but then some people are telling me c/2.

But anyway, I have to solve for the velocities of the particles in the CM frame, so how I do go from there.
 
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  • #2
What is the definition of the center of mass for a relativistic system of point particles...?

Daniel.
 
  • #3
1/M (x1m1 + x2m2) ?
 
  • #4
It should be the "zero momentum" frame.
 
  • #5
Then I really don't know what to say, but I would like to know, if you have the value for the velocity at the CM (which I think is either 2c/5 or c/2), how do I go from there to solve for the resultant velocities?
 
  • #6
You just need the CM's velocity. You've been hinted that in the CM frame the total momentum of the particles is zero.

Daniel.
 

1. What is energy and how is it related to momentum?

Energy is the ability to do work or cause change. It exists in many forms such as kinetic, potential, thermal, and electromagnetic energy. Momentum is the product of an object's mass and velocity. The two are related because energy can be converted into momentum and vice versa.

2. What is the conservation of energy and momentum?

The conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another. Similarly, the conservation of momentum states that the total momentum of a closed system remains constant, meaning that momentum cannot be created or destroyed, only transferred between objects.

3. How does the center of mass affect energy and momentum?

The center of mass (CM) of an object or system is the point where its mass is evenly distributed. In a closed system, the total momentum of the system is equal to the momentum of the CM, and the total energy is equal to the energy of the CM. This means that the CM plays a crucial role in determining the energy and momentum of a system.

4. What is the difference between elastic and inelastic collisions?

In an elastic collision, both momentum and kinetic energy are conserved. This means that the objects involved bounce off each other without any loss of energy. In an inelastic collision, kinetic energy is not conserved, meaning that some energy is lost in the form of heat or sound. However, momentum is still conserved.

5. How can we calculate the change in energy and momentum during a collision?

The change in energy can be calculated using the formula ΔE = E(final) - E(initial), where E represents the total energy of the system. The change in momentum can be calculated using the formula Δp = p(final) - p(initial), where p represents the total momentum of the system. These calculations can help us understand the effects of a collision on energy and momentum in a system.

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