Composite Particle Rest Mass Calculation

The equations are$$E = \gamma m c^2$$$$\vec{p} = \gamma m \vec{v}$$$$E^2 = (pc)^2 + (mc^2)^2$$You can use these equations to find the rest mass of the composite particle.
  • #1
zhillyz
67
0

Homework Statement



A particle of rest mass [itex]m_0[/itex] and kinetic energy [itex]2m_0c^2[/itex] and sticks to a stationary particle with rest mass [itex]2m_0[/itex]. Find the rest mass of the composite particle.

Homework Equations



Conservation of momentum and thus energy.

[itex] E_{bef} = E_r + E_k = E_{aft}[/itex] where Er is energy of rest particle

The Attempt at a Solution



[itex]E = m_{01}c^2 + mv\gamma + m_oc^2 = m_{02}c^2[/itex]. The first half of the equation there is a kinetic part and a part at rest, the second half is only at rest.

I am thinking I am supposed to be substituting the questions given data into this equation and cancelling expressions but i am not sure how to proceed.
 
Physics news on Phys.org
  • #2


zhillyz said:

Homework Statement



A particle of rest mass [itex]m_0[/itex] and kinetic energy [itex]2m_0c^2[/itex] and sticks to a stationary particle with rest mass [itex]2m_0[/itex]. Find the rest mass of the composite particle.

Homework Equations



Conservation of momentum and thus energy.

[itex] E_{bef} = E_r + E_k = E_{aft}[/itex] where Er is energy of rest particle

The Attempt at a Solution



[itex]E = m_{01}c^2 + mv\gamma + m_oc^2 = m_{02}c^2[/itex]. The first half of the equation there is a kinetic part and a part at rest, the second half is only at rest.

I am thinking I am supposed to be substituting the questions given data into this equation and cancelling expressions but i am not sure how to proceed.
What are ##m_{01}##, ##m_{02}##, ##m_o## (not ##m_0##), and ##m## supposed to represent? None of those quantities appear in the problem statement.

Your equation doesn't make sense. You're adding energy to momentum ##\gamma mv##. That doesn't work out unit-wise. I take it v is supposed to be the speed of the first particle.

Think about this: After the two particles collide and stick together, is the composite particle at rest or not?

It's best if you stick to working with energy E, momentum p, and mass m rather than writing things in terms of ##\gamma## and speed v. It'll simplify the algebra.
 
Last edited:

1. What is a composite particle?

A composite particle is a type of particle that is made up of smaller subatomic particles, such as protons and neutrons, which are bound together by strong nuclear forces.

2. How is the rest mass of a composite particle calculated?

The rest mass of a composite particle is calculated by adding the rest masses of all its constituent particles and taking into account any binding energy that may be present.

3. What is the significance of calculating the rest mass of a composite particle?

Calculating the rest mass of a composite particle can provide insight into the underlying fundamental forces that hold the particles together and help to understand the structure and behavior of matter on a microscopic level.

4. Can the rest mass of a composite particle change?

Yes, the rest mass of a composite particle can change if its constituent particles undergo a change, such as a nuclear reaction or decay. This can also affect the overall stability of the composite particle.

5. Are there any limitations to calculating the rest mass of a composite particle?

One limitation is that the exact calculation of the rest mass of a composite particle is often complex and requires advanced mathematical techniques. Additionally, the rest mass of a composite particle may not accurately reflect its actual mass in certain high-energy situations where relativistic effects come into play.

Similar threads

  • Special and General Relativity
2
Replies
55
Views
3K
Replies
1
Views
824
  • Special and General Relativity
3
Replies
102
Views
3K
  • Advanced Physics Homework Help
Replies
2
Views
979
  • Advanced Physics Homework Help
Replies
2
Views
590
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Special and General Relativity
2
Replies
36
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
1K
Replies
2
Views
803
  • Advanced Physics Homework Help
Replies
9
Views
1K
Back
Top