How do you know if the rest mass changes or not?

[sspitz]

My book says that if two objects collide completely inelastically, the rest mass of the composite is greater than the sum. I assume this happens because the objects heat up and this is counted in their energy.

However, in other problems the book assumes the rest mass of objects/particles is the same before and after collisions. Explanations are sparse.

How do you know if the rest mass changes or not?

 

[BruceW]

I am guessing this is a book on relativity? What mathematical methods have you been through so far? Have you learned how to calculate the four-momentum of a system yet? and how to get the rest mass from this? It would be best to understand it mathematically, but I could help with an intuitive explanation if you haven't been through the maths yet.

 

[sspitz]

End of a book on mechanics. The next chapter is more formal. I would just like an intuitive grasp of what the rest mass is and how to set up simple conservation law equations such as in compton scattering.

 

[BruceW]

hmm. I could write out a big paragraph explaining 4-momentum as well as I can, but I don't think the homework section is the right place for that kind of thing. But I can help with the confusion you had in your first post. Right, so the rest mass of two particles is not just the sum of their individual rest masses. I think this is where the confusion stemmed from.

Edit: Also, when several particles are involved, it is often called the 'invariant mass' of the system, and is usually just called 'rest mass' when only one particle is involved.

 

[asteriatic]

I would approach this question by looking at the underlying principles of mass and energy conservation. According to the law of conservation of mass, the total mass of a closed system remains constant, regardless of any physical or chemical changes that may occur within the system. This means that in any given system, the total mass before and after a collision must be the same.

However, the concept of mass can become more complicated when we consider the theory of relativity, which states that mass and energy are interchangeable. This means that the total energy of a system, including the rest mass and kinetic energy of its components, must also remain constant.

In the case of a completely inelastic collision, where two objects stick together after impact, the total kinetic energy before and after the collision is not conserved. Some of the kinetic energy is converted into other forms, such as heat or sound. This means that the total energy of the system, including both the rest mass and kinetic energy, remains constant, but the distribution of energy may change.

Based on this understanding, we can say that the rest mass of the composite object after the collision is greater than the sum of the individual masses of the objects before the collision. This is because some of the kinetic energy has been converted into rest mass, according to Einstein's famous equation E=mc².

In other cases where the book assumes that the rest mass of objects remains the same before and after collisions, it is likely because the collision is either elastic or partially inelastic, where the total kinetic energy is conserved. In these cases, the rest mass of the objects involved does not change.

In conclusion, the rest mass of a system can change if there is a conversion of kinetic energy into rest mass. This is typically seen in completely inelastic collisions, where the total energy of the system remains constant, but the distribution of energy changes. In other cases, the rest mass of objects remains the same before and after collisions, indicating that the collision is either elastic or partially inelastic.