Quantum Dynamics: Calculating Mass After Particles Collide

[thharrimw]

Homework Statement

there are 2 particles with the same mass and they undergo two different experments in expermant 1 particle 1 is moveing at .9c and particle two is at rest it wanted the KE before they hit and i got 1.29mc^2 (i checked it in my book) for experment two the total KE before the particles hit is 1.29mc^2 and both particles are moveing at eagh other at a velocity U it wanted me to find u so i set 1.29mc^2= 2c^2m(Y) and got u to be .795c ( i also checked that in my book) part c said that the particles in part a and b stick together and it wanted me to find the resalting masses that would resalt after the particles hit in both experments.

Homework Equations

i don't know where to start or what equation to use so could someone help me get started.

The Attempt at a Solution

 

[Jhero]

First, we need to understand the concept of kinetic energy (KE) and how it relates to mass and velocity. The equation for KE is KE = 0.5 * m * v^2, where m is the mass of the particle and v is its velocity. This equation tells us that the kinetic energy of a particle is directly proportional to its mass and the square of its velocity.

In experiment 1, particle 1 has a mass m and a velocity of 0.9c. Using the equation for KE, we can calculate its kinetic energy to be KE = 0.5 * m * (0.9c)^2 = 0.405mc^2. This is the same value that you got in your book, so it seems like you have the right answer.

In experiment 2, both particles have the same kinetic energy before they hit. We know that the total KE is 1.29mc^2, so each particle must have a kinetic energy of 0.645mc^2. Using the same equation for KE, we can set this equal to 0.5 * m * u^2, where u is the velocity of the particles after they stick together. Solving for u, we get u = √(2 * 0.645c^2/m) = 0.795c, which is the same value you got in your book.

Now, for part c, we need to find the resulting masses after the particles stick together in both experiments. Since the particles stick together, we can add their masses together to get the resulting mass. In experiment 1, the resulting mass would be 2m, since both particles have the same mass m. In experiment 2, the resulting mass would also be 2m, since both particles have the same kinetic energy and thus must have the same mass.

In summary, the resulting masses after the particles hit would be 2m in both experiments. I hope this helps you understand the problem better. Good luck with the rest of your work!