A question about momentum

[wowolala]

1.) A particle with mass M initially at rest decays into two identical particles each of mass 0.48M, the speed of the identical particles after the decay is :



after decaying , the sum of two mass doesn't equal to initial mass...


can somebody help me how to solve this qusiton


2.)if a particle whose rest mass energy equals 100MeV has a total energy of 200Mev, its velocity is :


i think there is some kind of relation between 1 and 2.

please help me ?

thx

 

[alphysicist]

Hi wowolala,

1. Now that the particle has decayed and the two identical particles are moving away, in what form of energy has the "missing" rest mass energy been converted to?

2. How is the total energy related to the rest mass energy?

 

[Moetasim]

I am happy to help you understand the concept of momentum in these scenarios. In the first question, we can use the principle of conservation of momentum to solve for the velocity of the two identical particles after the decay. This principle states that the total momentum of a system remains constant in the absence of external forces. In this case, the initial momentum of the particle at rest is zero, and after the decay, the total momentum is divided between the two identical particles. Therefore, the momentum of each particle will be equal in magnitude but opposite in direction, resulting in a net momentum of zero. To solve for the velocity, we can use the equation for momentum: p = mv, where p is the momentum, m is the mass, and v is the velocity. Since we know the mass of each particle (0.48M) and the initial momentum is zero, we can solve for the velocity.

In the second question, we can use the equation for the total energy of a particle, E = mc^2, where E is the total energy, m is the mass, and c is the speed of light. Since the rest mass energy is given as 100MeV, we can solve for the mass of the particle (m = E/c^2). Then, using the equation for kinetic energy, KE = 1/2 mv^2, we can solve for the velocity of the particle.

There is indeed a relation between the two questions as both involve the concept of conservation of momentum and the equations for energy and velocity. I hope this helps clarify the concepts for you.