Question

4. Consider the following two processes. In one process a mass mo is initially at rest and spontaneously decays into two masses m traveling in opposite directions with velocity 0.6c. In the second process two masses m are traveling toward each other each with velocity 0.6c and collide to form a single object of mass mo at rest. (a) Draw a picture of each process. (b) Calculate the change of mass for each process Am. (c) Are the changes of mass for each process equal? Why or why not? Why is the change in mass non-zero?

Answer 1

Particle decay process: a 0.60 0.6c 0.6c Particle Collision: m 0.66 0.6c mo

B) Change is Mass:

          When a particle travels in high velocity it exhibits a relativistic effect like length contraction, and time dilation, as well as the mass of the particle, is also changed from its rest mass.

                   In the first process where rest particle decay into two equal masses travels in the opposite direction with an equal velocity of 0.6c

So, the relativistic mass of this particle

massrelativistic = For the first process m mo =

me=2m mo? 11-V47c2 mo =- mo = _2m 7.60.60)/2 2m m, = 0.8 m, = 2.5m Change in mass Am = Total mass of Parent- total mass of daughter Am = 2.5m - 2m = 0.5m Similarly, for the second process where two particles collide and stick together to form a new particle which is in rest. Change in mass Am = Total mass of reactants - total mass of products Am = 2.5m - 2m = 0.5m C) Yes, change of mass for both processes are equal. Simply because of conservation of mass. Where in the first process, mass before the decay after they must be same. As well as in the second process mass before the collision after the collision must be same. The reactants and the products in the both processes are identical so the change in mass for the both processes are same. Change in energy will not be zero. It is because of energy mass equivalence. From the Einstein equation E = mc2 the energy and the mass are interconvertible. In first process a particle with mass mo decays into two particles with equal mass. In this process part of the mass of rest particle is used to create two particles with mass m and the other part of the mass is converted into Kinetic energy of the particle which help the particle to move in the velocity 0.6c.Due to high velocity, the particle undergoes relativistic effect and the mass of the particle increased so the change in mass in not zero.