Question- Two identical objects, each of rest mass m 0 , moving with equal but o

Question

Question- Two identical objects, each of rest mass m0, moving with equal but opposite velocities of 0.50c in the laboratory reference frame, collide and stick together. The resulting particle is at rest with mass M0. Determine an expression for M0 in terms on m0.

From what I understand, this is a type of rest mass problem usually given in modern physics courses. I came across this one day and tried to attempt it, but could not get anywhere because I could not understand what they meant by determining an expression for M0 in terms of m0. Is somebody able to help me determine an expression for this problem?

Explanation / Answer

The mass of each object is m0 The speed of the objects is v = 0.5c The total energy of the two masses before collision is Ei = 2m0c2{1/[1-(v2/c2)] - 1} + 2m0c2 Ei = 2m0c2/[1-(v2/c2)] Ei = 2.31m0c2 The total energy of the mass M0 after the collision is Ef = M0c2 From the conservatio of total energy of the system, 2.31m0c2 = M0c2 M0 = 2.31m0 Note: In an inelastic collision, kinetic energy of the system is not conserved. But the total energy of the system will be conserved. Note: In an inelastic collision, kinetic energy of the system is not conserved. But the total energy of the system will be conserved.

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