Consider the following inelastic collision. Two lumps of matter are moving direc

Question

Consider the following inelastic collision. Two lumps of matter are moving directly toward each other. Each lump has a mass of 1.500 kg, and is moving at a speed of 0.930c. The two lumps collide and stick together. Answer the following questions, keeping in mind that relativistic effects cannot be neglected in this case. What is the final speed, in terms of c, of the combined lump? What is the final mass of the combined lump immediately after the collision, assuming that there has not yet been significant energy loss due to radiation or fragmentation?

Explanation / Answer

(1) let p1, p2 and p3 be the momentum of the first lump,second lump and after collision combined momentum.

from conservation of momentum

p3 = p1 + p2

since p1 = -p2 ( each has same mass and speed and moving in opposite direction)

hence p3 = 0.0

hence final speed of the combined lump = 0.0 c

let m and M  be the mass of lump before collision and after collision comined mass

then from conservation of energy

E3 = E1 + E2

E1 = E2 = m*c^2/(1-(v/c)^2)^(1/2)

E3= 2*m*c^2/(1-(v/c)^2)^(1/2)

M*c^2 =  2*m*c^2/(1-(v/c)^2)^(1/2)

M =  2*m/(1-(v/c)^2)^(1/2) = 2* 1.500/ (1 - (0.930)^2)^(1/2)

= 3.00/0.37 kg

= 8.11 kg

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