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 0.500 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. from classical momentum of the lump is Pc = mv

Pc = 0.5 * 0.930 *3e8

Pc = 1.395*10^8 m/s

-----------------------------

Relativistic momentum of the lump

Pr = mv/Gamma

here gamma Y = 1/sqrt(1 - v^2/c^2)

Y = 1/(1- 0.93^2) = 7.4

so

Pr = 1.395 *10^8 / 7.4

Pr = 1.87 *10^7 m/s

-----------------------------
using addiction of velocities

Vc = (u+v)/(1+ UV/c^2)

Vc = (0.930+ 0.930)/(1 + 0.930^2)

Vc = 0.997 C

--------------------------------

Mtotal = gamma (M1 +M2)

Mtotal = (0.5 + 0.5)/sqrt(1 - 0.997^2)

Mtotal = 13 kgs

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.