Consider the inelastic collision. Two lumps of matter are moving directly toward
ID: 1732207 • Letter: C
Question
Consider the 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 0.880c. The two lumps collide and stick together. Answer the questions, keeping in mind that relativistic effects cannot be neglected in this case.
What is the final speed vf of the combined lump, expressed as a fraction of c?
vf=
What is the final mass mf of the combined lump immediately after the collision, assuming that there has not yet been significant energy loss due to radiation or fragmentation?
mf= kg
Explanation / Answer
a)
using the intial momentum
P1 = m v / ( 1 - v2 / c2 )1/2
and
P2 = - m v / ( 1 - v2 / c2 )1/2
Pi = 0
Pf = mf vf / ( 1 - v2 / c2 )1/2 = 0
then the lump must be at rest
vf = 0
b )
E12 = ( mc2 )2 + ( p1c) 2
and
E22 = ( mc2 )2 + ( p2c) 2
if it have same magnitude
E2 = ( mfc2 )2
conservation of momentum
E = E1 + E2
= 2 E1
E2 = 4 E12
= 4 ( ( mc2 )2 + ( p1c) 2 )
P1 = m v / ( 1 - v2 / c2 )1/2
= 1.5 X 0.88 c / ( 1 - (0.88c)2 / c2 )1/2
P1 = 2.779 c
( mfc2 )2 = 4 X [ ( 1.5 c2)2 + ( 2.779 c )2 )
mf2 = 4 X [ ( 1.5 )2 + ( 2.779 )2 )
mf2 = 39.891
mf = 6.315 kg