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PHYS126 Spring 2011 Homework 4, Due March 4, beginning of lecture.
1a. In lecture, we proved
2
2
2
2
)
(
)
(
E
mc
pc
=
+
from the spacetime relation. Prove this
relation using a different method, by directly substituting
2
2
1
c
v
v
m
p

=
and
2
2
2
1
c
v
mc
E

=
into the right hand side. After some algebra, you will get the left hand side.
1b.
The rest energy of a unknown particle is 2GeV, and its kinetic energy is 4GeV. What
is the momentum(in GeV/c), and its speed?
2.
A lambda particle decays into a proton and a pion, lambda
b
p + pi, and it is observed
that the proton is left at rest. a) what is the energy of the pion? b) what was the energy of
the original lamda? ( the masses involved are mass of lambda particle
= 1116, mass of
proton = 938, and mass of pi particle = 140, in MeV/c
2
. ) Hint: do it algebraically, then
put in numbers)
3.
If u is much less than c, the binomial approximation (
2
1
2
β
γ
+
=
) shows that the
relativistic
kinetic
energy,
2
)
1
(
mc
K
rel

=
is
about
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This note was uploaded on 03/31/2011 for the course PHY 126 taught by Professor Hobunchan during the Spring '11 term at HKUST.
 Spring '11
 HoBunCHAN
 Physics, Work

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