PHYSICS 2D
PROF. HIRSCH
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QUIZ 1
WINTER QUARTER 2016
JANUARY 15, 2016
Formulas:
Time dilation; Length contraction : "t = #"t'$ # "t p ;
Lorentz transformation :
x'= " (x # vt)
1
y' = y , z' = z
"=
1# v 2 /c 2
t'= " (t # vx /c 2 )
Velocity transformation :
ux ! v
ux' =
1 ! ux v / c 2
uy
uy' =
" (1 ! ux v / c 2 )
L = Lp /#
; c = 3 %10 8 m /s
x = " (x'+vt')
y = y', z = z'
t = " (t'+vx' /c 2 )
ux =
uy =
ux' +v
1+ ux ' v / c 2
uy '
" (1 + ux ' v / c 2 )
Relativistic Doppler shift : f obs = f source 1+ v /c / 1" v /c
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Momentum : p = " mu ; Energy : E = " mc 2 ; Kinetic energy : K = (" #1)mc 2
Rest energy : E 0 = mc 2
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Electron : me = 0.511 MeV /c 2
;
E=
p 2c 2 + m 2c 4
Proton : mp = 938.26 MeV /c 2
Atomic mass unit : 1 u = 931.5 MeV /c 2
;
Neutron : mn = 939.55 MeV /c 2
electron volt : 1eV = 1.6 "10 -19 J
Problem 1
The lifetime of an elementary particle is 0.337µs (in its own reference frame). It is
moving at speed 0.99c. Approximately how far will it travel (in the lab frame) from the
moment it is created until it decays?
A: 400m; B: 700m; C: 100m; D: 1000m; E: not sure (E always counts 0.21 points)
Problem 2
According to Prof. Hirsch's watch he was on time for the lecture, however according to
the students he was 1s late. If it took Prof. Hirsch 1 minute to get to the classroom from
his office according to his own watch, how fast did he travel?
A: 0.180c; B: 0.090c; C: 0.360c; D: 0.010c; E: not sure
Problem 3
A light source approaches you, goes past you and moves away, without changing its
speed. Its frequency according to you drops by a factor of 2 in this process. How fast was
it moving relative to you?
A: (3/5)c; B:(1/2)c; C: (1/4)c; D: (1/3)c; E: not sure
Problem 4
An electron moves to the right with speed 0.8c relative to the lab frame. A proton moves
to the left with speed 0.4c relative to the electron. Find the speed of the proton relative to
the lab frame.
A: 0.4c; B: 0.303c; C: 0.588c; D: 0.909c; E: not sure
PHYSICS 2D
PROF. HIRSCH
QUIZ 1
WINTER QUARTER 2016
JANUARY 15, 2016
Problem 5
375 m
The spaceship has length 375m and is moving at speed v=0.8c. For an observer on the
spaceship, the chicken is born (in the back of the ship) 1 µs after the hen lays an egg (in
the front of the ship). As seen by observers on the ground, the chicken was born after or
before the egg was laid? (Use Lorentz transformation)
A: 1.67 µs after; B: 0.6 µs before; C: simultaneously; D: 1.67 µs before; E: not sure
Problem 6
A mass m1 moving at speed 0.8c to the right collides inelastically with a mass m2 moving
at speed 0.6c to the left and the two masses stick together forming a mass M that doesn't
move. What is m2/m1?
A: 1.77; B: 1.33; C: 1.50; D: 0.75; E: not sure
Problem 7
For the situation in problem 6, what is M/(m1+m2)?
A: 1; B: 1.6 ; C: 1.2 ; D:1.4; E: not sure
Problem 8
Assume you know nothing about relativity and Einstein told you that the relation between
energy E, momentum p and rest mass m is
E = m1/2 c [2 p 2 c 2 + m 2 c 4 ]1/4
You can immediately tell that he is wrong because:
(A) dimensions don't match.
(B) the non-relativistic limit (speed small compared to c) gives a kinetic energy that is a
factor of 2 larger than the classical value.
(C) the non-relativistic limit (speed small compared to c) gives a kinetic energy that is a
factor of 2 smaller than the classical value.
(D) none of the above answers is correct
(E) not sure