Phy 133 - Assignment 5
Quiz A. 1.
2.
The question gives B’s speed relative to A, and asks for it relative to Earth, so
those are the two frames of reference. (As opposed to B being one of the
frames.) The picture should be drawn so that the moving frame of reference is
going toward the right, to match the picture on the formula sheet. The moving
frame is the primed frame. v stands for the primed frame’s speed relative to the
unprimed frame. u stands for the speed of the other object both observers are
looking at; u is its speed seen by the unprimed frame, and u’ is its speed as seen
by the primed frame. Since .6c is the speed seen by A, and A is the primed
frame, .6c is u’. u is what you’re looking for.
ux = ux ’ + v
= .5c + .6c =
2
1 + ux’v/c
1+[(.5c)(.6c)]/c2
1.1c = .846c
1 + .3
B. 1. KE = E – E0. Look up an electron’s rest energy on the formula sheet.
1.17 MeV - .51 MeV = .66 MeV.
2.
The question gives the small rocket’s speed relative to Earth, and asks for it
relative to the ship, so those are the two frames of reference. (As opposed to
the small rocket being one of the frames.) The picture should be drawn so that
the moving frame of reference is going toward the right, to match the picture on
the formula sheet. The moving frame is the primed frame. v stands for the
primed frame’s speed relative to the unprimed frame. u stands for the speed of
the other object both observers are looking at; u is its speed seen by the
unprimed frame, and u’ is its speed as seen by the primed frame. Since Earth is
the unprimed frame, .95c is u, and u’ is what you’re looking for.
Once you’ve got that straight, the rest is just dropping numbers in a formula:
ux’ = ux – v
= .95c - .75c =
2
1 - uxv/c
1-[(.95c)(.75c)]/c2
.2c = .696c
1 - .7125
C. 1. Since mass is equivalent to energy, giving a body kinetic energy
increases its inertia. (Gravitational effects depend on just the rest mass, but in
the sense of how hard it would hit you at a given speed, the body gets
“heavier.”) As it approaches the speed of light, m approaches infinity. This
infinite inertia makes further acceleration impossible.
2. a. 54.9279 - 54.9244 = .0035 u
To convert from mass units to energy units, E = mc2:
[
(
)]
= 5.222 x 10-13J
The u to kg conversion factor is from the last page of the formula sheet. So is
the J to eV one used next.
(5.222 x 10-13J)(1 eV/1.602 x 10-19) = 3.26 x 106eV
Ans: 3.26 MeV
b. KE = E - ER = 3.26 MeV - .51 MeV =
2.75 MeV
The electron’s rest energy (its mass in energy units) is on page 9 of the formula
sheet.
D. 1. (a) To someone on Earth, the astronaut is shortened along the direction of
motion, and has a slowed pulse. (b) The astronaut sees no change in himself/
herself. (but sees the observer on Earth as shortened and slowed down.)
2.
E. 1. The speed of light in a vacuum, and their relative speed.
2.
F.
(KE = ½mv2 is valid only below roughly .10c, as demonstrated in the lab/
movie. So if you tried using that and it didn’t work, that’s why.)