College Physics

Hugh D. Young

Chapter 27

Relativity - all with Video Answers

Educators

Chapter Questions

Problem 1

A spaceship is traveling toward earth from the space
colony on Asteroid 1040 $\mathrm{A}$ . The ship is at the halfway point of
the trip, passing Mars at a speed of 0.9$c$ relative to Mars's
frame of reference. At the same instant, a passenger on the
spaceship receives a radio message from her boyfriend on
1040 $\mathrm{A}$ and another from her hairdresser on earth. According to
the passenger on the ship, were these messages sent simultane-
ously or at different times. If at different times, which one was
sent first? Explain your reasoning.

Nathan Silvano

Nathan Silvano

Numerade Educator

Problem 2

$\bullet$ A rocket is moving to the right at half the speed of light relative to the earth. A lightbulb in the center of a room inside the rocket suddenly turns on. Call the light hitting the front end
of the room event $A$ and the light hitting the back of the room event $B$ . (See Figure $27.23 . )$ Which event occurs first, $A$ or $B$ , or are they simultaneous, as viewed by (a) an astronaut riding
in the rocket and (b) a person at rest on the earth?

Elan Stopnitzky

Elan Stopnitzky

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Problem 3

A futuristic spaceship flies past Pluto with a speed of 0.964 $\mathrm{c}$
relative to the surface of the planet. When the spaceship is
directly overhead at an altitude of $1500 \mathrm{km},$ a very bright signal light on the surface of Pluto blinks on and then off. An
observer on Pluto measures the signal light to be on for
80.0$\mu$ y. What is the duration of the light pulse as measured by
the pilot of the spaceship?

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Problem 4

$\cdot$ Inside a spaceship flying past the earth at three-fourths the
speed of light, a pendulum is swinging. (a) If each swing takes
1.50 s as measured by an astronat performing an experiment
inside the spaceship, how long will the swing take as measured by a person at mission control on earth who is watching the experiment? (b) If each swing takes 1.50 s measured by a
person at mission control on earth, how long will it take as
measured by the astronaut in the spaceship?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 5

$\bullet$ You take a trip to Pluto and back (round trip 11.5 billion km),
traveling at a constant speed (except for the turnaround at
Pluto) of $45,000 \mathrm{km} / \mathrm{h}$ . (a) How long does the trip take, in
hours, from the point of view of a friend on earth? About how many years is this? (b) When you return, what will be the difference between the time on your atomic wristwatch and the
time on your friend's? (Hint: Assume the distance and speed
are highly precise, and carry a lot of significant digits in your
calculation!)

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Numerade Educator

Problem 6

$\bullet$ The negative pion $\left(\pi^{-}\right)$ is an unstable particle with an
average lifetime of $2.60 \times 10^{-8} \mathrm{s}$ (measured in the rest frame
of the pion).(a) If the pion is made to travel at very high speed
relative to a laboratory, its average lifetime is measured in the laboratory to be $4.20 \times 10^{-7}$ s. Calculate the speed of the pion expressed as a fraction of $c .$ (b) What distance, as measured in
the laboratory, does the pion travel during its average lifetime?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 7

$\bullet$ An alien spacecraft is flying overhead at a great distance as
you stand in your backyard. You see its searchlight blink on for
0.190 s. The first officer on the craft measures the searchlight
to be on for 12.0 ms. (a) Which of these two measured times is the proper time? (b) What is the speed of the spacecraft relative to the earth, expressed as a fraction of the speed of light, c?

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Problem 8

How fast must a rocket travel relative to the earth so that
time in the rocket "slows down" to half its rate as measured by
earth-based observers? Do present-day jet planes approach
such speeds?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 9

A spacecraft flies away from the earth with a speed of
$4.80 \times 10^{6} \mathrm{m} / \mathrm{s}$ relative to the earth and then returns at the
same speed. The spacecraft carries an atomic clock that has been carefully synchronized with an identical clock that remains at rest on earth. The spacecraft returns to its starting
point 365 days $(1$ year) later, as measured by the clock that
remained on earth. What is the difference in the elapsed times
on the two clocks, measured in hours? Which clock, the one in the spacecraft or the one on earth, shows the smaller elapsed time?

Nathan Silvano

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Problem 10

$\bullet$ You measure the length of a futuristic car to be 3.60 $\mathrm{m}$ when
the car is at rest relative to you. If you measure the length of
the car as it zooms past you at a speed of $0.900 c,$ what result
do you get?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 11

A meterstick moves past you at great speed. Its motion relative
to you is parallel to its long axis. If you measure the length of the
moving meterstick to be $1.00 \mathrm{ft}(1 \mathrm{ft}=0.3048 \mathrm{m})-$ for example, by comparing it with a l-foot ruler that is at rest relative to
you, at what speed is the meterstick moving relative to you?

Nathan Silvano

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Problem 12

In the year $2084,$ a spacecraft flies over Moon Station III at
a speed of 0.800$c .$ A scientist on the moon measures the length
of the moving spacecraft to be 140 $\mathrm{m} .$ The spacecraft later
lands on the moon, and the same scientist measures the length
of the now stationary spacecraft. What value does she get?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 13

A rocket ship flies past the earth at 85.0$\%$ of the speed of
light. Inside, an astronaut who is undergoing a physical exami-
nation is having his height measured while he is lying down
parallel to the direction the rocket ship is moving. (a) If his
height is measured to be 2.00 $\mathrm{m}$ by his doctor inside the ship,
what height would a person watching this from earth measure
for his height? (b) If the earth-based person had measured
$2.00 \mathrm{m},$ what would the doctor in the spaceship have measured
for the astronaut's height? Is this a reasonable height? (c) Sup-
pose the astronaut in part (a) gets up after the examination and
stands with his body perpendicular to the direction of motion.
What would the doctor in the rocket and the observer on earth
measure for his height now?

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Problem 14

A spaceship makes the long trip from earth to the nearest
star system, Alpha Centauri, at a speed of 0.955$c .$ The star is
about 4.37 light years from earth, as measured in earth's
frame of reference $(1$ light year is the distance light travels
in a year). (a) How many years does the trip take, according
to an observer on earth? (b) How many years does the trip
take according to a passenger on the spaceship? (c) How
many light years distant is Alpha Centauri from earth, as
measured by a passenger on the speeding spacecraft? (Note
that, in the ship's frame of reference, the passengers are at
rest, while the space between earth and Alpha Centauri goes
rushing past at 0.955$c .$ (d) Use your answer from part
(c) along with the speed of the spacecraft to calculate
another answer for part (b). Do your two answers for that
part agree? Should they?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 15

A A muon is created 55.0 $\mathrm{km}$ above the surface of the
earth (as measured in the earth's frame). The average life-
time of a muon, measured in its own rest frame, is 2.20$\mu \mathrm{s}$ ,
and the muon we are considering has this lifetime. In the
frame of the muon, the earth is moving toward the muon
with a speed of 0.9860$c$ . (a) In the muon's frame, what is its
initial height above the surface of the earth? (b) In the
muon's frame, how much closer does the earth get during
the lifetime of the muon? What fraction is this of the muon's
original height, as measured in the muon's frame? (c) In the
earth's frame, what is the lifetime of the muon? In the
earth's frame, how far does the muon travel during its life-
time? What fraction is this of the muon's original height in
the earth's frame?

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Numerade Educator

Problem 16

$\cdot$ An enemy spaceship is moving toward your starfighter with
a speed of $0.400 c,$ as measured in your reference frame. The
enemy ship fires a missile toward you at a speed of 0.700$c$ relative to the enemy ship. (See Figure $27.24 . )$ (a) What is the speed of the missile relative to you? Express your answer in
terms of the speed of light. (b) If you measure the enemy ship
to be $8.00 \times 10^{6} \mathrm{km}$ away from you when the missile is fired,
how much time, measured in your frame, will it take the missile to reach you?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 17

$\bullet$ An imperial spaceship, moving at high speed relative to
the planet Arrakis, fires a rocket toward the planet with a speed
of 0.920$c$ relative to the spaceship. An observer on Arrakis
measures the rocket to be approaching with a speed of 0.360$c .$
What is the speed of the spaceship relative to Arrakis? Is the
spaceship moving toward or away from Arrakis?

Nathan Silvano

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Problem 18

$\bullet$ Two particles in a high-energy accelerator experiment are
approaching each other head-on, each with a speed of 0.9520$c$
as measured in the laboratory. What is the magnitude of the
velocity of one particle relative to the other?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 19

A pursuit spacecraft from the planet Tatooine is attempting
to catch up with a Trade Federation cruiser. As measured by an
observer on Tatooine, the cruiser is traveling away from the
planet with a speed of 0.600$c .$ The pursuit ship is traveling at a
speed of 0.800$c$ relative to Tatooine, in the same direction as
the cruiser. What is the speed of the cruiser relative to the pur-
suit ship?

Nathan Silvano

Numerade Educator

Problem 20

$\bullet$ Two particles are created in a high-energy accelerator and
move off in opposite directions. The speed of one particle, as
measured in the laboratory, is $0.650 c,$ and the speed of each
particle relative to the other is 0.950$c .$ What is the speed of the
second particle, as measured in the laboratory?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 21

$\bullet$ Neutron stars are the remains of exploded stars, and they
rotate at very high rates of speed. Suppose a certain neutron star
has a radius of 10.0 $\mathrm{km}$ and rotates with a period of 1.80 $\mathrm{ms}$ .
(a) Calculate the surface rotational speed at the equator of the
star as a fraction of $c .$ (b) Assuming the star's surface is an iner-
tial frame of reference (which it isn't, because of its rotation),
use the Lorentz velocity transformation to calculate the speed
of a point on the equator with respect to a point directly oppo-
site it on the star's surface.

Nathan Silvano

Numerade Educator

Problem 22

At what speed is the momentum of a particle three times
as great as the result obtained from the nonrelativistic expression $m v ?$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 23

$\bullet$ (a) At what speed does the momentum of a particle differ
by 1.0$\%$ from the value obtained with the nonrelativistic
expression $m v ?$ (b) Is the correct relativistic value greater or
less than that obtained from the nonrelativistic expression?

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Problem 24

$\cdot$ Relativistic baseball. Calculate the magnitude of the force
required to give a 0.145 kg baseball an acceleration of
$a=1.00 \mathrm{m} / \mathrm{s}^{2}$ in the direction of the baseball's initial velocity,
when this velocity has a magnitude of (a) $10.0 \mathrm{m} / \mathrm{s} ;$ (b) 0.900 $\mathrm{c}$ ;
(c) 0.990 $\mathrm{c} .$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 25

$\bullet$ Sketch a graph of (a) the nonrelativistic Newtonian
momentum as a function of speed $v$ and (b) the relativistic
momentum as a function of $v .$ In both cases, start from $v=0$
and include the region where $v \rightarrow c .$ Does either of these
graphs extend beyond $v=c ?$

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Numerade Educator

Problem 26

An electron is acted upon by a force of $5.00 \times 10^{-15} \mathrm{N}$ due to
an electric field. Find the acceleration this force produces in each
case: (a) The electron's speed is 1.00 $\mathrm{km} / \mathrm{s}$ . (b) The electron's
speed is $2.50 \times 10^{8} \mathrm{m} / \mathrm{s}$ and the force is parallel to the velocity.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 27

$\bullet$ Using both the nonrelativistic and relativistic expressions,
compute the kinetic energy of an electron and the ratio of the
two results (relativistic divided by nonrelativistic), for speeds
of (a) $5.00 \times 10^{7} \mathrm{m} / \mathrm{s},\left($ b) $2.60 \times 10^{8} \mathrm{m} / \mathrm{s}$ . \right.

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Numerade Educator

Problem 28

What is the speed of a particle whose kinetic energy is equal
to (a) its rest energy, (b) five times its rest energy?

Elan Stopnitzky

Elan Stopnitzky

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Problem 29

$\bullet$ Particle annihilation. In proton-antiproton annihilation,
a proton and an antiproton (a negatively charged particle
with the mass of a proton) collide and disappear, producing
electromagnetic radiation. If each particle has a mass of
$1.67 \times 10^{-27} \mathrm{kg}$ and they are at rest just before the annihilation, find the total energy of the radiation. Give your answers
in joules and in electron volts.

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Problem 30

$\bullet$ The sun produces energy by nuclear fusion reactions, in
which matter is converted into energy. By measuring the amount
of energy we receive from the sun, we know that is producing
energy at a rate of $3.8 \times 10^{26} \mathrm{W}$ . (a) How many kilograms of
matter does the sun lose each second? Approximately how many
tons of matter is this? ( b) At this rate, how long would it take the
sun to use up all its mass? (See Appendix E.)

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 31

\bullet A proton (rest mass $1.67 \times 10^{-27} \mathrm{kg}$ ) has total energy that
is 4.00 times its rest energy. What are (a) the kinetic energy of
the proton; (b) the magnitude of the momentum of the proton;
(c) the speed of the proton?

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Problem 32

$\bullet$ In a hypothetical nuclear-fusion reactor, two deuterium
nuclei combine or "fuse" to form one helium nucleus. The
mass of a deuterium nucleus, expressed in atomic mass units
(u), is 2.0136 u; that of a helium nucleus is 4.0015 u.
$\left(1 \mathrm{u}=1.661 \times 10^{-27} \mathrm{kg} .\right)$ (a) How much energy is released
when 1.0 $\mathrm{kg}$ of deuterium undergoes fusion? (b) The annual
consumption of electrical energy in the United States is on the
order of $1.0 \times 10^{19} \mathrm{J} .$ How much deuterium must react to pro-
duce this much energy?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 33

An antimatter reactor. When a particle meets its antipar-
ticle (more about this in Chapter 30 , they annihilate each
other and their mass is converted to light energy. The United
States uses approximately 1.0 $\times 10^{20} \mathrm{J}$ of energy per year. (a) If
all this energy came from a futuristic antimatter reactor, how
much mass would be consumed yearly? (b) If this antimatter
fuel had the density of Fe $\left(7.86 / \mathrm{cm}^{3}\right)$ and were stacked in
bricks to form a cubical pile, how high would it be? (Before
you get your hopes up, antimatter reactors are a long way in
the future-if they ever will be feasible.)

Nathan Silvano

Numerade Educator

Problem 34

A particle has a rest mass of $6.64 \times 10^{-27} \mathrm{kg}$ and a momen-
tum of $2.10 \times 10^{-18} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ . (a) What is the total energy
(kinetic plus rest energy) of the particle? (b) What is the kinetic energy of the particle? (c) What is the ratio of the kinetic energy to the rest energy of the particle?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 35

$\bullet$ (a) Through what potential difference does an electron
have to be accelerated, starting from rest, to achieve a speed of
0.980$c ?$ (b) What is the kinetic energy of the electron at this
speed? Express your answer in joules and in electronvolts.

Nathan Silvano

Numerade Educator

Problem 36

$\bullet$ Sketch a graph of (a) the nonrelativistic Newtonian kinetic
energy as a function of speed $v,$ (b) the relativistic kinetic
energy as a function of speed $v$ . In both cases, start from $v=0$
and include the region where $v \rightarrow c .$ Does either of these
graphs extend beyond $v=c ?$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 37

$\bullet$ The starships of the Solar Federation are marked with the
symbol of the Federation, a circle, while starships of the
Denebian Empire are marked with the Empire's symbol, an
ellipse whose major axis is 1.40 times its minor axis $(a=1.40 b$ in Figure 27.25$)$
How fast, relative to an observer, does an Empire ship have to travel for its markings
to be confused with those of a Federation ship?

Nathan Silvano

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Problem 38

A space probe is sent to the vicinity of the star Capella, which is 42.2 light years from the earth. (A light year is the distance light travels in a year.) The probe travels with a speed
of 0.9910$c$ relative to the earth. An astronaut recruit on board is 19 years old when the probe leaves the earth. What is her biological age when the probe reaches Capella, as measured
by (a) the astronaut and (b) someone on earth?

Elan Stopnitzky

Elan Stopnitzky

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Problem 39

Two events are observed in a frame of reference $S$ to occur
at the same space point, the second occurring 1.80 s after the
first. In a second frame $S^{\prime}$ moving relative to $S,$ the second event
is observed to occur 2.35 s after the first. What is the difference
between the positions of the two events as measured in $S^{\prime \prime} ?$

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Problem 40

$\bullet$ Why are we bombarded by muons? Muons are unstable
subatomic particles (more on them in Chapter 30 ) that decay to
electrons with a mean lifetime of 2.2$\mu \mathrm{s}$ . They are produced
when cosmic rays bombard the upper atmosphere about 10 $\mathrm{km}$
above the earth's surface, and they travel very close to the speed
of light. The problem we want to address is why we see any of
them at the earth's surface. (a) What is the greatest distance a
muon could travel during its 2.2$\mu$ s lifetime? (b) According to
your answer in part (a), it would seem that muons could never
make it to the ground. But the 2.2$\mu$ lifetime is measured in the
frame of the muon, and they are moving very fast. At a speed
of $0.999 c,$ what is the mean lifetime of a muon as measured by
an observer at rest on the earth? How far could the muon travel
in this time? Does this result explain why we find muons in cos-
mic rays? (c) From the point of view of the muon, it still lives
for only $2.2 \mu s,$ so how does it make it to the ground? What is
the thickness of the 10 $\mathrm{km}$ of atmosphere through which the
muon must travel, as measured by the muon? Is it now clear
how the muon is able to reach the ground?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 41

$\bullet$ How fast does a muon (see the previous problem) have to
move (according to an outside observer) in order to travel
1.0 $\mathrm{km}$ during its brief lifetime of 2.2$\mu \mathrm{s} ?$

Nathan Silvano

Numerade Educator

Problem 42

$\cdot$ A cube of metal with sides of length $a$ sits at rest in the
laboratory with one edge parallel to the $x$ axis. Therefore, in
the laboratory frame, its volume is $a^{3} .$ A rocket ship flies past
the laboratory parallel to the $x$ axis with a velocity $v .$ To an
observer in the rocket, what is the volume of the metal cube?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 43

$\bullet$ In an experiment, two protons are shot directly toward
each other, each moving at half the speed of light relative to
the laboratory. (a) What speed does one proton measure for
the other proton? (b) What would be the answer to part (a) if
we used only nonrelativistic Newtonian mechanics? (c) What
is the kinetic energy of each proton as measured by (i) an
observer at rest in the laboratory and (ii) an observer riding
along with one of the protons? (d) What would be the
answers to part (c) if we used only nonrelativistic Newtonian
mechanics?

Nathan Silvano

Numerade Educator

Problem 44

$\bullet \mathrm{A} 0.100 \mu \mathrm{g}$ speck of dust is accelerated from rest to a
speed of 0.900$c$ by a constant $1.00 \times 10^{6} \mathrm{N}$ force. (a) If the
nonrelativistic form of Newton's second law $\left(\sum F=m a\right)$ is used, how far does the object travel to reach its final speed? (b) Using the correct relativistic form of Equation $27.19,$ how
far does the object travel to reach its final speed? (c) Which distance is greater? Why?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 45

$\bullet$ By what minimum amount does the mass of 4.00 $\mathrm{kg}$ of ice
increase when the ice melts at $0.0^{\circ} \mathrm{C}$ to form water at that same
temperature? (The heat of fusion of water is $3.34 \times 10^{5} \mathrm{J} / \mathrm{kg.} )$

Nathan Silvano

Numerade Educator

Problem 46

In certain radioactive beta decay processes (more about ese in Chapter $30,$ the beta particle (an electron) leaves the omic nucleus with a speed of 99.95$\%$ the speed of light relave to to the decaying nucleus. If this nucleus is moving at 5.00$\%$ the speed of light, find the speed of the emitted electron relative to the laboratory reference frame if the electron is
emitted (a) in the same direction that the nucleus is moving, (b) in the opposite direction from the nucleus's velocity. (c) In each case in parts (a) and (b), find the kinetic energy of the
electron as measured in (i) the laboratory frame and (ii) the
reference frame of the decaying nucleus.

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 47

$\bullet$ Starting from Equation $27.24,$ show that in the classical
limit $\left(p c \ll m c^{2}\right)$ the energy approaches the classical kinetic energy plus the rest mass energy. (Hint: If $x \ll 1$ $\sqrt{1+x} \approx 1+x / 2 . )$

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Numerade Educator

Problem 48

Space travel? Travel to the stars requires hundreds or thousands of years, even at the speed of light. Some people have suggested that we can get around this difficulty by accelerating the rocket (and its astronauts) to very high speeds so that they will age less due to time dilation. The fly in this ointment is that it takes a great deal of energy to do this. Suppose you want to go to the immense red giant Betelgeuse, which is about 500 light years away. (A light year is the distance that
light travels in one year.) You plan to travel at constance that in a 1000 kg rocket ship (a little over a ton), which, in reality, is far too small for this purpose. In each case that follows, calculate the time for the trip, as measured by people on earth and by astronauts in the rocket ship, the energy needed in joules, and the energy needed as a percent of U.S. yearly use (which is $1.0 \times 10^{20} \mathrm{J} ) .$ For comparison, arrange your results in a table showing $v_{\text { Rocket }}, t_{\text { Earth }}, t_{\text { Rocket }}, E($ in $\mathrm{J}),$ and $E$ (as $\%$ of U.S. use $) .$ The rocket ship's speed is (a) $0.50 c,$ (b) 0.99$c$ , and (c) 0.9999$c .$ On the basis of your results, does it seem likely that any government will invest in such high-speed space travel any time soon?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 49

A A nuclear device containing 8.00 kg of plutonium
explodes. The rest mass of the products of the explosion is less
than the original rest mass by one part in $10^{4} .($ a) How much energy is released in the explosion? (b) If the explosion takes
place in $4.00 \mu s,$ what is the average power developed by the
bomb? (c) What mass of water could the released energy lift to
a height of 1.00 $\mathrm{km}$ ?

Nathan Silvano

Numerade Educator

Problem 50

$\bullet$ Electrons are accelerated through a potential difference of
$750 \mathrm{kV},$ so that their kinetic energy is $7.50 \times 10^{5} \mathrm{eV}$ . (a) What
is the ratio of the speed $v$ of an electron having this energy to
the speed of light, $c ?$ (b) What would the speed be if it were
computed from the principles of classical mechanics?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 51

$\bullet$ The distance to a particular star, as measured in the earth's
frame of reference, is 7.11 light years $(1$ light year is the distance light travels in 1 year). A spaceship leaves earth headed for the star, and takes 3.35 years to arrive, as measured by passengers on the ship. (a) How long does the trip take,
according to observers on earth? (b) What distance for the trip
do passengers on the spacecraft measure? (Hint: What is the
speed of light in units of 1$y / y ? )$

Nathan Silvano

Numerade Educator

Problem 52

$\bullet$ Cerenkov radiation. The Russian physicist $\mathrm{P}$ . A. Cerenkov
discovered that a charged particle traveling in a solid with a
speed exceeding the speed of light in that material radiates
electromagnetic radiation. (This phenomenon is analogous
to the sonic boom produced by an aircraft moving faster than
the speed of sound in air. $)$ Cerenkov shared the 1958 Nobel
Prize for this discovery. What is the minimum kinetic energy
(in electronvolts) that an electron must have while traveling
inside a slab of crown glass $(n=1.52)$ in order to create
Cerenkov radiation?

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 53

$\bullet$ Scientists working with a particle accelerator determine
that an unknown particle has a speed of $1.35 \times 10^{8} \mathrm{m} / \mathrm{s}$ and a
momentum of $2.52 \times 10^{-19} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .$ From the curvature of its path in a magnetic field they also deduce that it has a positive charge. Using this information, identify the particle.

Nathan Silvano

Numerade Educator

Problem 54

What is the speed of light in the alternate universe?
A. $3 \times 10^{8} \mathrm{m} / \mathrm{s}$
B. $3 \times 10^{6} \mathrm{m} / \mathrm{s}$
C. 3000 $\mathrm{m} / \mathrm{s}$
D. 300 $\mathrm{m} / \mathrm{s}$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 55

An airplane has a length of 60 $\mathrm{m}$ when measured at rest. When
the airplane is moving at 180 $\mathrm{m} / \mathrm{s}(400 \mathrm{mph})$ in the alternate uni-
verse, how long would it appear to be to a stationary observer?
A. 24 $\mathrm{m}$
B. 36 $\mathrm{m}$
C. 48 $\mathrm{m}$
D. 60 $\mathrm{m}$
E. 75 $\mathrm{m}$

Nathan Silvano

Numerade Educator

Problem 56

If the airplane has a rest mass of $20,000 \mathrm{kg},$ what is its rela-
tivistic mass when moving at 180 $\mathrm{m} / \mathrm{s} ?$
A. 8000 $\mathrm{kg}$
B. $12,000 \mathrm{kg}$
C. $16,000 \mathrm{kg}$
D. $25,000 \mathrm{kg}$
E. $33,300 \mathrm{kg}$

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 57

In our universe the rest energy of an electron is approximately
$8.2 \times 10^{-14} \mathrm{J}$ . What would it be in the alternate universe?
A. $8.2 \times 10^{-8} \mathrm{J}$
B. $8.2 \times 10^{-26} \mathrm{J}$
C. $8.2 \times 10^{-2} \mathrm{J}$
D. 0.82 $\mathrm{J}$

Nathan Silvano

Numerade Educator