Essential University Physics, 3e (Wolfson) Chapter 33 Relativity
3 3. 1 Co nc e pt ua lQue s t i o ns 1) A rocket is moving at 1/4 the speed of light relative to Earth. At the center of this rocket, a light suddenly flashes. To an observer at rest o n Earth A) the light ill reach the front of the rocket at the same instant that it reaches the back of the rocket. !) the light ill reach the front of the rocket before it reaches the back of the rocket. ") the light ill reach the front of the rocket after it reaches the back of the rocket. Anser# " $ar# 1
%) A rocket is moving at 1/4 the speed of light relative to Earth. At the center of this rocket, a light suddenly flashes. To an observer at rest in the rocket A) the light ill reach the front of the rocket at the same instant that it reaches the back of the rocket. !) the light ill reach the front of the rocket before it reaches the back of the rocket. ") the light ill reach the front of the rocket after it reaches the back of the rocket. Anser# A $ar# 1
&) An astronaut in an inertial reference frame measures a time interval 't beteen beteen her heartbeats. (hat ill observers in all other inertial reference frames measure for the time interval beteen her heartbeats A) 't !) more than't ") less than 't *) The anser depends on hether they are moving toard her or aay from her. Anser# ! $ar# 1
4) +ou +ou are a passenger on a spaceship. As the speed of o f the spaceship increases, you ould observe that A) the length of your spaceship is getting shorter. !) the length of your spaceship is getting longer. ") the length of your spaceship is not changing. Anser# " $ar# 1
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) A star is moving toards the earth ith a speed at 2-3 the speed of light. 0t emits light, hich moves aay from the star at the speed of light. elative to us on earth, hat is the speed of the light moving toard us from the star A) -.2-c !) c ") 1.1c *) 1.%-c E) 1.2c Anser# ! $ar# 1
) The special theory of relativity predicts that there is an upp er limit to the speed of a particle. 0t therefore follos that there is also an upper limit on the folloing properties of a particle. A) the kinetic energy !) the total energy ") the linear momentum *) more than one of these E) none of these Anser# E $ar# 1
3 3 . 2 Pr o bl e ms 1) Astronaut 5pud 6ick is space7traveling from p lanet X to planet Y at a speed of -.-c relative to the planets, hich are at rest relative to each other. (hen he is precisely halfay beteen the planets, a distance of 1.- light7hour from each one as measured in the planet frame, nuclear devices are detonated on each planet. The e8plosions are simultaneous in the frame of the planets. (hat is the difference in the time of arrival of the flashes from the e8plosions as observed by 5pud A) &-- min !) 1- min ") 9 min *) - min E) 11& min Anser# E $ar# 1
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%) Astronaut :ark ;ri is space7traveling from planet < to planet + at a speed of relative to the planets, hich are at rest relative to each other . (hen he is precisely halfay beteen the planets, a distance of 1.- light7hour from each one as measured in the planet frame, nuclear devices are detonated on both planets. The e8plosions are simultaneous in :ark=s frame. (hat is the difference in the time of arrival of the flashes from the e8plosions as observed by :ark A) - min !) 1>- min ") 2- min *) &- min E) 11& min Anser# A $ar# -?
&) As measured in Earth=s rest frame, a spaceship traveling at takes to travel beteen planets. @o long does the trip take as measured by someone on the spaceship A) %.2> y !) 9.%> y ") 4%.1 y *) &-.9 y Anser# A $ar# -?
4) An astronaut on a spaceship moving at -.2%9c says that the trip beteen to stationary stars took @o long does this ourney take as measured by someone at rest relative to the to stars A) %-.- y !) %.>1 y ") 4.- y *) %%.1 y Anser# A $ar# -?
) 5omeone in Earth=s rest frame says that a spaceship=s trip b eteen to planets took 1-.- y, hile an astronaut on the space ship says that the trip took Bind the speed of the spaceship in terms of the speed of light. A) -.992c !) -.>9c ") -.29c *) -.&>4c Anser# A $ar# -?
) An unstable particle is moving at a speed of %. C 1-> m/s relative to a laboratory. 0ts lifetime is measured by a stationary observer in the laboratory to be 4.9 C 1-7 seconds. (hat is the lifetime of the particle, measured in the rest frame of the particle Dc &.-- C 1-> m/s) Anser# %.& Fs $ar# 1 & "opyright %-1 earson Education, 0nc.
9) The closest knon star to our solar system is Alpha "entauri, hich is appro8imately 4.&light years aay. A spaceship ith a constant speed of -.>--c relative to the earth travels from Earth to this star. Da) @o much time ould elapse during the trip on a clock on board the spaceship Db) @o much time ould elapse during the trip on a clock on Earth Anser# Da) &.%& y Db) .&> y $ar# 1
>) A spaceship approaches the earth ith a speed -.-c. A passenger in the spaceship measures his heartbeat as 9- beats per minute. (hat is his heartbeat rate according to an observer that is at rest relative to the earth A) 2 beats per minute !) 9& beats per minute ") beats per minute *) 1 beats per minute E) >- beats per minute Anser# * $ar# 1
2) A set of tins, Andrea and "ourtney, are initially 1- years old. (hile "ourtney remains on Earth, Andrea rides on a spaceship hich travels aay from Earth at a speed of -.-c for five years Das measured by "ourtney), then immediately turns around and comes back at -.-c. (hen Andrea returns, "ourtney is %- years old. @o old is Andrea upon her return A) 1- y !) 1% y ") 1 y *) 1> y E) %- y Anser# * $ar# 1
1-) elative to the frame of the observer making the measurement, at hat speed parallel to its length is the length of a meterstick - cm A) -.>-c !) -.-c ") -.-c *) -.9-c E) -.2-c Anser# A $ar# 1
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11) An astronaut leaves Earth in a spaceship at a speed of -.2-c relative to an observer on Earth. The astronaut=s destination is a star system 14.4 light7years aay Done light7year is the distance light travels in one year.) According to the astronaut, ho long does the trip take A) 14.4 y !) %%.9 y ") 2.&4 y *) 1.- y E) 4.%- y Anser# E $ar# 1
1%) 0n their common rest frame, to stars are 2-.- light7years Dly) apart. 0f they are apart as measured by the navigator in a spaceship traveling beteen them, ho fast is the spaceship moving E8press your anser in terms of c. A) -.221c !) -.2>c ") -.2>-c *) -.29%c Anser# A $ar# -?
1&) A particle in a 4& m7long linear particle accelerator is moving at particle accelerator appear to the particle A) %12 m !) >2 m ") 1-4 m *) 2& m Anser# A
@o long does the
$ar# -?
14) A spaceship is moving beteen to distant stars at -.2&%c. To someone in the ship, the distance beteen the to stars appears to be (hat is the distance beteen the stars in the rest frame of the stars A) 94.% ly !) 2.9 ly ") %1. ly *) . ly Anser# A $ar# -?
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1) To space stations are at rest relative to each other and are .- C 1-9 m apart, as measured by observers on the stations. A spaceship traveling from one station to the other at -.2-c relative to the stations passes both of them, one after the other. As measured by an observer in the spaceship, ho long does it take to travel from one station to the other Dc &.-- C 1-> m/s) A) 29 ms !) %%- ms ") 1- ms *) > ms E) &2 ms Anser# A $ar# 1
1) A spacecraft is measured by an observer on the ground to have a length of & m as it flies toard the earth ith a speed 1.9 C 1-> m/s. The spacecraft then lands and its length is again measured by the observer on the ground, this time hile the spacecraft is at rest on the launchpad. (hat result does he no get for the length Dc &.-- C 1-> m/s) Anser# 4 m $ar# 1
19) 5ystem has a velocity u ?-.4c relative to system S , as shon in the figure. The clocks of S and are synchroniGed at t - hen the origins O and coincide. An event is observed in both systems. The event takes place at x -- m and at time t 1.2 Hs, as measured by an observer in S . (hat is the 7coordinate of the event, measured by an observer in
A) &>- m !) &4- m ") &- m *) &- m E) &1- m Anser# A $ar# 1
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1>) 5ystem has a velocity u ?-.c relative to system S , as shon in the figure. The clocks of S and are synchroniGed at t - hen the origins O and coincide. An event is observed in both systems. The event takes place at x = >-- m and at time t &.- Hs as measured by an observer in S . (hat is the time of the event, measured by an observer in
A) 1.> μs !) 74.2 μs ") 1.9 μs *) 1.& μs E) 1. μs Anser# A $ar# 1
12) 0n an Iatom smasher,I to particles collide head on at relativistic speeds. 0f the velocity of the first particle is -.941c to the left, and the velocity of the second particle is to the right Dboth of these speeds are measured in Earth=s rest frame), ho fast are the particles moving ith respect to each other A) -.>c !) 1.-21c ") -.>>&c *) -.9>>c Anser# A $ar# -?
%-) A spaceship approaching an asteroid at a speed of -.-c launches a rocket forard ith a speed of -.4-c relative to the spaceship. At hat speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid A) -.>1c !) 1.-c ") -.9c *) -.4c E) -.2c Anser# A $ar# 1
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%1) The captain of spaceship A observes enemy spaceship E escaping ith a relative velocity of -.4>c, as shon in the figure. A missile M is fired from ship A, ith a velocity of -.9%c relative to ship A. (hat is the relative velocity of approach o f missile M , observed by the cre on ship E
A) -.&9c !) -.%4c ") -.&4c *) -.&-c E) -.%9c Anser# A $ar# 1
%%) Three spaceships A, B, and C are in motion, as shon in the figure. The commander on ship B observes ship C approaching ith a relative velocity of -.9>c. The commander also observes ship A, advancing in the rear, ith a relative velocity of -.&1c. (hat is the velocity of ship C , relative to an observer on ship A
A) -.>>c !) -.&>c ") 1.4c *) -.%c E) 1.1c Anser# A $ar# 1
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%&) Three spaceships A, B, and C are in motion as shon in the figure. The commander on ship B observes ship C approaching ith a relative velocity of -.>&c. The commander also observes ship A, advancing in the rear, ith a relative velocity of -.4>c. As measured by commander on ship B, at hat speed is ship A approaching ship C
A) 1.&c !) -.24c ") -.%c *) -.>c E) %.%c Anser# A $ar# 1
%4) "onsider three gala8ies, Alpha, !eta and Jamma. An observer in !eta sees the other to gala8ies each moving aay from him in opposite directions at speed -.9-c. At hat speed ould an observer in Alpha see the gala8y !eta moving A) -.>%c !) -.9-c ") -.24c *) -.&c E) -.9c Anser# ! $ar# 1
%) To spaceships are approaching one another, each at a speed of -.%>c relative to a stationary observer on Earth. (hat speed does an observer on one spaceship record for the other approaching spaceship Anser# -.%c $ar# -?
%) A spaceship is moving aay from the earth ith a constant speed of -.>-c. The spaceship fires a %>7kg missile ith a speed of -.-c relative to the spaceship. (hat is the speed of the missile measured by observers on the earth if the missile is fired Da) aay from the earth Db) toard the earth Anser# Da) -.2&c Db) -.-c $ar# 1
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%9) At hat speed relative to the lab ill a -.%9%7kg obect have the same momentum as a 1.&-7 kg obect that is moving at -.1c relative to the lab A) -.244c !) -.2%%c ") -.2>1c *) -.2%c Anser# A $ar# -?
%>) A particle is moving at -.9c relative to a lab on Earth. !y hat percentage is the 6etonian e8pression for its momentum in error DThe percentage error is the difference beteen the erroneous and correct values, divided by the correct one). A) &43 !) %>3 ") &>3 *) 4&3 Anser# A $ar# 4
%2) 0n the lab, a relativistic proton has a momentum of 1.-- × 1-712 kg K m/s and a rest energy of -.1- nL. (hat is the speed of the proton in the lab D c &.-- C 1-> m/s, m proton 1.9 C 1-7%9 kg) A) -.19-c !) -.12c ") -.211c *) -.2&-c E) -.21c Anser# ! $ar# 1
&-) An electron has a speed of -.4&c. Through hat potential difference ould the electron need to be accelerated Dstarting from rest) in order to reach this speed D c &.-- C 1-> m/s, e 1.- C 1-712 ", mel 2.11 C 1-7&1 kg) A) 1- k$ !) 1&- k$ ") 1>- k$ *) %-- k$ Anser# A $ar# -?
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&1) An electron is accelerated from rest through a potential difference of -.- k$. (hat is the speed of the electron Dc &.-- C 1-> m/s, e 1.- C 1-712 ", mel 2.11 C 1-7&1 kg) A) 1.%4 C 1-> m/s !) 1.&& C 1-> m/s ") &.%4 C 1-> m/s *) &.&& C 1-> m/s E) 4.1% C 1-> m/s Anser# A $ar# 1
&%) 0n a certain particle accelerator, a proton has a kinetic energy that is eMual to its rest energy. (hat is the speed of the proton relative to the accelerator A) -.%c !) -.-c ") -.91c *) -.9c E) -.>9c Anser# E $ar# 1
&&) @o many oules of energy are reMuired to accelerate a 1.-7kg mass from rest to a speed of >.3 the speed of light Dc &.-- C 1-> m/s) A) 1.> C 1-19 L !) 2.- C 1-1 L ") %.9 C 1-1% L *) 4. C 1-2 L E) &.- C 1-& L Anser# ! $ar# 1
&4) @o much ork must be done to accelerate a particle of mass of
from a speed
to a speed of
Anser# 1%-- L $ar# -?
&) Assume that a certain city consumes electrical energy at an average rate of %.- C 1-2 (. (hat ould be the mass change in producing enough energy to keep this city running for %1 eeks Dc &.-- C 1-> m/s) A) -.%> kg !) -.&% kg ") -.&2 kg *) -.4> kg Anser# A $ar# 19
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&) *uring a nuclear reaction, the particles involved lose 4.> C 1-7%> kg of mass. @o many oules of energy are released by this reaction Dc &.-- C 1-> m/s) A) 4.& C 1-711 L !) 1.4 C 1-712 L ") 1. C 1-7& L *) %.1 C 1-74- L E) .& C 1-74 L Anser# A $ar# 1
&9) *uring a nuclear reaction, 1.9 C 1-74 L of energy is released. (hat is the resulting change in mass of the particles involved Dc &.-- C 1-> m/s) A) .1 C 1-74 kg !) 4.& C 1-711 kg ") 1. C 1-71& kg *) 4.> C 1-71> kg E) 1.2 C 1-7%1 kg Anser# E $ar# 1
&>) An electron is accelerated from rest through a potential difference of -.- k$. (hat is the TNTAO energy of the electron Dc &.-- C 1-> m/s, e 1.- C 1-712 ", mel 2.11 C 1-7&1 kg) A) >.-- C 1-71 L !) 1.% C 1-71 L ") >.%- C 1-714 L *) 2.-- C 1-714 L E) 1.% C 1-714 L Anser# * $ar# 1
&2) A relativistic proton has a momentum of 1.- C 1-719 kg K m/s and a rest energy of -.1 nL. (hat is the kinetic energy of this proton Dc &.-- C 1-> m/s, m proton 1.9 C 1-7%9 kg) A) 1.& pL !) 1. pL ") &.- pL *) %.% pL E) %. pL Anser# " $ar# 1
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4-) A proton in a certain particle accelerator has a kinetic energy that is eMual to its rest energy. (hat is the TNTAO energy of the proton as measured by a physicist orking ith the accelerator Dc &.-- C 1-> m/s, m proton 1.9 C 1-7%9 kg) A) .2 C 1-711 L !) 1.- C 1-71- L ") %.-9 C 1-71- L *) &.-1 C 1-71- L E) >.99 C 1-71- L Anser# * $ar# 1
41) A proton in a certain particle accelerator has a kinetic energy that is eMual to its rest energy. (hat is the momentum of the proton as measured by a physicist orking ith the accelerator Dc &.-- C 1-> m/s, m proton 1.9 C 1-7%9 kg) A) %.1 C 1-712 kg K m/s !) %.>2 C 1-712 kg K m/s ") 4.&4 C 1-712 kg K m/s *) .-1 C 1-712 kg K m/s E) >.> C 1-712 kg K m/s Anser# E $ar# 1
4%) @o fast must a proton move so that its kinetic energy is >-3 of its total energy A) -.-%-c !) -.>9c ") -.2%c *) -.2>c E) -.>-c Anser# * $ar# 1
4&) As a spaceship is moving toard Earth, an Earthling measures its length to be &% m, hile the captain on board radios that her spaceship=s length is 11- m. Dc &.-- C 1-> m/s) Da) @o fast is the rocket moving relative to Earth Db) (hat is the TNTAO energy of a 9.-7kg creman as measured by Di) the captain in the rocket and Dii) the Earthling Anser# Da) -.22c %.>> C 1-> m/s Db) Di) .9 C 1-1> L Dii) %.&2 C 1-12 L $ar# 1
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