You are in a windowless car in an exceptionally smoothmt *4m/t x(*wmh8yzsgr/ 8gpk train moving at constant vty(m4g/*hwx krm*8 gpzstm /8elocity. Is there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a rezz b0br1l:renw ;9845sjn ptyd light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinkirz 1bt4 zj wlryn:ns0 e5b;9p8ng that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroadw))2nn hb.z ed7ywy ek,i9zd)sjg 2m0 car, and throws a heavy ball straight up (from his 0y)by ,2 ) . )2g9enikhsdz7zwnjmwed point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say thaa:7f+imjt ci4 t the Sun goes around the Earth? Discuss in view of the first principle of relcit7j i4 mf:+aativity (that there is no best reference frame). Explain.

If you were on a space )u)odw9 *wp4 l(qijheship traveling at 0.5c away from a star, at what speed would )i ed*4(poljhwu w9 )qthe starlight pass you?

The time dilation effect is somr8.(x ewgt85aanjiy -gc 5u r+etimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affectingw(8r. gj g+ -t8r5u5aaiyexnc the functioning of clocks. What then does it deal with?

Does time dilation mean that time acukgc )n+ vi-b b018oyntually passes more slowly in moving reference frames or that it only seems to pass more sl) n0unvb ko+ 1gcy-i8bowly?

A young-looking woman astronaut has just arrived home from a long yxbkm+0 .n lu4trip. She rushes up to an old gray-haired man and in the ensuing conversationb+ m0.nylx4ku refers to him as her son. How might this be possible?

If you were traveling away from Earth at spees41(prl,sj.7 hp veomd 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth usir,v1e mp4. hpojs(l7sng telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, 8*rjh0eh(5 vr5ksx ktsay $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the 7 z;i7 rlyf da670jim6bk3msh relativistic p7z6y l0mi7 36ishkm;fad7 brjredictions of length contraction and time dilation?

Discuss how our everyday lives wouee0)s om7o wry.r x76hld be different if the speed of light were only m)6s.e ry o707rehoxw$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be wafgk j5o.,h0 used to indicate thah.f og0 k,aj5wt c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr s8 viav87p.p )khpls0 Tompkins, for whom the speed of lighhp8 v) .0sklia8ps p7vt is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited tv 3.pigcj8y ;w- bq:qto travel at speeds less than c. Does this put an upper limit on the momentum of an electronj pw gytvicb.;-q :q38? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain thdedj*0+ 5.w hst 0dwehe speed of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does thistrl4:z rga*za )(r.+ar )iks 9/edqna mean that a spring has more mass when compressed than wh+a/rd):a4 nt( r )agk9seqrlzz*ia.r en relaxed? ----待选择----yesno 

It is not correct to sa7 g-43a kii1wdt n gnj(3y,txsy that "matter can neither be created nor destroyed." What must we say inty ni-xd 3kgjna47 s3g,i(1wtstead?

  Is our intuitive notion that velocities simply add, as we did in Secti vy2/ fv4w)6dd1pv ddion 3–8, completpd61 fv dvdvwd2/4yi)ely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.23bvp wg.gkg*tkv(99 a m. How long would it kggt 3g (apw99v k.vb*be when at rest? $L_0$ =    m

  A certain type of elementary particle h10tu pfd0 gj2qqx5xn ahq89.travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals dependj :*rypeg8w8x on the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125www(bb4s1 k1w light-years from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime is measured odjszg/ob059q 8t./)j 1wfm 0xxtxm bto be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light-years away. How fast weuvt7xnc+/ 5u bb8p(9j tgp-sould you have to travel so that to5v t b9s p+npxg8u-7e/(jcu bt you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years awbe hzk4; :wsvs md)gdr (+m/br8gt m*9ay at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip? +hm9be*w; 4: gk rsd/d(r8bmvs g mzt)t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the Earth0/mln;zz4x oh is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

  At what speed $v$ do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.) v =    c

  Suppose a news report stated that starship Enterprise had just returned fr (nnp6bfmzv n-nv ,2e/om a 5-year voyage while trap2v ev(/z6b n f,nnmn-veling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. zu)3c.h.j 143uult.uqje lu mHow long would it take a spacecraft travel33h ulu c.)u.tjjulq e.z41uming 0.960c to reach that star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in heyj2k ;w1m 58e6cdaou:mmrr+mf4/ j nbr "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1. jamu5yco6n fm d2j;+ r:brw4k1em/m8 25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an avek(hlp nip45yti30 05t; vcxe frage pion be moving to travel 15 m before it decays? The average lifetime, ath p;34ylfit5iev0kx (cp0n5t rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travehlh2*m2 qkj:yy 8 5ydqling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twi 0 xhumg q3og-c.v-oo1ce its rest mass? v =    c

  A particle of rest mck)vvnuq 50/ xass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave,xut ,gab c-egw*2 d-;r btju)ls at $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent chaoo7:i 7d7owkdnge in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiresipfas0 07z*9e7 ei6enu 4ckcx $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaksg /n ji 0phs;..unhy7oqhps3: apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic p s/0nqh3ni ;7up ..hhsj ygo:energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in 3-(6iu aafwf6+okqm 4x4 y,5 clrgjjqjoules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest ma.i vk3pvebhxcvap0h/ipzm,t(+;sq e )./zk : ss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abouc:ax gwag 8 2(jv;qb6rt $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can bfz ilgquj / :qck14/itly/ )e9e obtained from conversion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic energy equwz :giq3: n1xnals its rest energy? gq: wni nz:x13v =    c

  At what speed will an object's kinetic energy h 5dfd zw ff-i ;( cxp(d.l;pi6*zc/pqbe 25% of its rest energy? v =    c

  (a) How much work is required toea jh q1lg3+i9bl ug s(z:h7,e accelerate a proton from rest up to a speed of 0.9+hbe,3(q gil j9ulh 7:sg ze1a97c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentu)e9+bj a bw ugg, hd6/5lgbd/cm of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750.:i)lbu* cd 6,t7kuvvcwuh cz em/;ol)hzc62-MeV proton (that is, its kinetic energy is 750 MeV)lc 6huwb.iu/; h,v6ztu *e2: zo)vcc )7 mdckl?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 Msb-3ed7oe:fd v. i f)0mcc uw5V? v = 7b sdo0:m cu.5-3 vd)cwfiefe   c

  What is the speed of an electron whose kinetic energy is 1.ww2sbv4 -9orh t7w-/orr8w6l svm7b c00 MeV? v =    c

  What is the speed of an electron just beforeugop9 j842ik v it hits a television screen after being ac24 igovk9 8jpucelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particz .j 287/xyow oqd7fcples of rest mass $m_0$ approach each other at equal and opposite speeds $v$. The collision is completely inelastic and results in a single particle at rest. What is the rest mass of the new particle? How much energy was lost in the collision? How much kinetic energy is lost in this collision?

  Calculate the speed of a prot e r:2qq8yrz.zon ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum o:x3tzeg )avk l-*p;*,c duqswf an electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,0yim 0kpegcn-j013(ul 00 kg is accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energc k( rnqye-w8*y and momentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleusw a-0 z dcm2z:i-4ki*pd: fxrd, $^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

  An electron ($m_0 =9.11 \times 10^{-31} \, \text{kg}$) is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.60 \times 10^{-14} \, \text{J}$. Determine the electron's speed $v$. v =    c

Make a graph of the kinetic energy versus momn-z:lwlmh) t7 idl)w4entum for (a) a particle of nonzero rest mass, and (b) a particle with zerwhw-i:z)lt) nml7l 4d o rest mass.

  What magnetic field intensity is needed to keep 998-GeV curans0jfx;1t2i d7, protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Uju a07 fc,xn2r;istd1se the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with aurff/fp2(* j respect to the Earth) observes a meteor come from behi* pja(fr/fu 2fnd and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, eac u2zw 2udrv5y.h with a speed of 0.50c with respect to 2zw dv.y5ur2uEarth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A second spaceship leaven-rkg + /xla7sjoc m tt2-yr33s the first mr - 3xktg jr7-3o+ a2nlst/cyat a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel ac6x*lo)eyb kqlts v*y ;1k8(tff.d /spproach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u = ;v y*y e6dl/lqbofscxts t 8f*k1k.)(   c

  A spaceship in distress slvth br3h+gl vex4+5h4q (h, hends out two escape pods in opposite directions. One travels at a shveg,4 (l b3rx5qhh+h+4lvht peed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth atn5:dtmuvh2n dh+fo74co-8adu ( ht /x a speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same d x8uvfht+2 nc /had57umon-4o :dh t(direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxw28)phtdq.k m ima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faster than about 0.1c is called reli h/cwz9/.yuw ativistic - i.e., for which the correction using special relativity is a significant effect. Determine /wizhc9 w .y/uthe speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) ----待选择----relativistic not relativistic 

  (a) What is the speedh3t+4 fe22mpc2d r pdkof;m3g $v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter wutaok p 0b92-aould have to be totally destroyed to run a 100-W lightbu9uoaabt-2k p0lb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce :uv ;kdf,zbe z8c67mw an electron and a positron together? A positron is a particle with the same rest mass as an elzu8dfm7:e6wvb ,;kzc ectron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon travelio; (7 ax9w f zgkwa*zw,kqk/p7ng at 33% the speed of light collides head on with a positive muon travel;pwak7w(xo,k9zz7afgq/ w k *ing at 50% the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino6j /gmu/jr-dxgt: e*j a dwlpu(.7/gx. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside thg lg* xj7 :r(u/gd/pxau -j.me6w/tjde front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate olm -btnvb:4db a84g9qx4,z iw*e hoe, f about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is me4wha7cse z7 qe, lj:g*asured to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to b 8om 9:64 :htscaodqcrreak a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding eneadh9ts:6or:4cm qco 8rgy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a car trkvxe5*sa 2s2 imda/*eaveling 110 km/h as compared to at rest? [Hint: use the biv sxem/sa2d aki**e52nomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0 bxu.iw lfxr4s,8if- 0.935c in the laboratory, are moving toward each other. De f4-xr8s 0wui,.fxbl itermine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle with momentuv9ti ;djyj;2dm $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterpr7 (p2mo8 abeptm0e v2kise obtains its power by combining matter and antimatter, achieving complete convers m ( 0ppo7mvaee822bktion of mass into energy. If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energ: ac1 ua,r)+y+9pjxhf7nq27sr vpqn .q tq+ mqy is greater than its rest ma+q7 )1qjym7qnh2rsx ,crt.+aqp 9uv npq+ a f:ss $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes t bn,-k.uw7 qvj0i0c xshat he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shv,ujxcik7 w 0-s .nbq0orter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogl .rnbt8)m*uaqrf3 : wen and one mole of oxygen react to form two moles of water, the energy releasedtw3f)*r : 8lu.anr mqb is 484 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identic11c2;yof h sqsal particles are created, traveling in opposite directions. If the ss1h2 1fyscoq; peed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship travesg+c* og +ez;kling at 0.75c relative to Earth measures his ship to be 25 m long. On tgg +o+e *cz;kshe ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. Yo 9lxxy7m 3yg3ru send a 3r3 gmx9ly7xylaser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupafu:89q y)br:kp6m2 x em9smhnnts have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spapx9rqk f mmb m:6s:2 u9h)n8yeceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. ogsb wq )rckrj- 3siwa:y.8( .What is the spaceship's kinetic energy? Compare with the total cwjbw . q-rkg8rs:o ).a3 y(isU.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 6.;lq+iirefz(6 0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this tr riqfe i+zl;(6ip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffness co3 ygtvj/ :ot;nik3(.mlw8o xd nstant 3 mt:d (;ixk/.j otlo8gyn3wvis $k=48.7 \, \text{N/m}$. If this system is in a spaceship moving past Earth at 0.900c, what is its period of oscillation according to
(a) observers on the ship, T =    s
(b) observers on Earth? $T_{earth}$ =    s

A pi meson of rest m6 hdf fi+uoh:i g.4pdhr*vf9( ass $m_\pi$ decays at rest into a muon (rest mass $m_\mu$) and a neutrino of negligible or zero rest mass. Show that the kinetic energy of the muon is $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.