You are in a windowless car in an exceptionally smooth s nc79 7l6trkxjt, uaf7t.5v ctrain moving at constant velocity. Is there any physical experiment you can do in the train car to determine utct6vrxf.l n779astc k,75 jwhether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of the 9 *utww7quvm- corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and rw ut7qv*m uw-9elative motion?

A worker stands on top of a movingjnrsj:zihenl0p;okc58 m: 3y 0m5 l h+ railroad car, and throws a heavy ball straight up (from his point of view). Io n;0si m5hc0zjmek h nj 3yl:8p5:lr+gnoring air resistance, will the ball land on the car or behind it?

Does the Earth really go arou*bic -8+u xqi1 0wvj(u,d3lntstz w1h nd the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is ndulu t101jn83w, i-wi+ zhxsc *bqvt( o best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what sphebbtm95.4d a tp 0d(,ylqk:jeed would the starlight past4hp:yj0,( mqbbdd 5e9 lat.ks you?

The time dilation effect is sometimes expressjg,t g1 y b;i4f0uumi5ed as “moving clocks run slowly.” Actually, thi5ijytg04m ,i u 1gu;fbs effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more f/e( zodix2+eb 6dbkf4od: c/slowly in moving reference frames or that it onk:f2 /ix/ dobe46dod+(fceb z ly seems to pass more slowly?

A young-looking woman astronaut has just are* )avi+f *hsarived home from a long trip. She rushes up to an old gray-haired man and i+ h* aiaevf*s)n the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a chh t,nnyv/2s1 uc,k f :siq0t6jange in your heartbeat? Would your mass, height, or,26 uq stv1f ,hni :scykn0/tj waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and lengt, hp3s q/+qpxwh contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relativistic1e7 go -oyiw qcn56zw5 predictions of length contraction and 1yogoz6q7nc5i - we w5time dilation?

Discuss how our everyday lives would be different if the speed of 4x-rducz2h1u light were only x2c4 u1h-uzdr$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas mi bkq *8quiw( gh)i*q.wght be used to indicb.*u*wq)(8 wqihq gi kate that c is the limiting speed in the universe.

The drawing at the start of tfr-z ,*inh 9r.gp9u+er8od d7i; kugihis Chapter shows the street as seen by Mr Tompkins, for whom the speed ofuhir gp.gzor, id7d+* 9re 8if-nuk9; light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c.; 6l7csrnc g01cmss(l5x xh /n Does this put an upper limit on the momentum of 071rn(sglmhs5n x;/ c6cclsxan electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of lifhc4 ee4-cmtld. /e8rgcb1:m gm 7hxw7vrw +-ght? ----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,sm ;76kvq8ly :)lzoyo does this mean that a spring has more mass when compressed than when relay ov;l8qzskl6 m7 :oy)xed? ----待选择----yesno 

It is not correct to say that "matter cakj kvzlr-+, fhm0a o +iv8 d9.yi6a/xrn neither be created nor destroyed." What must we sai/+a +f8r.ry6vl omvhkz ,0k9-xdaji y instead?

  Is our intuitive notion that velocities simply add, as we hq 9f1 kirn3lsq7t)g2did in Section 3–8, completeiktsn31q7 h )qgf2lr 9ly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 2khrl *s4:a6y j8.2 m. How long would it be when at resy*:rslah4 6kjt? $L_0$ =    m

  A certain type of elementary particle travkq *kv1 nzc;p,els 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 intervxp (2mz lib-d,als depend 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 125 light-years frfj ijzvy +8ln8wo68gww a6/t/om 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 lifeti6zu3so )k- ruhme is measured to 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 5od pi6:a)ut;ohkys 382 light-years away. How fast would you have to travel so that to you the distance would 6o)5s:u k;h3iyoptda be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed tur9(i/ z/y+oe e.e blpwup-c9hat tells you the distance is onlyo ./zwp( bup9/ -uyeec9lr+ie 25 light-years. How many years would it take you to make the trip? 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 Earth is o vc z7v9u*yn*$11.2 \times 10^3 \, \text{m/s}$. 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 thafr*gjt1m/xb4c h 9 yg/t starship Enterprise had just returned from a 5-year voyage while ttcgfxmr* jg1by h/4 /9raveling 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. How long would it take a v cws : ) 0dx;y/gxi:rtj0k)uc(l, vehspacecraft traveling 0.960c to reac(:cx) ljk g r0vh/dy ,vct)xs0:; ewiuh 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 her "Ferrari" spacecraft at a speed of 0.660)/lb cwmeg yz;3+e :qfveuk(b xq2 p8+c. It is measured in your frame to be 4.80 m long and 1.25 m high. +cp(zf3 ul2mb+q:wve 8/eyqgk e); xb
(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 avera as .:c (7rb0byxesvu;1nxox)bqv( .mge pion be moving to travel 15 m before it decays? The average lifetime, at restcm0uns x ;yvqv. s.(71oeb:arbbx) (x, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a pn p- c:4 y)fh,oehd1fxroton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s reln1ee 9sg,nhgrg59( obativistic mass be twice its rest mass? v =    c

  A particle of rest mait;e vkc3do r0 76pa1zss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a si8a-hkhrt0a nv+ 1p;t $v =0.10c$. 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 change in momentu69zq.oyc2xj7 a;tdd nkv*u 5cm of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiresyah7n krws2-lfi7x2mb-;ufmlv 3 7w9 $4.82 \times 10^4 \, \text{J}$ 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 breaks apart in the proc 95hy)x p6 t7r+lfkjhtess known as fission in a n j5t hp)ft7rh9k +l6xyuclear reactor, the resulting fragments have a total kinetic 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 joules at.rn ar2va. s5nd 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 mass 3exwgk mr.mrdi 2mk2: 5ri *0jof a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abu):gr6v xaqy j)t-b9qout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversionc xcpj(g2/tov1o m3o6 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 equk1g b3ce / s+c5a2wzvials its rest energy? v = v g ie12+a3/5bsw zkcc   c

  At what speed will an object's o/ v/(siq 5*v6bdbobxkinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a) ;x du3nx 3snd)jlwc5 proton from rest up to a speed of 0.997c? d3x3n)5sdc)njl w; xu W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton travemuijx+buj9 k m, :-f*rh dmp09ling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetic energy i8kw q tbg cz4:+cmv 0l2)rhog*s 750 MeV)hcr8cblvg wm0g +)4*z k2oq: t?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerau9 *;us.hphb 5fzw fp0ted by a potential difference of 105 MV? v =fs p50p;u ubw.zh*9hf    c

  What is the speed of an electron whose kinetic energy iw8qqt)x*s q*df3bh x 4s 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television scriw,-co*5 w8owoyxb q +2mvv*heen after being acceleratedic v,qm o8*bo yxh+w*wow- 5v2 from rest by the 25,000 V of the picture tube? v =    c

Two identical particles poxl zl53y5z 8yr1+ua 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 pt,3.2seqm:wztwhh s y22 pr7uroton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 of k 6z9v:0x r e7he*:wcj:dmm lban 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 27,000 kg is .l wimk,s uo j0j8 wn.7lacw4)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 energy and momjr5yfd z7g91lentum 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 nucleus,5:ijg+ om/ue q $^{241}\text{Am}$, 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 eno1/( f(v:wqdu2f g- eaepa-mlergy versus momentum for (a) a particle of nonzero rest m1oe (f/-qfeu( a m- adw:gp2vlass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to kef g) wtpn)d-2iep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab g-n2 w)dt p)fisynchrotron)? Use 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 respect to the Earth) obgc, :8csnp p+nserves a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor:c,cnp 8nsgp+ moving with respect to the Earth? u =    c

  Two spaceships leave Earth injiy.l( cmu(p2 b chj*bi2 h4d- opposite directions, each with a speed of 0.50c with respect to Earth. y*(p lbh 2jijbcm-4.dhu( ci2
(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 sp:a-l; ygyp;0ndp35zmhoj x7e aceship leaves the first at a speed of 0.87clj yzpe m0gp :oh ;n7x5d-ya3; 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 approach at a speed of xw )a sxne/8 p/+bbiy+0.60c. The Enterprise comes to the rescue (Figx+8b/e x)s +nb /iawyp. 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 =    c

  A spaceship in distress sends out two escape podc 6vs61vp j2qls in opposite directions. One travels at av 6qsvp1c6lj2 speed $v_1 =-0.60c$ 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 at a speed of 0.7xf+/;at35wnbo da, rk: a6qit5c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B3at+;q/ xratfd,k :nia w o56b moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima v-m1yohfn; n;/ s2 qq-vpqvx;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 se um m4qju(+brj; 48g1nj;zhfaster than about 0.1c is called relativistic - i.e., for which the correction using specemj+m1bj n zr4;sgh;j4 qu8u(ial relativity is a significant effect. Determine the 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 speeuv d 0s0j5 +bba17zcyt,f gg:/v(kxxyd $v$ 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 would have to be totally destroyed to run a 100-W light*4vojn jg.54syb,k uebulb for 1 ju44snj , bk5gv*ye.o year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce a9 sz ovdtt,)h tv3+y1gp,uc*vn electron and a positron togethe* tv1)yucsotpgh vvt9z +,3,dr? A positron is a particle with the same rest mass as an electron, 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 traveling at 33% the speed of light collides head ont8at 63(zjv wer4+ygl with a positive muon traveling at 50% the speed of light8we+vtajt zly63r( g4. 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 deca2t51aro1kaa37 u7 ih2 n vssiwy into a proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the othu rnsvka ti72a s5wa7o32 1i1her masses can be found in the Table inside the 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/)kno t;erla(+,p ip b+qb3xd of 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 measured to have a negative charge and a spee8r(ml.l02dl7 qy3;qoyfq xzx d 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 m7 zx): zd.6tjsj nq:6cotx6n to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron,cm q ndsz x.n 6t6:tx6o)zjj:7 and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mtww+0 mg933cfqe fgtnx+ n-d/ass of a car traveling 110 km/h asggntn/de 0ffwc+ 3+ x9q3twm - compared to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.9onp+p74l ) ryz35c in the laboratory, are moving toward ep7r lo4pzny) +ach other. Determine
(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 m5ke bk e1na7:9)ywqbxomentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship 4 m8(**yg1oplwji j46ksm/w4s8 jh ie p6fethEnterprise obtains its power by combining matter and antimatter, achieving complete convejik 4ge6y*f8j 6emi(s ph1thjm wo4w/p*l48 srsion 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 energy is greater than its rest8jlb1av .5fzi ma bv f8za.i1j5lss $m_0c^2$ 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 that he can fit a 15.0-m-long3/*ix2u ks gi+t t5sk ajw5po, pole into a 12.0-m-long barn if he runs fast eno +*taus skgpwi/, i5x2 jk3ot5ugh (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 shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one m.h m 8pj -:kf*f((la.ixgpcdta0a *2kntt u2u ole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this reactioi*l kax.g2j(ctpfkh8tfd 2t m.0 (n-a p:a*u un?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction idch( c7phvp6w;s 87w two identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the 8wch76h7cp;v ps(id wlaboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c d5km5+-)t+2; 4 ufw irevk9 kzozofjv relative to Earth measures his ship to be 25)z9of+;2+ itor5 v f-u54kjmvde zkkw m long. On the 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 .g 8v+s bx-ph v 1u:o+*bxxq)ix bu0vlaway from Earth. You send a laser beam toward the Earth traveling b 0pviu*xv x .v:qglhxs)b+ u1bxo8-+ at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a tz6r5hgr vr,v sg1b (h*- +mwbeotal 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 spaceship changes mass directly to energy. How much mass will be converted to energy to accr-bh mhz +rbgwvsgev6 *r(5 1,elerate 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 p1g ib+mqpckg,*a;0va speed of 0.99c. What is the spaceship's kinetic energy? Compare with m, v+g 0ckp;1piqab*gthe total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship i(9uz 3;s yrhw.wyf2q pqjq42i s to travel to the vicinity of a star 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 spsu ;j32p.qf4 qiy(qhwr92zwy eed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end osh2l lo0kmk9u4/m mi, f a spring whose spring stiffness constantil 0uhm l/k2m,mosk49 is $k=48.7 \, \text{N/m}$. 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 mas7clx tpkcz 8u-9br9k4 s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.