You are in a windowless car in an exceptionally smoothc/)udqf7esfsl , lc22k ry*+ o train moving at constant velocity. Is there any physical experiment you can dos lf7+, c2q2ry/l su*kcd)f oe in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the28bfzm1i) .o kn;mpg4f v7obt experience of being at a red light when, out of the corner of your eye, you see the car beside you creep;ntfpm1iv. 8kz o omb742f)gb forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving r8wram1gx -2q y,5 ewu2ylocn0 ailroad car, and throws a heavy ball straight up (from his pq8lm5wya1yu0 2 rw,x g2ne o-coint 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 that the Se uyvh0*2z+n iun goes around the Earth? Discuss inu v 0hy+ez*2in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at wha wx/m;/ ab(ygmt speed would the starlight passm/a (wb/gx;y m you?

The time dilation effect is if tr9vpqr3qs/7u //-htu c 7wsometimes expressed as “moving clocks run slowly.” Actually, this effect has nothin7wi ts 7r/tpq//f9q 3ru-hvucg to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean thw;hhp ,c lfx64at time actually passes more slowly in moving referencx6ph;4 c hfl,we frames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived homl: a xthh25ls8/wn g asy*x35z.9-tmkykf z( ie from a long trip. She rushes up to an old gt 2f855i /tzsk.(lza a9xsyghylhw:-3k *mnxray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earz6 omzrv r,3b ylqw5zr;*7xe;th at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline c5zxyzr lr e*3, w7vrm6oq;zb; hange? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, sayi)qh fr x(9 .nd0ig6gw $90 \, \text{km/h}$?

Suppose the speed of,gn fqlf0fyv2k *h. c5 light were infinite. What would happen to the relativistic predictions of length contractif , h vqnckf2f50*ygl.on and time dilation?

Discuss how our everyday lives would be different if the speed of u fqllk8/;uzgm0e**4r ml jo* light were only u*80 fm4kmr;lolq * u/el jgz*$25 \, \text{m/s}$.

Explain how the length co rd -agz11ai4f(e;fu mntraction and time dilation formulas might be used to indicate tha;fa4zgm efu( dr 11ia-t c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tompkin5hajb 3lem*4c s, for whom the speed of light b4cj 3aelh5*m 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 9gdl to8 ;( bus2lpcyk0por 1+c. Does this put an upper limit on th kytls (9og1d2rcpp0o8l+ ;ub e momentum of an 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 light?s25j poc)qgqoqz qgw9(9 tpi;47wpd 4 ----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 this mean that a sfc.+b9azk2 q yu1mkxa(g)t ,c gill20pring has more mass when compressed than when rela akikt au)clflzc.2 x, b 01+9gqm2g(yxed? ----待选择----yesno 

It is not correct to say that "matter can nep 32.20gpmhu+wfs jhdz: 4wmgither be created nor destroyed." Whatg:m0g2 pmzdf3j u.+ w 4psh2hw must we say instead?

  Is our intuitive notion that velocities simply add, as de l b7.da3k(z*pt-8zcey n3gwe did in Section 3–8, completelyee.t3pb 8n3- zdz7*a gl (cdky wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its yt+es7h8gs(b0 v9 y1kmley/ n length to be 28.2 m. How long wou(1e9y7 k+hb l 08y /mgtsysevnld it be when at rest? $L_0$ =    m

  A certain type of elementary particle travelszj.o d3u c8wro2ng5h - 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 dep .js8w(*kt gbnend 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 5q xpf8hva -r3 ql/g*slight-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 ttk 9h )wy+a4zoo 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 awayzc th) wmb.h + oaei0vem7.sfx /*y6:a. How fast would you have to .hmes+6x.aa* vefm w7ty cb:h0)i oz/travel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to nj3dgd8ln b 3tw8lw8uy b:mcm ,3v4:l8mq:j ca star 85 light-years away at a speed that tells you the dist, n3mugd: :w8jnl3388q8l4bybjdcc w:tl vm mance is only 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 fromkdz5lxf66o dhsu 34l( the Earth 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 from ab zbl,avb1c-j6qrs6v- n,bb2 5-year voyage whi, jrb -bs6nba216 bbqzcvv l-,le traveling 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.r,ye2fozllmb *ff;bz s8 ;f0+ How long would it take a spacecraft traves* 0l,ff;;fez2y+brbfmzo 8 lling 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 her "Ferrari" spacecraft at a speed of 0.660c. I0bg20ku ok, r.do2 mkarm3a-k t is measured in your frame t k,aok0br 2okk3-m2r0am. udgo be 4.80 m long and 1.25 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 average pion be moving to travel 15 m befo9:rs/hrra ,5 rp5nl tire it decays? The average rs i:/5rrrnp,h at95l lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelin3 wklu dvi2 y7k4,cy)pg at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass 5szp,4.dy)a-xik1 hdhqpq2h ? v =    c

  A particle of rest mifak555yj m0bass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels )dr,0zjy(ee+d;eqocyx *r +z 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 change in momentum of a proyrfcw0 n da2u xk+k2. -cu)kila 6+1futon that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requirrx008 n y.sl .blqpr5aes $4.82 \times 10^4 \, \text{J}$ 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 apartfhm-prhl 89ay2 t tz.+ in the process known as fission in a nuclear reactol.y+a t9- zp m8h2hftrr, 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 in9w iswgl*de(x2s )c9h joules 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 mass of3ev;tw(c:i x n a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States isa4, 8c8d k+526nfq tacb3f8 rmlw ndmk about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be o 0wy:1cy5mrzd btained 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 5a2 2grm tikx u4,ile/jz:vc;particle when its kinetic energy equals its rest energy? v = lgmtv5 ;e2zc,4ix2 ur/k :aij    c

  At what speed will an ob gqrlvmj .q:ak; /v9h/3cmp +vject's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to 8b:r1x +mlwk.7qh qwdg/yc;ma speed of 0.997c? W +1lwymkh ;/xd.mrqg8wq c b:7=    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 proto , *kvs/db0()*zoujsj, lst:s6sy y rvn 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-MeV proton (that is, its king5k l;cp .w)ihetic energy is 750 MeV)? gpi kh;lc.w) 5   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accele45/mp79sx ) rybpt rfzrated by a potential difference of 105 MV? v 94pr/ 5x tzfprm 7y)bs=    c

  What is the speed of an electron whose kinetic ener s3kb5qo0y5+ldo q: dygy is 1.00 MeV? v =    c

  What is the speed of an electron just befokrgl5vaec*y7m5 8;h jre it hits a television screen after being accelerated from rest by the 25,000 V of the picture tub8 eg7jkl5ym v5hr;*ac e? v =    c

Two identical particles of l ob: 3nl:0isirest 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 ofa8es v4j gw.(p a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 an enixrqx:, 1r0e lectron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 2;gq o9kpstl0 ji d pkfbno06+ya; ;5o77,000 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 energy and momentum of a proe7golqion 86jy+ /( fku3t4x iton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleusceie,cyu4 )zui; 4u;b, $^{241}\text{Am}$, 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 momentum for (a) a part/2w/pkru,e imxn( oa2rcqb 2*icle of nonzero rest masxpuemk rbirc,a*o2 n (w/22q/s, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons rev9 z7lzbp;n( itolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relz;7( ln tzb9ipativistic 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 Earthcgj+sj6 qj 0z0ucwh .ny6fv+3;( txsf) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fav+c .j uxn 0+ ;(6qffstzwcyjsj3 gh06st is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a 1zdk9 yu 3d )4v+udhdcspeed of 0.50c withdu4kzdhd13ud)yvc+ 9 respect to Earth.
(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 leave:f ) 1e2qvn.5o t9 ly0zjisbses the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth 9n5qfsie yjt0lsvz2.)b1oe : 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,pejp5lo 6 pvnze4 4/f 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? l/6zj5eo,vppe4n 4p fu =    c

  A spaceship in distress sends out two escape pods in opposite directions. One trp/ n,3je ueof5avels at a spf/,5 oe3upj eneed $v_1 =-0.60c$ 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 0.75c. At the same time, rocket B passe 40;vf 0l./3wce2axmtcdqvth s Earth moving 0.95c relative to Earth in the same direction. How fast is B moving rehcw0/mcx d0t4q2t; aelf .3 vvlative to A when it passes A? u' =    c

  The nearest star to Earth is Pq1d ;ylffi7ue9 -mpnsif/ 5* vroxima 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 traopzk: 16f7 of q m4hbt.yt.cr5veling faster than about 0.1c is called relativistic - i.e., for which the correction using special r c1 .hpr7t.fzqt:byfoo6m 4k5elativity 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 speedoqmp a- go wlr*haqsx +/jm7-9s3hp0- $v$ 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 h.iepvg *wag*; ave to be totally destroyed to run a 100-W lightbulb for 1 y *we*gpi g.v;aear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic ene g3d ff d4f/tx8lf5ww2rgy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as andf48dtx3gw fwl/25ff 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 rp)8w/t94.la wgr k:rw j/uqmspeed of light collides head on with a positive muon traveling at 50% the speed of light. The rm/8wr)wk/.pqt94l r:w j a ugtwo 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 decazz .x-69 tyl( ll1rhmby into a proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the fron(hyb6xl l m1 -.lt9rzzt 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 of aty (.unx76kf i 8y5vjlbout $4 \times 10^{26} \, \text{W}$.
(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 aeaoffa1c kmf 7) w3-,w 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 a cd:hzqr4z4cul sbw.d u+2h(p,w *o5 required to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a 4ou(w4*b2h, uwhd5lc q z:c+z prda.sneutron, 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) mass of a car traveliq ia*+i*n oivw/jv,m4 ng 110 km/h as compared to at rest? [Hint: use the binomia*4*w,n+jq i vv ioim/al expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in jlstn: t07k /rthe laboratory, are moving toward eacs0/ jtkrt :l7nh 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 rynf))jp 25rn particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining mattqj3vim l)rxg 64zh *9uer and antimatter, *)gi huz rmqxv9j463lachieving complete conversion 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 rest+ k.jy;nbf4 q*7*v:0qfmkxq( kvb woj mass (v kjbm+jx7 kkbq v.;*yqqo*n :w0ff4$m_0c^2$ 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-long poleds ndxhl:(ed5 b*m6;zdr 3xr) 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 shdl:; h )dex(dd6r53x n*rm bzsorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogeua,aix2 6 6o.nhmo0rdn and one mole of oxygen react to form two moles of water, the energy released is 48mi0ohd6 ru,a6 a xo2.n4 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 twx x p9.1rlq h41gh+im(n2mqc*2x szido identical particles are created, traveling in opposite directions. If t*cqdmxi1 hnpig 19+lxh.4r2qz smx2( he speed 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 tr+ :8jvvpyosr5aveling at 0.75c relative to Earth measures his ship to be 25 m long. On the shvysjp 58+ovr: ip, 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 , 7;+tucjobad speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observersauo t;7c d,+bj on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants qsc1hdkr 85fv 2ppy*,euw)0 w have a total mass of 150,000 kg. The occupants would lyvp8 s5qceuh 2,0 d1)fk w*wprike 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 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. Whmlz 0 zxwp:/;tat is the spaceship's kinetic energy? Compare with the total U.S. annual energ;/l txmwzp: 0zy 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 6,5ln *luiu9a tnn6 tp8jc7mo4.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work6 im*,at nn nu978lotjulc54p must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end 5c;cj,: pr bcvof a spring whose spring stiffness constant: ,vrjbcc p5c; 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 m)s6ssjt.v * l8ymjz9 o it;s;pass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.