You are in a windowless car in an exceptionally smooth train moving at consta(tlt( 0ol+t4uqt cd 18vpszec+r dx29 nt veloci dxz9l d rtuev4tq+(cl (2sto8p1 +0tcty. 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 red 5d8 vtgun .*ad le1:dvlight when, out of the corner of your ed1v:n a. dt8 ued5*vglye, 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 relative motion?

A worker stands on top of a moving railroad car, and throq-pf)h-t syq2ube2 e1/ec7qy ws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behindut pqf-se2q2/1yh-c )e7yeb q it?

Does the Earth really gozb aofl.ge:tdu /;d,5 around 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 no best reference frame). Explaidt :a o.zub;/dg5le,f n.

If you were on a spaceship traveling at 0.5c away from a star, at what sp 4ju vcgr7c675v: l)ry,tn8 nbutesu+ vsd (h6eed would the6)bd (uhc 8,c+ 5s:u47nye tgsv 7ujtr nrvl6v starlight pass you?

The time dilation effs+4w/ 00b(pj ffkgid xect is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the fdbf/gx 00k(i+ wf jp4sunctioning of clocks. What then does it deal with?

Does time dilation mean that time actual: qnnqm :anq*4ly passes more slowly in moving reference frames or that it only seems to pass :qq:nn4m *a nqmore slowly?

A young-looking woman astronaut has just arrived home from a long trip. p zy5 n34dus:2zhw(luShe rushes up to an old gray-haired man and in the ensuing conversatio2s u:dz(y 5h3luzw4pnn refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you kn8ng,vv0of/zz -bliezt*6o 6jxn/7 notice a change in your heartbeat? Would your mass, heigzxn8in t6/nvjb lzf*zeo- 6, /og7vk0ht, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, say x: rb.2 gt uo24nhps,sar4kd 3$90 \, \text{km/h}$?

Suppose the speed of light were infinite. /zve)x3e7p/v8 3wdz 7,at ob3bjdzobWhat would happen to the relativistic predictions of length contraction anoepzdv7 z3eo,bbb8/7 3jd/z) wva3txd time dilation?

Discuss how our everyday lives wou.c:z-sx1.y qg ton3s qld be different if the speed of light were only oq1 g:xys3..qsz tn- c$25 \, \text{m/s}$.

Explain how the length contraction and timeoj(*hqqs58rlg :x9 nkbw+jt+ dilation formulas might be used to indicate that c is the limiting speed in th 9grq*soq5t(8h b+w+ kjxj:ln e universe.

The drawing at the start of this Chapter shows the street+b h cmli5b8oq7.e v.zz9vq3h as seen by Mr Tompkins, for wh 9 z3lb5vv.hbq 8z. moi7c+eqhom the speed of 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 lesjs k63 /92b raj acu6dljfmj47s than c. Does this put an upper limit on the momen6 jbl jaamj2uk97jdf6 /cr43stum 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 lighfdjp s ryn*nuj+:sx ;3)- ;ujoc3clz*t? ----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 energtyyw9 ;:ie* x38ubjjcy, does this mean that a spring has more mass when comye: jcyb 8wj3*t i9;xupressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor b/qvuns :wz(.;3jn hpdestroyed." What must we q;bj:p. szv /h3( nwunsay instead?

  Is our intuitive notion that velocities simply ai)ybo:m4 vznto5ba. d*ee0 r 7dd, as we did in Section 3–8, completely wrongze ndmbibe5t*0:74) oy. a vor? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its u,ubn +;ol5 sbfdq;p 4length to be 28.2 m. How long would it be when at rest? b4o5l; u+,d;uqbpns f$L_0$ =    m

  A certain type of elementary p-hf;eu4ten4 p zo0lr-article 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 depend on t- )i fltt euz,l6rvi:0he 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 stu71 7e7 ygiuliar 125 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 /itrk +om 3b 1c8krna(its average lifetime 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 82 li.xir.8;zy(3 bx ciip qght-years away. How fast would you have to travel so that ti3ixpi; r.z. bcx(q8y o you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 lighitp- ;y 9*j*sp2a/ jmz8i ocr 8eetdm)t-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to mip- /eotj* pymia 89emj8z*)2t ; rsdcake 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 Earth8 kxw/fj-da/f 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 st gbfq(h)/ olq33 e-f4s2zwfqg ated that starship Enterprise had just returned from a 5-year voyage whi 34l gsqfgfwf 32z)(bqe q-/ohle 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-9mggzh pj jw55 p2) db6g9s+heyears away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured bg6)hp5wmj9sz5 hdp2+ gjg9be y 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" spo dmh yfn53) 1i::g0a+8f8kkhex0cg) wzqyohacecraft at a speed of 0.660c. It is me5yg+ f8 k1:dzxh) 30mhiay0g ) co8ewqknho:fasured in your frame to 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 averagd77vk)xi jxjd dw)g6 :e pion be moving to travel 15 m before it decays? The average lifetime, at rest,jk)x xw)6ijgd77 v:dd is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travel7fv x b;1xqm,wing at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativist15z7dw/p m8y7nqfwoe ic mass be twice its rest mass? v =    c

  A particle of rest masl4 yg+yboat mwas qd3**:t 1s/s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelsvu+,ecex():gesiei7 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 proton that acceleraya5vkn1-nlsc.x7r l dgcxoe :yzb d *.7 j9m3*tes
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactig19dt jlx6 e2non requires $4.82 \times 10^4 \, \text{J}$ 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 breaksd1tqi utg rovn) d7)nc0 +gt2nmsx/iomv. *+: apart in the process known as fission in a nuclear redv .tvx/7*2)micq10gd on:n t)irg+t nousm +actor, 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 qf e).-;k-p l/vr ox;ropt 6:fytbry10r 1 tbfan electron in 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 ma/(m(ouppy;)j *)yc hiq6kw yp ss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is ab (aeur+q bw+ 2l/4vknpout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversiod +,miff.1awk j4.k byqpvbv(5uu 8 g:n 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 p ;vb;xd4qul(iicqr:3 0i. ge wb0ic,darticle when its kinetic energy equals its rest energy? v =igc4.c0 bq(d,vbwd3 :lqxi;ur0iei ;    c

  At what speed will an object's kinetic energ7pod ;et4ev2ux;wz21l jj,prb 3zaci6-qzt.y be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a sppi6kkn4iq(v5-vrf3. d 6rsf 77db ytueed of 3rdtdq sufy k.4 vb(-7n765p6kv ri if0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy anr e3ugwu-: d4qd momentum 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 avwh qx0pum8,p +pr pu89t); uf;fwhz0 750-MeV proton (that is, its kinetic energy is 750 MeV)?)mf0r;pxp+w v; ,8p uzw8th9h0uq puf    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a poj8 zu3n ovq1t(dc;h 3ftential difference of 105 MV? v c38v uj;n(ho1zdtqf3 =    c

  What is the speed of an electron whosl+ 2n lpetn*tdz2i 5 o:0l1xgie kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen after + c9/uxjw ixo*being accelerated from rest by th/ju9+wix* c oxe 25,000 V of the picture tube? v =    c

Two identical particles of rest mass xv,ci3p2v1qrm (v3t q:8a afw$m_0$ 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 proton (fi x,;( q fx)id-4jrkw b b,2krk-*tkjv30nck$m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the mo7uodrjz/43. ouhe 0wklj, 92czym 0vpmentum of 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 2kq 786ke5 ixfu 0iv3xk7,000 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 pro9x r/26sxzi 13awupuqsr. j3oton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleuszy3oq ;.cm;m tq8pd 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 energy veq- ) pula83*6aalr guirsus momentum for (a) a particle of nonzero rest mass, and (b) a particle with l lu-iaa6ag)pr u3q*8 zero rest mass.

  What magnetic field intensity is nyf8 ljuo6,a8nj j05 c4 vjjd4rq- mh.beeded to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass 0jfcmrv j48ajj-h, u4l5bony8dqj. 6 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 respec+bkt9 by;g h5st to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u ghb5t;+b9k s y=    c

  Two spaceships leave Eartj z8-i7qa 9c h5,crsomh in opposite directions, each with a speed of 0.50c with respect to c9ra5z7m c8 -,sjoiqhEarth.
(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 spacesofcs5)( tbi)de/cyd kgq,s dna8j 38:hip leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with res3dif s(8o ))jta: deg,8nq ck/bdcy5spect 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 0.6v4 )6ggx 0odek0vc;c mf9 lm/c0c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving divkc4elg /c om;g9v f6cd0)0xmrectly 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 oub9kaw8 v5 (mnst two escape pods in opposite directions. One travels at avsnm 8(b k5a9w 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 *wv2s vo3y* sa t csdvo rd:)u6wr1n;3at a speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving rel:w vdrw2 *os)6 d1ovr *ssvcy;3u n3taative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Ceks g3i6*n9 l)8rizyyn ntauri, 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 qpzt*v9,(t 0 u 7:bmqc+ ehofhabout 0.1c is called relativistic - i.e., for which the correction using, h*z097e:mh+(tc up qfqvtob special 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 speedccsrv7u6 q 7l4 $v$ 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 eeb : d29woxx pakit 83(y5ju;o,;qjd100-W lightbulb for 1 year2 9p3; kot xqejeuji(w;xy,d ao5db :8? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of5fg5d5l)xj cb electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note thafxdcjb g5 55)lt 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% thg dz18-wdos;sw7 5ypzj,m l -he speed of light collides head on with a positive muon traveling at 50% the smywo7,hjsz d d-pwlg5;1s8z - peed 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 prot*p 7y ffal.gv6g1bvo 7on, 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 front cover. Determine the total kinetic energy shared among the three particles wh of1 p v77*abglg.yf6ven a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of ab n wr tuzl 2x5dcq*in;*j.s;/bout $4 \times 10^{26} \, \text{W}$.
(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 l4 cb*:cz ru 7pqcl(g*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 break a helium nucleus into its constituent)oaaf9 bcmk6( : 8d-c7nbmksbs, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 9 fd bn)kmmsbb o (-a6ac7c8:ku, 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 increasecze;v k9(boo4 in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint:9cvbo;zo (4ke use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving to4vc8rte,b9yg0 j wxx.ward each othe4e9c ywtv0,rx .x8bj gr. 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 momentum ;r (fkfbnr5 l/$p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matted+7,nv fro*( ut/cahyr and antimatter, achieving complete conversion of mass 7nu+hrv co,t*df/( a yinto 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 eut1fe q8q3u6 energy is greater than its rest masse18t6eufq qu 3 $m_0c^2$ 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 tha6 opo7sjlp 0g8t he can fit a 15.0-m-long pole into a 12.0-m-long barn if he78lopo6s 0j pg 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 shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one im yr,1iwt-o1mole of oxygen react to form two moles of water, the energy released is 484 kJ. How muc11yriit mw- ,oh 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 identical particles b ra);.aqw ba(op3c+z are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is o) paz bac;+.baq wo3r(ne particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measszc3 y-z xk8(jures his ship to be 25 m lzskc 8(yzx-3jong. 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 away from Earth. Youesygl(om 4e)ci h/d0+i 3/k ob send a laser be )+decm0s blye3oi/ig4k (ho/ am 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 occupants have a total mass of 150,000 kg. The ocflag,78-rdon pc*k0z cupants 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. Howa*p fl7 rok 0zncd8-g, 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 ar+ kw9n w9vwp, speed of 0.99c. What is the spaceship's kinetic energy? Compare with the totalpn+ wwv,9 k9rw U.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 *xkzlni , cm,,vicinity of a star 6.0 light-years from Earth. Passengers on the ship wan*zic,xnml k,,t 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 trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring r m4 k*pp 6ti, 19mwehxpwlv20stiffness constantver69,xw*lpm1h24 i0 p mptw k 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 mass )z57 swyv1lm 1)nukvz$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.