You are in a windowless car in an exceptionally sms sa ykum49 m x3.zycw/x71-ilooth train moving at constant velocity. Is there any physical experiment you can do in the train 3-saxci suy 9z/l1mwx. 47myk car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of lnnkmb -ditv92.sb :3 being at a red light when, out of the corner of your eye,nm bdni.s- b2l:93k vt 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 cqoqz 4. jyq)s69rd)m oar, and throws a heavy ball straight up (from his p4rq) yqm z.9ojq6o )sdoint of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the 4un:a.su l2rb Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of lusb4n a :ru.2the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveliv hfrb d-v1n64ng at 0.5c away from a star, at what speed would the starlivb4v-dr n1f6h ght pass you?

The time dilation effect is sometimes eyd)-iauu7/s 0l+tjrb xpressed as “moving clocks run slowly.” Actually, this effeciu )ja0 l+utr -/dy7bst 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 slp(i8 w86q cdy *q4v7*ghzseh jowly in moving reference frames or that it only seems to pass more slow e 6vg pqd748*8c h(y*qjhzwisly?

A young-looking woman astronaut has just arrived home from a l0mvbz j 7fu)*nong trip. She rushes up to an old gray-haired man and in thvn0* 7)umf zjbe 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 chana6ojzq)k 7 4i* muysgx mc410uge in your heartbeat? Would your a*4m)4igy q7 x6c0zoujumsk1 mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, say+a ;spzn m7y2nl6qxnfk80) do $90 \, \text{km/h}$?

Suppose the speed of light were infinite. W03zwgl;g13i1 btxyzb hat would happen to the relativistic predig 3zw1gl3 tb 0y;1bxzictions of length contraction and time dilation?

Discuss how our everyday lives wouldy3ff-esl)aaw lv;;nq.yl/h:8t89 z rudn u.g be different if the speed of light were only 8d sv u-q.l/ren;n:y)ltu3.l8 ffh9az g w;ay$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used3pr+r x/9x tkn to indicate that c is the limiting speed in the 9xrrnx3/pkt+ universe.

The drawing at the start of this Chapter , +1ejdt l;8*mx*jgjz4nzlwj shows the street as seen by Mr Tompkins, for whom the speed o e8 jlw+;j,m4 g1**jdtnzxj zlf 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. Does this putl1/hqjwb;bk i mr()vbzh.-0 f an upper limit on the momentum l10;jbkq .fh(vmibrw)zbh -/ of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero restymh 5 nb) zqdyd5m4+c2 mass attain the 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 this mean that a spring() .( dkvc kacdckuy :zwda3:2xy h-i( has more mass when compressed :h-3 (kazi2a:cdxv .k((cy)cdud k ywthan when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created xg9yd;bjo)i0c k a9x :nor destroyed." What must we say ia )bi9yjg09ok;c dxx:nstead?

  Is our intuitive notion that velmygdwtn.,r rp1 657lq ocities simply add, as we did in Section 3–8, comp m7 6.5nql,grwyt rd1pletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.te5 p8e4jztam;ux6 l)t4d e d/cd. s1r750c. You measure its length to be 28.2 m. How long would it be when atd 4dp demu);al6tej xs /t8 z45tr.ec1 rest? $L_0$ =    m

  A certain type of elementarf z,qv+o9i/3 dp/iepjy particle 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 depen, sy1z8bbgd b+n:g*o sd 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 1.jacyr v0 /f b2oig,/t25 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 measur izjd oe):wh imh7g ..r1t)ih/ed 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 light-ye)8b7 xoau6.r hi0,osz eun0tiars away. How fast would you have to travel so that to you the distance would be only 35 light-y o ais,b07 zn)xu8 06turieh.oears? v =    c

  Suppose you decide to travel to a star 85 ligh1*h fu mv8z2w2n-vg aqt-years away at a speed that tells you the distance is only 25 light-years. Hg wvu2 *na8 -vhmf1zq2ow 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 t.rtwhbkv 5k1/kw os s72cr k5,he 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 return prg.pgca7f6dby 6 33q(cve3d ed from a 5-year voyp6rceg(6qg733.vd fay c d3p bage while 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. How long would it take a space bmuxfh0a+/gs4uzg ))craft trave ghzu+)ua)0s m/gbx4 fling 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. k ch2 pe+z16jhIt is measured in your frame tp 2c6e1h+zjhko 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 average9 dgbafj8q-esa .4lv/8q4n.; e i pcwa pion be moving to travel 15 m before it decays? The averageg8/ wqe ;4a.b-qcln.4v e ijs8da9fp a lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protor 4jwu/wlkz8+ n traveling 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 ,qao2kqa9qn g61u+ cj8xem2c/omy5 z mass? v =    c

  A particle of rest mass g1*ina 1is8lv $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels all 7m 59;z- 6rfpl2ow fixc8xlt $v =0.10c$. 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 ac8z+ da ptfl6f0celerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reacnni 90d 7tmkt-npu* g3tion 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 breaks apart in the pexlwv+4iy j* o5h .rj)rocess known as fission in a nuclear reactor, the resulting fragments have jrwvy+ije54l*)x o .ha 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 +v mlmlq oir1xc12 ++mwdvv3)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 mass of a r7+jl4rhet2. r4sn y llf x5,bproton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the U* 5 77d;pydz4caxjlywnited States is 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 obtained from conversion of 1.7mghhm d a09 xdnrlda-crvd ,b.*) m.,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 kinetix iji7k11+ zijbc6p0fm zb)zc1kla 1 5c energy equals its rest energy? j5zl1 kx016z b+1zkmi j1c iicf7a) pbv =    c

  At what speed will an objecg)9f 6pq6qbn hcyy-.it's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required umn2,s g-sr4 kto accelerate a proton from rest up to a speed of 0.997crks, 2m- 4gsnu? 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 traveling 9w/(kvoh( n merc cl(*$2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-thr9;yur(q ;+s:ym ks MeV proton (that is, its kinetic energy is 750 MeV+k yr hr (;9qstuym;:s)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potenti7xp 6 5gqgea, 3qnis*dal difference of 105 MV? vq6*5 n7sig ,qpxea3gd =    c

  What is the speed of an electron whose kinetic eneo j- 4ca :c1rl cy)nhmk8ot.+1lfpi .8uxazi0rgy is 1.00 MeV? v =    c

  What is the speed of an electron justm sm lokm0lkz77c8zbbf k6 ;u+:*q/ pv before it hits a television screen after being accelerated fromsob*fzm 7uk mv7 klzm:6 bklp 0c;q+8/ rest by the 25,000 V of the picture tube? v =    c

Two identical particles of restcyeuff ,6p7k.i.iv u 2 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 protc8 sv31wzd1 p3).mylqi4au iton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the m3*tdse aunqkyc* *cusuvpa/ : 2/l9g3omentum 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 27,000 kg is acceler: -rw(sdkxih9me -3f tated 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 hy (w2oh;; msqmomentum 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,rkyw 6 cf+l w.n k40s;3fmuix6 $^{241}\text{Am}$, 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 vers7uq)cb;) pr mph3;jfe ;5aubj us momentum for (a) a particle of nonzero rest mass, and (b) a particl)qj3;j7m u5phe ;c ab)f;rubpe with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protot9ap,b y;.dy jns revolving in a circle of radius 1.0 km (at, say, the Fermilab synchryt yp 9a,bd;.jotron)? 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 travelipan7gnjx +mi f.qbz.a 0e l0x.)+) voing at 0.50c (with respect to the Earth) observes a meteor come from behind and.a)x+na .p j+00fz)io.l xegim bq n7v 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, each with a speed of 0.xk2*jl2 km9vjb zc ) 8xfv;d9o50c with zkx) vfbj k8oj*cv ;xm2l9d92 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 Earts+nfuanl 33j y 6nf+*qh traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the firstau6njly +q* nsf+n 33f. 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 Earth2.l o(wgsa2t o nl*q58-z ewkz sees an alien vessel approach at a speed of 0.60c. The Enterprigoowz2 -.2l (astn* qz5lk8 ewse 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 =    c

  A spaceship in distress sends out two escape pods in opposite directionm y;7 vsyen2k3s. One tra72sevy3 mk; ynvels at a 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 specs0v +)fszsi +ed 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 relativ++)sfvcs0 zsi e to A when it passes A? u' =    c

  The nearest star to Earth is Proxiuu6-:08gwph c zqqq r-ma 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 hjz 7v 0nv/eiafmq9*,is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determin j0av* hz/,mf7vqn9ie e 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 speed cr(;kuwn40 z 6udjtgos:a1h 3$v$ 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 wa5to ylyc/pq31 rgh-(ould have to be totally destroyed to run a 100-W lightbulb for 1toh-lca(p yr3 1q gy/5 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of :i* lkf.kul5a electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same r.k fukl*i 5a:lest 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 cozqox gn et6d+0oe* s*3llides head on with a positive muon traveling at 50% the speed of lighten dtq6g0* 3*eoxsz+o . 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 protbrxe z/ndjyg7a5u77nh2vn+a . kb2 8g on, 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 g2 v .hnb2n 7d8bzjrn/k 75ay 7e+gauxcover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a raej1w)pm7/g;e q-g u:erkvl *y te 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 isa ti9u +y,8tb7 eqjaks8w9r w8 measured 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 break a helium nucleus into its constij og+u, xm91sgtuents, 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 c9 gg+,m jso1xualled the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a ci(bsxl0;ag jzm 9 +xbssn4 2+aar traveling 110 km/h as compared to a90xbxssami; nlas4 + 2bz +jg(t rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in 6f6x66qpdmgzzn;nh ny o1 / 5jthe laboratory, are moving toward each o/p n666 5nq zmnx1zfo;gd6jyhther. 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+ 2pq:s-1mthzez s(j d with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powe9w 9uju(jbwpr/0 j ml,r by combining matter and antimatter, achieving comu juj wrj90mpb(, l9/wplete 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 ;y/s5 md i0 ozyk04evothat its kinetic energy is greater than its rest mas y/o5v k eoy0id40zs;ms $m_0c^2$ 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 bej+rbf g gib*:3q;e d8olieves that 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 bb:j+g;bqo 3ie8* dgr farn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxy svq qli 6k 1ddtt71i)fu3u:9x9,itrpgen react to form two moles of water, t qt qd7tf3t 1d1vu9 p69i,:si lkrui)xhe energy released 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 identical parti,5pk24,*jib mu )l umwjbt*xicles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative tbjmki2u , ,wpj* 5xtb4u)l *imo the other particle? u =    c

  An astronaut on a spa(6ugme jj3 nb9ceship traveling at 0.75c relative to Earth measures his ship to be 25 m long. On j(3un9b6egmj 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 fr05 h wuedt 4/e8 x9*,efygyshaom Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do obs 8xuf tw *d4/y,0shh5yee9 gaeervers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg.9;4b mt q-okeb The occupants would like to travel to a star thaeb4-b9 q tokm;t 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 ofy qe.yucwzj),0.vtz+ 9zlh+pi,6hu y 0.99c. What is the spaceship's kinetic energy? Compare with theu c, ejy v.)lph.yyith,+qw6+u z90z z total 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 vicinity oq,gb1/ialv 91aksg fg;k5 x,9p1hgo64h ve w bf a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.vp/;,g1bbog fk1q6gv1s 9kial5eh xaw 4,9 gh0 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 stiffness constaniw8utzqq5gn 8 +v(6b ct i8(i6u gbtnq +8zwcq5v s $k=48.7 \, \text{N/m}$. 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 mlm el 1.j/;wxsass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.