You are in a windowless car in an exceptio f1l2r/(flmn mnally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car lr mf2nl(m1f/ to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of thevtp w3b.:qh *o 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. Wh *w.qv:bth3o pat does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavlpo(a1v7/vkx) 6x n woy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behind ito6v7knv l1/)(x oxp wa?

Does the Earth really go around the Sun? Or is it also valid thf2.a t5t;xjnn8l8n v o say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference j2h8 fntxna; 5.vntl 8frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speevb8etc9vwn+k6d6h8 f d wouldcbw8he8dvnvf+ 6 t9k6 the starlight pass you?

The time dilation effect is shtrj/e(-/d*flz bhs2*ra5 mnometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do2bm-aj *etrrh/*d5s ( /lh znf with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actuall r2nwg,ocwu.e/g;ss8 y passes more slowly in moving reference frames or that it on2gwe. ;gunrocs sw8/ ,ly seems to pass more slowly?

A young-looking woman astronaut has just a yer- oqu76fj8rrived home from a long trip. She rushes up to an old gray-haired man and in thqr 87j6-yefu oe ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at spej. o)u qa gn uj0p*cdb*;)pzw7ed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or w.d 7nqoguaj; *pj 0)pb)*zucwaistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, ,47zqem 6)rarszixo-d 6ck1tr: h g 2osay $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the rf zscmofu /r vh)( 02,an3dx*felativistic predictions of length contraction an of2d*xf,h(0 m/far 3)uvczs nd time dilation?

Discuss how our everyday lives would be different if the speed of lix1dnw /)s5 koaght were onlw/ 15dosk)x nay $25 \, \text{m/s}$.

Explain how the length contraction and time dilatio4e3i,9 kqy u dn5s1;-jm hmwszn formulas might be used to indicate that c is the limiting speed in the z4j q ds-n;iywes1,um5k3m9 huniverse.

The drawing at the start of this Chapter shows the street as seencj-g +vv,po jx4l4yq 6 by Mr Tompkins,g+, q- j6l yvcx44ovjp for whom 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 less than c. Does this put an u :s+8:r)wt)hyvqcp ol pper limit on the momentum of an electron? If so, what ic8)ywo :l r :phvt)+qss this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of light- 9y marxz7 d287qygck? ----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 has more mass when ckkiyvw-. ufy3rpbt-: n0 w+s)omp-ryv:3 .k-ik nfsw0+pt byu)wressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destpdz9ilx -2n:q8koh8fjmd- (yroyed." What must we say instead-(dq- 2 n8mzxihjd9ykf pl8 :o?

  Is our intuitive notion that velocities k bwcthy1l/, gngu5n ob-1h2)simply add, as we did in Section 3–8, complkcn )121gu hn -5lhb/ ygow,tbetely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its ll(m +qo8 jx(6cw+o(tzc4q mu-1sxkx eength to be 28.2 m. How long woulj8- cxwt o( qe(qm +6x1 +4sxukomz(cld it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels3phcs4 g m3i)a3 yi)kh 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 the factori;uk k7p/yqa9n ys-; :c)jqd* pl7wgu $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 from Eatf 27.6czdm(ir e8sos k(rp 2nrth 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 to be j.(z 9;fsm10tgnni xq$4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light-years away. How fo uwv/ohrs:hln3 6 ,z2ast would you have to travel so that to you the distance would be only 35 lig hw,vo2 /sl3:ozu n6hrht-years? v =    c

  Suppose you decide to trave).j1iizcu1g t l to a star 85 light-years away at a speed that tells you the distance is only 25 light-years.icjg. u1z1)it 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 isps 8mq ska q:5)ko6vm8 $11.2 \times 10^3 \, \text{m/s}$. 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 froma)azi81x5 cju a 5-year voyage while traveling ajz8xc1 ia a)5ut 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 a 7( ula b8142 gdwkajke7py5esway. How long would it take a spacecraft traveling 0.960c to reach that star froupakksj 7 (74w e5db2el8a gy1m 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 spenpjyqq1+br -(azx; hqp; dr:;ed of 0.660c. It is measured in your frame to be 4.80 m long and 1z(;; :x qp-pbrqa1 n+hydr qj;.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 1 tvo,0q+gfdp gg iusf/ 7)qd415 m before it decays? The average lifetime, at rest, is ig)+0tdf4gs/,d pvq1fu7q og $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of +sd; 98t s2 nik0:j4n uojdmbno h;ji+a proton 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 mass? v =7gb4lugnspw b,z(7)x    c

  A particle of rest mass :cdvz7b/f3 .i2 rbkw9lhz qk1k m6uh ;$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at .1 afdchp-wag cyhpi ,jer.4)m t0;p+$v =0.10c$. 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 inc7tg3u9+o6.sl j-zoaajbs (v(ws 0m u momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi2oh1b4z v(mo g6*yvr sres $4.82 \times 10^4 \, \text{J}$ 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 process k.xlm( +96yl7gwmmt c 7ifolv8nown as fission in a nuclear reactor, the resulting fragments havlmom6xf(vgy.il l8 +t9cm 7 7we 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 jz3) uns: 3j+**wk l twdyzry6soules 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 3qu)db/dbyft8kfj:9z 21pmjm k;ti6 of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Uxaeq8ozv/.u +q ps9 hg;:,l ;/gr aercnited 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 obtained5lk.xj 69m f 0iqa/bjjeh*s+g from conversion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle ozpgl /k:i 5:fwhen its kinetic energy equals its rest energy? v pfg/ki o:z5l:=    c

  At what speed will an object's kinetic energy be 25% of its rest e6ly. uxljxn09gzh 0 :nnergy? v =    c

  (a) How much work is required to acceleratilhd3 trhsmvf .v 3i(xqxow ; +k1wa.8 cyp762e a proton from rest up to a speed of 0.997c?+ h1 ys(i 8kd ;v.mixf6hlqvo.wtr2cw37axp3 W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic enek/7eb hs5vb) brgy and 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 a 750-MeV pr4 lnb)( kwx x6/rii9ynoton (that is, its kinetic energy is 750 MeV)? 9i(w4n kbri ly)x x/n6   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 4w bg)uaclw+ s08k3 roa2na3b a1qlj(MV? vqsun3 l 0jao blag8wb) 2c r1k3wa+(a4 =    c

  What is the speed of an electron whose kinetic energy ieu.s vg srwzm t.,.sybv ;26-gs 1.00 MeV? v =    c

  What is the speed of an elec :hz 0nsu;on 0 )/3ws vs3wgb+zus7xahtron just before it hits a television screen after being accelerated from rest by the 25,000 V of the picture t snbwus0 w:xzhgsz 37h);u v30n/a o+sube? v =    c

Two identical particnek*i(*9q gb w +5zkucles 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 pj6lk6jsb/q2 tc77 msaroton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 aur7lu9; pu 7m.qg*zv en 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 27,00cv0 d gqq-*oe00 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 pz4 a 3-ickofzv l(zy26sd5rs3roton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleui 5e:fbg xf:ut0kb7 hw4t .9uvs, $^{241}\text{Am}$, 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 parti /ci5.fdfel7k;+tst jcle of nonzero retecdfstj ;k il5+/f. 7st mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in d .;xzvyog,4hrt8gu; a circle of rat4zr o;ggy x, .u;h8dvdius 1.0 km (at, say, the Fermilab synchrotron)? 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 tr r64;gok+d odeaveling at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she mg +;rd6od4oe keasures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave n+non3;b(y akEarth in opposite directions, each with a speed of 0.50c with respect ton( nnb3+kyo;a 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 leaves the fi-qkrkg t7s-;4 vk tls2rst at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with req -kt2st;rskv 47 gk-lspect 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 q1 ucic 2.39qoykvgm0a speed of 0.60c. The Entek3m.q0 vq ou g1c9icy2rprise 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 inx.9lyuzre sif x;hy7zv.p(/ : opposite directions. One travels at fys (.u;/ hxvrz.i7y: lze9x pa 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 0.75c. At the same time, rofd95i/woi2)0d .uhhy(e jeoou(3elm,vci +c cket B passes Earth moving od/2.(iw +cudecivm)lu f3 o, o e50 (jyeh9ih0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 ll+l +ggg 7il:pight-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 a;xf2zfc.(3he fen. yg(tpxb9/.tw qa bout 0.1c is called relativistic - i.e., for which2ef c.nfzb.; ((h3qxay.wp /g9xettf the correction using 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 speedbt ;qxk/r2g *m $v$ 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 destro*,sg n0-ask qcyed to run a 100-W lightbulb for *sk- c asn0qg,1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electcldx hj6q;/ o:bzv,yws ni,. 2romagnetic 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 that ele ;6njq,zc bs2vx .wiy/l,do:h ctric 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 travelis.hb .sp x5b vez sictgw.z4+l48,4 qung at 33% the speed of light collides head on with a positive muon traveling at 50% the s5c qbs4tez .4w84x.s ,zhu.vpil g+bspeed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, anrtk0 gdn* np;t-v*6cqd a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Dn 0rn-ct6v;p d *qtkg*etermine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at /a*emt2jog10 y y3p 8 l :vzkk3:umehma rate 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 fcr4rs w1.bv* fk24o zand 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 nucleuqauhdy( eo6u62p w 3)xmtx r77s into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy2tx3 xwepur)(7q 6auyd o76 hm difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass oyi; qhx pa(yvwy0)iujx.88+l f a car traveling 110 km/h as compared to q;up+88i)iyj (y.xl ywvxh0 aat 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 tkdr-d rhay sc)8+-4v ehe laboratory, are moving toward each other. Deteya-c)h8v +4 krr-esddrmine
(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 part zp5;owm:ei9s5v8ai qicle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powe/b -nqq)qq7ul8d )xd yr by combining matter and antimatter, achieving complete convers)du-d y/ n7qblqq8)x qion 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 rj2m gwwb +/qk8est mb+ qgjw /kw8m2ass $m_0c^2$ 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 pole into zqei)cd++;oca 12.0-m-long barn if he runs fast enough (carr+ziocdq; e+c )ying 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 hyd b/i dcmyhq0ow9pb 13b -9;iizrogen and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elemh ;d b/ yq-wibb 9z0cpm91o3iients 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 64k89fvr acg yidentical particles 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 to the other partic 96a cfgv4ky8rle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measuresvs pmjd,kyly: (g7n(1 h8; q jnrbx4a2 his ship to be 25 m long. On the ship, he eats his lunch in 23 m2n dyja1;rgb(,(k h :lvp qy87xnm js4in.
(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 Earthdov9v s :zo st1l+;w.b. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the lasto ;1z9b.ovsv s+w :dler beam?

  A spaceship and its occupants have a tota4khv 8a*ytxn48 uoox+l 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 spacesh8x4utk8a 4o* vxo y+nhip 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 le4ql 7 02oyi,+ 19d tvjnekf4j ojv5qnpft Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. v79jjoe q ,fynni450 2q+ l4 1odvkptjannual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a s.+t xmcmd1eq6ecr.,2c 3d03 lzhj xvs q(t0qktar 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than d2ehrlqt 3jes+ 0mt, .q1cqm63k0dzx c ( .cvx1.0 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 springs5(nm;vx 7nj m whose spring stiffness constant xmm;7vj(5snn 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 masecbm5uoi:9c zurx 6,-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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.