You are in a windowless car in an exceptionally ssf* x *) birtr628oy h.jiz1qpmooth train moving at constant velocity. Is there anprb r.zh)x*iotfi q61j2 *8ys y 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 fwzw0 ;qyu7* ra red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say ;wfqz* 7 wryu0about absolute and relative motion?

A worker stands on top of a moving railr;w y*e85bteyar94eth oad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball a*t5 yrteb;y89 hw4ee land on the car or behind it?

Does the Earth really go around th exfh,r -m)2;5 ok*m pqbyn+mhe 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 frmo;5bh2e , r*+kpq yhm-)xfmname). Explain.

If you were on a spacerfts,o ink)u,nptd 1k32ehpw.:eda2mom ; 4+ship traveling at 0.5c away from a star, at what speed would the stp poi21s+o r) w,:;3h4,ft 2mnuddkamekne.tarlight pass you?

The time dilation effect is sometimes expressel*xo zyuv, ztwv,t* +r81qt-td as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. vq+ yu* xov tzt-rlt,,z81w* tWhat then does it deal with?

Does time dilation me2sj t*.g)b8/a uqamq van that time actually passes more slowly in moving reference frames or that it uq t 2*/bgsaav).jmq8 only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She elykt -u3nrm*t /a48p1 t:hxarushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. Ho/x8r4utt* :p thaka- elm1n3yw might this be possible?

If you were traveling away frondvr3:t q,6c:tx rok: m Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say abtr:qv3: x o,n :k6rctdout you?

Do time dilation and lengt-q6nzw 9plhnu0z .*e nh contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light we1glkcx9k -7 ljre infinite. What would happen to the relativistic predictions of length contraction and time dilatio9lk7c -xjk lg1n?

Discuss how our everyday lives would be different if the speed of lik(bkpkdu y1(s+ z h,hn0-dpj(ght were only kzpyn kjd (sh-1( b0pu,khd+( $25 \, \text{m/s}$.

Explain how the length contractwe(qst )5fu (kmagckb4 5ki:5ion and time dilation formulas might be used to inb)(t5w me45ukksq5:a gkic( fdicate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as se3lbumpa +n /5clxjro+ ;es)e6en by Mr Tompkins, for whom the aejpn6+ll3)r; ume5/+ bo sxcspeed 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 cjmf6c2pw)bcz,(ep2 upper limit on the momentum of an electron? If so, what is this upper limit? If not, explain) cbp, epc2mwz(f2c j6. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the spr; da zc)p7)jxeed 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, don0*w 4yirpgn c)mq, e0es this mean that a spring has more mass when compressed tha,)cmnryi0w4 pnq0eg* n when relaxed? ----待选择----yesno 

It is not correct to say that "matter can nei 5swx.*ijfdrx3gwm2 w5mzt4( ther be created nor destroyed." What must wm54 wiwwrg(j*m 5.tx23 fxzds e say instead?

  Is our intuitive notion that velocities simply add, as we did in Section 3–8,u0uj:v e*p (qm compl0 jmv* eu(u:qpetely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.2 7m* vj.,jvjo cm. Hoj c,jv .v7o*jmw long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travel;n:ka;r 8g i9- 6sprmfdb.s qes 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 intewf+026viz-wevskb3er, es6b rvals depend on the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from Earth5fw.rs1/u mm q 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 averag01kr)u9l wy uie 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 light-yea/wwd1( nkg9ie rs away. How fast would you have to travel so thk9g(w 1iwne/dat to you the distance would be only 35 light-years? v =    c

  Suppose you decide tocquh9x.min kf+ pss1w4/g4 z 0 travel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the t0fwz 1+squ s mx 4.ikgn/9h4cprip? 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 fromb rf,1z9iar* 4ncmtl3 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 aqd0k b*u7vn2u 2vnr3 had just returned from a 5-year voyage while travel20v 2aun3d*nqvburk7ing 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 j33v32lu 3gwwzr/h+d1a .wxpuhi3 qnspacecraft traveling 0.960c to reach that star from Earth, as measured by observers.grnv312puwwi 3 /z ql33x hw h3aujd+:
(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 yo6wb 4l7ia9se3wz6q jtu in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m4z6 6wwatjl 3s 9ibe7q 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 bef0 ep;p/qtlmw (ore it decays? The average lifetime, at rest,(mt /lp ;pwq0e is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton tra1 x9xlkspw7z 2veling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s re .afurr pd+ :9o/ffx)mseb76elativistic mass be twice its rest mass? v =    c

  A particle of rest mass ys l+3b*mkp *sfibh wy h0vt,1g,1 +ji$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at 9 gekvwy iifvsi/jm9rhl;37r c7l 2,8$v =0.10c$. 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 odb 8c4jp)c)r of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical r )*prmz tlx)n k-: hon+2b2axneaction 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 process oekg 97dt(++8vxqgaj known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost i+dt a7qek9vg+x(j8 o gn the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of a ai v:4vs(v /h8kqyw4cn 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 mass of a proton 8az+pvza83w2klue2og, gu l; in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abog.4- lk, tat4m5lnrhktmfk27ut $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 1.0 /a5jetr9j teqe r3.s* 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 w 6 o6wc0plfr,kb di3;jhen its kinetic energy equals its rest energy? v k ;,rpdi36wjfo blc60=    c

  At what speed will an object's kinetic ener4m(uhe8 ggo qy8w*ds-gy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proun4 yq j eo*,v8dbvmua)4lp74ton from rest up to a speed of 0.9u u , 4da4*)8enlmv7ovjb4ypq 97c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic esvgrkfwl5+0b- 36v zn nergy 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 proton (that is, its kinetic energy is 750 Mn1atw 5,, v1mr-gysd seV)? awvr- 5n, t 1,smysgd1   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MV?(dkd kd5h.9ix k8c-3wn0xv g4x /ahtv v vv/-tx9xwhd (kga 4h.0kdixkd3c 8 n5=    c

  What is the speed of an electron whose kinetic energy is 1.00 Meurd5oyzu,w8( jc 2t/hV? v =    c

  What is the speed of an electron just before it hits a televiub e*u4eaxg8w wf9: n(sion screen after being accelerated from rest by thxneguw4w:* 9b(8eu af e 25,000 V of the picture tube? v =    c

Two identical particles of l1 h(zzlh-kb oh o;bn 00gy3.zrest 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 ofh 9k.tg iiy4j7 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 momentuaprg-4gr s-pu a/xs7*uor n2 -m 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 accelerated to 0.21dd0rn4fs 6tc2h w7 xm)c.
(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 kinetize8 ovld4+v68hz ps3w.ba5ut c energy and momentum 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,ko(k),/qnk qg $^{241}\text{Am}$, 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 particle of nonzereopcdc9ri )1 3o rest mass, and (b) a particle with zero r9i3pr decc)1o est mass.

  What magnetic field intensity is needed t5rt r78 npi/mc4gk8v kzon(s9o keep 998-GeV protons revolving in a circle of radius 1.0 kmo k7i/n8 vg (rsmt845rcpz nk9 (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 travelx+)9we ue.tc*kh ch i*ing at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0..)xu +9*k techc*hei w50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directjhb(p a91+gzt3a g-klions, each with a speed of 0.50c with respect tolkh( 3aa9bj 1-+ggzpt 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 fir2p+h9qcazuc-l0 x)vb 0l- mef3pnibl9pzk 55st at a speed of 0.87c with respect to the first. Calculat ) zac- p-ll39b 5v+x5 pl2ukei0 nh09pzbfmcqe the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speed of 0.60c. The Entebf yb1nj(,xn s*3jb/0bq py(crprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed ofb*bxp 3(jyb/ j nn1,cbq(s y0f 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 gy)oe-s 3l0dm o u67ydin opposite directions. One travels at a sm u3s0l6dyg )7 d-yoeopeed $v_1 =-0.60c$ 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 sa7ctoc 7j61, kfw+ qf wl6w,jpime time, rocket B passes Earth moving 0.95c relative to Eaj fq7lt,iw ow+, 16c 6kjfwp7crth 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 light+ y-ym if*7mkvg dl;w ss+sce, (reo) 0mu*v6g-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 isi7k8)q7 t/vomkr2ym 2l;z wh b called relativistic - i.e., for which th qwhmv7o/28irzy b)tkm 2;kl 7e 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 speede0dspmj9 6un1 iyy-y gcq 8)ae p3b0x6 $v$ 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 10-fq rpx +txz 4bw.j/r80-W lightbulb for 1 tpbx 4q /w-.8+rjfz rxyear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electro2e sy,vv.wl2n magnetic energy is needed to produce an electron and a positron together? A posi2vvn,ws2ely . tron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collides he;in-jhwiyye8wg.i0 9 3z5 wv 5tzz 8nrad on with a positt85zz 8ygw5wzr- nyie i9ihn 0vj 3w.;ive muon traveling at 50% the speed 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,+xa e i0*ljw)6,no 7vlyzfus , 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 energ0ji +,l*yo,6aeu wvnzs)7xlfy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about e*7 aouc,rkd:$4 \times 10^{26} \, \text{W}$.
(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 negatik 8zpsrj,sber f,*o ((ve 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 wouldl4wr dnb gsc2lz4- dj,a;iz8gne( ;.n be required to break a helium nucleus 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 energy difference is called the total binding energy of thewa; e,cn2gb .sl-8n4dzjig(lz4 ;rn d $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relat60c74re+j ,cfrrhdcnw(vvp) ivistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use tnp0c ( e cd7fv64ch),wvrjr+rhe 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, ar.lppwv(qh oy- x 3j,: 6rgr9cue moving toward each other. Determine ovxpprw. r:3y(hc6lqgj-,9 u
(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 wbfhi ; -b/nubi9h2yss4.c 77xm tbu8 cith momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power b j9ckaqq(7xqp9 zr: mj,+r 2tdy combining matter and antimatter, achieving complete conversion of mass into energy. If the mass :z a(9rrj+9cjpq2xqk d7,t mqof 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 ki7foy:rd51+rb, o re rxnetic energy is greater than its rest m:x+ ,rr dfreorb75o1yass $m_0c^2$ 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 cb 9r d,uumk52oan 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 detai uuokb d95mr,2l. 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 g1su.yy9o.i+h+ks q;cjy3ib mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the ma9i 1g ko ybhuq3jcy ss+i.+y;.ss 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 are create-(x y1c ph ck.2jzosn1d, 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 otherh kjx1sn(ypc1.zo 2 c- particle? u =    c

  An astronaut on a spaceship traveling 1b7ff on m, lkwqe-48fat 0.75c relative to Earth measures his shf-leq w8fbof17 m,kn4ip to be 25 m long. On the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away p6isl76 h*c0d1wa nvmfrom Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers 7*win0 6h61alpds v mcon the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. Thed1 pz2ygswz6oo:z(p2,zx es 6d9i8w c occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will ozzpydxso8z,6(sz w21w6egp d9:c 2ibe 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 cukw.mvt// ;:pxtf5k1v 4km s of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consump;t k1ckmk/x sp.umvf5t 4 wv:/tion (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 6.0 lightaz9t xw, ,)r ediy5k la f;xnw(oo8k+)-years from Earth. Passengers on the ship want the (one-way) trip tek5;yz)o a(afko xi ,+dlw,wr)n 8x9to 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 oscillaf ykt0k 8;x6iztes on the end of a spring whose spring stiffness constant is i; kk 8f6tyz0x$k=48.7 \, \text{N/m}$. 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 9wdt5q8rpik sss 48+m$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.