You are in a windowless car in an exceptionally smooth t gzhvrp6juh6)gu 7d,:w d ;q/irain moving at constant velocity. Is there any physical experiment you can ru qj6gh :h7 wd)/,vdziug6p; do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being andmk((ol93z 3u, -u/h7rdpzt q ojrw0t a 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. ( 0p uql/zzoj3,dnu dw (7o39hmrkt-r What does this say about absolute and relative motion?

A worker stands on top of a movingm7e2ghu fn3:h)6 vtr* iwpr,g railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resisth: p6ft ,v nhgg2 *wer)iur7m3ance, will the ball land on the car or behind it?

Does the Earth really :r.j) ml+fzhf px8swq6-j x+pgo 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). fpzh) sf+6wxx:m+j8pjl -rq. Explain.

If you were on a spaceship traveling at 0.5c away from a star, klt9r7 o7 7frz5yypy1at what speed would the str71 y9ytf 7 zlorp75kyarlight pass you?

The time dilation effect is sometimes expressed as “moving cloq6 b ,by,iqi,ecks run slowly.” Actually, this effect has nothing to do with motion affecting the functioibey,q, i6q,b ning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in1gc 5oq2.b jd mrju,qm5, nk1x5)xwnj moving reference frames orwm5,o2xqn.jx5cdnk5q ), u1g r1mjj b that it only seems to pass more slowly?

A young-looking woman astronaut h9hzi;f t b37vuas just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possiu 7fvti93 zhb;ble?

If you were traveling away from Earth at speed 0.5c, would you no,dxptnk 85 +kv22hm udtice a change in your heartbeat? Would your mass, height, or waistline chan+p5dm8vhu22dxk k ,t nge? What would observers on Earth using telescopes say about you?

Do time dilation and length contracti,dxvk* 8d :tn5jr 4bgfx9a3 pmon occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What woul6d)f /efxh4g xd happen to the relativistic predictions of length contraction anhd4fe)6gf/x xd time dilation?

Discuss how our everyday lives would be different if the speed of ligh w dn2.rm/(bert were only/ m 2.rnrwd(eb $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas mighx .z24efdjtj mrmtk :.616cad t be used to i. xacj2tz 6f4met:djmd.r16kndicate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen jp 07foks l2b/*w (lui.s lr1oby Mr Tompkins, for whom the speed*(j1wfbl0ur /ksiol 7ol 2. sp 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 trave6ipa geuz,y u1nk) nq5bh:p7;l at speeds less than c. Does this put an upper limit on the momentum of an elect qn ;hp :bpz7)k51iyg,a 6uenuron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed k hbqgf21(t6 bof 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 rv l;q -pnqd:)has more mass when comq-l:r v) dpqn;pressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed gg2 l.x1h+mwy." What must we say ins h+m12gwgyl x.tead?

  Is our intuitive notion that velocities simply add, as we did i9 j p)qd9.5bh sd-1lpmyi+xqen Section 3–8, completely wrong? dlqp my1.x5p-ji99q+hebsd) ----待选择----yesno 

  A spaceship passes yh.ulokwoh tw 8.+mxlkpd *(7ww4 ;z2 jou at a speed of 0.750c. You measure its length to be 28.2 m. How long wood o74z+lhp2thwl m.8w uxw;k *j.(kw uld it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels9p,.b 4iol u3yyo0- innl,yi q3mazb8 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 thez-nz1fhzl :hbc 2k6.md3l9vm 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 Earth at mhphc) xk 5)8ra 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 a-2e.u m wnda8uv5gsx9 verage 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-years away. How fast would y(ynhfm i h :p jhj6*.wxx44qhs 8w2+lxou have to travel so that to you the distance would bhxnhp 4*qw6s4hy(xxjf:i. jm hl2w+ 8 e only 35 light-years? v =    c

  Suppose you decide to travel to a starg/s nj:v6 r-dx 85 light-years away at a speed that tells yvnd:gs/x6r- j ou the distance is only 25 light-years. How many years would it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the E4qb pi5p4yzj8arth is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

  At what speed $v$ do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.) v =    c

  Suppose a news report stated that starship Enterprise had just returned from and i(rs;mqwl/eh5/bfc ew /)( 5-year voyage while travel///f d) b(m l5;rhw( cenwseqiing 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 womk1 -)/j k9,d dy ttw7l(io2l6nyttcc uld it take a spacecraft traveling 0.960c to reach that star from Earth, as measured( 7mcty1)-6o/nj,k2cyktl tl dt iw d9 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;e6rx +h u8z+/ulyo: m6quf uo her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and uuf/ 6o8 leu+yz x6qrm+hu:o;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 1q u1n,fy5nf om before it decays? The average lifetime, at resqfnou1, yn5f1t, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum mi86d/zii tx) of 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 oi-b3 tk4r3bi *mqt3 ymass? v =    c

  A particle of rest mvn-(h ;w+zam3y 5vg5 4awor xtass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelsc u: ;)jvuym,j 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 pricr;: 9kw 9cfuoton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction require6h+xcb/ge nwjhz(- e(s $4.82 \times 10^4 \, \text{J}$ 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 p ypr 6:ggoe:6ry,val6rocess known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy orv:6lpya6 6:, yeggor f about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest entb66 evz 2fzjn0nd f6es75bi2ergy of an 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 offf3wtc++rvc2 t;*k yo a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Statk t.u t*hz t;qnl26v4fes 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 fr / yom4,.rjysbillp w3h 6 ,j37wf)icnom 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 when its kinetic energy equals its rest.a.wyqjp40 bjs djn (- energy? vab- 0jjq w( .4dpnsyj. =    c

  At what speed will an object's kinetic energy be 25% of its relwuky m:ag ;5oxkm2):st energy? v =    c

  (a) How much work is required to accelerate a proton from rest u 73uu (+ggdjpg;f p(g1zlms2.p u7oa3 p 9uaezp to a speed of 0.997c? pga zz;m( p.3p +uof 2l1j uude 7a(p7s9uggg3W =    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 protogdz l-/c1 vjp 6t3,snon 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 enermw( u4,s f 6gc+n6wzgzgy is 750 MeV)6g4( wz+zcswg u6m, nf?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a pote62rk m )fwf4yiwo1)ukntial difference of 105 MV? vwf1miry6ko)fuk 4)w 2 =    c

  What is the speed of an electron whose kinetic energy idegz. ,dt1g( y(p7vofs 1.00 MeV? v =    c

  What is the speed of an electron just *vo+ ) xzntq+w.oml0qqhf+8a(p zl1rbefore it hits a television screen after being accelerated from rez o+.vnwph+*l az1qt)0olmr8q( +x q fst by the 25,000 V of the picture tube? v =    c

Two identical particleo/zb1a93 r5;i hlvw,q 6qzshls 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 p3y,tbr pe4x )groton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum of an electrw dt/ a6fq8a64f- l1 czhepwo8on ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 0.2l/pcf, q6+lqxm is99d1c.
(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 anwe4/4ulz* ql0wxr5bn .f4kcb d 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, wey3 q/3;7kde)zmxr7m m1 lrv$^{241}\text{Am}$, 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 non 6rxf+(cihz +dzero rest mass, and (b) a particle with zero resz(6ih+rfd c+x t mass.

  What magnetic field intensity is needed y7ql ;fx0cd3 jt4h mx)to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the q 0;xdlm)jc3th 4fy 7xFermilab 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 traveling at 0.50c (with respect to the Earjp1n5b -hzi y5e5 rp60x ct(xhth) observes a meteor come from behind ane-hx5i( x0nyhp5 5jc1 zp tr6bd 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, ehbn o5.eghl.qyce + )/ach with a speed of 0.50c with respect to Earth. hc/.ohelygn +b5) qe.
(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 ead r29hp-jtmy)gi*5 ;e5n xesecond spaceship leaves the first at a speed of 0.87c with respect to thex-*9 eh mpt aid)jrnyg25e5e ; first. 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 Earth sees an alien vessel appro8c;9(uv qqrq-9pswxk+atzu l k 379jqach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed p+l7q(w k3ku za8r- 999vtuqqj;cx qs 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 directk 3f(c *5 a83kx.nsc,jjhp7nmm r q- rrujn7/wions. One travexsnj/ 5 mr,qkan *n7 fprch w.j73j(r8k m3-ucls 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 speed of 0.75c. At the same tigf ex+x.vt3vt + ep 28-m5hrx2)jq yybme, rocket B passes Earth moving 0.95c relative to Eajg xyvrvf2mp xh.e+253xy) qe+ -8tbtrth 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-yefeb c(iq ,c5jh16 st/dars 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, anyth4 2oomkmpt f)j ibwe+8j5n7- ;madz6z ing traveling faster than about 0.1c is called relativistic - i.e., for which the correction using sz-ao7+j n mktm dopz;42bw5iejm8 f6)pecial 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 speedzwy+ny)sv 5a -sw. w+mbvu4 ;y $v$ 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 destroyeprz8a oa nf3+ 13 )8cykuhs/fwd to run a 100-W lightbulbzrfc/3nkhaw) oy 8p38asfu + 1 for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is nydi n)5vdx 1t,eeded to produce an electron and a positron together? A positron is a particle with t )d,vdyi1tx 5nhe 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 travelin:5v ct.;b 7flfxj- jvhg at 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest matfh:7 lvxj;.j bv5c-f ss $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, lc5li 1.e;e t/heq i/nan electron, and a neutrino. Assume the neutrino's rest mass is zero, and the otle iq ln/ h.eet/i5;c1her masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about;(jru5rcg mo2 $4 \times 10^{26} \, \text{W}$.
(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 and a speed8 4wq,qjn( 7v yynxyd7 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 requihqy *ih hi0v:wb6j b :c;5n5arred to break a helium nucleus into its constituents, two protons and two neutrons? The rest ma56bj:i 0 i; qhrc:nhy wv5*hbasses 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 the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relaez35bl,b 4o mhtivistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansion.]l,h3e45bbzom $\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are movin6*yw2gas z cwo+ japa3oh,4s -g toward each other. Determigo sjaapywzw+os4h6*3-ac 2, ne
(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 tha;:g8tugwl0+ vpy 0z uqt a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combinins9*duzd.c, mc u4mde 3;z9 d wbid;on-g matter and antimatter, aczdim wc3b, dod z 4u9s;;9* d.-cdnemuhieving complete conversion of mass into energy. If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energ/yll c4a0llj8 y is greater than its rest maslal4yjl/c 0l8 s $m_0c^2$ 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 int/ p8es/du7e rio 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 idse8 i 7u/r/edpea 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 mole of o56 ncrh 9otiom0(r/bmxygen react to form two moles of water, the energy released is 484 kJ. How0h o/rm69 imn5rbtco( 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 particles arez9mz ayn054xvss:4qg 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 particl 4s:9x amzzv5n04qsyg e? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures k4ufoin 8/ix(;*-at po+jm umhis ship to be 25 m long. On the ship, he eats his lunch in 23 min.o4k omun(8/ m-;x+pj*iaut if
(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 :( r(y 3 (bkraqhq-qxvspaceship at a speed of 0.85c away from Earth. 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 lase r3qrqkb-h(xy((q: avr beam?

  A spaceship and its occupants have a total mass of 150,000 kgn1aw1j 6hpq r:. 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 spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship tr wha nq16j:p1o this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. W l.yqji hf cjg*2+a*bgcq9p9,(jlr2xhat is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumptionqfj g,lq.r h gc*9ij2l9+ja2 cb*pxy( (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 6.0y9jf4 b b5gnc(d70 pjm ca5o a:b+m0rt light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must bejmpa0yb0r+nf5cb d 5(m:ogjb 7 ac9 4t 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 consfvq6;b4amvosyu: x ; rs 148xwtantv:;r14m 4ua6f;xx oys8 sqvwb 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 ma)eteie0jvcnijw ;-t x/e4j02/k boj3 ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.