You are in a windowless car in an exce aoxoz.;w7rh sbt)h;)yo 7i *fptionally smooth train moving at constant velocity. Is there any phyiobxhhyf7wo; o ;*s7 z).tar)sical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red lbk(m l8jfommx9 d 50*xight 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 doefok9m5*dmlx (jm b08xs this say about absolute and relative motion?

A worker stands on top of a j ti0b7 t/h )fy59msotoo9n.f( mn us2moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, o. 5f 2mtt)t sy79ns( oon/ h0bm9jiufwill the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say tb1;g ccvczrm:ra4j :* hat the Sun goes around the Earth? Discuss in view of the first princcg j*zbmc;r:v1r4: aciple of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at:4mdlk jd(8vz/x qc-f 2t aqh, what speed would the starlight pass/jx mh,q(d fl: z82vaq-kt4 dc you?

The time dilation effect is so(8u 09zgeri3k6jtsn mf,7x phmetimes expressed as “moving clocks run slowly.” Actually,3( fperx0 mhz gisj8nku97,6t this effect 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 moww)+.dt- mln)u7obt-kk qqx9v +op,ure slowly in moving reference frames or thatw+9kduvt+- pl) qnuk)7xq . ,o-twmob it only seems to pass more slowly?

A young-looking woman ax4 1d6e twdd1kstronaut has just arrived home from a long trip. She rushes up to an 4d 6k tw11ddexold gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed dzuxw: 03jki m,bfw4;0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What woul mbd;,wki0uz fj:3x w4d observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, +qkt5+s yo,zvsay $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relativis 8r)sr(v4nchx tic predictions of len rr8v4cxs)(n hgth contraction and time dilation?

Discuss how our everyday lives would be differe9 z 9nu0uoew8ntu w77ax:6 neent if the speed of light were only e a0nxnw 6uu978 eoz9eutnw :7$25 \, \text{m/s}$.

Explain how the length contraction and time dil/ ss yuli-ehrwe765e 1bn q bge7vp52,ation formulas might be used to indicate that c is the limiting speede71-2phu5sne 6e/7 rg b, qwy5iev slb in the universe.

The drawing at the start of t3u) bjr7*8nuz rbi e7bhis Chapter shows the street as seen by Mr Tompkins, for whom the speed of light)ub7i8z3b ue rn7rj*b 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 putpa2 z9wny64uesznr c/c(t-l 0ktz 81 t an upper l8zku 2c-(/azr n yttetn04zwcl 96p1 simit on the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero ))q npg1xu5xog-e 9js rest 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 has more mass jcdvz h18y4+qnx9z0k onulm 29 fu,q1 when compressed t21 y zk90u1n v9jzdnfoxq u+ 8m,qlh4chan when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither q9xfwt*4w z0u, b2.7ktl y kxth(ksz8be created nor destroyed." What must ukwxhzfk*b2zlq(tt , t.0y9sw 8kx47we say instead?

  Is our intuitive notion that velociti p yr; f5s3essr5wr8vv38 *se/nj:ssyes simply add, as we did in Section 3–8, completew8/y;3 ess 5v *8sejr vp3frs:sns5yr ly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You mjwn+o 8+uo *z 1)zlsbueasure its length to be 28.2 m. How long would it be when at rest? j* o)lz1zuuns +bw8+o$L_0$ =    m

  A certain type of elementary particle travels at a spev2 4cab4tali 2ed 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 tfvl+c ys c bukyq03( uj-+5b wnh8o..yhe 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 s 4)vhmiwc t(c2dy4 .ydtar 125 light-years from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime is measuranx(rp 5 d+x*um2y*fsed 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 wou l g.2 j,qlt-2cpzo7zvld you have to travel so that to you the distance would be only 35 light-years? vt-,c7 lz2jp2q lvg.zo =    c

  Suppose you decide to travel to a star 85 light-years away at a speed thatbej5 +h. ta e1*nl :m08xxrgssnlwn66 tells you the distance is only 25 light-years. How many years would it take you to make the t h6n0w:5 sse*1xbanjexn+ .m6r t ll8grip? 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 kaq l091 g 0b j 6l)dpxlugn+wgk;-agw 8tr91gis $11.2 \times 10^3 \, \text{m/s}$. 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 Enltj (q 6joi4a8terprise had just returned from a 5-year voyag8 j6tja 4ol(iqe 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 ldrwqn )29d:2+adzyooc w4m6 l ong would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observ mw:d2r+la2n )o46 qozw9dydcers:
(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"(.xv p 6eql,:jtvhxb1 bzd5w wj:i0 6v spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long andbevzi (dbxx h:pv 66.5: vt,1lwj0 qwj 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 average6n )2w cww6d hjtkm5s8(r zgxy9.z6o w/e uc9q pion be moving to travel 15 m before it decays? The average lifetime, at rest,c6knd u e 2wr/jts9 hcw)6w59mgw(6yz z x8.qo is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travejt pz//e+eb*h ling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s re )yrg29dbooc8r.xu p; lativistic mass be twice its rest mass? v =    c

  A particle of rest ms (* th-yvmc:lass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle traveyfkb 5 9k+b 5jgqb.pcfj :nn3*ls at $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in momentum of a proton that accus( -9:tpg r5cdzty 7uqli5y3elerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reab w02 l42n:6p zdimfvlction 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(uildcm2rk2g,) hu codb 83h* at rest breaks apart in the process known as fission in a nuclear reactor, the resultih,hdc(dcmk rg*u bl3 u2 )82oing fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joulebi7 395k rpt5q,td*mlrvs,k m s 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 mados+i/3p k*j(k f-pk) sgp; k lk*n(5 bipe)svss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in ti,c/4 pwqb0wcn(nx m:he United 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 obtxi mm+i wgg)1 b 9nf:)qca8.ucained 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 when its kinetic energy equals its rest exl 1w7m: 0wn6/ gc ozol9v;juiaov6b2nergy? v =m lv l2v/iz6oacw0 xj;b:9og7o16 nuw    c

  At what speed will an object's kinetic energy be 25% of f4r+qra x w65mits rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest p9gv+ lv;fx1m*jm ;mqup to a speed of 0x;f +9vmqmg jv*m;1lp .997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentuypuic q4s7.j8l8kre bh.7cam(uj (1 om 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 p)zn3 x7 pyf- 5yq0kfq750 MeVpqzy-)nf5 k 0 3yf7qpx)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 3y,re dfy :ujw 2d)+ec105 MV? v =2d:wr3,f)jyecyu ed +    c

  What is the speed of an electron whose kinetic energy is 1.00 7ao pg+6jd0sx MeV? v =    c

  What is the speed of an electron just before it hits a television screen abp(r))1rx k2w5b5 a+py qir .lxdsck:fter being accelerated from rest by the 25,00))q15apw5+yi(d blk xbr2s :rc.rx kp0 V of the picture tube? v =    c

Two identical particles of re npfjym/rf(8t/b m5z0st 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 prott1-p0eo b)lwya5 ga w4on ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the moment;m jh, d6sw)/wf:mlp +w/jstaw1 b k/gum 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 0.21c. een7ujkx7+ k,lm68dc7 jj p4 fyi zd5/
(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 and9e bzl m*0c0fkwdtj /5 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, t4si /en+p*y u$^{241}\text{Am}$, 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 0ayj2tnk i5+a) a particle of nonzero rest mass, and y +n0ki j5taa2(b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in a c -n2ydj n5oqtz 7 yn/:ch70:vjpm,gg7*askgh ircle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The pro*-n:q:nyzgj oh0sayh g 7/ ,d77tcmn52 pjk vgton'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 travelin 0ja)c6qs wwn*g at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteaq jw)* 0wscn6or moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite direc0duld. 47ku lptions, each with a speed of 0.50c with respect to Eadl4uukld. p0 7rth.
(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.m;tm-)- 7h ayimkp ai(4ah k7m A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate thyha47im(k tmma-pk- a mhi );7e 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 e 8sw8zsqvqg7 uu ,+u4Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed ofvqss4uwuegu 7z ,q88 + 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sendapqf4am+c 8vczi2m r 68 q5s(ss out two escape pods in opposite directions. One travels at a speei+ ssc q5cza mapv 46f88r2m(qd $v_1 =-0.60c$ 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, rocket B passesp2*skw 78 evzs Earth moving 0. ekss2*pwv8 7z95c 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 E.(r q9k.0sgi jfmma,3c5eqpv arth is Proxima 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 0.1ce hjnbb524mqkcr:mp 5v(/h0j, q d0iz is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the vq0jc: eh 5,hmbz2bpi(rm5qn 0kd j4/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 speediyls q(d / sj+m)7xo4p $v$ 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 totallydxs(.i:s0w qpkf0v8v r;qtz4 destroyed to run a 100-W lightbulb for 1q x0s40; vwsr:qz.(ktdfp8 iv year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount ofannn v g8i cqws itu//1m-(.y; electromagnetic energy is needed to produce an electron and a positu/i(qy/;w1t-8mv.a ncs ni ngron together? A positron 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 head oh/p inhlut, 9q:7y 8ukn with a positive muoh:q ,9pt7/ ulnhuiky8 n 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 y5ik1fm:7qjjcf n-)d, and a neutrino. Assume the neutrino's rest mass is zero, and the n jfj5i) -71:qkdyf cmother 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 ratea.vwo5dr *ug(q dv,di6b+es 6 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 and ax/f64d955 oovu i+s ekgdq 6qg 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 requi.v6s1e q lyf/ f.ht mk fw. trjm8db:/oi.4.prred to break a helium nucleus into its constituents, two protons and two neutronfhdlm 1ts4k.b/w : ..fr jy6qr.p/ fiov.e 8tms? 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 the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in thzpfo o(k/ q3ve: 5+bzhe (relativistic) mass of a car traveling 110 kh bv(o5po:/ +fqzk ze3m/h as compared to at 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.), 8x;z a/o:pta42cftdjhyou 935c in the laboratory, are moving toward each o, 2j td/ taf a:u)cp8;4oyhoxzther. 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*8-twm ,9h*n:g3 y5czujonh kvd:yiq 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 combining matter and ,e1m)r 2fqbrce pg bus +k:++santimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approxb, s +)gfrq:21eu+c +ermpskbimately $5 \times 10^9 \, \text{kg}$, 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 kz q3lk,g47nos inetic energy is greater than its rest mo 4,kngs7zl3 qass $m_0c^2$ 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 canj2,ws0puf xi* 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 thespiu,j f0* 2wx 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 mole o*mor lxpe7p46 )g1unuf oxygen react to form two moles of water, the enep1 m7npo) uegu x6rl4*rgy 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 particles are created, travei oip26)q,kx3-am gjaling in opposite directions. If3 pg-qo) jax i2ia,mk6 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 particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative ttkwybnqe aa9 d(f3/q(al76b 1o Earth measures his ship to be 25 m long. On the ship, he eats hitwn9aekq y16 /3ba(7 (f ldabqs lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. You send a7clfg7pinfj98 xm( zol0 9(ra f(l90ga lcfp nrzo97xm (7 i8jlaser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mas nj61e3 qa/jvvs 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 spaceship changes mass directly to energy. How much mass will be n jva1vjq/e36 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 spaceshqm9 qd ddqt5pba c(x t14050rxip left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the tota0qp50d5crxddxb q ta1t 9(4mql 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 of a star 6.0 light-years frc a 9k32tj(ss*uaxm3m om Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 yc 3x*ajkum( a3st9sm 2ear. 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 n); qjnv9 .m w2xegu.w ajx.eo46e1pvspring stiffness constant isvao2e.v.jx6 mp)ejun xq w w;49eng.1 $k=48.7 \, \text{N/m}$. 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 nomphd(+b7j9x3dyq3 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.