You are in a windowless car in an exceptiou arxxts.13 *ameu8 d9nally smooth train moving at constant velocity. Is there any physical experiment you can do 8xd3. txmuusa 1*re9a in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience ofe3x7k8 j5opz+2zo2lx zqby0 h being at a red light when, out of the corner of your eye, you see the car eyz5jz83p +xooh k 272lxz0 qbbeside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throwsf wv5-jmsl,axbcf*dr1q9( x/ a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behiwx( b*1lc, xv sfda5/jq-r9fm nd it?

Does the Earth really go around the Sun? Or is it also valid to saei+ n,p +s p2qs(p*0wysf4xzuyo2h 5my that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is ,mfhpo *qn+p z0yy2s2+wsu(x4ie5sp no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c awheskvz/ -2wmxj-/ c ep3 q:p/hay from a star, at what speed would the starlight /w/eq pcv3x- z:jmps-h2 keh/pass you?

The time dilation effect is sometimes expressed as “moving cl/m 28uzat)rhs ocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What a uzrt2h)/ s8mthen does it deal with?

Does time dilation mean that timf:k1r wmtr 1yo)ssn12e actually passes more slowly in moving reference frames or that it only seems to pass t swm2 so1rrfnk)1 :1ymore slowly?

A young-looking woman astronaut has just arrived home from a long trip. She qqn+7yq 1nn0y 8o6.q lfhd)yfrushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?7f h+qnq1. f8 yyynqodq)l6 0n

If you were traveling away from Earth at speed 0.5c, wolqi,z:x2g, - y8u .b/qzo eovuuld you notice a change in your heartbeat? Wouuq:8 v,ilx /y g uqbe-.2oz,ozld your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and lengthkj/p f:/em .s mgsj61se 5p.ey contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light we7x j+b6:xxmf wre infinite. What would happen to the relativistic predifmwbx6 j +x7:xctions of length contraction and time dilation?

Discuss how our everyday lives j, iq.ozy h(/dwould be different if the speed of light were only i.h z /qdy,jo($25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulab9tv-2,zccg 60q yqrfpk2d: bs might be used to indibyc-q b2 zg9r0kdf6cqt p2: ,vcate that c is the limiting speed in the universe.

The drawing at the start opjx79i /,4lswsr p6 b f07xl(odz0bazf this Chapter shows the street as seen by Mr Tompkins, for whom the speed of l0lj xo/4al rxbz7ps06i(9s z,pfb7dw ight 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.1bgv ,et805pof8qg ua Does this put an upper limitu f0pg a1,o bqtev88g5 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 rest mass 9ovv;i qnc+w. 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 when cjhrss),m0qhz i44 +wuj-p:t eompressed than when 4)t :0hi, 4pjsw-umqsr+z hej relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither bynaxj:tk zr ys91(9+ke created nor destroyed." What must wezx: rst9k1k ya9n(jy+ say instead?

  Is our intuitive notion that velocities simply add, as we dkkh78rv1 qq,isdl;e2 (sa7c nid in Section 3–8, completely w v,s7lchknkqe71s; (ad8q ir2 rong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its pvmwdmtek*8ls+ ukg/0.*w- z length to be 28.2 m. How long would it be when at rest? ewgwm-d.v*/k slm u0 zt*k+ p8$L_0$ =    m

  A certain type of elementary particle tr4w 1ra9jpmi vht24 9dravels 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 fact7b) 7e(s5hqfk/tmv xvp;non) or $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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- mvz;a. e8+,kqscg)zt 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 average81 ) whaoh9pla 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(so-u7 irtz tfc9-s)l away. How fast would you have to travel so that to you the distance would be only 35tt uf --9o 7rc()izlss light-years? v =    c

  Suppose you decide to travel to a shmyf,6)tp2a )3k4c ; hkqckprtar 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 trip? t =,hr)ckk h3 y2cf;k)tpm a6q4p    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 isof0p925-mhntpn e1 pe $11.2 \times 10^3 \, \text{m/s}$. 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 statb js 3ld/v83/efzz.nned that starship Enterprise had just returned from a 5-year voyage while traveling at 0.84c. e zln 38.v/3fsbn/jdz
(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 spach0ah2ddz 5hh*5f;nzx ecraft traveling 0.960c to reach that star from Earth, as measurhndz2dhax5*zh0; f5 hed 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 yo9ema-db8x bxsc x;2+yy0vdqh ,18xvw u in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. 8ydvb1v2eq w x xx- ,+y089s dm;hbaxc
(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 1i9jbo yz 4u;7p5 m before it decays? The averagej9iubo yz7 4;p lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling at 5:c33 oywuz1(iou+q n-i cork $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass6*e h:/9(rk;cgew kp qllod t4? v =    c

  A particle of rest mass h, h3oawks)c5 , l5cyyg. gom8$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels anznu;t rz-*g n rg-xk;5-vo +:ezq1nn t $v =0.10c$. 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 momentuhhli p3oe0.czgy *q1(7sq 9vem of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requ;)ne+m ja*cia ires $4.82 \times 10^4 \, \text{J}$ 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 known a ia0yex+ecy4 )s fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the processae0 )y 4ciyx+e? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules an;poaca tt v z0b +c3;.l.a;dnpd 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 massjyvay), 4dq;z2 a qi*g of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consump5ja 658k nzkkition in the 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 ou2ru+aw4 xa0lbtained 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 vm4gqt,8emms );6p vsf7j(o70n : ff2mtu mb ya particle when its kinetic energy equals its rest energy? v v2t; fvumm7f(mpsom6y f40 q,7em :jgtns)b8 =    c

  At what speed will an object's kinetic energr u:i5bpm/rtofs7hr 4 j p(7,ty be 25% of its rest energy? v =    c

  (a) How much work ist *.cb*fcnam pvv7y/z3ex+ 93ww f5yc required to accelerate a proton from rest up to a speed of 0+9bz a/femc7w33n pcxytv* vcf . 5w*y.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy anddl fq;my3qo nig0 *i/+ 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 7o db:;0i7ix ff50 MeV)? ;f xi0ifbd7:o    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a p eb8yvs 4 g9)aflu;a r44bcpe(otential difference of 105 MV? v = r 4g8lac4 s;uby fe 9peb)v(4a   c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v = cp.4v swy7cm (   c

  What is the speed of an electron just before it hits a tzflf/5p ueaf3jbz+/ 3s tr1.melevision screen after being accelerated from rest bba.f1fm/us zef+ rztlj /35 p3y the 25,000 V of the picture tube? v =    c

Two identical particlesj adyn5-+tbj8 f-nhp3 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 )8 yv1o..ara lle)bfvz6y1xrf *p-yeproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 ele: pz4 yb2o-xkictron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 iir, 8bc me+xv 2uy lhy*(s()-j+jzuwis 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 prfw/,6ot2b8c8rsaq n pc0v(bsoton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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,rlhr7r *t dk(8 $^{241}\text{Am}$, 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 part:tuj;a7qy )6e 5x,naxzx vet)z-dxl m ;5t;i jicle of nonzero rest mass, andjx5a56;e zlt-i:x; n ;7xut x)evzqajtym,d) (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving i te2e((,njhs) xy y6-k kzbpn5n a circle of radius 1.0 km (at, say, the Fermilab synchrotrop(kh ,eyez(-y2 )njxsbk5t6n n)? 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 Earth) qa *5.w83tghyuta 23y0m tlpq observes a meteor come from behind and pass her at a t3t*a52.qua3pyy8lt0g mwh q speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each wp4y l*iv1bdi , k6tz-eith a speed of 0.50c withl6yitbz,4v*ki e-dp1 respect to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth(we:o9 qpa os. traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calcuosp.w a :o(q9elate 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 hev t/adz 4:rnu(d 45asees an alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a spud:ve(tr /h aazn454 deed 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 un0a+ 0/df/ql rbq0fzmmt )6 kopposite directions. One travels /u6zt0nqka qbr 00/m+ mfdl)f 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 th2 pxs 0biut 8223wtugmr0v ln,e same time, rocket B passes Earth moving 0.95c relative to Earth223ug 0vp02 i8 w,tbtmlrsu xn 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 ddrw u0gp 53;b(q)kt1wu1wkelight-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 is called , l- ; cex5zliv(c6bsgrelativistic - i.e.,, zc(xv lli;b6seg-5 c for which 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 speed qfv*u6urp tl+kf p:nab,7ws t 6nv4 59$v$ 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 b75ee d,qg 2k8fxzm p6 iic5j2de totally destroyed to run a 100-W lightb5 2zjmq 5d7 dx2ke,ci8i p6gefulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an xh ywhy n)os,c0 p,2p*rr4z/celectron and a positron together? A positron is a partippzchrhs)o/02 ,nw yr4 cx,*ycle 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 collidesqy2(bwui75fe37lyyas5qw -x4f4u ,va diu h0 head on with a positive muon t(5d2x4u4f lh53f 7v0is a ,7iu-qyawywqubyeraveling 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, and a neutrino4mh5v5 ixx,capsifl7ti 9 7-r . Assume the neutrino's rest mass is zero, and the other masses can be found a 747vi,prmxif5cis5xl 9th- 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 al6qiu7so c/;.jni7) u7vsdxj bout $4 \times 10^{26} \, \text{W}$.
(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 speed ofetq.9 ix ak5mxu)y9qy ,-wo3p $2.24 \times 10^8 \, \text{m/s}$. 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 7f kz(*lpc w pq0uiy/+cx5r*ra 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 brq cil7z*f+5pyxw(/pk0u*r cinding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage incr5cz-wis7mkh /ha/u(d 6rc(h b j;0n jtease in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial exp7/kbr 0hcs z6(u i;cd/nwj-ajh(m t5h ansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in c l(to yxe65f43qe:ux/kus +4uhke s +the laboratory, are moving toward ea4 ky:6ul 5x4us f+ohqsxteukc/3e +(ech other. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle withouhk.km57a *ljq53 6 gt3h7zcinem h8 momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combion: j2/3m+ nkbi uukt+ning matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterpbn/+ nj o:2ik+3uumtk rise 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 kinetlq3x de:zlz/l:gp2 8w oav;l8 ic energy is greater than its rest mas /2ldqz 8exp; lo:v8za3w:llg 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 bf1 2.rpv(z7 ohezlv 4nelieves that he can fit a 15.0-m-long pole into a 12.0-m-long b.r 1holpv e4 (zz72vnfarn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxn7k,q 9yn i*nvygen react to form two moles of water, the energy released is 484nnkiyv9qn 7*, 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, traveling in oppositz( z9dn47ba nwueo;4q e directions. If the speed of each particle is 0.75c, relative to the laboratoane7( n ;qzou9z4wbd4 ry frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75cmy .a ,6 faie8jp9jm.wsc4o o+ relative to Earth measures his ship to be 2,9wj4f ap im8 6m.ej+ay.ocos5 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)cb 4zw wp(h8o a spaceship at a speed of 0.85c away from Earth. You send a laser beam towarhcz bw8p(4wo )d 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 mass of 150,000 kwm:lnh(io jy 9i0 79g+io eqg ,x3zo-hg. 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 093zimq -o+ho(xew: li7j, hogygi n9to 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 Ea+vwe n nexd,*22 xmo:ah*;lwzrth at a speed of 0.99c. What is the spaceship's kinetic energy? Comphv ;ozwx,nx 2ael:nmed* w2+* are with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity o5 9sg3nok ofh:f a star 6.0 light-years from Earth. Passengers on the soo3 nf:h59kgs hip want the (one-way) trip to 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 oscillat ccg 3(a9:()uxgwo vwwes on the end of a spring whose spring stiffness constant wxu(g:cv )cw(9oga3w 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 mas2vdsy 5qy1 e 6sk1kdt6s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.