You are in a windowless car in an exceptionally smooth train moving at constant a5qpjh9*sbu:b xv n0;4oq; ccvelocity. Is there any physical experiment you can do in the train car to determine whether you are movcs obn0pu*;vcxqqb9a;:5j 4 hing? Explain. ----待选择----yesno 

You might have had the experience of be nhngn( 3a19jluq up6 r2(pl8zing at 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. What does this s (n3jpqr9upu g 8nlanl1z2(6hay about absolute and relative motion?

A worker stands on top of a moving railroad car, and thro*v xd)74oxmh :yc5m fp6bv3b sws a heavy ball straight up (from his point of view). Ignoring air resistance, will the bmsmx3v6 vb*h )c7fpxoy4b d:5all land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to0tnlem:x(ohon*(5a m g u:wvrb;w.s 3 say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explainm:o;( ng0 ab5uvxw m(wr. *h :slto3ne.

If you were on a spaceship *ija ,puh hh7:traveling at 0.5c away from a star, at what speed woul,uja*h p:hih 7d the starlight pass you?

The time dilation effect is sometimes expressed as “moving clocksye2 pz)r 5mcv9b4o(fr run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks.z(fycp9e4bmor5v 2 r) What then does it deal with?

Does time dilation mean that time actually ib1j6g ug7wjz4 h-1oapasses more slowly in moving reference frames or that it oi ojb1g6 4z71juwa-gh nly seems to pass more slowly?

A young-looking woman astrot t1niu rjsg1-cs0z w.-w f(laz,qsg)h+; y*i naut has just arrived home from a long trip. She rushes up to an old gray-haired man and in thejs*i1 z-w+zgrh)u sg. t10q;snc-,a( lwif ty ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away frok j483. -,f zpf*m dkgfws9npem 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 telescopenjp 8,4k fs d.w 9gk-ff*3pzems say about you?

Do time dilation and length contrarmsb;:ne4 2 umction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite s d,84leuxmcy- -*afe. What would happen to the relativistic predictions of length contraction andmscl-*xa,e8u-fe y 4 d time dilation?

Discuss how our everyday lives would be different if the speed of light were sb+o/ba1dws6j g/s*n onlyo*ba 16g//wdsbn+jss $25 \, \text{m/s}$.

Explain how the length contraction and tq xg1 4i1qdl1yxx- a-qime dilation formulas might be used to indica-qxygi x1dqq 14x- l1ate that c is the limiting speed in the universe.

The drawing at the start of this Chapt)l 6l+s 4us0uhv: tyquer shows the street as seen by Mr Tompkins, for whom the speed of light lv4+uq sytlh60 usu):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 spurm3 p0a5bd hbfu +q17 4shc6seeds less than c. Does this put an upper limit on tup3fcq 71dh4+s5h 0usrb a b6mhe 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 attain 1ntp f ji9c ab7ctis -qf78*wul6 ,q;bthe 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 wbk- ivm9y0z9r hen compresskb v r99iymz-0ed than when relaxed? ----待选择----yesno 

It is not correct to sayj9z zb4g ec3 vx;xtcdk;:o5 x1 that "matter can neither be created nor destroyed." What mbc; xv; zjd :c4z3x1txoe g5k9ust we say instead?

  Is our intuitive notion that velocities simplpa- r0 6ippum;)bi7 ngy add, as we did in Section 3–8, complet-0 unp;bp)7p gr6i imaely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c1zya6-6 qgdrd . You measure its length to be 28.2 m. How long would it be when ad 6gd1ry-q6 zat rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed9mkj84d2en(:vvu (dpcr2 nqx*ic: pr 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 o xurv9o.5b -oi*ue k5b4 om4men 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 tuiez/ ; 8ss1bwo a star 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 mea)qkbxs ld;x+sk 2 g. o1oe6rq(sured 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. Howt9 j-hkieo.p0 fast would you have to travel so that to you the distance would be only 35 lhkep j0o .-9tiight-years? v =    c

  Suppose you decide to5qu9g+y;+b 1af5 nz)vlpmtl k 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 trip? 5tagyb;n+f+m )q 95 lz v1ulkpt =    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 y6;;w/1x en txe-vqtsEarth 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 d.yoo 4hv5* ,u(b z8ort x9wbrstarship Enterprise had just returned from a 5-year voyage while trave, v8dyoz.oh4 r*59 bxwub( rtoling 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 wooewrmlkn j76;u04 5av7/* hbrm : y;n.znvluquld it take a spacecraft traveling 0.9606 l;v:0ar*jk.wl7y/eo 7m 5mrzuvb u4q;hnn nc to reach that star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecraft at a speed of 0.660c. It is sn8oro qz,57 dmeasured i 5 rz7o,8odqnsn your frame to be 4.80 m 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 before it ehh2 o;qb:4kmdecays? The aver 4oeh:kh ;m2qbage lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling +g5pl 1o;chl qk4 nk+ lv/rfl5at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be h.a*zr o2ynit ( ulim(1r5qx, twice its rest mass? v =    c

  A particle of rest masp xxrc6ayd47dh;pr ez*l0lr ;mz ( 7+ls $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ata2 bmfh8be.w,r8t 9do $v =0.10c$. 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 hs s/na88.x3 5s:qne gjdwbxr8m2+ 8u,fyxba change in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical react*l*zdyn2n yvq5z u*3jion 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 pr e m*b gk6oadt8,sp0b8ocess known as fission in a nuclear reactor, the resulting fragments have a total kinea b 8dkp8b,06go mtse*tic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest ener7 )qqf1 5dpvnm j*z+yjgy 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 of nlmq 7/iw hb x3ft c;7jhk8,uxr3-sb8 a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumpti bjw7397- n1q x-ik*zeuv rhxqon 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 obtained from conveb* i4hr.a f-wbrsion 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 energy? h5xsq 2byfkl:2i5r+r v =b5xfrqrl5y h2s +k:i2    c

  At what speed will an object's kinetic iohmlvh-h iah4dd, ;9- )pw7henergy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a sriq8m/ fthf+ -3ywwu9egov*: peed of 0.997c?- r:yug+8fv q if*/9we hmtow3 W =    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 v7 )prxgkwe*u2l,v. xproton 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 ib5n 5+wc x) vfsva3,drs, its kinetic energy is 750 MeV)? )5awfbn5rvc3 x+ ,vsd   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 4y4p i fxl-/vss. xil,MV? v ilps4 i/slf xy,4x -.v=    c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v v x2 z)h7qub75xpc6zq =    c

  What is the speed of an electro5fo o trh4x.n3n just before it hits a television screen after being accelerated from restt 3fohx.5o4rn by the 25,000 V of the picture tube? v =    c

Two identical particd2 6j(4 g:x)lfpmwg tv -u1grples 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 3kmq:.6zg1dl d,h-tjmcq.d c 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 and0 tu s8/ afir+ls24ejs the momentum 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 t zkr)rqtrl;+2n* a5l of mass 27,000 kg is accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic uqo7b pz1;a ye)bx k38energy 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 nucleusas bw1rz-mws/q3ex5uqq:p lw u9;; 2v, $^{241}\text{Am}$, 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 ener7zwzknym 0 d 9;ckuhr967u0y *rawc g:gy versus momentum for (a) a particle of nonzero rest md:kwn km0czwa0uyy g* rc u h9697;z7rass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV proru qgl+3v0k(t,t5v j0 z. spjztons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotr. l+qgz,tjjtkp00 vsu(3r5 vz on)? 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 ag 5;e w3qxwq3gejm9zbx;f41t t 0.50c (with respect to the Earth) observes a m;1e5;4wzwx b qqfm x jg33teg9eteor come from behind and 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, each with a speed of 0.50c wicufv)88-lt)f8ykukswj hx4+j2vg. :t8o pm eth rhk2fj:8ptc-)88ywg.uv8 mt sek f vux 4olj+) espect 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 traveling at 0s kkbpnj 6m1m.twx 4/.ehs+-nw-ae;l.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respesmx ka-n4bwsp-e.6kt.jeh /1+lw nm ; ct 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 j+4imrr- f/wkat a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u = -m+w4i f rr/jk   c

  A spaceship in distress sk94n7 (7 bkylwu+e owcends out two escape pods in opposite directions. One travels at +497 ywwno (7kckbe ula 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 h;qxg 9.mm:oca speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth ihx .qc9m:o gm;n 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.b-4 oiq -rb+xt3udrvears 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 r1bdc* s*n5ljfaster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogen atocs5j1rbnld** m ($v \approx 2.2 \times 10^6 \, \text{m/s}$) 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 b+;i;a ows;ky ka+ gkp /i/b8v$v$ 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 destroyedsrlztvwgexs 7o 96lyunpd c:9csw .1(*g / 79p to run a 100-W lightbulb for 1 yearl:/g.grze9(n9 ostdvu w6w* 7csy ps7lcp1 x9 ? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetwypvov4o ,. kez ;jg3+ic energy is needed to produce an electron and a p+eg3o4 jkpvo;, w.zvyositron 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 sug2eo5 w/wxj,peed of light collides head on with a positive muon trav/w jg,uoe5x2 weling 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, ang u-es l4 xfg3ni)q*n,v u*(o*px/jyv electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front covfug)n psvn x, qixyel-*(/uv j o3g**4er. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a racaad +m;r8b g :vks*l*te 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 nnk(sdiiqg gm f ,+0:l: vzrz27ypf(-t*ahkd)egative 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 would be required to break a helium nucleus iggf:(s0u:gxk m a+:uvnto its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respecv:f: +asgugxg(0 mku: tively, 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 (relativistic) ma7kh3 drawv b3*ss of a car traveling 110 km/h as compared to at rest? [Hintw3dhkrv3b7 a *: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moviniq40 ke *5rgzxg toward eacr q 0exzi*k54gh 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 pfov 4ysz+)v7 di4 ean4article with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combi4sca)mkybtzaj;8 .y c 2rh- +oning matter and antimatter, achieving complt+j2byrk4ys -aacc;) moh .8zete 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 )u df+4-62 5(xfdjylujl rfuvenergy is greater than its rest mass y -fvxd5j4 26f+uluj frul)d($m_0c^2$ 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 physi)pvzs3t7 ueh) jg;g 0hcs believes that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pshup ge 7h03 tz;)jvg)ole). 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 andpt0t3)ui0*np5 rs obych(d8d one mole of oxygen react to form two moles of water, the energy released is 484 kJ. Hp pi0do(n5sr3b* 8 uyd0hc)ttow 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 partiw9wr9 rd, * 0gqitq5vhcles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to thewv99r,5* ht0iw qdqrg 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 relativdb: (px.6( s jf3/pgyccrfep5e to Earth measures his ship to be 25 m long. On the p(d p /xj5 ffp3bs6cr c.(yeg: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 awie u-5semw rt09k bz4j4whe-. ay from Earth. You send a laser bea40.swb9 wuz54ji hee e -mrkt-m 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 totalcy 70kn1bq iru s8:x: )i5kqvg mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the nu:c851xsv 0q )q igy:rikb7kengine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0./d; k-h,hwur0mqj v3b99c. What is the spaceship's kinetic energy? Compare with the total U.S. bh,dq 0 /vj;3hru-m kwannual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a s jvz00zgof+z--rzg+h tar 6.0 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 be done on the spaceship to bring it to the speed necessary for thisgg- z fvo++ jr-zhzz00 trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whoty : bj*i7fxq;se spring stiffness constant if:btj xy7;q *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 m w p 1qyiqh.m7yjd2l75ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.