You are in a windowless car in an excepti*brmzjw nmzzh9g*4v u46v5*)at3fhr eqf1 h1 onally smooth train moving at constant velocity. Is thjmu qm h*v9r6va w1gzz435hh*fb*1ft nez)4rere any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had t .9)4e -( +ftwmow.ghdw enzz/;xt tjjhe experience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you sto )tdjgz9+-jw.fme. xt4h/ z ;tnwe(womp 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 throws a heavy ball stro 8ap.wpt*gjx b; 8 czl1cg:t.aight up (from his point of view). Ignoring air resistance, will the ball land on the car;.gt .tl8* z8op: ja 1pgbcxcw or behind it?

Does the Earth really go around the Sun? Or is it also validq8e jsgzdu 4g4nt 1ii/+* epr, to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that ther48qg+d1rt*,z / iseegni j u4pe is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what sperf m3q57pltr)ch 492sc g yk6qed would the sta2q)ryf c6thklgq5r9m4sp c 37 rlight pass you?

The time dilation effect is somem ezb6 9;9jf7+lnyd :deno h4atimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the function9m6b nyhaj:9 no+dez4e;fld7ing of clocks. What then does it deal with?

Does time dilation mean that tj*.evb89+( kf: q6aippefy b jime actually passes more slowly in moving reference frames or epe6+k(q *8vipa9yjbf :.jbf that it only seems to pass more slowly?

A young-looking woman astronau-z7ncnv41 /db w9e asit has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to s-cn79ewb 1 niv a4/zdhim as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, uq, v1v6zoh0 f:t4 kiocd3+vkwould you notice a change in your heartbeat? Would your mass, height, or waistline ch :v+k4 utvfdv k1 6o0hi,q3czoange? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinarl ov5 u p.o94sjdx-4pny speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite.nj7vnf,8+ fj-pt g o6)5. iq5 gburnxx;/gw hd What would happen to the relativistic predictions of length contractionxtv8ibqpu)g fogg nj j 7+xnf5 ;hwnd./r,-5 6 and time dilation?

Discuss how our everyday lives would be different if the speed of l mbicc8 a,0iab;7nq;right were onlybian;m;7c c a0,b8riq $25 \, \text{m/s}$.

Explain how the length contraction and time dio11q6qgy3iblr w i4i1v 85/pn .enk zqlation formulas might be used to indicate that c is the limiting speed in the 31w1nq.4i rgqqvn8/b z5kpy6e l oi1iuniverse.

The drawing at the start of this Chapter shows the street as seen by Mr Tomgujg1hi5lu+ np8m4 q-pkins, for whom the speed of light imugu n5 - 8gq4ihj+p1ls $c=20 \, \text{mi/h}$. 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 thm 4dc7l u1ah(:un14isi n- tdgis put an upper limit on the momentum ocd7d g4ilhst4:1 uam -(u1 nnif an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed oa *ttgv0*s t4ff 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 2 u-(:cexh5 j37lslv bus.texwhen compressed than when rela5es lcux ux3t7(hs:j2- bl.e vxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." 5dex r, -uurxep)ipr mq20/s (What must we say inst ur er 0s2(pp/m-u,5deq)rxixead?

  Is our intuitive notion that velocities simply add, as we did in Sectidf .wcs8gft(r1(uk0 l on 3–8, completelyr fg.kl80fus dtc1( w( wrong? ----待选择----yesno 

  A spaceship passes you at a speed pz8p;i t w: i6yyh2/qyof 0.750c. You measure its length to be 28.2 m. How long would it be when at rest?pq6 z8/t;iy2pyh i yw: $L_0$ =    m

  A certain type of ele4f/yl ,rumq s7mentary particle travels 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 9k,4wv nirzc6factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 frbrk ,*rkg8ea 8om 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 pk s+f/moi-f)it , 2czpion if its average 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 stag;1-coygu thk v5j2u ln7mc* *r is 82 light-years away. How fast would you have to travel so that to you the distag-vgtu u **c1hl;m okny25cj7 nce would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed that tellsxd zh-xc+v:(j;b,dzq you the distance is only 25 light-years. How many years would it take you to ma v(+c:zxj-qb,xd;z dhke 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 3sxm7.9lqjg,bv4xepthe Earth is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

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

  Suppose a news report stated that starship Enterp8sjv,y1/ juuf rise had just returned from a 5-year voyage while trav 1ju8,jyfvs /ueling 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 aw a1m* xhq9 c2,skzop*1j gv;xgay. How long would it take a spacecraft traveling 0.960c to mkv *gsg x 91* 2;jaz,1phqcxoreach 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 4 ksp q,f;mc)l0.660c. It is measurmq l4scp f;)k,ed in 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 fa3d ,inz.yyk(5j( pzu7nt dhu9m f08m before it decays? The average lifetim,0un tz(a9 dfpy( k7yh.fnimjzu5d 83e, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelink yug04b1w.n fg,uoa 9:pq8 gag at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an objekd,t xjolv* 6vry-(/mshfk9z k 4z,x*ct’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mass4uy k.p eo1hm- $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a*m9( q 5lnzibyt $v =0.10c$. 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 momentufe os (v3sa8e0m of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi x ufi3+i3bs1ires $4.82 \times 10^4 \, \text{J}$ 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 pro w ;jhgv8*7mqxcess known as fission in a nuclear reactor, the resulting fragments have agh 8*wvm7x;jq 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 electqkoeop 3 :, 1oe(j-ags/lrkh:ron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a protcwz( ux +lf(p:on in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual ener;2e7 9sdgu revm8bcu (gy consumption 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 conversion of )8zcut26pvgu n1-qe sh+lg)e1.0 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 ener.vix*)uhguf h1 ,awl2gy equals its rest energy? v huf1x2.l ahu*ivg, w)=    c

  At what speed will an objec qqfq.6+/gdwb/.acgz)ajl e 5 t's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelera:fsp cy**yb 3 kw:2aea k+jwm9te a proton from rest up to a speed of 0.997c?k:* +fjp3yya*kc2 wbwe:9 sma 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 oe-5 +u:i axez6+lnm tnf 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 1pxy1.53hiq9brxqi fq( k bu. 750-MeV proton (that is, its kinetic energy is 750 MeV)y5b1qf.h .3xbi p 9iru q(xq1k?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a protonj )jj q8hdaeyiaguva (n )6;t)g 6lj)9 accelerated by a potential difference of 105 MV? v =a)l;u)a (qdjhg6t i g96ejj))vjyn8a    c

  What is the speed of an electron whose kinetic e/wnunw ;*h- u+/z odvjon:5osnergy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen *hc5p 0ihbk)9lb:tt p after being accelerated from ph tt c)9 pl5*i:bb0hkrest by the 25,000 V of the picture tube? v =    c

Two identical particles eq gl1hera;180x9,l7on- ww5bxwj lnof 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 proton *0 sha c0(ipnnyzr0u 8($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momenqsr+:dsjzv8p* l ys1z;,mh k 7tum 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 accelera xnh nqc(s40keb hq.f;ib9v+5ted 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 pr(feamum25g3ox g+ j+ uoton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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,iyono30bazdh4 ;:k phv2*: cf $^{241}\text{Am}$, 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 energyt0vsx8j3;)vdm 7c7r d5wyy( zb fmb;2u4t xli versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zerosr7 v(t vi du4 yw8xj;cl 7)dxz t2ybm;fb3m50 rest mass.

  What magnetic field h6eop r pno vy5,2rh, w94/ijuintensity is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the,2 rovw5 oiyhne4phu96p/ rj, Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at-d zmp2+ *gftj 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. jmgt2 zd +-p*fHow fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50scg( 6ph vfy3pj:z:dy0kx8w; ou:/ zoc with respect to Earth. v/d u6cj p38f( z:hoy;z :oyxk pg0sw:
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A second spaceship leaves the fiuq )m d. *ij5t iy9/f)kwj di.vbz64y(/aac qjrst at a speed 4baj*y qfm6. azi/tjj)i(ckqi)v/.5yuwd9d of 0.87c with respect to the 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 approac0il1 xx f x3dkjtrf/rc33*c)gh 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 of 0.90c relative to Earth. What is the x x1/x)l3kif3d rf3*jccrg0 trelative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in q1j2penm f,/y h++ beuopposite directions. One travels,ybh+u+f e1mjp/ e 2qn 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 timeggo8*vp :c;5e(pwa hh, rocket B passes Earth moving 0.95c relative to Earth in the same direction. H(acvhpoep5h* g ;g:8wow fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proximt jj-y)jfk; 7tak)g j/wnx:q;a 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, f.g i1 qqk5o9/c-ib;jcuqc; sanything traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of bifi;qqks qc-.9ccj5ou;1g/ 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 speeduz aq(xu q0)q. $v$ 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 matt z)cgy3k0 jbwri3m2i9 er would have to be totally destroyed to run a 100-W lightbulb for 1 yrm3gc9 )3kzyi2wbi j0ear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic4du6+nll5o)eslx f,nhv- 7 xf energy is needed to produce an electron and a h l sf7 n e,x+lx46lduf5-nvo)positron 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 lightchq y5 1g,*erp).b9qwcu 4nk i collides head on with a positive muon tc95q,wp.) ri4 kb1y*qcnehguraveling 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 n7oycs2 kcp 03seutrino. Assume the neutrino's rest mass is zero, and the other mac co37k syp20ssses 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 ag btwhvv bse49-,5al l9kv1e3 rate 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 k pm*kdu 6zan,m/;8 j nhkeq/+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 into its constitue8xfb3zw .q-z5 kvvyj8 nts, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.0z 8wbvz5 v8-x3 .kjfyq0783 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) mass of a car traveling2*zh40qgacyk qv0 f4q i75b9uw 0flnr 110 km/h as compared to at rest? [Hint: use the40nhgu f5q4 0fizqkv2 cblrqay 7w90* binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in t /ey.kpy4ugk ,he laboratory, are moving toward each other. Deteu/k g.4ykp, yermine
(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 particnwz pyky) *r4:q)mz7fle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starshi-y19an/k :t ipcsxi5 wp Enterprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass 9i ans- 5:1kxyw/ tcpiof 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 energy is greaterkvh jtp,:vj* +*pv*z r than its rest mass jtjvkv+p *v*r*, z:ph$m_0c^2$ 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-lkg bi 31y0j,eh/*ifhq7 kju d.ong 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 the idea that whejj b3 hyg7 k hkuifq0/,1.*edin 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 mo5m(dkkcp06,hx) fh7*r crhemle of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements ,rmkh 7 0k ph )rfmce65x*c(dhdecrease 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 iden w(l)deozq:f f+*8dtw tical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particlef)z:tdw8w q*f(dl e+ o's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relaz,w 9yhy0e- wb3dn apvky.v:/tive to Earth measures his ship to be 25 m long. On the ship, hv0awz.d,3 vk/y9-w eynb p :yhe eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. You se)9b 7ogcn r7rw6t q,jcnd a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the E6,rjb7nr79t owc) cq garth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. Txct6qei:i yfh ,c.f 5,he occupants would like to travel to a star that is 25 ligi,f xhc.5cif ,:ty6qe ht-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 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 spacedm.a1dt y6h;bship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (about y m1; athdd6.b$10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of vrnyl)c ng 8or0 y1z8)a star 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 b)1yl80rn zcg oy)vrn8 e done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the enda249w4/sod j jc.spvx of a spring whose spring stiffness constant i4 2/j9jcss dao4.vpwxs $k=48.7 \, \text{N/m}$. 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 massqm3opy9 mb4 -h $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.