You are in a windowlesu 74ns ( bftyari2.bt.se/-cfs car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to - r tbc2sb7.( s .f4ty/eniufadetermine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of bei 5m1wgn);w03erx0rvv/+5r 0d roizt 4xxcy iyng 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 350r w4) e mr10 /odx tynxr5igcvvi0 wx+yr;zthis say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy ball stwu 6xtf mo0vv8w:4wt0raight up (from his point of view). Ignoring air resistance, will the ball land on the car or behind itt0 v w4 txfovwuw:0m86?

Does the Earth really go around the Sun? Or is it also valid to say that bwe 23rto4y:-bpd6 sm(usz- r the Sun goes around the Earth? -2(p3e rs:dobyb twru4s m6z- Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceshiw 1()t+ x bza1.t)xen0iknztdp traveling at 0.5c away from a star, at what speed would the starlin .d at nk(t)iwb0tx)z +1zex1ght pass you?

The time dilation effect is some0(q:fe 9ot y 2p8ceacttimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the function:8e c 9o(ftyctaep0 2qing of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in movingt :r/p9b hxd8f reference frames or that it only seems to pass rf x/d8:9tpbh more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She rush5b-xxrc8/d skgy twj1z(ren( 1 q2 pn)es up to an old gray-haired man and in the ensuing conversation refers to him as zgk swyj d)(e- 1r1c2p n8qx x/btr(5nher son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice g63l;bc z/coc a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say abo/zgb 3l6 ccoc;ut you?

Do time dilation and length contraction occur at6:eo gztc,o,s(4r jc z ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relativistic ipht , 79c-dxqkar95ag5cod 4 predictions of length contraction a4 cgdd,co t-99x 5ip5ahrka7q nd time dilation?

Discuss how our everyday lives would be m2ovhjj(,s, - 8xemdidifferent if the speed of light were only-exm(j,ih d sv2, m8jo $25 \, \text{m/s}$.

Explain how the length contraction and ti w50y3h2re 0,ulrte8swffo4.9i gxmome dilation formulas might be used to indicate 4irmx .90 owrwye ,tfg0hs25 lf u8eo3that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the streen dm)sj le5(8iwv:ra0-r n-eqt as seen by Mr Tompkins, for whom the sper- 0-v5jw)d8smni q(eerlna :ed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Does this putu7.qlokb00xmjja64hzpialp c .bm;p.l .1 z. an upper limit on the momentum of an electron? If so, what is ibj6llb0z7.pc 4mlu;p.oqa mhj p 0.azk..x 1 this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of light?qux fgnv4a,q ;i,i;m/ ----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*vzblr:, y,nj mean that a spring has more mass when compress:yz* ,jrbvnl, ed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroy)kpqtk qgh )a6/:fi qnr53:ew ed." What must we say ins6aw tkgnf: h):5r/ekq )q3 pqitead?

  Is our intuitive notion that velocities simply add, as we did in Section 3*r(y 1op9zxsim, whz-–8, completely wroi9s,1y-zhrp(wz o *mxng? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You meas-gx4yy bj8, eb-s;p leure its length to be 28.2 m. How long would it beje-4sbbgylx ; e8y- ,p when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a spemo(d:dvl)tq (c*0 opsed 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 interval dq+8 jied7sq wjz8kc1 hm-8:ts depend on 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 to a star 125 light-years from Earth at a speemx t)pu )*noyz 0m*9c/6a2b gwlp 5qfud 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 p gg ,of0ue18emion 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 fiu.k./ (+*kirfu+cn ( hputlframe, a star is 82 light-years away. How fast would you have to traveluikt+h c+l rn u fp.iuf*/.(k( so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speedlepr1he g 4s.kp9petrm 36:q+ that tells you the distance is only 25 light-years. How many years 3+4epq ekep h9:lmgtr6ps.r1 would it take you to make the trip? t =    y

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

  Escape velocity from the k-674uc/ t1u wmncgr gEarth is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

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

  Suppose a news report stated that starship Enterprise had just returned from aglgk/aemm ka q9,597gn yjlwj; 5/, jl 5-yeakjgn9gq 57 lk e/ag/ llj m;95y,awj,mr voyage 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 l1.v2t hailx(/o x4 iphight-years away. How long would it take a spacecraft traveling 0.960c to reach that star from (hhp2vto1/4xx. iialEarth, 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 spi6l(lfs sbc e2u4t0 jkcxa(3ze0m 8.seed of 0.660c. It is measured in your frame to be 4.80 m lc sb(ual6c0kei(0 f83j 4.xsmstze2 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 decays? The9 : xkvw905 tybkahf)x average lifetime, at rest, i x b:kv)5xfy0wh99k ats $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton tr1iiq0c 8dfln :aveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rk(zvb) jro,+c est mass? v =    c

  A particle of rest mass h)ter pu)/gw0yab8 d2$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ato b6 ohg2x)e/uf,fik 8 $v =0.10c$. 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 ov7 r v.+op kv(m8ulrf0f5+urhf a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi 9+ 1c.kyqhwmsres $4.82 \times 10^4 \, \text{J}$ 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 proceg pla 1gw 3coq9n+7/klss known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the processw+1locl93gaq /kn gp7 ? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energyn3+c jo.m5 vix 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 a prct: l)vnbj-ngjqv7 6(oton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United0 8az1ps0n2 9gafqggu ya*n+j 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 obsu0o4gt2,r3a 7mir v stained 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 4nowboy6 i +vee91*jt kinetic energy equals its rest energy? v =4woe*jonei1ty+ v69b    c

  At what speed will an object's kinetic ,lpx.2*g4 ub lyqb/whenergy be 25% of its rest energy? v =    c

  (a) How much work is required to acr5i l9612 w *rb nusdxa9:xc2v8hsactiglo,3 celerate a proton from rest up to a speed of 0.997c?rxlsn1 ogbxl ii 9,r:vh3d 68 tcc 5w2aa2s9u* W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and mo0vacj)f7 -;lfo0h7q 6uvarmxj30lfz mentum 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 p/. jgbz: q,dm v7xrk ve3u6t;hroton (that is, its kinetic energy is 750 MeVg,qr6xz7/ uv.; ej 3bkmt:hvd)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentiati mdral( 2g (rf:*rs*l difference of 105 MV? v = a trm*r l gf(:s*(i2rd   c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v m/)1ibbz+ lmxw i i mtc (+w8)-t0qleq=    c

  What is the speed of anfng+ekkdx 2y/8hmy 2* mgs*:f electron just before it hits a television screen after being accelerated from rydx2*f:h 8ymmkg* kne 2+s g/fest by the 25,000 V of the picture tube? v =    c

Two identical particles 4j tt /e(td -qf0s3hmuof 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 ;ss+;.in fk7uc yo pt5a 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 and the momentum 8danu6zv :pa*8j4 ef uof 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 onyydcz5:.j l3 y7k: mof 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 energy aioz5yyfm,+q +k x8:wv nd 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 nucleuf te3q4c6*z:npzjh a:s, $^{241}\text{Am}$, 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 particw08 hcbrb:lzo0cu/+cc3u l6 wn v t(g7le of nonzero rest mass, and (b) a particle with zeroow3cuchl bcwbgu 0n/:6t7+c 0zr( l8v rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in a t.9is//skr + .; wvxjw+wa9 y:msmupacircle of radius 1.0 km (at, say, the Fm 9 ;iwj/sv+s.krxm aw /uap+.t 9w:ysermilab 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 traa848v fx0ynxr3l zr r8dv0d1u veling at 0.50c (with respect to the Earth) observes a meteo8n3z 8r8alv u0y0drfxxr1vd4 r 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 oxs8rjy j91pk:4r (rrx pposite directions, each with a speed of 0.50c with respect to Earthjry:prs xr (9k8xr1 4j.
(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 seconjw 98 b*vs8ei7gkutat p,z6iw8 fcj-*d spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the spj wt,zs7g *i8akc-8 9v 8jpfwbe*t u6ieed 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 c rs( b.j4i1q7 l,gbaco0ckq/ 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 relative speed of one vessel as seen by the o.0coqcc 7 ,/ qjgi lsrkb1a(b4ther? u =    c

  A spaceship in distress sends out two escape pods in opposite directionbtmd)86 p4m5wzlo b l 5*rqqj,s. One travem8l4pqt6 5 moqb),dl5w * zjrbls 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 r)darb+8 9ft +sjx 7o1q g*glka speed of 0.75c. At the same time, rocket B passes Earth moving 0.s+xk89)dj +1gtbrrlq*afo7 g95c 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 Earth is Proxima Centauri, 4.3 light-yeau;-reu b2ttdor q j0-/rs 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.h3p0lz,p mot71c is called relativistic - i.e., for which the c o37,0ml tppzhorrection 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 h7gmg8 ly 3mh mrw.w( 3cnh5-y$v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter would have to be totally destroye* phmc yq1y 4k33wwc: (wp3rmed to run a 100-W lightbulb formc (yphk*wq3:w3y 4pw m erc13 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy cfm p0c)yuemm49 d5 t/e2a:jois needed to produce an electron and a 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 ttj4):mc25f cm o 9/eaeyum0dp his 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% mz29n/vc9zq(lw cedo::o/ch-- nr jx the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muonoc el/2h z:xv9(/ n :nzr c-9cjdmowq-s (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 6nx(:d e(2dr )uze oiqinto a proton, an 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 cover. Determine the total kinetic energy shared among the t ui2xre()q 6 d(n:ezodhree particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy a6p+*0oyqt1 9l 0psh7ea/bjz.gtv w eg t a 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 chh2 e-dc40hvej; u v1rj n2u;+lpf *ivyarge 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 pkhs z037s3) lajob,hbreak a 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. 3a,k)07ljh 3so szhbp00783 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 asy;5;of nza0traveling 110 km/h as compared to at rest? [Hint: use t;zsaya0f ;no5 he 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, l)k)i6qq. 37lvwz u*7nass xiare moving toward each other. Determine * 6lqsivi)) u7qxklzwn7 as. 3
(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 partioq-g:teqk ) (n :szf2hcle 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 antv l mnn6k)1bb:imatter, achieving complete conversion of maskn:n6) b b1mvls 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 accelerat6zw)-eyaw 4k br-n.a1 bytvxc7+bkt -ed so that its kinetic energy is greater than its rest masse+yaz4awx b-cr w-vk )6kt 7y1b-nbt. $m_0c^2$ 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 aa5.y-tj pr bt- 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (c -.ayt trb-jp5arrying 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 molea,kb;soc5 q /c+p5yiud-y1n q of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the m/p b1 akn y ;y+5c,uidcsq-5qoass 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, traveli2 iyk+ c w *io h2b.i9u;ha;se;(ph2iam +aqveng in opposite directions. If the spea * hsh 9;m2p2icekywi(.e i+va iqba;; uh+o2ed 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 an ( jhu)klq0u)qy++mst 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch inq )unym s+)k(h0ul+qj 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 spac/( afc8p5 tvlmeship at a speed of 0.85c away from Earth. You send a laser beam towam f/c5a 8p(tlvrd 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 kg. The occupants wo qjd(i l; 1ue+przaff0k2w9f:z0v w(muld like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this spe0z+a muif(v2 fw qz(lkjd r09pe1f :;wed?    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 ;3xtqc1j ;sn. mqkok0a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (about qxo. 3qn1cjts; ;km k0$10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 6.0 light-yeae 4-p, qcimq 37gfa/blrs 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 necese gia ,qfmqlb3-p/c7 4sary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring .e +do, qo*du( u)ydzhstiffness constant is y+e.,uddo( uzdq)*oh $k=48.7 \, \text{N/m}$. 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 mydq 28l++lp i;dw jf9ycf/f 2bass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.