You are in a windowless car in an excn/xz;* nfn kpk:q*nn-eptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determk xn /qn;np*-kf:z n*nine whether you are moving? Explain. ----待选择----yesno 

You might have had t y -7dc6qqjobqd44/6 0ut wml8l.p qixhe 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 stomp on th-0.lmcq /4bpdoi x 8qtd47lqjwuy66 qe 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 st ayl-u1x m77f6uh1w/ bujo-haraight up (from his point of view). Ignoring air resistance, will the ball landlh16aou1/7 uh7ya-xbwj muf - on the car or behind it?

Does the Earth really go around v)( n6jl8p2otk sbjh7 the Sun? Or is it also valid to say that the Sun goes around the Earth?8lpv j(ko6bsh n7tj )2 Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c vkm5jm5r y35) ul:aribiy5t,away from a star, at what speed would the staram i imlr:y)5t kbrvu35 5yj,5light pass you?

The time dilation effect is sometimes expressed as amru2f z;od6*“moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it d6a*m ;d2zr ufoeal with?

Does time dilation mean that/ude (e wh.xkc 3.t+af time actually passes more slowly in moving referencde xhc./f k+3uw(eta .e frames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a lon2 n j;)my:zu/ks1t98aauebe9xa;c z:-wc c k fg trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to hibae2kuzt::/j8 f1kz- c cmu)n;9yw s c;eaax9m as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a changttqa;( b j-6jge in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telg -6ajbjq ;t(tescopes say about you?

Do time dilation and length contraction occur at jiwgbocpzs 0*y, o5lg21 2xs)ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to thf)j 60 ezoyt;qe relativistic predictions of length contr6zo0yef qt )j;action and time dilation?

Discuss how our everyday lives would be different if the speiwd-f /wi ix2x x1b++oed of light were onlxw wi-x /fdx+1+ii2o by $25 \, \text{m/s}$.

Explain how the length contraction )b x1vd8kf lwq// j8 8n6fvzljand time dilation formulas might be used to indicate that 8vn/l vl68fdzkj1wx/b q 8)fjc is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tomh3:2lkj8zv ;uqqsb+a2 o3u8 kvzh v3upkins, for whom the speed of light isa+u8joqh vvqv z8z3:lb3uuh3;s2k k2 $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited tp-e0 bzx w:us4o travel at speeds less than c. Does this put an upper limit on the momentum ofe0u:w zb-s4 px an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of non lphdcw867gz i boe5rpi 3z;n *;bi+b,zero rest mass attain the speed of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does this mean that a spring has more mass sh0gnvn; 906mp,i m1ckw9n:vtx8lt x when compressed than wh, t9xcnnhvsptl08: wk01;nm g6xvi9men relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created mfcj6m )ft( w ;ir,ew/nor destroyed." What must we se/6 twwjr;f,i mf)m( cay instead?

  Is our intuitive notion that velocities simply add, as we did injcra- zv.2y;r5ey n 1r Section 3–8, comple1v5y2. cyra- zrnje;rtely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0. dkzqqk4f8hjyf6u is*9ja+ 7 2750c. You measure its length to be 28.2 m. How long 2 6ih7jjzq *fq akdk4f sy9u8+would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speeylc ndxa- 8996c)dihkmcs,- 2lv ra:ld 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 f7lwi;j lv/a. kq3fsl9actor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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-yea1ypcct+x -8j eo/7pe/*owmcti4 ylkit.o3 7n rs 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 averakli4y- ce9 xd;84ftu 9ew5j 6runwit:ge 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 stwnidvia/c pus 43g5zm9vcyj x+p9;( +ar is 82 light-years away. How fast would you have to travel so that to you the distancwn4 cdi3s(+ mpuc ay9 9 p;vxzig+5j/ve would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed tha+aw+a,cp v f3ht tells you the distance is only 25 light-years. How cv3 ap w,f+ah+many years 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 Earth8x7sdv 5 pby58shn ad. 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 r k87iaziy1* s r.mw-ceeturned from a 5-year vor*7w.18i-yazmi s k ceyage while traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would i1c+kbbb *;zc st take a spacecraft tra;b z+c*ksbc1 bveling 0.960c 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" spk wrk;)+puqu-z +h5waacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m hig zh)+; u +kuk5rpa-qwwh.
(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 averagfv,mtys9 a10 8u7,xcmwt(+a vl mht(ge pion be moving to travel 15 m before it decays? The average lifetm9l vu a0f7tmvhtsctw(8+, ( 1xg ya,mime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton tra:5au )t :xtgqjaoyywtrm z +/fy8c2+1veling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an objecte;gi5t.ym,ci-ioat ;ui 0,ae’s relativistic mass be twice its rest mass? v =    c

  A particle of rest m3o*va f )mcge:ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at p:1e)3s oiftg $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in momentum of a5s223d(lwjvgo jikr/ lt) ux 5 proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction req etsnv3a3tt)j:;z, kdhgd d **uires $4.82 \times 10^4 \, \text{J}$ 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 as fission2,ntmbvppt8 wd7g6 b1 in a nuclear reactor, the resulting fragments have 6p bmtg7v28 1ntwp,bd a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy/t-.ocq5h u6xbea a c* 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 m)0 amved1vg,t6zjcc mph;7c3ass of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Sta/5 z;iyei wq58f ip7ko 5bkf+ i37kzlmtes 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 i* (8gt bxh,wsof 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 equal0lc+oeht*x*yz l zx, (s its rest energy? v = x,(hxezzllt0* y*o +c    c

  At what speed will an object's kinetic energ:4mdllu l/wn) y be 25% of its rest energy? v =    c

  (a) How much work is requij7 o0k spcriog 936,jnred to accelerate a proton from rest up to a speed of p, 069on gji3 7roskjc0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kineti/-yp.gpbs 3nhisd ;ef,ha f5 pb vaq32q9n 2v6c energy and 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 750 2f;/ct v xwfhwab7xq99h)+ ymjq3e (tMeVvtxx fae /7 +2 tf h3;hbcqy9wqm(jw9))?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentiuxc3oq mln8i;e yus+g 6v(c+ :al difference of 105 MV? v e;q x++n:im(g 3cysvuuc8l6o =    c

  What is the speed of an electron 369+h n 4kmktzf .r1cxzod mcmyc2p)7whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before iltf wq6u5(3pk;*-bk q gxp553ey pmket hits a television screen after being acc5;mgx*3 6wu5ek(p fyel qpp3bt5k-kqelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particle y*fi yuwz6d2;fda 0j(s 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 proty lv;2mb*-t vton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and magy jf:d, **cthe 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 of mass 27,000 kg is accelel m ug-vu jg3car;;x,8rated 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 n6ygh 2yc l3d l*a/0mtof a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleus, *n1, 4 ts(jvgdxwtwk4$^{241}\text{Am}$, 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 k 055xvy k 8;vk(bkdof n1w/rbxinetic energy versus momentum for (a) a particle of nonzero rest mkr 55v8wn0k b;(yv1kd x/fbxoass, and (b) a particle with zero rest mass.

  What magnetic field intensit4kvf;*p-n rvky-3 ifq y is needed to keep 998-GeV protons revolving in a circle-iy*p fv-rk fkq43n; v of radius 1.0 km (at, say, the 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 travesv me;)xam ,ynn4evbu- q5w,- 7;rejcling at 0.50c (with respect to the Earth) observes a meteor come from behind ands)5 4vn vu;e;b,,nq7y- c- a erejmmxw 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 directd:vt t3j9.6ytvh kk/omb: e 2iions, each with a speed of 0.50c wit9:t 2votivm:h kkt3j y6.bed/h 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 traveling at 0.71c. A second spjll:on 2qavys 6;4;)2 xlxc jbaceship leaves the first at a speed of 0.87c wito4c xxn)l6lv jq by2 sl:2;aj;h 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 q 5*iw6ls.lzean 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 speed of 0.90c relative to Earth. What is the relative speed of one vesswe. 5*ll6sqizel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. Oyj35w d-nu/j0 jjo9uz8h4 ygf ne travels at a spju9h jjo3uygwf8 0jzd- yn /54eed $v_1 =-0.60c$ 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 if2- -m6 p)qxtbw w1.mfjgi+u 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same directgtq x1i. )fw bip-+6m-juf mw2ion. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, nctvr,):n5th 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faster than about 0.1c is called rdxnydv(t;9 j10 o jl/yelativistic - i.e., for which the corv /0 9xyo d(tyj;jdn1lrection 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 lr x,xnlwz1z85*57d1g wveei(mh l(h$v$ 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 matterakk:fmiszlz),;r4 -+ hud ; yb would have to be totally destroyed to run a 100-W lightbulb for fz4ky ;r;a ism: huzk ,dbl+-)1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic w :tx ysc h-(3d8.qozgenergy is 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 conservedy z3o.g:wh(xd 8- tqsc in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collides head on with a posi)s (jncfa1o ;;pte7b/u ovtv-tive muon traveling at 50% the speed vun;j - c;a(1 /oos7bveftpt )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, and9py x0i h,tn/1k6t jxy/-e jowj k).ba 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 th -,tj.toxk/ bk ei9y6n0)h1a jjpy w/xree particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a ratgdx1t7ai ,eh0 e 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 ch/sjsn .)ri -8 k,kaftnarge 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 requir,luxo+lghffs2 /uh3m yzh. p:8rx)z52 uewq+ed to break a helium nucleus into its constituents, two protons and two neutrons? The r 23zuswpg/+x5mf)2h.:uuh8 ,+ye lqoxhlzf rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increavc81mupg 0 ;8mn9)e4qd 4(so2lfto 6p vihyd dse in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expa dslv;e0y9dm8)pdmniou 4c1 hf 6p8g(otv4q2nsion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in thep-vv 9p kj8,gq laboratory, are moving toward each otg,v9v 8qk-pp jher. 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 with mvf+rzjdw fvk-o /a8hv43nh (( omentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter and ant7/ ryc4zb5 iiwimatter, achieving completi /r57yz wbc4ie 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 energy is greater than its z oxh cw.e)*s:u fhl1lf(l l,kv),*qzrest mass *w. z )k*vul(hlq),c,zf1 xs:holf el$m_0c^2$ 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 pehuc ba3sr08/c.( ybshysics 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 pole). Can he do it? ea80 y burbs/3ch(sc.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 oxygen react to form two moles of c09wa /vv6 *ox3amx bxwater, the energy released is 484 kJ. How much9 *x/ owxv6 3abacmv0x 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 createdcz 95t:mfqn9q , traveling in opposite directions. If the speqc:59q ntm 9fzed 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 y6vyu- qkxa6yw c(4: rbbmc)/ traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he ea:6cmq4)/- uc y 6(bxyk yvabwrts 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 Eart rq :s.lbpq;k1 s++o8ly e(viah. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed .(qle1 r+asyqp:iso+8kv ;b lof the laser beam?

  A spaceship and its oct n:ek20 nbr j;cb0p -3leym6ocupants have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a spe62btnl k3rynb;0 0e-:ocpejm ed 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 spaceship left Earth at a speed of 0.99c.- 0k6,h pi )bcht4vermvray9 ; What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumptioneh6);mrck,i4b - 0vrpv ha9y t (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to traveld*kro /j5j) (4y wsnxys g6+kt to the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) triy +4otdkj6*krjs n/sxg 5 yw)(p 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 oscillates on the end ofomc9nybzr(q aj lxci (cd, * c4;wx150 a spring whose spring stiffness constant is cxc05rwcndmo (baj * y,x(q1i4zc9;l$k=48.7 \, \text{N/m}$. 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 massg g g0ocb1;ku8fb2o, u $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.