You are in a windowless car in an exceptionally smooth train moving at ,:x.eek9t(w watxm/ uconstant velocity. Is there any physical experiment you can do in the train car to determine whether you are movi a(mkwx w9 ,.et/:txeung? Explain. ----待选择----yesno 

You might have had the experience of being at a vv;wkhe / 6ci s+2zk93ikohk1red 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 does1s2k kk 36he;+kc9w/zvh ovii this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy ball strjn y /(5z1lsfqaight up (fro/ 5yz(lj1qsfn m his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to saklro* :v0p0k0k.bidny that the Sun goes around the Earth? Discuss in view of the firstdi0b0v:l.rpkk n* 0ko principle of relativity (that there is no best reference frame). Explain.

If you were on a spank8p 6:tbt+gu,myhu,ceship traveling at 0.5c away from a star, at what speed would the starlight pass:8pth+y ,,t mb6g kunu you?

The time dilation effect is sometimes expressed as “moving clocks ru6;aj ( ecgo eo :qj,f2lw))gxpn slowly.” Actually, this effect has nothing to do with motxg;,:e ja( w g6e p2ol)cfj)oqion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly i a;yta5yu;n3zw5xl j:n moving reference framesla:n xy ;j5;3twyzau5 or that it only seems to pass more slowly?

A young-looking woman astronaut has just vmhe1txw 81; nxhum3q2x :p1uarrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him vu pxx; mhhntm1 1eq 3:28xw1uas her son. How might this be possible?

If you were traveling away ,n9e11iha )i kk+alrxfrom Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observerk11+anixi k,ehar l9)s on Earth using telescopes say about you?

Do time dilation and length contraction occzmsm3z7v 2*p6-q ktou w(x2wpur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infin*i,ov*jiosuqjptt,v-, 7 om-ite. What would happen to the relativistic predictions of length contraction and time dilq-p*ms*-,o o7vj, t ivjit u,oation?

Discuss how our everyday l+c;knm*vzl)wac ow(t 2k5n9fives would be different if the speed of light were onln(v)n*m +coc5 29katlzf ww ;ky $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might cu:*e,.ctdq+dhm i 2ybe used to indicate that c is tcu *2c:.t+mheddq ,iyhe limiting speed in the universe.

The drawing at the start of v omg0l 9/0htxthis Chapter shows the street as seen by Mr Tompkins, for wh0/ tvm g0l9hoxom the speed 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 speedd)f8 k3 yb1 +sxfqi5lds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limitsb l 3f8 did1qkyfx)5+? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed oo y,y ix)teps 4ic9;lk;k4ze:k+b 5suf 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 ener8vum 3qen/a o ,wil58egy, does this mean that a spring has more mass when compwo,/ m8ei e583qua lvnressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be hz 66 hs,d6 vmav2lhic.yw*3icreated nor destroyed." What must *.3vy h,ah66d mwsihz2ivlc 6we say instead?

  Is our intuitive notion that velocita;*bc rs kd9f8snpr5ja: f+ e,ies simply add, as we did in Section 3–8, completef:kp8j5re,crs9*n+ s fd ; aably wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. dr8 :. *oz1hmv/1fsou nkf/j tYou measure its length to be 28.2 m. How long would it bnj ofd :ho*svku1/f/. mz8tr 1e when at rest? $L_0$ =    m

  A certain type of elementary particle t; +1v.nm tla-gwgvxn3ravels 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 favch) 49l(bnj -wxxed4ctor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 spuqryha.bibu z e*4,::eed 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 ib cs /qqhd3k sp2c( z7ucig065s measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light-years away. Howqr13d xm1.; g-)mjddbdm j o)a fast would you have to travel so that tommd ;-1q.dxr) ao)3bmg 1 jjdd 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 speed tha(fgkz3t+e7dg wzg6mvn;v8 6 u t tells you the distance is only 25 light-years. How many ym3tgk(f6n6dz7gg ;vw vz8eu+ ears 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 tdukp+l nv;) )phe 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 Enterprise had just returned fro,du9+l+qy gwk m a 5-year voylg qkd w,+9u+yage 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 lmh-qz xb6culr :*w 46xg/mhejl15m4 a ight-years away. How long would it take a spacecraft traveling 0.960c to reach that star from Ex 41465 ulwz/a rlhqg6m m hec:xj-mb*arth, 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.wb -m y0ti,co at a speed of 0.660c. It is measured in your frame to be 4.80 m long aw imbc ,o.y0-tnd 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 je8,qo7d0 hfr fx2avsq74ltw +z z;:g pion be moving to travel 15 m before it decays? The average2d,wf4qghlxos e7v+: fqz7a80;tzj r lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling j k4eft(tajb/yj91 5cat $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass 7hoi9k+a.w ylbe twice its rest mass? v =    c

  A particle of rest mass 2qsuxjxng 5/0c7l n7o$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at 6ndiofyf -zqszpis/432d .0 w y1cp p.$v =0.10c$. 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 a pro u ga9/2t3uhrvton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires02s4r 2pu4in tafjj(z $4.82 \times 10^4 \, \text{J}$ 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 aps+byif bsq1t;(eyeho(nz : 86art in the process known as fission in a nuclear reactor, the resulting fragments ha nb s(tqhs eiy+:(eb6zfo18 y;ve 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 of an electron in joules an xvib( 1x, 5a 9cxjyx04fe:llpd 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 6ksn)81zvv wb 8rpbms x 1p-f/proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in th a kz(5wkve5x4e 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 i xb4* mydn+ s7qyt;+eb9lt x8conversion 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 +oq5k 5whep ak-i z3-rits rest energy? v = 3zh-k-e r5po5qa+iw k    c

  At what speed will an oh3t p :e-z,s;cs(wo 6a wk+qshbject's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is requicphgpf/.qefj 31 jle*. wo+o/ red to accelerate a proton from rest up to a speed of 0.997c? W = c h/+j/j .egpwo1.olf3fpq*e   GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energ f1zhw1x4sn x2 zid4 yz4h.sqwh t*y5:y 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-MeVoa osyk48k 17ynw r i-a lcxgn4..um80 proton (that is, its kinetic energy is 750 MeV)? -slo.y4mcxyn7k w auno ikag810r4.8    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of gppnwmd8 v..a9 /be-z105 MV? v = 8g.nbzep w v. p/-9dma   c

  What is the speed of an electron whose kinetic d oee1rh/60eq energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hz 6o cc7vtuktj53o k;, 1eqo8rits a television screen after being accelerated from rest by the 25e;j t83 ucorocvko75 ,k 16zqt,000 V of the picture tube? v =    c

Two identical particles of (izxlm4lr/pl0h*y+j 2qic ;z 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 o q4l9l*ofh3i2ncwva te4s . -df 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 and the momentum of e ae.elfm2(3k 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 accelerated to 0.21c. ycjs3+2 uc7 u 4qdy)sp
(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 proton (*sf7:k5a sdtonze .bry:n *, a$m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 vwkpj5baf -4*+gdr wmlz hv16+(i*.on x qv.i, $^{241}\text{Am}$, 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 momentubu uih:ihp5t*w c)(0vm for (a) a particle of nonzero rest mass, and (b) a partivtbu iic(: h)w0 5*puhcle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV p4b i(gzxgb +jd x4rj;1krlm7s u)*yd -rotons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The protonbgugrdlxz4bs jjxmyi -;(1 +r)dk7* 4's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with respect to the Eartzhqv4x0-b0atn7oe.o1ilfqu b:r +n 2h) observes a meteor come from behind and7x4hni1 0v u+zo0 .enrbotf- lqbq:a2 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:l j.7+i8(vuh a-cy 7pkfypto with a speed of 0.50c withy(vp7a7lcjt-+k h.yi:8 f upo 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 50xs1n a2 nx(*pnzfuf0.71c. A second spaceship leaves the first1af5f(pxnsn2uz *n 0x at a speed 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 al vq,mzo5dqp+8e +rlgr py;t 20ien vessel approach at a speed of 0.60c. The Enterprise comes to the rescueo ,q5d e+g qyzl0+r8rt;2mp vp (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 =    c

  A spaceship in distre:knwtjfc4 k/n:w ;2ehss sends out two escape pods in opposite directions. One travels at a hnctk:j:nw2 f ew;4k/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 st,u/; jm b w+t+v2rokqag9ru+knt*q+ peed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in t9k;v q2t +bqk ruaj/n tog,wrmu+++t*he 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-yto ;9 y81ioh nit*yw2q-gbu:sw4r e h*ears 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 relativi. bea(tjh4uj94q4qbq stic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an elub j9.hqt4(4 aqbeqj 4ectron 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 b jq++ ao+o5ql5boj +c ;s3ahx$v$ 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 ma hgd,2v2+ro6s; hovlitter would have to be totally destroyed to run a 100-W lightbulb for 1 6d2ro,v is2hlo;h+ g vyear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energ efzmvc;d-y .8y is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but ha8-zym;ed.vcf s 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 ligh9 or q)dr 1wiafi-d ; ,8wim2aa2guzt6t collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest mass ;2qo zdmu9,g8r wfi wa -16) 2aatirid$m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can deca,mg 3xtfv 6nc.p p.jzc (32dgqy into 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 3 pdq,g6mfvpg3 2.tcn.j x(czthe front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate ofhj(* qpo )9z +ednh 3wg;/pbaa 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 chara1p yzwdf+8* wge 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 t7 .n:lu i86wav6/er5(mc:j gooahuvro break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an igc6m .:nlo(r7a/u 8heawv: r uj65voelectron), 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 increase in the (relagg10q tr( joy:tivistic) mass of a car traveling 110 1 q(0ggj ort:ykm/h as compared to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having -svss x dc/21t(r 7bh,ofho gqp ,5m)pa speed of 0.935c in the laboratory, are moving toward each o(2-bs ,sr hv1ctm,oqp ) h p/dg7soxf5ther. 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 parioxf4zws 8 f xsvcj88//nk *:gticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by 6 (qtg/x/2fi2 lw mth ax2w4v+u. cy1pi pj;wscombining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approxim.2 /vh12js4pi( w+ixgft/a6tw ul q m2 ywc;pxately $5 \times 10^9 \, \text{kg}$, 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 res wtvwj; sn up5vsc,0d fm):3j2o: +ksrt mass s 2kj, 5)3wt: ;uw:m+vsd nrcspv0jfo $m_0c^2$ 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 hefi tn ,4yl(w( s3vqj8f 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? nijfst(4w,3 8( vfql yExplain 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 i .r /pwi)cf8 j9n3ued3bg (jqof water, the energy released is 484 kJ. How much does the mass 839q/( cgfdrei)pj.n bjiw3 uof the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling in opp ct: sp,no)ay rswum1l; 43wa6osite4pou 3:1 ;r wt,yslmsa6c)wa n directions. If the speed 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 travelingh4bvh qq3 )qjj,7 es0d at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his ljbq h)dj0h,q v4s 3q7eunch 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.7a7t fc4m.h2liv kza 4 You send a laser beam7ahzi2.c7vaktl4 4mf 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 total mass of 150,000 kg. The occu; d3rg6+msr1 fn9mjr 0b, n1xizzlpn 3pants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the space3l+ j6r1gzdnf3 rs mrz9 ,nx01nimpb; ship 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 atncmgloi+ dn3c0i)h ;7w1:j 4n n/jutr a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annuu7)jilhtc n0;1n wo:j3nrcm/+ id4g nal 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 star 6.0 light-yeard4r : lon3bx7js from Earth. Passengrdx 7 ljon4:3bers 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 this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose s an ;rxn(-jx7is4mve5pring stiffness constant inv;em( ja4x rns57 x-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;tvzvszm64s .yzp 9( :7gwoqdass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.