You are in a windowless car in an exceptionally ,dl; sje;:tudpma r dlz7;c3;smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to de;a;; l; td3r pdducs:,m7lz jetermine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of the cornek5i6ki:jc18xra)jq 4pgt p6 rr of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about ab 5atj pri6iqkj4)1k6rx:c8p gsolute and relative motion?

A worker stands on top of a moving railroad car, and throws i6/y st)smyc2gbp / b+a heavy ball straight up (from hi ms/ s)cp2/ytb+yb6gis 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 + 5jt;xh42t/xw(ok lf q youz.valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativiwtl.hx+y x fko/4 tjq (zu2;o5ty (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.,q9ljph 6ib7 n5c away from a star, at what speed would the starlql bnh6j,i79pight pass you?

The time dilation effect is sometimes expressed as “moving clocks run slowlo .s71 d.rhjekb8nm v-y.” Actually, this effect has nothing to do with motion affecting the functione.7 hbd-mj v osr1k8.ning of clocks. What then does it deal with?

Does time dilation mean that time actuallyj 9, s-hcjfy2y passes more slowly in moving reference frames or that it jfcjs2,9-yhy only seems to pass more slowly?

A young-looking woman astronaut has just arrivqdjox;n8rwxto oal4 q-. e/ se4o825oed home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversa4l8. jt2ore xwqo/nxso;8o 5da o-q4e tion refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, ykcz.2u r 4fu,would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using ter uzcf.y4uk2 ,lescopes say about you?

Do time dilation and length contractio ;scruf+g54 ewn occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light werex.s5+ 92fsau5smwy7 j: ajnrc infinite. What would happen to the relativistic predsr9sxy: msf5c u.27+5aj wajnictions of length contraction and time dilation?

Discuss how our everyday(p8 j:m plv+ /kvefdemj8 gu.0 lives would be different if the speed of light were onl0l (dmjuevm. :p+ v8 pk8/gfejy $25 \, \text{m/s}$.

Explain how the length contraction and q9xgnufg 8*dx c*ww0c x 0)k8htime dilation formulas might be used to indicate that c is the limiting speed8f) hnw8uwdc g0 cxgx0 xq*k9* in the universe.

The drawing at the start of this Chapter shozr4,d:myf 70 jz 9 fctxhqm9vyjn 9i1yi.6dl;ws the street as seen by Mr Tompkins, for whom the z. f;j1 9yd49vi j6hd,fyxli:rt7y qcmnz0m9speed 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 put an up 5c6pjqqrhl(* per lqcpr (6lqhj5*imit on the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzer h+sb sw(is2k)o 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. cx.jlz j* lkh,bls05 mean that a spring has more mass when compressed th jjk.c .x0l,lsb5*zhl an when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be 7tddf)f7 c- mycreated nor destroyed." What must we say insteadc yf)d7m7tf -d?

  Is our intuitive notion that velocities simply add, + nl07keaojk/smaizdx(wxk71 m)x++ as we did in Section 3–8, completelyksmnjmd xa+ix7 w7 ++ akxz1/) ko(0el wrong? ----待选择----yesno 

  A spaceship passes you at a speed of9 8 f6;zlvh) x2ywf bpw7pbxb* 0.750c. You measure its length to be 28.2 m. How long wozlyxb92) b xfwwp7fbp6;v *8huld it be when at rest? $L_0$ =    m

  A certain type of elementary particlil dbmmp(r.3,/e7 wnwe 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 factosygsvq+7:5/il:indy 1b ov s ,r $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 Ear2o c(rm-+w ot uiraulnfzno9 -y.4, u,th at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime kd ky uwfgv + jl25yk0zjh-x ul5590n4is 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. How fast woulj0wi 7lf 3vtvbs3ap6 5s,7yd, ddmq3xd you have to travel so thi,lt sm xqvfjwsddbda5 63p,vy73 03 7at 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 speed that tellw7*w-mq/wz5evg 9g b0b/qai es you the distance is only 25 light-years. How vbbg7e /ww q5qw/0gi ze ma*-9many 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 Earth is gfu3y b4co1 i)$11.2 \times 10^3 \, \text{m/s}$. 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 return 6w75fjr/ vbgled from a 5-year voyage while traveling at 0.84c. j7rl5vfw/g6b
(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 4d29rgpcb* jway. How long would it take a spacecraft traveling 0.960c to reach that star from Ea92j4b *pgwrcdrth, 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 fadm: mv h o,x l(9/+b+ydg5ebma 09yain her "Ferrari" spacecraft at a speed of 0.660c. It is me9:/gf9avyodbx++(ya5b e lm m ,dmh0aasured 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 m before it decays? The avepzt x6k bk,f/4rage lifetimz4 p/bx,k6tfk e, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelinn9riq6;om svp0-zh8 d--a6x ll/ dvh dg at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass?4n3am e- .x;j whzuo-g v =    c

  A particle of rest mass t)w0+. zpvwhfxg(pz*$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at2iu)(vfnjq *yp*xy qv.t2wfyb/ 2y-s $v =0.10c$. 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 injlt xmm*ft 9nc9 o3ollhi03 3z,o 4rq6 momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction afm,wnmc g2/o,:.gv s requires $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaks ap u b,dz. gvbew+lq8++sart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mad+s ubv,+z+q wlg .be8ss was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules ar)oa yhh*mj+7jou( .mnd 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 pgc-xh.un 80cidhotid , 0j+d8roton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consu1jaatj;mlaqj.vw6 v ;4 kv7,h mption 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 be5r/oq mcx(f9r obtained 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 kinetic energy equaou/8lac6 md pt512u iuls its rest energy? v = i opaduuut5 61lm8c/2   c

  At what speed will an object's kinetic energy be 25% of it9 z4:fzgzcq7is rest energy? v =    c

  (a) How much work is required to accelerate a proton fromh d2 u*ea*xw6h 0qtb4 cbt8zg2 rest up to a speed of 0.2ab 26t8bch qd4tz*ux0 ewg h*997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momexy6w nh10gfk8mei1e 4ntum 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-Me1 h8ekcp th/-bV proton (that is, its kinetic energy is 750 MeV t8/bph- hc1ke)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a prov.qk1,,c c58rjdr4t djmvm8j ton accelerated by a potential difference of 105 MV? v 4 dc8k8t5 j jmjm dqv1r,,crv.=    c

  What is the speed of an electron whose b ;u;4f 5yxbk-s6 ztkwkinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen after bm(;x.u3jvv6n xu1w s xeing accelerated from rest by the 25,000 V o1xvuuwvx m 63j (nx.s;f the picture tube? v =    c

Two identical particles of rest masssg):tcn t+ ebh0x5xx2v oc5p zis,m12 $m_0$ 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 p7u: xu*kv* w*wwglf(r roton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 an electronsa 63vw(y l(s62v qkhh ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 )ufc:eru :/loplr)d4 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 enernf 4e 3/-gbf+ i3ugvujgy and momentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleuip7s 1r8 0r .ib/jkrenfw,kcwpq3).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 -,-5ua sorx; lsz.gzx versus momentum for (a) a particle of nonzeroxalro,-sg;uz .s5-z x rest mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998--eihy;,ssfr c(cx l 3/GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's res3 c ;x/s,i -(fhsyelrct 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 reixy95 n6p wfw1spect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How ffipny w 6195wxast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions,w-q+ fhx r gfp(a+kv/) each with a speed of 0.50c with krph -qvwf +f ()/a+xgrespect 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 seg, z7sqe *xcq(r3y+hm cond spaceship leaves the first at a spee ehs (+q*3yc,x gzrmq7d 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 approach at a speed of 0.60y5w 4l(: op 9rl7jvy)9e yy+cxwxdz q0c. 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 vesselcy7dzy0xyrv4joq 9:l 5x w e)y+(9lpw as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. One h:8cqxqy( :lntravels at a spe8 q qn:hl(x:cyed $v_1 =-0.60c$ 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 timew 3+hhg0 )2tgmencw7f , rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it pass7 h23g0 nwtm+hefc)gwes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-ye+6cvq8t8i*r j )vi+hubeq q7oars 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 travelin w k7p aal,rw6)x/f6csigl1iemu/:7 mg faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effal,mmi6 fu)e: 6/i l1s7x7kw/gw cp raect. 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 speebs0ueatey2f3m::tm ux4o2k * d $v$ 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 ck71njxevo7k-yp-z ex2n, z* have to be totally destroyed to run a 100-W lightbulkpk7yxexnzv-c 2 , e*jn7-zo1b for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnet v5 d8rfa jk7hh(:b-ypic energy is needed to produce an electron and a positron together? A pvf d5yb:j-par7 kh8h( ositron 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 light collides head on with a pof . jhkc3)ap91gd ev, (qb,br wcluu77sitive muon traveling at 50% the speed of light. The twoh73 vb fbk)7,ugalc9wr, ce.p ud1jq( 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 neutrino. Assume the hr48k hyjt e0yqz9 ;6pneutrino'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 three particles when a neutron dz;e yr9t jh8h6qp 4y0kecays at rest. KE =    MeV

  The Sun radiates energy at a rate of +k.h2h f azlkot17o 22*c kzqaabout $4 \times 10^{26} \, \text{W}$.
(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 measua4lwtoef g64z)f ue3/ red to have a negative 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 constitudg y,7:v+ j:h(iacghtents, two protons ac7: yg( jh gt,vhad+:ind two neutrons? The 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 increase in fr4qnq1cyc yk,2a /8 2b)i2 zaxvw.nwthe (relativistic) mass of a car traveling 110 km/h as compared to4.b2)rk2 a/ c cx8n,wz na qfvywiy12q at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving n/ ttxxjdl mj cs*2;(.toward each other. Det/*cxt l.jj xms( n;dt2ermine
(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 paht7f *5gwh(nqg 2sz5 z a)gw0vrticle 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 amq8a. q bc9gs0 /8cpx6 wgxb+and antimatter, achieving complete conversion of mass into energy.gqagcp. q86sbbw0+9 mc xx8/a 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 accelera 9dby4v407wyxb7mt n -xezlg 2ted so that its kinetic energy is greater than its rest mass ynbe742 w -xy704mxldb 9tgzv $m_0c^2$ 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-long polsyq 8q2w bw)0we 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 ww)8q 0q 2ywwsbhen 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 tn- roscb1eak4o6v1jk 2*b bvq-77iewwo moles of water, the energy re24n-kca be wiobve1*jbk6oq1 v-s r77leased is 484 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles a:uq ,v/t0beahy9k m/pre created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed rely0 tuhv/pq,k:a/9 ebm ative to the other particle? u =    c

  An astronaut on a spaceship trak* +ryyyu 2i:9aok701svp ftz veling at 0.75c relative to Earth measures his ship to be 2y1r y +k7 fsy9zivk:0ot2 au*p5 m long. On the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85cdwi b g,sqw46)y5 fvk* away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the sp ,*4gd vw)wfkqisy b65eed of the laser beam?

  A spaceship and its occunxbzetj s)xz1r7v0 )-pants 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 speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be convertnj01z-t v)bs r7 xxze)ed 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 l1l u lpw5p2cm(xlf-8 veft Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption ( wmlupx8v l l1f-p2c5(about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to +dpn ws1. hzlq z*k2-wtravel to the vicinity of 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 be done on t+zs-dkh.lw 12w p*zqnhe spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on thenaho wfw+w a*8 y2o,o* s+i6ke end of a spring whose spring stiffness constant is oy*+w8,ohi2sa wo wf+ *6n aek$k=48.7 \, \text{N/m}$. 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 m6hfgg f26d z5hass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.