You are in a windowless car h pb, uwkw06d7in an exceptionally smooth train moving at constant velocity. Is there any physical experiment yopwb6 hkud w70,u can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of theck 4p6 rx7hal8z y2wo74 rz3zg corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the bry 7z ko2 rw8axz4pch 463zgr7lake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving rauh9brwrrudvm re 5b3 6/)7o0eilroad car, and throws a heavy ball straight up (from his pointdr b7u3 6v0hru9 or)/me5berw of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Su)qxikc(b95s-5m w( tnr tk0opn? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Expl5- ((m9wcbq)s rtonx5pktik 0ain.

If you were on a spaceship travelin8rde6 e)c i/h- 4otdvjg at 0.5c away from a star, at what speed would the starlight pass yc e4-/ hddv)ier6o8j tou?

The time dilation effect is sometimes expressed hk6 4lp roz:tl g-6xk4as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the fz hx6-lpr gl4k6t: 4kounctioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in movinge;+2qvqd4ap ejk0 8t a reference frames t+;08 qk4 qva2apeejdor that it only seems to pass more slowly?

A young-looking woman f ofvk5 og12 5rtxh5 du+9mj7sastronaut has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers tfu gxjo2 k5 dv7fh51r+9st5moo him as her son. How might this be possible?

If you were traveling away from Earth at spee1l(tl1qg w,b 690ewc1.y pgl*nsobdwd 0.5c, would you notice a change in your heartbeat? Would your mass, height, or wae bo9d*y,b.(qll 6wglg1 tw01c1wns pistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordy:h3ijqm l hw-,sx--lpxys-cl 4w3l2inary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What wo *y dr 26g c,lwkz++fljx 1sn0kt/;xdruld happen to the relativistic predictions of length contraction and timk0 lzf+16 tg,clj;x /xsy2+knw*rrd de dilation?

Discuss how our everyday lim+ dicq1v02 atx,f. hrmumcmdg3t3,k m./ 8 qbves would be different if the speed of light were only .02m8d3tf m ,+vmb3ram cdichmq .,guk qx/1t$25 \, \text{m/s}$.

Explain how the length contract)e :r2 sjxz )/axog7feion and time dilation formulas might be used to indicate that c is the 2 ))/ezxao jsr:ex f7glimiting speed in the universe.

The drawing at the start of this Chapter shows the stl 97pnqti)f n3 9v1voh l/pf7creet as seen by Mr Tompkins, for whom the speedn7q v/1pl9hp9t) nfofv7c3li 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 anf)e7axl2( jv5plf n*a upper limit on the momentum of a*a p7x5 fvn (l)j2alfen electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attaikk zau /5uvmc93vl1l;.p9 fgcn 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 spvqk+ k:-oe57 f(aft tpring has more mass when compressed than when relaxed?o:tkqt( +fpv ea7- k5f ----待选择----yesno 

It is not correct to say that "matter can neither be creates,oe1u gav 9/cd nor destroyed." What m,uec as /gv1o9ust we say instead?

  Is our intuitive notion that velocities simply add, as we did in Sect90vsaxnz c6.rq*rm - bion 3–8, compl v. mrar-cn 90xqbz6s*etely wrong? ----待选择----yesno 

  A spaceship passes you atbp (v s. - x:qvit4s7:y6lxerz a speed of 0.750c. You measure its length to be 28.2 m. How l r4sxl(vzv xey6 bit sqp:-7:.ong would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed oq) bq4 l.ji3myf $2.70 \times 10^8 \, \text{m/s}$. 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 factor q(o fop4+5ugt$\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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-yea3ivk,0nj,lw 6jyqddfi 2 nx 0: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 ofo(oh o2 kw9gpll+wt)pz1y l0) a pion if its average lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star)g d2aa6pq;2 pczx-ik is 82 light-years away. How fast would you have to travel so th-2dacg62 zi ;p)kxpqa at to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-yearq0wcaxx5 ne* ,s away at a speed that tells youw0c*,5 qex nxa the distance is only 25 light-years. How 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 n5 vt:)u*p0,z ; ahdnbly(qm:nf0uipthe 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 f)rn:-acly ye48sn5tqeay(3 that starship Enterprise had just returned from a 5-year voyage while traveling at 0.84c. eaa nry:3ty sc-f)(8eynl5 q4
(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 it tm: a8eu+nrl- nake a spacecraft traveling 0.960c to reach t a-:l uner8nm+hat star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecraft at a rp*g0+zal-t espeed of 0.660c. It is measured in your frame to be 4.80 m long and -eg+r*pt zal0 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 piphl4fkyswnutn.*,/rp;7 y wa + tn/-xon be moving to travel 15 m before it decays? The average rk;h*ap /7wt ln4x ,nps utw+fn .y/-ylifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling at x) r;;8/+haz0s7obu bvt 2oomhx +qtu$v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass? v = f18zd e:yzp2 c10ivxkkfg .a+   c

  A particle of rest mass wu*8*h ptdy2v$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travee iq;qub 2k)rl:ggv; :ls at $v =0.10c$. 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 chanlbf(9976hr-vlsf d xuge in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactiondlx2vk2 w :8wb a +s(u3:mnm0dpcu4h h 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 apart ing): q5(phslxp the process 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 process? (phx5) :sglpq $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energ,c,e: yo up7fuy 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 rldx s-5j a0. owsvfl zg,73h9a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abpcd; o( zb(k94f)p vywout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 1d+a 5dy2* satt.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 its rest energi 6ex:nb/r 46cy,v 8i3sc gyzgo 78flny? v =gz ,8b3v y66/siy 4n8irexofc:cgn 7l    c

  At what speed will an obje)-:a)s9w*orn 3 gllqi s(w ggo le;z0act's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a1 ; fm4c0ag wn*gmad6fne. (po speed of 0.906md (pa4cnag;.nm*f1ewf g o97c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton t-y:r rmk u7om1y i2g;k)k7+ube nty*oraveling $2.60 \times 10^8 \, \text{m/s}$.
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,kghwjzv ld yi(-1q5t,ivxa b:- n i76,lpw06f its kinetic energy is 750 MeVkjgpl,xi 0d1w - il6yaz6vhw q ftbn:5i(v-7,)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of0 k+ *s/old izh(oj,q /dagflw2 4i:kn a proton accelerated by a potential difference of 105 MV? v =odqaldkk j4+z0*f glon :is2/( i,/hw    c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v =j4b9dbbn *6. .p oiugh    c

  What is the speed of an electron just benl:l 5cg,tb6z fore it hits a television screen after being accelerated from rest by the 25,000 V of the picture gn,cl 5 t6z:bltube? v =    c

Two identical particles o.y5pd2e adq z)f 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 yb;9unp jt,uv0r92txf 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 an electron dov euy37o:kf+p2 p 9szbws:)($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft o5b8:u 7eqp )yw5rih rkf 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 and momentum ofrp; 5ov tg,pv nc.tl;;rsmiz8x9i43n 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,5a g /2/xcc-jmcy:ng f $^{241}\text{Am}$, 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 particle of 9iea :5vyh2canonzero rest mass, and (b) a particle with zero rest mas :iy ca59veh2as.

  What magnetic field intensity is needed to keep 998-GeV prozg 8,b /q*zkegotch0m.s: fge u5c(p02l2 jyjtons revolving in a circle of radius 1.0 km (at, say,cyh cu: , gb5f2z2.e*kegqstl j(0j zgo/8m0p 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 traveling at 0.50c (with respectyx: u(wc4h2 f:pz6:(+.igufc xfsqmk to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with rezy wsc mu2xi6u.xgchp( q f+4f:(: :kfspect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50j-cvdk*xug +a3/,ljzver .a5c with respect tgejcu5+vdk*z l .vr- a/3aj ,xo 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 spa 8 lx*il5 j*f-dmhsj2gceship leaves the first 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 firlhfj8sxj *m5d2-l gi*ed
(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 speeufkrfl*8i; l5ogq9- jd 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 Ea9 fo8ju;rfql* g-k5lirth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. 4kst0u nwms+ ibc*l4 ,One traveuw 4+ckilb 4n st,*sm0ls at a speed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth at a speed of 0.75c. At the s v n;tr7whykpal-amh.+ fjm32/20 etc ame time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A wha/fh; wmpnk ch+y7mea- 2tvr jl.2t03en it passes A? u' =    c

  The nearest star to Earth p/.aw43 u1td7d:pudx f ph0e vis Proxima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faster than about 0.1c isl.w w5 od0uq3z called relativistic - i.e., for which the correction using special relativity is a significant ez 50. 3uodqlwwffect. 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.a/fh/e /hcyh $v$ 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 tot(m8d )u(oxtx2 bm5ny php+ri3 ally destroyed to run a 100-W lightbulb for 1 yea iux)d hnombr5p8xp(y (32tm+ r? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of elec 4k -gco*uve :mauj; +on1wn.itromagnetic energy 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 chojiw ka+n.v cog;14 -:m eun*uarge. (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 ata,:f fowrz/ m/zp9xy1 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each o:m aof,1f z/zp x/r9wyf 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 pro. . rb5pdtvltacce /kv59;hqi(8 gmu+ton, 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 three particles when a neutron d9 hvtr5gtl;/ c.+(.que 85pk vbmcaidecays at rest. KE =    MeV

  The Sun radiates energy at a rateai/l 2a6z e-z +yixvi8 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 charge and aqa(l:u (hhdwt41n .bm 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 cz*v3 /dkna lm-onstituents, two protons and two neutrons? The rest masses of a proton (includn lmz/3ak- *vding 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 therov+,uu;qn-k- b*irs (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the bi;ris bko-r *uqv+ n-,unomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of mx(i6 j p39qfkk2d/obktp46k 0.935c in the laboratory, are moving toward eac62ipmkk /fdqtbxj(po 436 k9kh other. 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;n)qq0 y-qge+1 qful7e,fjg x particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its po/z4 oysor48jxwer by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Ent4r 4zx/o8sojy erprise 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 i7dr kzh5 : 4otznjgm.;ts rest mamthz57d j4gok.z ;n:rss $m_0c^2$ 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-nr7 f0/6yb00t; lc ggnqhel3 g+ bch,hlong pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the3h;glb0 e ,l7yc/rf gcg+n nh6b00htq barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one msu1fg+8 ns, 9g r--+.fa tft7encm 9nkgnqr)mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of tr a +) mnftngg .-n9s1+sutmg -enqf, c7kr98fhe 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 reactioh( n/:nym xadi33q ,cqn two identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other partdya3 mi/qn,h xc3qn (:icle? u =    c

  An astronaut on a spaceship traveling at 0.75ceec 9f;ee6iitbq1u4d ,f a -g3 relative to Earth measures his ship to be 25 m long. On the ship, he eats aeeq ,gid6t314ei;f -9fe cb uhis 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 a-: 2(excmm qlit a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do obse:q il x-mm(ce2rvers on the Earth measure for the speed of the laser beam?

  A spaceship and its be mj*v .mx.h qpo;l 4j.e..fjoccupants 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 convertedj ..h ;q*4. bxjpv.ejlmfm oe. 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 35)r+sxu fv ulur.y+p 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy con+uuxrp+ .vusyr )5 f3lsumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel t+sewyrx,8ua.- .dppd o 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 the spaceship to bring it to the speed necessary for this trip? u u8e. +ps,x.w-drd p ay=    c

  A 1.68-kg mass oscillates on the end of at.pkwekyep. p t p.u)d/ wf+(. spring whose spring stiffness constant ipdw+ p/te )(f . tekykp..wpu.s $k=48.7 \, \text{N/m}$. 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 mass g.j 0i+7sx b2rye6igry. 4edd$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.