You are in a windowless car in an exceptionally smooth train m1,vgk*f3vz5wysie uigka +- :oving at constant veloks3 a i*e-:z +kw 1,ygvifg5vucity. Is there any physical experiment you 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 tkl 8 w tp*gaorh1/c/r8he corner of/1/h wtr rkpc8* 8gloa 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 absolute and relative motion?

A worker stands on top of a moving railroad car, and thr0 fntxi0kj 1tw046 rlxa+wq -oows a heavy ball straight up (from his point of view). Ignoring air resistance, will the b6xn+0otwtfia4-rk qx lj010 wall land on the car or behind it?

Does the Earth really go around the Sun? Or is it also cwpns mb +4/sd b;x-es9 r4-dvvalid to say that the Sun goes around the Earth? Dis ss; dms+re -/-4n9bwbdx4 pcvcuss 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 away fro n0rj) eknfpdj+sbfe10q ka5 0m6 9.bxm a star, at what speed would the staref9 mdjp) .kje05 r6b0k 0+sxbnfna1qlight pass you?

The time dilation effect is sometimes expressey n-1- xnl5t-/fa6jrydj)mho d as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does )lt -rynd n oj5ja-f1y-xh 6m/it deal with?

Does time dilation mean that time actually passes more slowly in moving l2 kno;fh)kt0on0ll) reference frames oo))lt0 l0 nfkhl2; onkr that it only seems to pass more slowly?

A young-looking woman astronaut has juruvf,t .4ggl v8e .a5fst arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to l.f5g tvag .e,fr 84vuhim as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, 3qeh1ifrb4; dz8lj x1 would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes sahd1zqxjre3 lb;1i8 f4y about you?

Do time dilation and length contraction oc/ l 67mzuieki4y ov/ 1qbh6b*kcur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of ligjc 0)x;7cp dv0ko 7xipht were infinite. What would happen to the relativistic predictionsjo7ccp kixx v;pd7 0)0 of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light were 8sgpjc;m24;j pss91mn5 ro0x/f xmcqonlymj 1 nspm5o9spcjx/mfr0;sx; 2c 4gq8 $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used to 3jq/q/ 05 8gru8/ltw n5vtwy eelsfg .indicate that c is the limiting speed in thef/t u /8eygltjn5 egsrw qw5.80vql/3 universe.

The drawing at the start of this Chapx; 93,ovqcn+auoz a.) 4x niv03gstxlter shows the street as seen by Mr Tompkins, for whom thv4ngsztn)xc9x ,0xolqva a. i3 +;3uoe 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 speeds less than ryh9e2b d2x54br,jsu6o jlr ee*w 8(oc. Does this put an upper limit on the momentum of an electron? If so, what is b lh4(r2o9b5xjue*r s 6,ye2 jdore8w this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonze+:fiqm lw bc13ro 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 me7h uk4fs7 ecf4huaz79an that a spring has more mass when compressedfa47k4z 9euchu77 f sh than when relaxed? ----待选择----yesno 

It is not correct to say that "mattey ;ew/d+nd4yzn 2b+ uvr can neither be created nor destroyed." What must we say insteadz++ud2enyy 4;wn/vbd?

  Is our intuitive notion that velocities simply add,nsmqy on/*3r/ibh*7z as we did in Section 3–8, completelyn/o yqz7 ns/m hb3i**r wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its lengt(cz m3ofk;7m)mbhj 4t h to be 28.2 m. Hm7;kh )tczf(mj3 o mb4ow long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels atji:a. bzas7l(5ys(aux: dhf g86sj,t 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 facto7ze;ffy*, j0zac)b v7j/kg mvr $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 l9b -ju :chtim8y*sn 6l-q9tft ight-years 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 pion3m6in)sz0y1/ zraz 7c oc t*cwuxo-w) 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 is 82 /*tlovi0 +bellight-years away. How fast would you have to travel so that to you the distance woulv*l eb/l0o ti+d be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed that1 8ri: m+p;ktif6oc qi tells yq:it c8 f+m6kio;r i1pou 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 the Earth is9/vnz 5px yw/x $11.2 \times 10^3 \, \text{m/s}$. 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 q,mbbo+r;7i 4 hbaxx c23py.e from a 5-year voyage while tra.,oya4b q7hpbe mb x;x3cr+i2veling 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 so12wh vi ws5/w)kx7llong would it take a spacecraft traveling 0.960c to reach that star from Earth, as mlssh 1o5/2kxi7ww )vweasured 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 "Fdi 6+a7y6q g73gidjf +; jadx5 incb,kerrari" spacecraft at a speed of 0.660c. It is measured in y+jq d;665+i fd7ydagxjia bkg c 3,in7our 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 movibrks7 vdx+n.c6-la; tng to travel 15 m before it decays? The average lifetime, at rest, ivrlk -;bn7 atx+6s.cds $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveliusdpnzae:.26uput 7m) d5 t3 ong at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass etmwb- l2:w)h3mqq .f sy7:qnbe twice its rest mass? v =    c

  A particle of rest mass hg;q3xdrhrlpy o-0n(r *7,zn $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelefbr2 bhc 74j3m:f d,hgly2 i+s 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 change in mom*.ep18 0mohmgj bt f2tentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction j,+of f)h wv/1et:vcorequires $4.82 \times 10^4 \, \text{J}$ 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 a*cf narfzs4:,9elp 22vg+ixhj. tya3part in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 2,3 ylf jghea4.t9v r:*c2nfxaisz+p 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 joule.z3 * zx3xvpjzs and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a pro togge.ct82xe:apez91 ;2p9xmz5jw wton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption i 9kyaow.5not )n 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 be obtained from conversion of 1.0 gram of mass? m9c 2yqv poya1fu 9n,.   $ \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 ( 0l26l(zt ;,qndauvbtq)yi uits rest energy? v ya)2q tti (;uvnd,qll6 bz0(u=    c

  At what speed will an object's kinefze;7jyngy /ce9k3 +ge / itz9tic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton frz6j iubtj9)l)om rest up to a speed of 0.jjl 96t )iz)bu997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kineticz0bnbr04n8/ gokk 0z r 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 energ7covog .49q2nqs hr. sy is 750 MeV)r sn27c 9q4o .qhsvg.o?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a )3lq cmi6v5x(1i g* kata; ptipotential difference of 105 MV? v = i k563l() acm i*viaxg1;qpt t   c

  What is the speed of an electron whose kinetic energy i.u yu/,orwn;ws1 ram- s 1.00 MeV? v =    c

  What is the speed of an electron just before it 3 vml9 g saenuvs., s/;hf)v89q)lhvj jy(- qnhits a television screen after being accelerated from rest by the 25,000 V of the picture t9jl./ (-sjn)esv3svq) mvn 8a fghh9 qyl,v;uube? v =    c

Two identical particllw.7 porlv4y1) cdwjgu-e 7w:es 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 protxb6c,py/w.+ 7etjurnf: p w t4on ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 owe 37/ee)+i9frpct ek5;agk tf 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 gxn/6,hs 2a z.k1edta 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 xr ebg/02u1 mn0r j kv+iawm2-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 nucleus++ 2la1d, bqs +2rcj/escrxqv, $^{241}\text{Am}$, 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 x6bebtjnrnn.8495xov r - 8yr (a) a particle of nonzero rest mass, and j vxnxe9 ntyr-b86r85bo4nr .(b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 99qlq)g19eskmp m1 ;,t n8-GeV protons revolving in a circle of radius 1.0 km (k)1 n9mm ,e;tsl1pqg qat, 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 traveling at 0.50c (with respect to the Earth) obusj9j s)j;/m dserves a meteor come from behind and pass her at a )/ 9jm uj;jdssspeed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite direct25fbu/s wwj ya-l yo0.je-8poions, each with a speed of 0.50c with respect t5 8 -/s e-fojo.pyb0ulwjaw2y o 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 Eart cq8nvfulp:2)h traveling at 0.71c. A second spaceship leaves the first at a speed of 0.:q)u cnv pf8l287c 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 vesse 1j)py at ep6p*t+nxf4l 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 spee yjp)p n tt1xa+*pfe64d of 0.90c relative to Earth. 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 z03 ihej e :eeuc89nl)directions. One travels at a speed 3ee8jc:nu e 9l0zhe)i$v_1 =-0.60c$ 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 samed;q 0fz2 8yqag a u2v+--pi2eeywi0re time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u'2qz 020y8-pye - wgvu if;+ aaqr2edie =    c

  The nearest star to Ear4ax(n b8mfoh.2*dr k +ies7tn th is 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 bmm91kq2 zy ; yh/yi;y+9gosfis called relativistic - i.e., for which the correction u qgizok2+s y ;b1/9yymhy9fm;sing 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 warp;bt ri3e 8kc:d9($v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter would have to be totally destroyed to run a 100-Wa/ldtq - 31teg)s0 lan lightbulb for 1 ye)0tq a3 / tnglsdea1l-ar? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is ne; x qmq2i3kvuy:l4m5xeded to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has thvkml5qi4 xx;y 3uq2 :me 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%hiqumotx m puhjvv.1)-1;+-l the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each oq . t-v );-mvl+jmuhpio1uh1xf 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 electronx6/m*yzs 9w s54tn zqj*iaj5m, 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 kinet* *9 twjy5/xaqm sji6 45zsnzmic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy afq d :qn (8v.w2tlr5k;3yt atyt a rate of about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is mealhxgp) cns h5u,.;1sb sured 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 heliu gc9sq x3yc3p*m nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.x9cp gsc* y33q00867 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 the13rflef-vq sf1 sjy4yy -4rn0 (relativistic) mass of a car traveling 110 km/h as comparesffyrv4--nf0jys 1r1 ley 4q3d to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having cvh 6d4ay 4xt,a speed of 0.935c in the laboratory, are moving toward each other. Ded4v4hc6xy,a t termine
(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 psi*iuxkt7rd(a ,ma-nto918momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matm 7/7bg6nscpbter and antimatter, achieving complete conversion of mass ipm6cbsg7 b7/nnto 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 itge f60bzuy,bhzote4;tw d.i(0gdj 7 . s rest mass .ht.e g0; 6ub4edfoi(ty dz7wg0, bz j$m_0c^2$ 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 p- m s pygar,;j9pj5z*+hxml+m /7 jhwqhysics 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? 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 pp5,a9jm/jqhg*+w xlys z7j-m r ;hm+ m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react i -u26ev+g l3lwiru (pto form two moles of water, the energy released is 484 kJ. How much does tl(63i2iuwrv -eu p +glhe 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 created, traf pc:tvgo 3m0-veling in opposite directions. If the speed of each particl tmvg:p0- 3cofe is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Eaun)zcg )drr3 :rth measures his ship to be 25 m long. On the ship, herd )uz: 3)grnc 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 spadgal /w24: mejceship at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c eja/g2ml: w4d 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. w5z+s c/ghkodk v)0z (The occupants would like to travel to a star that z0dzk)+hgc k/v 5osw( is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this 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. What is theb2r4g33z9inh9 jop3qj fb6c(/rl27nfniq ap spaceship'n7 n62gicporfq 4f/b(39jjl3z hri bp 3a92nqs kinetic energy? Compare with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship itdm7 s:bo zcu6p (ef3o7gu0e0s to travel 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 w0 c0pue7dsfotb7u6ze(o g:m 3ork 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 wxv yiv3c ,i,x0hose spring stiffness constant is3iy 0x,vxc,v i $k=48.7 \, \text{N/m}$. 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 marcr v/xyih pix roh48/l4xg31:lo1 q0ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.