You are in a windowless car in an e+il2hmf 38ss .wne vrd/ :fe)nxceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to de3n 8l)fs 2/.:ws+fm hidevn retermine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light whend o( o;2pmrc;0/)tp- o ih;1iqvabwkn, out of the corner of your eye, you see the car besidd pinv;)a-kp/o w2( o q;1mh0brti;oce 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 movin8ub u,ae2 fpb5d7 agd6g railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air aadug6p8bd b5f e u,27resistance, will the ball land on the car or behind it?

Does the Earth really go around the y*s72hkdbu59:8 w mb men8ecu Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that therne dewbh2:umy*s7k u5b89c 8me is no best reference frame). Explain.

If you were on a spaceship travelinv.(eix;f b8 w,zy0h10 hgvbo bg at 0.5c away from a star, at what speed would the starlight pasfy1 b;0x0,w8 gz v.ob(ibhv hes you?

The time dilation effect is sometimes expressed as “moving clocks run s3rg3yjk- d 2 4fagih/fhiilry:/-d7( rqhjd/ lowly.” Actually,dgdhy-ik(l h4d jrghr3237/q/ fiyrif j-:a/ this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually pace9a .u7rif : h0p7rj/cd.bei sses more slowly in moving reference frames or that it only seems to pass more d 79fe: a hij7r0u.cbr/ cei.pslowly?

A young-looking woman astronaut has just arrived home from a long trigitg0ez 0/9 yyp. She rushes up to an old gray-haired man and in the ensuing conversation refers t9e0zti ggy0/ yo him as her son. How might this be possible?

If you were traveling away from Earth at sp,p f/ceh (b d- j/yyv q.t1xunk-yj3:deed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would obse d,yce nq-3yf h-v(/jx k:py/ 1jtbud.rvers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speesy-nco y7a ;a4ds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. Whail5 w4dmj17 rvt would happen to the relativistic predictions of lj7mw5d1riv4 length contraction and time dilation?

Discuss how our everyday lives would be different if the speed h4n bd ov,v -1ju:vxw.of light were only 4xwv1u o:h.j-bvdnv,$25 \, \text{m/s}$.

Explain how the length contraction and time dilation3 o ;(8hqstm 7b9dgkjx formulas might be used to indicate that c is the limiting speed in tth7q9gb3kj;d m8o (s xhe universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tompkinu 6jb,01hgmky +aydnsjmt.;+s, for whom the speed of jgyta mysj+m,6;+bd u. 0n1khlight is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limita5huhirwy 7gj 75gg;;ed to travel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not, explain;wgih57y ra7u j;g gh5. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of light?0bb)al*n xky z02ci.5yln:y0dj. t7d5r ou iy ----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, do7fq 7 kktst -rsp3:y.res this mean that a spring has more mass when compressk-y7:kqtr. tp 7f3s rsed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destr)ihbm(kr sniwto/ 2,/oyed." What must we sa2mk,r si/iow(hn /bt) y instead?

  Is our intuitive notion that velocitiem0xhs(2- v /yvwbzsoa9q 4 8mfs simply add, as we did in Section 3–8, complem/fqvox2 0 ab4w- 8h 9szyvsm(tely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure it))hqct t5pnkh3h*0l(uqo ) y fs length to be 28.2 m. How long woq3ho5)qp)thn 0k ucy)hf l(*tuld it be when at rest? $L_0$ =    m

  A certain type of elementar86w;uomg3gh k :it an3,qib7 zy particle 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 depe*a :44l5 ard**nr blvtj.mxww nd on the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 ligh z)erhoi-n.z; unx e. z0f9p0uz1) ditt-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 pion if its average lifetime is measured )o,e t6yv4en pn4(cdpto 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,w:huw ow bab/a*1 -4kt a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years? abb w: /4 wuot1*w-ahkv =    c

  Suppose you decide to travel to a star 85 li n *xt5cu9;f q(yz;q8 kjqn2laght-years away at a speed that tells you the dinky5lt8;j9qqzan ; c(qx* u2fstance 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 is /p4r;gjzfa9p $11.2 \times 10^3 \, \text{m/s}$. 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 Enterly p0f orm yx.qj(:m(+prise had just returned from a 5-year voyage whilm( qmpr.y:0lx yjf+(oe traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a spacecrafk 2d3h voq5ar.t traveling 0.960c okhva2.r5 d3qto reach that star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecraft at a speed of 0.663cyt6 0iv i7eusw:jb3 0c. It is measured in your frame to be 4.80 m long and 1.25j vit:ius76w30ebcy3 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 6cpx3q: ( kx*hyl :mlw37dh lhmoving to travel 15 m before it decays? The average lifetime, at rehqcl3p:h 3m7k6w:yxd( xhll*st, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of pdy(.r 9-m5 rulvtq/q a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativisti i:(ti.nce +5c v7ivqqc mass be twice its rest mass? v =    c

  A particle of rest mn*dvwunj145 o ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels asy tx+4b xcsl9tc/15st $v =0.10c$. 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 protohpo qi5 apr,282aag7 mn that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical r4ahr hlg w6* imly uj9+.39fzceaction 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 restmdter-j i5l lm1- 9mw0 breaks apart in the process known as fission in a nuclear reactor, the resultii9 jwe-5m drm lm-l10tng fragments have 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 ffvi07ev rl..iz/q ce3sl/(q 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 a p4gpi 9chppv7. mv bx2;roton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consid8f1714 k gqg ah,wdsumption 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 be obtained from con a+bred. s) 1mok(ke:gversion 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 parcwkdk2(zwmw1 (xjc; .ticle when its kinetic energy equals its rest energy? v jdw.c w2m1;wk( c (zxk=    c

  At what speed will an object's kinetic energy be 2/2vbffb4 i+co5% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up tomcbb*z,wx*wb a u*5: x a speed of 0.w* *bxuw5mcb :baxz,*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 momentum of a proton trav4wu8 1 oq9gzzdeling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV protoqr 5x5pvuk3 1xn (that is, its kinetic energy is 750 MeV)?5x r5u3q1xpvk    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerjew *j- q52emr8ta(w v:ct e;wated by a potential difference of 105 MV? vtw8 v:;weaje(rtwq-*cme 2j 5 =    c

  What is the speed of an electrondxn anv3 6a6gyhf5:g * whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a telekt;ewdrs xqq 92k3 ntw5 j;jtoz, z,8;owo0e0vision screen after being accelerated from rest by the 25,000 V of the picturz t50kq9ortedw o2 8,0xwkw3ejs ;;toq;j z,ne tube? v =    c

Two identical particles of rest u* ,-5qagg-gh // xfguxp (hvhmass $m_0$ 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 v21vixy -/wsnkn7; j za 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 th etfdkdt:7*q:hw( it ;e momentum of an electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft 0pd.:cx9 iusyof 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 enerrpvz2j/:wz zo-ru0- go2oj va)k,op.gy 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 nucleus, 8vh t08rm;7n2e kmaly6(y mjg $^{241}\text{Am}$, 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 nonue,j+txn3h /wqemwlu 94rqk m :*jl5 *zero rest mass, and (b) a particle with ze 4 elrnlueq wtjm,k/hqj w+9m:x3 **u5ro rest mass.

  What magnetic field ikvmlc3 . /e6.0v)itggng+ :r*ahddlbntensity is needed to keep 998-GeV protons revolving in a circle +)e0gdvnmkdt3lg:*rg.v i h 6/a.l bcof radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with respect to the n 4m er+tyj x1vq,-y7kEarth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with resp- m yqj ntev,xy+4k1r7ect to the Earth? u =    c

  Two spaceships leave Earth in oppv911h;zm l,;p,wlvf m g62xtfo lmzw;osite directions, each with a speed of 0.50c with respect to Earth.w2z lmp; vtl6 o gvwhmlfx9;f1,;,1 zm
(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 spa3qaw9xgm w+p0 ceship 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 iawgqw0+xpm93 f 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 an7w;w xa 9hz3mt alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overh73waz;9 m xtwtaking 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 distress sends out two escape pods in opposite directions. One bptd ok:hi8+; travels at a+kb:;8tp iodh 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 p3p+3 uu-p isv 42djz-aymxxkpewoa9qt;+,6 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction.uva6-xe z2tdp a3x+ p3,piwm-s+ 4qu9 oy;k pj How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 nrocb1 9di1jvwul w2ti7typ/57je+)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 0.1rb5eu5ijx/p0 ,w t5tgyn.f1 qc is called relativistic - i.e., for which the correction using special relativity is a significant effect. Deteqnewrf gpx555y0/i,.tb jt u1rmine 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 speex9 4unw6 6iigpmb(s3gii17x pd $v$ 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 cu-gp dt(x/5 znbcbzhs0z:d97, 3qh i to be totally destroyed to run a 100-W lightbulb for z(si/ cg,t qudp5 : 3dbxh0zn-9ch7zb1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an elek6(pq* ihnyc5f9jei73 2qwyj ctron and a positron together? A positronn7f3jw*y5jqik i c he (yq9p62 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:(h(uw bzrf-x at 33% the speed of light collides head on with a positive muon traveling at 50%rwx( : (bzhuf- the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino. Assum+ tfvj wsw/h/.e 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 pa/hv/ f.jt+wswrticles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a ratenxq35en2qcx(cdkr.8h r61e a1 yhk:p zw7sr9 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 wjl8 u.bv63 2tnbf*lq2 rv/d 8-anvmi 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 dc6jkttm-u 7k: (hca9u o*oh8be required to break a helium 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, 1.00867 u, and 4.00260 u. (This energyotck7 9kt huo( 8a6jmu*dc-h: difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increazf em9cia )77jse in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hi 79m zj7ceai)fnt: 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 n fty r08iahz.g,2kz,j0au r.y -sx1kthe laboratory, are moving toward each otheyryr.,g t jkx2hz1na0as .0z 8i,-fu kr. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle witei8m)z/ir y2i,5c+ijl /l xjfh momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power/shv+6 5-y 5s uslzndz by combining matter and antimatter, achieving complete conversion of mass into u5vh6 5dsssz +/zlyn-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 gy( za+6jpr4 iqbx6i-njd ;1qb-ktorm4q x4 *wreater than its rest marajytop qqb1zm *+k (wibqxi;x- 6 4n 644r-djss $m_0c^2$ 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 15.0hze/ k12/ok cjjn0em48 ciae+-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do24eh8c oka/ / zkj0jme1nei c+ 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 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mol-;+ k6th9eistzxe6 rn e of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the nrk -sxe96i;e+htt6z 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 particl:j7 . s9p bgby det43jcm(mi8bes 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' pmic9btb d( : 7g3b8j.4jesyms speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c rela;ar3t d8s:,aaauxw j my,t1,ltive to Earth measures his ship to be 25 m long.ta;t jr,asd3waym :a l8,,1u x 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 pf;uy h/y2 u5j bbcz7)0.85c away from Earth. You send a laser beam toward the Earth travelf ;5)ypz7juuc/b hy2 bing at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupa)ge uer:).wmztxla q k- 9j;l+nts have a total mass of 150,000 kg. The occupants would like to.r)-t+lux:k 9ga el ;)jq zemw 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 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 h9g-2 5c+o0mz f080 jk qrkia8pviuaoEarth at a speed of 0.99c. What is the spaceship's kinetic energy? 0f2j8-ik kpq0m ho9iz08v5u agco+arCompare with the total U.S. annual 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 sta s2b4lo e1o u;m5l.fsy -jm j*bcwb.j/r 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 spacess;wbbo l.ycusj *m lboj21- jm/ e.f45hip to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on ql)jsg :du1qcv1 mf:/f he)g8 the end of a spring whose spring stiffness constant ic8f m1fevudjg /lqsh)1:q:)gs $k=48.7 \, \text{N/m}$. 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 mac69 cvb ,3uq2 )xyrfnass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.