You are in a windowless car hbj6b3f q;3t u0wzy r4in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are movingq hjz6f3uwbry 40 t;3b? Explain. ----待选择----yesno 

You might have had the experience of being at a red ligpsxg 5k3,)eozi4 4psex( *9kl c:ebokht when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this s4,pe)kibxl4( eeoz 3kps x: kcg*os59 ay about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy --i(n - c b(bx3hfvgd- km-rziball straight up (from-i3cxvn dkb --( -ig(-fbzr hm his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also vx9d; wov;,:oqg.k de54 mmyb malid to say that the Sun goes around the Earth? Discuss in view of the first q m g9e o,5;v.od:y; wbd4xkmmprinciple of relativity (that there is no best reference frame). Explain.

If you were on a spaceship a rk,oe h6-1eci gbys6/g6iela6 3om+ traveling at 0.5c away from a star, at what speed would t-eicoh3 kg661 i , ol/6+raye6eambgshe starlight pass you?

The time dilation effect is sometimes expressed as “moving clooz6c c6kkn 35ncks run slowly.” Actually, this effect has nothing to do nnokck663 z5 cwith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in movi .stuugr9 mz+hi501zjng reference frames or tu ujr9 mz1g.0iz+5tsh hat it only seems to pass more slowly?

A young-looking woman astronaut has just arrixld z,wjd sjt.(26z1cge 8d ,aved home from a long trip. She rushes up to an old grada xz6sdet 8jgdw1lc ,j.(,z2y-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling auulyx ffy(c6 0 6 g0,j2j6gmxvway from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observ6f 0, f6yj6j2gum xuly0cv xg(ers on Earth using telescopes say about you?

Do time dilation and td4n n: pwr92wlength contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinqlaoc 9q.e(k5ite. What would happen to the relativistic predictions oflc eo9qka .q5( length contraction and time dilation?

Discuss how our everyday lives would be different if the aiq 2(:5 srodl+; zh- jpjxr:ei,fjg6speed of light were onlaldjj eq6j2(5p+hox, - r :g:;i fzirsy $25 \, \text{m/s}$.

Explain how the length contraction and time d om0 n:)/vkrjnilation formulas might be used to indicate that c is the liminonk): 0rm/vj ting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tomp0s5 curv(esdjxqx64vh.b 7 6jkins, for whom the speed 5 uej7qh (sx60bjxvv6 r4.cdsof 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 speo6bj)go.)yh,pr ur 8zbp*s h 9eds less than c. Does this put an upper limit on the moryg) ) 8z.js*phb6po o,b9ruhmentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero );.jh ea r3qrmrest 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 mean that a spn8u:s 1t.skk / k usoxj).2vjvring has more mass when compresn2vk /tujkv u8jkx. so. ):1sssed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." Whav5erzx3ll. . st must we say inst lvers.lx.3z 5ead?

  Is our intuitive notion that velocities simply add, fo4,l rh p/wb*5h8g,62fflmtmrpw.h as we did in Section 3–8, completely wrong?frfpol2/gtmfphlhr ,w*5bm,hw .8 4 6 ----待选择----yesno 

  A spaceship passes you at a speed of 0.750cgcq-snohqi2g ;q. c, q8h+9oceq)/ lc. You measure its length to be 28.2 m. How long would it be when at;.s nc),oclch qqg2ci9 qohe-q8+ /qg rest? $L_0$ =    m

  A certain type of elementary particle travels a x0scnxs)g07idve /-bt 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 fd 51flsc:hlzqp) 52e xkr) t;depend 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 (9quk)bjw 7r.s7 nc oaa star 125 light-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 zaq3)k 17 qtgw+s30svgn an,k 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-yeai ocot3r6 2mdh6r12bsz) :cc rrs away. How fast would you have to travel so that to you the distance woul62od o r t) bc6rsrzhc23:c1mid be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-lykb; ++dwo *ayears away at a speed that tells you the distance is only 25 libad+ow+ly;k * ght-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 Earth3 1zqb0pflsg d0 bmh(* 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 state/e-w+7x f91vv jiw,g iyrk8ju d that starship Enterprise had just returned from a 5-year/e,vxv-wf9uy jg+ri j71k wi8 voyage while traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-ylw qi8 +a )(u;koljb;sears away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as aj8su i +lbwq)o; l(k;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 hehjh;4q+v5s3j* q pbg4 pgok-hr "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m longhpjj4;vp3q* s oh -qbh54kgg+ 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 ia)0mb)aslag,ch-*lyr9 g ;y gt decays? The average lif s ) ),0hry;*gglbalgc9ay m-aetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a prlzu, (ybl0j7 ,5snbrdoton traveling 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 ma m3/rs,kfkt,v( xywq(ss? v =    c

  A particle of rest mazbpf px)4;u7 uss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels atk 1pir+th 826v muyyp/ $v =0.10c$. 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 proton that accelerates* un 1u6j 5tjfup39s-)v eju*apmqqu;
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction r0d2 db;8eqbfvequires $4.82 \times 10^4 \, \text{J}$ 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 in t6m 6.nxuc/vnq 8/q jmeuv5az *he process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 206x.m mavce/u5jvz8n*qn q/ u 60 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of qhrc4x z-m7l: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 a prd u j hqxczk/7rj:3x1y+2 rau3oton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumpt 2 6udqu*tina+ uy3gw2ion 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 cn0xs0xt425 dsa4a l sdonversion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic energy equals its rest ei b4xxdj qe k:wq2/s58nergy? wks:8jxd 4qxq 2eb5i/v =    c

  At what speed will an object's kinetic energy be 25%u; yi-7r s*czc z/-kwpy37qye of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to aq:luj;tly9px,91 f 9wvez ) ba speed of 0.997c9 xetf q pvb9wl9)ya;l,uz:1j? 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 pro nbmoc *sf8;r z/g),lvton 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 energy isjz/xbrk 7p -bpvq:c 0: 750 MeV)?x r vb0k-j:p:/bp czq7    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton acceler.(y*hzlik ;o( d ceb5uated by a potential difference of 105 MV? v iy(e lcu5h.z(*;odk b=    c

  What is the speed of an electron whose kinet 7ad86 n*b7gmzpl:ylk ic energy is 1.00 MeV? v =    c

  What is the speed of an ;1jt5fj jqvx0 electron just before it hits a television screen after being accelerated from rest by the j1 ;f tqjj0xv525,000 V of the picture tube? v =    c

Two identical particles of rest fw-2st63 ccdi3sy( im 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 p d.eht6d dvl(: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 elq*0 moxvu5+i pf0: u9 qp+iltiectron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,08(.c suzpuuk2 00 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 kineti6ifiv: f xr1v.c energy 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 nucleu 1; -fdapf-dmpf2nm8bi s4 ay0s, $^{241}\text{Am}$, 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 no2tf,i*k c: 2 bystxw8l e zkiq0yn0,c1nzero rest mass, and (b) a particle with zero et0is 28*,ln izt1q0 ,kcc 2xb ykf:ywrest mass.

  What magnetic field intensity is needed tysp3mzsk4t th6f0 v;4o keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. T0hz fvmt6;344kpsstyhe 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 t( lusml /golj0u:(yr3o the Earth) observes a meteor come from behind and pass her at a spee msl:uu l(gr0o( y3/jld she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50c wi*cbqr*gwyz6 1 r*yzgb6*1wcqth respect to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A sez d--dk(fhfadp7sn4r:vw9i0 cond spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respdwzna ki9d0-p- :rfdfs(hv7 4 ect 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 atp xkzmqf/ a///9 9btgel9mg q+c ,ks*z a speed of 0.60c. The Enterprisf e/a s9m9z+9 bt clqkqkpg/* ,mzgx//e 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 vessel as seen by the other? u =    c

  A spaceship in distress sends out gkuk9 e/a+7lmn,avp. two escape pods in opposite directions. One travels at a sv7 k/k mle. ,u+pgnaa9peed $v_1 =-0.60c$ 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 sayjo7 ec:)l332wrwpmoj3 blv) me 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 pass)eboyvj3rwj3pol 2ml :7 )cw3es A? u' =    c

  The nearest star to Earth is Proxmal;, ;7tebj6s t pii,ima 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 ujd;y,d()c1y iu *ypgtraveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity ic *pg 1)yy u(d,jyd;uis 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 *4eh ixmi(rd2jytb -/txav+-$v$ 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: kb/r5ldamh 8 have to be totally destroyed to run a 100-W lightbulb for 1 year? :mbrh5ldk8/ a$m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce ane ojj6ay7me51cta vgp5 r 8.o) electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this procerjmtc. p 85ayooj6)a51vg7e ess.) 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 w )c lgpz o2;v5wupkln/t,d, f;ith a positive muon traveling at 50% the speed of light. The two muons ( kp,g lznd ltfv/u52c;,)owp;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 e) *kz-eornx-dtm mh,7lectron, and a neutrino. Assume the neutrino'*r)hx mnt -dke ,7zmo-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 decays at rest. KE =    MeV

  The Sun radiates energy at a rate ofjzs- )ptjb9: c 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 me vb ;xg-n(rsg,w6 zsc*k;2 aieasured 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 nucl6wjf)w h i 3248anckau. lsz 0jjd/:gleus into its constituents, two protons and two neutrons? The rest masses oflwl aj/)034n.8h ij acuwfz 6gsk2:jd 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 the (relativistic) mass of a car tra/f,o-re d45plp mga)j st:4 reveling 110 km/h as compared-rfrdp 54/)see oat4,glp: mj to 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 laboramfeb 0xyw)c0 7eabv5 /tory, are moving toward each other. Determine e0 y0e5 w7v)mcax b/bf
(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 mome n5u s5)naoaa)ntum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power byt. +-zals ahn2g- 5)c1bdza,geb7wz s combining matter and antimatter, achieving complete conversion og a. -glcz-zea7a5s,sw d1bn h+ztb2 )f mass into 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 its rerp/-ooc(0wau w7l6 enst maop0own ar /-(l7w6ecu ss $m_0c^2$ 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+tn vgm0-q/af+jf;fexgqh98 xw+b+ w 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+w+/+ fqnf0 hf mtgjbva+; g9 xxqe8w- barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two moles ,gh96xf+juq m u xs 0pd784jzom)t3t+wfl (juof water, the energy released is 484 kJ. How much does the mass of the elementlf,+ufmjd0(o68 )+qgxhump szt7jutx w 49 3js 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 v4xbxazt03g y*;m-amue py,* two identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the l- t*a xv ,04;xuey3m*azbgp ymaboratory 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 relx -emymcsh:;dchy *w 2e8 c;z6ative to Earth measures his ship tom-s* ye mhcwy6c :ed8hz;x;2c be 25 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 0.85c away from Eart-49l(4qaj gmgw jf1txfa2. fs h. You send a laser beam toward the Earth traveling at velocity c relative to you. What g4jwgfaf91-at l2f qsm4 .jx(do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its o-5k0gpkb03u wl0h4 ti zaw jf3ccupants 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 spb- jl hit0fw3zgk3 400 akp5wuaceship 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. c6t9m+.gccznrp,w k06ln5 l jWhat is the spaceship's kinetic energy? Compare with the total U.S. annual ener5,gjrcwm 9pl.n z +6knt6l c0cgy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 6.0 lieg/l k); v0fvhght-years from Earth. Passengers /)k h;0vev glfon the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on lay2h*- gig kc+zh+o: the end of a spring whose spring stiffness constant z2yc kig-:*lhg+ ao+his $k=48.7 \, \text{N/m}$. 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 +,v2 uotcuimel(: 8qwuj1if/$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.