You are in a windowless car in an excezzog -qxo6f5+ ptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train zqo+o6- zxg f5car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the 2to4.1. wto 6uchedrid m v4*zexperience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pt12u*o cw 6. mio .dzv4dht4eredal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a q k+-ts aj(rnub9jx(qbrg-); moving railroad car, and throws a heavy ball straight up (from his point of viewbn+ qgb(9a)sxu k--qt(;jjrr ). 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 vn3 nx i:cl/,tcalid to say that the Sun gcc t,/i: 3xnlnoes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship travna-1i v 7kc.gyhpf9*celing at 0.5c away from a star, at what speed would the starlighkpc* fcg7n-1ya 9.i vht pass you?

The time dilation effect is sometimes expressed as “moving w 89(:bv ykx2+geyaz;/:l oheru,wvpclocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does i /vyx2o zk+ ry(eb9p:wugl :hva;ew,8t deal with?

Does time dilation mean that zr fuh.r2,9t (dng kg-time actually passes more slowly in moving reference (uzgk9rrghfd .2tn,- frames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived ho * x/bgnu:w; ;l2mlbadme from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be poswld; mb:a;/*bx ngl2usible?

If you were traveling away from Earth at speed 0.5c, gqme6 -z2qk9 dwould you notice a change in egqd 92-qz mk6your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and lp 6q +yftjl ,mk1*qnx/ength contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happeb pe y5tnibih 2q/h56r*w2nc*n to the relativistic predictions o tic5rq2h5nn /62 hb b*ip*ywef length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of ligh )2oh9ua9 xgewt were onlyu 2x9h9agew )o $25 \, \text{m/s}$.

Explain how the length contraction and time4 o(gunpx1( a0a g(gfnv65ldq dilation formulas might be used to indicate that c is the limiting speed in the universe(5g xo10(d(avglqn64agfpnu .

The drawing at the start of this Chapter shows the street as seen by Mri8n4,dmtxd p 3c;*co g Tompkins, for whom the speed of *m ctn,igpodx c;d 483light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limite.9 pmc/ou1p)ffi t 6c v)vjib2d to travel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so,mp pi6vj boi/v) cf921f c.)ut what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the spee4 -;jbp vktbt5d 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 mdfbial/s0 z9-ean that a spring has more mass when compressed than whz- di0b fsa9/len relaxed? ----待选择----yesno 

It is not correct to say that "matte8. me.vnn-i6j 7 *roedm2 pacume (f9ir can neither be created nor destroyed." What must we-2aj m i.m8fdv uen9*no.ee7 p6 i(mcr say instead?

  Is our intuitive noti xl(bq,7dzr-o6 u/lhl 7) exawon that velocities simply add, as we did in Section 3–8, compl()e7x,/ho q ll xd 6brzuwal7-etely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. :wl sko/;6vn hYou measure its length to be 28.2 m. How loovshl :/n ;k6wng would it be when at rest? $L_0$ =    m

  A certain type of elementary parti.5uge/xbir gg(6n .mtcle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals depend on t0u0k7x(2. bpfit y nhvhe 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 light-years from Earth at a 6x u kf* kwvakmbi-:kyj*h:+* 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 4iufv0a98hgg wz6lc 3w : qpz*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 is 82 g6f*pjbjonp p92h 7,d light-years away. How fast would you have to travel so that to you thn of7 2bd g*h6jp,p9jpe distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a spee9 pli-m-c 80atm4b.omfv q8ted that tells youo-m9ma tciv88em4-qlp 0.t fb 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 Eartcm8x s- igi5 wkry-1e4lh+zu-ott:n3 h 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 that starship Enterprise t5l1e6ctph-z8 n *fyz ;sdzh.had just returned from a 5-year voyage while traveling at81hz yd ch ze-n6lt*.5t;szf p 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 spacecrafb*4; zozcpvt2*9 qabkt traveling 0.960c to reach thb2t oak94*z ;b *zvqpcat 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 azn 6 +tugmii:0zx4q o hav98(mt a speed of 0.660c. It is measured in your frame to be 4.80 m longx:aq 8h(0z 9 4o+inimtu6 gmzv 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)sqpy39 c t/8tp9x eu8vww;hs travel 15 m before it decays? The average lifetime, at rest,vcsut;sy98 x )tp9h8qp3/ wwe is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton lp6my4+ /yaemtraveling 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 masue4cx pc-dyk3 v dvq,/di4bons0;(6 w s? v =    c

  A particle of rest masg3xvcgbnzt.d. +s6x 9s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelsdq37d+cm9;shuf e 3eb 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 momentum of 0mq8, 0l pjtpwa proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requkfnem8 l3 y ;a5mbz56sqr6i8bires $4.82 \times 10^4 \, \text{J}$ 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 the process known as fissik1x,-ffc vdq(on in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process-k d cv1xfqf,(? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of q/ l8ostt cw2ju++v2fan 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 pr-dw oif4 63lbldoqlu) nr,x-3oton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is ab cr/a;21qeqzmh.7nfpout $10^{19} \, \text{J}$. 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 mal20kldnj)c* y ss?    $ \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 energy? p/jbpm1 a f1:svj-l9wv -fslj 1wbp/j:m1v9 p a=    c

  At what speed will an object's kinetic energy be 2*b8-y :v. yvkl)dyq mb5% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a (lhf7k- 516zy.a5wlnjor z zispeed of 0.997c? W z 5kz 61-7z(n lriy.l5faojh w=    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy ann8x,0 iwskre7 d 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 isk/6y)ao w n.u :krpp qomt(,o0, its kinetic energy is 750 MeV)?0tkor w.ypp,6 /o mko:an)uq(    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of f5; nzdf-kjg: 105 MV? v =-5fk d;njfgz :    c

  What is the speed of an elecz hya1n fra1vkw9aij( 0 s+q6(tron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen r/+lnee v2jorbt6i; 7after being accelerated from rest by the 25,000 V of the picture tubo ev2nl6ie/7;r rt+j be? v =    c

Two identical particles of rest mass mrc*:14 (briyhscq .a $m_0$ 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 protonj 2 5p26 norkj11plgj vwg4-6h3ylg(h p 9obnm ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentuzka0 o3xeuqpf45 x ,jp:vqu ,owq ,.v6m 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 of/d+x7*lo kjpv 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 of a proton y79bjd z1gk6)zyc):e/r put t($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 8c30+ kqh5zonj 7bexba,sp,ls, $^{241}\text{Am}$, 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 pxp 0 ej-lgyl+e5fd2:particle of nonzero rest mass, and (b) a particle with zero respg0f5lj:d p- 2ey+exlt mass.

  What magnetic field intensity z /f+5slzxzez7kb ;o58. kjbx is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab sy .f5xjk szl/+5bzboxke 8; 7zznchrotron)? 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 : gpral.a1rr4respect 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 resl14par . ag:rrpect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, ee 1sqayp.ryz 6.l2 hy*(e +zozach with a speed of 0.50c with rey+zl(q6za .zy.s 1erep* y2hospect 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 tvpny)b*wd u) -k :x obzm46)bce5s*giraveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to th )y:vdpmu)ekb n5iz 6bw)o*bg * 4s-cxe 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 seg)zjl k 2c;w1 hl:xj.0s xnu/v2)vtf luzh/ .jes an alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Etl.0hxv2vzx.s n2) k)/ fzj;jh1uglju l/w: carth 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 distrnm,wxp4okz7e6 vs *r5ess sends out two escape pods in opposite directions. One travels at p4*, 7xvnwmko5 sz e6ra 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 same time,wgr1f3a9q2ilz u u r;/i8zwz9 rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to zi r9zua9ugw3rfql 1i 82z/ ;wA when it passes A? u' =    c

  The nearest star to Earth i1ijp smrwa:floj90 x4z( f w5)s 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 t 2ewy tc;bis/g,8u6vmraveling faster than about 0.1c is called relativistic - i.e., for why v 6ubem8i/sgw2,; ctich the correction using 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 a +m ).o:u cctw z)yqjsu1..mj$v$ 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 1 fcg8x3b 0 gf4qrhx)ea 100-W lightbulb forxe 0)3rfhgxg b48qc f1 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electrzim4i*y*iv1*ku9 jaod(uoo 0 38iud domagnetic 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 opp * v (ou9z1ami4ij3kydid8*oi*d uo0u osite charge. (Note that electric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collides head o:awk*)7 usgp an with a positive muon traveling at 50% the k: apawg*u7 )sspeed 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. Asjnc1bmf9+g. :xsjaa 1sume the ne+.:cb1ja1 af9nm gx jsutrino'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 ratr,h9w.m blz:r 3ti hwqt.rf46e 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 negati ar(7r ej(ts9iz 6yxcw ec*ta:.wf(2eve charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to break a helium nucleus into its constituentz/ao- ;qr yz;os, 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 eny ;; razo/ozq-ergy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass mf hk1:da j-vjh49v9l of a car traveling 110 km/h as compared to at rest? [H:4 f9jlkav-9dv h1 hjmint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.2o;t)r(d tqc i5ls/ kne2( wye935c in the laboratory, are moving toward each other. Determ) es(/ n;eityd2o2q5wrlct (kine
(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 v.-lrd(z uxq8xo :z *rhrxv.6with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter anq+ jzovs-pn 15d antimatterjz-q1 5onp+ vs, achieving complete conversion of 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 bdjs3 v,ka:2s.v2bmqc 3fjc3greater than its rest mass ,cafbs3 2 bjc .dvsk323:qvjm $m_0c^2$ 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.+ i6o nwao-f9n0-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 ev96o-fi n wo+naen shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxytt 5v1t: /bxshgen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decreaxs t51htb t:/vse 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 ideyn dpd;38re1 l8hvip2 ntical particles are created, traveling in opposite directions. If the speed of each particlp;nepd rv iyh d2813l8e 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 tnn c0cj)d)icb* xj7gj1 )ruazr/ap3- raveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in 23 mica)bji jcgxapnrn)j)cr-01 */u7z d 3n.
(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 c:bz;(muuc0/gl;i i u.q,/zcm wz uv.h. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for ; z ccl,bi u/gqmv0(wzczum: /iu..u; the speed of the laser beam?

  A spaceship and its occupanm0) k4jg vu9yr zu3dm1ts 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 converu3vk 9 dmg0jm)41urzyted 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 spvh)*u+ct wc1-n s4f ytqyx9 9qeed of 0.99c. What is the spaceship's kinqc4+tf99)hvcs -qyt 1* xuywn etic 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 is to travel to the vicim:/punsf :t b123)kj8cqp mwm nity of a star 6.0 light-years from Earth. Passengers on the sh nbc13tfmw/u2 : q)jmk8p msp:ip 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 on8eak i( w,ebz5- n9 xsoq9m9au the end of a spring whose spring stiffness constant iszo9 ,89eab 5ks(nxw -e9quam 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 mas(tzk d/pg6:z es $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.