You are in a windowless car in an exceptionally smooth train moving ab ,/ vp2t(cz5 .skljljt constant velocity. Is there any physical experiment you can do in the trainlvj cb/ kp.2t5(lz, sj car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being onu. e+5nehayfjvp/7gu.hc h) :v .-y 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 pedal, thinkinh.j y.)5uv h avo-:+./nhyc u7pfeegng 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 th ( phm-zwvd(i7 h60hprrows a heavy ball straight up (from6pp-h hm7(wr h v0idz( his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go7-s,fi 2nky9 fb7vlgn around the Sun? Or is it also valid to say that the Sun goes aroy-79f7nk fn,s2l vibg und 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 traveling at 0.5c away from a star, at what sq kfm z-t)3+w0fvrq5)dyi1xupeed would tvk3+-iz 0x) mfqwy5)fr1udqthe starlight pass you?

The time dilation effect is sometimes expressedn:a u;+gb)8gfcvtg3f as “moving clocks run slowly.” Actuallyb g:8c;agfv+)u f tng3, 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 mg:f gr 8nb+o5actually passes more slowly in moving reference frames or that it only seems to pass more slowly+8g n5 mbogf:r?

A young-looking woman astronaut has just arrived home wzw g(m+ .dfc+from a long trip. She rushes up to an old gray-haired man andmc+wwzg(. df+ in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away 0/(mv5q w1huk jb+vlr from Earth at speed 0.5c, would you notice a change in your heartbeat? Wojvrm(w+ql5h0bv u k 1/uld your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length;7iz5 d +qpd o-a lxhnen gv2qy3h1e6; contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen mf( vo h*lfx4q3iyk)2to the relativistic predictions of length contraction and timeq3v (24xmf*y hli ko)f dilation?

Discuss how our everyday lives would be different if the speed o5xsid 7es9 (.kasa5ua f light were only ssa (95.ea7adsik u 5x$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formpuny rqqyb.k1g m(z :3 p2st:;ulas might be used to in;qbrtyu23g :q p(ym.k snz :1pdicate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the streqh /.m2, jbjgzet as seen by Mr Tompkins, fogb2q . mj,jzh/r whom the 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 tottqpc 1v 1qa08q8becub)(ls 7srr59o 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, expl( bosrtec8pvl) 19587qab1s q0tqr ucain. ----待选择----yesno 

  Can a particle of nonzero rest ma7lzn3m ebd u-*4o0 fkcss 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 enerrk4y*jl( 7pvos- p) yegy, does this mean that a spring has more mass when compressed than ( lojrp)sy - 4evyp*k7when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be qkg* f1el6 wjnmc,(/ajx:l5 p created nor destroyed." What must fgmq6/l x *5n1c, j e(lawk:jpwe say instead?

  Is our intuitive notion that velocities simply add, as we did in Sectionse7 -2bx5:wrr ae5xyc/0 zu vm 3–8, completely y2zx0mr5a5 we/7bcr:sxv-ue wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. Yonivv6pa+ sx(04g: to tu measure its length to be 28.2 m. How long would it be when at rest?(sp v6+ n4tax v0ogti: $L_0$ =    m

  A certain type of elementary particle travel3j*okd ; vwb8sskevenj ,a*36 h)gxz7s 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 the fa/lpb6mt 6k*dictor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 ,mso6np0d 9hn 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 ,+j8yk:.0wob nzvbio 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 fraad a8vy dndx3x:b qoj)2,y+8pme, a star is 82 light-years away. How fast would you have to travel so that to you the distance would3x,dxn 2qd) j8 oydy :a+ba8pv be only 35 light-years? v =    c

  Suppose you decide to travel6k dw*;q9jwok)i/d oj to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many ye)k*o ;9di6/qw jwdkjoars 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 theex 0xr16 3h;r+h nbrfv Earth is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

  At what speed $v$ do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.) v =    c

  Suppose a news report stated that starship Enterprise had just returneo3khr;i 1gf q,d from a 5-year voyage while traveling at 0.84c. q;k 3hg,rof i1
(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. d7t-m r i3owvytpe9;,How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured wm;epy rtditov 9-3, 7by 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 0.66c79d irsa1rhs 6ma(f+0c. It is measured in your frame to be 4.80 m long and 1.+di 7m961 rshc(afsa r25 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 pioj3un z3 uzw kb. 3o(fs:zru /g1rv(d,fn be moving to travel 15 m before it decays? The average lifetime, at rest,orvu g u,dk:33 zbf. zsunz1r/j3fw(( is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a eephq 2.l8 uyo) kvw)m 3a4t2gproton 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 mass? va-dd*qb;rsp fil a)l8i lozw0l sp- t56 ;1j1i =    c

  A particle of rest ma*d2 5kqot:r+9( aun.r j njzdsss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelszm)zj 0-du w9w +uk)6xgm dmk7 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 vhp f1-usm1 u3ze3e3qmomentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical rbt92;elb s ,q9 yps3yoeaction requires $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest bt;w br gv3)wm0reaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetivbw) rmw3g;t0 c 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 elf66mzou g7 25y+utusuko+(ilectron 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 mh5p+ k/nwu)48j l xtmkass of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States ;ty:g28tso9qbp7 (wt:mfk dd20htgu 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 obn:- 7vbws ps4ytained from conversion 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 equaln5; x/uzd:bru s its rest energy? vbuznx r/; d5u: =    c

  At what speed will an object's kinetic energy be 25%1x:a04i ern )du 9xkbl of its rest energy? v =    c

  (a) How much work is required to accelerate a proton frvs 6dbf.1 wat6om rest up to a speed of 0.997c? W =1s6 afvw6tdb .    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum o h,n; /s6avuhz g.g0vkf 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 enerde7-gpdh31)x7 ch l irn(tma2gy is 750 MeV)il2gr-adhp7 3t hdn )e1m(cx7 ?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton a8jhiza/ , a+co)gm( vhccelerated by a potential difference of 105 MV? v =,/ha 8aogij+vh(mz )c    c

  What is the speed of an electron whose kinetic en/er -wq-q6 lowergy is 1.00 MeV? v =    c

  What is the speed of an elecoo7qeo 0pyb)t a,lahou 78t9;tron just before it hits a television screen after being accelerateq apht70t,bl)o oae;o87uyo9 d from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mass yoi62* c/ r03 ym-y,eyf /cm2k- pfipf wo8uwr$m_0$ 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 a74qzg+6d i qyf)0 y2bj p5esai proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum of an eledcr9 )ztd h,v2ctron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 ach +em ;cvkjy: pp:f-8dcz) ut2celerated 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 momm5)+.ghz 0os3d6kqvky4z i ngentum 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, +:0bzx e 2npvbw2z :tx$^{241}\text{Am}$, 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 zh 9twj7r;+um nonzero rest mass, and (b)9umhjrw;7 t+z a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons rcq;4 i-hp d87,h tn jmongn3(eevolving in a circle-mdpe qntoj (gcnn h;,74ih38 of 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 rj6 1(izsprl t+espect 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 respect to the Earth? z1+lt ir6j s(pu =    c

  Two spaceships leave Ea yvy*9b :/e9qwo 3fhxnrth in opposite directions, each with a speed of 0.50c with respect to Ear*yqfw39:x9byo v / henth.
(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 ar7rsedo hx1;hh 3v3u4id79sqih (/pf t 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respec;fo/xisih73 vdhu7s 1(q43 h ehr9pdrt 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 at a speed of 0.60c. The Enteuy9fh2 (obcq *kz 6(myrprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What isu( hoy2b(qcz my *6f9k 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 c;1gf;:a;(jvbfukhu t q: o3htravels at a spehf:3ugt(c ovu h;q;a:jk;b 1fed $v_1 =-0.60c$ 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 xw )s:60x;b*qd yckq ya speed of 0.75c. At the same 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? ubx)y06kd *wc ysq;:qx' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years awa:v6edesx 5k6/ m8nt;y jxfa :hy.
(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, m b-l (fiuk,61o *zmsuanything traveling faster than about 0.1c is called relativistic - i.e., for whic*zb fu(o,s ul-1mim6 kh 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 5 o002njny.rs1pu ybh$v$ 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 9 -3cni1 -kkhdz0gblc be totally destroyed to run a 100-W lightbulb folg0in-kc d b9-zhk3c 1r 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic ener+jutmv39w a2z bq4gq9gy is needed to produce an electron and a positron together? A positron is a particle w43a9qbj2u q+ zgm v9twith 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 at 33% the speed of lig3975 i yzxrh, kt4hja tgjr*i0ht collides head on with a positive muon tt 9 * 54zgj0ajxrkyti,rhhi 73raveling at 50% 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 pdffcti kdj;7 2+wfe/ 3q se*-sroton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in *2c;i-te/ jsef7kwd 3+ fqdfsthe 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 energygtefu8ts9q 9; at 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 measured to have a negative mfp v7-hbho6p20ha v:( ykvu)jr*gp7 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 constit1 tk qa-yi.mn (b0,6te .vflrtuents, two protons and two neutrons? The rest masses of a proton (including aniq,.m a6kf yt t-rb1tl0ven (. 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 (relativistilc4p*q9vav)i x l8o: 4l2ti hlc) mass of a car traveling 110 km/h as compa:q*v 4h2 l l4l8ic)itaolp 9xvred 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 l33z+xg 4h,mjuc,wsw caboratory, are moving toward each other. Determisxjw4mcc,33 wzu h,g +ne
(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 mowt6q8 w2as ih.mentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by comc/w/5 (fqq-8jnef*nijswe ,p bining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise iw(qw* eq iensnf8 p5j/ ,jfc/-s 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 thatpvlf 9h x2a6rl6 ;axm; its kinetic energy is greater than its rest massmxlarvl; apf96;x 2 h6 $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-long pole innxf4 z( / wl0g:80txrnr au.fyto a 12.0-m-long bar0w:tln4r( rxn/xfy zgu8.0 fan 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 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form3,i wh1w)9hkw: qfd gr two moles of water, the energy released is 484,g f: qiw1 d9h3)wkhwr kJ. How much does the 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 creatl1+v )w70od rfcwubc4 ed, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame o4fvwc1wuo)0 c7d lbr+ f reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relatiet:br,7f q)wv/uu*ws ve to Earth measures his ship to be 25 m long. On the ship, he t qwrw:seu )u *v7,/bfeats 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 awaq6y w( g;c0x3u; e9ejpb4oxmg mh:mb5y from Earth. You send a laser beam toward the Earth traveling a4myc6obm egmw0 :;bug(3 5j;xq xhpe9t velocity c 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. The ocly)59e ,uj n +dk f:r/;:tfqx0gofslpcupants would like to travel to a star that is 25 light-years away at a speed ody/ullp, f+)kq:0 ;rn9ejf o x:g5sf tf 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 t k-k3ip4w;,ew d eu9rat a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consu r e3pk4kt w;,eudw9-imption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to th7:usmd*,c5n;jx cy ske vicinity of a star 6.0 light-years from Earth. Passengers ju: , 57*dk;cmysncxs on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the endc0f/ r5w:6g 1xcom* f2c8kvach5e mzz of a spring whose spring stiffness constant isfcc*5r e8v2z/m:xgw15 0fzc oacmh 6k $k=48.7 \, \text{N/m}$. 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 i 7k1n.ee8 fdav0epw3s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.