You are in a windowless car in an exceptionaj*m2mm yquc-9d r:s*illy smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are mov c9m*is q*jrm2du:-ym ing? Explain. ----待选择----yesno 

You might have had the experience of be , mly,rmjs)0ving at a red light when, out of the corner of your eye, you se)j sr0lvmm y,,e the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws auo hyp1fo b )oa18*cum sj:1i7 heavy ball straight up (from his po1i yjhs7*ma8ufpb1c1o )u: ooint 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 valid to say that uv .t; lvvs(n3the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explai;v (s lnvvt.3un.

If you were on a spaceship traveling at 0.5c away from a starhsl.9n;l s:x)y eokyof/(ao* , at what speed would the leof*y ya;o/)s9lk no :xs.(h starlight pass you?

The time dilation effect is sometimes expressed as “mooec 7z z5apbsf*-d0u 3(q c4hrving clocks run slowly.” Actually, tbp(fo3ecd a7u-z*5c z04qr hshis effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time /wza m ag4ug3uocv14m(/gy2g actually passes more slowly in moving reference frames or that it only ggya u3(1/caz24u /wm4vm ggoseems to pass more slowly?

A young-looking woman asttj6k:xyyg 0:f1v f k-:rzxge1i3o nl)ronaut has just arrived home from a long trip. She rushes up to an old gray-haired m nx: -)11lfzyvi3eo g6x:yj:0 krktgf an and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice sd q-+v3g bs2ra change in your heartbeat? Would your mass, height, or waistline change? What would o- dbs2 +rqsv3gbservers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary spe5jonfa3-c hq-ebe.p0 eds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the rep;0qlyn9r dhia,l:v4 ifr( (mlativistic predictions of length contraction aplr9 i;0ihy( ,nlq r(vf:da4mnd time dilation?

Discuss how our everyday liv. tp.jq(4;7 xkit j/o;isjczces would be different if the speed of light were only ; j4i ojkt;7 q.siz( cctjxp/.$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might bpu o 4x* vt/- w( ,1qzhxmfmac,ked:f7e used to indicate that c izap*fh7qc d ,mxf/ok: 1evt4w ,x(u- ms the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tom6;hbbh2 5p kncpkins, for whom the speebkc6b ;n h2hp5d of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less cqad s)f0i o)tqyy:*,than c. Does this put an upper limit on the momentum of an electron? If so, what is thi0:q)) , s yciotf*aqdys upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attaikd hbbiez 4qz:*/f+n4tl s9:q p .,brun 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 enerku2b e043 o +lnmp:uffgy, does this mean that a spring has more mass when compressed than3mp :ufn 4e+k02 oulbf when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be c;tm.:n m fvxqmkau 8puf* ,9+xreated nor destroyed." What must we say insteadtm8u ; m9m.vx nu,*:+kfxap qf?

  Is our intuitive notion that velo kb/h y3zg1 0u4by(zsocities simply add, as we did in Section 3–8, completes(o4 gb /zby1yukhz03ly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You 4ds1mth;m t3 w sr91zxmeasure its length to be 28.2 m. How s19t ; xrtszd4h1 mw3mlong would it be when at rest? $L_0$ =    m

  A certain type of elementary particle trh4y s5aydk :,g/g .oaw m ,v-o3gzks)favels 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 intervalxhkm3 y.xg/ hq:kr:1 zs 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 a star 125 light-yv9 7vm xftv;z0ears 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 to be; a)5 0n 4u;gqobkuczp $4.10 \times 10^{-8} \, \text{s}$? 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-years awaytqqt;1/gdzv.; .e ddcpzh :h, mj *f2v. How fast would you have to travel so that to you the dist .q:z vtdzjm cd 2;,1v e.*pqdfh/ht;gance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 h6e3 5)r9 la7mb;;tzrozv azilight-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the ti5)a3e;7zb9ozvh zm r;6lr at rip? 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 Ep;1u x l d8g6ldk+1axlarth 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 847ame bqvt9sreturned from a 5-year voyage while traveling at ev8qbatm 7s940.84c.
(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;i+2zcj vvbm5 *ktl)e away. How long would it take a spacecraft traveling 0.960c to reach that stc)b*j+t ;m52kiz vlev ar 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 0.660c.7/nnsvper ar89x+t4lai )8e i It is measured in your frame to be 4.80 m 7 lsin)89+tx4p/are ai8nevrlong 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 pio 0. ;bim*3kffhozvn 0bn be moving to travel 15 m before it decays? The average lifetime, at rest, is fobzn; .iv* b 00mh3kf$2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of adohyx7y 6d+b 1j8 mbg0 proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relat . u3v:pxutm4civistic mass be twice its rest mass? v =    c

  A particle of rest marooz q dy,;.dfsuv)m- z5ajnz 70h+t/ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels /q-o cz9r 1dsbdf h2.iat $v =0.10c$. 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 tsc ogbyn +s(h2.o00.jugjq*
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires mi61 tan l lqz.twc50;$4.82 \times 10^4 \, \text{J}$ 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 fission if+det 8ss **s8r w8(awsq-vfbn a nuclear reactor, the resulting fragments have a total kinetic energy of abotss v r-qb+ *fws8*8(s8w fedaut 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an el 82ro:*u5agpdt 55 dcruh(jr xectron 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 o/2/nqhtwx1 o lf a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Uyd0m*j8 9bm5(1cl m j.ciwzi-/ywlpinited 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 ob5oa -t. fktju.3wp*a4 r p9kiztained 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 ene i-t33u;(. k mix1yh po)psvwnrgy equals its rest energy? v-pn1 (oy)pkmvt 3xi ;3h. iwus =    c

  At what speed will an object's kinetic energy be 25% of itcz2qs mlkdp5 (w8 8gp3s rest energy? v =    c

  (a) How much work is required v38) lpolw.e8t6 dr fu;gvdk*- 7nfhrto accelerate a proton from rest up to a speed of 0.997c? W =rvk 6ldwl.f*h 8;3od7un8gpfe r- )tv    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and mom3rm46v1rrfq d entum 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 auzee3 9bdwhywz2b ;0b5mc r(25 s9hkg 750-MeV proton (that is, its kinetic energy is 750 MeV)52 z0( yz wkbmuwsbe;d 5 hh29br3g9ce?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 M2z 5isb9wi5 ruz):si1v 9 eyyjV? v =:s zj )u9yr5 yi2wsvzb15eii9    c

  What is the speed of an electron whose kine)n1v37 ebmp ektic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen9 sb8e 1okp2b/. autmd after being accelerated from rest by the .s ep2m ko b1/da9u8bt25,000 V of the picture tube? v =    c

Two identical particles of rest massv xsnl-dvqytmy: 3/;( $m_0$ 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 0fcf4 uxx-uhns.m j1ugt.f+ 3proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electr;.hci47a*9v86t ,nla*qinc iov x alson ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 accqyeb8.+ , 2vulst9u ihelerated 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 ; a+j++ic iydzof 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, hp/0t8uvw el4ygeo54u4jm f/ $^{241}\text{Am}$, 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 f*8yfyzrs;sy, or (a) a particle of nonzero rest mass, and (b) a particle wityy*; z8, rsysfh zero rest mass.

  What magnetic field intensity is needed to keepsqs.,q3 5sc ,tizjvd2 998-GeV protons revolving in a circle of radius 1.0 km .sizcs,3j sqq2 td,v5(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 Earth) observes j;gg4cc,hmai w*3w8 na meteor come from behin3cija *n,4w;wgc m8 ghd and pass her at a speed 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 of9o-gjdrx l/t d 07adm-b h.tr9 0.50c with respect toojdr9.- d -b7adt gr/9m0htxl 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 second spaceship leaves 9(-yjxqd m6xqthe first at x(9x q6qjd -yma speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vesso j x+m)qk *;;rzaa 9d2ma8znuel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens 8 rzn qja*xum2az9;)+ kd mao;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 o h 5l35sne-wi 4us2rpj/7,v,b slxiwin opposite directions. One travels at a spew-rsx5b/no 3i s ,,piljleuv2 s754hwed $v_1 =-0.60c$ 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 9 j/ge x4t,gq6m1eahpthe same time, rocket B passes Earth moving 0.95c relative to Earth in the same directpeajet4xm, g/g 96 q1hion. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centaavm -cbwo(kq-, q 5s3turi, 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, anyd8alk+ )et2ce4m m8githing traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the sde8mgkm2 tcl48a)+ eipeed 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 spee96/;a p3+fqu9ivqmsx (;eyaa v2hlgpx i )*dyd $v$ 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 destroyedy 9i.dda-j-ma5j*rp p to run a 100-W lightbulb for 1 yrpdi9 -5ma. pj -*ydajear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is g u5)nnun kxh da/8v*jrjl7+3needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. l8na un+/uvk jjh3)5ngr *x 7d(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 on wita6/ m8gv+qqm.m/kdt3s*v kkphrpk + *h a positive muon traveling at 50 * gp /mqpkh3s8v+r6 .tk+qam/d kv*mk% 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, 9wox- -ripakr, s-i-x 4gu xu6and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =-6,r u w- o-i ax9ipsgkrx4xu-    MeV

  The Sun radiates energy at a rate of aboutod0 )8uklhm; g (*nr*gwj4f rn $4 \times 10^{26} \, \text{W}$.
(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 charge and a speed9o 9qdf4*u)mur10qe,t h b w40 ynpqsjm d;,wy 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 chyoo y;lei2 -fgq75(7t8 m jrbe required to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including anfye-7o(; 5yjlgqc r2h mt8o i7 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 tr. b;hxi /1heuraveling 110 km/h a uie.;1bxhr/ hs compared 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 laboav0w0 is 8e 6zzct*7rxratory, are moving toward c0r8ze7w a sx6tvz*0 ieach other. 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 v3zrcq(6droy2wt 71: ( u kbrpwith 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 and an8rz hr8t)bq qjcmpy69*. w r)mtimatter, achieving complete conversion of mass iwrqpr96z y.rmm8 *) hj)8ctb qnto 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 acceleratewt9bx;(sz u bql t,yb(+ha8)ed so that its kinetic energy is greater than its rest massz+9a,u btb ;b h8xwlys)(e(tq $m_0c^2$ 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-l0(k letc ap0,wong pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he c,kt0wel ( 0apdo 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 form two moles oiwtd0 6p 6rqr8f water, the energy released is 484 krw0t6p 6 idr8qJ. 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 reactioncw fvnqt7i q*+ow1q., two identical particles 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 par+qwfqc.w v7o* ,1nq titicle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Ear m7eq(0vs/b htvu8mfs g(,,frth measures his ship to be 25 m long. On the ship,h(fsqbv/7 r 0 t(eu8gm,,fvm s 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- zj 7vl+i1j)lx subj8 spaceship at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for bsxj1 l)v+ 8iz7u-jljthe speed of the laser beam?

  A spaceship and its occupants have a total mass of i5s2h(ynprhu-j *x8op6i+g9- wjqc e150,000 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 direcox( jj*- eg8u2hnywps ii p5r -hq9+6ctly 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. Whp 0;r-itl* blklri,j; at is the spaceship's kinetic energy? Compare with the total U.S. annua *lk,lrrpitbji;; 0l-l 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 star pf,++*f*iux iq k+gnc 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 +cfgui xnf+pik*+ *,qthe spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscill oaq2ymd- (7du)ydh )iates on the end of a spring whose spring stiffness constant is )oqd uy(2dah )d-iy7m$k=48.7 \, \text{N/m}$. 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 m. l es g:s1msn9yadk14ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.