You are in a windowles9iqh/ qqxc-z (6)eyv1dag0x )v 3hg (iuo0 vhks car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment yxoicv1dh v3iayu -gk (0)h 9he60 qgxvz/)q(qou can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out oico g h3 tbbxy8+il-x( rj81)of the corner of your eye, you see the car beside you creep forward. Ix3-(8 1b bgiclr+) oyx8ohijt nstinctively 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 a heavy ball stra bm6e-/2.ev fazq0-a5 wy)qng7g gwjkight up (from his point of view). Ignoring air resistance, yf5 begq/kw7)vnma -z.62 -0aqjegg wwill the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to,.ksom sj+ 0aaza53cq say that the Sun goes around the Earth? Discuss in view of the , kassja3acz 5oq0+.m 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 spbqn sfy,:niu y,x,b,+ eed would ,q f,by+ iu:ybnsn, x,the starlight pass you?

The time dilation effect is sometimes expressed as “moving clocks run slob-(x byg j*(v.7 xymkzwly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then doeyb7zm.x*gb (x v kj-y(s it deal with?

Does time dilation mean that time actually passes mo 5+k)9wgn.ud gez3mz hre slowly in moving reference frames 93 z+ nh5z.dg)mugwekor that it only seems to pass more slowly?

A young-looking woman as qb,j 8- 8t;yk icyz(ru-ib,ebtronaut has just arrived home from a long trip. She rushes up to an old gray-hair8qr;z,(bj cb ,yek8 --iutby ied man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling jvhx7- t-hwr ck5oi2e6+ev,s away from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observervsx56e7e,i -ct+hvwo k j- h2rs on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, c e1 cz-.e2 no.yh)isfsay $90 \, \text{km/h}$?

Suppose the speed of3 kl2vf de (/uoer*k*e light were infinite. What would happen to the relativistic predictions of length contraction and time die/*ke u(r*o fdlk2v3 elation?

Discuss how our everyday lives would be different if the speed o70r p aur;.iovenarcy8a( )-u f light were only ac;uu earoy8-7na).p 0 r( vir$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used top/m j./hld;a y indicat;j//. yahpdlme that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tompkinsvq.d.er ;a*o wx8*. tmwusk.z, for whom the spee *savok.m ;wuw drx8tqz..*.ed 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 atk+-(o6hn( w,(zfg wm tla)eepf+w nt7 speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this uphetlf(wmnz gp7 fw(+an),t+ok( 6we -per limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed o supe8v9cygpjj/; 9* kf 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 thahq 754rj+mwbob-m hc)t a spring has more mass when compressed than when relaxed?-+b7wr4m) hmq5b jch o ----待选择----yesno 

It is not correct to say that "mattegg .+1rsuyf3h. 5v38aobrvllr can neither be created nor destroyed." What mustl3g .srv+a 13lfg b.yv8o5ruh we say instead?

  Is our intuitive notion that velocities simply add, as we did in S1 lgg7 sju5mo a4lqq3 5m7+ukhection 3–8, co g 4galkq+o7qu hm55us3jm7 l1mpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. p5k5;;rhb ew 2x5yghwYou measure its length to be 28.2 m. How ;h2k ;ewxwp5y 5hrgb5long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at b ug2, 4dh*;v0mu-nok*meo vv 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 intervalo,xf,f eij7l8kil, 0es 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-year,/5v;paiz.rjy 7zs d us 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 itse,tzm2blx- vcpt,vi3 z4q 7 -e 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 stac: dx9)qi)lc)tadxn5 n*x-6znvxk*e r is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years? v n)xd-xcict* 9q5*6l)xnn e:z vdxa)k=    c

  Suppose you decide to travel to a star 85 lh1e 30:oyhs fzight-years away at a speed that tells you the distance is only 25 light-years. How many year f1:0sy zheho3s 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 xb. :vpqbzae: q q+:j7w/1qmd 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 thaz:e *sqrikcbw3+yz -a;*h (okf1*-hn6ivk ebt starship Enterprise had just returned from a 5-year voyage while trayk+6kb:*b ze w *1i-c a s eo(*hrkzq;i3h-fnvveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a s: xjbry, 4 :crztb9av;pacecraft travelx tr9;cbr j:4yz,v ba:ing 0.960c to reach that star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in*q m e5b4eypx/j5)hxi her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame tohpm4j eq * )y55exib/x be 4.80 m long 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 trave93dm/w wvn(3gpc * kxfl 15 m before it decays? The average lifetime, at restknfvdpm3(9 *w3/cx gw , is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling aj0;fd cuhls3.t $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mascgs5x.m/ irm g11v5yzs be twice its rest mass? v =    c

  A particle of rest massog:w3;y uyh9xr owoz 8-e/wd 0 $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels (m ry 3ka+/ guhoq1if-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 a protowx8+qee)ij3 3-o qh jn:eo+ydn that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical rea7r8u4 : m*7eekibyj eyction 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 breyj swtuk2xd 6: /6xkw.aks apart in the process known as fission in a nu6: kudw/.s kwxjt2 x6yclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electud es2,on4z;ohop .++kcv x/bron 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 malcnzi8d ;og o ax0z*xv3,,sg-vz.x9* g-q fqiss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Stkl9(v x 09efohrrr3.yates 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 zn(w x55*eimz obtained 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 eneoqj1r.*mdv ba6y . jw,rgy equals its rest energy? v =. q*wb.yj,oar6jmdv1    c

  At what speed will an object's kinetic energy be 25(p+gj/foc dp *% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to g50b3u yg ;568c0bfsjaei weza speed of 03fe8buj0gwe 5g6 ci; 5 ayb0zs.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton travel-tfhf.7p q3jm -gk ,muing $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV wqii/ r5zx0-e:h 6 kinbys+7c proton (that is, its kinetic energy is 750 MeVezx0i:qs -cy7n6 hw +ib/kr5i)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerateda1,)qk/,mvzrpx.s i0k j o-ko by a potential difference of 105 MV? v = k.0ik)/mosk,vqz p-ax o, 1rj    c

  What is the speed of an electron whose kinetic energy is 1c8.qy(t5wg wb8zh, e i.00 MeV? v =    c

  What is the speed of an electron just before it hits a teze /2woqnb/ckplyn v3w6+ch ;j,c t, 5levision screen after being accelerated from rest bzcj+te cy o; /5hb /n,6p3klqw,2ncvwy the 25,000 V of the picture tube? v =    c

Two identical particles of rest mass bd)*ac wes1x*9zray. $m_0$ 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 proto;7p3yef+inhgc oo39b)ge9ozikl d - 4n ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 o vrk4rnps j+uki :.z8.f 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 mass 27,000 kg is acceleraoea(- 8-jr uk-i:*kef t7hwmlted 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 adxhhel-6 r4vux5 l;f. nd 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 nucleus08h j xn shy(*zu(7ozq, $^{241}\text{Am}$, 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 m(w.51 qhb kxzf8,1 ktofrak9xomentum for (a) a particle of nonzero rest masfxx195kk(z 8,qkhatbw.1 for s, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to kee;zrgeb1+.c sj p 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic+z;b s 1c.ejgr 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) obser+b 4w.5-hmfpfu v.o9lp+z n lnves 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 E4lw ++mzpf5vfl.up-b 9nn .o harth? u =    c

  Two spaceships leave g8a wx,t6./d .ths 8bir 4rxxgEarth in opposite directions, each with a speed of 0.50c with respect to Earth.48r.,w h8i br6tt/. adxgxsxg
(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 trx.us8u sg+z, eels6n-aveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the f-.sgnu8u z,lxs ese +6irst. 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 vessel approach at a speed of 0. stjy lz(0z)8 bd/ nskxflr-6(60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens wsdtz- bz nr 6s ly8/)f((kj0xlhile 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 distresbmp7b aa 46jp0l.d:ogud*s a 0s sends out two escape pods in opposite directions. One travels jb:a dadm g7p*.6lubao0p0s4 at a 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, rocket B passes xu,8bzckg 6 zk d-e87wEarth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' gx ceb6d -88zw,zk 7uk=    c

  The nearest star to Eart(g4t).s8ah q*ezc upx lmg5n-h is 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 traveling faster than abgf4n p gtq5wl/in2clr(*)c z4 out 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effnzwfl )*25n4g irc4(pq/gc t lect. 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 speed9edax xjezn6mm*0 -9n $v$ 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 rxi;vxf:7sq6i un a 100-W lightbulb fo qixfxvsi; :76r 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromaw k; 49;rcggjagnetic 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 opposite charwagj ;;9kcg 4rge. (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 speafi rf;st(d;l :a9u2nfy;eo 7ed of light collides head on with a positive muon traveling at 50% the speed of list ;an2d:; f;e7fuo r(if y9laght. 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, 33 :fl oeq6xwean electron, and 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 33wx:o felq 6ethe total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about xh 9)ztaq.*,2maz nny $4 \times 10^{26} \, \text{W}$.
(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 andtykq 13q47ucp c2jos5 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 heliuwpw(+kl63xpwg * j f;rm nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and herf6g3 pw* (xjlwpk;w +lium 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 (rela3gst ga kun:jq zfr/(i2;4z5 ativistic) mass of a car traveling 110 km/h as compared tot4kq /aaz3f:sg n5;z2i rujg ( 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 laboratory, are movingw3qhqo ;.fv9 z toward each other. Deterzowqh fq;.v93 mine
(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 parsqxd1i;e r0u.xb w31q3a tqc -ticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprisefs9;c hy ip50e obtains its power by combining matter and antimatter, achiec pse509ify h;ving 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 itslh-l; wb*ubs/w -9dvv kinetic energy is greater than its rest mass;v w9 ls-hdbl-uwbv/* $m_0c^2$ 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 th-g2o h( ,ply-y n k/y;ex4wtt/9fibd wat 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 doe;h-py(9 4t2-eib/ o,kyng/ flwdtwxy s 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 wn;3 y2x ufhh6to form two moles of water, the energy releasx;6 w 2ynf3huhed is 484 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 identicdm6 l. .dqi okesz35tf 29sm4nal 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 particle's speed r ek4i sq236s9 .lnmfo5 zdt.dmelative to the other particle? u =    c

  An astronaut on a spaceship traveling at a 4 ypc:9cdef)0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats:p4 dy)aec9f c 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 spaceshipv1i nt/bjhr.nnt,1, u at a speed of 0.85c away from Earth. You send a laser beam toward the Earth trave,j vrn b1 n.uiht1/tn,ling at 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 occuk2+mf c r+(ibrpants would like to travel to a star that is 25 ligh2m (+fc irkb+rt-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What is x1bjkg,en0x*h /gxf:the spaceship's kinetic energy? Co g/1xb :xk*x0j nhegf,mpare with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 63o6k piz(k*2wmgfj)rptmt * 9.0 light-years from Earm 6*otk*9 j)rp3i2wf t p(kmgzth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end ofq7v ;g 4ahml j;crtbms86lid56u5 tm0 a spring whose spring stiffness constanttdm56utl8q4hg0 ajb;v;65smcmli r 7 is $k=48.7 \, \text{N/m}$. 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 yh,cl )3-fyi swoe 21ab,r8 yziy4tass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.