You are in a windowless car in an exceptio /*cnpjya 4k8anally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to pjn8k c4/*aay determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of jro (hn9g0l -0-yhv ribeing at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively yojhgn o0-9( vrhr-y0ilu 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 ls 0 9vyikzp;fmghpvun j( *00e:0qq3a moving railroad car, and throws a heavy ball straighm vni0f0:hvqp*30plsg0ku y9;qze(j t up (from his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say that the Sune 7.la+ d/oon.h+nx --fiw lad9be9hd goes around the Earth? Discuss in vi oeddn.f i+ h/.oh9 aenxbw--97+ dallew of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceg.2cc)y dxb 7v ps/zd39o zjp)ship traveling at 0.5c away from a star, at what speed would the sta /.zyp7g)j )zbxdo 9pscvc3d2 rlight pass you?

The time dilation effect is sometimes expressed as “moving clock +c nmn1(im-aos run slowly.” Actually, this effect has nothing to do with motion affecting t1mc-inm+( naohe functioning of clocks. What then does it deal with?

Does time dilation mean that time actc06c/r cgkn0dually passes more slowly in moving reference frames or that it only seems tgkr ccd/ nc006o pass more slowly?

A young-looking woman astronaut has j *1cwf f9xddcj6tf35p xkqsy 68tjf 06ust arrived home 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 migh9j6k5 fjcd1wx6 p3cf8yxs 0 td6tfqf*t this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a changei x r ,;ft2ezzgye4h10 in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes 4ef0 2xzze, i1yhrt;gsay about you?

Do time dilation and length contraction occuduj*hhsh9 35q r at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the reqy4dr pp9w17 elativistic predictions of length contraction and p 7e4d9py1rwq time dilation?

Discuss how our everyday lives would be different if the speed of light werc+ru26 . jw39yrus pfie onlu+ upr.9 cj32sry6ifw y $25 \, \text{m/s}$.

Explain how the length contraction and tim6pu -hc*gr 9 nn:hapa*e dilation formulas might be used to indicate that c is the limipr9apnha-gh 6n**c :u ting speed in the universe.

The drawing at the start of this Chapter shows the-a, 8boqks1u w(rtclbb-ag ) - street as seen by Mr Tompkins, for whom the speed of light18 t k) b(rab-a- bgscq-l,ouw 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 than c. Does this puts xq. z t-9k7m:i/fjc,t*n cdi an upper limit on the momentum of an electron? If so, what is :s/cinfkmq c -d,*7 txj9t iz.this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of light?ptn+n r2yh/2+ o;)w lgt,rynk  ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does this mean that a spring hasu9ef g8 trs.;t more mass when compret8eg 9.r;ftsussed than when relaxed? ----待选择----yesno 

It is not correct to say that "mattwtx,jp j2p az mljyc89n 41g1-er can neither be created nor destroyed." What must we say w8 g 4pnm9atp-jzy,l1 jj1xc2instead?

  Is our intuitive notion that velocities simply add, as we did in 3c; 1w(jnq8 ouiqm 5g5:ns osqSection 3–8, compleu;5sso3qcgm85:n q1iqw o ( jntely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.2 ,ns hptwa65hascx(23 xkq0k r31: qfem. H3c f:,kh(awhr 20qkxsxpq1a3t se 56 now long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle tr0 5qay xx;pd: dw4qo1ravels 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 depeu))pg :lcgy0r7o tfb1 gic++ dnd 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-years from Earthj1e1oyw w7kwz l6,r; v 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 pio.q79drlcb xke 5lz5k:4qv;l5n:v eam n 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 lighw;.sx )kas9 i:tht (bmwo.m a7t-years away. How fast would you have to travel so that tow7:9h(xk ) m.oiatw;s .atmsb you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at azew e 1y 3zkqz66,h ntdu-0ske0 14igf speed that tells you the distance is only 25 ligh1s-0,0tyneqz 6zkk gfeewzhu 6d4 3i1 t-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 fromh93,2hc*zcqn 7syb r f the 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 starshikx d)d*(k 0ngbjwm: je6b39lk p Enterprise had just returned from a 5-year voyage while traveling at x:6* kdkem(j3djg 90lk wnb )b0.84c.
(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 woul f7bs;g) gy)fcd it take a spacecraft traveling 0.960c ty) sfg;gf) 7bco 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 her "Ferrari" spacecraft at a speed of 0.660c9r .j no pae*0viyl+tixtzjg,n .a3,;. It is measured ina.xai*z0 y +3 9.gn tjior,p;ej,vnlt your frame to 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 travlew8r7 54 yvfdel 15 m before it decays? The average lifetime, at78dy4 wl5 vfre rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a l,cgkd0gy1 f p6sp7a:proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relati0;q9t( ,lwnd:fjua4kmbv 7xuz;h3 wr vistic mass be twice its rest mass? v =    c

  A particle of rest mo6l zm*zbm( 3+ ly(80jrwybueass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at z8 rma5 kcl n;lbfoqg(4k *(s($v =0.10c$. 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 protonr:wa r4d -1jtr that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requirei f,uej. 2mcy +y;1xam s .u0ww2j:wfss $4.82 \times 10^4 \, \text{J}$ 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 br xwtq*ub+awmul9- vd6*teu+5 eaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in th+e+a-vquw bdtl5u* wxu*m9 6te process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules and ahlt*a)lkx1+ d q5qz0 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 . v33m-;xx wu)jsmoauchp0m 3 a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption i9gp6:je-l6hvsxa* yu0 xq:fq n the United States is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conver xqo.z3;lf1 /njn (4bxjvuk* jsion 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 pars +v(( s8,iwny h lak3zjxn9t8ticle when its kinetic energy equals its rest energy? v+ 8al siv ,x(wk3(9nhsjyntz 8 =    c

  At what speed will an object's kinqe2pqml1 d2v4 etic energy be 25% of its rest energy? v =    c

  (a) How much work is required t9jm,.uhzi g *to accelerate a proton from rest up to a speed of 0.*im z.j,hg9t u997c? 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 oph o8 42pvcq9rf 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 kineti (cnbze:to 0-xc energy is 750 MeV)?: noe c0xtz-(b    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated a9+byp s5ddz:6 pw j1oby a potential difference of 105 MV? v9 +os16zp 5aydb :jdwp =    c

  What is the speed of ans5(5fyikqczz)y * g q* electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a lt.sis* r 9+ektelevision screen after being accelerated from rest by the 25,0.+rsetsk* li 900 V of the picture tube? v =    c

Two identical partic w9aw)scx44h bles of rest mass $m_0$ approach each other at equal and opposite speeds $v$. The collision is completely inelastic and results in a single particle at rest. What is the rest mass of the new particle? How much energy was lost in the collision? How much kinetic energy is lost in this collision?

  Calculate the speed of a protoa :upe:y*j yx+n ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 id1t y5x/- n r)*,m,jvhnsd )fdqkmn3electron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 accelerated to 0.21c. ed/ b.fm+f8l,hxa2 jbrn62f/ r milt8
(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 kineticp u : r+:+u5uuv(qenfrtq-ot(z;3 wti energy and momentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleum i)*dwa)i)a ys, $^{241}\text{Am}$, 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 kig 7oykl z1e3z2f. hl;cnetic energy versus momentum for (a) a particle of nonzero rest mass, and (b)ghz 3zfl le;y. 21okc7 a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV:n*gd 6y ,;oa j27 zeutqjrf6o protons revolving in a circle of radius 1.0 km (at, say, the Fermilnu6 zgojoq6d;j7f*:,e 2 ta ryab 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 a mw0; yacxr 1p+p8ww: kreteor come from behind and pass her at a speed she wwayw c:prpxr0k1+;8 measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.5cimqi o i1pf0:)sml8-0c with respect to Earth. i:108-lp q mioimfs) c
(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 spaceslqc4w 2 hc1 (h(ijp4/s5rvl bchip leaves the first at a speed of 0.87c with respect to the first.cs/p5l qlc4r1vh2 b ijhw(4 (c 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 ap0 .w8d ctqyrk4w mh9+eproach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the 8cq 0k rym4+w.t9hedwrelative speed of one vessel as seen by the other? u =    c

  A spaceship in distrtqg/ pymbrg9p0)g4: pess sends out two escape pods in opposite directions. One travels at a m) q0p gbgg/ yrp49:tpspeed $v_1 =-0.60c$ 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(7pbb,r q )bn.lzxwk3 B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B movix),(nkbr 37qz bbl.pw ng relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-yearju9 t f08a5 cjr/re*ehs 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 about 0.1c is ca,ds +bz 1h7kf7unr0mblled relativistic - i.e., for which the correction using special relativity frk7 b1bzmhu+d,0n7s 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 48lwm r2)xofmc53 fo o$v$ 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 d 4k5o pxp7n8qrun a 100-W lightbulb fo7n5oqp4dxkp8 r 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic d v5 :9tpruw27kbdp1lzn6qi 7 energy is needed to produce an electron and a positron together? A positron is a particle wit ip:79kd2ru5dp76wz l qbnvt1 h 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 light collides head o-j q9j ukfr1xsc0;6 xtn with a positive muon traveling at 50% the speed of light. The two muons (each tur jsqk61c90 x-xj;fof 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 elect(76 jdwnlgp,am. v kk*ron, 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 the total kinetic energy shared among th6kp*lnj .md7,gvwk( ae three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a ralgrc pf3h2 y/atlzi-8ye7jvag.- (w; te 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 measi(/n8 ynmp 7fgxh0)nt ured to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to bre, oq7t7cy3nypq3 0*l- fkgy +joh ubb6ak a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, resjgo k+7ct633by *0 ,qo-ulhbny7yfqppectively, 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, dj okoy.*c a-++vr,wg8mjyr car traveling 110 k,+jkmc,o- v.r ga* yy8jo w+rdm/h as 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 laztj+1m1 3tdy tboratory, are moving toward each other. Detert yt1zm t31dj+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 particle with momentum j:0+z0 nq fyzy$p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprisehvl-a9y,8zvb+ct d7q8 ;uh; y fw +dae obtains its power by combining matter and antimatter, achievin;zqfd u8 hy+dy l7hb+;a-t, 8cevwva9g 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 energyu t 1., wisnp*:pkojjfn9 p6a( is greater than its rest manpo,ks6. ufiwn1 jt *a:pjp(9ss $m_0c^2$ 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/h)g gctvqm1 q j- n:y9.5elwx believes that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Expw. v/1 9lx5n-qh e) jtyc:gmqglain 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 fo;7dxl6y8-xh/ czsf ;zssi9g k rm two moles of water, the energy released is 484 kJ. How much does th/gcds 9x8kzxs ih f67;s ;zly-e 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 partir bi z()8zjj v,shnovl8b9bzr ke*+ 6.cles 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 relative to the otherk*ir lzeznj s96r)b8jv z b ,+.(v8ohb particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measur(h4 yln m5re/:nmf p1zes his ship to be 25 m long. On the shi1: plhe5f(n/4ymzn mrp, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away frop 4wb8j-21l2ox1 b1p og/vc;ofzljp mm Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the b p/-boo11z j2o12;lg8v mxcf lp4jpwEarth measure for the speed of the laser beam?

  A spaceship and its occupants have3 m p0,gzs(pezy7 yc*y 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*zgpz(yy y 0pc7,em s3 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 a(0o ;mrx2+ wic2ou/oo0khau it a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energok(0 +ihrx 2mu2wuc aio;0o /oy 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 stavu a;s-2(zbjor 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 worja -2vb(s; ouzk 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 o *+ /8pselvl u47qmaaend of a spring whose spring stiffness constant is7s*/4qulmoa+ avp 8e l $k=48.7 \, \text{N/m}$. 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 massd* vb9 w7360 7crrlhothq*w hk $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.