You are in a windowless car in an exceptiz zqdhze(8.rzwul-rbyst/ 2) c1h-- ionally smooth train moving at constant velocity. Is therer. czz )b-qzutdiwrh 1s- y2l-zeh(/8 any physical experiment you 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 1(5aji 7 n:mud*bxj nx3r,nhc a red light when, out of the corner of your eye, you see the car beside you creep forward. Instia1um3h (5njirjbxxn*: ,n7cd nctively 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 rlk; :ma h7rh -v+9v*nitoa)txailroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land ;x: +7khvv)haot9inar*mlt- on the car or behind it?

Does the Earth really go around the Sun? Or is it alsoy,ancy8i5 0 yn valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explcy85a y0ynni ,ain.

If you were on a spaceship traveling at 0.5c away from a star, at qzizf b4; )l)kyr 7+rt wh20ybwhat speed would the sbzyr ybz2+4;) )tw0 firhqlk 7tarlight pass you?

The time dilation effect is sometimes ex8 vb35;hhihuh 5ig cb6pressed as “moving clocks run slowly.” Actually, this effect has nothing to do h 3b5;i6 hhi85ugvchbwith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving referenwd;y6y/ (ve irt s05n wvvy-hb0*lzh7ce frames or that- y/w7tw;dh0ivv(s5 brhe n 0vl*z6 yy it only seems to pass more slowly?

A young-looking woman astronaut has just arrived h-wf6tjfgk /2 iome from a long trip. She rushes up to an old gray-haired man and in the ensuing conve6wij/ kft 2fg-rsation 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 a change .df(3eaf--0t y/aqxvq(fr r jin your heartbeat? Wf v(-d /e3a0yrqx j(r.aft-qfould your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation ande3 ui+4nou4l ntqwp8 , length contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relatiys-p 4z7 xk:(yer0ji dvistic p- dx7(k :z04rpjysei yredictions of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light were opq62bysno-) o./v3o +vyf b8xvihum/nlq /o/b.v ybufo 3ixp)2-smo 8v+vhy6n y $25 \, \text{m/s}$.

Explain how the leng1qoa;ay8t h2( wp,jf ;nzta2rth contraction and time dilation formulas might be used to indicate y ttzpqfr8(oh2 awanj ;21;a,that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the strop 67y3 08v*f . tz/ wvuxrqiw,wb;xfbeet as seen by Mr Tompkins, for whom the speed of light isovww/tr* 673.;bz p, yxquixvf 08bwf $c=20 \, \text{mi/h}$. 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. Dxmn t)5 hjw6byqkn710 oes this put an upper limit on the momentum of an electron k0qb6 t1j)mnh5xn y7w? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of ligh3 u ;.kqftb3c5si m/hxt? ----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 thai.r/) h8ursaq t a spring has more mass when compressed than when relax/)sa qhr.ui8 red? ----待选择----yesno 

It is not correct to say that "matter can neither be created nczi c6(..;qxclsl 4 7gp nvj9yor destroyed." What must we say instead l.liv(c cc964gsqz xp;.n7yj?

  Is our intuitive notion that velocities simply+) tknx+przr6+9c*o5g vzy ez add, as we did in Section 3–8, completely wrongzz5 ++ g rrov 6+kpy*9)znctex? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length t3rsnlav;ef7)+5x i *qsha u5p o be 28.2 m. How long would it be whes np ulq+fri )es7a5v5*a xh3;n at rest? $L_0$ =    m

  A certain type of elementary particle travele-r qgt5(.q/ 0f u qadum,wj/as 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 dddhyv//;t b wdj2khlszk+5 d6* j0.dkepend 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 Earth at a speed of 1;j7w/ j,yfxbb ks)to$2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime is measured t hwnd4pb w nkq08b(1)n,bsz c6d.9xnji)x3 geo 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 light-years away. How fast 56y f18lbvp+0c xwbxp would you have to travel so that to you the distance would be onlyv1bc5bp 06 wy+xp8lxf 35 light-years? v =    c

  Suppose you decide to travel to w- ej8om+ds.z a star 85 light-years away at a speed that tells you the distance is 8o- m.swz+dje only 25 light-years. How many years would it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from t ecwhzm: h3a7epb*w.8he 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 sz-+u/e2 jzt0kyeyvprh l- rt67j/9po tated that starship Enterprise had just returned from a 5-year voyage while traveling at 0.84c. -rveztlj-960e//t2jyz p 7+ho upr ky
(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 spacef2jlg 3fz )7u9qdg,xmp at9 )xcraft traveling 0.960c to reach that star from Earth,3zq 7um, jf xgl)tfp 9)2xadg9 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 00vit-6b a*yps) wcp3 z.660c. It is measured in your fram*0 p-vi tyzw6 )b3csape 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 travel 15 m before it d+(ry(ebp /x/c)sh kznecays? The average lifetime, at res ychbs r/xnkz+)(e(/p t, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelin+kz t4fvfc2u.x2i: k zg at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice it kf +eaf-zmp3 3q)3uaat o3aj1s rest mass? v =    c

  A particle of rest mass hj/uh 8*aa/gm ussk x *7rc1;g$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at ii uo.;x/nu7;surds) $v =0.10c$. 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 that9vsbs 0avwu4 - accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requrn1 m /99hlpxrires $4.82 \times 10^4 \, \text{J}$ 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 fisszd .tc8j5+ n6hqk6 ao x0txka3ion in a nuclear reactor, the resulting cdh+3k5 za8on06 axtq.6kjtx 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 acr2i+f. e3gu knj+z k9n electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mavgh o0 t2-g :bpc2u n;yh0wnt+ss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption y* ( p*x2buscrfig t3-in 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 conversion of 1.0 gram oyq,0(s x wt)1gi7u abof 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 equals its rest en72m( v3vkqge)a j 7mqgergy? v(v77 vq qekgja )mmg32 =    c

  At what speed will an object's kinetic energy be 25% of itsad 2e8 o9t(gpf rest energy? v =    c

  (a) How much work is required to il sr 7k2a9i,raccelerate a proton from rest up to a speed of 0ail2r ,rk7i9s .997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy anvig2yjbn t9 ilt- 9:q+ayx01z d momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton :f*eluw0((i lshdln0(that is, its kinetic energy is 750 MeV)e*h0i(nsl( d0uw : fll?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential diffeo:)093jyxlunmpm (tprence of 105 MV? v 0u xjlnm9p3():o my tp=    c

  What is the speed of an electroqwh9 co:h 4yn /l ev528ixhju)n whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron ju aacn7q5 q/hgr.9a 2uwst before it hits a television screen after being accele/h9gc .qna2q7u a5warrated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles o(afi-pho,ah;fetb 0nsc3 f2 7f 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 proton (ngcifjtg/4n- d3q: d+s ;xi8v$m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentdu 9 wz o3*makol)s82eum of an electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass psh65-1yqg21bt osvh 27,000 kg is accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energy and momentum x70/(s ah: ;r ce+vtp7wramq qy)/unqof 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,1wn,w)b q krbu:i 6fai7hhj/l ;4m .jx $^{241}\text{Am}$, 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 fsq7efb c-qaz1 x nx+w)6pi hcr+wj+37or (a) a particle of nonzero hxbi -j1pw7c)r67ze 3+nqqxs + aw c+frest mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving6ym*knn uupk/r 0f*b , in a cukbnmyu,/n6 rf0 p**k ircle 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 respect to the Earth) observes a -14v+sx( psj bjs0opymeteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with re- vsp1s( jo0ysb4x+pjspect to the Earth? u =    c

  Two spaceships leave Earth in oppz8 fbv) c qwwrfog/t() a8h0q6osite directions, each with a speed of 0.50c with r6vt/w80qaz rfwgc h)8fq)ob (espect to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth travelind+s5crlf gi 0oq+47de6f zbx5 g at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the seco6d i ++ c074ffzd5lrobxg5 esqnd 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 ofyj4)e3*5pp l4e ws-0hfexmt x 0.60c. The Enterprise comy 4f pse4tex0 le)5xw*3hpj-mes 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 relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sendsck wg-bx ko;j)s;2u 54ef0f kj out two escape pods in opposite directions. One travels atc4 w;ju; )0 of5kgs exkkj2fb- 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 0.75h/m+xufp(jq 4c. 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 i/mf(j4h pqx+u t passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years aw z z2 f9p6wl ,hxxddm,6.dt(wco9 p1ctay.
(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 callbadme3-tazp)gdc .-i( l g6 o1ed relativistic - i.e., for which the correction using special relativity is a significant effect. Determingd 61(lp )a - b-idt3eco.zgame 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+yx5-el v*/1l:hys:uf1ktgu jg )eh g $v$ 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 t;59wq6tliyic 66res+xw2s soo be totally destroyed to run a 100-W lightbulb for 1 year?;6iylw6 c5e6x t2oiss srw+9q $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produo.5pxo6:vygi(i wey9 f6zhp k0 iei; .ce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge xwfii5; g66.0ho:eyvz.o pe 9yk(piiis 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 collid6sb2(k wd; cyfes head on with a positive muon traveling at 50% the speed of light. T;y6(2 csfkwd bhe two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutr3vv 8vg 3*w1gn1sf dgn.9dfh iino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the8 g iwvh9gs13vnd vn1f*.gf3 d front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate off4j+-0f kpte- ghfpx)9v xg .n 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 c v5c lu9tl6ur+a 7k v.ghw)x.gharge 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 cozsvn); 8fo1bfybgoe++u*k ;w nstituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the +kfsu)w nvby1+ o;8b ;*o zegf$^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increasulkd4enrfmr;4 a c .86e in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binorc. ;d8f6 ka4n4mre ulmial 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 moving tl; becsin w7 -:2hl.iha8oo(q oward each other. Determiq2a7bnh:w s lic oh8lieo;(.-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 withre u i19 yy./oav+ha) mo,vi1d momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its p vp/2lzi3lwtpud 5/5xower by combining matter and antimatter, achieving complete conversion of mass int2xtzdilw/3 v5/ ul5p po 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 end8s l ox;i-ap)ergy is greater than its rest maso8 x-psa) d;ils $m_0c^2$ 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 o*v 2jl2,ctk l15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explainko ,ll2* 2tjvc 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 oh4uhc. 1hgwsb*qofr*4-ga* tbk.b.mf water, the energy released is 484 kJ. Hog4*4hf- ugbq .1t. *hcr*baksobwhm.w 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 particlejj6yswv pk:1s6pm 5 o/s are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, wh/p:m5 j spys ojv6w61kat is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship t09bevhewr n28 d8 fb6jraveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his luned8e9b86jhr2fb w n 0vch 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 speef2 w52rv2z8qr: gzn0ogg / xeqd of 0.85c away from Earth. You send a laser q0x2z825ngre wgrqo:/ vgzf2beam toward the Earth traveling 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. Thec8ram,q (pksj( hj0 k. occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to e .ark8q m(pjhk(0cj s,nergy 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 th)wf+itk1 *y +hpcogb7 e spaceship's kinetic energy? Compar i+1 g*+wkyocp7bt)hfe 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 v.u kac-7 .7narr )-ht1y/wbu mbyz0 qvicinity of a star 6.0 light-years from Earth. Passengers n -rryu7zaua)17hmvtc /wb- byq.0 .kon 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 onp1i1zp.4o82pq 5fwysf)i/e:u jjk ) uhi a5ir the end of a spring whose spring stiffness constant is )/.iaps8 55ki4: i 2h ji1q zyfe1jppurowfu) $k=48.7 \, \text{N/m}$. 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 mk gr**/2iu bfh8fztx+ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.