You are in a windowless car in an erd- rmuev34+vtq5zs 5xceptionally smooth train moving at constant velocity. Is there any physical exper+metrvdr535 s-vz4qu iment 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 a red light when, os3( ekgxgh;p m*(peolhq-*: z ut of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinkinhgeeglkp(pm-sx*3:* z(ohq ;g that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad caryms 86n(ka;ep 46d0,txunim k, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land o4 0m,(6sxkamndit en ;yku8 6pn the car or behind it?

Does the Earth reallz iy1hrc+ ko+ybj(r:1 y go around the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of theh1oz+kjc(:r1 yb +riy first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling 4r8:96 duoy4 orllw* k)jxa x,wjuczz 2 2,hfkat 0.5c away from a star, at what speed would the starlight pa)2cduxl4h 2u,l ,y46fo kj9k8wro zx* jwr:azss you?

The time dilation effect is sometimes expressed as “moving clocks run slowly.” Agq 6tc9zc ;u+xctuall9;+6q uxc cztgy, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actualza- s)dv4 :mkoly passes more slowly in moving referencem)dsz- kao :4v frames or that it only seems to pass more slowly?

A young-looking woman astr tdj0d8 vkqe)+onaut has just arrived home from a long trip. She rushes up to an old gray-haired man and )dkv8+tqe0j d 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, w/tb8(1f nrviwould you notice a change in your heartbeat? Would your mass, height, or/wfin bv(1t8r waistline change? What would observers on Earth using telescopes say about you?

Do time dilation andx/ kqllc 3k5b wfj/lxz 7ce*u7 tz(e*7 length contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happj;( az+o poy6zve awm7;/0gq oen to the relativistic predictions of length contraction and tim +w/;ao qy 06e jvzzg7am(o;poe dilation?

Discuss how our everyday lives would be different if the speed of light wer. 2xtuge rih0:zb;qc q. z4o,d4kzsl/ e only s; 4bzzqzo.ei. dl 0 c4hrq2x/tukg,:$25 \, \text{m/s}$.

Explain how the length contraction and time dilatn 4cwh;qgonz;,9 ot l9ion formulas might be used to indicate that; g4 9q;9nh,lozoc nwt c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tommmhe br.nzo v*q5;7 sqp vq698pkins, for whom the p r m 57 q.96b8*s;nqqvhvzeomspeed 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 than0 5 h 3)tjfbs;yrk+rej c. Does this put an upper limit on the momentum of an electron? If so, what is this uppe +e) r5 fkh0jjr;t3ybsr limit? If not, explain. ----待选择----yesno 

  Can a particle of no2e,l cmvp43m9 1hpots nzero rest mass attain the speed of light? ----待选择----yesno 

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

  If mass is a form of energy, does this mean that a spring has mogye:)yv cx,b;afe h, /re mass when compressed than wh,y x:fg ;ev/hbyace), en relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor des.. qctxxr +h:jtroyed." What +c.hx:trjq. xmust we say instead?

  Is our intuitive notion that velocities simply add, as w6,s tu p56nio+1skh ; px1irdme did in Section 3–8, completely6,ui6os1h5p +;1 dnt xmrsk ip wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750iz4cfznra9)) :b/ kq tc. You measure its length to be 28.2 m. How long wok)/ ac9:)n q4izbzfrt uld it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a spw 5u3nzi3 rpp2eed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals depend on thjm4oasn.da-37l) n p2 k)dbuqe 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 frj (rj ;-tv:.fe+vokm)7sih ht+bf+ghom 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 azwv(2im x4us2 pion 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 light-yea, rk0ha :9cp 0z: xnrw1aes+arrs away. How fast would you have to travel so that to you the1 cr,aea x:0z 9+ns0akrpw:r h distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 8-eltr99rh hfa/ x7-8 n;ctd e6x-ejdb5 light-years away at a speed that tells you the distance is only 25 lb ;xtret-8 r-/9- d hnel76edaf jhcx9ight-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 the Earths5*-j2fr i eea 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 h4 r/:l4b0heusc4by 3nfv .hhgad just returned from a 5-yea4rv4e/yu. :bg 0h c3n slhf4hbr voyage while traveling 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 5:pkvostn2jv kl:0v 8 spacecraft traveling 0.960c to reach that star from Earth, as measured by observerskotk25 s8pl:0nvj v:v :
(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 c6s/u l j25(gizvnfivqq27 i2speed of 0.660c. It is meaqu2sqli/( i 52vic zfg72 j6vnsured in 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 travel 158j7bqfkp h8 z z;l(nn1 m before it decays? The average lipzqlz;8b1hfn 8nk(7 jfetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proy-m ,q dc7)bcoton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice .wjw t+ p2jxzhoy3e5ui b1. m s37wey;its rest mass? v =    c

  A particle of rest mass xx; t89u ls/pf;ywnm ip3 7f3l$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels x67g)m58e b rqo4 iaz5bwaz4p 4aex a)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 proton th.dscr2s9:h (zot tya1at accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction ts odoc1ne: 3m361uij 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 restji5yi:tnv7k,+s- st b breaks apart in the process known as fission in a nuclear reactor, the resulting fragments hav5t:s -jivy bn7k,ist+ e 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 electron in joulb83,z8,wkdmqfh3n +tb av-cddoy/ n- es 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 of a proto gr l6f27;ka) ,sifgd vps4p,ujj j5*vn in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumplrrl j)y *r twu r((,izmbig8/f 1ly* dpv1h*.tion 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 conversionf8spccbwyh;fu 05 47h 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 zt 6,.y.jftkl(*pfnh kinetic energy equals its rest energy? v =fn6t,. j k(lt .pyzh*f    c

  At what speed will an object's kinetic7r1of a .yk+ ;l 0yyd+bs(yjqn energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate aj19 34hv.xpw-eqay qk j)o,mf proton from rest up to a speed of 0.997c? W = ky)ej,oam1x3 q4hpw-vjf9. q    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energ6 o51y gfc;myd*j csa-y and 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 (that is, 59 v0tdgv,c p /vgojx7its kinetic energy is 750 MeV)/dgj90v, vt gv cp5x7o?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelera5: non:uec 188pmtnhbted by a potential difference of 105 MV? venn bm:p8 n8 u5h1co:t =    c

  What is the speed of an electron whose kinetic energy isrn +u.sw70is/pei qs- 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television scree+orflv o(*mh oci 21(pn after being a ifo*m1h+oc v(olrp2( ccelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rei)62b eagrv/6 7ml5** /tzl jonadlfxst 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 protq/rs a3;kx0qh1x dp eh:9xk4uon ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momw(2ro 6+ cr 7bnp0fbz (*oxwuie*8spientum 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 27,000 kg is acceleraf:c7bhg3c1l 3oeq v :zted 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 ener -ty/ d-d+wsdqoe/g+o gy 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 nucleuej32hn9anca6a3 *w 8iu)raz ks, $^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

  An electron ($m_0 =9.11 \times 10^{-31} \, \text{kg}$) is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.60 \times 10^{-14} \, \text{J}$. Determine the electron's speed $v$. v =    c

Make a graph of the kinetic energy versus momentum for (a) a particle of npo*; y++cd.r f d gt*-sfv:vs0 +qjbvyonzero rest mass, and (b) ap+g*; :qd-v0bvf* .s+ +vo fjdycrtsy particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons(s a/t mr tvg-t343swo revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton/(t vtg33sw-4tomar s'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 3otbukm(w(239mout u 0.50c (with respect to the Earth) observes a meteor come fr2utu3o u3(tkmwm( 9bo om behind 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 direction/j mb(*k hl+ gxhqtvi-bj0*d,s, each with a speed of 0.50c with respect0 /d, hkv( m*-lqji+ghtjb* bx 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 traveling at 0.71c 0*yr yjaq0550ti* *ocoov ,yezmvr*d. A second spaceship leaves the first at a speed of 0.87c with respect ty0oy*tqmra*0cv,ji5 0*o *e ozvr5d yo 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 a;-qw m 1p upsk1phv))dn alien vessel approach 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 relative speed of one vessel as seen by the 1dk) hv m sqwp-);ppu1other? u =    c

  A spaceship in distress sends out two ,gsa(97 v xj jh/xxltwa11dn qm+bv;7 escape pods in opposite directions. One travels at a speed +ja1wl(q b1m9xxvg xt;ha 77,/sdjnv$v_1 =-0.60c$ 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 speg 7n-vpr3reohb 0gpudbz : 3f;tn;,b: ed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. Hv:pbo bdzue b gt:p; 73 gfn;rn3,0-rhow fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri,qv lvrh 9sj22* 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 about 0.1c is callizy3x xv *r+uc9gk4(m ed relativistic - i.e., for which the correction using sp+irgvx3c u4k( x9*mzyecial relativity is a significant effect. Determine the speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) ----待选择----relativistic not relativistic 

  (a) What is the speeyh7 i8 ru4,xutd $v$ 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 run a 100-W ligot(b0,rq.1z i:gcz kahtbulb., i:1gtza(r0qz kbco for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produtm0o(s hd(c ,( ly5z6lzku l4gce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite chayloszlzl50m6(4 ( ( dkg,cuth rge. (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 s in swcori*p8f o0x23;peed of light collides head on with a positive muon traveling at 50% the speed of light. Thfoc0ri 38*2i w;ospnx e 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,ioy8, u:3tla;ruqj+,n. so m u and a neutrino. Assume the neutrino's rest mj ,;trunm.+u oa83ls:ou ,qiyass 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 =    MeV

  The Sun radiates energy at a rate of ab dxnp85v( e0y33g sx yy*tqo;bout $4 \times 10^{26} \, \text{W}$.
(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 havee :pq*o-c+wve.)-virnki +uc 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 r7z6r+gu e ubt*-bi: khequired to break 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, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This eb-ru:t+bki6u*ze7h g nergy 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 travg;1mj uzdlcv:q1j u-0eling 110 km/h as compared to at rest? [Hint: use the binomial zl; -1mj u1dgq0v juc:expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laborateyf,t 0n q84tlbsx-+i ory, are moving toward e+t fs,i 4 enl8q0yb-xtach 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 particeb;lnxz/3 b: jbmrjd,8z3.ld u 77sdcle with 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 ,x1 t+oyekh.iand antimatter, achieving hoi1.kye+,x t 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 energy is gre+bl sd43jj s*fater than its rest massjs4 f3+jlbd*s $m_0c^2$ 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 lkm)n.be *2pa 99fhgican 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 does this fit with the idea that whenb)alkh .em 9i*fpg9n 2 he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydr2b. :2lu bq:(ayi/ wwqx(oticogen and one mole of oxygen react to form two moles of water, the energy released is 4 it2 ib qw(:2 aqby:lcxuwo/.(84 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical partj;jy uirl:z6yr/q,k :icles are created, traveling in opposite direy/kjyq uzr6:,: irj;lctions. 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 other particle? u =    c

  An astronaut on a spaceship traveling at 0wrrj+ ;mn/1zx,-/fd xzw;d at.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in 23 m1zd/ / jr-;wtma fxrdnxw +z,;in.
(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 sp- .74k-ki cxhk qmimjd.( bvyn2.bmz9aceship 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 the speed of thei 27imzk- 9kxcbj n4y.mq vmb(.-dhk. laser beam?

  A spaceship and its occupants have a total02h-ma ;muyqs pjt(b 7 mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, t pausbm;jt7m02y-h(q he 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 thjf z1zrgb))f w1 5;stde spaceship's kinetic energy? Compare with the total U.S. annual w 5 rzz)1t1s;)gjffbdenergy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to traveltstz h426b,c;iw t xq12+1odzdw6 khe to the vicinity of a star 6.0 light-years from Earth. Passenge+tq6t;e cwik6 d1,h sz1 d ht4xzow2b2rs 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 of a spring whose spring stiffness consta4qrf1oi (unx7k e-8etntru1oi-8e(qftnek 7 x4 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 mass l kvf 9hx./svmcp *g+2$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.