You are in a windowless car in an exceptionally smooth ;k0z2 fcpg q) 7ykz-nkx.f sr7k*0irktrain moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are m -igysr k0*c x kfzkknf;20.7 7pzkrq)oving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, ou*zz9c p5-n) uecndjw7x4lw9b t of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that yowzdl99cn*4 n-u wc )zex7jp5 bu are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving rai9xz *8- ovnew ;vs.pcllroad car, and throws a heavy ball straight up (from his point of viewsex9 8wvl o.z;vp n*-c). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it negqq12ee: ue4,7tme7lk)ac7rul n 2also valid to say that the Sun goesq7n emr1el27k :nqelu7)e tcau2,eg4 around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceshz b *:hiks vbk;b551c(xkrq- sip traveling at 0.5c away from a star, at what speed would the starlight passb kqi1c5:xvhbr(kb *5z-s ;ks you?

The time dilation effect is sometimes expressed as “m sds87-+a:drrczzc1xp,mg ; i q )2xtcoving clocks run slowly.” Actually, this effect has nothing to do wxxc:7c+q gz1mp r);cidst- dr2 8,zsa ith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving ; gsqw31cn; ut 3w*:ikauca/xreference frames orwq;k3:au/i nu;cxc *g t3was 1 that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home froml gvclo 0sb,9 ,hy+ig) a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this 9ibvl g sgc ,l,0)h+oybe possible?

If you were traveling away from Earth +nl5g5bi xlwact* )n5at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Ea5gln5t*ic nl)+ w 5xabrth using telescopes say about you?

Do time dilation and length contraction occur at.;xf+q4gxyn eh) d r7i ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relati mzqsi.cmykzj1 4t6bqu) ,7*vvistic predictions of length con *cz4sij1q7zbk tv)y m6mu.,qtraction and time dilation?

Discuss how our everyday lives would be different if the speed of light were o ,nzcuc2 ;0 c8bcf/th4q 1ld8chu qv.nnly 8nu4cbhvc 82f /qcc .,nd;z ch1qu0lt$25 \, \text{m/s}$.

Explain how the length contraction and time dil0e k3.b gh0 lrx7,opjdation formulas might be used to indicatrh7,d 0b x0lgkopje.3e that c is the limiting speed in the universe.

The drawing at the start of this Chapter 8.u jiji;tn(r shows the street as seen by Mr Tompkins,ujtr ji(8 ;in. for whom the speed 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 les4z g/.ed(vgb9 e+o rcmc18wcf s than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not, explain.g er1d/v.f(94w8z+ec b omgcc ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speeotlvw/o.- q .q f7o0cp5l/v nvd 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 more manj2 ,sf0uo5f htqjrm5*0 h.fdss when compressed than .m0qhfh uj 5sd0nj f*2t rf5o,when relaxed? ----待选择----yesno 

It is not correct to say that "matter kzua,(/ iei3qcan neither be created nor destroyed." What must we say i ( z/,equi3aiknstead?

  Is our intuitive notion that vels(cef3uoaq3 sd ,+ 6dyocities simply add, as we did in Section 3–8, completely wrong sc6u+fas3d y,dq3(e o? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its lengtevo-s-9 3jt6m j+nqtj h to be 28.2 m. How long would it be t nte 369o+sq-v-mjjj when at rest? $L_0$ =    m

  A certain type of elementary particlg3 vf rzfue 2d;a44m5kuj +.rqe travels 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 dependauc ,xw,t2,wru0 pe3 n 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:oyqovn)n8 ; t star 125 light-years from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its av 1 -/*xmayuo:q9bunca *jvv(herage 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-years away. e+k u3n0i8)temfnd -jfrjyulwm 6v ms 52b562How fast would you have to travel so that to you the distance would be only 3 )rb0 m6 8f 6lyfnvee22tmjus+wmdn-u5i35jk 5 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a s + t0oyn ze2tkn*3bgb;peed that tells you the distancezg0yo *n;t+ 3bbnk2t e is 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 the Earth lqx2j.9rxs x )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 tw*n)dd1)p4kao 4ksjq u9 j6g ehat starship Enterprise had just returned from a 5-year voyage while travel ne14q*6ps4kw)jkg uadoj) 9ding 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 worv, f :1lnu fd557hsnruld it take a spacecraft travelingr15r,f slud5:7nvh nf 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 her "Ferrari" spacecraft at a speed of 0.660cea-(xa 5fxhs4 d7xaqwd6*ds+. It is measured in your frame tow-e qax5*7h ass(4d fdd+6xa 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 movwowae -0)m 8e4-cape iing to travel 15 m before it decays? The averagapo- 8e0em-)4i ew wcae lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a prsl+ xgc9+cm: xoton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will axz7a vo,6(+t/fcwp p ;9 ua ldsh9wpr9n object’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mass ;m ,utqnw*h,vo x1s*s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave d)k6 bwrmg232zhx st*ls 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 o-* pbxmt) +zcef a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires+ym :ahj* n.ux $4.82 \times 10^4 \, \text{J}$ 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 proceqxr.dqvp7 1+yfz j:mj7z /*lw ss known as fission in a nuclea+d f7w z:7qrj jzxvmy*l. pq1/r 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 elect+9m*qp n+e cumron 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 mqr :v7rqpi,)- f dguq1ass of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy co 5 kvthzu9bl33nsumption 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 of mass? g+j ej;mao)i)-zm.pat m27 /xrlh/ zd    $ \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 p2+o 4bx0qiovvi; a+3eo lks.aarticle when its kinetic energy equals its rest energy? v =b3s4ex;v o 2lvq i0+oa+o.kia    c

  At what speed will an object' )zwlt6v(-of js kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from r56 g,okoogmd 70m u4mlest up to a speed of 0.997c? okog5 m,oldm0m7gu 46W =    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 travelnlr mzg*3 w(t3ing $2.60 \times 10^8 \, \text{m/s}$.
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 kinetic energy ikkqbui.pj8,y +f+q6k im:. me98m kans 750 MeV)? ayqkq8k:+puk km.i 9fm6 j+. mb,ne i8   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 1cfq1)dv;w 0wf /ci;yi05 MV? vi1/c)c fw0; d;fqwvyi =    c

  What is the speed of an electron whose j -lbfp4e2b ejc3+hf/g+ perwn 70pu1kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits au7; e 2i5ec ,d.yqvbkz television screen after being accelerated fro7qvzk ecd.2;u,5ei ybm rest by the 25,000 V of the picture tube? v =    c

Two identical particles hyd+fie6.n yq;-; *-kdbywz d 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 nww).mw. ht6z,naf/cl a8+g i of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 ez3 hu1u0-rghajp2 8u llectron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,nay:;0,x:w9en e xu :l rmwzz2000 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 ene yvdcofa5 *se479:n vumn 7(vprgy 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 nucleus, b 1bl.h jzy4,zhx4b.j$^{241}\text{Am}$, 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 mv d7yxjb x1.hmqc(/s6e1ku7 lv2t0 a qomentum for (a) a particle of nonzero rest mass, and (b) a partjvsb qqma 721cv1.x7 kldu(y6e0xt /hicle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revox r; vtf.:,q vzd,pwagh,k349t rdj;llving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic : f,axrk p t3,rvg.4td;,;w9zvh q ldjmass. 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 n5+gugg); ham Earth) observes 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 E m+ga )5ggu;nharth? u =    c

  Two spaceships leave3k q6+fbkvmx 1txt1hsy*i a:: Earth in opposite directions, each with a speed of 0.50c with respect to Earmkf3xisb:t k1 xay 6*1q hv+t:th.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A second spaceship leaves the9vq*ybl/r.srdd wh,. first at a sdhl,r . yq*./rsvw db9peed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an n2/xcgrv+d;i/p 5(cf2v zb3;hlw qa xalien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while movin(gc/fhv 23 p+;c/rba2linzx 5d x;wqvg directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in qxycx; onq12 12 a *ndah/1p+i1nrg rzopposite directions. One travelsnp2ydz/1q rrn1xco 1x1ig a2* a+nhq ; 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 Earth5 xed 6i9- (tnmwm( 9mcb;,f0sipvixe at a speed of 0.75c. At the same time, rocket B passes Earth mo9(i9 ,m5i;vdmp be0fcxwsm en(-tx i6ving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proximpxnqe97tkpu:l. u2r 0 yqsm) 3a 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, anyny9jen0-cerfbi ni. 6 6qem4d (n gz22thing traveling faster than about 0.1c is called relativistic - i.e., for which the correcticed6g.(62n9zeb n4y j- qiiem 0r2f nnon using special 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 speed 38h+vbxts-0l xf2(1jyisc c c$v$ 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 woujk9lrk: eop:*wrp x2/ld have to be totally destroyed to run a 100-W lightbulb fo:p r29o*kw ejp: /xklrr 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed t ykwcui.ik3xcp2;u ( *o produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, ik*u wc cp.i;uy2(x3k 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 on with a -yeo-c4-b3p8 swqx cepositive muon traveling at 50% the speed of light. The two muons (each of re 8cyw3x--ee pcqsb-o4st mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can deca3n:vi11xjz anumz ul, tw0/ +by into a proton, an 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 the total kinetic energy shared among the three particles when a neutron ,:zm0 nuziv w1tx/ lu3+ab1jn decays at rest. KE =    MeV

  The Sun radiates energy at a nbykcz):/ d/9 zeqv9wbh /g769zsdv 4 rnpro 0rate 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 measured 31b rmy 11lruxto 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 break a hehhx3 qgd;w-we/q8w4(hfy1qa lium 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.3-4w1f a x w/dqq8hwqg;yehh( (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a car travelinggtaj.77 r. y,+i8ju vd7fjoac 110 km/h as 7i+ u,jda rjv8ycj7ogt.a7.fcompared 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 thfpfr56j zpz3 (tc6 lt8e laboratory, are moving toward each oth8fptpf6zt z3(cjr65l er. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle with momez6(wxnxoo. ef.*z * ayntum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power r5ug 1ff3ov+z by combining matter and antimatter, achie g1zfu5r of+3vving 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 ene zvy7/zbu)9iwk1 xz+g rgy is greater than its rest m9u/y w 1zbgi+z7k)vzxass $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-long pa5(c e0jnye ox0ry 6w*ole 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 when he is running the barn looknw yj0a*c06ry ex eo(5s 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 mnk1v vrv v943boles of water, the energy released is 484 b v493v1v knvrkJ. 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 particles are created, travelingj*9er :, ovqcn in opposite directions. If the speed of each particle is 0.75c, relatq,*: cveojnr9 ive to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceshipf)64 (d6u2llb tndi4lc4/pfl l dl 9rz traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eatun(4lzpll46 9l26l)fd4 r dd/ cfiblts 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 / j+ 2b0)hla(qjq d3asdsw(ag speed of 0.85c away from Earth. You send a laser beam toward3a hs )/ ddgjj+0b(qwsqaa2( l 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. T5syox1 ;pefx 8; 2,aymoqq z1mhe 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 to2,e11xx8momy;az5; ps fq q yo 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 aeu p3 /m:a*4-izmk g .irsws)ht a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual rmz-:pim 3u w.k s/h)asg 4ei*energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to traf sts 1oal 5lj*.q vnnlp(+nq;04mw;evel to the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip * 0me f4olnvtls jnq na (+5wp.s;l1q;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 stiuyg2jz5hlw5o m 98bky *xxk 70ffness constant is lm79k*y 0w5j kh 28yxu5obxzg $k=48.7 \, \text{N/m}$. 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 massf(p wiv nzxl;tn 3t.y-u,6z7r $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.