You are in a windowless car in an exceptionally sm-c7rgpxf8 wm+8;4ztg1e) o0kcvi o w sooth train moving at constant velocity. Is there any physical experiggpkcmw8 owec8i -;4v+r o0 1st )7zxfment 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 ligr , ss(yr-3le+rg+,/;*w j iis wwi)tim0uvekht when, out of the corner of your eye, you see the car beside you creep forward. Instinctive,si;j0iwr3 w-eyr sgkev tm(+is) +iu w lr/,*ly 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 opo 5yy4rol ts0 j)bd8-f a moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behy)0by 8j-tso5d l po4rind it?

Does the Earth really go around the Sun? Or is it also valid tih-)ww2;v gn-zxx8fg* yk1a so say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best y* snk f2v-g 1a)8-hzg;xwxiwreference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a sta0,zqx 7h k +4dpz.yxfxiw qj,9r, at what speed would the starlight pass you?9x.,w0 ifxy4 qqpxh, z dz+k7j

The time dilation effect is sehez0 17*:ior : pvhrfometimes expressed as “moving clocks run slowly.” Actually, this ef:7hr1:ei*epr hf oz0v fect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving referenc, 2e x6xfz3l;y*gnujk ge;u*k,3 l62zx fxny je frames or that it only seems to pass more slowly?

A young-looking woman astronaut has just a 3 )t zimwdmh:cs6,q:srrived 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 might this be po :hdcs:,s3)mt q imzw6ssible?

If you were traveling away from Earth at speed 0.5c, would yo ;wt-q5 .a9uady1fox ou notice a change in your heartbeat? Would your mass, height, or waistline change? What woaqof.-t5od w 1yx a;9uuld observers on Earth using telescopes say about you?

Do time dilation and length cn: tv382q mvdvontraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relat3a hjivxks2 a(hk1vdh2jr 9*(ivistic predictiorh321((hs*hxkk 9va2jd v ijans of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed ox.up9,t uicx9f light were only .x 9tx p9icuu,$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be qojmn2lv( /t wi;hom (cq23+pused to indicate that c is the limiting speed in th ( t+pcqlwomj(noq23h; m2/vie universe.

The drawing at the start of this Chapter shows the street as 0iw,r sz/4rzn2 w m.p6y yvbv/seen by Mr Tompkins, for whom the speed of yp0s2/v6wir/rz.z 4 wyn bvm, 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 tra4ws4x.4oxj w;u nh0fd vel at speeds less than c. Does this put an upper limit on the momenwjo4 04d 4.nx;suhxwftum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attainnfyt)dnnqwo:g7d4 h )45xvl+ 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 m,b bax*; ox:ern 9xp)kore mass when compressed than whp)e :9n;ba,*xxkrxoben relaxed? ----待选择----yesno 

It is not correct to say that "matter can tmt*1e. wuf q;3)ojnfneither be created nor destroyed." What must1otuj.t)e;fnq fm*3w we say instead?

  Is our intuitive notion that velocitiescnwx:lw 3-mbpz2m +te; ok*y ; simply add, as we did in Section 3–8, co lb2;opy-nmk: *t we;3wx +mzcmpletely wrong? ----待选择----yesno 

  A spaceship passes y a;xxd*nnq2yekm4 .s7 ou at a speed of 0.750c. You measure its length to be 28.2 m. How long would it be k ;7n.xm4qe2 sda y*xnwhen at rest? $L_0$ =    m

  A certain type of elementary particle travels atj6)vav xnhg ip.p;10jj++qe t 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 depend oml :lfy9;, gpuuf5gb1.min81ot+l osn 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 f u .3bc7s(9e0r fswghjjv-mbl w616pof $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime isjhh/(0dul9 d e 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 5i,foa0qi(r o 82 light-years away. How fast would you have o(r faqo ,ii05to travel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-year.ykktva(b h+4unvy0 o55a w 1vs away at a speed that tells you t0yk nw5 btvov5y.+u4v(ahak1he distance 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 thu ry- e9cm86eo .4zisc,2whbqe 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 starship Enterprise had ju3u7rb 5apb6z sz sz*,yst returned from a 5-year voyage while traveling at 0.84c. z7ya 5z,br36zb*pus s
(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 t w7 iee 7qy,.6m-qdbueake a spacecraft traveling 0.960c to reach that star from Earth, as measured by observers: qdqe w7ye,im 7e.-u6b
(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 tr,k(yl57 m;zkpj0k iher "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m l(zr0;tlk kp 5j7 mkyi,ong 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 1t of0serco+7 65 m before it decays? The average lifetime, at rest, is r6 +ctos7f0oe $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum x2-j/v7y+fa spx hde/of a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativiste:pu.j xh. s+dic mass be twice its rest mass? v =    c

  A particle of rest mass wb3t /1 mb*nk6z3nlcy;gcsu 7$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels jep n5 2tj0qn*zerz67 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 that ayskk+ xm 9((z(s/x il qt/9qyjccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction rzghq bx+. -*lp 0we2nwbxp;h1equires $4.82 \times 10^4 \, \text{J}$ 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 bre isx u/.nv lg(+-zjx7qaks apart in the process known as fission in a nuclear reactor, the resulting fragments havl-q/v+jg( zs.iu n7xxe 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 joules and5tm 3kbxps4xa1 ryz;4 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 o k g5bn mhkar2lwa 9*:f-h8t0qf a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Sd-:pp ag7r q)1ttv wbpa*r:c*tates 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 4x)5ckfzh1f3t(tw k nwn 5ra9 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 :nswn4df.:2(0 2z kx p)szc3llcjkmkits kinetic energy equals its rest energy? nx l:fkd)3w2ccn jz2k klzm0:p.4s s(v =    c

  At what speed will an object's kinetic energy be 25% j7o47h; k-7g)w at1mvij dqbyof its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a -+e3gds 7ty mwspeed of w d7gy-e3s+t m0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a pro h9+ topzqefpnd15e;5ton 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,:ss 1w 7di(hz;v6 vomg(las8i uw5 kc5 its kinetic energy is 750 MeV;og8 6s (1vli(swzicmdk57w sauv5h:)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of vcx;v l yzmf9k iop:ubwx.40v4:jm:+ 105 MV? v pwc:;9: fj kvli vo:vz bu0y x4m4+.mx=    c

  What is the speed of an electron 25*k csqce:nfrxv: t/whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television62 qv/madx2o plji* q4ete xq;k.(0cp screen after being accelerated from rest by the 25,000 V of the pictu0co k6* j t qq;dmxee4.qv/ (aplix2p2re tube? v =    c

Two identical particles of rest ml)i4na q q5bp5ass $m_0$ approach each other at equal and opposite speeds $v$. The collision is completely inelastic and results in a single particle at rest. What is the rest mass of the new particle? How much energy was lost in the collision? How much kinetic energy is lost in this collision?

  Calculate the speed of a proto 1ya- 6ya -9g-/l9 gzpysrlgjsn ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electr- v8rxbuo p.i6)uor6yon ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 a a3y15fibqr5*;qa3vaul + e b)i6qebkg 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 kineticqv ( w7ps bti8ap1 2zx)6sav/c 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 nucleus, sro6u qwl4o l06*c5zf$^{241}\text{Am}$, 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 +25qiom,r1n-uio *2ofl p);ch utxjx of nonzero rest mass, quf p+)oi tj noxi*1ul-2xr mh,2 o5;cand (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolvi6*zm+z1 e5ibwli1v ogng in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proti* +5mv1zb lie6gw1zoon'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) obseroi1xgyu1j6 50l* e xgqves a meteor come from behin*j o uxqgey 15lg0i16xd 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 directions, each with d;9h6 6 meerl lyprd3 tl3ik507o6cfra speed of 0.50c with respect to Earkc7plirh0de633llrt ydo 69er6f m ; 5th.
(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 seg.q fs: 3go;bw0g( umjcond spaceship leaves the first at a speed of 0.87c with respect to the fir3 ; gm:w.gfuq0j b(gsost. 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 sq/eacipg3h *9v/kau2/ n c8k bees an 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 a2*kkn ge/c/9vchqub38ap/i vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposs g ik +a. 26qf-g/lhfve(g5knite directions. One travels 2fe5sqni kagvg(h/-6kf l g+ .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 Earth8l3fld0 fxgt 7 at a speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving rel x7lft3lfgd0 8ative to A when it passes A? u' =    c

  The nearest star to Earkke*6p3 al qb6th is Proxima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveli0fgf /ox ao2s9ng faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogea09g2fxo fo/ sn 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 9r2+m*hy9:tpd;e8x1v x z zwlw jc2 cg$v$ 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 ligur4/bazvuf-u6rld+ 3* wziq vt 51yp4htbulb for 1 ye* p u6dia3t fvl+1q44vwzub-uyrr z5/ar? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed tebau ,;zp00qf6. 7rosshu jd6o produce an electron and a positron together? A positron is a particle with the same res, eo67 prs6;u z.b0 hfqasj0dut 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 colc+br*xxq k t 2tq5ti*7lides head on with a positive muon traveling at 50% the speed of light. The tw*2tqc7r 5k+x*ix bqtto 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,d1 t3yhqr 0yb20qrpj8vr: 1cz 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 decays at rej01r c2 r rz0q:d1 v8hypbyt3qst. KE =    MeV

  The Sun radiates energy at a rate of 0mexd)tf:. kq)jgs0e3z1 t vpt m+;gyabout $4 \times 10^{26} \, \text{W}$.
(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 havebtq)dclc7ii z+w 5l:w1,a/1 fhbij4c 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 helium nucleiz9,ft 9yb-u7b3tup eus 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, 1.008b97e-fuz,i ypu3t9t b67 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 (relafq*pd705: pldg q0v7glsd:e vtivistic) mass of a car traveling 110 km/h as compared to at rest? [:gd0 e v qg*pd7d5:lql pv70sfHint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving toxurih kr(/ r3v6 nj,by75:un+ suj+j ; whzba0ward each other. Dun7wjh0y6j n 3ujaiv ux+zr/ 5rk+b(r,: ;hbs etermine
(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 particloyd btb+*2 w s.x:iv;fe 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 and antie sd*i 4dyeq+y jqa4 6u8bo7e9matter, achieving com q y4+siyuqe a8b76*oe ded49jplete 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 i14ksw)d m+cij ts kinetic energy is greater than its rest majmdc 1s+)4wki ss $m_0c^2$ 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 physe jf2l)o( 6essics 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? Explain in detail. How does this fit with the idea that when he is running the barn looks efe6l2e(s) sjo ven 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 22al3kg z,jsjof water, the energy released is 484 kJ. How much does the mass of the elements decrease ins3, 2k2j gzjal 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, traveling in)jbz yqk h39(7ha za p2iv,0ie opposite directions. If the h i)ah i,3pj70zz(b k9eayvq2speed 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 *lipw8r bl in 74(so1cat 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch inr nb ci 781si*lplw(o4 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 spacesz.5t tmvql8am ., -boqhip 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 the ,5t q.. v-mmb8qtlazolaser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occupants wouy62 06:k xa k t*rt/xtqkshg1uld 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 x 1r2g6kxut/ka*kthy06 tsq: 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 the 2geisno5sj;3r1w.m r z4mdc8 mj -s8wspacesh3s5 n2w-reic8 ow.rmdzg 18;msm jsj4 ip's kinetic energy? Compare 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 -3eh wla;a im5to the vicinity of a star 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 work must be done onwl ;-iha a5em3 the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillate /p7m.x pa8kyns on the end of a spring whose spring stiffness constant 87/ nmp y.pkxais $k=48.7 \, \text{N/m}$. If this system is in a spaceship moving past Earth at 0.900c, what is its period of oscillation according to
(a) observers on the ship, T =    s
(b) observers on Earth? $T_{earth}$ =    s

A pi meson of rest m g r+(0pq8djgu7wffq. 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.