You are in a windowless car in an ex+.96czo fre wcceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are movineocf .r6w9 c+zg? Explain. ----待选择----yesno 

You might have had the experience of beingks.7tt 2d, *bo+ kjy +qtii,yl at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling bay d+ti2ti.o,,y j7ks tbk*ql+ckward. What does this say about absolute and relative motion?

A worker stands on top of a moving rail2g.w 0mhrs* klikm8 ;oroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball la8s.;l k0*2hmgmkiwo rnd on the car or behind it?

Does the Earth really go pa/h)jq c4-s j/lbdu 4around the Sun? Or is it also 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). Explain.lbju4/qa d-jps4 ) c/h

If you were on a spaceshipbmg o witu*8.; traveling at 0.5c away from a star, at what speed would the starlight pass you?iumo8b*w.g t;

The time dilation effect is .okp b phnc-x+. woaaz:e8k13 sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal wa. 3 1b+woax8c- zh:noe.ppkkith?

Does time dilation mean that time actually passes more slowly in moving refere41sg/4hrnt4p 3ruapx nce frames or that it4gntupp1/4 srr3x4h a only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a lse fxn pfkxy9ihvw0+xx/a0)2* :l w2oong trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. Hoa2xkwsxw 2 0*o0n:y/xle+p)f9v ixhfw might this be possible?

If you were traveling away from Earth n,8/9g(dchpxyf :yad:p*fman3 q x ak nph,.3at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or wanc pmdfp3aa: qyhgp.(,yf x*n:x8a3d, 9/ hnk istline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary spzbb 7k (b,y(meeeds, say $90 \, \text{km/h}$?

Suppose the speed of llsdkfcs;fu80;o7 qa4 ight were infinite. What would happen to the relativistic predictions of length contraction and time dilation?fac d; uo8lfqs; 047ks

Discuss how our everyday lives would be different pz ,m,k/jpjg2p02r 4unwu q:aif the speed of light were only qjk: na /ujpmzpp4 rwg,,2u20$25 \, \text{m/s}$.

Explain how the length contracdm6.bc e +x+ibtion and time dilation formulas might be used to indicate that c is the limiting speed in thebd .c6e xim+b+ universe.

The drawing at the start o (:0 8coxrsliq 2b9gmlg/sj9if this Chapter shows the street as seen by Mr Tompkins, for whom the speed of liossi 8/m2l i:j0g9x crb(ql9 gght is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Doe p *af;msvahjvu9 fd0y69cc ,(s this put an upper limit on the momentum of an electron? If so, what is this upper limit? *f0fp9 sa9hm6a vc(,j;u dycvIf not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of ligqy9ub) f ,yi7 y/q-ezps 8gl)kht? ----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 mass whm xgl2jl4a .7jen compressed than when relaxaml j.47l gxj2ed? ----待选择----yesno 

It is not correct to saq q7be dpxe;2+jc;5vpy that "matter can neither be created nor destroyed." What must we say instea;ec57p +d;peqqjb v 2xd?

  Is our intuitive notion that velocities simply add, as we did in Sectiobhrq1 *d(kv1ume/q p1ydi-z 9 n 3–8, completely wrongqzb/ yeprdk1(9h dvi1 u qm*1-? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be o7zyx 9rc ,,lk28.2 m. How long would it be when xzo9rl7 k, yc,at rest? $L_0$ =    m

  A certain type of elementary particle travels at a spl2 u8zjz tqnl4kwu7*0eed 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 1tv ygt46spe,z8x 3-zja(9pqtv6fd jon 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 frfiu-+9 qd/9 wbj n:qjie kk)v,om 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 average lifetime is measured hlt l4aya,(om y5 i)qrzbh m3/),8cza 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 s+np m1*fhlen5;b8om3 ) cwvbr3f7 bjframe, a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 ligh71fcl n)+ovmfp n8 msb *33 rwjh;eb5bt-years? v =    c

  Suppose you decide to travh5+dwfpk r y64w8)hqyk bd.:del to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to m 4by586pyk):dkqd+ wfhd wrh .ake 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 is)f l yjce,ezt2,u 2f9b $11.2 \times 10^3 \, \text{m/s}$. 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 just returned emq: 7khtl cqg0 w59y:-f zi8pfrom a 5-year voyage while tra l y:cw:-m9ip q7t50ezkhf8 qgveling 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-year fub+meocia467u9ngnpc6)y0s away. How long would it take a spacecraft traveling 0.960c to reach that star frneaic6u0ng c+ 9)puy mb4f 7o6om 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 0.660c. It in mu2m:py)a t(s measured in your frame to be 4.80 m long and 1u2 p m:natm()y.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 itrq: wdg+-/pz w,02b bm nt*mjd decays? The average lifetime, at rest, isdww pnqbm0+ mr:2g-d */ ,btzj $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum 3+r ;rwrvrdd z)wz1-(mtas. f of a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its : pzw/ot4nc rs8*jx a3i(nms5 rest mass? v =    c

  A particle of rest ma 9f gpqzfm*)gqf;w ,yqrs79/ tss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels e-sa(- v7vi+zdgxdd j;rot:;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 mom o* hw+utm4qh:l/f) ixo u4fs,entum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requ3xui -6rygom+ires $4.82 \times 10^4 \, \text{J}$ 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 fit/fkb14 (g:*acpf ip i3k0m8 s5d uxrcssion in a nuclear reactor, the resulting 1pm:g(5bpfxcfrdkca0ki 3 s8 u*/t4i 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 electron in joules and 2nrub*6q av 8zin $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a pp-p 2bn1o xlj(w5re h, wfn/8aroton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Uniteks,b8z iy, n,rd 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 conversgg40j u x1,6unv:2d p4,xvqfp/(apixyddfb4 ion 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 kinetic energy equals iofnrr 44c:sf6u6 b)m qts rest energy? v = rfn s :b4m46uf)6qroc   c

  At what speed will an object's kinetic energy be qyum )7m.ic;svw8y:e 25% of its rest energy? v =    c

  (a) How much work is required to acm ynb9 k;y7m*f.e qoyz.b jq24z7sc5t celerate a proton from rest up to a speed of 0.997c? W =k2zy7sbeyb;ynmo9* q7tfcz ..jqm4 5    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 protonme h3 sed9ae 0ivz,)2y2chy 1l traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetic energy is 750 up y+po0 mopln/yyj2v 3e*. ;fzy 1j,rMeVjlerpmf*o ;n1p0 y ,juo yz+y/py3v.2)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differen+g t0 dcc8m/mxce of 105 MV? v tgcmx8 /+0mdc=    c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v sy 4*ambb kp1* =    c

  What is the speed of an electron just beeblq;r6 v sfdj5wl1 g;a*g*98avf f;t fore it hits a television screen after being accelerated from rest by the 25,000 V of the picture fj 5glr;;; fegl*91 t*f8wd qbvs6 aavtube? v =    c

Two identical particles of rest 1j( l, wvcqobm.y((wtykc1 2fmass $m_0$ 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 pro g)y9/r 6 )/t3pg fbxljhlovj-ton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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/olk/3 .yy0ycgn k 9cc 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 27,0kpcf 8)19( azlf q9kohhc8*rv 00 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 of ama(6hnsiav+p5jwr rgk 5isk36 *0w 6x 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,bnn4 z1b7du0h $^{241}\text{Am}$, 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 k -tu4qaofs3q5inetic energy versus momentum for (a) a particle of nonzero rest mass, and (b) a 4fq5 soq3u-at particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV prq9+zjb8j8vxf otons revolving in a circle of radius 1.0 km jf +vzjq x9b88(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 (oo2n *pn8(-(umlsy tcwith respect to the Earth) observes a meteor come p(n( uso y co-l28*mtnfrom 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 leavei6k vg0b:0 nje 7krkc: Earth in opposite directions, each with a speed of 0.50c with respect to Ear ibk ergkkn:6j 70:vc0th.
(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 travxx0 t p v9a(a0ac:f7 2s8 nvsrlcj)ys8eling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with 7sy)p tv2c9a80fx:sax8n jvs(c lr0arespect 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 au2 cds4lfpn/d5 4dk 0 60h*kb rqyq kz:4gjq.gn alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overh4dkqz qcsyp4b05 rn*d dqgk/k24fgu6j 0 .:ltaking 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 distreu(zl-yjru(xke9 c d-mg,:,wfqpt 4l3ss sends out two escape pods in opposite directions. One trag(:3,9u tfzx-muqcp - wl 4ld (jk,eryvels 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 Earth at a speed of 0.75c. At the same time1qamuqku3sa w)9w4x1fqo0xzw9/x0 c, rocket B passes Earth moving 0.95c relative to Eawcusx1uo0q9fq kx9a aw 3 )q/z140xmwrth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Ea6 sgdw)j)8sb; e;tuhs rth 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 traveli ;rhvc:i.i(; tsamrm 6ng faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity i6 r;hrti mav;m .(ics:s 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 wbc3zq9cc8 n )6sq v/y$v$ 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 wou +/t:m(c agv o qf:q,+rhau3hxld have to be totally destroyed to run a 100-W lightbu:f+goh3t/a vq ( h, uac:mrq+xlb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to producr3m(v 5j)u zkyy4g 7oce 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 (zr jvy)4y35gc k7omuelectric 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 spz9v4by n zqz:)d odl25eed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest massny4d2: zzzbo5q )9l dv $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino. Assume the 4cz 5;8y*ink,i; 3jcia b jjshneutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the5bjyz *i4n 3ihj8; ;sk ,cajci total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about5 ox cww -w01x6(83 kslgdbwhd $4 \times 10^{26} \, \text{W}$.
(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 k3sc:/gpq4bv l*ps p;.+ wzbnto 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 hew are;gi, ;0mvhhs w:4lium 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 vw:a ; m 4e;rgh0h,iws4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of5z 4tmsh:;x2qhu*7fdyc 2s zsg7wzg) a car traveling 110 k4ugzzf qmw2c2 hd5t z7xssg7sy; :)*hm/h as compared to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c 3-fr m--x ;yk4uho*they.g axin the laboratory, are moving toward each othax gy*k4hyh.ef-m-r-;t 3x uoer. 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 a9u06mjmm(6* m yf he1 yl7omqz particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its ppos,ss-uhey4 irf 217 ower by combining matter and antimatter, achieviosfuh 7erss2,y p i-41ng 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 kiqw*;;h lo-nnm netic energy is greater than its rest m -o ;nqmn;l*hwass $m_0c^2$ 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 polc)pwg) fh no)d(d j2x,e into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does tcp,ox)whd)n2gf)j d( his 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 o tikp; fzb1 9z/kygal(.pe*. sne mole of oxygen react to form two moles of water, the energy released is ky;f*.p1pti . /sgbz lkz(e9a484 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 particles are created, traveling in opumzuh963 +m ,el zzvte5tk;9dposite directions. If the speed of each particle is 0.75c, d99vhz ,+m; tt63e mke uulz5zrelative 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 0.75c relative to Earth measurejf 2n 5yj i:-3paze)cgs his ship to be 25 m long. Onip y:jgc2fjn5 a3 -)ze the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. You senor p-wo/-mw -,ooy ynad066okd a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Eartp--a-w,oyooo w6yo k6d0n r m/h measure for the speed of the laser beam?

  A spaceship and its occqievu(9 l/ss 8upants have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, tv8i( q/u9lses 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 spn6 l am08uif+xaceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total f i0mu+6lan8x 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 vicini;z 4g0kxr 8x8h dw;bb 3f1dnakty 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 on the spaceship to bring it to the speed neces x;n 3b0k ;h8kadz8bfgr4 wxd1sary for this trip? u =    c

  A 1.68-kg mass oscillates 0bvn*6 f (wn dcrv)r.:jn m(i 5u ;xlvsx8r2wzon the end of a spring whose spring stiffness constant vwn :rr(l0z*bx2vx 8c. srn jn;uf5d6miw)(v 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 lhpw gb2dqy-,-lfnpi4dy* (+$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.