You are in a windowless car qucw(dw- ) x,2cxwtq7z yh+0yin an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the w(-uqx,t2yq)0xczhy cww7d+ train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red/bh,;o utah/wh qc ggd0,+s-n 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 backward. What does this say about absolute and rel dh-tb,;+a,g/ hgqocusnw 0 /hative motion?

A worker stands on top of a moving railroad carf;izkkc j(k/a da5tc47 6s8ny, and throws a heavy ball straight up (from his point of view). Ignoring air resistnk8yt47(;5a jka 6kci /sd zcfance, will the ball land on the car or behind it?

Does the Earth realloql g:zr3 j17),ba3l o kcb+o1jvd3n qy go around the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss io koqblv 7go+cjr:jz1n l3b)1d,33a qn view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what spedp*t.p,6t n8z 1k ky2xg,kvdeed would the starlight pass you?e 2.tkt v kp,8,dxnp1k6zdg*y

The time dilation effect is sometimes expressed as “moving clocks run slo)cr3i hkt)ia5z vrj pp)-0*pxwly.” Actually, this effect has nothing to do wr-)i3 ziv )r5pjap)txc0 phk*ith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes morb+ v tojnw9w*-e slowly in moving reference frames or that it only seemswj -wvob+n*t9 to pass more slowly?

A young-looking woman astronaut s-wh t j-i 6i3unp2c;gns+zg)has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conver+j2g hniptcs)gsi6 -u;n-zw3 sation refers to him as her son. How might this be possible?

If you were traveling 4nythh p0nb1/r.tp; mf)09 w dx0kifyaway from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observenw. yyt0hmtrbp)/ 0knx4fp1hd0 i;f9rs on Earth using telescopes say about you?

Do time dilation and length contraction occur at oryuf, glmfp.gff. , n7+dinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the + /;i /0h;dzck atdy-4d znhk ja1;pmprelativistic predictions of length contraction and time dilathn 4kz/ ytzh;pdd;apj+ic/; kd-a0m 1ion?

Discuss how our everyday lives would be dp+ 0z:a rw*ibi4j3 +a3db gdctifferent if the speed of light were onldba z4w*d cabgt+r+p:3jii 03 y $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be uob5 iyevn gfd1s47zc* 21tf8csed to indicate that c isne s4 1c*57yz8if otgc2v fb1d the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tompki 79cs9x8qls rbns, for bxs89lc7 rs9qwhom 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 less than hfj .j(x.5hpu c. Does this put an upper limit on the momentum of an electron? If so, what isx(5 .fju.j phh this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero v ;eh;144cbl qetn 0gurest 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 u(zapy 4kvp81 spring has more mass when compressed than when(4zpvypuk 18a relaxed? ----待选择----yesno 

It is not correct to say that "matter can nei+zmrpnz72/)qq 2 wvosther be created nor destroyed." What must we say instead?pmwnvzs )zq7+2o qr2/

  Is our intuitive notion that velocities simply add, as we did in :c.) k t; 0)nnxipl2sd4ivbg lSection 3–8, comp4xni:;b gtvc2dl) nl 0s).ki pletely wrong? ----待选择----yesno 

  A spaceship passes you advcr+5w/v 2mat a speed of 0.750c. You measure its length to be 28.2 m. How long would it be when at restw25 cmvva+r /d? $L_0$ =    m

  A certain type of elementary particle travels at a 8mji ;nm+ww)h 1p;nuzspeed 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 the qgp + rp--f4smfactor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 li4fmp4q, vd.ikbt)kb 3 n:qih4 ie.e*hght-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 ikhb9-je d:c k kx:cv( g ,t:as-q5btj8f 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-years away. How fast wouldu*g(uf9 k -s)alhou +fjypn t48f *c5x you havef+ c*okup sfhug)(uyna48fl5xj - *9t to 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-years away at a speed w1m:ivx:x 8ldy 91qxkp(mn8x that tells you the distance is only 25 light-years. How man9m8x1x1:qxym v8(x: nkp wlidy 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 thx )43ev/pye ws /m6eage 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 j4e*uzwe.n,/ljld dq2ust returned from a 5-year voyage while traeuwq/l *4.zlj ,n d2edveling 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 awbcv-5ji; d z97f9db avay. How long would it take a spacecraft trave9 baf-;c iv7bd5 9zjvdling 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" spa y8;tmfxqx6z n/(n1z scecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. 6q1x8nt;sn(fzz xm/y
(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 pq5qh 8yl*1 az:piu s.it decays? The average lifetime, at rel:5 us8iqh.yqp* p za1st, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a v8qapi1pv-;4wn: kscmg x 6d /1l.ceu proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an objecty ec7n5n p-99vi6c( 8ql rz c,,xtckyp’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mas 9qwyx2bwuk(9y(;*rb if e 8rjs $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travev;moi6 rtx:m5r.dxl qi nxs q6/nd.7) 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 momenfa3h4qz r kx6hda/k +:tum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires* xev klry.+xtyn0)*k $4.82 \times 10^4 \, \text{J}$ 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 fissio1iwed4mab8hr 8 y9/gu n in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200b8w4 e9mhd18gur/y ia MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an ig.t).b:r oq2gb mvv9electron 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 mass of a protoz 4a4)4z dqxhrgu; b2dn in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Statebug62+(gw* lve rl7sm s 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 bhjp7n*lkenel ;, 01c de obtained from conversion 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 ki +.cwa4hg y8o31lwzbr netic energy equals its rest energy? v = 1hac gzy. blw+43row8   c

  At what speed will an object's kinetic energy be 25% of its rest energyq)(k qcgfyizf46)h7 y? v =    c

  (a) How much work is required to accelerate a proton n 2 hbsi eo(3i.n 7br,it6y+xqfrom rest up to a speed of 0.9 ro2 +s7 b.enyi,i(3btnx6ihq97c? 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 protxd1jizy)fjs :u9 y75ex2w 4ijon 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,,ziof9) 6djxgby 8s(6 hqum3vq +k6 tc its kinetic energy is 750 MeVmj )q3uyh6tv89 bc zgqf ,66 sxidok+()?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potg:npnlg/j q b frm )8lt6(0k.eential difference of 105 MV? v =lk gnl reb.pm:g(0fqj )n6t8/    c

  What is the speed of an electron whose kinetic energy is 1.00xq 8 l f6wf(t+cl srm36z;ace+ MeV? v =    c

  What is the speed of an electron just before it hits a television sd0lg/dcqq 1b zn:.o +ncreen after being accelerated frqdzcgn /:.o 01ln qdb+om rest by the 25,000 V of the picture tube? v =    c

Two identical particle;v6f81actlnb s 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 of a pro1zt 6cc1u vz2p m0 l1y*l7yvxoton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 elec sg e(raup;5p.tron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 accelera12eu ojd a23ow4fxwb 0ted 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 ofgv z6t,rk gu)d91d+cj 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 nucleu02t;rgl d4 ksts, $^{241}\text{Am}$, 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 on,ailf/d0.r mzae4w n )9ur,of nonzero rest mass, an,rlru zd. a4f/,n ewima )09ond (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV viux7 tvg5:bgzg6o5w7vyin z 8/xn6* protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's re*uxt6g y/z 7wgo85z:i g vvv65 xnbni7st 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) obsek e 5ka; d6js60tr2gjkrves a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respecta k06st6k;j52ekjr g d to the Earth? u =    c

  Two spaceships leave Earn-64w lofukotn/ e )c hj+;u g8blno,)th in opposite directions, each with a speed of 0.50c with respect to Earth. f4won l8e+u /cn) g o;,jl)ktun6-ohb
(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 the fiuwhkn0m.(w k 2ufy4 q-rst at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fi 4nkh.u f2wkqu( ymw-0red
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth see-iy2a :cf5wxuk0h) p,enxnw: s an alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Bf-e50a2kcx :n):i wx h,pwnyuelow), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends rs s ffu)1y(t s,2v oocdo cgi((,24qdout two escape pods in opposite directions. One travels at a ss,41s cf)u(2soqr gv(coo yitdf, 2d(peed $v_1 =-0.60c$ 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 time, rocket B pas 6.eaafwgodj xw37:0eses Earth moving 0. 0da3fjawg.w67 eo:ex95c 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 P f4wvwc l8 1tye2v-m)droxima 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 traveling faster than about qg .*6*ybzq h4hbzwh:0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine theq6*:yg*qbz4bh .zh wh 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 po/a ce6ua kj)-llw3 uh e7)s7$v$ 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 wofma3xk 5. xlgecut9:i2 4 hj*suld have to be totally destroyed to run a 100-W lightbulb for 1 yeaf x:49 xhimsk*.5 3u2ectlgjar? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is neede4 c6m 5xe-jpm;jk7 gwwd to produce an electron and a positron togethepjkww jc7gmx5 -m;46er? A positron is a particle with the same rest 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 c:gxqc- mk68lv;u uyt61 (ibejollides head on with a positive muon traveling uutm k-e8(c 16v:jxi gbl6;qyat 50% the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and j wbm y zvj+-ydz5l; bgu(5g-h5s d6-xa neutrino. Assume the neutrino's rest mass is zero, and th5ugd+y(g bmxy -d hlz6b-5 wsjz ;v5j-e 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 abouygv+iaf* :emn:q q +v1t $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a negative charge anp9 jo. 8r0l5u24akjki d s,j*voldi:k d 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 toejw ,.zuxdp5p f ;ui;7a bg24o 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 energy difference is called .z4 gpae2id u 5wxo,j;u7fp;bthe total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a cq7x(qj;0-b kkx p9uvw cys:1l6tjb 8d ar traveling 110 km/h as compared to at rest? [Hint: use the binomia- jct;d j:0(6x1ksl7k98qbquwy bp vxl expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the6i i gyh.p4v5a laboratory, are moving toward each oi a4h.gp 65yivther. 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 thatcjl m,nvh tr ;+xq274f a particle 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 andlxkfq 5dy5sga0/eig i5/95ze antimatter, achieving complete conversion of mass into energy. If the i5s/ky/e9 5f ggedzaxli5 5 0qmass 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 greater than its restw2p)y;hg79,u prt fig mai2; ),y9wgp f rgtuph7ss $m_0c^2$ 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 physicsh p s78eay(ek87l j*j6co ,trt 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 itp*l,ekt acr(t7sy6jo 7eh8j8? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form w5qkiiy ek0ffw4 :)+etwo moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this kf4w50)e yqfew:+ki ireaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
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 crychr0zg1hsgiq 691n l*7zo. k eated, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the labor 76 qon 11izhg9rgys lhc.k*z0atory 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 h 54 v y-i7foy)k6xuyrmeasures his ship to be 25 m long. On the ship, he huiy57vf 4)oyyrx - k6eats 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 spaceshbbbg5;t 6( x kmod 40l)3u vow,mhm,neip 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 kn)de ,mx4,hv bm o0l3b6(bw otmu5g; 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. The 9f(x1 spav9 khoccupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spac k1(x9vh9pasfeship 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/q2y0k1 fovly Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compak0o1ylfv/q 2y re 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 )h8afudm,ib l vx,*o (sa2-ejtravel to the vicinity of a star 6.0 light-years from Earth. Passengers)*lj8 hfi bm,-s,uaxv o de(a2 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 springqals b9,yga387 ma6 gsget0,e stiffness constant is lge8gbasg,yt s7qm3 9a,0 a6 e$k=48.7 \, \text{N/m}$. 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 bolq+y) u,v-lp9c+wlm uo.c *$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.