You are in a windowless car in an exceptionade.:;h il+ .:if tg6eguf 3 tyokzj.9hlly smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determinegff: +y3d9etohiz .ul h.keg j t.i6;: whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out:fafd1 x b1ad* 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. W ab*xdf f1d:a1hat does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throdb6)wh82ynvos q*sf , ws a heavy ball straight up (from his point of view). f qs6h v8dbsowy)*2n ,Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? O gowe,8de s+/ir 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.d,w 8s+/eei go

If you were on a spaceshipo u*ri/mgc1uh q+ p,3s traveling at 0.5c away from a star, at what speed would the starlight pass youp/c h1is* goqum ur3,+?

The time dilation effect is sometimes expressed as “moving clocks run slowly.w h5uwaop0 i5rp;w0 j:” Actually, this effect has nothing to do with motion affecting the functioh5w puwp0jwa:5io0r ;ning of clocks. What then does it deal with?

Does time dilation mean that time actually passes t c2+ftsppb xo15-tz. more slowly in moving reference fra1fztt 2pso pxb+-t5c.mes or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. Shez2z 7hlev)- n-t8/kjlu 85qkbpqwsw 0 rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this bk-w8q 8/ 0ulswv qljz z )hbkp27t5-ene possible?

If you were traveling away from dad*ek()mg: rEarth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using teles(: *grm kd)aedcopes say about you?

Do time dilation and length contraction occur) 9di: f2xbcbj w+jx+:3m2fcg xkpv k4 at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infgj g0/ :ydt4em vkyu,0inite. What would happen to the relativistic predictions of length contract:/ teu gvyg4km0d,0jyion and time dilation?

Discuss how our everyday lives would be different if the speed of light /zefm80tco6k were only/k60 o efztcm8 $25 \, \text{m/s}$.

Explain how the length contraction a.r .ny6zyoqycz7 9p)z nd time dilation formulas might be used to indicate that c is the limiting speed in t rc.y9p 7zz)6ynzq.y ohe universe.

The drawing at the start of this Chapter shows the street as sq; ,ub bhgd :dhgu+t;p3rv9e; een by Mr Tompkins, forhhpet v,:;bbqu ;g;du+d rg 39 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 less than c. 4/s 6bzvl +zdzDoes this put an upper limit on the momentum / +zz dvs4lzb6of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the spee;h a:2 u2,rrsod s(9pw9khadlst*aj (d 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 mass d a 9nw4- 7u)ejae+kzc+jf:cqwhen comprqzc+fuen+jac97a w -k4: )edjessed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither gsiefc4ojxvb )0flz( 3s: stp,j(k; .be created nor destroyed." What must we say instesfozv jxp si0jl4)f(c,steg;( 3:. kbad?

  Is our intuitive notion that velocities fz wezc,1gz5m7 nlo5)simply add, as we did in Section 3–8, com)oz zn175mzw, 5lc gefpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to z- u4duxxaalw .y7y5:j5y2s p be 28.2 m. How long would id7x . l:axwsuj 2uyp-yayz545 t be when at rest? $L_0$ =    m

  A certain type of elementary particle tj2aag rx*yvki-l ;9y/ ravels 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 intervalss s y 5:j2 9rxcv67+6nv9d uups.us)l;oyg eko depend 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 star 125 light-years from Ea.wb7cg2pqi i6 rth 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 lifetiopzc o k xk7* mpcp6p*h,4ah2*me 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, bxko3 9.pv clj 3ci8c3a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-year.ox9bikc 8lp v333cj cs? v =    c

  Suppose you decide to travel to a star 85 light-years away at ah(ysinr9/ ci;k0by z) speed that tells you the dis0 kns(/h9zyir)y ; cbitance 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 fromeyu,; q7h3itu pj*6 hw ,qa/wy4: cube the 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 just returned fr i3say zo1,/is9uko zd* 6dqwg54qvc6om a 5-year voyage whil1wyg 6,i6ik q4uood qsv9 cs5dz*3z/ae traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. H*bqs6sf; e+qw ow long would it take a spacecraft traveling 0.960c to reach that star from Earth, as mef sw;s b+q*qe6asured 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" spadmran-a4vyn:a0 :.l gfjd* *tcecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long-d nj rnl.f td0::my*a4gvaa* 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 x2tar y4gzc 2u) q*eh0bj+f0m15 m before it decays? The average lifetime, at rest*h0 bt2mjra4c yx f0zu+q2)eg, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of ixz)o7k+o h.r a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativi3as- pxl,7y+ rzz. abqstic mass be twice its rest mass? v =    c

  A particle of rest maszlm.k f 6u;-jblzi: za*u8tz4s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ak5:)ieui+sw+ pg0 bar t $v =0.10c$. 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 ttn5,:g9bor3)r:5xi4 m hzmzj s:c lp rhat accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiu ul+zobgjale/ +j 3(:res $4.82 \times 10^4 \, \text{J}$ 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 ap,x-mbb)f 9 7a jfxje0wart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of a70 9wfx)baj b ej,x-fmbout 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy a1g+m1ol1 qbz5g/wlqer7 wo:hhrt(*of an electron 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 proton*+n/v:up 0 ,vjd vvmkbed59dn in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United tizbi 4mqv4;3 wi :m6lStates 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 obtainev xne5eur05w+d 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 kinetic energy equals its r7tq 5e. 9m2efyw/glcxqe1qh,est energy? v =q5qx f2mlgt1yw/ eq, he c7e9.    c

  At what speed will an object's kinetic energy be 25% o (86/2omysw:ivi8xgml4zw u+i q uu+gf its rest energy? v =    c

  (a) How much work is required to accelerate a ri, sj-hk,pu znxp4*- proton from rest up to a speed of 0.997c? W *j ,n-4 -uirzpk ,xhps=    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kineti4r4xw7 tioy+vc energy and momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, kj2cv 1q/+oe6tabmh +its kinetic energy is 750 MeV)m +hj/k v6obc1ae+q2t ?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated b.1fr+ z o1f ijbbnjzji/ ;h 83oy)mzt y2ny4,xy a potential difference of 105 MV? v b1fjt 3m; n o.h jf8z2zi )iyyx4zjon+yrb1/, =    c

  What is the speed of an electron whose kind yup9.iahc(a hv xt5( e:9c+netic energy is 1.00 MeV? v =    c

  What is the speed of an electron jus 46l-iap wh2fxt before it hits a television screen after being accelerated from rest by the 25,0h- ap4l2xiw 6f00 V of the picture tube? v =    c

Two identical particles4sng)huzq a18r s-w*y 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 proton ,ma8pwiwze4 yk0* dym g/ c01a($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 a5w1 89ts:fy )ush; k)ibbkjnen electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 kg is accelerated to 0.21c. 0mfk 9l7/cs/ drlmb) h
(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 ++sxmg 2 b1apm*f+q7cez3pcs 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,o.-gfkh6 q(7k3 y.nwrl7a)wwkqclr2 $^{241}\text{Am}$, 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 parti*/vdx 8nla,f xcle of nonzero r x8dv*na, f/xlest mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to ke0b5/iray* u nlep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. Thenura5l /*0 ybi 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.e gs01rhyh l ); or;a)tw-q-ik50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. Howrhl)h-tk;r;iy o)-wea01 s gq fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, eachv.2oq*:dc : l k6j)yauriok8l with a speed of 0.50c witor: id)u8l 6l v:kcjkq*oa2.yh respect to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A b6*vd:ocou,0x j/b cssecond spaceship leaves the first at a speed of 0.87c w:vxj ub 6 sdc0cbo*/,oith 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 alien vessel approach at i3vd/7* vgxga gno46 wa speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by 73gw6vv in4 dga/go*x the other? u =    c

  A spaceship in distress sends out two escq lqn59x4qk olgb .4;tape pods in opposite directions. One trxo 4 ;qqkb594tllq.n gavels 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 time, rocket Bbxs)bt ,h* vl; p4 m.e1qt4iwv passes Earth moving 0.95c s*i,wm.b1)vpqve4; bx ttl 4h 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 Proxima Centauri, 4.3 light-years auh) u r2m-/tgaway.
(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 huuactdz2pq 7m1 p r0.ax ,+7l,homt0faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is aa,oh+ru,tl p p27amhu0t1cz7m dx 0.q 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 speeuil - oejnf3l vm,e0a(;7d5ocd $v$ 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 c fl2ym 31/qnw9(aaom6ksj jlnnw*-3 lightbulb for 1 ye(1 /n2jwka9mcnsl qfam on -3lw 3*j6yar? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electiiv 3:i,yb9)xk xd/g3df 7r ep/fufa+romagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposifkvfu + rp :i3eybf,7d x/9/ xgd3a)iite 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 33un2ixc 3 +e*z+w (vptq, z0swp% the speed of light collides head on with a positive muon tra2(v q w tcw3*xp+zisnez+, 0puveling at 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, ag7obyk5gp 42q4f.co r-. jaqmnd 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 neu4pfg qrm y bkag5. 7-.ocoq2j4tron decays at rest. KE =    MeV

  The Sun radiates energy aadvc.wd+.q /hn zc rsl1c8b 1:t a rate 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 to hpd oc85b3 v3qhave 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 :fseuit.l c/,jf6iw5x51d oj to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u,wfj/l ie65f,u5j1: tsdc.iox 1.00867 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 (relativistic) mass j/+e9xk79vqxlrr2ig r *8z rfof a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansionrfr r299qj z *l x7kv/i+xger8.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are mod no ekk0;.h+xz1y ;vpving toward each other. Detdzx.v+10 k ;kypnheo;ermine
(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 uuu076gk,m,snmhkf ;jo ( +ju7i2n ghwith momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtaine jvi*v2sazrh 2r57u (-cl1xb s its power by combining matter and antimatter, achieving complete conversion of mass into energy. If xzbsaurviljv 7re1 *hc52-2 (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 e;len xlcctmi+m-; /llnzq; 9 )qqu51unergy is greater than its rest massu5z qqqm;unnc;t;9 x+mel-)l /li1 cl $m_0c^2$ 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 t;)be9e:l w , tkr8uq25smoovimrypn:2p):n 15.0-m-long pole into a 12.0-m-long barn if he runs fastm: t);ek2sr8neo5 :2v 9oiyn,btwup): lr qmp 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 even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one(kzodr ckpc/ 77qj* u. mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the el jrquo c/7.d kz*(7pkcements 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 parun29udk rk/pirx*glmj26c 51 ly2z r-ticles are created, traveling in opposite directions. If the speed of/d r1n9zkx lilrgpkc6 2y-uj* 25rm2u each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earthvo he/- 84 qzo/tgosw, measures his ship to be 25 m long. On the ship, he eats his lunch in 2g4 q- 8we/hoov, stz/o3 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 Earthso732six1kwog8 m6lr . You send a laser beam toward the Earth travl gso m831owxs7 ik2r6eling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupantsgttvsi6xb e+v.6a gngv72y wn ch 932, have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 lighgci97gevbtt n vnw,+23.asv 6g2yx6ht-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 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.f 45r22, o1hy f,gz0w ogsemvn,yha )k What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption k my hghyn5a s f4z02ofr2 g,,o)1evw,(about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 6.0 light-years fa dt0q3ocr /*)lw f3lcrom 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 necessary for tow3l)d30cltaf q/rc * his trip? u =    c

  A 1.68-kg mass oscillates on the e th-o/ vg d6pbh+x-1y8r (aqqend of a spring whose spring stiffness constant ibth+8d -a(vo6y1q qex-g /hrp s $k=48.7 \, \text{N/m}$. 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 ma /xz,62ydmyqrss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.