You are in a windowless car in an exceptioxfa;f /5vpfuix7o6 )s nally smooth train moving at constant velofv7a ;65f )p/isxo fxucity. Is there any physical experiment 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 light when,i35gtysc u/3 4j( 1.efyea jnl out of the corner of your eye, you see the car beside you creep forwardt3(cs/1f 5j.au3jigy le4 ney. Instinctively 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 of a moving rafnexyh*n 1kv+yo/ob.-(* wah ilroad car, and throws a heavy ball straighh1a*+xknwof- /vb h*yey( o.n t up (from his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around ,- w1,vgrs*hy)j cupvthe Sun? Or is it also valid to say that the Sun goes ar*p )1rvv g,u-c syh,wjound the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship travelinp 0kmm:o d0zlrg.00freh sm20g at 0.5c away from a star, at what speed would : p0mle kgdfr00m0s.mh2 o rz0the starlight pass you?

The time dilation efnwu)sg/svkdb-9ls o*r8 u b; 7(r2bcmfect is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting thgln72;9k(r -vb/ r8 dosumuscbw*bs) e functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passxhvi 9 wmu5)h9es more slowly in moving reference frames or that it only seems to pass mmu9iv 5whhx9 )ore slowly?

A young-looking woman astronaut has just arrived home from a long trip. Sz6 x25goi9 ;fdth0 r9tlmqz f4he rushes up to an old gray-haired man and in thfz0i9t6fmxo5zr;h9t qd 42 gle ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Eart:rj xeg1h-07a1qtsqth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observerx0-hq rj1q1etg7s: ats on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds,f r7yp )9p4wia say $90 \, \text{km/h}$?

Suppose the speed of lr6*as0mcqrr,fuy)ll, 7 fas 6ight were infinite. What would happen to the relativistic predictions of length contraction and time dilationl7fa lur6) ,sry f*cqamrs ,60?

Discuss how our everyday lives would be different ifk 7ptrsb56a2 gm3i km1 the speed of light were only3m pkg216irsa7bk5 mt $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formu 6y ;s1shiu tpj,:eyn8g5hagx6g*er1l,n8 g dlas might be used to indicate that c is the limiting speed in the un;erggj ,hssx5ig*,yt1yg 86n8n eu: 1dp6h laiverse.

The drawing at the start of this Chapter shows thcvs xcwn6s04.wx9vp pifp: t- 08e ty1e street as seen by Mr Tompkins, for whom the speed of e 0.pc s:y 4wp6 ftvcniwx9vt1-xs8p0light 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. Does thi rd)xvj )m2ue mrx.v8vrc4+z+ s put an upper limit on the momentum of aj4x+ve cxzm2 8)rm)drvvru+. n electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the sp019x zymbzc 5jan 1k*n;q0slw eed 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 edoc3nm y*3wv.s a9pvo7vif3* sfafl 1 z06h+cnergy, does this mean that a spring has more mass when compress*aw 3vnva7i.s3 mz0yofpcsv 3 o6ch 9*ffd+l1ed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can nei 2au7c)5 di o+iovzhzxn):zt: ther be created nor destroyed." What must z)ozi:i nzv+5 uh7tc 2ao:)xd we say instead?

  Is our intuitive notion that velocities simply add, as we bglpjpx8; v.1-k, pmu did in Section 3–8, completel8,kp;u g1 pjlx vm.b-py wrong? ----待选择----yesno 

  A spaceship passes you ;) 9bc7rt6qf t .oqengat a speed of 0.750c. You measure its length to be 28.2 m. How long would it be when at rest qnt;7 qbo g.9r6fe)tc? $L_0$ =    m

  A certain type of elemen9jzf7+ry 6kd ntary particle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intewo/1x.ts0bgt2n/do p vv6mf/ rvals 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-year ixq.. ou(rbu:n5n a8xs from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime is measured to be cto:2nzyy(eb-d m*w7$4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light7jaaemn699c c -years away. How fast would you have to travel so c9n 7ja6mc9ea 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 speedun +u9t.vt+i/v7 tp xy that tells you the dinxv+u tpiv7.y+tt /u9 stance is only 25 light-years. How many years would it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the Earhe-3swi9d 6c n:oq f1 ids7y)rth 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 had5 r01 *rhiynqrc ;,.7vsa iypo just returned from a 5-year voyage while traveling at 0..yr70i r1vcs5pr;o n,aiqhy *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.ucp4cu/1a0vbk zaw :6 6 light-years away. How long would it take a spacecraft traveling 0.960c to reach tkv4 z6buac :p/w0ua 1chat 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 "Ferrarv gm.fup;m 9h3iw i)q5i" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m lq5mupm)higv9if . ;3 wong 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 h)c.j(xfm 4ld *hxr+a 15 m before it decays? The average lifetime, at) m4a cjxhf(x+hdr .*l rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton; nwpv1ku8v3 oejk 8+*b :zw; wmgmz2m 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 ressbe- obp8 n.)c s6ya1 dbbd-,tt mass? v =    c

  A particle of rest masf ,q n:qv.tes3s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels aqdg,p,(yxr,4av g qd /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 chana)hwm jhvks8u6s84v - ge in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requireq(+fv - yq-)w1mcwq dls $4.82 \times 10^4 \, \text{J}$ 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 re 8ic2g a0huz8pst breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a higp2 ca8zu80total 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 in)y fg*bb4)n x0st-kn d $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass ofve6zqx7ieuia9cd )c598ll ,p a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United State jsjt(jw0l,)yqf) bmd:g8 j*e dp* a0js 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 convfy +fa1cgbj3fg d,6u9ersion 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 enerky2mhx; 9;k *vhkptdd pw-+7y gy equals its rest energy? v =k;ht -wkx +;dv 9d hyym*p2pk7    c

  At what speed will an object's kinetic elhd zp;2 2nvhuog 1s* y-/7tw*w6ulyenergy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from r,1p 62qwrfl+mq g+8ec1z ri jaest up to a speed of 0.997c? q1pqragclre62, m+ j iw81f +zW =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energti 7: 5hjufw3,ol*ttt y 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 (thatrndblsp4onm6;+5h 0 b is, its kinetic energy is 750 MeVm d4h5orbs ;nbl p0+n6)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential diffe p/o*,h *i n-py+ wew:zau;oglrence of 105 MV? v =/hzo+p ui*a py:eo;*-l wngw,    c

  What is the speed of an electron whose kinetkq t)81k7qf w:;uwl vwic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it :vxr rs7 b9n2;bc q1ikwo:rh6hits a television screen after bei hs2xkb:bciwrn; r rv16 q:97ong accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest m-aa1yec;iedka 0(ko gp6r: e. ass $m_0$ 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 protom5f ,8wx x+i 0bdmh(hvn ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electron (k s /u,dzf3h2r$m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass qy2-r+ h svqd/27,000 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 kineti p27 lvum csj4h-i,l*ec 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 nucleusv ly p*ngr/j)ll3k7z1, $^{241}\text{Am}$, 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 mo +fhe,s kqj(c,ibd 6k:mentum for (a) a particle of nonzero kj:b6+,fc s(qie khd,rest mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to k8sl)q 1:lo 7ppetac r;eep 998-GeV protons revolving in a circle of radius 1.0 km (at, saa o18tpslc: lqe ;)7rpy, 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 0.50cv d/3 8yjqf*pr- +lqlk (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving wi- /rvf+k*8 dp3jlqyq lth respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a s w948+4zxh i+,qoa bfbl+z nkqpeed of 0.50c with respect to Earth+zkhf 4o,n+xi zwab9bl8 + q4q.
(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 firstsa1x 1i 43r -z+n5q1kjrkug hp at a speed of 0.87c with respect to the f p-3 1z1xr4saknghu qk1i+j5r irst. 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 n3k 6,8mc*vutkqnpfy+ip na3w x1/p9 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 vessel as seen by the otpn8 3m61nakpcqynf/ p k9wt3vu i, +*xher? u =    c

  A spaceship in distress sends out twollk.tgyxg* kl34(+w*zzla 9v escape pods in opposite directions. One travels at (.wxl3*ly +zazgg 4l kvtl9*ka 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 B pjt my zj-ye,+7asses Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it pae,-7jyjz y t+msses A? u' =    c

  The nearest star to Earth is Proxima Centaurm s.2ob,kyboj25q:vbu ft c yk78l6:bi, 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 fasejwkw68pgjjf xx169r+ch22 i ter than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determwf8e2ix9j2 6+ k61gr ph wjcxjine 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 dnfdum.qg*7 ,$v$ 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 de.demy ;e;q6wostroyed to run a 100-W lightbulb e;qo 6em;d.yw for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagneti6* i;x eadgr4b ilyb)y2x2 s:hc energy is needed to produce an electron and a positron together? A posit2i2: xhlg r4bi;*y 6ysxd)abe ron 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 collides hes+2t nuioncgjh 1f// 1ad on with a positive muon traveling at 50% the speed of t/on+11 uj nfihg s2c/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 intgq ibncu6 ker .)955lko a proton, an electron, and a neutrino. Assume the neutr9.5)lkkr5 i nueb6 cgqino'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 rest. KE =    MeV

  The Sun radiates energy at a rate of a0l9 f5 jscg4hmrs 6-ulbout $4 \times 10^{26} \, \text{W}$.
(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 and a spee pkffl)x -*c-.x,fqqq d 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 heliept:8re wm -3e5d (fbxp(a +rmum nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an e(5(mt 3wpe epa+fxdmb8 rr:-e lectron), a neutron, and helium are, respectively, 1.00783 u, 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 percentagb d hoix)*si;i.1eqs;e increase in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use ido1qe i. s;sib;h)* xthe 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 , dvs70t ow-2mx2ezhkmoving toward each otwh,m okdt70-ezv 2s2xher. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle wrttp 4 5/1nidotvvd+6ith 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 antia+m1ok 2 j)y1cd1mz bfmatter, achieving complete conversion of mass into enej2 obz) f1ma1ky+mdc1 rgy. If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energy is greater than i -m8bxkyp/n6rts rest ma8mr6-k yb /npxss $m_0c^2$ 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 poleg5rs +9;c j 8jy)azll98grsdpcuu,z2 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 la,ydj j8+rlrsg uuc g9;2)8zclp z9s 5ooks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen rfqph4pel2 9gp f-0f; seact to form two moles of water, the energy rele fqffp0 -4ge9;shl2ppased is 484 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 identi:a,1itgzgi0fa qoz2f p6*x;ocal particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other paif g20a6xf*i,o pz1:otgq;z article? u =    c

  An astronaut on a spaceship /uo0k, *2pxrkqz(glr traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch irq,*g kp k/(zx2rul0on 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 of3cfcy 5dul52 zsw:pi2 0.85c away from Earth. You send a laser beam toward the Eayf3wuc2c2 p5:islzd5rth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000zqgfnqz 1i-087p;i6jabv- s b kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceshi1n7pzjvz- ;6s qabb0- 8qfi gip 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 lef-tze6xu0i5 g*a.qz fq t Earth at a speed of 0.99c. What is the spaceship's kinq5g. i xzzeq*f-a06u tetic 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 to th0at,xxzp 5v4,ta ck 7le 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 on the spaceship z vatx475ktla,0,p c xto bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates o41d/s r u : jclu)nfuf,fbm l kw8xth)(5cl*6tn the end of a spring whose spring stiffness constant irf us ):4t d)cxfbwjlt*,fc/1(u lum8h65kn ls $k=48.7 \, \text{N/m}$. 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+ )+imuq bd5rzss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.