You are in a windowless car in an exceptionally smooth tra7amqm- fy9o:q,unlt9 in moving at constant velocity. Is there any physical experiment you can do in the train car to determinlty:- aqqmuf, n9 m9o7e whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of the corne + um /r;iubsng18en9qr of your eye, you see the car beside you creep forward. Instinctively you s/u91egms r;q+ i b8nnutomp 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 railroad u9dty9s( rc i-car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or y9iudsc 9-t (rbehind it?

Does the Earth really go around the Sun? Or is it also valid t/u8b qu9x2lhao say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). a8 b2 u9l/xhuqExplain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed wou :ko3 yy2ou w9n-(iuzin y2-3iyu9(ko u: izowld the starlight pass you?

The time dilation effect is sometimes expressed ots r 1+tkq6ipu 2*66uud1hj gas “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the u 6u ost16u 6h1+r dg2ji*pktqfunctioning of clocks. What then does it deal with?

Does time dilation mean that time actually pashkal 9.nj2 u3eses more slowly in moving reference frames or that it only 9 2ejaknl.u3h seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a longilmey73 k+ dzb0ade-7 trip. She rushes up to an old grek y70mdaelzb-d+ 7i3ay-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you n1 vsp2j.vd2se(nu0pnotice a change in your heartbeap2u1dnj( p v2se0s.vnt? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contqo9 kp-3v-l+lu idl5yvz lsx6j v7:v+raction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light werz +f6 nt jrtk8i2hrj((eq-j.ue infinite. What would happen to the relativistic predictions of length contraction and time dr k zq.n2f(jjji6tethu-( r8+ilation?

Discuss how our everyday lives would be different if the speedb 2q56s.ahsw i of light were onl5w.26ssqi hab y $25 \, \text{m/s}$.

Explain how the length contraction and time kpwheoq8 v s: h5-;br5dilation formulas might be used to indicate that c is the limiting speed in ther ehs5;wqko:8- 5vh bp universe.

The drawing at the start of this Chapter shows the street as seen by Mrbv8uxmw:z-de fblh31 :2i3gh Tompkins, for whom the s:- fmz w3xe3vlh8b2gd 1u:ih bpeed 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. r4zvfha3l5x: myy)r .Does this put an upper limit on the momentum of a). :fr3z4 yayxmvl 5hrn electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzeriapk*oy qj-/ m9msj j-.:w4 hgo rest 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 spring hr+w. xt18yqcg 0wur,t l fe2a*as more mass when comp w*8f,q.xut2lcr tywarg + e10ressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created l2nk 44crii9m nor destroyed." Whatr9lmin cik424 must we say instead?

  Is our intuitive notion that velox0u: -34. ihlrho 1erbk6kjpmlnw,.l cities simply add, as we did in Section 3–8, cojb-por le mhlw1xkl 0.k,h43r 6nui.:mpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to b :ru15xegd .qne 28.2 mnd5e:ru.gx 1q. How long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speedv djwar9c/jh6ugt:96:mo7 hs 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 intervalse*sv 8 *g2eojj 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 light4e,uixlce w4 8-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 if its average*dq*(lly(x(nl lrs j4 0z+stu -hqrx; 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 uks ;z;y07i bm82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-yi;s7m;zkub0y ears? v =    c

  Suppose you decide to zki(6n s84 gmdteuc 3awxm988travel to a star 85 light-years away at a speed that tells es4g8n(3mdcm9txu k 86 zwa8iyou the distance is only 25 light-years. How many years would it take you to make the trip? t =    y

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

  Escape velocity from tqgx2aeae- u o6 9; atcxv0p/f:he 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 Ep 2eni:jym;k9nterprise had just returned from a 5-year voyage while traveli9ken j: y;i2pmng 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-yearvi 8p ; dv8qnq ,h0gtioae+d.i:/wq5us away. How long would it take a spacecraft traveling 0.960c to reach that star fro 5.qv dii+w808p:u,dqqon he gai;v/t m 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.uo0kdxqc/q+; x5tod 2 It is measured in your frame to be 4.80 m long and ;50o/t+kqoqdd xx uc2 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 t l.v3: rvnix1iravel 15 m before it decays? The average lifetime, at rest, vxv3l.n:iri 1 is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling ua da y*1yw l1n.g0n/uat $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic)1thke,th71m n(lo 6)pto2s tsni q+a mass be twice its rest mass? v =    c

  A particle of rest massv 8o6p7d:.btrd 67dn9 dul mxq*iw,uck, vob2 $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at 6r1ryjn hx2n: dtx,q) $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in momentum of a proton that acchhxg)kwk-+i 9;hli )vf1qnhs0w 5 v8 belerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactionq0 z2tbq(x4r3 noy e;i requires $4.82 \times 10^4 \, \text{J}$ 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 f: *q8lapkwk0sission in a nuclear reactor, the resulting fragments have a total kinetic energy of abouq8* ka:swkl0 pt 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 m grvag-8(8c y0 7kasnin $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of aq(edkmqds /,*rqu zfq 6: 4k.n proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption inti2zl3 (bvy . )x8uuid the United 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 obtaof8e(, z8twzb ptti49ined 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 rest energy?+ b .aaky7gs*q /n*lz /jcavq: v = a:+jy*bs7k/qcaa gn zl/v .q*   c

  At what speed will an object's kinetic energy be 25% of its rest/h*1/pgwgx a k energy? v =    c

  (a) How much work is required to accelerate a kg.js5 mwngn/;8nhy) yd. 4qnproton from rest up to a speed of 0.997/yw)5sqnnnkmgjg 8;h.dny .4 c? 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 o nyp:mn44ei q2f 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 j( 0f s7z.gu3n1bqpwbproton (that is, its kinetic energy is 750 MeVqfz7w0n 3 sg u1bjb.p()?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential diffet.dabv 58tm87a o; vt *g(vpdmeg;m-n rence of 105 MV? v =bp78 d8gdvet*n;o-t;.mmtv5va agm(    c

  What is the speed of an electron whose kinetic energy1;we 4bcd e,qtfmck; 6 is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a televisxo0z rbi/uc1: ion screen after being accelerated from rest by the 25,000 V of the pio/xicb0:zr 1 ucture tube? v =    c

Two identical particles of restfn4o/vis0w 0 r e*ekl; 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 b4tbm;57bb1tx 0ctr fproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 eleuoekl9g2ay3cn 34 ah;f qi0m.ctron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 acc7 .p-l8h-wgbj/ uz kz:p5u ukfelerated 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 a pmk.,wnyt ,l6bl) gsx 169cr dyroton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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, p) apa+ ;m z1nj 5b;-a0lg0o*cyu kffl$^{241}\text{Am}$, 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 (ap tz35tnry)-j nl /yj3) a particle of nonzero rest mass, and (b) a particle w t-5j/ynyj3lp)tnzr3ith zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in aal2ty,pqax5(9fz+gdo2a ) l(vukz x+ circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativtv)+u5g2 qzaxka,a ld (2o y( fx+9lzpistic 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 travelinnv3q)ke- ls/)* wpj fhg at 0.50c (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 with respect to the Earth? u =h /q*)snfvk3j ep) wl-    c

  Two spaceships leave Earth in opposite directions, e b x g;3u7c 3:ya),(jzb lvt6rkhp;nlmach with a speed of 0.50c with re6yprmbhjz7 t x,bal 3;:;gv(cl) n3kuspect 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 travelin*23 89qpoap * 9(jlxez uy:j*u aicuqvg at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speu aiju u9 qlpqcz:93e vx8aoyp2* *(*jed 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 vedpd g7 jvi p+.c y6s/)w++xwgqssel approach at a speed of 0.60c. The Enterpw.dp/ +xc g6jg y+ )vdpq+i7wsrise 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 other? u =    c

  A spaceship in distress sends out two escaeqc240t(lsmt pe pods in opposite directions. One travel( tetc0lm2q4ss 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 B passes Ely l70dvzpvfnuovz)g46q / ue 0f.) +harth moving 0.95c relative to Earth in the sf/p)hv0 )q dl+6funo7u v4zgyelzv0 .ame direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 8secxxhq-wjylc+w n6 *ra- ok)r-* 9p4.3 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 tra 8ok(/3a otmtqveling faster than about 0.1c is called relativistic/a3o 8oq ktmt( - i.e., for which the correction using special relativity is 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 h 6) g.lf /q0brr2ufb 0vsrl(r$v$ 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 tkb od o 3r:hi6 in2hm rf.+;lkf5/gjb/o run a 100-W lightbulb for 1 year?2;hf :.il /rb53fgoioj6d+k mbkr/nh $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnet481bny i4nl) w5c ikhpic 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 c 84n4i w1khn b)i5lypopposite 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 travelin6 gyi qs8kc)z3gsnm:*g at 33% the speed of light collides head on with a positive muon traveling at 50% the speed of lkz8ycn g3i*s6q: sm)gight. 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,mf 4a*/g44irvsss9:ve i f,hb and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cs*4 ,gms:f /ib9v4e 4s fahrviover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy ac1 5n,1bkpgu.kbdk2qvh; 6hn 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 have a neg-s5(g 2ize:ewvdv a;e ative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to break a helium nucleus into its constii d/q2t,-ul sdtuents, two protons and two neutrons? The rest masses otls-i/ u qdd,2f 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 the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a ax 9p:f;o w;np j(ccet,7,bco car traveling 110p,:p 7 xejwb ;oc,9o (ccfant; km/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 + 0ip 3edffl6c4), td0ku+tfr zn(dgf speed of 0.935c in the laboratory, are moving toward eac6ikup+4d+0 ftncfr0z, (det flf )d g3h other. 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 with momentufora:i: h97 tpm $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powsk9vrnde qox9 /s3t0en 1 6vzdb-7xe,er by combining matter and antimatter, achieving complete- o939 vv/kexe seqzr x 6ds107d,tnnb 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 accelerate uxt /mm.y,9zkd so that its kinetic energy is greater than its rest mx.mmk,9 zy /utass $m_0c^2$ 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 /lf /iua-hre5nd3gy*believes that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter dl/ f3y5 n-ahuer *i/gto him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrog r7zklkl8xh8 *en and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much doeshkl*l r88k7xz 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 indx6 b a,*;w-zgxjq+zm 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 parti,bz;d wjxzxam q+*g6 -cle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to+j:pp. h/wcjv Earth measures his ship tow pj:p.h j/+cv be 25 m long. On 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 spaceshiz /0jhpaunt: 5p at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relau0 /nhj :azt5ptive 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 150,000 kg. The occupants worzav6i;8e(: vtr;sah yh4c 3, surd *y5ss (rduld 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 spaceshirszci dyr*hveh(;6ra85 sdut ( sy:;4 as3vr,p 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 Eaf: -3gn6kd5e gx 2c azjd,e1j*3ymrrsrth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with th2,1gk6gr:aj* xm5j f -dy3r3ezdne cs e 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 the vicinity 3knp/mgh 25rk 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 kp5k3 gr2mn/ hdone on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the enwvs80 7xf/ha w skt+:cd of a spring whose spring stiffness constant isv7a8fx h0:wtk +/ scws $k=48.7 \, \text{N/m}$. 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 mg1r5 k;: ., skgxudil0xbkp0rass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.