You are in a windowless car in an exceptionally smoothl fr ajkdxoj5:(- zqk..tu j;2 train moving at constant velocity. Is there any physical experiment you can do in.k ojlj 52ta ujr-.:xqfdk;z ( 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, out of the c:zjp ob0 rk99lorner 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 tb:09k9 o jrplzhis say about absolute and relative motion?

A worker stands on top of a moving railroad car, an(jnw*)afk*jxep -s9m*3iaj6y knx t)d throws a heavy ball straight up (from his poit k **jpxs jw3na))*fx9( ekja6-mny int of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is itd keya l bhv/n5)s /h1qg:w,;b also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativ1l : 5hg)b;a ybe,qkn/dws/h vity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speeeern g+ i:c +0wrim54dd would the starlighi05ic 4+rr+wn: egmdet pass you?

The time dilation effect is sometimes expressed ab j412zwaj /rmc3iy+gs “moving clocks run slowly.” Actually, this e4+gwizj/a3rjc2 1 my bffect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time jl7 . yud(m+ajwoaqda(;:+ smactually passes more slowly in moving reference frames or that it only seems to pass more slo 7ysjadu( .q++m;mjl:dawao( wly?

A young-looking woman astronaut has just arrivedhi:--irw(p dugxad: k aiuzr*b+w1s qbj). -8 home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?ji-zwub- )r.+i d8 abg: h*da-qu isrp(xw 1k:

If you were traveling away fr9.xdn d8wo98m z/ ql+kbv hmh8om Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What hoh +lxzd q w.n88dvm8k9b/9 mwould observers on Earth using telescopes say about you?

Do time dilation and lengthbw*8 i5 zw. h9y /ng +m+(gbnui2rpmst contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would habn9oh9sb gk i,3m +a07*pqyoh ppen to the relativistic predictions of lhpm7*kb h0 ,9bgoy39qo+sinaength contraction and time dilation?

Discuss how our everyday lives would be different ifw xk-nn)69mes *)idom the speed of light were only omxn* s-) 9wkem6nid)$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used to ioa4ehx7 */mk qndicate th/eo*akqm x74 hat c is the limiting speed in the universe.

The drawing at the start of this Chapter shtf 31/s/sqp.9i bjp thows the street as seen by Mr Tompkins, for whom the speed of .tj q/ipsstb3/h p f19light 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 cq oq :9ut*ey9at speeds less than c. Does this put an upper limit on the momentum of an electron? If sqyouq :9 tec9*o, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain t4ohe18thwfec5+st p 2he 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 has more mass when co,6*f:t+ kka(* rd;*dehlddsxbxf , rzmpressed than brk *d*tdd*d+;kh a,(6zlx : e,f xsrfwhen relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be creatnf)p 5y+prjh.ed nor destroyed." What must we 5py.rpfj h)+nsay instead?

  Is our intuitive notion that velocities simply add, as yfrv :rq-lzbgb.(8 4e*z sjt0we did in Section 3–8, complq8f0z.zlb* g(resjt 4- bvyr:etely wrong? ----待选择----yesno 

  A spaceship passes you at ala6hdyav ytg 4 ;d1,+f speed of 0.750c. You measure its length to be 28.2 m. How y;v dtgaf+6y,alh 4d1long would it be when at rest? $L_0$ =    m

  A certain type of eleme+e*emzt.nw .zntary 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 intervals depend on the fz4ud;7 ,bpfm6 jpz6k)nwj i1factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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-rj nfcl(./80 m qqyj2oyears 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 measure-d pn)du3+o*flmcqr*d 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 fs+k ijl;d5) okast would you have to travel so that to you the distance would be only 35 light-years5olkd jis;+k) ? v =    c

  Suppose you decide to travel to a star 85 light-years away at a spe6v1mipguht4t/zb9c 6 ed that tellsb1h6/m ctuti4 6pzv9g you 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 the Earth i-s uwnrwb.v *)s $11.2 \times 10^3 \, \text{m/s}$. 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 returne9rgu*dqe5cmo-i (* j kd from a 5-year voyage while travelino*gc( iukd5-em9* qrjg 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-yearbt3h+kpu 3.a fs away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observers+3ukbfpah 3t.:
(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" spacecw 5c+bw6ug+gpraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long an+u5cp+bwg6wg d 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 15 m before it decays? The otyi-4c t my/6)uu yi1average lifetime, atoyi- ) u4 6yy1ciutt/m rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton tq p43zomla47.k+fsjn raveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic masl t07e7b:m lktu*6 jcri,ivt7v:fc 0zs be twice its rest mass? v =    c

  A particle of rest mass tcxkd9 4s(ygcv5 v2h (+evvx)$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ak6z1 5jij x(zit $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in mom 6 vv,0gjpfl/ iqjfb)t.smt ;,;qch k)entum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction o wm( 0, kr+i h.(oy44h-zfjclfgk 4cyrequires $4.82 \times 10^4 \, \text{J}$ 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 hvra.qlb 1 m r8 ,xfa6tnm6+5din the process known as fission in a nucle8 . md +6h1rt nralmxfv6bq,a5ar reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joulesoa- ;k y,dcah. 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 pror;ie*3,) 6s eksmsp-;infgru ton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Uni/vd)3o q4xhv2qqlkmz2 r0e i7v-.x hnted States is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from coqr7h. phtsup(ku0/nn8r 1 6iuht y))*of3f tvnversion 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 pf,:p/ 22ker 382qx omodk hxyenergy equals its rest energy? /dr82ky qh p2o3 xopme:kx,f2 v =    c

  At what speed will an object's kinetic energy be 2zl qx2:ni7fo 1 vng8icn3::tgfsc f 375% of its rest energy? v =    c

  (a) How much work is required aaec/+sk (+ve e;yd7 rto accelerate a proton from rest up to a speed of 0.997c? s;e7 rekd/+v(cye+aa 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 ve lhaa*y ,3vp1,uq2dof 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 (tha-q4, jfotk4m kt is, its kinetic energy is 750 MeV)?jkt q-fo, k4m4    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accels) lgv;gr5 ly0y8se: se6s4s uerated by a potential difference of 105 MV? v = 6 u slrsg;05selsyv8)y4:g s e   c

  What is the speed of an electron whosehqcfd6u70cq 0 ta:k e0 kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen afte7, vtjj2(jg xcr being accele x(,vg2j7jc jtrated from rest by the 25,000 V of the picture tube? v =    c

Two identical partic2h8shhd2xt/awymhg:p p;8 +u1 9sdhi les 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 proton6u) iq.bdpfw p;;f6ku ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentu h jstjne99) et;jj-8hm of an 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 0.21 nt5x.o ;,biom(j1*e aemga1jc.
(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 enehcn;cymyu7:f85ru p .rgy 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 nucleugxkqjwegw)m42m+or q6.b63l v7; q dpm 52nnzs, $^{241}\text{Am}$, 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 of nonzu q+:upkuvs*hh33+ ne ero rest mass, auehv 3sn k up+u3*:q+hnd (b) a particle with zero rest mass.

  What magnetic field intensity7m9fj5dc6.9jy hf ehq n6q8js is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativhm f dh6jq 7jse969jy.qc5f8n istic 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.)tifd:uv ,n;4 jzx3h)aag3 cq50c (with respect to the Earth) observes a meteor come from 4v ;x3zf) uaghncj:a) t3,qdi behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50c t gl++t* b6ee r6:fujgwith respect to Earth.u:r tgt+ge+ fb*jel66
(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 0.71 wpxxx/+0f(wyc. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of y0w+(p x/wxxfthe 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 a speed m .; shwuwzg0)of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while movinwh.;0s gmu )wzg 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 -.nsf g8rvh d9a+ k+4g0se,tzwag 6 evtwo escape pods in opposite directions. One travels at a spee++n 09s6,arv f etzggga8dw 4-h.ve skd $v_1 =-0.60c$ 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 0cx 7iz/*4e z: fxb; 0azer4caj.75c. At the same time, rocket B passes Earth moxi jefr0b 4/xca7;ae4:zcz*z ving 0.95c 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 i edd*lhihxr;/3s o(wvvj*j- / s Proxima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling fastex-cv 1+4 vaxuzz0 hqg9r than about 0.1c is called relativistic vga 1zxq+4u 0vxzc9h- - 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 spee.gt ),djm:+2m 1onkaokob; cm d $v$ 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 p5s h8u ;:9lhlig.r(fkpkee2 be totally destroyed to run a 100-W lightbulb for 1 year gpusef89;hi5 krl e 2kph.:l(? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electrom1ju;lbf9g+ ery r. d0qagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electr gj9f0eur; l+ 1dqry.bon, 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 trave9+g *g:b2c4kia *csk s* kopdd-:tkij ling at 33% the speed of light collides head on with a positive muon traveling at 50% the sosd a tkggk:k **sc:jb4i9 -*kdp2i c+peed 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 a neutrinihi ,lo3i)a 2+f,iogrc, uic 6o. 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 pa6co,)iiou3,+ ig fcahili2,rrticles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of abo aen;,caf9+my ut $4 \times 10^{26} \, \text{W}$.
(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 spe-lfts fo)8; tfd ha2b0n)r:nyed 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 4-,d;l/q 12mbpjcb6fsu vgqq 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, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of f4v;b d/j l-bsg1 2pu q,mq6qcthe $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mahq*; 2 rhlej7zss of a car traveling 110 km/h as compared to at rest? [Hint: use the 7 * zqjr2hl;hebinomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a s.(cmcy-aaq9 h 0ebd 8opeed of 0.935c in the laboratory, are moving toward each ooec-aa.(mb c98yd 0q hther. 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 wix*mduy+a 9 am-teem5+yb+;km th momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by 6ko(doah 7 iz;js9+v.5oh qa v- 6zlihcombining matter and antimatter, aziahkhozv5d v 6a.oh6l 7oi +;js9(- qchieving complete conversion of mass into energy. If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetz+y*+f1c n yqiic energy is greater than its rest mcny y+ f+iqz*1ass $m_0c^2$ 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 thc ma)s3)/ck pkarhwhnly0- .*r+sp+sat 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?.ks)a ws/rlc+)p rma-k3 hh *cp y+s0n 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 two lxqa 86kk )bv ,mq.m aysi86q.moles of water, the energy released is 484 kJ. How much does the mass of the elementb.)xyks,aq8 q8 v6m6kl i .maqs decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling in oppositeo0+tkvo7bg:x directions.ovxt7:+gkbo 0 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 particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measwj8 uf t8fa(zs**v td 3an.yu7ures his ship to be 25 m long. On the ship, he eaw8 j8nduzs .tua(3y*fft7va*ts 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 spl:x6oe9/ )e;q jflawe )g4 coozgw;7xaceship 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 observers on the Earth measure for the spee/age o6;j)l 4wefw:geqcxx ;l)o z9o 7d of the laser beam?

  A spaceship and its occupqd el.ws*.pqp4v /9dlror, n,ants have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerap,eq4rvw ,ls./.nod *pl q9d rte, 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 d91erhs2 n+shspaceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. anseh9n rs2h+d 1nual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceshiic 0u twz.87mdkwi.ihi 85 np3p is to travel to the 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 spacei7.0m npu3kchiwd z8i8ti.w5 ship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a ) +mmh yfm(r;rspring whose spring stiffness constant i;)(y r+hmrfm ms $k=48.7 \, \text{N/m}$. 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 mq )kcb(23inx - tuolu(ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.