You are in a windowless car in an exceptionally smooth train moving at c-.k ()ydxyi*: dl53 ru n;(bh gwidycuonstant velocity. Is there any physical experiment you can do in the train carn-dhy*(bu ;(u yix.gkr y) dlci3:5d w to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when,po: 5 7)e sc/5gk4rddpdlua/r out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling 7rd/cso5du/e4) prl:5p gkadbackward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heimh e qck13p7 wqv/t,c k:f+3ravy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behindt3 kv qe,i+cp:/m1rq 3h7fwc k it?

Does the Earth really go around the Sun? Ort*om/m +yru5*9zccu9) 7sn2ugr- -dkdw jo cv 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.ory*c)7+9mdc/-wusrutck *5uvmz njog 2d -9

If you were on a spaceship ten53vot n-o*v i b:kn;raveling at 0.5c away from a star, at what speed would the stnn v5tboo3*;:n i-kev arlight pass you?

The time dilation effect is sometimes expressed as “moving clocks run slowly.” ge)u: ,aekj*e 66rlsqvqej9 9Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it9), 96j rvqlj egek6s:qu a*ee deal with?

Does time dilation mean that tim9hxi ig a5dztrnt3 1 :908iguke actually passes more slowly in moving reference frames or that ita5d:ig8i tk0hz9rg xu19 it3 n only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She r w1k)d)ooj hy2ushes up to an old gray-haired ma yjo)w2k1odh )n and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at spee7 icc05di:vqqd 0.5c, would you notice a change in your heartbeat? i:ccqiq5 v0d7Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speey::lq5fi+ ftbmtmw3sl oc0am4.uc ). ds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinit 9, dyuo7f eu3i7fhj1)g ei3gyy-z .rie. What would happen to the relativistic predi7yhz, yyu 17i9.fo3jg erd-ie) g3fuictions of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of lig.4dhd7qa9nh: -i e:cl3ldg yh ht were only l7a- .l3gicn :h:hyd94d qehd $25 \, \text{m/s}$.

Explain how the length contract83zau+mxer2x ion and time dilation formulas might be used to indiczx8u xmr3e2 a+ate that c is the limiting speed in the universe.

The drawing at the start of- 9llqhvf79am*kj)p e this Chapter shows the street as seen by Mr Tompkins, 9p -ll 7qmhjf9)*ke avfor 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. Does wk :y.)3kl ywathis put an upper limit on the momentum of aly) yk.3a:wkwn electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest masi*oes f k-/qs6s 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 has more mass 9*cs fhx;lhm:when compressed than when relh *shl9mxf:;caxed? ----待选择----yesno 

It is not correct to sw,n-lfu*o nyu wsy-7(ay that "matter can neither be created nor destroyed." What must we say y f ws(n7--,*luny owuinstead?

  Is our intuitive notion that velocities simply ami-fs/+ 0vj6w(0 jxix+4v-ubqdjhp :re u r:mdd, as we did in Section 3–8, complxbqjh vds/:46-furi 00+wpv:m j+uxe- m (ijretely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. Y on0q2+al st2q i4os0xou measure its length to be 28.2 m. How long wou0ixo q4a22nq 0 +tsoslld it be when at rest? $L_0$ =    m

  A certain type of el2 aaee q. vuv1eqf im4e;u /dj-h7g,q8ementary 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 fpekf/6, q;ng bactor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 Earth at a speed ux r dfnj5f1mnbh+d- l4prn 526ov3ix97t vw3of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its ave no,m6 w7ga1morage lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 ligwr2z e q,g 9o ;nssbxdf32e(3ght-years away. How fast would you have to travel so that to you 2g egx9rnz,w3f2 dso3sqb e;(the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 )jphst fwe+ )un+*a(pi db4yc-;6ah rlight-years away at a speed that tells you the distance is only 25 light-years. How many uhnwph (yd+fja-r+ie)ps4 b6t c*) ;ayears 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 Eartydpjsbz9yk(g2 -u * j9p,okp 7h 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 thatwrk *nmbxb8l;2ga;y 9 starship Enterprise had just returned from a 5-year voya*m;r9b ;8k agy 2xwblnge while 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 li in9+oo9znc dv)xt*i0ght-years away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observer*dx0)nzn v99oo i t+cis:
(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 youc4x kb--1anr1ey *w*lva 8jmcr29hbu in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m hibv*mcr4hyw--r e9 *cjk8xl1 2buan 1agh.
(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 itw(ol5hy-f3m0f yu0w t decays? The average lifeti0m fy-(woy utwh5f l30me, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trava9dhc qo5b8( h bvcf,93,itq feling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object cq6 zydjc+84j’s relativistic mass be twice its rest mass? v =    c

  A particle of rest massnhm2:pglk ( 3qsll,0 a*utd,g $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels 3ute6t-bzi7a :z dsdu3 uzwcqn,)u 1: ;g3aem at $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change ui:m.z ss/ec)in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical react wpnp36 cjs:4)vcq-o9 l7rfm bion 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 av9yg u3osn ;i6part in the process known as fission in a nuclear reactor, the ryoni 9u6;gsv3esulting 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 eleaz8.v+ im9x/p /.poss2vvcoh ctron 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 pw5 8k2utq:syt roton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in h-hx7 khq 4fucs1yz0 5 qnqfw18b*l( bthe 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 obtatl +n os+1p0qained 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 eqi,l, g rq;2paeuals its rest energy? v ,2;giel qr,pa=    c

  At what speed will an object's kinetic energy be 25% of its rest energy 1s dl1kuu *yw9q;amw1? v =    c

  (a) How much work is required to accelerate a pron 0v.4se5 iifuton from rest up to a speed of es0v iu5n.4 if0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton travel.an 28jt7qwq)w.llf n ing $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is6 /yd7tsvlb5 s s4yoi8, its kinetic energy is 750 MeV)oyvl7/d4 6st sb5iys8?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential dvz(w:5jan (zdifference of 105 MV? vzvjz(5 n ad(w: =    c

  What is the speed of an electron whose kinetic energy is 1.q qc0tnbm7+.,b/tzu lw ,s0ux00 MeV? v =    c

  What is the speed of an electron juo.,zy,m az 8fast before it hits a television screen after being aa8o zz fay,m.,ccelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mr syc:v5 cw660t0f1j 1d ;ccyer yqk.cass $m_0$ 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 ( x:cwlh,l8i) g$m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 (p -7nzrbf*: xmiwd1/ vxy z.a. sqr7l6)wrbl 2$m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mac mn ow99 lz0wh,/;be m(et-xew 7;qosss 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 kinetic energ:4au9 b qsku9f*l8 h:+u :2nyq*w-etlx zlspwy 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 nucleuejzhfo85v66vlp ;q c04p vwcw2o 4 h3us, $^{241}\text{Am}$, 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 nonzerqm*gp*:ht(c75 ),zqw ijb wl qo rest mass, and (b) a particle wit(ljqiq, :)w7 b*m5qwzc h*tg ph zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protb 91*2cdaw qlfons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic ma bfcl*12dwa9q ss. 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 0.50c (with respect to theqho6 ,hpc)-g3yym +ha Earth) observes a meteor come from be3hhapy,m c) h-y6+gqo hind 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 wignjfgr g29g-6wu.q+z th a speed of 0.50c with gnggj6zg9 +r.fuw 2 -qrespect 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 (j8iu2o 4g4f vgppxx1 3dxq7s traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculaupv7sgxg3 pqjf8i41 2x d(4 xote 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, 3( gyfrr/aa4 8v8jd0zypywv an alien 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 relativ fa w,8j g4yyv/vyrzrd8(3pa0 e to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress senf6pbt 2c sm:y.ds out two escape pods in opposite directions. One travels at a spe.: myf2cb6spt ed $v_1 =-0.60c$ 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 Ear b ntjk(pht,8msmzl j,*d*-)ath moving 0.95c relative to Earth in th tlan *jt hs b(mpd,j8,z*)mk-e same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, nr.; d,j 3ojn8i9cwwz4.3 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 travev 6n0mp65:owjju1 06 pisecozling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed 1m pojo5jwi 6v0zn6epc0 us:6of 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 spee1pm2u+ ( x u:xlaia)yxd $v$ 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./aa( t 7fzjqbpa81n p to run a 100-W lightbulb fora a(j81 ./bfan7qtppz 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an le, 9 y;m;ay/akdz aupcmpna1,f 5qqv0;w56g electron and a positron togethermpd 9gczaf0nam 1;e6,q /ayvl5 ua;q,py5w;k? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collides head on with af:wqcr 6j9/ ju positiv9cw6:uj qj/f re muon traveling 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 ;tl q6jg* laropwc445electron, and 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 amonl4c jl5w4orqa* tg6 p;g the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about+i4ro w v1kx4 6cu8qzs $4 \times 10^{26} \, \text{W}$.
(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 zt: 0kyr(veyfq9 l4 5shave 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 to break a helium nucleus into its conshxhcu ig8h5u1jm9gp bf)e;xc(:*u 4 2znms;dtituents, two protons and two neutrgh5c hxidz ;uemf bc8;(2u 4)*9ngmjpus:h1xons? 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 the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (re- ,ajf(ei +/dt qd4lxtlativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expans tjaelfqtdi4/(x ,d-+ ion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c inannv.u3t3jgx1 ,o9 zclx4e 1v the laboratory, are moving toward each ote9.34uo1zx1j nl3 tgcvvanx , her. 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 mg.xd0p fb/(lghb)ds( omentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains pbjd678kp5 mnpf/xr7 its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approxfj p5 r87xbdp6/nk m7pimately $5 \times 10^9 \, \text{kg}$, 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 iw+.c; h7 ktpxyts rest mkp+7w.ht xy;c ass $m_0c^2$ 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-3xyh -rs kult2+cx8 g1long 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 fitgyc 21xsuk +3rh8xt-l 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 3nv) ,ewq 2h5: ks) ;.dbd,kd 2m1mpqettjm qgtwo moles of water, the energy releap dt1 q 23e ;msnbm) tkgvwqhdem:d, jk,)2.q5sed 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 identical particlej v a;zm ti vz)-u8*kyvg5bc5dw k5+c,s are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to themkiwdu cz 5*)bv+ a5j kv5c ;z-gtv8y, 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 ref3 y7pcee504* msxvy.uxjps49(mo0b j. gosr lative to Earth measures his ship to be 25 m long. On tyxpp ofbs5(xce90mo jrs.40u4s.gy* 3e7 mj vhe 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 spaceship atvzuzyzqt-x2 , ) k)9wm 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 observ, zz2kxtu vzwy)9q)m -ers 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 occu*k hdl4 ur tgn6+(t6ukpants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To 4g(6nk rhtt6 d+luku* 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 spaceshicyu1 1 9i/yey4:xl fhdp left Earth at a speed of 0.99c. What is the spaceship's f/yx91 u 4y yld1h:ceikinetic 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 the vicinity of a star 6.0 light-yeardlga(g y58v+ws 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 spacesh8vl(gga dy5 +wip to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffnex2x p l5e-kkxh (tqx3 n/jpc*.ss constant i- xxl* k(tpxjh.325cpe nk/xq 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 mass 6 nn6uazlj7n l8xmsf8m,cwy) 5y yx( yk/cq;.$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.