You are in a windowless car in an exceptionally smooth train moving a*c it8m ty:qk2v k; lo+87nsra1td -eha8+fyrt constant velocity. Is there any physical experiment you can do in the train car to determkey8rf8o a ;l8 y-ics12k atr vnth+md*+7q t:ine whether you are moving? Explain. ----待选择----yesno 

You might have had the ex7a)pqz 3 doui0perience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctivpi7z3q )0au doely 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 movingogvj5,-r 6 cph railroad car, and throws a heavy ball straight up (from his point of view). Igoprghc6jv-5 ,noring air resistance, will the ball land on the car or behind it?

Does the Earth really go around theaym q:z ;aa9x(ul4k ,f Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (thay mafu(q,k z:4; lxa9at there is no best reference frame). Explain.

If you were on a spaceship traveling ato+g v2t* frhp: 0.5c away from a star, at what speed would the starlight passt+f* ohvpgr:2 you?

The time dilation effect is sometimes exprec uxldba,9w l1f(sy78ssed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion ay9d cbxlw7(,81sulf affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving ref.oyu8dnti48 nd 7w m gqi5b0k8erence frames or that it only seems to pass mo ndidwt gi4.uk5n887q0 bo8 myre slowly?

A young-looking woman astronaut has just 0l/g r(z pqroeb)cp,1arrived home from a long trip. She rushes up to an old,1 gqbper0c olprz/( ) gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were travelinb1r5p,4i v az. pdv3lnzdwp500gsf*gg away from Earth at speed 0.5c, would you notice a change in youfsg pbr1, vd5lw vd zp0g5 *34.zn0ipar heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and len; np k6fizyr+b)3wv;p499sfkpg8 nc tgth contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite.r *x jt,7jhu3i What would happen to the relativistic predictions of length contractiut ij 7x*jhr3,on and time dilation?

Discuss how our everyday lives would be different if the speed of light were oni(j 1v3 6qfc /fxae;nvlyx/i 1cvfaq6 (v nje;f3 $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulgxh f4d:ot3g ;as might be used to indicate that c is the limiting speed in the unive;f:gdo h gt3x4rse.

The drawing at the start of this at9a9bde + iau(,+p/uc idjw0 Chapter shows the street as seen by Mr Tompkins, fad ja 0 ,+ pte+d/iucab(9iw9uor 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 travelx91ebe 0ztp4f/7 )z ybwpe6ui at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what ib1zby p07ie /fwe4pet6) 9x zus this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attjoa:qu rmmyw7:isqh5 2fn)jsc 0y7/ 9ain 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 hase) o5mv. +: /dpyvxows more mass when compressed than when relaxe)/ x:s+v5 p.meowvyd od? ----待选择----yesno 

It is not correct to say that "matter can ne +4u+d 54ggiqq koy(ieither be created nor destroyed." What must we saye4iqod yui45g++ qk( g instead?

  Is our intuitive notion that velocities simply add, as we 0l((cc bahnx 1ak (k5zb 6ao djew5/8adid in Section 3–8, completely w xb(jhe c6zkkn1c(d aaoalw558a/( b 0rong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.2 vca,srk*b.4s- vn b 8om. How long would it be when at rest?bck- v sosn v.a,b*4r8 $L_0$ =    m

  A certain type of elementz jk00hcrsp 1f6wgi9/ary 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 d o. p ,k8w1xrvmbijrwk20oj9* epend on the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years fromxy(3evof f :z9pwa0 9o 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 ism2qlp dtl4(o pl 0q-c6k-(rzts average 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 light-years 7nw:.wtovde; away. How fast would you have to travel so that to you t:.;odw n7 evtwhe distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-ym.;uvm7e,1 arom8 j ydears away at a speed that tells you the distance is onl,amdym vu.m;7e1jor8 y 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)0-y e faq5 u:ux krrujsm(m2np-8tc*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 Enter3yg m v/9gri 7tv; hi,0)csbsiprise had just returned from a 5-ye,;ctbrvvsg g07i/iy) 9hs3m i ar voyage 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 cj)-vuokz31v: wm yu- light-years away. How long would it take a spacecraft traveling uou:jm3kvwy-)-1vzc 0.960c to reach that 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 "Ferrari" spacecraft at a speed of 0.660c. Io3e1whhpbr7uad itmr2a;/ 30 t is measured in your frame h 1hra2dt7m pwure3iba/;0o3 to be 4.80 m long 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 15 m before it decays? 8z v n9yyb7s /mcts7c3The average li8y3/9vzs nsmc7 tyc b7fetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton tm0sn3agn 197bm(q2 r ygnv ns-ail4 l(raveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relati/er5pgw) bkcg yz5m;;vistic mass be twice its rest mass? v =    c

  A particle of rest mass hwp m.otivw/)::dvr*$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels aol)dz y8 q4/knt $v =0.10c$. 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 iwf0ez:,y hdmjz2 :/vaccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction rpq ry1e-zrhh hm)ri60f8 (2aj rjn6u 5equires $4.82 \times 10^4 \, \text{J}$ 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 fissdmrbi.f503dk ion in a nuclear reactor, the resulting fragments have a total kinetic energy of about 20k. i dd0m3bfr50 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy od . ,ha-7n ey*rwy8wmwf an electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a protb mh dy75b .bczy88uai i3 7r55l7jixfon in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abo -2/bbg/zj qhxt;*5 znsvd yx,ut $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion )h2e- p1mjypt bz r8. 0dco+p ho7z.sgof 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() r huy9hef+ ,xkufk) kinetic energy equals its rest energy? v = yf( f)hk+euk rh, ux9)   c

  At what speed will an object's kinetic energy be 25% of its rest treb;t9g/ti* energy? v =    c

  (a) How much work is required to accelerate a proto;9b xu 28.j3lwzzi ffgn from rest up to a speed of 0.997c? W =xwz lj23 8 f.z;fibu9g    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and71fzt t0liq)h momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kineti( lzx-4jfc3f fc energy is 750 MeVf flx-(fz3j4 c)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentialsx)z m,zx)m3m-v. z3q eb(bst difference of 105 MV? v)-t xxbem,q).s3sm(zb 3zm z v =    c

  What is the speed of an electron whose kinetic energy iw7vps 0zfz:n h2*ty 2ks 1.00 MeV? v =    c

  What is the speed of an electron just before it hi+;5jwwzousnp,aks h ()f4j:w+f0e al ts a television screen after being accelerated from rest by thsw+kwh)4(oezla: u5jns+w,af; f j0pe 25,000 V of the picture tube? v =    c

Two identical particles of rest masste6,;uqgmn- s $m_0$ 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 ahoe+e. wraw jki.d/.8 5ohkq5 proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 ms)*tsqr a.xoj ev +ou7h yi4kb(9m** ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 acceleratgu5s c 3uf9t,wed 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 proukrm(e*) 1xl may0p8 wton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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*vub,gmwe-v34ktr ;4n tz (fy, $^{241}\text{Am}$, 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 paylo*vvkwud kibm kvf63:6d)k/: 3to 0rticle of nonzero rest mass, and (b) a particle wit k:3kvy)*v otlkidwdb: /63uv fm0k6oh zero rest mass.

  What magnetic field ip45 erh-sy6jn ntensity is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The pr h4j5pr-y n6seoton'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 0.5 tp4wjhaful5v5va5 5.0c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as a5h5uv45t v wjl.fpa5 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each wi 8fsulv:vl8c4c*w94lm 2n ljeth a speed of 0.50c with respect to Earth. 2lnjvl*c9 f84c luesm48wl: v
(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- v8c xwpq.tybl -9qqv58twu: the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if itvqyvw.: lxtb8 pt5 w q9u--qc8 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 of 0.60c. The En3gw53vtu 4c uml9 qay(id/c3cterprise 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? uc9cu(iu 3cl 3md/5 a3vtg4wq y =    c

  A spaceship in distress sends out two escape pods in opposite directions. One twmpt-fiu-py /9l/ ;uw ravels at a speedu/uy/i;- 9-pwfwpm l t $v_1 =-0.60c$ 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 04arly;)c l5;:v)di hlpd e4 oe.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth li ;yalhldv)p; 4:oecr4)ed5in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years awar,kbfa0g- :om*t u rb+y.
(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 trave.4j 6hjuf o,46owi ucmling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of anojfou,i46 hjwu m6 .c4 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 speedg5rdker ):9im $v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter would have to be totally destroyed to run a 100-Wv;vn)0/6ynp qc 1g-iqo.as emdluz** lightbulb for 1 yd;l- 1ezcoq.sv*u0 6n *ym/gq av)inpear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to 2n5ju f ang:90uz8eds produce an electron a0:2f9jau euz 58gn ndsnd a positron together? 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 comq*-zd5p b,vvvt0.nillides head on with a positive muon traveling at 50% the speed of lig- v.d pv,vn0mb qi*z5tht. 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,- 1j: gvit.dq(glsoa. 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 among the ta.o(vdli-jggsq:1.t hree particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about0k(y(z7aum8xp iaj gc p;5 p(g $4 \times 10^{26} \, \text{W}$.
(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 measure lnbas38dx3qjt.q s*t 2prg,-d to have 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 xif5kke-(l m9rz.m* wnucleus into its constituents, two protons and two neutrons? Tmfwmr e5-li*9k (zk.xhe 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 (relativistic) mass of a car travelingsp yh8wzl-tsl1 /,3zo 110 km/h as compared to at rest? [Hint: use the binomial expans1z os 3- pw,y8slhz/ltion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving to ggzru.l(xhe/o -*oj7 ward each otz7.gh oe(lj-gx u *r/oher. 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 wi 36+pwbp +l35lpctxhjth momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powjog )v a p)rc:.n9h et-kfd03ker by combining matter and antimatter, achieving. g :)k3vd0 rte)jfo-9n chapk 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 accelerati8(og* ah 5av.p 9wu w4xz+eiqed so that its kinetic energy is greater than its rest ma*ogx 5h9eww.vaziq8p i(4+ ua ss $m_0c^2$ 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.cwcd(1. zzee3 0-m-long pole into a 12.0-m-long e.d(cw3ez1z cbarn 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 to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen andga, yb5qu 32y8:dykl r one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease inb2yqu8 r yakgy,:dl53 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 cphkldcw77lr c0( -j*oniqxu vz)7 a .1reated, 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 sc( ) voh qz1ucw-7*lnpdr 7la0kxi7.j peed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures hi;( 2aty 3b8 ;scxnzibxs ship to ;cxxb28is n3a zby t(;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 spaceship at a speed of 0.85c away from Earth. You so 6i0.:y9e(wbo- sixortv m9gend a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the o: -to9ygi vibm9es 0x.6r(w olaser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occ 379ky(glu+ frjso/n cupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To acceleratekru +gonf9yl3 sj(7 /c, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship le0 pf ss 15x j 9gggh(wdgr:6i+1aew:peft Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare wi:6jrggf9 de5(xp: ss+agwp0e g w1 hi1th 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 tg gl bh0qq5a8y : (1z4xy9j xt)yyht*lo 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 spaceship to brib(805:9 tq* 4z)g lhxygh1jyytaxy q lng it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffness c 1vs/nt3cuyq- fics-j*,,jicezha4 -onstantu3yfz ih4s,csan ,1cq-vjj-e / c-i*t is $k=48.7 \, \text{N/m}$. 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,:a d/4s1rqm+ abocgt $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.