You are in a windowless car in an exceptionally smot*y, l8fnim(wjpp. 6 af c*16:lbideeoth train moving at constant velocity. Is there any physical experiment you can fl* 1ien(*ewat:c l d ,by6mij68pp .fdo in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, outa9ay740wwtuggbs 4 7p of the corner of your eye, you see the car beside you creep for7s4uw 4wt0 yb79 ggapaward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy ball s ldmdn(x/ wft0j/57 cstraight up (from his point of view). Ignoring airs 5d x0fj/(mtdcw/7n l resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say that the Su6 fm gzutwx:d1f:ug ng4 fdx(1r(6oi+n goes around the Earth? Discuss in view of the first principle of relativity (6z:f n+11g4ft:wdx mr( (uf6g iogu xdthat there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed:h*mkslo pjk,oxp 7r j60z,a0 would zkj rhl00:7sp,, xoom*6 kapjthe starlight pass you?

The time dilation effect is sometimes expressed as “moving clocks..hg-bqzvc)f2 bi:v a run slowly.” Actually, this effect has nothing to do with motion affe-:ha v.b.z vqfic)b2 gcting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually pablbw 6i+ +hvsfq;jt2*sses more slowly in moving reference frames or that it ++2 vbhs it6qlfb;w*jonly seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip.o9yptr.-ga8 ;qk 8- w-n7mjhzntk:rg She rushes up to an old gra t. :7ygotqkj w8rn gan-mpk8;zhr-9-y-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 notice dc5z+kub4db3rm*k q 8 a change in your heartbeat?qk58m 4c kdrzb *u+3bd Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contra2 a)qx(lv(e ovxv9-j2 f: iqxrction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infyj2* pe9ttr .3xy) pdninite. What would happen to the relativistic predictions of length contraction and time dilatioy2pyr*.dtjx39en) tpn?

Discuss how our everyday lives would be different if eth7kbi/ hg z +/v)0d-0uutdx the speed of light were onlyuhzdvhg-0 d+b/ i 0kxe7)u/tt $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might b,dfthqo u835uy/jq k j8z +1rue used to ind3ju 8u5 ,jqfduqk/+zytoh8 1ricate that c is the limiting speed in the universe.

The drawing at the start of this Chap duny1 h 5lll;a0bz5l-ter shows the street as seen by Mr Tompkins, fol;u15n-a0dlhl by lz5 r 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 tr5b dmdkobd/ hxn++d9icy9 : s8avel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper lx b +ddyib:s99k /dnod5 8h+mcimit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of light?jxhl/+sn3k k lw,i3bpde3, -e ----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 thdtwn.wh gfw4 3: rw85cis mean that a spring has more mass when compressed than when relaxedr w5ww4. chgdwt:f3n8? ----待选择----yesno 

It is not correct to say that "matter can neither be created xq3o kp m60rvccp6n1y2mne9: nor destroyed." What must we say insteadv nnx260 y 9mck6r1:c q3eppom?

  Is our intuitive notion that velocities simply add, as we did +gqym g/wx6gc1i3n. x in Section 3–8, completely3c gy6w1/qmx .xni+gg wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its l*5w fk .-noevaength to be 28.2 m. How long would it be when *n.ovawk-5fe at rest? $L_0$ =    m

  A certain type of elementarw xyudpb 67:0my 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 factor g v)r +szt 9, ,8y 6gnncdok/xirkwh1+$\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 s56khfp a2t+./ b-hywum 2ylk lv57xzcpeed 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 lifet )zfp,cit *y,vj 9dqu;ime 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 away. How *i nonz(b oe3no( 5zw5fast would you have to travel so that to you th3*(oob 5 z iozn5nen(we distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-ye4st7(e2kvo rr ars away at a speed that tells you the distance is only 25 light-years. How many years would it take you to maksvt2r 7re4o( ke 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 cel0 8s dy/u:*+jgub*pj(cvethe 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 Enterprise hadd yrl fk;w7s*p4 1p9qr(- tkxa just returned from a 5-year voyage while travelingpws yx q(ld749-pf k;kr1t*ar 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-years away. How long wouly 0;uv7: oq1)mlt fyl, (wiyvkd it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by (vly w1yiu) 7:k,qmy;vfl0to 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" spacecrafy 7 n63nogjtsn-ovl,-t at a speed of 0.660c. It is measured in your frame to be 4.80 m long- jlvgn3n67os tn ,o-y 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 dieb2;r cx-y2 q id2p s0-zz1fqecays? The average lifetime, at rest;-i 2q0cp2yqx -ri zs2z1bdef, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proh5 /l(; tl/aiqbtbsv0ton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativisp9d q0,sl *epe 3;pqectic mass be twice its rest mass? v =    c

  A particle of rest mass ;vu 81ri ax 8y5-;dllo5qpv4w2tpgz s$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ao l)x:whwg cq .y:,3qjt $v =0.10c$. 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 momentuml 8 rd/59rdpfk of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requireqhj:s y0jzb .*1d 0 p9(wsjodqs $4.82 \times 10^4 \, \text{J}$ 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 fission int9whhv u781hmz+s ;k8o+qy w i a nuclear reactor, the resulting fragmensz+h+k wt;w q7o89v1 ym8 iuhhts 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 anzz48zw-:atn9k 3 97 u wwywtuz 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 g,g2i/ttv n 724hnn kgproton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in thhdz25-pkuli1 9 mzc,qd;wy d td:6e3ee 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 obtained from conversion of 1.0 gram3us 2m1ve*gehsg3zx)w z9 d /0trmzz1 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 e,3,hcgis+cl1x 1*smqj c*qsa quals its rest energy? , g3m**1+qsqicjas c1 xl,chs v =    c

  At what speed will an objee s95bjaoan s25- ago f2j/qgr1g;v u3ct's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a speed m3 ;(b8 (vz otth7ze7r7ketxoof 0.997c? W7rbekm; e(vo z(ttx73h8to z7 =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy p. 6f67t;. r rhvevbzland 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 (t*+ 08ykho:s(si bnz whhat is, its kinetic energy is 750 MeV)? +ok 0( y*sb nhwiz8s:h   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a pv ny5t8ou( +lows3 9o1wq 5j3qr9hiw4 qojhz 6otential difference of 105 MV? vvqo4nzs9t 9 6 l5wjuhoy1 iw(qo353rqwjoh + 8 =    c

  What is the speed of an electron whose kinetic energy is 1.00 ndgvjy;- 4:y y(vo g7tMeV? v =    c

  What is the speed of an electron just beo cwz/ ga;-sm/hn93qs ,/dnoh fore it hits a television screen after being accelerated froh3;o snzs- h/nwc m/o, dg9a/qm rest by the 25,000 V of the picture tube? v =    c

Two identical particles offut*i.1 q8nec 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 prx3l:caz9o r:cjg+1ibimu -) ioton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentuf 7gpsn-wa43erj 1p +hm 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 jc m 9hm-try+++s3 qjo1 -ijv +qzqx7aaccelerated 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 1vccxpm:3e6my 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 nucleus, by6x ee fh)nm3t2 )z,dww9 5bx$^{241}\text{Am}$, 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 ki6mgkd0u 83 +d1extsolnetic energy versus momentum for (a) a particle of nonzero rest mass, and 63sd0m18 +xetodklgu (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolqi,u0a;; x*kqo ea14uu/6invi l2k geving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? 6gix lika*n iu ,ae ue;;/vqk 2o0u14qUse the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with resperxf2 0q9,3j ei2xt r5khh fjv(ct to the Earth) observes a meteor come from behind and pass her at a speed she measures frv (hi0e5fq2xjj3khx, r92t 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 0.5hb-20e a3a u1hvol3r f0c with respect to Earafharbl-he v1uo20 33th.
(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 trav)d -4m)mvtknc eling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Eav)mt4kmc- n) drth 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 vesselesl wh;sbn2b5j0j.. :4r 6wyk j mf9ea 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 spe2yj .j.9srebbhk s:6wa5em;lnw f0j 4ed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distresc/ya+qmy;4:wp(k u c w uivk(4s sends out two escape pods in opposite directions. One travels at k44 :w;y(ukp+ci(yc vquam /wa 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 Earthscqa j, y8oh-) at a speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction8 q)cos-hjy,a . How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proximqgq e zg89vys3p m (o)j88pa(ka 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 faster than abob*c h2sn, c-squt 0.1c is called relativistic -b2,csns* -qc h 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 speeb;dyhs1r0h .;h0zt.z xqj9e y 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 be totally destroyed to run a 1l q0h.sgoba*q,: u.ly00-W light 0h uy*qla.: bsq.og,lbulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of 58/)y xjyw+il 0 avwaxelectromagnetic 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 opposite charge. (Note that electric charge is conserved in this process.) E = ywa 8x/xa )+ iv0w5jly   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 hel: /w3 y,i4m. ey c)z5hrbozwaad on with a positive muon traveling at 50% the speed of light.y o5izmc.l z3r:ew ), hawy/4b 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 am ro6,sz :(*tswmuw xbi,r -y8 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 totw,imut: -6z rsw, x8*(ys bmroal kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of /)1faj,e tcl6c)nxt/ho1bx uabout $4 \times 10^{26} \, \text{W}$.
(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 sp wa andt.ba( t)6-0ktheed 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 co , -tdjerov56xnstituents, two protons and t re6d5 ,-jotxvwo 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 the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a car tra7* 8zf. zgla1umsahj u-bx15i40 c xytgg*3kt veling 110 km/h as5 agxk h*t3bt gu za0s4uicz -*ym.lf8g117jx 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 speed of 0.935c in the 1xuev vzgv 0,35okfg 9laboratory, are moving toward each 3gog ,ux0 19vk5zvfev 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 th*dl)x;b0(qoz4d-x h3y lxoml at a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter a/do,ydr (d mf7nd antimatter, achieving complete conversion of mass intod7 dd/(r,mfy o 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 kinetic energy is greater than its dx 4o.hj: b/v ywn1*uerest massxnb jew./:y4v1oudh* $m_0c^2$ 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 15.0cr0 h0 k4*zb4t:yih9s ;kmhzt-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can hh4*r09kzi: ;4m0t tczk hh ybse 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 and one mole of oxygen react to)hfx+ 4y lyew1zi8 e.h form two moles of water,1eh+4 f) xewzhy8yl .i the energy released 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 particles are created, sxj wmo0m6 sq0s) y 0nw,-joz-3y es2itraveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the owym,owjzs2)-0sym sjn3e0o6 0s -iqxther particle? u =    c

  An astronaut on a spaceship traveling +jj+o- / xj5xcbopj,q at 0.75c relative to Earth measures his ship to be 25 m long. On the,p/-cj jq5+ bjjxxo+o 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 sgga/q ).2 ova8)0j ap n:fkjmyp*g6y qpeed of 0.85c away from Earth. You send a laser beam towgjq .v 6a apg)fmpnqa )y oj:/2y80*gkard the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 -hhvykwv 4-o7 kg. The occupants would like to travel to a star that is 25- 4hv wovy7-kh 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 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 left Earth at a speed of 0.99c.lbh r)m3ub*:dc/dp ; -exf dt: What is the spaceship's kinehd ec:umdt-/df)*p x: r3b;lbtic 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 tv2 gy.molk /.do the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more thayo2g/d lm.kv. n 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whox3yt:1 q,bgtke*(wukse spring stiffness constant is k:(u,3t qbyx e1gwk*t$k=48.7 \, \text{N/m}$. 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 masf i,py gm3i-j/s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.