You are in a windowless car in an exceptionally smooth train moving at constsews3 -ak+8 s1an - co(djy4hpant v+eop3cnj-hwk 1 s 8-d(yaass 4elocity. Is there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of beines ,4 *f3qrkgtp/l8kme,z,e ug at a red light when, out of the corner of your eye, you see the carmq8, s4rzgel*k ,3,keeu/p ft beside you creep forward. 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 raiv3s87a l em vl,ev.5lylroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behind it?el7svv.y3ma ,5v8 ell

Does the Earth really go around the Sun? cgi(a28 4 se ,jkcdonlh;qc39 Or 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). (kischq d , c9cej4a2n ol8g;3Explain.

If you were on a spaceship traveling at 0.5c v;sooy+c1( o2wla .gh/nh23bdn. fnq away from a star, at what speed would the stl .bon2a/.+ ovfhwhg;3n s12ndc(yqoarlight pass you?

The time dilation ef8w066qlvn6f5f knr ltfect is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do wnt0w nl5 6k6qfr6 8vlfith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation me.c0k)fbhrqw -l +/mbyan that time actually passes more slowly in moving reference frames or h kycrl+m .bqf)b/ 0w-that it only seems to pass more slowly?

A young-looking woman astronaut has just arriver q n 2o(3ej m*oojj(z.d/s*sqxpz ,6wd home from a long trip. She rushes up to an old gray-haired man and ix2erzs*on (jq o o/ w3qsz6mp dj,(j*.n 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 a ;dlya sf(h3, vwrtu/+ change in your heartbeat? Would your mass, height, or waistline change?t au+ylw hd,/( fs;3rv What would observers on Earth using telescopes say about you?

Do time dilation and length contractip7b7-wx:4x o+vdc rv*ky+ wfnon occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relativistic 2eth .kd8i( lgwzmc)g3s /,vgdtw.t0predictions of lengt0m,82lw.cstgdk thi dte gv g./z w)3(h contraction and time dilation?

Discuss how our everyday lives would be d pcui5ak pzr2k(x* +gvcg1 w63ifferent if the speed of light were onl u1c +xprpvk *g3w z5g62(cikay $25 \, \text{m/s}$.

Explain how the length contracp,c .kqs4fd m/tion and time dilation formulas might be used to in/p4smd ,c qf.kdicate that c is the limiting speed in the universe.

The drawing at the start of this Chaptew*vwp )y)6ouqp)4un5ya:hkhy 4 pv4fr shows the street as seen by Mr Tompkins, fp4ufnup*6wwv ))kvyyo 5 :q)hy p 4a4hor 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 this put aost0tz(/kz (-( pq tp9vecfx1 n upper limit on the momentum of an electron? If so, what is this upper oet-xk/zq pp 1tc (f9tszv((0 limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of l/ ulv rw6qubw co85,m-ight? ----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 spri6+1 yysio vvt0ng has more mass when compressed than when s+oy0iyt6vv 1relaxed? ----待选择----yesno 

It is not correct to say thattuv+a a+(sj6mcmv./,)mj b9 oweq dw , "matter can neither be created nor destroyed." What must we say instea q9u+badmo/w(6w eat ,mm), sjc+vjv .d?

  Is our intuitive notion that velocities simply add, as weiih3n0l; 5.; ky.s-nbac bm ps did in Section 3–8, completely wrong? c;lmbn.s3y ah i-sk.5p ib;n0 ----待选择----yesno 

  A spaceship passes you at a speed of 0.750q dvlr +b4fni0nv.9/ jc. You measure its length to be 28.2 m.. 0ndn/+vvl i4bjfr 9q How long would it be when at rest? $L_0$ =    m

  A certain type of elementary .p4apq0k /1ke1yyxrt kehti-vfc pf. 3e- h44particle 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 k3;bur;v k ta3the 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:vj.jn85w xo c( /hlkz 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 lifetimi 6wuedaspl(// pfk8;e 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 +yx shf2y*ad1(zpvjj40z9(c l52nugc t+i q dframe, a star is 82 light-years away. How fast would you hc( +0pyt2*u49ncd1g qaildx zz5jh2( sf +jy vave to travel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a t zc2)lfga; : ys/ma7g9s)asc star 85 light-years away at a speed that tells you the distance is only 25 light-years. How f )azma79sl2g:;ygs)/ s cactmany 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 ijz5yw mw bix2 ud/ du -j)+sf2hc.(-lus $11.2 \times 10^3 \, \text{m/s}$. 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 returnpwd(. (nrco; zi)nxn uv723t bed from a 5- uwi nvr(c)37xt(nozn; p b2.dyear 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 lb b+e *yx(rj,ru5qx 5fight-years away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observxf+,eu bq55 xbr(*rjyers:
(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 szh*6hx ***epkv jd 4uopeed of 0.660c. It is measured in your frame to be 4.80 m lpd6* *e*x4 hkzj vh*uoong 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? The hdp8vp5q;v3 haverage lifetih3dv p8p;h5q vme, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of axw15i uiq3 l;y 0sr4ym 2uyr13sf4eqh proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relatijg p i:r*/f4qtvistic mass be twice its rest mass? v =    c

  A particle of rest m yz+zrxs pde8r6h,,-awf v,l/,9bcptass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at mg9a9fqbi 3/te-xzq6g(te8rua r9t +$v =0.10c$. 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 proton0omxtkvx yk+4ie dd x8joyye 11nat78+3 e b7. that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requx xn690 btfevlolf( :lt:e/.d ires $4.82 \times 10^4 \, \text{J}$ 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 apnu3jn lp(2yrd-s 9x o2art in the process known as fission in a nuclear reactor, the resulting fragments have a -9ryxus dl 2n3j2n(pototal 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 of35 7elk8zieziva9 8x j 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 masbq. r-5u 9wdvtjgl;q o): la:x+pdh +ss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is4twt 7qpb ncxt0znj)1/-+cmp 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 obtai,n,pxqrt8i(* qw* pgi ned 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/ iu05hvpkqo (sc5ku3 when its kinetic energy equals its rest energy? v = 5503u/ i(qk oc hkvsup   c

  At what speed will an jke.p1ol-lnms 9bahr; 193ks object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to av1)u1)x wyve uccelerate a proton from rest up to a speed of 0.997)xvuwu)vy1 e 1c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momny b+u o.*r+t4x /auho*hxli3 entum 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 e+dpdc: 21gan,uy jx:a 750-MeV proton (that is, its kinetic energy is 750 MeV1+py:un exag,dd:2cj )?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential diffe y3ryvxbzx,f1kd h0mowl omm+ 6k/ zpp1,100srence of 105 MV? v 0y pwfo13 6xbmr +,zsm0h1mp x k/ovly1dk,z0 =    c

  What is the speed of an eleft uhd;t z-y8 f9z3(jjctron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an elecz+g/p 4i-q(wp 4odrem8b7 udvt5s- jstron just before it hits a television screen after being accelerated from rest by the 25,000 V of th d -ubv(goz re7s54t-s8wp +d/m4jiqpe picture tube? v =    c

Two identical particles of g6av.a(:s f qcrest 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 protobfonllb vq:f0-9r j uy03(;mc 4 0sdhdn ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and th/7tb l2s(p0z ins/t,j-zp rl 6owz8dne momentum 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 acceleratgrxfpn*y.f+s 5c 7 w/t6xn;yped 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 d-p+ld/ ohnz 4and 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 nucleu4odplim 2rh2o k385cl s, $^{241}\text{Am}$, 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 ekch0zu(n - ju2nergy versus momentum for (a) a particle of nonzero rest mass,0z-nj(u2hu k c and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998 fq lu3ht8s28x+c p3*wcbi) ba-GeV protons revolving in a circle of radius 1.) i +c3 asw2b*uf3xlt88bcphq 0 km (at, say, the Fermilab synchrotron)? Use 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 respect to the Earth) obsoyk ng/2+ ad7qef1uq xy )-:onerves a meteor come from behind and pass her at a speed she measures as 0.51-ky o y2 o)q7dnuqeg:x+nf /a0c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each wmb 47si1o51mk 6v q.i9s sx/ppujb :tzith a speed of 0.50c with respect to Earth1 z6is:mo4pxvuqib/t s5 m.71b9 jspk.
(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 03 lhm3tqxly* second spaceship leaves the first at a spl yh3t3lm0xq*eed of 0.87c with respect to the first. Calculate 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 an alien vessel approach at a swwjz)sq32vp .;eeh 6s peed 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 relative to Earth. Wqe 2hszv6.)pw;ws3e j hat is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite dirl c4cw,j()e00tf egnoections. One travels at a spcje, c 0)f w(4eng0ltoeed $v_1 =-0.60c$ 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 E pj0sswuaw/: 2arth moving 0.95c relative to Earth in the same directia:2uwpw0/ss jon. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 lighti blqcp9 1djzh/ f4)a7-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 fas5naxg. 3:ptshj2n : qeter than about 0.1c is called relativistic - i.e., for which the correction using spee3gq: 5.p h: n2xasnjtcial 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 speei5+x) b(xihq u5sgf5:0sk l bvd $v$ 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 hri jtv.pp9jw393b y-9tjy4 uwave to be totally destroyed to run a 100-W lightbulb for -bt9jjrww.ivyt 349 yjp9pu 31 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energyk8m g:w2b*oh f 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 ele8og*h :kmwf2b ctric 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 travee)6rd9b( r ta;tfb cf3ling at 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each9d6re a )tcbf3tf(;rb 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,-,.* o9sb7yxrf gef 6 yisbr:r an electron, 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 . 7bye*,irsso:fx6-bf9rgry among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energya 5etwtvibo5 /8 h73ks5y q2sm at a rate of about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a nk ;n4xkews ga* om6a75egative 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 requirez4ty ew9; n-ty9mok3 bd 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 4t ny 99o4w3;tebz-k ym.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) massh kuaq:+my; ,a of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial h qa;myu:k +,aexpansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, x7 jm5uw :6.qyris7xware moving toward s6wrxu .wqyix :jm577each other. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle with momsx0 y -mm,au 8mlt5x)sentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combinxn 9e-mrvso(.,ep m;z ing matter and antima xn9zo,erpsm(e;. -mvtter, achieving 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 kinetic e (mc )hfxin6d/nergy is greater than its rest masshc)/ix6( nm df $m_0c^2$ 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-lo+vcnd rz+8s n3ck:6h 5xt)bxtng pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea thatn+xbvtcx386r+ktzn dc :5sh ) 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 ,m r/ jud9)hgz4udg8hw le0o 3react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decreasegh/d 8u4 eho09mj, ug3rzw)ld 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 a --up)t(8s;kep-2n2jzvxp bku v9 rb gre created, 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 speed relatij22-u x(szvp r p8- etv9u;-)pbnkbkgve to the other particle? u =    c

  An astronaut on a spaceship trl4/i:k44q0zfyuwze2sir 1dd9l 6sog aveling at 0.75c relative to Earth measures his ship to be 25 m long. On the slfz:d 164do g4lksuw qy/i20irz 94 eship, 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. *kfmha8lcrd84s v8j 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 Eart88d a.vlk4frh 8cj*msh measure for the speed of the laser beam?

  A spaceship and its occupant*ib kdv.g6(y6 t 91xo/d5u a fvapy9xws 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 accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship tu*xfy. gv56d9ot a(bvwd/y9k x 1 pa6io 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. Whp7t6ym3cmvl*,mo:f 4seh r x4mjq;.pat is the spaceship's kivl4;epmc rsyo,6mj .:xq3hftpm7 4* m netic 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 th qd*q rfpv; 7*yg3s5h(-xrwx3 mzs;wg e vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take norz*p;v fr mhq3sy7wq5xgs-g ;d *wx(3 more than 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,*enbpodqc::5 gog;hj ky 0*w the end of a spring whose spring stiffness constant is gj:o*,e5o*c;0bdyp:h w q gnk $k=48.7 \, \text{N/m}$. 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 m)s x zywb15kk,l4;jlwass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.