You are in a windowless car zdxbld) df 6afpo*k1 a4iz.0 7in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whetlfba o 1*f4. zkz7d0ia)d 6xdpher you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a rznq (cqg +(dlug 0-zmztxs /1:ez ,1qfed light when, 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 backward. What does this say about abssgt n 0q, (1zz:e/zqx-u+gd f1mq(z lcolute and relative motion?

A worker stands on top of a moving railroad car, and - 9kgywun:s-i :a0de:- zigjrthrows a heavy ball straight up (from his point of view). Ignoring air resistance, wiug ak:9y-r isg :-i-wn j0de:zll the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it ; ,f+ q/z.tl4sauec4o)quttt also valid to say that the Sun goes around the Earth? Discuss in view of the first prin/ftt4 qtzq u4+;, oa)luets.cciple of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traqepie al:a,l+* 0u)uaveling at 0.5c away from a star, at what speed would the ste pu+eq )a:*iulaal0,arlight pass you?

The time dilation effect is sometimes expressedh 6k ,lz ozlry22g,y1z as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the f6 ly gyzz2 h2z,r,1kolunctioning of clocks. What then does it deal with?

Does time dilation mean thato 6)g*a ep5cmp time actually passes more slowly in moving reference frames or t)p cgoepa*m5 6hat it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from ar+qydz z7/ 7sdmz j5:z long trip. She rushes up tz /zrdq+ z77zjys:m 5do an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Eorl l2xf2 kv3o99lte -arth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? W lk3o9o l9-tre2lxv2 fhat would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinarg)ng/- l g7tlioz j: c6)dr1zuy speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite.ak/ 9rw (7bnpvl.u8ytwn1o8b What would happen to the relativistic predictions of lengnv wrtn197a/bu.bw 8y pok (l8th contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light werea i+kv nt(uw6b.:xf/n onl:iu(fb x+n/w tv6nak.y $25 \, \text{m/s}$.

Explain how the length contraction and time dilation f 0 gpe6.wo(z7fknzl5n m; lo(sormulas might be used to indicate that c is the limiting speed5.ol0ml (ng (6z;esfwnkp7o z in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tompki w0ec(:-uqyyqx p3 2xans, for whom the speed of liyyx -c(3:ew0xq q2 upaght 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 pvb ea4ct zh+4r*s.6, posk ; scdbwq72ut an upper limit on the momentum of an elscpre+ 7od6.a*q s 4s4;t2kbb ,zwcvhectron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of lztem8p*a(m; ,v ur0 o9jh2izuight? ----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 tha vmd..0dc lwekazs.5, 7nn 5wmt a spring has more mass when compressed than when relax 5.mwwenv .klsa,mdd5c .z70 ned? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destro9t ouhwcp m8fink+5j96gx8 j 0yed." What mustk tpo08gnjw8iuj 59x fmch96+ we say instead?

  Is our intuitive notion that veloci4pil5)lt :imv ties simply add, as we did in Section 3–8, completp: )t5mill4v iely wrong? ----待选择----yesno 

  A spaceship passes you at a speed o9hev c-ick p -cztx1 1z0dw62nf 0.750c. You measure its length to be 28.2 m. H2e9npz6d -1i xk0hvw-c 1ctc zow long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle trav wxt/l6kgsi 7lfn/.xl io: c).els 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 intervax (f4guc* 0j (djj;z h8tb8b(mohck.yls depend 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 from Earth at a sp2buedkt ( + 8ae0m cd1d,pl. af,oan*weed 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 lifetimebt4u*o e ap: * qqh:yoc-,qf0y 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 awa5)ie .kw pfko6y. How fast would you have to travel so that to you)5f6ie p.k wok the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a spee x7z,cxl4nur yv n 1kxxna-933s,c(t ud that tells you the distance is only 25 light-years. How many years would it take you ta4l9rn x zxn-uyt3k, 1xc3n v(,xs7uco 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 t-7o z9arhkfg 9 4gcy9bhe 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 had just re*)eao4pnv 6 /gkjxjx5 turned from a 5-year voyage whjg)6 45jkne/ xx*apo vile 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 light(-j t-z:sr*mt ymk trya5e qo0i0nt;;-years away. How long would it take a spacecraft traveling 0.960c to reach that 0mz: ;t-ti 5 y rmrntj0oeq(k-ya;*ststar 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-*f 16t*r 6le/n5g zhasnuldrjrs (/u" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m ha1s*-j/6rl/(unh*6f 5 ugdnzstlrre igh.
(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 befmt9i9-y* ; z8gb.vnapi0 gfsgore it decays? The average lifem0 9 *iapgi yb9g;st ng-.vzf8time, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protxtw5ak n 6ny78on traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass;yg,9e okwjk kc4x6w 583e plf be twice its rest mass? v =    c

  A particle of rest ma2kyu6k( xk*fhy62rl* rg5kjqss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a5h+p/s cklr s8t $v =0.10c$. 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 acwu : (4v*v4 ekhc3yxorbf. /bpux4.a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction4gsj3kq lla5+e4y (x+xw19 j rfbb eb6 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 apart in the process known as fis .lczl(j+ t xra5ys66lsion in a nuclear reacto +5l(jyc6tl z6lxr.sa r, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules ann 9 qyrtbco3 5ik;t+*;)cptgvd 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 l:j ,dtosmg7)fo faa r:v/8t 8of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy cjm d) ) -jqkzv1jz24;tf:effponsumption in the 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 obtaine1bhc66n hz*gbmsw3g*a y;xbq:l a )2kd 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 kmxsx5uv1: ,lz inetic energy equals its rest energy? v = uvm1,:zlx 5 xs   c

  At what speed will an object's kinetic energy be 25% i p ,zngmkt;mu6:x5f) of its rest energy? v =    c

  (a) How much work is requ+k8vjtd d6x,c o;ia0lired to accelerate a proton from rest up to a speed of 0.997c? W ;+d 06avocld ikxj8t,=    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and mo8:fuo +8jb 1/jqr 5 qsi7qh7zhita.zu mentum 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, i;h 2r/9s0dzztw lh :oots kinetic energy is 750 MeV)? d: r 0s2lzt /hwooh9;z   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerai 0j68/sxbb-f b8ao nvted by a potential difference of 105 MV? v = jbnvx f8bs/ obi0 -86a   c

  What is the speed of an electron whose kinwle js 0v)e+fndt j 0k(zc45*yetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a televis z ,p)l17 b.q xcdx1d d205yuuolaw1dj6pdi6 qion screen after being dup oby2,qdxdd1z7d jxaqlc 056.w ui1)pl16 accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of re/zbba+*o rsw m)3p* v4fbpid.p:r .best 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 o;l4av;ksthw2rg j4 8a ke *.ulf a 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 elect1bvn:l:j mkb ce auypo(woz6 ,4,,hy9 )wnm8iron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 kg is accelerated to 0.21c. j pkd/o50e:dr
(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 mn c -wt. onym3 8lic:66-e3 umbatf/hgomentum 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,:siysi:4sro 5s5m++s zj rn4v $^{241}\text{Am}$, 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 momentu.bx:5l0loav h m for (a) a particle of nonzero rest mass, and (b) a particle with zero resvoa0 5:h .blxlt mass.

  What magnetic field intensity is needed to keep 998-GeV rmucyhuxef: m2-bea ;w0 z:1*protons revolving in a circle of radius 1.0 km (at, say, the Fermilab syncyubzm;x m:1er- w ce f*:uh0a2hrotron)? 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 Ea fk-hrublw1 9,l83d frrth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the metef krlfb w1rh- d,983luor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50c yhxos/ b3r+s iy76+p dvlaq,2with respey7dy 2hps,o+q is+ br3vxl6/act 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 traveling at 0.71c. A second spaceship leazm9psj:+dc 4 w , (umkssrp(/mtsts.) ves the first at a speed of 0.87c with respect to the first. pw./ s:tr sju, sdktmspm+(9c4sz)m ( 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 speed of 0.hkx hdk, l20r3* 4tb;odfxhf960c. 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. What is the relative spe 3dh xhrkodt2f09kf4l;hb *, xed of one vessel as seen by the other? u =    c

  A spaceship in distres+k ud9 rw w43 .2ecxb+daltwo,u8 .swfs sends out two escape pods in opposite directions. One travels at a l..wdwa ru43b ,8tku9xw wes+o+c2dfspeed $v_1 =-0.60c$ 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 l+bndsb *ydu8 s87h)e at a speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth *sd bn)dyu8+ ebls87hin the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proximr77lpbcwwg(n ;ru xn;5h4t :ya 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 tcbd31rs e8oa egg/i-wd4k0d3l y3 a3hraveling faster than about 0.1c is called relativistic - i.e., for which the correction using speeh3-o0a43 g3dlgy38 1c w/e bdia rkdscial 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 speebve+j vimy8k g0d1 d1siu*z)6cdc .i9d $v$ 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-W l2 qie 9pz6c-xfightbulb for 1 year?q2 6z-fpeicx9 $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needciw7m ab4+ zp6(ntislhi:z97ed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has:+7ia 7si ni(btc 64 hzz9pmwl 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 speedcm ymh.xw 65:jvzt;k- of light collides head on with a positive muon traveling at 50% the speed of light. The t6-k;hy5.:mzm w tvcjxwo 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 )gxcz3m 5ag*s m,ypx) proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table insizg,m *ag)3 cxs )xp5myde the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at ac.,+kx wv .hmp 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 negative charge and i80ust4jl51ygq go l0a 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 requb70j5 dot )ob-j9cw:ce k/y ljired to break a helium nucleus into its constituents,tj-ow/9 l5jc0c7b yk: debjo) two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a car travev-tw(- zoekz( ling 110 km/h as compared to at rest? [Hint: use the bi -otw (zekv(-znomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving towarom :8nb nk/68qh( d +b)g7pxdbsw.grwd eacbnxwwr.(h:d/ od bk pg7) 8b+6smn q8gh 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 paspr5d.m i6 qv)axj e44rticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its( r7yt to1k 6(ps+eywy 20gpnfr2 bx1t power by combining matter and antimat((k1 ty7 s0x +w ptngt f1rypbro6ye22ter, 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 o -y*d ,xslleam+jl( h;23e cnkinetic energy is greater than its rest macds,mxhe2eo3 jlal y ; (+*n-lss $m_0c^2$ 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 bq uz7)r4vy/6k0dvik 08.22gieuy zuruj h6h that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when h2 j76evyhy k kvi/0u. biurug8q6h0dz4 u2 )zre is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two moles of wat vlc*rgbtmm3j,k 4/6rer, the energy released is 48 ltjck3g*,rr 4mb v6m/4 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, traveling in opr,/v(nt qywt29 txlf87 sewpe9k( jj; posite directions. If the speed of each particle is 0.75c, relative to ;(ktwnw etj(f79 eq2 8lrxty9 sp,v/jthe laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75v3ico6tyu 6j8 c relative to Earth measures his ship to be 25 m83iov 6 ju6cty 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 6t1 5r ia/icmmyl- 1vhEarth. You send a lasi1ti/1m y-vh5arcl6 mer beam toward 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 kg. The occupants o 5ni4uqjw634,g avzk 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 spqongw,6ui4v4k3z ja5 aceship 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 lk, )l95 byy. oe pv3 a4/u7qqbl(sylsveft Earth at a speed of 0.99c. What is the spaceship's ki llp,yv9 kob ss4e ( q)3/yul7qayv.b5netic 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 to8yayr5cb5y4 zhm*qows /q*m 8 the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to takes yzh5mq ao*5 8* 4qmb8ywryc/ no 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 the end of a spring whose spring stiffness constavp ge6kx/bqpl aa a2 dne38m+ ui9v-*2nt i3 -d euv*x/vgb 69n+lqa82ep ikpaa2ms $k=48.7 \, \text{N/m}$. 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 magy- ;3utdeo 8k iua8v9ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.