You are in a windowless car in an excw2th7 lkg73v leptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the traiw h3v7 k27tlgln 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, out of toed t cm+6plzy;:yz ;0he corner of your eye, you see the car beside yop6zt: 0 m; cyldoz;ye+u 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 ni9w3hv: f7*8ls s ypqrailroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistanc qnf9w h78s:y3lsp*vie, 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 jp6fbq4uakwsj .6mqm 3)2*big-, fejthe Sun goes around the Earth? Discuss in view of the first principle of relativity (that thersm ,b i q q6fuj4-g.3m)j62jkwa*bpfee is no best reference frame). Explain.

If you were on a spaceshiytb6y so 9jo ezp9v6)r gzm19-2 tl9xmp traveling at 0.5c away from a star, at what speed would the starlit 9mm2y lvsj9t6b)xyp19ez zgro9o 6-ght pass you?

The time dilation effect is sometimes expressed as “moving clocks run soudm f0 bz:,6j2- zvba: ikq0xgzn/)jlowly.” Actually, this effect -)b6 q,0 :zu0/:2b fikdj jzxavnogmz has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually pas*k l-8 )6r pzr-l:cgi4azx mznses more slowly in moving reference frames or that it only seems to pass p* rrx:l nlc6m z -zzki4-a8g)more slowly?

A young-looking woman astronaut has just arrived home fromed:f6g ,q 2djo7e3e esxlihi0, 3 jw*y a long trip. She rushes up to an old gray-haired man and in thejy33xi7 ,dh f l6qg w2:0sjede ieo,*e 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 c6 y+( degu(huyhange idy gu(eyh (+6un your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contuhs9bw i ljok -or, :;8a0x2puraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relavjm7cdsoev2cl04aimy: (7t 5tivistic predictions of length ic svc42m moyaj:vd77e t 05(lcontraction and time dilation?

Discuss how our everyday lives would be differentkr1q i gf- qcr0y4 0fx6 fdnbn9sl;a1, if the speed of light were only n4fq91;,60nf ldacs rbf kyr1q0-gxi$25 \, \text{m/s}$.

Explain how the length con7y st*,oh5ymcsd ,,qqtraction and time dilation formulas might be used to indicate that c is the limiting h5ssy,mo,tq c 7 *,yqdspeed in the universe.

The drawing at the start of t x/8,r(mhf 9 yuz)v mg+q0pouzhis Chapter shows the street as seen by Mr Tompkins, for whomvyrhf89)u (gm o,q0mxzpu/ +z 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 tor9 izmyp(mki so9l4,j0wr t2.;+mqjm travel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not, expmrq4+t smp.lz; kr, jwoi jy920m9m (ilain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the .ztkzbatx. z p-3jl.h(;eul ) speed of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does this mean that a spring has more msdkkvf12mp)4h7 xj 0 xass when compressed than whek xd1k hj2)pv0sxmf47n relaxed? ----待选择----yesno 

It is not correct to say s5creammbz(z-4.bgi/p c / x3that "matter can neither be created nor destroyed." What must we say ins3em cmi4(p/5.zbcazgx r -bs/tead?

  Is our intuitive notion that velocities si /n *+ikr) ovv/m6qujgk4*rqc mply add, as we did in Section 3–8, completvv+qirun)jc*q /m6 k4k rog*/ely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its lengy-uxxo +jt:o,a/ysc39qd w s 0th to be 28.2 m. How long would it be when at /9oj3w: ct +0yaoxxqdys-u, s rest? $L_0$ =    m

  A certain type of elementary part :zu;rgxclwq w(j/ 67kicle 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 txrg 7l :l d7pw 3u(g-(z1br)q0 pjl.lq+rlnf 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 17hfoi bwj1z--l 8 a0wm25 light-years 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 averagehb (i.,bl2nvs-gbr th 1p c3)t 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 f:emhl g:tek.5e,e vg+j*1in drame, a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-year.ej igh e*gk:dne,+l vm 1:te5s? v =    c

  Suppose you decide to travel to a star 85 light-years away a :n /kiga*0e8vpnqc1t yjg 2 mr,5jv;bt a speed that tells you the distance is only 25 light-years. How many years would/ *81;j n0aygbqctrg52 j, inpmvvk: e 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 thv 4:)rnn+mk+ 7 ecwcu1w)cfx+)+zdgai ofb 5te 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 Enterpa pq0vh*n8h e5z+ gh:xrise had just returned from a 5-year:v+ 8p*h 0qzhgn5 xaeh 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 light-years away. How long would it bqv)8 z7 jvu /r16biwurha67h take a spacecraft traveling 0.960c to reach that star from Earth1ah8 /u7ru6 7qz6)rbbwv j hiv, 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 kv;mo ld)dk1- 6mh6mx h2dfd3"Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1-m;k hdkd3f)62ldmohvdm6x1.25 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 moving1.oda.s 2v/;xp g; +vxqkut gq to travel 15 m before it decays? The average lif;udgsk+v v p .;q t2xgq/1xao.etime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum o4pxo soa/)cgdq wkr:/1frg, p/qe3i 6f a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relatieg* f-hz8fmp rvac4 w5 w0mlb(8c *nr-vistic mass be twice its rest mass? v =    c

  A particle of rest m( )i9voa 6ubwvass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave4vhz qr ek+:ap+i4 :yxls at $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in momentum of a proton that accsc-pfo80h) bcelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactionypqwa. 18e 3 *clkue7o 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 ho)ccw8c 4kbvpwe3(iu k( f m: j.he23the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lo c8 kih.ow2ecb :(wcv)e33u kf4h (jmpst in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energnrm *ct1i -vh gd2,+syy of 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 masgs (tgxo )jk/38fjg ;as of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is aboutj/1c3cz5ki d yi.is 2a $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 18p,7ypnh gxj 36 mbgj-.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 kineticj,qir1v8l*45oc v xb8*qkxsh energy equals its rest energy? v =ixlj41 8cvr*ko *sh,v58 q qbx    c

  At what speed will an object's kinetic energy be 25% of its yddj/rpt::hup +( s1g1 qcr7nrest energy? v =    c

  (a) How much work is required to accelerate a p3 s aop6xw-9ol /qaid4roton from rest up to a speed of 0.997dao/soipw x6-3lq94 a c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetinoltwk)an8 m06 /,x8cj3ctyz c energy and 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-Me.vv2,2o d iexsjybe- +V proton (that is, its kinetic energy is 750 MeVv2e, b2ij yed-xos .+v)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton acceljwxkg dt6kkwqx;k, 1 2,0rlq)erated by a potential difference of 105 MV? v = q jl1; kkr)xkxwqw t02g6,,kd    c

  What is the speed of an electron whose kinetic energy is 1.00 fdjl)6b om(l ,/05alfmk hk:fMeV? v =    c

  What is the speed of an electron just before it hits a television screen after b(w6lzq85 qhs1 ia5 pzxeing accelerated from rest by the 25,000 V of the picture tu 1ip56ahw(8z qs5qzl xbe? v =    c

Two identical particles of;p1h wzg:n,ic 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 u/rfnss *67mk 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 c: qy/n2w+zghn+v (ucan 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 accelerated toyy5a 7n9r9evgo 3cc/g 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 proton xabe ue z2).zw cx uyds1b./u*af y.-)($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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,28 /a8xvwkesw $^{241}\text{Am}$, 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 vb,x2slvkbzi+6 l3pz 8 dag .3oersus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rx6l3bv28b z . osak gipzdl3,+est mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in a dd wnc :4.db,pcircle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The propcn dwd4,. d:bton'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 tv6 ft97v*es jhf*(1 uh9 knn9p5yuncto the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving wvjhn(97shttfu yeu56 19 9pfnv *kc*nith respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a cww,brb8vwar- ,j 2 6zspeed of 0.50c with resbwc8 r,,zvww6jrb 2 -apect 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. zfr)q3 y 6o ,zdik 9ayw(j4e6zfgx+h+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 Earth ++g) fwi6 4djozzay(z xk93yf6,her qif 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 1(grlaxnefky,jn y;w2h*a;nb 6x1 5bof 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. What is the relative speed of one vessel as seen by the fb *eyx;y,b1 lk(6a hj ;awnrgxn521n other? u =    c

  A spaceship in distress sends out twf2p 2*z y/ bvjomd,bf-o escape pods in opposite directions. One travels at a spee22mbypdj *,v ff z/bo-d $v_1 =-0.60c$ 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 E8gaap25bjr gzj ,lnxk /tw+5- arth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when ixj+5aklz 2t5wn agpr, j8g-b/t passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years ak, f)f3 b8xkipway.
(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 about 0.1c is called relwj8q*l a6va ii(u98kdativistic - i.e., for wiv8ka(qjdw *auil869 hich 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 speexn9m4 zc)1d6 agis v:ctbg ;c;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 ruk6x8m sb u szks.,vbxh5t.;w.n a 100-W lightbulb for 1 yesxvth,skm .sz 8x.uwk;6 . 5bbar? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is neededy;m048 l6)b er(o4 pwzevxqstylm7/-c)bhdr to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the oppositeelc87wmye4 )z; s)/-o4y60 mprbq xtb(hlrvd 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 traveli .x6 uvruuh./ys h,ad/m ch4s8ng at 33% the speed of light collides head on with a positive muon traveling at 50%/,am/uyd ..ur6sc8hx sv uhh4 the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a protg0o 0;, cy:/jsotssah sh *mg9on, an electron, and a neutrino. Assume the neutrino's rest mass is0*h syoag9;mts 0hgcsj/,o: s zero, and the other masses can be found in the Table inside 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 a rate8 olp m;2 ahgrs)v-mwk,2j4 nr 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 a speed of-.gsbci6u)* - n vhpyn $2.24 \times 10^8 \, \text{m/s}$. 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 inton /tgiz pxz 8 puy1t)royb9s94 e,7in; its constituents, two protons and two neutrons? The rest masses of a proton (including ,z/9 z9nteyi)u7sg;n 41rpp8yoxi tban 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 traveling 11se.7 pj8 iux,a0 km/h as compared to at rest? [Hint: use the binomi87.ajesui px, al 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 s n5ykr(zs3+x-b gg,b, ba/ hjoex(k- moving toward each other. Drs xak,,-+(g bjhxogskz yn 3( eb-5b/etermine
(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 wit/u ale2.lj pr)h 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 and antiqy+-ppq n4 of.dz s/sywwb**7 matter, achieving complete conversion of mass into energy. If the mass of the Enterpq*ypbp- *wy 7ofzwds q/n+4.srise 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 kinetikw.,6 ywy6u/i qz b a/rbu20qvw:5qkuc energy is greater than its rest ma: bkqr/ 2,.6uybv q5iqwu u 6/kzw0aywss $m_0c^2$ 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-long pole into a.e0., co/ .xf yh;k yekwwnoh6 12.0-m-long barn if he runs fast enough (carrying the pole). Can he hxfew y;c,n0. yw.oke.h/ok 6do 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 mol+9l3olo 6 m kvvea1x9 esax./xe of oxygen react to form two moles of waterox/l9oe e.x 931k lxmsvv+ a6a, 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 idlgz+ek e8ask,6lr9x 7entical particles are 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 relatig k8zsel ela6r97+x ,kve to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative t tcoyr:c25bfc- x)p4t o Earth measures his ship to be 25 m long. Of rctbpto5-cyc)2 :x4 n 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 send b sotzc079uww: x+f7fa laser beam toward the Earth traveling at velocity c relative to you. What do observ0f+:z9 wcto7u fw7sxbers 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 occup( wo*y9ev-ep mj9 zcw8ants would like to travel to a star that is 25 light-years away at avw*e- oyej9p9 wmz8 (c 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 0.4,7w6 g dubnrq99c. What is the spaceship's kinetic energy? Compare with t6b n4rwu dg,q7he total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 6.0 ligjwze 1;v .. 8vusod 2gp;kfsp5ht-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 bring it2wsdp8.g;vvu k;e5op. jf s z1 to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a sj)j5pj l(*- o6yv miujpring whose spring stiffness constant iso6y *m)jjjli-uvp (j 5 $k=48.7 \, \text{N/m}$. 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 2zma ffr+ksqvapzip-7 f0, ;zrha7 ;, $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.