You are in a windowless car in n2o*c* dfc,oop 4z2w 5m wdr1tacm e*3an exceptionally smooth train moving at constant v omcomcfed 3*dt5zw 2*2ow4p 1*nrca,elocity. 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 being at a red light when, out of the lttbv g/ 47 26oqbn*b;kxu.hvcorner of your eye, you see the 4;tbq oh klubx7/vt gb62*.vn car 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 railnrtdl8+ 7 :q t3f0lztmroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behird08t lt3t+ q:7fln zmnd it?

Does the Earth really go around the Sun? Or i m120j z3ynujy()54rl rujqgcs it also valid to say that the Sun goes around thjj rg mu2u5y l3(1zc)0qynr j4e Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a 1* p:7 2ss) adv1mbb ;)5wetsfozqfbc star, at what speed would )md1t;:275)1 *p s fbvefab o bczqsswthe starlight pass you?

The time dilation effect is sometimes expressed 5z rysku; yntdiziw -s*u- )lf*a7w,m c.d .+cas “moving clocks run slowly.” Actually, this effect hfzu)-tz*7dau-iny*l .wic k .;,cm+ w dys 5rsas nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time a.al3opu1 p(y6)ehgroles ; 4 rctually passes more slowly in moving reference frames or that it only seems to pass64yp.g )h3rrelo;1se(l opau more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She eb4 -t0liqwt )rushes up to an old graybi-)wqet 0t4 l-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 t4.sfuos i9n3 speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth sf3o9 s4ut. inusing telescopes say about you?

Do time dilation and lengthg/y 0.-jsoqd* wl)qy v contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed ofps8mb /rkb 6)5 arr*c5yvn,xtswb+ i 8 light were infinite. What would happen to the relativistic pred5,mbv y*kr8wbn s t8 rp6/ixs5)a cb+rictions of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light u26;ij b2w-i; ggdw0koje11ymjc2w kwere only 1ieow 1ww 6-0ky2 jg;c22gukbm;jijd$25 \, \text{m/s}$.

Explain how the length conps rn; .vys x72(oyr10+ jxoyttraction and time dilation formulas might be used to indicate th+ 20(opytyor rx;vj s1.ns 7xyat c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mroiv)48f*q6d3u1x v .c g8zg wewr2ptv Tompkins, for whom thx 2vu3.z6) owp rtgq4c 8gf8i1*wd vvee 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 an uppe)j0 d553j6-4xzvsncdi w l;nxhqjo1tr limit on the cv sid;4oxnq0t1l wn)5 xj5 j36djhz-momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speka32 ab7j)ji vq/7sq*h/ c xvzed 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 tx u99hgz9. ( o*pyde1kv)axbhhat a spring has more mass when compressed than 9bh91exz)*gp yah dux (9o.kvwhen relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." Whj fk e ;c) 3hgzfwlw ;3q-y0oy;z,k2ehat must we s 0k z;e,3 wh fy;c)q;-ek3l2jwzhfg yoay instead?

  Is our intuitive notion that velocities simply add, as we did in Sectiontl9u)vef.dh3 q 7mvf):os6 pc 3–8, completelyl v36.)dft)mfhuep7 ov:qcs 9 wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. Yomi +5rs/vod 5ju measure its length to be 28.2 m. How long wouldj+ i/s5vr5o md it be when at rest? $L_0$ =    m

  A certain type of el4og4 tljr7j4q etqt::5n(yljementary 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 fact 8. oqix*cek-dor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 trave.i:s ,: vrgoral to a star 125 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 lbbcnbk hxmu1.2/5wvmv;s2yw 4:h-kits average lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a sc wzoz9; kh978icb 8lptar is 82 light-years away. How fast would you have to travel so z988lokpz h cbc; 97iwthat to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light 8qhp 1*d rk,cyh)t8 .ibsfo1/h/sdga -years away at a speed that tells you the disthy8ksi,qdda8./*c p/ sb1 h 1 hto)grfance is only 25 light-years. How many years would it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the Earth isbu wiy:iug* .*u1 j6qv $11.2 \times 10^3 \, \text{m/s}$. 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 stars/xu1o:ep1d zps 8fqh.ru. ;mmhip Enterprise had just returned from a 5-year voyage while traveling at 0.8d..m1u o 1:sz 8upr/qmh;fxpe4c.
(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 lodajm h*4h7re/ s k1 +l5u- thawczlgcc*(/9qtng would it take a spacecraft traveling 0.960c to reach that star fro1/ul/ wa5c+lh rj47*g (*hsaktd mt9cc -zqhem Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecraft at a speed of 0.660c. It is mb*c 4f5gfj-i peasured in your frame to be 4.80 m long and 1. 5fp-cj4igf*b25 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 decaysf+7z 0m-rh 7 tg6divdp? The average lifetime, agf7dmz0 +6 -t 7dripvht rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trave b 3)gapol zg l2vpc4-80sd-xxling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic+xei b91a 5ihe mass be twice its rest mass? v =    c

  A particle of rest mass bf-e6yp/ys3 ,5tiaa)pty,i ;ow0 mdq $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels atv6 v: cja8kru: $v =0.10c$. 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 momentuu.)tqsla hq, v,hn5. pm of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi hkj:us3. s1idniuds9 92hcv2res $4.82 \times 10^4 \, \text{J}$ 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 apad7,jx5)dsyit2 4 vc xlrt in the process known as fission in a nuclear reactor, the resultil dxidj5x,t)4 s27cvyng 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 o ;kd3y+z.iy u*q6ghsyw i9mt3 f an electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of mgnk. 1kk cu9sb u3;mru u)-h.a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumptio)yse hg6*80x1xaa;gofsp ; vf n 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 obtained from conversion of 1.0 gram of oy2cu:pdpmcr/p6q9+ 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 equals its rest energy?u*(kao5oliu 4f 6hsw8 v =kosa*(li5 6 uow4f 8uh    c

  At what speed will an object's kinetic energy be 25% of itsul .,w1jn 2q8bgc-emd rest energy? v =    c

  (a) How much work is required to accek(e,4s h43trxmr sq*h lerate a proton from rest up to a speed of 0.997c? k4,t hsh4x*mrq(s3re W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of abs30t uvio dz2n.x,.l proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetic energy is 750um2,() 8qcoy-qa /j das b5eju MeV)? -2a jmqu ,o(jb8)u dq5 yesac/   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a po7/ugt:) ez ; mbxmk6zftential difference of 105 MV? v = : )m;bz uz67x m/ekgft   c

  What is the speed of an electron whose kineticx*yt5 5w03xkc mwam3;hp 8mlz energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hid/i5x2r ;c*3 s rx9zb gfhho/nts a television screen after being acc*/bz; r9xx3frdh2n /ho s5igcelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particlearsd8 vndm0 y-fn:):ys of 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 k)ywcn vnu ,o a9,ga 57a1,w0vw9lxy pa 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 momentu 1nyi29 /oxmukm 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 27,00q28 d.0xu:5cauv;ri ea * huos0 kg is accelerated 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 ecppww.r0s, /2 shlkwlz h *5j(nergy 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,(jg,*5b 5: f*hszkf/ur mr iyu $^{241}\text{Am}$, 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 energixx (/3:cskk ;9uckwmy versus momentum for (a) a particle of nonzero rest mass, and (b)mikscxc w/x:3k (ku9; a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protonmf(e8a56vg9g,:unevh tk j; f s revolving in a circle of radius 1.0 km ;n e5 kg9:evvtfjm6a hg,(f u8(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 E.dm p;g3eht1u q-)l8xbrxrpc9: b yo;arth) observes a mete pdu :8ghp .qbr9xb3;m) ;-1t xcleoyror come from behind and pass her at a speed she measures 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 )b.ajjr eh5ax8xi l)ta4ix m674kx x;a speed of 0.50c with respe)xji a4bh eit7lr a 6.mk )ja;4xxx85xct 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 travelin6vm 3up(a5fb)z.smi:u.)epyqie wcn*6rs 7i g 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 Earth if it i6)y5m pz7*wasfpri6:.3sm)uqn.cvi ebie(u s 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 speeiq4-4b xyxoukn.gl7) vf;8 wed of 0.60c. The Enterprise comes to the resc u ib)xflg7.4v4 8yxw;eq-n koue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opp pue3m322pr boosite directions. One trae3 b3 o2rpmpu2vels at a 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 Earth at *xh5i u rhm1g2a speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it5mh1x2* irguh passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-y:- 57 hygzirjp b -r44yja-etoears 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 about 0.1c is called relati9wkyt b2v1c/h3r/e3ykt ir )avistic - i.e., for which the correction using special relativity is a si aywr)3tkb1cy 29krv 3teh/i/gnificant 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 speedzmn e/x-,l/10lzipn ao y8s*c $v$ 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 ie.cpd 9xelp)befk1 bmxjw5 (:ct1 .6-W lightbulb for 1 ( ieebt.1d9m.)w f le:5c6p1bx pkcxjyear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an n*- f+kqvvf uw+c60lxelectron and a positron w-q0 l cv+ fnfkvx*6u+together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the ,xr dra,,4hyd3j /bxa puse53 *vchh- speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muxh3 ,j5br,cr ,43e-* yhua/sadxhv pdons (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,*w ;c*p 8sa5grb)- iuubki o/l 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 among gr /8 k)cilb;w* s5buou-a* ipthe three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of 3)o.ey26ezaqzjk(vyi/g bt .xw 59gw (e,sai 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 i rxp3a6sna:4 8y1x *jxdhu2cws s15b bs measured to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be rea1w-zhhe8tf )or 4att 6 -)ro3qnd*h zquired to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an elect8fz rq4n )tht6-how)zd t1oe*aa3r-hron), 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 2 i7, yv lob 2j7kyukie,2fa)0qv)9 xoztcq3h of a car traveling 110 km/h as comparey o uv7)70li3ki,tzo b ja)exqchv29,f22qykd 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 t ;t:h6 fjepj.laboratory, are moving toward e p:.f jh6et;tjach 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 particlrmi *x6 w0+6iormn:8vcpb 2gfe with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise xq1ru3 +yat c5obtains its power by combining matter and antimatter, achievin qyt 51+xaucr3g 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 thar/szss e:x+u9 t its kinetic energy is greater than its rest mass essz9/x:us +r$m_0c^2$ 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 j,v d- rvy05jlhe can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Cr ,0vlvyj-j d5an he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two moles of, wz93+h 26 l0zfujxqreq. uynawh)9x water, the energy rel36f0,uh+axq ww2)zlzn9jyr uxh 9 e.qeased 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 particl1 tgkz53/xoo b:c7q hjgf-,ade/imq ;es are created, traveling in opposite directions. If the speed oj odcg7,ib-5f;etg qkq:3ma/zo xh1/ f each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spacesh9(o*wjf l99sczo xhjej b5 0:zip traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his z 9sjj 9wjleo0(x c*:hzo 59bflunch 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 ab( 2bqabx k4(yt 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 Eb4(qax(y 2b kbarth measure for the speed of the laser beam?

  A spaceship and its occupants have a/j* 8ynv 6f7fwkjg;oy total mass of 150,000 kg. The occupants would li ;nyw jfj6fy*v8 ogk7/ke 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 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 sp)* uex id05habaceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annuxd)u h*50aibe al energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vic6ow0vvwp8a2drz ( hz/ inity of a star 6.0 light-years from Earth. Passengers on the v6d2/p8whz 0ao(rwz v 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 it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the- 1af l1ph:fl lbf-wlzrv9)7h end of a spring whose spring stiffness constant is 9v)- :rhpl alzl1f1 wff7-lbh$k=48.7 \, \text{N/m}$. 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 ma y3+2ybyrpjr+sn o )w)ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.