You are in a windowless car in an exceptionally smo lzd-)l080r kwk7gksl 9-ycmn oth train moving at constant velocity. Is there any physical experiment you can do in the train cw) 807ncmsk-ylz - kd9 l0lrgkar to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light wh0- (.2n ml d5hl0vfltxbxhjl,en, out of the corner of your eye, you see the car beside you creep lf0nbml 2v- 0x.l txlh d,jh(5forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad dj2s,i 89* ( jkg p-ukcsnt,gxcar, and throws a heavy ball straight up (from his point of view). Ignoring air resisu-8s(j,*dk2gs gt,ikx n p c9jtance, will the ball land on the car or behind it?

Does the Earth reallyj*xhr6+fb;o tn 1 v+twr ;zxsn,b q0r: go around the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first prinh+,06rxsj:;rn1xbt orf q*btvwz;n+ ciple of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c aw*/8v/dac.k ew pfb.kfa j7 +ahay from a star, at what speed would the starli ck+/7 8e afa/bjfpkhv.w*a.dght pass you?

The time dilation effect i45 ,7lqwr .vyr 9eubcls sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does 5l lw.cuvr4er 79b,yqit deal with?

Does time dilation mean that time actually passes more slowly in moving referjngoc 20l mxi no)ld/mq1n3-),i*t cmence frames or -0oj)lqtgino,/*i mc)nnclm3xm 21dthat it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a qb/xufe ye9h3vi m 8*-long trip. She rushes up to an old gray-haired man and in vq9bme*h38i x/ e-yufthe ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth afeeux4v wrx.(v0* cs9grwo z0,+5emzt speed 0.5c, would you notice a change in your heartbeat? Wo 0cwxw5gvx90v,*srz.(m4fze eer o+ uuld your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary sped84wg( ougcap fk .7x)eds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What dcgk +brys()i,mrr .)3bjj *b would happen to the relativistic predictions of lengtr.rc*b dim jyj(g )s,rbb) k+3h contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light wh .mhky* l:f9gere only h h*mylf:g.9k$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used 1 t.46vwwvc.8j r;nr,jwu almpazudo11 6su+to indicate that c is the lim;t.josm6cd .v v pn41ra 6jawwz1u+8u,uwrl 1iting speed in the universe.

The drawing at the start of th qzq):77kdzbfis Chapter shows the street as seen by Mr Tompkins, for whom the spee7 z fbz)k7:dqqd 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. Doeh y p8z zu1trl c6e(+c99gr/ahgx +he6s this put an upper limit on the momentum of an electron? If so, what is this h chz l96r8zc yt+h9rg u pe1(a/+exg6upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero qvy1v6gkou*le k):p1zf1 b9ahgt 3 *srest mass attain the 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 mass whmu*;e;g80z)hxtcycz- )e. hacd;erhen compressed than when relaxed? ;h*)truh ;h)dz0c eac-m.gzcyex8 e; ----待选择----yesno 

It is not correct to;.zs)oodxs2ex4 j ef(wkz 7d. say that "matter can neither be created nor destroyed." What must we say instea7zosdkjef ws4o; x2 ( x.zde.)d?

  Is our intuitive notion that velocities simply add, as we did in Section 3kawkzd a31ax0 ..2jpluln 7 (a–8, completely wrongu(l31xak7 . 2pwaz 0ka djla.n? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You meas sqi , 4k50)2b(hzn18inoiyd-)k iaysf+s locure its length to be 28.2 m. How5z 04os) hfqon,( ksbi21)ka+ csiiny 8l dy-i long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travs qchf,1 d8ag/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 intervals depend onspj r/vd7me zc-c1t;( 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 ffpl -g:2+ nxejrom 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 z/k4t e u7z3kilifetime 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 +n p0nef0:pecerh2n t0uh1 m1frame, a star is 82 light-years away. How fast would you have to travel so that to you theen 01h0rte ue 1nnp0+fc 2:mph distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a stal 0t2 n:huin+jr 85 light-years away at a speed that tells you the nj2i:nlut +0 hdistance 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 Eartexc- k58(dpnr7s za r*ki /y/ph 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 returned from a7dztl:8 f bk(z8krdpsz2j w,( 5-year voyage whil rt,zkkdws jf pbz2(z8l:(8d 7e 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 woulde*t;8m xb,mp) )o6.umq xqpuy it take a spacecraft traveling y beu *x.;o8)pqqm,pxtm)u6m 0.960c to reach that star 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 y;lo:zem7yk0"Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m o lky0;:y7mze 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 movilo3o3k nm.qk +;v3* draxb.1j2e y jueng to travel 15 m before it decays? The avera+.j3ex 2b.y lk m3kduoej*noq3rva1;ge lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveviojn5b 65alc:yrk o (/,h kc0ling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass?ff5. x * a7kufiejrl4auy/, 2k v =    c

  A particle of rest mas o m7i): u81wyu+rnlsds $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels atz-99j6bt pgn j $v =0.10c$. 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 g:nv wm*9os *b f8lqo+momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction r)1 ly/f4 wpvneequires $4.82 \times 10^4 \, \text{J}$ 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 bc,cc1wwp32 8h-bc iiknown as fission in a nuclear reactor, the resulting fragments 3i8cb2wpchwicc- 1 ,bhave 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 energw.z(+r5af6xg py3t gr y 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 mass 94x6- z1lmw f/ r,z et2rnhwcgof a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Sw-sc(:-b onhhc v -jq1tates 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;r30c :flwr gu9+ yfkzr3th2s 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 ptcsjsx9w8z/( zx1 0q sarticle when its kinetic energy equals its rest energy? w8xqs sxsz0(t9jz1/c v =    c

  At what speed will an object's kinetic energy be 25sa+gq we+mtdho64iev;/1vl 8% of its rest energy? v =    c

  (a) How much work is requirx-ojso mo*yp 6ngc; k h,()5fhed to accelerate a proton from rest up to a speed of 0.997c pn,hcx6;k)soomyj-ogf*( 5 h? 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 a p*u88(kl aw bozpv0(jxroton 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 79ap04y9 nyvu 9kxcnq 550-MeV proton (that is, its kinetic energy is 750 MeV)? 9k0ny4vqp na cxyu959   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential diff w5kpl4 0tb2a6 pdnbqyn4pq3 p,nuy..erence of 105 MV? v =24 .pul3kwpa 6p54nqypn bdyntb.0 ,q    c

  What is the speed of an ele 87e /h*uj+owaigc afwy1a9 7mctron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a t)gxa5z 7 +oeqg c.1zepelevision screen after being accelerated a7 g z.zqep+g)xc 1oe5from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mass s 65jyja9d:8nf9; ezoju9qpm$m_0$ 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 protojyk cq5 24,be+j9rdfm n ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 ofe6.n v od. ub:p)ya8iu 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 accelerat7v pud*l,s q+xuz+1 sbed 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 ener5gx + z60 j usp8x)wie9dap6h0o4p nlg,jioy*gy 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, d x+d4:w8* krtcd wo isal asd1h.0r,8$^{241}\text{Am}$, 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 6-da,erlkxhfm /3+ arz7xi 4aenergy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest mass.xlki3/ +4xa, -adfahr 6ze7mr

  What magnetic field intensity is needed to keep 998-GeV protons revolving in yl .o+:l4rg aq5dhn 1ba circle b1+. qal5o :gdrlnh4yof radius 1.0 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 0w xj-6,.p rpy7xhc;-xzdm,lyv / aw*d.50c (with respect to the Earth) observes a meteor come from behind and pass her -r, wh7myyx- v;wjlpcxa6d pdx .z/,* 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 a spapys-g. h*hg 5wee i/gw5 x;g9eed of 0.50c with respect g; 9/pwgw igshg5eh.ae5y x-*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 spac tx)wu qvivi2 )(8z*haeship 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 is faz8x(h)* 2iv t)uwi qvired
(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 or8wf p5-wct2sx qys+4 f 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 see +y2ft sprxq5cw8-ws4n by the other? u =    c

  A spaceship in distress sends out two esc/t o yyp2o9gpfl4+ . 3g7.jq:vwha rfkape pods in opposite directions. One travels akoqhfoga+.wp9 7 3:.vf jg/2l4yt y prt 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 a speed of 0.75c. hnyuog4 3 p+pz(t l3n2h.b tf:At the same time, rocket B passes Earth moving 0.95c relative u(3gn 3p yolt+t4z bf:2nhph.to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Eartc /73iixn)aun h is Proxima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faster than about 0.1c is call i1o8zyr.n* knqx1r)p7wl*e (0(vicwq ht h2ued relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed 7e 1kw2r 1lvx 0h8qrczo(unt*pi( iw*h yq).nof 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 spee1d7nmw zpob o8; ;7dsrd $v$ 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 totallya97r 2x nylrmz0.y 6bp*)lcqs destroyed to run a 100-W lightbulb for 1 m 7a.szq2n6 9br*yrp)xcy 0llyear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energyi4mnoq5 vur7 oj /,6lnlx.7xp is needed to produce an electron and a positron together? A pmx nxp l/67.4jqnoioru7,v l 5ositron 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 speed of light co(vv6- titvd sg *7u5jullides head on with a positive muon traveling at 50% the speed of light. The tjugs t*5- vuv (7dtv6iwo muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, , u xg+1,axh13kjzcmpvo(y jyt( 6f(aan 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 co yv13((,tc o jx,ajkuxa6 p1g(yhfz+m ver. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at( *o nf)oek5ty 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 negative charge and a spy9:q9ve(n9herxu d : beed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to break a helium nucleusljkq;anl5xx )oz4 q 07 into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium arql)xq0 zkjn54;al ox7 e, 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 percentage6ndmyh4 ,iv x: increase in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansion.,dv6y ximnh 4:]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed os 78qsr /cov1mm4) .h rz:lzsh/cldm-f 0.935c in the laboratory, are moving toward each other. Determm7z rr/8-c:cm z .v/ss4loh mh)ld1sqine
(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 pam)p iwuvn j9t9;4n(b prticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by db brqb* (su/-l 4lpa3combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is /*raul-bb q( b3pdls 4approximately $5 \times 10^9 \, \text{kg}$, 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 accelerad.ph 9/dm bx3(w le tu6 fskk;:nw;zn3ted so that its kinetic energy is greater than its rest mass h6ld:b.kw/(d kwt 9pu;;esxnzf3nm3$m_0c^2$ 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 c5(nfqwvfh s +*fc0a(i s;: wknan 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 he is running the barn(s+a5q*fv: ;fc0( i nnskwhfw 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 twozg vdkj 9n0i s87:6lmo moles of water, the energy rel79zdmi6 g0:n ls8ovjkeased is 484 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling ina4i e: bb ujd;o3(ix-f-+vhny oppositeo n+x :fv; b 4i-uie3h-ajdby( directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0 .ijccp uj ) kwgv06op3kh)5twzl.)e8.75c relative to Earth measures his ship to be 25 m long. O)e)co jk 5 l 3wpjv. cg)08uk.6wpizthn 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 wotho52) pp/z0.85c away from Earth. You send a laser beam toward the Earth tra5/tw oo 2zh)ppveling 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 y(y2b8r :rvp0 qr37b tno aen+p3wz7mkg. The occupants would like to travel to a 73zn+rt( y2y: nr87 mqpwb 0earo3bvp 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 spaceship left Earth at a speed of 0.99c. Wh9pb ,tb*l q 5v-m7jjbjat is the spaceship's kinetic energy? Compare with the total 5bvjm9b,q7 *jjl p-btU.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 vi, kilgmder 70-u0 *bkdcinity of a star 6.0 light-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 it to tbl,ue *i0 7krdgkd0-m he speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spn 8x 8ocqxkpufo8o0 kp4.j/f+0f 0itoring stiffness constant 8/04fj o q no0fku8pic0x +8otkf.xpois $k=48.7 \, \text{N/m}$. 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 maz3e gb.1ui5ioq9q 4c lss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.