You are in a windowless car in an exceptionally smooth trai e;evjmtwr z6h+5- -u-d uo8phn moving at constant velocity. Is there any physical experiment yev--+ -jt5mo p u;huz8re6hdwou 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 cornopho jwd8c67,yqc h 94er of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, th9 qdy7,86o h 4wcjchpoinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a movingp7cm w2csn2tnvc -+(x railroad car, and throws a heavy ball straight up (from his poin(2w7 cm xcv2pt csn+-nt of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid tow 8fiy f *u)as4(btp1u say that the Sun goes around the Earth? Discuss in vie*4wf aupyfsib1u)8(tw 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 star, at what speedcnqgu7 *d*q sov15 o)z would the starlight passv cu*57*n)qzo q1dgo s you?

The time dilation effect is sometimes expressed as “moving clocks bx9iel7; ho83qyq * ayrun slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal qb; y8 oi h7ea9xyq3l*with?

Does time dilation mean that time actualv - 0+(khlu/1ex-x ygdjd8v paly passes more slowly in moving reference frames or that it only seems to pass morev dxx-- + vk0ej8( gyluadh/1p slowly?

A young-looking woman astronaut has just arrivedkz3rn ie5d6st;wy8 + s home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might th+56s8y3tse; kwi nrdzis be possible?

If you were traveling 8 .c4 pm lpp2xe(gu5air(db3jaway from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth usinuc2pbirlpj. g(43 xpe8d5ma(g telescopes say about you?

Do time dilation and lrd-)* xjzc:fa6 0oi bzf apo/6ength contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of ligh*h*se csw vj27t were infinite. What would happen to the relativistic predictions of length cov ejs**ws2c7hntraction and time dilation?

Discuss how our everyday live88p7wr 01 g cuixig(jcjn 50ims would be different if the speed of light were only j8n5g7j p8imi(c iguwcx1r0 0 $25 \, \text{m/s}$.

Explain how the length contjre;pewdqp7 63m/ 7xnraction and time dilation formulas might be used to indicate that c is the limiting speed r3 ; pdep xw67qen7/jmin the universe.

The drawing at the start of this Chapter sho6ka,s d30mgl4u2 a(ym;gom biws the street as seen by Mr Tompkins, for whom tk0g4agoymb l m3 s,m (62;uidahe 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 paherg7 ; ,m/5lu unc+t,t6qejut an upper limit on the momentum of an electro;r,/5n+ejuu ca 7,tt mhle6qg n? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzernq -yo9d z7r;qo rest 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 h tf4;fwyj4f -bas more mass when compressed than when relby;t-f4 w 4jffaxed? ----待选择----yesno 

It is not correct to say that puj 4uha-yyxd)tt5 9toa6n:d+ y, +tt "matter can neither be created nor destroyed." What mu ja4u-9tytdoapd+6t+uttxyny ,:h) 5st we say instead?

  Is our intuitive notion that velocities simply add, as we did in 6vynzib zs10hwn;ds u9i( m4k9,emx(Section 3–8, completelnvd(s6wi ; s4 xh19zeuk,9b ymm0zin(y wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to ,-2kea+jqw1y 3 w kyhjbe 28.2 m. Hoe3awy 1 2+yhj,-wk jkqw long would it be when at rest? $L_0$ =    m

  A certain type of elementary paeeaug4 3bn84n9u7l s wrticle 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 depeh :rr. dpee sl j6,g evq*cf28zsr43fz, )xu*und 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 travelccu()/0exh dw 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 its average lifetimb4vr*i+ 1hgl*f mn ob5e 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 pk,t p a9 1rpb tw9h/q2/t9c7k 2jaziblight-years away. How fast would you have to travel so that to you the distance would be9akh2t1jkr p9b/ 7 t9q2c,ip atz b/wp only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years z llp2cojua /z01-u9ub38ktt away at a speed that tells you the distance is only 25 ligzub-kl jz1t0uou2t9lp/a 3 c 8ht-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*hs.n5*uzks f the 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 justaz+qwyu k-(fq 9 jf+4d returned from a 5-year voyage while traveling at 0.fd (u yk+q qjzwa94-+f84c.
(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 a(kbj6yl ijl;5b n5gt+way. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as mtljib5+k(b;gl6 5y n jeasured 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 i6 4py/mzap qv0lw4c0f . 80su j-kdzzes measuredfepl-/zzk4ayp0 q4u . v6 js8z00cdwm in your frame to be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to travel 15 m*, 7ax;sfizy n4)fw c ks5pzd( before it decays? The average ln id5 w *pac4fz7yzk),sf(sx;ifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton t.c01o qsd3 vtnraveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s rela q8y ,xxi/lnk3fgd/0ltivistic mass be twice its rest mass? v =    c

  A particle of rest massbacv oa*+p7 6w $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave )gu 3g2bgy,nqls 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 a d -m j.gpw/, k(jd :effxn.kp:7eb3agccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiresydu he.dqh i.e1kt2h vx3x 70, $4.82 \times 10^4 \, \text{J}$ 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 fd nw8i8 f v li2..uov(l564,xenbvp bapart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about odlu4 .n (fpwvbfi28xelb68 n vv,5i .200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an el;. uxvpb-x)fq *6d dc/v5rz1 i un3kkyectron 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 a ps3k1 jlv;c oo6roton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is ab1gm8yhqcb;h..be;r x out $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from c 9n*.) 8sqi q)dxcl sr0gq;vmronversion 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 pf /ue9d( zha*t fh/um0article when its kinetic energy equals its rest energy? v ht/umuda fhf9z (*e0/=    c

  At what speed will an object's kinetic energy be 25% of its rest enb(nsl8bmwz j21 en8g id v-r22ergy? v =    c

  (a) How much work is required to accelerate a proton from rest up to v43jl.q; myrv(rz;uh a speed of 0.9973yrvvm (;.ljqh zu;r4c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and b8,l3cy 2kr xonp5ig)vvb5+ jmomentum 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, its kinetic energy is 750 MeViw f ,9dl2inx;)dilfxn9w , 2i;?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differenc i)pe-s4on)s q6)e v xo6/xlyee of 105 MV? v = ve 4ol en6eo/xy)pq xi))s-6s   c

  What is the speed of an electron whose kinetic +tquor5u zc9m5)w+y . kg3kevenergy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screenm( u (skd85nbp after bnmdk(ps58u b( eing accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of restzi wc r: 1 b82cqqb5q2cyrp::c 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 proton - 0gu4o lzwc/ pwgx.;s($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 7itoxib*cup-0)q4qjbxg 23n 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. 16tlmlf;nw1.ib cfh 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 io2: k4l4t7;xe,kkw ea en/ cxenergy 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, ot(m nfgh/v0 1) u0 grykhl4(s$^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

  An electron ($m_0 =9.11 \times 10^{-31} \, \text{kg}$) is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.60 \times 10^{-14} \, \text{J}$. Determine the electron's speed $v$. v =    c

Make a graph of the kinetic edtw .oq9r p7+2ijt;pknergy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest mtp.; w 9krq72pitj+doass.

  What magnetic field intensity is needed to keep 998-GeV protons6a g9avez(rn dzc/:2tc 3) ndy revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Us d yzagr) dc(a 6/e23z:n9tcnve 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 travei(q- aq4 ,;pkm)da rbrling at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her apkq(rb r,aai qmd;)-4t 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 speed of 0.nsg+.:f q;m ii dc-e)hv:dfi; 50c with cfei;q)i+::; vnf-d mdhg i .srespect 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 lea;ues 7mpu )e*+zk+c yu04k jwnves the first at a speenu u+ ps4)em+u;c7 *kze 0kjwyd of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speed of 0.60c. The Entez4+ m6pe/jjhab5wz m:rprisej6me bz4 w /jhzp+5am: 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 other? u =    c

  A spaceship in distress sends out two escape pods in opposite diwl2ld :nj 2.iorections. One tr2ow.d :n2ill javels 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 a speed ;fp 9t,w;rak ucj5us6of 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 it wscat fu,;kjp5 ur;69 passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.u9 /lz8abx(dr3 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 tqvc o9 ua(w79hhan about 0.1c is called relativistic - i.e., for which the correctiowh99aco v7 (qun 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 speedmviy5x fy2sv ;g8hhxa)2rg1 . $v$ 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 ha0qfky9k-ewdat fmzr kltk* 1i92 .k,8ve to be totally destroyed to run a 100-W light tke 89fqrkm9a- 1dz 2,t.y *i0kkklwfbulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of sv8 vzj20-sxnoe3u 0(1uwk kwelectromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with thw3e0zj n8s1 u2(k owkuv-0xvse 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 collides head on f17jg.tq hvc5with a positive muon traveling at 50% the speed of .qh71cjvgtf5light. 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 pr o j,r i /)td0w s5.ydnlhtyed0ho;*4voton, 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 the three particles when a neutron decays at rest. KE 4 drwyhs0. e* nd5/)d0toot;, lyjivh=    MeV

  The Sun radiates energy at a ratx5ts jgrzb5.qsj tm) c; 7j2)se 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 mnywnqu--.x/ w ku69hheasured 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 required to break ae+ nhho,+ o.eod7s bq+ helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (inclu en,eq7++ hbo+odoh. sding 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 percentavz)3n3u4q4k dd rir1age increase in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hi1dkv) zau43i 4 rqdn3rnt: 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 laboratory, are movio nfwspz6zx)4 y,0 qm:ng toward nsw)x0m z:6 4p zfq,oyeach 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 paiw39q40zcl;v z ,mxt zrticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power byetcq m+25b0z (ruz p(d- igiz, combining matter and antimatter, achieving complete conversion of mass into energy. 0zdz(+bu e 5(i z rq2g,icpmt-If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energy is greater thanl)7i(()yi 7bhmj ea*b wvmtl * its rest mas (lmy()*teb lami wvh*7b)i7js $m_0c^2$ 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-q2m vf*t*xuj6 e-se-g dhwe;15e2 lnr8o pns 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? Exq2-1l; o-ng rdxewh vne8efs- p u2*6es5tmj* plain 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 wabtgt/kg*p:-qvq lezwe 5 n- 18ter, the energy released is 484 kJ. How much does the mass of the elb t:8nlv p-q* 1tze/wgk g5q-eements 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 i1x7tir mswn:3ae* v)jdentical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to thxas31) 7imnjv:w*e tr e laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth m4jwsl /wst 3i.idmguh2; .uj(easures his shipw2j g/ii(4ums..3jw shlut ;d to be 25 m 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 b0c,o0c2 dckaspeed 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 Earth measure for the speeo,dcc a2cb 0k0d of the laser beam?

  A spaceship and its occupxq+ 3e*pcm1ybants have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to ene 1qcpe +x3*mbyrgy. 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 038c)kpcef::u-c j e un.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy cnceu- j c8u p:e)fkc:3onsumption (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 light x7 q)(bnxdh5r-years from Earth. Passengers on the ship want the (onn)rb75 xh( qdxe-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 oca5 e2 1oy:xeon the end of a spring whose spring stiffness constant is :a1ye cxeo2 o5$k=48.7 \, \text{N/m}$. 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 mk vk:fsv j+pts2wk5(xtvb.*5ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.