You are in a windowless car in an exceptionally smooth train moving at const4ggtdp u0qa:hy4( + uys32syeant velocity. Is there an4yp (hy+yas0q gt2s4 guued 3:y 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 b0sb8seh4k z b+eing at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on t 4he+zksb0s8b he 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 car, and throws a heavy bayx tm)fzm y*1(/feh m5ll straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behind it?/my1 h)mfm z *(5xtfey

Does the Earth really go around the Sun? Or isq;yeuxb9s 9ys q9;2l v it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (thayly;x9e vs2qsqb;99 ut there is no best reference frame). Explain.

If you were on a spaceship traveling at 0s x ir-yfl)3pot;rk./kzo0,m .5c away from a star, at what speed would the starlight pass you) xs pryl3ork/ - i.fm0,tk;oz?

The time dilation effect is sometimes expressed as “moving clobbf/b2u (u046 ntqskgcks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with0g2b qb (usfb64tukn/?

Does time dilation mean that time actually passes more slowly in moving)zi2pytc x/9q reference frames or that it only seems to pass more slo)/p9qt xyczi 2wly?

A young-looking woman astronaut has just arrived home from a long tp) k 8i0s6y,aiyj;cvr rip. She rushes up to an old gray-haired man and in the ensuing conversation i,) y6k ri0aypcv8; jsrefers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you n5 9y5k4l9t;kl+bke9s lw s vqrotice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth s l9bl;+ v k9ts955wlr k4yqkeusing telescopes say about you?

Do time dilation and length contractiox) f(f rzx/11oiqdqv3n occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would hapi+osmk44byz nd s.b+7 pen to the relativistic predictions of4bsmd7+sz i b+ yn.4ko length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of ligo::qdxiuq 5s. ht were onlyo:xdqiqs 5:u. $25 \, \text{m/s}$.

Explain how the length contraction an,u04t p6o nja -ldrxlke f.(h(d time dilation formulas might be used to ind lnlxjae(6kr0- uhf do4(,. tpicate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as a7a ;ny d5hhl*seen by Mr Tompkins, for whom the speed of lightn;y la*h7a5d h 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 abf;;u bkjn ,ey/l gz o+r3k1*tt speeds less than c. Does this put an upper limit oy ;*blnk;reb u+t zog1,f/j k3n the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nopwjniw:tbek;) t-7 h 3nzero 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 hasj + bsle9du.w-9mcg n1 more mass when compress+cw .ejl1s 99n-gubdmed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed.d+.cduizu9)lu7i/o;jj r . su" What must we say ilj u/jdc);. s+duu. o9iri7z unstead?

  Is our intuitive notion that velocities simply add, as we did in Sectiopzc9xn n; /yvtnwe:2,3a+ pugn 3–8, co3 n ep:x/tac;w,vzn+9 yupn2gmpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length g1yhd/9om6p1w9go*gw mdz2y to be 28.2 m. Hodm*oogy gpd/92z9w1y wh g6m1w long would it be when at rest? $L_0$ =    m

  A certain type of elemen 0vz(iel co2vosn+2-k tary 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 depentdh2 .bqd pw+ j1 aawj-3s*sr9d 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 travepw .:m yz4vby7l 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 lifg.u6wd5flb(bj f. s5oetime 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 stqeozo7:x/t )aar is 82 light-years away. How fast would you have to travel so that to yo/ z7x e):oatqou the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed thfttm ydnjr-531// /df +pzk crat tells you the distance is only 25 light-years. How dr1ftc /d+-j/n 3mp5rfkzty/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 Ear*pp/cz 1)j mt:-duzy ath 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 fromigk6 9wm/ 2ci+lorgo l :aep;e -r:3pu a 5-year voyage w62pmi/ge: +-k lo9opir3ca w;lg e:ruhile 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 ii o46jcku 58(. fdysjht take a spacecraft tra(. k c5od jij846yushfveling 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 "Ferrari" spacecraft at a spee7rs. bcm eg04 aadso1,d of 0.660c. It is measured in your . 04a1s,b7m dceoag srframe 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 before it decays? The avrljt9gi c/1qf h(,ls7erage lifetime, attc7 g,h9jqr lf/1l( is rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelr5jrj/ qj2)p uing at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object fy*ewzc)cto w/n1c*m,*f qh/ ’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mas ;zswsihi d9;(ocy2 *ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travel yp/ ln;4als+75s ,beenhq)i gs 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 bg0 s)65kxg n+utpo1 jproton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requ vqnajgo )4.ty+3.)x ldxlzv+ires $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaks apart in the process known as fissm+ 6a 3 zea:j9bx*iitlion in a nuclear reactor, the resulting fragments have a totall9*: azet+ia3 bixj6m kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an ele r8 +mwvip fw/ wo)ahyrl2681zctron 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 ayhhbaxm+g s 0zes u;+9 uu ;-n97:ixvt proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United kf+ zqaydg)94States 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 ob9 w.9ivi3tit) s) jq:;p dqoastained from conversion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a parqmpzefvd-st/) vo*+g - rg. +s5iql2 rticle when its kinetic energy equals its rest energy? veodgpm. rvgs/-+5+f-qsl q2 v*zi t)r =    c

  At what speed will an object's kinetic energy be 25% of iehm84c 0 -fzycq*,ntp l v-x9avh6x9d ts rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to pa ;+kvhy-2+ ouow di(a speed of 0.+-wik+huoya o2 ;( pdv997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy andka:lxo:d35tt 7o. mi s 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-MeVplol- l0q ;(, mp:nd0l tospe/ proton (that is, its kinetic energy is 750 MeV epl00ol(d pn:;-tp, mlo/ lqs)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 fyc(y+ *umc4*xt 25y1lx fns, 7yi csuMV? v = 5* uci+ uyymc(y2 ff*y71lcsn t,xx s4   c

  What is the speed of g7wkrj1 ;ds/aan electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television sv3 zxx/o1d 9zwcreen after being accelerated from rest by the 25,000 V ofz z d39x/v1wox the picture tube? v =    c

Two identical particles of re-, 9n5rxmv ryhst 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 ou);e8tmn-r l ud/l07 b prbyd3f a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum of eol 9- i2eupg;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 accelerated41)*/) rauql ;n8fm nkvf kilg 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 energy and momentum of a proton ( 0ef2mgep0p t/$m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleus1od* s0- gtjsn, $^{241}\text{Am}$, 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 ver v5k* hh.s0m n8kv7mxvsus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rekhxm0 vnhk7.v s85*mv st mass.

  What magnetic field intensity is needed to keep 998-Go2u-9 zmr g,enom( ,rdeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the duo92 rrg, (,emz-o nmrelativistic 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 o6 j*xobcxkh;/4j v p .pcyeo,3 c ;u.zafr4w/traveling at 0.50c (with respect to the Earth) observes a meteor come from behind43rxpa y/x46 co pb/fococh ;j;*, . wejkzvu. 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 o86 ahrrwy4 *.cbjc4 h/q,upn opposite directions, each with a speed of 0.50c with respa,h./p ubhrr6jn44*co qc yw8ect 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 0.7p/b(spva2k3m 1c. A second spaceship leaves the first at a speed of aps b3/v2m(kp0.87c 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 speedfxpa q 8pk ,tn*6gc)1h of 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 1hnptxag c*6)fpq, 8 kof one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposit)/ qz(,:r2v .nhtfv l/ln nr wei,f3pte directions. One travels atfl/ ,irn,. nvz2 )hw:qnvt (3pe/ftlr 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. At the o ms(s-lrat w3,9+m hg.ss 0pssame time, rocket B passes Earth moving 0.95c relative to Earth in the same diroha9mpt- lsgr w( ssm s.s,0+3ection. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years an3x.k-g7m fx,:ggean; zn :c+i a hnj-way.
(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 traveli:hg*p /l,p mq,wyijp3f7/ q s )*bsnonng faster than about 0.1c is called relativistic7bppiq/hjspqm s :/ g,**)3ln ,ownyf - i.e., for which 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 speedec.bk w. 6dqx/ $v$ 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 1002n;p *cnbb8rk ;/jwq d-W lightb;wj2npqbr cn*bk /d ;8ulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce q0zal1lai () fr0 ob7zan electron and a positron together? A positron is a particle with the samolza)faq bl7(10 r zi0e 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 speenw: rbb9 gsbv5qk.ip.qc: gzuk/ qct5-h6q.2 d of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of reqqr 5itbck:ph.cqvgk5 2-. g.w: 96u n/bzqbsst 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, an ewjuong ez:(f (o;hh pq oy5,90lectron, 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 = ,uw hjq9oh y (0(o:; ng5eofzp   MeV

  The Sun radiates energy kt9iv ;wwaf ra8og-7 ta( p3u,at 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 measuu22a;l i5r amared 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 a helium nucleus i6 syh w5sc5oxd;k).vr nto its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the s dscxo rv5w. 5;h6ky)total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relo,wfebz- 6lt9n vuq(pk o.z 35ativistic) mass of a car traveling 110 km/h as compared to at restq f(v e3- pbn 6zko.5t,z9lowu? [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 laboratory, are moving towardo 09y9afd g:ct each other. Deof9d0a9:g tcytermine
(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 th;,+ufeu v fanq0i4jvti7l:d .6f 9kdyat a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starshir x d8q60m7nuip Enterprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approxirdm76iu0nxq 8 mately $5 \times 10^9 \, \text{kg}$, 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 isb si hlnhwq wf,w;3t- gw7:;*mqd.j7a greater than its rest masi hl;twq7dw g- ;asq3,7:mwh*jn .bfw s $m_0c^2$ 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 c0k 7ojuz5s tks5hu)-yan fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Ca) z70sks55y-tkoj hu un 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 hydq(pl 6x z4pfooo :ra7-rogen and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in plof4p7rzoq-ao6: x ( 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 pek, d/5mkkg f.articles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame oe.5g,/dmkf k kf reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c kud1me 7bro.-n5(g u zrelative to Earth measures his ship to be 25 m long. On the shipr(uzd.-5k1on um7 bg e, 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 frvgu.r,)2irch: j46lpl *m pf lom 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 speedf* gm p6.rrl)ui,j2:4lvclh p of the laser beam?

  A spaceship and its ocyi wf5 tsh7z*7cupants 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 5hi*s7 7twy zfof 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 spa ji. ,8ik6nt+ xl4,lt0m faop5)tsjhg ceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with themi s. j+io,86ha5 fl)k tj pgt0lx,nt4 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 light-yea ,un 3 ph9e5/pi tr,rx6mkg2pyrs 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 the spgmh / 25 u kpn,3ip6p,exy9rtreed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the+k8 qvu3g b:rhn*kbj1 end of a spring whose spring stiffness constant is 1b:b jn*3ku gq+ vr8kh$k=48.7 \, \text{N/m}$. 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 mas e34(myocfe7g8bw u a1s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.