You are in a windowless car in a cbzp)pt slo+01p.;ex n( zx,hdqk:t:n exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the t qc nt, e0oz.p)(z l x:x;+hs:dbppt1krain car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at ft/e xj/ ;+axo1d6cth 49kl-3eic xpea red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this saco+jxtpafik6xe/4 tx/;h 3-1c9 e edly about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy ball1 / waa+gi1u*i ef,xuz straight up (from his point of view). Ignoring air resistance, xi*,gw/+a1 fzu ua1e iwill the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say ogg7ex),gf;4m (xdkhthat the Sun goes around the Earth? Disxe; 4g7fxo,dgg h(m) kcuss 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 25 h:n*zwfznpa star, at what speed would t*2zz wnp n5hf:he starlight pass you?

The time dilation effect is sometimes expresf8z czn-1h.z8a3 a*nrbjra w 7sed as “moving clocks run slowly.” Actually, this effect has nothing to do with h7afwrjz3zz.b1a8 8 ra*n-nc motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually 0p+/-vftzuxp lq,6rlzn0 j l+ passes more slowly in moving reference frames or that it only seems to - 0tlp, /qlv +pnj r0xz6lzfu+pass more slowly?

A young-looking woman astronaut has just arrivedw-w 7gr- cur:k0s gt1e home from a long trip. She rushes up to an old gray-haired man0ur7 w1t -gw cgr:kes- and in the ensuing conversation refers to him as her son. How might this be possible?

If you were travelin 8w bm0f/0uokc,uf, 2,vbvgvtg away 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 usfm0ok t/vcf ug,b28vb 0v,w,u ing telescopes say about you?

Do time dilation and length contraction occur at ordig js .racq7zsd6go snb)tz fd7e0- 89*nary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What woupg*oyp-7r a6kwv4: mnld happen to the relativistic predictions of length contraction and time dilation? 7m*gok4r-vpa yw n6:p

Discuss how our everyday lives wouldadri:l-p. pq4 d+diz; be different if the speed of light were only iqd4pp: -z rd;+l.aid$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be use aff 1bd*4xj0qd to indicate that4xjadf1*q0 bf c is the limiting speed in the universe.

The drawing at the start0udgc 51d2ssa of this Chapter shows the street as seen by Mr Tompkins, for whom the sped sc2ad0s5 u1ged 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 lew95apf poo+ 1uss than c. Does this put an upper limit on the m f 9uo1pawo5p+omentum 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 speed of ligm1 tdal/j1n kqx-h6f+rh kd; 2ht? ----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 mam h 3bzd)f3ug7mr3r: pss when commrm3:bfdpz3r 7)h 3gu pressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." Wha kxz j w+hewf*t 27t+s7sb4ad:t must * sz w+dws+fb47kxjt2ea:7t hwe say instead?

  Is our intuitive notion that velocities sim nim4gt8(;tr)0 craueply add, as we did in Section 3–8, cor08ar i tteg)(;n4uc mmpletely wrong? ----待选择----yesno 

  A spaceship passes youyf-+/ xt+abq/msee .z 8h: +dk/cozv m at a speed of 0.750c. You measure its length to be 28.2 m. How 8syc+kz/t a+ze o/ :xvqmh/bf-me. +dlong would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed ofmi36uto7 sm/t3/ mij7 b;isgt $2.70 \times 10^8 \, \text{m/s}$. 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 inter(4ham+gs0k-qioh-w d d: ( rs+qnri9tsxr( 4k vals depend 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 travel to3cd7v rddpp j2r7zw 61+l/phf 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 lifetime b8aw*z.jqvf2 v1g:v h 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 light-years away. How fast w(wvwulys 5yj;7t8w a3 cqi g(3ould you have to travel so that to you the distance would be only 35 light-years? v csiy8l35 twy3a qujgw7(w(;v =    c

  Suppose you decide to travel to a star 85 light -hnaqgyqpl5k1b7 1( s-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to ma1 h1qkq5ns(bp a7- ylgke 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 Ea; qvic. q(ikw;rth 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 from8f g9jq*5qd(9hic uao a 5-year voyage while traveling at q9 5jgh(coi uq*a8 fd90.84c.
(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 wo29 fcn,xyof zcf09oax..icf* uld it take a spacecraft traveling 0.960c txf9 zy2a fx 0*f.. f,ocn9coico 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 speed of 0.660c. It isvqxz *my,w+ d: measured in your frame to be 4.80 m longy+d :z qm*xvw, 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 moviny sp3*q:9iddsa:++dnl /s msy g to travel 15 m before it decays? The average lifetime, at:dp/siyd9 + + n*q:m yl3ssads rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trav6w vxeim2 dt8,eling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its restk0v ieict2yujjdz5;u ,ae)y4kg 0j:. mass? v =    c

  A particle of rest mas xv4-9o cxlikdw2 *si*l*ft+b s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels asx (d mnht9q5j 1j04qyt $v =0.10c$. 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 ofku y 3 hh(j51:p+xeaqt a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requir 53kg :ndxp8umes $4.82 \times 10^4 \, \text{J}$ 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 reso, 0: bivovo plfv*19gt breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic enovfo :po,gl1 9*biv0vergy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest enq( wzku, m:bj5yh84,xucc6 fkergy 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 of0nnn.j3il4:d eq. r glks:(l h a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in )rvr; g(x *rmfjl(qdb t/y,s 8the 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 frox /vouf390ty mz3f d5ml d;hf/m 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 particle when its kinetic energy equals its kvvs0uowl2 9we*g y// rest energy? v kw0 olvusvw*/ /2y9ge =    c

  At what speed will an object's kinetic energy be 2i :fedd f)*; kh:.noct5% of its rest energy? v =    c

  (a) How much work is required to f(4ixav uot2mg1p jg8sa 881n accelerate a proton from rest up to a speed of gmft ao8 sia1(881g2pxv u4jn 0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic ru( lnl,qe0 yefl9 x+1t r8qs7energy and momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, islsxne1:) t)axecf(0 ts kinetic energy is 750 MeV)s ))sc ea0letxfx 1(n:?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton acceleratejhhnvqo ) s 4nm1-a:7md by a potential difference of 105 MV? vao m1)vs-:h4nm n7jhq =    c

  What is the speed of an electron whose kinetic xu t g*d jsmke/*)(u ) :dgz*d:b2wyxienergy is 1.00 MeV? v =    c

  What is the speed of an electron just b r(i rnyvc(n/px.,) jlefore it hits a television screen after being accelerated from re/ .(p(iyj xrr,nncv l)st by the 25,000 V of the picture tube? v =    c

Two identical partic.4mt vb pvf zs7(ru)s cu/jb+4les 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 a protonjzx nims ),;x7 ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 anuzy.(ki, 2xf )i(jdzm 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 accele, nczj(,qt+ nsyirs614i 1jj yrated 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 ma5) rtpgtm 00gomentum 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 nucleusgxa xbpq(l v ruu(7 *fvrv;l/.a2) a0y, $^{241}\text{Am}$, 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 ene u,, lgohoum+2rgy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero g ,,2o+uumohlrest mass.

  What magnetic field intensity is needed tojekg1t g5az7 3m)*ejx keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, t * 1zkej)ggx3j a7mt5ehe 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 travelin:fa0wkvq do3*r97/y+as6mf p (cjlfug at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? uwa9m3q(0 f7ro6ykvfp/*sj: +l a fdc u =    c

  Two spaceships leave Earth in oppo(ehi/.zaa- kiph0c , osite directions, each with a speed of 0.50c with respect to Earthh /aeick 0ohz-,a.i p(.
(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.pn0c1nj 9 mlq*7hjurt,xj: l;71c. A second spaceship leaves the first at a speed of 0.87c with respect to the firn *: jlq1mu70 n x,c;lhtjrpj9st. 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 set8p-bgh,dh od oc)+i+v/ hd7j es an alien vessel approach at a speed 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 rela7h-+od ogt, 8 p/)ivh+dhjbdc tive 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 dirvx2g/ t5b0d, gokc7e uections. One travels at a s20d xebv7g,u ct5ogk/peed $v_1 =-0.60c$ 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 sg2 (gbr 4kg8gyg)lfoe1r,:vapeed 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 it passes A? 14o:8arve ,l2ggkfy r g g(gb)u' =    c

  The nearest star to Earth is Proxim1;qa dt,d,l/ 8rrakhpa 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 trave8j5l9 dc pe;uiling faster than about 0.1c is called relativistic - i.e., for which the correction using special98 udji;e5clp 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 speed 4zhlh (xsurq+auj696 $v$ 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-W 5ego/ m gc(px-lightbulb for 1 yea g- /ecxg5om(pr? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of ele 4t9,hhw:zk.)y uxz qcctromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge )yhzq9w4u:cth,.zkx . (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 lig hr,8, oql6ng5 gik(ico/sd :+m7vvvmht collides head on with a positive muon travelr, sg,ci7k6vogvo+q(: mv/n85 ih mdling at 50% the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, 2. neux2z3.p czzkp 8zan electron, and a neutrino. Assume the neutrino's rest mass is zero, and th2zxz 28zp uep.nc3.zk e other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about ,s y zyerux8wa./4,yk $4 \times 10^{26} \, \text{W}$.
(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 hav;.m 5dw;qi4 pt;unh h aezsmb1r: 2n4je 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 faj2+*s)g utrbe required to break a helium nucleus into 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.f*2ausjg +)tr (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in thrbp1j(s (sjv m9 pur..wp57cne (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial (sbrpc9nujw1ps m.v(pj.75r 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 / v22pf)fjgj xxev7z- *hs1kj toward each other. Determfvp )zx2k-x*h72/e jjfgv1 sj ine
(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 i7s)n5nn1 feh a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combini.t6b :hxbarkl 51 x.vls+qm8h ng matter and antimatter, achieving complete convtkh81x5qa6l+.xmlh v .bb:r sersion 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 accelenu1ttqo bff/09p :pfgg3,kt9 rated so that its kinetic energy is greater than its rest mass 1o9 fp/fg3f9but g0 pnk,q: tt$m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-lon 6l 9v-m4a:ohd*9zm1ytbe-k woe o(pyg pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he d hem6b-wo oapv moy49-d9 1zey t(*:klo 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 jsbf:g *e*a5q of water, the energy released is 484 kJ. Hosj5*e* :aqb gfw 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 ipu0-q4nv q b.identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the lb 0q 4inu-.pqvaboratory 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 t2z7z 1fiow)nfzwx 92do Earth measures his ship fzw1 i zx2z7dn9o)2fw 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 sp*z 6d h;fz1qfjaceship at 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 Earth meaz*hzjq f d16;fsure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occ/ v:*gzck;trbz iuk, /upants would like to travel to a star thak /:* urvtgz/bik, z;ct 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 lefor0lt4- eb s*ht Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (aboutb r04th e-ol*s $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 6.0 l h;) 5advwvk3sy3y(n2 g.3 qte 8vihcvight-years from Earth. Passengers on the ship want the (one-way) trip to take no more thyv5sq8;3 c )w3v(dvne y a32hgvk.it han 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 end of a spring whose spring stiffness constanx;z54ollr4s in tz:k 3t z5xs lo l triz:3;4nk4is $k=48.7 \, \text{N/m}$. If this system is in a spaceship moving past Earth at 0.900c, what is its period of oscillation according to
(a) observers on the ship, T =    s
(b) observers on Earth? $T_{earth}$ =    s

A pi meson of rest mass h8g/3: oookmf$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.