You are in a windowless car in an exceptionally smooth train)4ex* )orzq 3kq acbv:b,b qo; moving at constant velocity. Is there any physical experiment ex; bo,ovca34:qrzq k *b)qb )you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light09jc7mxn nacd,s0 iq6 when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal,n09 760sa dcjicqm,x n 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 ballrfx9yo *52 auhv2d(uf straight up (from his point of view). Ignoring air resistance, will the ball land on the car or bedr 9 (5 2fyh*vaxu2ufohind it?

Does the Earth really go around the Sun? Or is it also valid to say that the Suncw- eb;sx9fyeetw. l+-1ie 7w goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explaic;wb9x.1yw ef - -el+et wsi7en.

If you were on a spaceship traveling at 0.5c aw hln )h/q1 t1oqxe(q7tay from a star, at what speed would the starl ()qtoq/17qln xt1heh ight pass you?

The time dilation effect is (k59,m* zsay,xisoem: z kx+d sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motik, xdzm*:imsox,+a9z (sk5 y eon affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that timmu6)fl 1 ocg5ne actually passes more slowly in moving reference frames or that it only seems touomn 5lfc)1g 6 pass more slowly?

A young-looking woman astronaut has just arrived hc)vi;2 6ta,efgc ;fomome from a long trip. She rushes up to an old gray-haired man and in th6t o i),gcmf;v cf2a;ee ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would y-y+k7pajev4 *bn4xx4d oy l l9ou notice a change in your hearax 7e okpb vl-ly 4*y+n944jdxtbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordivt7+ r(s.iy. h wybg0qeq5y4mnary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infini.vzhsw8mq:q;c+p :idr-xzq)te. What would happen to the relativistic predictions of length contraction and time dila:.wz-m;s: r pc )8vxhdz qqqi+tion?

Discuss how our everyday lives would be diwby p 8f;*:v- s;u:srnmm aku4l 4yf.ufferent if the speed of light were onla:uyl4fnb4 f.- 8ms:; um*krw su vp;yy $25 \, \text{m/s}$.

Explain how the length contractp5tc k0 ci6q0 vudab-tzsf(+;ion and time dilation formulas might be used to indicate that c is the vt qk+z-fp a(c5;0s6ic0tub dlimiting speed in the universe.

The drawing at the start of tnsb4m1fw8 gme )cgta 9o*5hv)his Chapter shows the street as seen by Mr Tompkins, for whom the speed of mhnc wo)4 )fmga5t9be*v s1g8 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 :kri j/x xx3r.less than c. Does this put an upper limit on the momentum of an electroni:xrr x/j3x. k? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass aib;i /w9e1lvkx98 rv httain 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 morerjdxjz) ) (n,t mass when com xztr),j)nd j(pressed than when relaxed? ----待选择----yesno 

It is not correct to say c4oadf41v/5yh rd+3buck/io that "matter can neither be created nor destroyed." What must wodihrdkoau3 c5+14/f4by v/ce say instead?

  Is our intuitive notion that velocities simply add, as we did in Sec7ydy-gxba iknp20jnwf0o 1 ):tion 3–8, completelyxny n fdk217a0yi w-pobj) :0g wrong? ----待选择----yesno 

  A spaceship passes you at a speed oftke+j)zlyi4 9 r;rb9 8w jow0t 0.750c. You measure its length to be 28.2 m. w 09tlj4e 9bz ;)rk8iowt+ryj How long would it be when at rest? $L_0$ =    m

  A certain type of elementary part+pjfjp v0uu7, icle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals depend cfb 02iui9rhnzfyk4.f t;54con 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 from Earth at a sp) wv(jrl 8* nlmzjd5 n*5j0kjeeed 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 is measured to beep o2xos,r-w; $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a 6rtg )+xlxxl1rypsvhe5hc 2u * 84ly1star is 82 light-years away. How fast would you have to travel so that to yox st y2+ prl6vxrl1c*8l5ux eh14)gh yu the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to*bzccd a+wpx8*x; r4u a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to mzcd8*+r* pw;bax4 xcuake 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 ty7/ q;yebdl8 a4ok3nyhe 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 just retok ez41u,ymt66gj/ pt urned from a 5-year voyage while yjo 6epu1/zt g t46,kmtraveling 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 it take a spacec7q)+f*(vlqk n6vb(lv v jk ywe2d9y(fraft traveling 0.960c to reach that star from Earth, as measured byy *j e(vfvv+w)y6 n9qkqdf( ll(k27bv 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 "Ferra ec tf/y93 *0x7mztvpbbw m.5jri" spacecraft at a speed of 0.660c. It is measurm bx0eymc9p7w5tj.tbf 3vz*/ ed 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*xjg9q8z x5mxuxnldw, .no0pm * .yg+ moving to travel 15 m before it decays? The average lindl, u.gnmq mojp **zx+yxxx g9.w085fetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling aiu*9k.vy j;e9ph hy oj1g setq4n32l,t $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an objes3wi3ll+v5h3pa l ) tsk)7ryuct’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mazbbhd: +h n+a5ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at (6nmxvg7 0ikl$v =0.10c$. 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 ofi rmiues14m: bgq)4v:x p*id+.:gsxe a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reacti+((evtsla5aydw:1 bnon requires $4.82 \times 10^4 \, \text{J}$ 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 ip t4ck*b* qvq+n the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. q kb*4+pc*vtqHow much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules and in ,ow 1 qkea1a5g$\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a p(q k2e pta3 )3n6fpgqh joey29roton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumptx5q(n8gbt d,xion in the United States is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained fro 52q/np tgxl8om 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 of6 lptim dq1z.2iny)h wq0 m3rl7g81hr a particle when its kinetic energy equals its rest energy? v =h )ly1r018i.n r i t7 hlmm6wdz2gqq3p    c

  At what speed will an object's kinetic end bb6am+j xt:/ergy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a spee fup/no3 v.ck xw8vgx y.7*zx*d of 0 z3c.vfw.y8*oxux7nkpgv/* x .997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momeqiclb r0 ly4 i3i44) 3mz0tlvlntum 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-Mbvc,)a yz+go3eV proton (that is, its kinetic energy is 750 MeVz+3)byaov c ,g)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated b(1: g im:p0mf/hqcxtov.-v xdy a potential difference of 105 MV? v =gdtpx:mq1- m f/x (0.:c vohiv    c

  What is the speed of an elei*b1n n2/k *x/v mygpectron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screi)r( 5fa ac4l5*rls op .vwq8ven after being acceler(fs v pr8a.5)ll *vco ar4wiq5ated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mafmbdzt11p5/ euhx; f( ss $m_0$ 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 protond,c7i8glgjxn3l/ c ;wqv ,; n h7nw0of ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentumutf( bb/09 w8 jvh *j3.efpy:q oqj/hu of an electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 kg is ack d5*sr,)bftk7cu.jafm ,i+ ycelerated 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 +p-+tq0k1vsw t itj)g energy 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 nucleu fiz4zwo w9+y o6t7ia )g)ihc8s, $^{241}\text{Am}$, 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 y 7i: )qwbvf.mkinetic energy versus momentum for (a) a particle of nonzero rest mass, and ()7 qbyv:f w.imb) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-Get:h 4govpk;5)hp /f laa6wkp ;V protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's re4:p)w;gpa vho;/l6t ph5kf ka st mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with respect to the4aehvj38v4 ; ko + -ocn3zzud;yg nh:w Earth) observes a meteor come from behz;zonnu;4vwg: v +-ackh3oj h3d84yeind 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 leave7 hdx0;2fhk8ro vfy3k6 p(mwz (aq3d l Earth in opposite directions, each with a speed of 0.50c with respef6ko lv;7 2wrm(pad03fhx8q z3( h ydkct 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 travelihown9i4t avr-vr c6.1s 0u-f lng at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second shis-1 c46avnv0.rfhu 9t o r-wilp 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 vess )nl2 t3 6wjq7*kcjusael 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 relative to Earth. Wh al6csj7w j2tu)3knq*at 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 dis3 :f.b/1h on*a8va wss8jszvrections. One trwoj abshv f1s. as: /3zvns*88avels 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 of 0.75c. At the same time, rocket B passes Earw ag14y /vpx 6p;uv9xwth moving 0.95c relative to Earth in the same direction. / uvygxvpxwaw4p 619; How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Eara5 22ahyv70jwr:uic( qilt ar )x:(dbth 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 tfxs i(g1sj(b 10i28uf kv me4araveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogen eg jf u(akv1s21i4b8ms(0 xfi 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 speed9a59i5n6yd .obzs2y 9sed:awii 1lxa $v$ 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 wouldp*4hz0k cbbrefi)k1d2cj( n 5n6lw3h have to be totally destroyed to run a 100-W lightbulb for 1 yb*rd hj1) n(36whckpl e0f5 i2n4cb zkear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electrs d*; a1kdjz7ron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opd jkdz1 ;r*as7posite 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 li:kc.fhtvt )a0er,z63 nw)toj ght collides head on with a positive muon traveling at 50% the speed of f, 6tke.j3 vtcot znar)hw):0light. 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, an electron, and a neutribgeh/0m/ mt..iy t ij-no. Assume the neutb//jte.m0.-ih ym gitrino'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 =    MeV

  The Sun radiates energy at a rate of aboutld+er uf/w70.ku l-hu $4 \times 10^{26} \, \text{W}$.
(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 speedmy(26rk o6 lka 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 nuclek i-hw* t x46awstxu,6us into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, res *-txhi xw,6ua4t6swkpectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a )o d73i(tbe qecar traveling 11o tdeeb()iq 370 km/h as compared to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in thextv .m9u44ixd laboratory, are moving toward each ux4mx i9dt.4 vother. 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 particle wiy0h98lg 0 xjh gqbj/5z+zyjz: th momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprisehs(tz :2)xrfv s- enj6 obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If thes6hn-x() :fjv s2tr ze 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 accell e9w2,;i 4axhe bo :dxvpb.p(erated so that its kinetic energy is greater than its rest ma bx; 24d:e vl,p(epoxabih9.w ss $m_0c^2$ 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 phyvh *dlql-p69u sics believes 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). u9*hdl-v6lpq Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen wuw7j l,o:zsi/-y: mq react to form two moles of water, the energy released is 484 kJ. How much does the m/muw: wyq-,:sizo7 ljass 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 in okiucei5) j*i zd+( a(vpposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed rel cdz)+(iuje5iva( *ikative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75jx1izfao*a-t a,iugz v .wls+n7 r/6)c relative to Earth measures his ship to be 25 m - o/.wxr1ua+ljtiaf z)zv76 a*sn,gi 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 speed 2 xzlls0w 2fn.of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. Wzlf2 2sl.0nxw hat 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 kg. Thewk5ia - qo,5 nd1uu4jmxima+0 occupants would like ad u,aummo5jkixn14 + 5 w0q-ito travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceshipszgyl-wzs+ d7ahuw; e7(* l wr));nimop e)i , left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual);w uwy;)*g )il+e ,wriso - mz7 dze(7hapsln 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 f:dr eclc)vzra 3:tu z*+,x,r 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 ,z vut ca+lz:c :r3 e,*xfrr)dwork 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 stiffne-k kl65 g0.07 )l8ltkzfflj5sxyywd kss constantj xtl 7lfkk k) 50yfs8g-.5 6lzdkl0yw is $k=48.7 \, \text{N/m}$. 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 mj;.ky0uw yc e7ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.