You are in a windowless ngq, mrca57rcl .pj+ ;car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you c nlrr5c.qa,;mj 7c+p gan 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, 4 5jkjy*wx 97m9hcrkx,+ qpbbout 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 say about absolutebh5p 9 jj,mqxw+xc49kybr7k* and relative motion?

A worker stands on top of a moslt((p,- qqr 6 ud yy/h4yg,hcving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistancetu h- r6y(hgqy( l4scdy/,,qp, will the ball land on the car or behind it?

Does the Earth really go around uz /ov7-f7 jx sgz/n3ng,ot+qthe Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that3nqg gt-u zxs/z 7on7v/j+f, o there is no best reference frame). Explain.

If you were on a spaceship traveling yzy , hke )+,rjqe-5ovat 0.5c away from a star, at what speed would the starlight pasz, y,+roe kj5 yv)q-ehs you?

The time dilation effect is sometimes expressed as “moving cloc04to ;jio) +hq(dskuv ks run slowly.” Actually, this effect hat4 k h(o ;viusj)oq+d0s nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly ink5;we3. z adwypd ed7wo: q-2z moving reference frames or that it only seems to q pzww-od.kz dd27y a53e;ew:pass more slowly?

A young-looking woman astronaut has just arrived home frmgg sbf6jm.*0 om a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to h mfbg0*sjm.g6 im as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c,d p0be f.gu ( vhbs*)aj25pbs1 would you notice a change in your heartbeat? Would your mass, height, or waist 50 *hae.pbsdbgb12 p vj(su)fline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at or tts ln9g-c/h;dinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would ha v:wrob,j yf0lmw9 0i)ppen to the relativistic predictions ofrwv) :iw09jobmlyf,0 length contraction and time dilation?

Discuss how our everyday lives would be different if the speed o3aoj3, imw 6hyq4s ij5f light were onl om6s33,jiahwy4 5i qjy $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used to)5sr-ui+ r07 pnoz. t5xf 4atg.e gmgy indicate that c is the limiting speed in the univerf5 m g.7 0 xt4t5)py-. u+gieraszngorse.

The drawing at the start of this Chapter shows the9fve 0osj,-dq street as seen by Mr Tompkins, for wqs 0df ovej9,-hom the 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 put an upper lt kk 96o goenbbs/2e7/nf9ju 3imit on the momentum of an electron?ubknb o7nte ks396 g/2jfeo/9 If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzer pe2qpkke:i8i -c9n 0ho 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 akjq s5g.6 ac8t spring has more mass when compressed than when relaxqkg5ta j.6 c8sed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." W p* f*vbl+sapxk3q1(qo4c+ivv(9gg r hat must we 3l* a cgxv+ivv*orkbq+qp19sg p4( f(say instead?

  Is our intuitive notion th zjb9/4d x2eoiat velocities simply add, as we did in Section 3–8, com b 9zdoeix/j24pletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0h0w7hzhq3.3 m e17ac qob zke9.750c. You measure its length to be 28.2 m. Ho7c1he9 zeaq 30bwm7z3.hqk how long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at3sv v,t,. weqz 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 int. jky gk.vt (4yxg14y y2jyat3ervals 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 to a star 125 light-years from Earth(thj zb, gtf98j+ luj2 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 is4cte (nlnh1 1x 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 sta 02wi i5qs8mhbl* ;+ 6woskrejr is 82 light-years away. How fast would you hav *be;5+6wmlr 8iss2w0hkijo qe to travel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to tr5xfoo ph;h4g( 2ra,b ravel to 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 make the trphgr45a hf r,2x(;oobip? 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 thg37qa*wstv :me 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 returned from seg(ywlkk8 30g60tco2mbtw ,qs,xw4 a 5-year voyage while travelin ,y8ow3 (gwgsb leqx 00wm tt,k64s2kcg 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 spac+lg h6k,tj9yl ecraft traveling 0.960,jh+lg y96ktlc 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 t9s)7a dt3hbu speed of 0.660c. It is measured in your frame to be 4.80 m lonst3thd )a7bu 9g 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 .p84j c+epfz/ 6ro maxs;srn wm, .p9d15 m before it decays? The average l;mr w.z9 m p,sn+.4ppe/ fja6orsx c8difetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelingd .mci, g ,, 9,t7xpsrzheeh.d at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its re++d fe:fjzkr 622k lvest mass? v =    c

  A particle of rest mass,cas (8zh.xq r:z0cv 6zonn3w $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a+pf 2 2watn58k )9gyxbfi0dp0wu oj :zt $v =0.10c$. 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 o u am5:xe9q3nr: xw-5c1csdgmf a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires ked-xsla6b 4 a8 ;:awo$4.82 \times 10^4 \, \text{J}$ 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 knownzfczu qc)i*ov5ti.v-c: q r4) as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in thv-zcrq i*4o t .:vicf)u5 )cqze process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in 6ydm-x hte zh507iab.dd2 qp2joules 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 pr,x a f-c1xekb+b6vx6boton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual ener wm ;*dh 4s8z)xi an.e787 inbdbchf,jgy consumption 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 from conversio+0cy(p k( zzlvn 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 itswz+l db i2*r) (gef0nq rest energy? eq)g w0drz+i 2blf*( nv =    c

  At what speed will an object's k; 1)eqrhlkbc do ;1zglg*/m p6inetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton fromerzy *d)/r 3zge-vd4 a rest up to a speed of 0.99a dde4zr/z -y ge)*3vr7c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic )a ,g4.ybcr n.dhwa6 6nwnlyg+m; b4 penergy 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, its kinetic energy ic kia0, hbh,i7w gsw:/s 750 MeV)?7kib/ ihh0w sw:g c,a,    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton acceleraty 1d 7oh:hm5ra5du*(s4 snzqved by a potential difference of 105 MV? v = *nz7qr5hyv ad: (sh5du1mos 4   c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? vyzq c7vod433 j =    c

  What is the speed of an electron just 3ei/ 97p z9y/ v9gj qrswji:udbefore it hits a television screen after being accelerated from rest by the 25,000 V /79wu93 yd9q:j zjpv siegi/r of the picture tube? v =    c

Two identical particles of rest )8yno 2 *dpnkamass $m_0$ 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 protoc h.pp t,px cefk/2t4+n ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum of an eld6 demvaa5/p,zap7,: ii x,jyectron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 accelegzp0+yu85f)o zzj f+q rated 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 m+sd-y cd6e wflew; ys92ehj0(omentum 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 nucleusza(( /4xy4sjlqnr nn f4 luh;/, $^{241}\text{Am}$, 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 versus k ,u zjbp/9tu.momentum for (a) a particle of nonzero rest mass, and (b) a particle wpk./9b zjt,u uith zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in af-e v;.dzfnah8wpi cbzw+486 circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the r8af ;8pi+nvfz .6hcwz 4wbed- elativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with uj1(hexx b-idy fr+*iz y4.d,respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. (rx ,ehydf4i-.ydz1 j*uix+ bHow fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in oy 72j4di (oy:*fmd5 jdm4optimf t*3ig/v) wwpposite directions, each with a speed of 0.50c with respect to Earth. fjd7(yojmw/i* :g4i2m5ptf4*3y)towmdiv d
(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 sechou lc*vp0f0- w3e) iaond spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with0l0o)u-w f ve* 3cphia 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 cm p,-cx on/gt tqz,,ztx(q*) alien vessel approach at a speed of 0.60c. The Enterprise comxzqg)m/zot-c, q*ct, (ptx, nes 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 po;qzek5s5hlu9 e nj1 yh7a8n: rds in opposite directions. One travelyes z9h;alu5:r7 8nh1qe5 nj ks 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 t isct:i.zh /9lhe same time, rocket B passes Eart9 ./hzclts:iih moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centru7c b c h lklo.8h7x8;nhqr(,auri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faste8 j0yi+3s0xxxsash r-r than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a signifxxs+si - 3sa 0r0xy8jhicant 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 speep a9 pfth95rs-sxlc ex:)*z4id $v$ 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 *2kuw7i zo/,:vhoyf w a 100-W lightbulbv7o :yh w,ouwf z2ik/* for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnet 3ftee1ii/q,m ic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass q 3te/1e,if mias 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 c. 76p9bxb8.*cz1pmzv+a f s0ccvmqu w ollides head on with a positive muon traveling at 50% the speed of light. The two muons (ezm.bv a cv*s 8q 6 +p0cfbzx17p9cm.wuach 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 *eh/0dqs 8:4yfcswyqa 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 rfcwssy : e0hyq48* d/qest. KE =    MeV

  The Sun radiates energy a,q.d b8xaxb. g+i3*pyo gvs (ht a rate of about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a negative chariwzapj0cvmr3a 7zw9-vy4 -j* ge 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 reqoh 9k8s-i2dpw5 f2 axkmlh,d0 uired to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (i,k25 mlad2h8i f-p0x k shodw9ncluding 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 percentage increase in the (relatig: 7v4 ard.isul7gz 4uvistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the a:ur7.g igz4 4luvsd7binomial 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 movikwi;sb8 d2 8fxng toward each ot wxfd88;i sb2kher. 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 )zqen6fgtax4cc :. f4particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtayizet 5yceed73lwxj(: c.kht/z3(-oins its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approximatelw33e7ytoeiy e.h (/xc:-lt dkj cz(z5y $5 \times 10^9 \, \text{kg}$, 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 + cwf,hb0c r):2*rjv 2grbutvso that its kinetic energy is greater than its rest massh+cbrr0b c uv2, v2:grj)*wft $m_0c^2$ 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 believesny5a2gu0 5-p saj;d ob 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? Explain in detail. How does this fity2dub5s a ;j- 05gnpao 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 wh 1isc ka--;s;am;uvone mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much dwh; im s1-v;-uk; casaoes the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling in opp6 foibvc)tsn7v0. asd.0 rf5 bosite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle'6b0brsivo 0f ta) cf.ds.75nvs speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0 qj2py0n0b-yquk6q (yct8a9t*lnm 7(rdt(qr .75c relative to Earth measures his ship tt(tuq2*(6dqk j y qm(l8ny -r9 yq rpb00tna7co 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 speed of 0.85c away from Eart f z2rj;wamxfv : /j;diov8p14h. You send a laser beam toward the Earth traveling at ve1x28 fr4jzw f:/ m;ivv;dpaoj locity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a t(0q:z-kf /efdi i3fdbotal 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 e/3:ikd(f-f q d0ebizfngine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What is -v(bcf f b )fc8m1)hf ua-man:the spaceship's kinetic ec(v- : mfm) auff )-bfhb8c1annergy? Compare with the 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-yeaz9/q(lqx5gt3m x ;ggy.p e o-urs from Earth. .t/3( l ;9xmeq5yz xggq u-pgoPassengers 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 speed necessary for this trip? u =    c

  A 1.68-kg mass oscill(fo-c*vdvt 8 lates on the end of a spring whose spring stiffness constant v8*(fod -tcvlis $k=48.7 \, \text{N/m}$. 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 ny b 6d:frf/(;5dbavq wgcbwg-2(9 dn$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.