You are in a windowless car in an exceptionally smooth train moving at const5*ou0w / 5flx zqc+qg (a:mjshant velocity. Is there any physi:ljs+c( o wf5q *5h/0qxguzam cal 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 being at a red light when, out of th45drdmg vh*)p) 4fthiq8 c; nre corner of your eye h 4vr)5rmc*;t4h)nip q8ddf g, 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 absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavyguw(zbwg+9b :z46bra ball straight up (from his point of( g9zb wz+gu4abb6wr : view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also validwx *-, e5xuok-o xnsa u)/dk 42paf/lx to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame)/xo42 kl afox5 nau )e-/s*xu,xkdwp- . Explain.

If you were on a spaceship traveling at 0.5c away from a star,hqfk0/x of1 q xur.p7n*p8mp bp3, f9d at what speed would to/,.kx p0 f*b3pdf7funp qqp19h r 8xmhe starlight pass you?

The time dilation effect is sometimes65lgr)o ty*li expressed as “moving clocks run slowly.” Actually, this effect has nothing to do w5i6 )lygtol*r ith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving refd /tq2k;1na adi08ek verence frames or that it only seems to pe/1ndtad 0;qvkia 8k2ass more slowly?

A young-looking womag4-5uz) izf5c xj4 4qmvw3 jlmn astronaut has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as hej5z5m z4w mq) 4l-4 jgi3xvufcr son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you nofae- dl1z;ve5 lh+x(p d-ag+sda(; r rtice a change in your heartbeat? Would your mass, heightxela -d (( va++ rhfa1l5p;z dgsdre-;, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occuygq a 0 :usuuy98j4-3zz/pepx6ap)ptr at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happenc m;( req2yqze47e(f l to the relativistic predictions of lzmqr((cqe y l ee2f74;ength contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light y4k,zweh:ql4 were only 4e4hq :yl,zk w$25 \, \text{m/s}$.

Explain how the length co.sny5 4w.8(;a) 7pl.jg k nwruzvidxl ntraction and time dilation formulas might be used to indicate that c is the limiting speed in the ( zu;.8 vlikjlrdxn4)p.s 5y.w 7wn gauniverse.

The drawing at the start of this Chapter showsgzgakv 3egxf 06,,y. f the street as seen by Mr Tompkins, for whom the speed of ligfgggfyz k.e, ,a603xvht 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 tcovsye: *(b4 this put an upper limiots(v 4ce*y: bt on the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero 3/5 fw o6hryi(vb0 fo ndfhptyp7/+9wrest 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 has more mf;c z1v 7vb 7w kmoaeb: cy:)+cr3kv/rass when compressed thana b/z3kk;:wyr7cvcv)o r bmc:f17 ev + when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroye )s5 d,t cixmc9c,ge7ed." What must we say insteacxed mc7,5g i, s9ce)td?

  Is our intuitive notion that velocities simply add, as we didoe fa. e w93)noy4vb:n in Section 3–8, complev yno3e:.won9f4e a) btely wrong? ----待选择----yesno 

  A spaceship passes you at a .hs6g5mf k em4jd2lb, speed of 0.750c. You measure its length to be 28.2 m. How lons l.jh5k6m2 f d4e,bmgg would it be when at rest? $L_0$ =    m

  A certain type of elementary particle trabmiz(llm- 76z j+em9uvels 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 dh 18hul tpqb,w,rwz)0epend 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 stte g37 ittdwy4 :r/ha-ar 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 averagi9nag4 ll+ +oo 0m*(y cwvor.fe lifetime 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 st5.u*8 evryhodaibi27pniz) 8iz m i86 ar is 82 light-years away. How fast would you have to travel so that2 m8 ipob5ad.*uvi)yi8 7ir8i enz6 hz to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away gled(.) en wt*at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip? t = lentge)d.( w*   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 Earth i/jbhev8 c:n uyrk:hx/ dm/(l:o,qse * m1*xfns $11.2 \times 10^3 \, \text{m/s}$. 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 vgb,m 67k9khk xswtf -ewm484 just returned from a 5-yeag9,tbmxf kke 4h-vk msw4 867wr voyage while 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 .l s+d2m4i8vfk s9pe/gy s*mt long would it take a spacecraft tra2s/ .v*iskys8 4tdem l+g m9pfveling 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 speed 9o,ilj:w vk 9sof 0.660c. It is measureivo, klj99:wsd 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 mo zqfcj.4u0. *vle 9xkyving to travel 15 m before it decays? The average lifetime, at l0u yc*v f9k.xzq4ej .rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum ofzjygop b510r2 a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its 1le n1j3aerbfa-5 l(b i8; zcirest mass? v =    c

  A particle of rest masu10 zby:;(-o28bon. ap (exlnqnqet a s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at61 lixftz2ofy 4l:;9o2ic60ef vj zos $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in momentum of a proton that ac k ;,f1x4d0kovy z .h)6gczihrcelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction rer l:k+(*e; qxl,ywits quires $4.82 \times 10^4 \, \text{J}$ 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 proe 765yecfer p3cess known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 Mepe3e efy7cr65V. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron10 (7ee oh pewa4ruxmc)ms2j3 in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a proton i rv *emxry94w* :k-rfe+c1c.tw.pfuin $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy con9vx6 s,v 4bhae6q rf1qsumption 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 bekealj(lpmw6rlict omy* :s9z 1g -2 84 obtained 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 particle when its kinetic energy equals its re35+cbv y y (yqg)o0z4p 2upcvmst energy? v = co zygmp4qy0c3v2(5b+yu)vp    c

  At what speed will an object's kinetic energy be 25% of its rmv9 l)),(4 qpeecl xasest energy? v =    c

  (a) How much work is required to acceleratehz n1yfxl,/ 8ictfw7 - a proton from rest up to a speed of 0.997c?fczlw7i n,/xfh y8 t1- W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic enefc5ljbhmy7 1v/di 0o 0rgy 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 eneru,mybz guw5kg2gs ..tr0sv-1 -3fijmgy is 750 MeVy. 2u-ijrs1.3u,vz-0ks f gbgmmw t g5)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by aa1ybvnj/8-yq+az .*t2ad vgr potential difference of 105 MV? v a-d rty avg n+/ab8zy2.1vj*q=    c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v = )+ o re+n6rgvl   c

  What is the speed of an electroxivx)vj 8a ho4n:3n3b n just before it hits a television screen after being accelerated from rest by the 25,000 V of the picture tubej vi3xx 3n8:)b4ho vna? v =    c

Two identical particles okkzm pok3 +5b0f 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 prp8) d-os b+;wip v6cyroton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 elepdw 5kr13-ft4p cq5lnctron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of2kt(kr* n7pkfo, al(xt aij0 9 mass 27,000 kg is accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energy and momentum of a prol ry00s .ua7ukp s )wobb(4-cyton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleus,7eh hjr 3q /ulvllb: ijdj2)2- $^{241}\text{Am}$, 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 qk6-4xau( awesus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zae4u 6kwx(qa-ero rest mass.

  What magnetic field intensity is needed to keep4d bo;9k;jb ho 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relao dkbb 94hj;o;tivistic 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 0qx gqt,t7/ p:f.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 re t,tpgqf7/x :qspect to the Earth? u =    c

  Two spaceships leave Earth in m5yw)zo x+ 7s6u*fe b ueyxu2b9h9n81mobaa( opposite directions, each with a speed of 0.50c with respect to ws6 m57moxb+1z 2oauhe9n8yu xu)faeby (b9 *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 Ea ;ry*gh yf2f:9yyh4+ r3lnv(hqy4m aw rth traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to trahmy4wy:y3 ;h4(+2fqrvfhy* ly n9 ghe 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 : 6cy3+klra ymm3ch2 6pzsno+sees 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 a6 cyal63y rp23+nmozm+ :cks ht a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. da-bvi)fmp:fo9iki 13t 3cj+ One travels a9 a 3dfijo)k3cbp1iv: itf- m+t 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 s k*iof.m(lpc5i21 h lspeed 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 Af5s ih(2pk.mi lo*1lc? u' =    c

  The nearest star to E ft5(-nb.+ arh5hwuhv arth 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 traveling fash ts7x 2mc c4v8jtud yyj(vr1u 7ms253ter than about 0.1c is called relativistic - i.e., for which the correction using spec8u2ys( t2mjy j c3 svdtx7mu7c14v5hrial 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 ozh hefv++(t5ji +y - dn p s.*(zg(vw,gzgs-y$v$ 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 )3lthiva0 jrq.p,c e /to be totally destroyed to run a 100-W lightb3i) ac0jq lp/r.vh ,teulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of el 8k0.- l09wf wayj,d9bepb lqeectromagnetic energy is needed to produce an electron and a positron togefbwq.8d, - 0 kewe9pyl 0ab9jlther? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light cov26 epjivza 46llides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest mjpv6z6 4iva e2ass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino. Assc1+ 4ovz q./vw )g;hhxa m;sm lkbpi48ume 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 ener. 1la mks 4 )ch8pgwmoibvv;; /qh4+zxgy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates ener ,1kwyb+dia 6h xid gvr-2u:m2gy 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 measured to :;bo wu n 2hc0 pda1w6cvqb++jhave 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 into its consti nrbjqb+aj3cg82( .cituents, two protonscj+ i .8(gbb3rjqnc2 a 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 total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a car,t :2qvqdb6 ax traveling 110 km/h as compared to at rest? [Hint: use the binomial expansix :v2bat dqq,6on.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speedvz*zf +.2:zybgcc j(io/-) ,it ouu zb of 0.935c in the laboratory, are moving toward each other. Determiif ) izugzz2bb,c*vj :yu-. (zto+/ocne
(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 pa-+tb ,ee--s sx v)tlmrrticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains it 1+qmrw;i(eazs power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approxi +; q1eiazmwr(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 as-:.w+ wjjv;em tp -sso that its kinetic energy is greater than its rest mass m j-wjt. w-es+p sa;:v$m_0c^2$ 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-long po vxlu vy1 e7,iyok*;l1le into a 12.0-m7 xu,*k i1ve; yvoyl1l-long barn if he runs fast enough (carrying the pole). 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 react to form two moles of wl*yv+ je7*oym) yj5sv ater, the energy released is 484 kJ*oy ymvs* l +yje)7vj5. How 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 identicalgb,fhb gu w6 +nfv4)k; particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one,fw;gkfgnb v4u)+h6 b particle's speed relative to the other particle? u =    c

  An astronaut on a spaceshi86)qeatsk 0wrp traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the shiste w0ka)rq68p, 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 awa) eujw 0y*4pxnc2d yn/y from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth/ ) pu*cyndwxjn 0y4e2 measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. Therfjbdcq 1c140/v w (ud occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceshbv dujwrd4q1(1c f /0cip 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 yo2y:0phn 9 9gwjng(ythe spaceship's ky (g9y:no0j9gp2nhw yinetic energy? 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 lg3oio5zrth2e wv:/e1 o m*c36.0 light-years 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 speed nvel 5m tg3coih *1ooz :w3/r2eecessary for this trip? u =    c

  A 1.68-kg mass oscillates on the 8xorg2fg k6/a end of a spring whose spring stiffness constant 2k8r f/xagg6ois $k=48.7 \, \text{N/m}$. 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 massa*j if*2hbrzz3 /z. ot $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.