You are in a windowless car in an exceptionally smooth trai. bohu 3w 3dd0pi(j+bpn moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you a dopw du30jb.b3i+(phre moving? Explain. ----待选择----yesno 

You might have had the experience of being at a ret 5qvn5+1ti)tnp-; npv zdyd)d 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 say about absoluttn; v5zt +-t5)vq1n ydin)p dpe and relative motion?

A worker stands on top of a moving railroadi;2 ,:ym*w,8twebwgq+zq m j e car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behiniw8e+wmwqg*y , , z:jq2; tembd it?

Does the Earth really go around the Sun?u;r+nmby)yojl r5/*c yd(e/abki 8f2 Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first pry 58rmj+bbdfe/)(a/n oiy ; u*2cy klrinciple of relativity (that there is no best reference frame). Explain.

If you were on a space* oa wss(zvenq-h;-4rship traveling at 0.5c away from a star, at what speed would the starlight p*he as-wv oqnrs;(z-4 ass you?

The time dilation effzr 09 q1d4ul/rmk0:6rrjnif fect is sometimes expressed as “moving clocks run slowly.” Actually, this effect has notq6zff9l rm1 ji4r rk00unr:d/hing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that )0npf,grx )tte: qrb6 time actually passes more slowly in moving reference frames or that it onlpxrgq:nt,0fb)t6 )ery seems to pass more slowly?

A young-looking woman astronaut has just arrived home from ag0 + +wus :tt:fwie0tp long trip. She rushes up to an old gray-haired man and in e+0tp: uf :g+0tistw wthe ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, wrbyz-fx d zrz q4)7ri7,;hq(yould you notice a change in yoq4fr 7b iz; r7zdyq(y -zxhr,)ur heartbeat? 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 ordinary speeds, s9mxrr75w13llp y7*mz py +6d; vsnnwsay $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What wxfc:)ymu t(c+6an/ qhc1dh 6r7xtr 7 lould happen to the relativistic predictions of length contraction and time dilation?mcaqu 16r+xhl7 t67dn t()ycrf/xc: h

Discuss how our everyday lives would be d8 plzk3 (7qp n mxymr(:v5xa ,-*hvgutifferent if the speed of light were onlv txq 8ua:kp mg7 (m r5y3lnvhxz*p-(,y $25 \, \text{m/s}$.

Explain how the length contrat9kf m:11sb6uv r 0by/fajk1c ction and time dilation formulas might be used to indicate that c is the limiting speed in the univk1 afr19/byfs0um6kj bct1 v:erse.

The drawing at the start of this Chapter usyj u6lpw8k :b+- mh0n+1gcq shows the street as seen by Mr Tompkins, for whom thpmk qs:0yl1u jb6w8+ch+gn-ue 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. Doeq;vb 7f6n jn9ms this put an upper limit on the momentubn;f 7v jqmn69m 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 th2bfyo 0p, /awqe 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, d*4m4o-ch blqmoes this mean that a spring has more mass when compressed than when relaxed?4ch4mq l*mbo - ----待选择----yesno 

It is not correct to say that "matter can neither be created norha(j47*d-cwm; oq p7 jt)elvp destroyed." What must h7td(*;pqcwe j p) o- lja7vm4we say instead?

  Is our intuitive notion that,gz 2hw9fav8 t velocities simply add, as we did in Section 3–8, completelh v,wt fz892agy wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.75 djly3/wbw. f-0c. You measure its length to be 28.2 m. How long would it -dwb.3 fwyl/jbe when at rest? $L_0$ =    m

  A certain type of ele /unekf8gx*c2 lyh,1 -h-e vzpmentary particle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals dep1bb 19a:xwb1p g 5cl4sb6tw-d pz,yikend 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 at a speed 042s a5k0utf w nk;hagof $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average b)sm5n+y;+;xdds 8siy h.v7/r hxhvh 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, :nef pw; muv ia,4p.q0a star is 82 light-years away. How fast would you have to travel so that to you the dismf0e p:v.quw;,4na i ptance would be only 35 light-years? v =    c

  Suppose you decide to travel vp2b);s ei an.to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years woul spb.)ei v;2and it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the za+oxgoc8rs cd-(4 ,f 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 Enterprisx-(/j*txuok3aq -v +uf zip)tlb(k9 ye had just returned from a 5-yeajitafz b tv-k /k-xp*+ u ql9)((ouy3xr 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 tqm j83dos9s vkij:4 ;away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as8 mv3ki otsq94j:ds;j 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 / ,rm-ufw.5llhkc c;j "Ferrari" spacecraft at a speed of 0.660c. It is m. c-5w;jlcr ,/u mhlkfeasured 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 avera;nlmp/c-jg yk ew5;j1+kjky0 ge pion be moving to travel 15 m before it decays? The average lifetimj0;1 kgnjjkw5/cl;-kye+m py e, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a+b7h x,wp wo hm9y:w5p 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 reiyn(,+ xzvwcc ; oew9)st mass? v =    c

  A particle of rest m7g)xrl40h g kr2poto5 lzx2 t;ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at4p +w:2 8fi td.bzheok $v =0.10c$. 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 accelerac6l0g . stlzmtug-13;xhf 6ea e19prxtes
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi72rv)/5 6edxp x imlferes $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaks apart in the process known as fissionxv9o3 *s4n x:p h(e ntiwl -,3p. ztwes4f4joo in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was v 4w3ji9pos,:o-tx*x l.(e es p3thnwof4 zn 4lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules anb 6zcm2u/d. uqd 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 57e-2mg(n xui)znhs n9k-c rbht: p2fa proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumptioepe4f d xk8.t ):.xpkpn 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 conversion of 1.0 gram of m+ 2njf)tgb0 umass?    $ \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 qfio luf +n*t6e4bg u7n9(wk+-vjv2t when its kinetic energy equals its rest energy? v f+(jq*itbnn-+ g42tlw6oek7 9vv uuf =    c

  At what speed will an object sksoew:y,-x5's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accev-sseudh2f)( m73 7sspxcoc;lerate a proton from rest up to a speed of 0.997c? W = 2(s c upcv)7-xmfhsdo37e s;s   GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton travl hcpp(0q 0;rsu u;j.qeling $2.60 \times 10^8 \, \text{m/s}$.
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 u x(c 9xf+o1zpr6 mh,st0 n4x;jfoqt3energy is 750 MeV)?m0 1;o(9 36 fnor x+f,tqsxputzh4x jc    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerateb,+ahy(n h5/hbvkqp/ d by a potential difference of 105 MV? v 5 bkh,q/np bv(hy/h+ a=    c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v (f-m7t 4 bmhprr1 2eiqs1sq dq3 zy-g7 =    c

  What is the speed of an electron just before it hits a tegt erx mwcc4s:h.)2fq0tj7 h5levision screen after being acceleratedch:x5 0qm7 h )ctsr.2 tf4wejg from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mathd zcrb*llq01c-1 5mss $m_0$ 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 o o:matwgb.0-4w ql2eof a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum of an 2let9 eh,h3w/g u1lnvelectron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 9og ngqh4y6mk di- 21g2 jtl)bkg 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 mikq4 cr) x// zh,:7zn-h pzmbjomentum 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 nucleus, ,y8f2z eq+v g+)wqpjc $^{241}\text{Am}$, 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 momentum for (a) v6v +1gt))gbp w jvi6 q*lerc;uj 3my,a particle of nonzero rest mass, and (b) a paj1r* vwe6; u m6 vljc,y+piv)gqb) t3grticle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV proeq6 ,5ql2.o8b ww ndqhtons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The 8oqewdlw5n,62 .qhqb 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 respect to the Earth) obserxbq 5 ,c7pzi9n a;.o; pukiiu*ves a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor monzi p;ux. i,koia5u9c p ;7*qbving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, )-,lwh.arkcp each with a speed of 0.50c with res-c),hapl w .krpect to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A second spaceship leaves b-6o*a5-zehhn s c ,4wsvv lg4the first at a speed of 0.87c with respect to the f4n gzcsw-e-v hosa64b l h*5,virst. Calculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at ye hy0:.wlsv9 *,g n8etq:( n9wvzeb pa 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. What is the relative speed ofye9 ,ghn:( eq :svy.twpnveb*8l9 w0z one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposit b5)o:k sjh:ete directions. One travels at a skte ):jbsh:o5 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 speed of 0.j1izet z0y*/a9; wlxr 75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relr*l0j;txi1a zwey9 z/ative to A when it passes A? u' =    c

  The nearest star to Earth is Proximaj zs1l1d7qnbm t;y 66e 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 faster than 5mb0rrti a (6pabout 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speedi5rb(0tpa mr 6 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 speedeq v+9,lf i6mu $v$ 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 dm7 jwrgfw8h m0/7aqio06 -mzkestroyed to run a 100-W lightbulb for /7ij6qw 7k 8za0r0mg -omfhmw1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic e bgn0ht+9 ow 3(x3nvvbnergy 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. (Note that e nbv3(9x b3ot0 hwgnv+lectric 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 collides head on wijv vo-vdj i( *8.ab9nqth a positive muon traveling at 50% the speed of light. The two muons (each of resbivjqvjd8 (9n .vo *-at 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 electzq z+pmg(ksno j3(v4.ron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table iz4+oq(jzvkmn g(.s3 pnside 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 rat q8qez1e8*8 ifxj 0lgle 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 measurepsh(pscv,xh5.0) *an b y0wzhd to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to brea0hf1 jre6ysrvo1 o:q q63m kx-k a helium nucleus into its constituents, two protons and two neutrons? 1qj61rx y0 - kh6frq3osvo:meThe 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 traveling qlxa ow 4(*+xyh mzj(3110 km/h as compared to at rest? [Hint: use the binomial ea43oxz(m+y xl *h(wjqxpansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the la; xh)ubxd gg:nnh -.)0tgd g+mboratory, are moving toward each other. Determine gh mdgt+b0- dgx ))x:g;nn .uh
(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 witkg,w9f 5h fto.79whjk*b 9xom h momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtainsbtq -rj i gyq31yyo-.0 its power by combining matter and antimatter,gqy0bq-3i y y1. rt-jo achieving complete conversion 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 accelerated so that its kinetic energ2izidngu23do ilm j t51.9b6zy is greater than its rest mass i2dbd gt3uz6 2.ioi9n l1jmz5$m_0c^2$ 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 pole int03surkpv n0as3)6of m4 iia9ko a 12.0-m-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 a)6i 3onsua3kskv0 9rp 4fmi0 barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxm;a,ifm p:bb /4cetj01k k (yaygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this r b;mi: emj c,4 a0(f1kk/ytabpeaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
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 opposi6y3c:kkouca iz trh(0s co,*0te directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is tr,:czucsh60k*a coo(y0k i3one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship tr,y8zbf;oujz .d+q 6l haveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats 6oq+8h b;lf.ud, z yzjhis 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 ;cw+h( k3acc+d zik1r08b4dgh vu /ei of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocitawz+ck(8g;hii0ue4hcd/ kd 31cr b v+ y 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 total mass of 150,000 kg. Tekcc4xdn:e nuh1*h-r7 1c- cche 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 direhx:c*u1-4k71 n nc-rd c chceectly 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 /ruzxr9zy (3w x);xjf0.99c. What is the spaceship's kinetic energy? Compare with the totaz3j r9;f()yr w/xxzxul U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to trhcu, jg9o)uztfb ;*5gxoc 0 rzyx(c;, xm/6 jvavel to the vicinity of 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 work must be done on the spaceship to bring it to the speed necessary for this trip? u =g;*h6 ;/zoy, o xug0zfbxcc(u vcjmt5, x 9rj)    c

  A 1.68-kg mass oscillates on the ehqk/ j m/q66yrqbodtk (2m 4;and of a spring whose spring stiffness constant is 4bd m hj2/t qk;a66oqmyrq/(k $k=48.7 \, \text{N/m}$. 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 mng +6 xjxz9n*had8wofv/p/:mass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.