You are in a windowle 761ffy)t +;r .u,e yis.hdg lrc5)mx-znpudh ss car in an exceptionally smooth train moving at constant vednp7x ;rezt+.hmchl fr5)ug y1i,f6-du.ys) locity. Is there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had thebyu b18ejv 1fx62 rlca1h-te / experience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does th b1cj 1b 6t/uafx hv1y2lee-8ris say about absolute and relative motion?

A worker stands on top of a moving railq 8xe19ro* 5uf zyn;kmroad car, and throws a heavy ball straight up (*519u y onzfrme kq;x8from his point of 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 valid to say thooqg 65x4e 6.r0i)/ton,xxdfsu t p; +9kdhatat the Sun goes around the Earth? Discuss in view of the first principle of relativit 9xiaed; 5tx)+66pd0t.h uq ko,f/tso 4xno rgy (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed7 p*in9l: .w6uujv rzx would the staw: jx7r*p lzuiv9nu6.rlight pass you?

The time dilation effect is sometimes expressed as “moving clocks run slowlb0k/g*dwkf l:o(t) qk y.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then dqd /kf0:) *gkkow(tb loes it deal with?

Does time dilation mean that time actually passes 7 5 w0fu;zhubt(-nadn2 b(bn umore slowly in moving reference frzd20 bf ;tan7w-unh bn( buu5(ames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home /b8 h/nkt ;+ hng:nm4a,plz mzfrom a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this b+,nna;8:4m h/zlhtm gnk zpb/e possible?

If you were traveling away from Earth at speed 0.5c, would you no*aw5-+mwn t rtq *z9qctice a change in your heartbeat? Would your qc wtn rw 95a+*mztq-*mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contractv w ae:vr(0ka e4oq8:ydk0edfz6y+n 0ion occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the ret0o8dnj+se x7lativistic predictions of length contraction and time dilation?+xstd 8ejo70 n

Discuss how our everyday lives would be different if the speed sh4**oe0u e7fcdat,m of light were onloc4e ta0d uf*hs me7*,y $25 \, \text{m/s}$.

Explain how the length co6c.e,t kcuypt.9 o2 mjv8hr (gntraction and time dilation formulas might be used to indicate that c is the limiting speed in th9 huty.c2p6.egr vmjc (t,ko8e universe.

The drawing at the start of this Chapter shows the street as w6s xqhpvs,c0 fn 8q)r vl:q.;seen by Mr Tompkins, 86 s,wcs:h)pr q .fl;n0vxqqv for whom 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 thisrijqmag ,c 9nv,z;mm 7c5*ws4 put an upper limit on the momentum of an electron? If so, what is this upper lgcv ;w7m4 nr,* 9msqc,miaj5z imit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of lightw3 jp+ hf3(gt5dkkzg: ? ----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 mea-/w)p( ne: popcvhfh 3n that a spring has more mass when compress o- (fpcvh:p) wnep3/hed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be )yuj+/ v) r4o -bbznqfcreated nor destroyed." Whabr4q-)fyzv+ j nou/) bt must we say instead?

  Is our intuitive notion that velocities simply add, as we did in Section 3 kpcx:eqhs(1w13-uyp –8, completely wr qpcsye k1hp1:x-3uw( ong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You my fqvtpcl13 7/ar 7s6p2u2 zuceasure its length to be 28.2 m. How long wvr2l3pa7f z6y q/tccus72up 1ould it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speieaq: b3y)/aavv qp .*ed 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 det6l2 z)str-ozu2pe l y 1/qk5spend 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 stm.1fck+adktc-. 3g vgsm d8: mar 125 light-years from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime i mc1npg*vnao6 u ;2lg8o/fv4us 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 frampjkvg.ade:fk23e 2(d e, a star is 82 light-years away. How fast would you have to travel so that to you the dis dje2agv ke(dk :fp.23tance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed that tlx ti3)5 zg*(j6d dlnqellsx)dt3dl(q*i gjz5nl 6 you the distance is only 25 light-years. How many years would 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 tmu4*h fr1ge1cph7 qfc2p3m 6q he 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 fr/8f)q w 0cunja9 )cajjom a 5-year voy89)cu/fn aw)jcqjj0a age 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 .u-vc p zqs+ (taqa(zv)zqg8(ong would it take a spacecraft travv-zv. +qq 8p)z(cz(saug q ta(eling 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 of b +ev5o 16hxq+h i,qgi0.660c. It is measured i1x6+qv ih5h +,q oeibgn 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 moving to travel 15 m before it decays? The ave1b o2vd h8trkxi4r6f1frt i 2b d4xv6k1o1h8rrage lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protonhnhn2) wv(te1 traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relati8:8 o*zio/ pvt, r8rki.foma bvistic mass be twice its rest mass? v =    c

  A particle of rest massk qzsr2j i0-6e $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels 5 s,b4 bbzsxn* 3r(vwfat $v =0.10c$. 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 thav)tyct88y cpif c+yw 0bj7)9wt accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requz28jt9cj vp-v /y7jil ires $4.82 \times 10^4 \, \text{J}$ 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 restema y2xd y;:46yq 2sb0x cwo/q breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of aboy0sb y2yx /d 6qxow:2e;aq4cmut 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joule -zrr 2avbnv9c7 6z,ym.qwcj-s 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 mas*yj,n3 ych)sh s of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energ(ii.,mf1i98i nggbd b3q xg0vy 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 f78w4j7wcaiw4k/qid 2np avh-rom 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 5ntv0;/kgpm.j o4 jvxaz 6gl ,energy equals its rest energy? x4l/ ; jg 5p,akgtvojn6m0zv .v =    c

  At what speed will an object's kinetic energy be 25% of its rest energyh)v q 3x1j+h /+e*jgyr :wcbg3kt2xwe? v =    c

  (a) How much work is required to accelerate a pzzmvox 1)+e0wroton from rest up to a speed of 0.997c? Wzmoewxv1+ )z0 =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy anui2m ;gkq+ct7d 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, it660-3b:fsqh g xwv+ v(t;grl9r(mcj fwa5 i fps kinetic energy is 750 MeV):gamq0r fpl xh5wt63i6vrsf9 (bjg ; +(-wf cv?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerat )2hf7 t- z)7beir.efbbjtpsv2 le* q)ed by a potential difference of 105 MV? v = v2h 7sz)fef7 leibebt jt)p qb.- r2)*   c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v ,0ms8 vstsk;og 5v w(pdj8cp2 =    c

  What is the speed of an electron just before it hits a tx(wv3.dn1 dzdg*2lvk elevision screen after being acceleratedx1(nk.dl 3v vzwdgd 2* from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mass e,nwe-pf opn*,kp:+ev7 xkf i/ r2ss-$m_0$ 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 x,r7f0cez, ,wwq4jxu 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 mougnx++rgqxx :afw d/1der 88 )mentum 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 aqbjsg// uvf :0ccelerated 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 afegd*wd/;yi 8 yv (9bdv4.yr bnd 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 nucleus, a d 3+z6hcc4oy$^{241}\text{Am}$, 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) a particle of nonze9zllwg vb7. j*dakk ce2/8)zmro rest mass, and (b) a particle with zero rest mass*/zl9 dljmab zwk 287kge) vc..

  What magnetic field intensity is needed to keep 998-GeV prbd;s mq8j.fytxi2q). 1+rj w zotons revolving in a circle of radius 1.0 km (at, say, the Fermilab s.qjm;z+. ywxf j 2qstr1i8db)ynchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with rzp xv+gn,f -3 d,4shvrespect to the Earth) observes a meteor come g-pr3nv 4,v +zx,fdh sfrom behind 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 leave Earth in opposite directions, each with a spee3ud 7;4po8yagg.1wwmqz lj *jd of 0.50c with respect to Eartlwj3wod;gaz m.1pq47gu8jy * h.
(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 srtz0do 4f7 szf/i/w;n rr l.8bpaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship wi;8r0f4f rdzrns/w/i 7zb otl.th 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 approa w1w4 wzgq.4gdch 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. What is the relative speed of one vessel as seen by the ow1gg44q zd.w wther? u =    c

  A spaceship in distress sends out two escape pods i68p o) sob,8iewlv z;jn opposite directions. One travelsw8 e ojp,8ozs 6l;vib) 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 t4uepw:5kxek95n qjp 6z 5)y0a5dt fsaime, rocket B passes Earth moving 0.95c reksafey9k qudnpw 6ztj e5x 55p)4: 50alative 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 Centauri, 4.3 light-years away1 6/qldipx7wq.
(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 thanif 8lu6tnf67 m about 0.1c is called relativistic - i.e., for whn6f it mlf786uich the correction using special 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 speepxslu6s*l2 u-d $v$ 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 txdm 3n t4xhs3)otally destroyed to run a 100-W lightbuh3 s d3nx)t4mxlb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic )vshx hl pzda .7d.8g)energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note thalzgd)7 ah 8dvs.)xhp.t 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 travelural3o eq5( l9ing at 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (r llea9u5o q3(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 p9o7iz2d gd9uli46daw4kt b4 g :4y7pvebgo ;a proton, an electron, and a 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 particlespydg9g:4 2 e7b6 44d;abipzg 9do tokiv7l4 wu when a neutron decays at rest. KE =    MeV

  The Sun radiates energy a/lu 339mb8 kjrll 5uszt 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 5k(*sedc t:ol 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 break a helium nuc k6ck*bjhh 8hzu+m 5)- kg4tyileus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy ofjk4zh b56c* gmt+khy8)-hui k the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mask4ixx. +5 u fm1jl8liss of a car traveling 110 km/h as compared to at rest? [Hint: use the bilsxx 1+lmi 8 .5ikjf4unomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speeth /nf0l8u s,td of 0.935c in the laboratory, are moving toward each othensl8/u ft0 th,r. 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 with momentum ke b,inw.go ;ccm-.0g9r t(bz$p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining may(x 4 pfu9qcan 4- y2y7dt 8w:hgc0noktter and antimatter, achieving complete conversion of mass into energy. If the may gd2x9:p4 o(a7kn4 ch8q-uwyy tn fc0ss 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 energ 23+,remgqk-w ncbaa7 l,qov7y is greater than its rest mass +gn rob2eq-vw,q7a,mak7c3 l $m_0c^2$ 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 believesveiq05q+ 9uj2 rq(6 ctxqsf- b1l klz5 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). Ca quqez q ti9 cr2qj0l+-5k x1blsv(6f5n 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 ;s;(t;vwk kmi sxk+i , (1nhwmof oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass o;k;vtkws+i n(khm ; s1,(i xwmf 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 rqlmgh(1 xyzqn 7-kok 673a8bopposite directions.yo( bq7rhx-q8g1kn m6 lk3z a7 If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceshiaywtav gi5.;bz*;htai4 6/6na/fau ip traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunc6 f ihaw6*gt / y.z4na/i vtaaa;biu;5h 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 speeikz n85powqdt5-h(0w d of 0.85c away from Earth. You send a l i(h50wk58zdtoq - nwpaser beam toward the Earth traveling at velocity 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 mqno2o7, ihiz 7ass 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 engine of the spacihqo 2onzi 77,eship 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 isxe,6(xjmbx t6zqwo3m ; 5g6 mx the spaceship's kinetic energy? Compare 66q , m5xgwo xxb;jm3xmzt(e6with 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 traphh 0 o26:pyifvel 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 mf062iy:hpo hp uch work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscily9wz2p)he6i;9;d q ik (shfjdlates on the end of a spring whose spring stiffness constant efjh z9 h26;dw;k9iyi) dp( qsis $k=48.7 \, \text{N/m}$. 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:;x m j sbdba8+u- tsill(aj03 $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.