You are in a windowless carmawz0*t wc 2r:vdpi/, in an exceptionally smooth train moving at constant vrtm*w z0 a,i/c2 dwp:velocity. 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 the experience of b, d y2kmem0gml:29cp reing 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 tha0: gkrm2clmdey2pm 9 ,t 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 heavy6ny0 m tynns/qh 2dr8: ball straight up (mshnn6n80 /r: 2tdq yyfrom 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 thatxr8k vm mz-i/.l1mh8 y3+fvle the Sun goes around the Earth? Discuss in view of the first principle ovh1 8m8m m lx.fziv k-yer/+3lf relativity (that there is no best reference frame). Explain.

If you were on a spaceg se 6y5v2va/xship traveling at 0.5c away from a star, at what speed would the starlight pas5evs2g6av/y xs you?

The time dilation effect is sometimes expressed as “movin6d- wd:.hn6:m86ewt gdjwb:kpn ve 4;txbwo;g clocks run slowly.” Actuallx:wbe ; 6o;wwhdb-d:j en6wdg6k mt v4npt8:.y, this effect has 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 in moving refergl s/p aqfy0z6 6xor x6gd(-;dence frames or that it only seems to prd6d ax; gs0po6yg- q xz6(fl/ass more slowly?

A young-looking woman astronaut has just arrived home from a long t2ch59 ;/rdmlk0wkp k erip. She rushes uk259/ml w;hker 0dk pcp to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a ,m mw.5hugaxu idy;/ctl5h +0change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth usint/h lxu5mmduh;y 0ac, +iw5 g.g telescopes say about you?

Do time dilation and lf+q g2p-(nhdkz+j)zb 0fg am4ength contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light wi:e xz.rugr9*cxtfybv 0 1f1 5ere infinite. What would happen to the relativistic x1:eftgiu9 r .vf5*b01 rzyc xpredictions of length contraction and time dilation?

Discuss how our everyday lives wov,, zyegbn30i zq0mrg n;wt 05uld be different if the speed of light were only 0mr ,neqzgy0,z5bvgt i;w3 n0$25 \, \text{m/s}$.

Explain how the length contractiq iyfs vd:r +bu xtd.j16t()y0on and time dilation formulas might be used to indicate that c is the limiting speed in tdj:ys fy x).r 0u t+db61vtiq(he universe.

The drawing at the start of this Chapter shows the street as seen by M z( jq,1o(atjjwdpm54r Tompkins, for whom the speetm,(zwodjpq 4 5a1j j(d 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 bv5ndss2 5 0nuc. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not, explain.0svs55 nn2u bd ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed ofm:m.7trq wq0 p 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 mb2huxqru vc( zg ,v72.ass when compressed than uv27x(qz hc.vgr b2u,when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be creathjx+w 7do wk-*1q 10.vsyih-b znogs)ed nor destroyed." Whaty+s7 ) -b.z1 ko*vdgs-i owh 0hqjnxw1 must we say instead?

  Is our intuitive notion that velocities simply add, x6: or8e (glwxhv0l- tlpv8kq h2-w8vas we did in Section 3–8, comp-x:vq x28 v(lewlkh0 8-tpv glo68wrhletely wrong? ----待选择----yesno 

  A spaceship passes you at aynm :kfaey* (. speed of 0.750c. You measure its length to be 28.2 m. Hofek ym:.a *yn(w long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels arg c;e f*cl;e;to pp.7t 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 intervalsq ,rxhi cq7g 6x.d0gr- 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 at a spen b8fyj m2z,d+ed 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 i;4 ylz+sft:gwm 4rmqo ;-ghlif)w9d7f its average 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 frh 3toiu,yztew8 l o612ame, a star is 82 light-years away. How fast would you have to travel so thatoh3 wte l8u1,6 iz2yto to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel 4i b,g mlfxvyfmu /:4:to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years wouldbu4,/4 mm:i l:yffxv g 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 s7a2//h v9v glq -nx6ectf)pw the 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 Ent dn(dj5e * hrwf2;u6zmerprise had just returned from a 5rj*6me ;ndhf uwz (2d5-year 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 long would it takn++j vvsm0nwqn7dzq 4cg3 //l e a spacecraft traveling 0.960+3/cq jqlgnns vv w47 +nzm0/dc 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) dw,jd yoipaim: bh: ,fel*/* of 0.660c. It is measured in your bw,had pe* )ij,m*:yoldf/:iframe 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 de5t-opls)i:d7jbo-d r cays? The average lifetime, atdoid:-r7bos-t lp j5) rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling7azppfpba , 59 )ndnmmrz6k o5/. ar*e at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be tst3s36 s;rfk gwice its rest mass? v =    c

  A particle of rest mass lid yp *ari * bbg0792a1(liyr$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelfmhc656*r+tbctdcxs24yy 1 zk(w;s b ;t ) xrls at $v =0.10c$. 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 momeu8 qn.b3lmgyx ;0tf xw,h3d ,rntum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactjth we.667zn xion requires $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaks apart in the proce s7nl)n:qt0tkq;18qdin*z:dx ( pvgyss known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of aq0pkxtnsz *tqn 7g;d:1dyln)8(i:qv bout 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest ene0lih(mfumea i ,bf1+rcjj6 : 7rgy of an electron 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 1wykyb m3fckkl25p ai,/m0u(in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in ;,zvyrb6gw(jhc l*8 othe 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 mass? 972bvzn 3nusm    $ \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 r xexvsbar8+jq(sz1 a*t68i *qest energy? v = t8q r aav1zx8 +* j(b*esisxq6   c

  At what speed will an object's kinetd 58*f:iaj-v+ (wdhw4g tcy teic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a sl7q lm)-iqp c6peed of 0.997c? W qq7i m-)pl6 cl=    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 proti18.s+y cf kryon 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 eneyp bw xcr-pi 20q89ze2rgy is 750 MeV)? zyw-8 p eq pbc0ri29x2   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of v i3y(18azxdh. utr.i105 MV? v z .r i3h8a1xd y.v(iut=    c

  What is the speed of an electron whob*juv.xq(*y./g ysho emf1x. se kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a televismnvn+cr :u cl8d.(3 mjthl2r 1ion screen after being accet3c2d1jv. l8 :crh( mnmu+nrllerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of restjl m4 o0v-sai6d0i(be c57)mtvdk - dz 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 protonwqu9n*( z /u+r-s(fwb9utl th ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed andhina u0 ()2 5wx o6wxvsj.bj*d the momentum 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 fsfd v n/bis;9;aw :4a27,000 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 zwdqe)2cc )6w;kx-qf energy and momentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleus69 eeetu)alqmy0n- czh: tgr-1 nbhk3k9wq. ., $^{241}\text{Am}$, 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 vers x /6+*j 8zqnkzkm 5+ mbxmwqbb)*3xzq oy*i.uus momentum for (a) a particle of nonzero rest mass, and (bo mxi ) *bmbxym3*6k.k+x*z/zzq qnwqbu 5 +j8) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-Gkk;o(a:v7h o ceV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The :okv;ao7kh( c 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 Ea 0lo:7ok 1lkmcrth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the metek 71ll0 oc:kmoor moving with respect to the Earth? u =    c

  Two spaceships leave E d q()i7hsd+wbarth in opposite directions, each with a speed of 0.50c with respect to Earth. b7 h)dwq+s(di
(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 traveli:b6 7o)wc1l5wuz fpmbng at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the seuo bwm b6lp:7)zfc15 wcond 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 andnb/sty7(tvv8cbw; *.zcdyn 1 ;, 3k-iwe ayz 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 at a speed of 0.9bwsi;w(y1bt knvdz-e/ v z7ny c a;c3dt8,*y.0c 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. One trewwssamj3r2p3 zl 7nhpb 96w sb+0.:oavels at a spw9s 3.o73jepbw 6 0h+m:al s2rwbsnz 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, *)kpji ay )zolm-c; n emib4*yfq2h1 of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the sa*h*bf2m ,py;4eyaki )qijn )oz1mcl-me 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 away. *d- g*w /cguuz
(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 travekoli:/2v.o e ha w5npg /sv(;oling faster than about 0.1c is called relativistoel; o5 v:2 ho .a/(snv/pgiwkic - i.e., for which 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 speed c gany157 e7ft$v$ 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 h *czat 5hn64ilave to be totally destroyed to run a 100-W lightbulb lc564nt a hz*ifor 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electro) ww3kz0)qwthn and a positron together? A positron is a particleqw) h)wkt w30z 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 cobu8 18io5c ehw6by+ 5bjosya5 llides head on with a positive muon traveling at 50% the spbuw55o 1+ij 8o5y8 bhbycs6eaeed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and n*/ jyvi zl:7wa 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 whe*inzl/vy 7wj :n a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a ra o410e6lzdxtat4 nc8)roiv +o te 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 to4 9u3 zw,drquo 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 required3z tbyc09bl*vx5ttw, 9ggkb+ a j*a) m to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and heliumm l9 , *j)5ba+ 0 tvkab3ztcg9*tywbxg 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 travelin6 ti6o:gy/l5ds yh xp..l+ndpg 110 km/h as compasd gph/oyyt+n 6.lp6x: 5ldi.red to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving toward :qhce 4g(3y apzhf .5heach other. Deterqhh .(pz4c35gefyh a:mine
(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 particlerf0n/w 78 tpss with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powerrl7s7x*n/ey+kq/ )8u sk zpmg by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Englyxrkemqk8zss+p/ ) * n7 /7uterprise 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 e nlwqtvyz*lh5 ;vv u(b4j6dv, 1i;yi5nergy is greater than its rest masdq5lz vw hb5li1 v(nuv*j4ty6 y,;;vis $m_0c^2$ 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 ir sxd/v.-q, 9.mko qzpnto a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he -v.k qo.dxm 9r,p/szqdo 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 react4gau9zo+n5sg 2zwb kmo.o. r7 to form two moles of water, the energy r5g 2 .r wnkg+a.o4uo7o sz9mbzeleased is 484 kJ. 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 identical particles oa2p(+ (h jfnyare created, traveling in opposite directions. If the speed of each hpj(a+yn2 of( 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 spaceship traveling at 0.75c relative to Earth measures. *owqyt+e t9:fuldv 8 his ship to b.otfdlqt :we8*+9 vyue 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 awylb 42pbh 5uuwkc/bi;u1d0wl897 u fqay from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measudkw4; 15 q bhy ul/7cu u290bbfw8lupire for the speed of the laser beam?

  A spaceship and its occupants have a total mass o m.n-5ez rph7)b/ kyief 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 spaceshi iz)kmbh- /n7p.e5e ryp 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 inih dv ummec;-0.sl 10s the spaceship's kinetic energy? Compare with the total U.S. a1imndh-ucm0el;vs . 0nnual 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 ofiay k (jo7(3w8:r cxlight-years from Earth. Passengers on the ship want the (one-way) trip to take no more thj aiw(:87ox(y fokrc3 an 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 oscillxzq+)9x,nbh8( ghfr izs9 ztq 4(wn +9riqw9eates on the end of a spring whose spring stiffness constant isxq9 8) gh qz,tnwqrnrb+ (xfzez +ws9h9i( i94 $k=48.7 \, \text{N/m}$. 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 79ph65 ,ek5,z fwasa ayh;l of$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.