You are in a windowless car in an exceptionally smooth train moving at const ffz87x: jd5pxant velocity. Is there any physical experiment you can do in the train cxff857 d:zxjp ar to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red u6wct+ql5e a; snb:j ,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. Wceu lw;bqj,na5:+6 tshat does this say about absolute and relative motion?

A worker stands on top of a moving railroad ca cizv ls.q8 e4gxw+56trz. ,kbp/bcn8g ,lp +gr, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball lanv .c/ zlts gx+, ke8p5biqnz8,blggc4 w p6+r.d on the car or behind it?

Does the Earth really go are+ 98h2 ndwy68our rv*xwxo.nound the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no bes y 9 dv8r2 n6x.xhuw8+or*oewnt reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed f9)zis zt)mh(su, -akwould the stai, t f) -k)azs9(shumzrlight pass you?

The time dilation effect is sometimes expressed as “moving clocks run slowly.” /ot8sp ;)wushActually, this effect has nothin otssp;u8 w)/hg to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that t;)ep zdzbx) u7*9qbneime actually passes more slowly in moving reference frames or that it only seems to pass more slowly?ne b qp)z9e ;uzbx)7*d

A young-looking woman astronaut has just arrived home from a longa 3mk(;iuuvweml.elcw(m9 7, trip. She rushes up to an old gray-haired maw(9k (a.;7ul3imwm c u me,elvn and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away/f5vq 55j+ sk9gvaqjn from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waist5 5 fj95vvg jan+k/qqsline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary e4q 1 fd5xa(sdspeeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to thsk r6cs 7ye-a 1h-y.ddkz.vz +e relativistic pre7-shrcdk.z-se ka d yv 6+.zy1dictions of length contraction and time dilation?

Discuss how our everyday lives would be different if the speenm)rr 5tt m3k4h4s9wx*-ur2zzsc 1e t d of light were onlyzn5zt9mhmtsru4s* 2tr c 3ex1r)-k w4 $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used top6a6 iwdo hij47)a 3sa indicate that c is the limiting speed in the universe.i6p4a 7o 6s jiwd)3aah

The drawing at the start of this Chapter shows the street as seen by Mr T+r(pelj))o o0ldb *pmompkins, for whom the speed of light is )b0j)l o ld+m *o(rpep$c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to tra buhc6)g2a;rcq0dctz007u ojvel at speeds less than c. Does this put an upper limit on the momentum of an electron? Ifuj00z brght207 duo)c6qacc; so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the -u5hwo,ei , ouspeed 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 meako09juv 61q 9qlx/hh+r)quy t ;y bgg5n that a spring has more mass when compressed than when rel+1hxk5you h)bjq/9u096vl gtq qgr ;y axed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor d3hl*xaf rbp(07qh asgl)2g+ gestroyed." What m+xrhpfbla gga *073s(h2ql g )ust we say instead?

  Is our intuitive notion that velocities simply add, as we/2zvx t1 a4v o5gke8yc did in Section 3–8, completelyexz2/og1t 85v acv y4k wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measqhyi;9- 4x1xvxh dh8 eure its length to be 28.2 m. How long would i8h x-hx ydx ;i41vqh9et be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a spar5:7xqr z :yyjlqotq, .w/z)x2a-vkeed 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 intervaq0xedtgukswn4xg , 8c. 67f gh69qzj *ls 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 tos1(acxom6q v 9 /sbsl p2mj,1k a star 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 is measured to 49llh13nzcoxq )s7*v ynk w,a 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 frame8gqb luw*zlj7dxq :q8f:y ;h7, a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 ligh yqhl8ugq;lwzqfx7 b7 *8:d j:t-years? v =    c

  Suppose you decide to travel to a star 85 light-years away d-sx/*3 0t43ksl bspks z qe9tat a speed that tells you the distance is onlss4e0*k q zs3 tpdl9-ksb3 /txy 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 the Earth i*gf5p23t7)ss a hurxw2 bupv+s $11.2 \times 10^3 \, \text{m/s}$. 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 stkgbd 2wjn+3djo q92k 4ated that starship Enterprise had just returned from a 5-yea+dgjkk jo q4bw 392dn2r 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/jc6+ vbmn,v lb-8hzw light-years away. How long would it take a spacecraft traveling 0.960c to reach that stjhzb b+vmnvw- ,8/c6l ar 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 05tro+mcyl36 2mfjebk8(;u :bsiwc( si)im3 y .660c. It is measured in your frame to be 4.80 m long and 1.25 m high. 6mbtm( f 2y)ms+is3w 8o:iky;b(ru5e3cij cl
(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 ct54 m1 s/bpqbbe moving to travel 15 m before it decays? The average lif5/csq4t p bb1metime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a prooju cn2c.x anpgg;o/c5 .rkek9)7 ce2 ton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic (/xt cby d:-, qtxy,al. fk1nwmass be twice its rest mass? v =    c

  A particle of rest mass+7r nevqxq 3 (up87ttu $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels )14 mba;yr69e hy,k vyzloiq*j b*y6jat $v =0.10c$. 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 accel f/axf.0 nftij:b3l+derates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requireszv3.2glx1sj (u8 jdog $4.82 \times 10^4 \, \text{J}$ 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. :2)dxdudu1 m eoqmh0 as fission in a nuclear reactor, the ru emx d1duh2dq m:)o0.esulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of axd8km b3xkmkctv(k1j,1dk8 yx:x5, xn 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 protoo ng/v:q (c*1tjbj sb-n in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consqnz, )*)wenr 37lpktccbgo / -umption 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, k8j:0 16otipodbez 4 *08 munoxs4rwjasjy 0ass?    $ \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 part02aen y0 1zawqicle when its kinetic energy equals its rest energy? 0qz1 ewa y02nav =    c

  At what speed will an object's9wi ibmogp;qu /1q(xem823 hu kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to *g9po3ecq md*a speed of 0.997e *9dmqp 3co*gc? W =    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 tra+-,p497 m(ck g4boiuiukh p6aezbxo (veling $2.60 \times 10^8 \, \text{m/s}$.
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 kinetomfwoqb3hx5/b* /)z6pi +x9qx q ,uen ic energy is 750 MeV)?+xx * ux5qim3h/e, zq wobn9/ bfp6oq)    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a prva6rprl x// 1boton accelerated by a potential difference of 105 MV? v = rv/xb16/lr ap   c

  What is the speed of an electron whose kinxi2edn:p06d qf8oc. d+,twz xg;q n k1etic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen afterleo 8) m w5mfl(ct;afm;n* bb0 being accelerated from rest by the 2bfal)el;mwn8o5 bmt cf* m(0;5,000 V of the picture tube? v =    c

Two identical particles of rest mah .squ/ djm+y ;78iupzss $m_0$ 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 proton9 kg*um,l,x alche1yid j9)) w ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 t3rzxaoq5 s,0hss )d-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 accelerated toc gp c cs3*q/l:no,)qa9h,kd p 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 ofryga h4id3m (/ 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,mif r ue tq9k2/gb+2i6 $^{241}\text{Am}$, 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 ozxz*l iv7x 49j8yi y,vf nonzero rest mass, and (lyxy8vvzx4ji,9 * zi 7b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving qv5s8zw2l0ye in a circle of radius 1.0 km ( 5z sqvy80e2lwat, say, the Fermilab synchrotron)? 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 (r 2pmsotux6w/4lu b 48with 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 witt m opbswu/l846u24xrh respect to the Earth? u =    c

  Two spaceships leave Earth inlo8e gdbhq4 k+oy16om+t 41 jd opposite directions, each with a speed of 0.50c with rg q+411+o64ho8 yblkmjoted despect 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 Earadozzn/77g v- th traveling 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 second ship with respect to Earth i7v-odz zn /g7af 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 a speed ox 4jcp 7*kxg:qxfl 9w w)1y0aqf 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of *kl1 4xj9)qa xw0q: gpfy7xwc0.90c 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 es l e8x5zg7ln g*-bbxi8cape pods in opposite directions. One travlb5xn 8xelg giz*87- bels 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 time, rocket B passesd5tzz9rz .atnnl; b 5v1ms b,3 Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative tobz.5m ,9az v 5;rdl1n z3tbnts A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-year3ccx xu7 -v,cus 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, anytuj8 l;4unn6qvx f2 sd9oxbj6vm )c5d0hing traveling faster than about 0.1c is called relativistic - i.e., for which the cc6 6 4nslx925d;foxjvnu0bd m )uv8 qjorrection 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 speehdh/i jm; lyx (df86)hd $v$ 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 wouonqk ;lh:wx33ld have to be totally destroyed to run a 100-W lightbulb for 1 yea3 q3hln; xw:kor? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy i3; e.hpy4coz( lq 9dfts 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 electric charge 3.9pozlhcetq ;ydf( 4is 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 rclu,* n 19-z:hwswexspeed of light collides head on with a positive muon zu n,*l es-wwx91:c hrtraveling at 50% the speed 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 proto8fc.yr7f h)+ svgxir: 4dqw7 5 sl t5+ndkk1hkn, 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 particles when a neutron decays at rest. KE =rl)r n.sw1vts7kx 54hgd:5ffhkc k 7+ dy+qi8    MeV

  The Sun radiates energy at a rate of abouth/dy).mltaq8fu n g i 4:2yxu: $4 \times 10^{26} \, \text{W}$.
(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 zl5u kzy+-ha5to 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 edf:s1n rl)5 c/p; eznbe required to break a helium nucleus into its constituents, two protons and two neutrons? The rest pc)fe/n5 e lz;d:nrs1masses 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 increa3z3vywq k(akwq a7z j/+- x4p8ja8ysfse in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomi8xw48yja yvzpjz( ak7a-k s3 fwqq3 +/al expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed os/o0 d h096n4 o vvwmspq:au4 j(y(xidf 0.935c in the laboratory, are moving toward each other. Deteh:/6su0aq vxns wy pj4odd4v (0m9( oirmine
(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 wit168doqjp oxrv c d:pt+o f3(l2q*k 7tteu/ex-h momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter and anc*n -0/ gld;vhik3q :s hkxz6atimatter, achieving complete conve0 h;xsqz/6kc3 dvik: *a-lgnhrsion 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 , ;t62ifv-zd ki ucc.othat its kinetic energy is greater than its rest mf2d,ctc;.ik 6v i-uo zass $m_0c^2$ 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 believ3 a/rrv8ghg w4snmo ;z-:q/qe-(m xtees that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is runn;tq3z4w-q/eg/ersn-vm( or x ahg: m 8ing 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 1-em9ta) yx69puz j zuform two moles of water, the energy released is 484 kJ. How much does t1ey6m p-zzxu99 aut j)he mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, tr 1rjk 8 a7u3io-xddrw.aveling in opposite directions. If the speed of eachrkjwr 3.o-ixda18u7d 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 .r j-v ckq 1on*z-c-hnqj /.rzrelative to Earth measures his ship to be 2jzcr qh r.cqn--o-nk 1z/*j v.5 m long. On the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. You seuxmp-a:xxlgi9y 44z3nd a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of th3x4 im a xl-4u9gyzpx:e laser beam?

  A spaceship and its occupants have a total mass of 150,008(kba 8vv msp7zs6,rs 0 kg. The occupants would like to travel to a star that is 25 light-years away at a v 7s(m8,kz s8sa bvpr6speed 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 spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What is rdo 8 ,v egm, qx11c4zqpo8m-g h4npm9the spaceship's qr dp eq4ohgx,81cg9mmn4pz-,8mvo 1 kinetic 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 i8t+ek f6*/gs p 0hv vrzvqwak gmgb a)6il*.32s to travel to the vicinity of a star 6.0 light-years from Earth. Passengers on thrtkwe3al)*2+f 8h /g6v.vqbiap v mg szgk 0*6e ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a .cr, wn(4htjm) vy)ehspring whose spring stiffness constant i t,v .en4()hhr jwm)cys $k=48.7 \, \text{N/m}$. 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 mk*v;eiqd0 qwte; e8 * qnb2ir9ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.