You are in a windowless car in an exceptionally smooth train mov g kxkrjpup61bv; /+)ping at constant velocity. Is there any physical experiment you k1u+/rjppxgb kv; p6 )can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, o9rf nm2eap.l5j- xc6,uc te2hut 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 doeh292pern f. 5jec-atcxum6l,s this say about absolute and relative motion?

A worker stands on top of a moving raihpe;k6g,*mv) dn5 h bhlroad car, and throws a heavy ball straight up (from his point of p6 k,h*hbnvg5;h ed) mview). 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 that the x9 oei+gu:yd 3Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best referen +dy 39o:uxgiece frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed cuott3ez5wi amm*0 /*would the starlight pass youu5oz*m cei0 wma3*/tt?

The time dilation effect is sometimes expressed as “moving clocks ru 0vbh5io;9v3skj( gyof *:obo n slowly.” Actually, this effectjo:goo0 f5vkyo3bsb9 *i v(;h has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually i)oxnupt(s29 t 6cv q:passes more slowly in moving reference frames or that it only seems to pasp nxv2i9 qs(ct )t:o6us more slowly?

A young-looking woman yj9lx)3mypo1 kj u mk(dq8abl0 c9:o9astronaut has just arrived home from a long trip. She rushes up okdl 3lxo(u90): 8a jy 91jpmcmk9qybto 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 spea.vu/x xyl-p/ed 0.5c, would you notice a change in your heartbeat? Would y xyvupx//a-. lour mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinar8a/mqgwi i4 6ry speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. Ww.. x9 )sfxjfk4oz,l rhat would happen to the relativistic predictions of lk,xl.9) ffxzowsr j.4ength contraction and time dilation?

Discuss how our everyday lives wou) wbpaq kkywa,p 1vyo;8i-r1.ld be different if the speed of light were onl.,8-1) yoiwpp vb ;r qkayk1way $25 \, \text{m/s}$.

Explain how the length contraction anpe(6ny5zphb v w v(b a4o073ifd time dilation formulas might be used to indicate that c is the limi7p b ( wbnov fi3y64vh(azpe05ting speed in the universe.

The drawing at the start of this Chapter shows th8 **e juil 7 )n2e6/czzgwwyx4l epev/e street as seen by Mr Tompkins, for whom tl vw8 /2e cxzy *u7n jeizelp/we)*6g4he 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 spel-)nr 9 k8 nh;w2wmtz y32zvl9-s o;z3wam abneds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not, expa8 ;w-t b)nanr w- nh3m2yzl;vszok9m 32lzw9lain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speedt(e a9o8opq 8cgw g,o* of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does this mean that a spring hasra8 ;82cw t8u f,ajovn more mass when compressed than whv;t8n2 j ,8ru acwoaf8en relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be cvi) m l2 qmkhgb(49cs1reated nor destroyed." What must we say ins(21) m9bhklcm qv4gsitead?

  Is our intuitive notion t )n 5 iba(gdz7m,prz)uhat velocities simply add, as we did in Section 3–8, completely wroirmz)dg 7)npab 5( uz,ng? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure itshisq2--o d0 iop2io7i length to be 28.2 m. How long w ospi20i oiho2q-- id7ould it be when at rest? $L_0$ =    m

  A certain type of elementary particle3 e0ds ;otewx* 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 intervhr4(b.4bdldvp 9(itaals 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-x(.hyx0 i-j 3hq+j:5nmjxryjyears 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 lifetis**sq)p q z/ceme is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light-yv+( t- av8yrhoears away. How fast would you have to travel so that to you the distance would be only 3rv -avy(8+hot 5 light-years? v =    c

  Suppose you decide to travel to a star 858 rw57s v92puwu8dctd light-years away at a speed that tells y ct 8 spuw8dr792vuw5dou 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 v,)w,c gx(rth 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 Enterprise had just ret9o0u /1zumljq,dk4 rev ,p tc.urned from a 5-year voy. /4mqdezv9,j0oc u1lrkp,utage 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 wouldin++ i,9lnj afv1vxdy-6 e ,jf it take a spacecraft traveling 0.960c to reach that star from Earth, aiyje+l f,ijn1-f+xv69,nva d s 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 rua59: kjn 5e1 yzwx(znmq0l *at a speed of 0.660c. It is measured in your frame 5y x95ea ku(l n*wnqr10:zjmz 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 traup7khdiy 1k myc 3hs5q/.5 d5mvel 15 m before it decays? The average lp/73h1hi 5kdy. q5ymcudm ks 5ifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protownw, pf rph-.yd uibi7 +-n:wc+ulb3+n traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be+dez:h; .2 x8 tnzntt0y176fagn) c axyrk(ia twice its rest mass? v =    c

  A particle of rest m3mr gq ,gg.00ieor3fyigprw bs;71/vass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at jn blk3p;* t 8;q ssk ;,w1ks+/hzzjdw$v =0.10c$. 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 c / rc+ob xn7uez tn9hdu58ssq)b* d+2xhange in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactionkekqu/w9+b 1 iu)rr7n 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 pry(uo) u-8khtkocess known as fission in a nuclear reactor, the resulting fragments have a tota(k o)u8-tuh kyl 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 an electron in joul 2wnpcqq kdpv 7*o;w9b/vt nw3k((sp7es 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 l -1f9xnk1o16: mkcsh qlgf )ca proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy cq9iwiwo )u 9z. 5.xa m/d,jmiionsumption 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 convemui7 v a976iqlsb6 j-zrsion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic energy qn/9o4m m xkr,xg(hq5 equals its rest energy? v = m5mxrh,o4n kxq q9 g(/   c

  At what speed will an object's kinetic energy be 9yd0, ext l8ia25% of its rest energy? v =    c

  (a) How much work is required to accek5 kjr:h.izp.gyh01fk2h( s jlerate a proton from rest up to a speed of 0.997c? W =gskh k:..y irphj02j5hf(k1z    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 pro k h+n:4he1nuyton 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 energyaxc ztw0( 9axe pt:.)j is 750 MeV)? 9axe ):(t. t c0zwxjap   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a protow 3wpx* ,woze+6hlgm( n accelerated by a potential difference of 105 MV? v +oxgp3 *w(w,elhwz 6m =    c

  What is the speed of an electron whos ik44j hyzrs19e kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just 4bgvyv/u+6h xlu ze4,before it hits a television screen after being accelerated from rest by the 25,000 V of the ph4v6ue+x4,bu/y gvz licture tube? v =    c

Two identical particle m0zp7s) g+l8/e3fvu+t qkwacs of rest mass $m_0$ approach each other at equal and opposite speeds $v$. The collision is completely inelastic and results in a single particle at rest. What is the rest mass of the new particle? How much energy was lost in the collision? How much kinetic energy is lost in this collision?

  Calculate the speed of a pro sv zh4)4njx(sbsazclu9r0q)55 n 4kgton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momg/2tbgyfb uuednxh6d83q;/0 entum 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 m2lyfpu eu* )urg-q*zial le610 n l.(nass 27,000 kg is accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

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

  Calculate the kinetic energy and momentol:pwa jfqm qo6nj+i ( 82c5x(um 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 nucleus0b u.tzs2y3 lv, $^{241}\text{Am}$, 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 nonzeyt t3x33lc ,qdro rest mass, and (b) a particle with zero res3l qdtxc, yt33t mass.

  What magnetic field intensity is needed to keep 99em 39xnaaze3/ 8-GeV protons revolving in a circle of radius 1.3xnea9 ma z/3e0 km (at, 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 (with respe; ;n (zkt2ofgusv whjc, 5h)u5niy t1*ct to the Earth) observes a meteor cji;czunkt*y(n5s; gtofuwv hh2 5 ,1 )ome from 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 oppoo j e7xt73.+-:e4t 6zb qybalfufqhc/site directions, each with a speed of 0.50c with respect to Earth. 7ful b+ h4 a 3tzqxb7fq-e ye.6o:tjc/
(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 spacesvq6ommo/t w,ka b7 uf 0m/b46lhip leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to E/tbl omfqu7 o m6avbm64 /,0kwarth 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 a .q-y:sd :izqfw)z*j opproach 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 fod*:szzq -) w.yji:qEarth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escapem ,qq4w2 +x -cdd(dy owa6/y:g 0dkkex pods in opposite directions. One travels at a sx/w e6cdkad(y odw d+x-gk0q m2y,:q4peed $v_1 =-0.60c$ 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 passes Euehp2g,pbk7 +arth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =7uh+ bk,pge p2    c

  The nearest star to Earth is Proxima Centaur;lf1 -)7fijp+9zk b8ny2not tuqney :i, 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 about 0.1f (0x2 .kxi4 y /(rxiq-dwfqftc is called relativistic - i.e., for which the correctioixi r( /yw2d-f4xt0qfxqf.( kn 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 speed5 r7p-(+o 09: 5qbudq -nuqjvlin txkh $v$ 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(g sz2.ne.kj,pgm1 ig to be totally destroyed to run a 100-W lightbulb for 1 ynz.2j (m sp1kge igg,.ear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromiqx1q. ( (n)vy)ercjgagnetic energy is needed to produce an electron and a pog q1eyxn(q.(i cr)v)jsitron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

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

  A negative muon traveling at 33% the speen4mth:iq5rqt4 -f hr4d of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (hr:hnf4i - rq5m4 tq4teach of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can dec6x37xd- z gwgsay into 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. Determin g3gsxd7 wz6x-e the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates ene.voxdr- k,*vi.o ce8g rgy at a rate of about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measureh g(98muxtv .xn6ew.,z+ owopd 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 break a helium nuczj7826xem xpn5; 5opz w xbvi3leus 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, a 586;2jnxmvzpe5oxwb 73x zi pnd 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 traveldw-9:eqgqy. 7s6ngt c ing 110 km/h as compared to at rest? [Hn :dc-q. qysgg76we9t int: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having zpaq*jnp66dy -og ;*(gyx oz+ a speed of 0.935c in the laboratory, are moving toward each other. Detero jn;6y* zz+xgp (do*qgay6-pmine
(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 mom cda-tk + 8idrfi.33ezentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combiningch)7tn2yj.:(k/ a,qqpet:d6ljjof kyph3:r matter and antimatte. ctla : qekyp:j2 7/pfh( kdrny3q:t, ohj6j)r, 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 energl15qwz)e- in)xkus 7my is greater than its rest mass m)7-z qlw5k1xesu n)i$m_0c^2$ 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 1(x m1vy)t4bbbo:tz 5 g5.0-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 f1bzt5(bo4bg yxt) mv :it 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 relfqnxbq+p jy o055d,+act to form two moles of water, the energy released is 484 kJ. How muchb o+qj5dyx,0n pf l+5q 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 identicabz,,fb:6.q0/y xxgk(1no rxlubp+wlv:y / rql particles are created, traveling in opposite directions. If the speed of eachvb /nx/06,p fl kuy,bo(xql1y:.zqrr+gb w:x 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 tra(3vi-tmw1)2u dpmr + foxo du9veling at 0.75c relative to Earth measures his ship to be 25 m long. On theo 2dv+1d po(9wu) 3i-xfurmmt 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. kk.;dyww dcl7 k((r(e85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the lasw r 7k(edkwl.yck;( (der beam?

  A spaceship and its occupants have a total mass of 150,000 kk+;q59w xt bk;c.-fxc4z neu cg. 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 spaceship change tq knxc+;4cecux- 9zbwk5;.f s 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 spacesh9l6gz a *jnls /4+ c1(zbl*zcxwdp.rtip left Earth at a speed of 0.99c. What is the spaceship's kinet *zx91a t b(sw4z/* rcjpdl.+l6nz glcic energy? Compare with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vici,7r v6fvhkiuyz 3b j;gw8a-l- nity 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 ;6z3wy-fl,kv8javrg bhiu-7 it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a sprq-vh8 g+uml-u.zumo/qe m a/:ing whose spring stiffness constantmm/ -eq+om/u hv :.lgu zu-qa8 is $k=48.7 \, \text{N/m}$. 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 zu7ak3a ygth+h tsl93,p4h,u$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.