You are in a windowless car in an exceptivg l)yxcoda*:7vt .)gonally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whethevcgy .ga) xd)*:lt7ovr you are moving? Explain. ----待选择----yesno 

You might have had the experi/s/we ha-jx4 jence of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Ins/ej4axs/h wj -tinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving hrdt /+ge7iq9di ) oq1vlo(2v railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behind ito1vrv72/+d oqhgi)9q t( diel ?

Does the Earth really go around the Sun? Or is it also valid p.w ,hkzfh48wto say that the Sun goes around the Earth? Discuss in view of the first principle of relativ hpkfh,48.wz wity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c h2mmx v/4l 6jsxy lauy p:hinm490x+6away from a star, at what speed would the starlight pas4xyhs m6 uhmpavm 6yx/2lli:nx+9j 04s you?

The time dilation effect is sometimes expressed as “movi ya+ //whxk)8 jj-oczkng clocks run slowly.” Actually, this effect has nothing to do wyj +ax)kjc8/k-oh /w zith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moviol7 r3lr/n8os t*9hgong reference frames or thatot 7sh9*oo3gn8l /lrr it only seems to pass more slowly?

A young-looking woman astronaut has just arrived hot:prc(z +- ouj2h; 9ra9x/q:ye7halu a hyv/ pme from a long trip. She rushes up to an old gray-haired mt/p +e (9uzoaj /a7ahyrxyur9q:- :lcpvh2h; an and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earthu/7uro7 g -leh at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline changee u7/rhu7gl-o? What would observers on Earth using telescopes say about you?

Do time dilation and lex m +83gymfda7kbogkzq9y2 -5ngth contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were ik:kc2 ,9yqdcrie e- ,jnfinite. What would happen to the relativistic predictions ofqe9:kye j d,ckr-c,2i length contraction and time dilation?

Discuss how our every t nx*+hia)tg-. r4qlzday lives would be different if the speed of light were onlyxnz) +rt- tlg.i*q4h a $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas mightlbfw 56+n)exzyvfs 8+ be used to indicate that c is the limiting speed in the univers5wef )xyvns6zflb+ +8e.

The drawing at the start of this Chapter shows the street t;uwo7sywe1pc 1 r08a as seen by Mr Tompkins, for whom 1 7e;swtu cwyp0r1 8oathe 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 this put an uppero4owqb/ h w0fhc)8tq57;ixxq limit on the momentum of anxb qc/45hifxq;qwo8w0h7t)o electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass amwzgp,i5k m7031k *yj itks* httain the speed of light? ----待选择----yesno 

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

  If mass is a form of energy, do+ guuas 7+r 8pnvrwo4u.ub;* thms-m.es this mean that a spring has more mass when compressed than when relaxed mpm t .+guno8ha- vu7r+4s*suw u;r.b? ----待选择----yesno 

It is not correct to say that "matter can neither be7xc/p-y6cdf6(b eq3ac 1e n zw created nor destroyed." What must we sa(b pzxc e1ewyfad 6-q6 /37nccy instead?

  Is our intuitive notion that velocities simply add, as we dido*gd )e 16badl jgwk-l7xl:5r in Section 3–8, completely w gal l5we1-)lg6x j* r:oddk7brong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to bw ylztreys2 m-1z5v2 cx2p x;5e 28.2 m. How long would it be whe- s21 x5; v trzxpc2zylmw25yen at rest? $L_0$ =    m

  A certain type of elementary particle trav q;znvn1ry l8-els at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals depend on the factor 1jo9o(- p qcso$\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 a2;s0qn aqi j)t 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 measure k a6+seua39rftvnyh77,*ux ed 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-years away. How fast would*nn gsm.gyw6 ; you have to travel so that to;y .gn6n*msgw you the distance would be only 35 light-years? v =    c

  Suppose you decide to trp9coy9 3p6 ai-)c:ovx(9*febz ry f uaavel to a star 85 light-years away at a speed that tells yzcfy9yf-vp 9)cr3 (o69 iu*ax:e paobou 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 the Earth iou1jz;l j40 56 tyec:x 2y5bd jcyts)ss $11.2 \times 10^3 \, \text{m/s}$. 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 juge zv -gkbub0o2brs cbzrlz+455/d. 9st returned from a 5-year voyagezog r .9/0uk-rbblgb4eds z55vbc+z 2 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.4 zn)0z zzyfl. 2a,asl How long would it take a spacecraft traveling 0.960c to reach that star from Ea.)az szf2nz, a0zlyl 4rth, 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" spah1 rc*+r tkf2vcecraft at a speed of 0.660c. It is measured ch+*vt1rf k2r in your frame to be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to tgh/ 1dxw1vcy p(yufma 4p)+b. ravel 15 m before it decays? The average lifev gb(1.a4dw+ p)u/myp1fh cx ytime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling a)6 rpj4b nf*gnt $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice itsg9qz4q.ir3z a )g p0ey rest mass? v =    c

  A particle of rest masuyny k4/b lt9i5jl 8e,s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelh7sxnojrr a,2zi86)8 nv zx 2os 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 momentum of a proton that acceleratec11fogj9 .phcs
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical revims r9lw9b)6y9g5oi1 zb :tq4t plv5action 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 apohf6(rkpcvzj nkr0 lo9 x 49ufs0897wart in the process known as fission in a nuclear reactor, the resulting fragments har 6h 0zolfwpx9 j9s8o(0kf ru97n4cv kve 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 an electron in joules and in3p 9); yal,fjmteyg6p $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a pj0 dzpshd+ 1k;roton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption6rooewvs2 l k) r81sv1 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 t,kkp: lm:6 zlobtained from 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 parti,oi tsrliq, jx:m:++j+get .gcle when its kinetic energy equals its rest energy? v jxt eijigr.mql go+ +t+,: ,s:=    c

  At what speed will an object's kinetic energy be 25yb63u+ln k7uhow mwq +4n b5.m% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up tof f sf:)j eovvh/155oq1fnna/ a speed of n5no)f h5a svf1f/j/evq :fo10.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and moment*qsyd oo 8:5m2st* b9hu jbkt:um 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, its kin 3,a5byno9scz etic energy is 750 MeV,ny 93bosa5cz )?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potent63(i jnfo; u*k bw9s n2e+z* mnen4irsial difference of 105 MV? v = jnoues2nk4 iwn( bs6;m3+fir**z 9ne    c

  What is the speed of an electron whose kinetic energy is 1. 6znc;vzes( *f00 MeV? v =    c

  What is the speed of an electron just before it hits a telev95v)gb*xcaj-rm b -dtision screen after being accelerated from rest by the 25,000 Vc95m*jbg- avr-t) xb d of the picture tube? v =    c

Two identical particles ob 9s ;baa .u:fk9gx* pbfyc::yf 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 proto 7 1;jube zacyaviy jur2/828on ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 o9; rn / qbwcffyc)8+frf 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.k;s;taq3q a n 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 e;pw* fwde+xq5gnxcx .* 52r9gdfcy3 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/z(; 6zvw or6 ax* dyfwvf9ib3, $^{241}\text{Am}$, 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 momenxb23t-e1r d e3ihfnr; tum for (a) a particle of nonzero rest e3xtd2i3 f; b- enhrr1mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV prub(.i:dg4 *k v)cewn ubeot jn+j:g.0otons revolving in a circle of radius 1)4e. d .*tg(j+ibwv :cnkoejnub 0u:g.0 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 respeco h-4zq,nx1n ht to the Earth) observes a meteor come from behind and pas 4hqh1,x zon-ns 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/c+ (xzj ;wuxv a speed of 0.50c with /;xxvcz(uj+w respect to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0. )hzjuimy9v 1(71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second si9zvj)1h (u myhip with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speed of 0.60ci 2 ipc,0l8h-k;fsnb /kezn5 a. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Eartz k,ep5icbf2hkl8; 0an-s/ inh at a speed of 0.90c 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 escape pods inttkea/v)9t99sdfzago5 4az8 t od v:; opposite directions. One traveg 4/99) 5kda9ovtat:vdt ;zezsoat8fls 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/d(qi)z 6. iauqm d 9abe9h,a0.tnujj.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same dm.ahje9nz(q/i 6. dqd9uiab 0,ja)t uirection. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proximg)y gi/j29u 2ofzjn3 xa Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faster than about 0.1c is cally ng1jj58yxp nc(acvm t)9t-( ed relativistic - i.e., for which the correction using special relativity is a significant eff (9g)yantv(p cyjjmnxtc851- ect. 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 spee6 udwgdy* h55ibwr 3,qd $v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter would have to be totally deat; 4jiz) dpk*fon+ts d(d.e w,hu7;kstroyed to run a 100-W lightbuj4u7 d *ewtktid,;s(;.zdf)+hpo anklb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount a:y*wud6/jnbecyv m., a0 /b gm)lsz-of electromagnetic 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 that electric charge is conserved *6/)se m-gm /zu:ywynb 0b,alac vdj.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 ofpf-tl6;d0kkgba 6 yv6 light collides head on with a positipy6k 6bfk6dal0t-g; v ve muon traveling 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 proton, an el ku-)ak 6- 01lbl)q3 qlkngibjectron, and a neutrino. Assume the neutrino's rest mass is zero,)-akl1lqi6q-3n)ug b b0 kj kl 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 =    MeV

  The Sun radiates energy at a ruz*bam j gwr( cj 9s;ym gkvl3v.b);;+ate 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 have lso3is8z ajof3ie0b ;s.1v : ya 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 nucl)+ce17 n11 egkmbr xpgeus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutrocn7gkb 1 x+1e)1ergmp n, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relatiq8k2v1ld;a r y bkjg)*vistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use thvl2b* qg1ykkr )a8;jd e binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each havinei5i :qtk geh 02(kpa tf(ks6;g a speed of 0.935c in the laboratory, are moving toward each other. Deesk6(0gq5: ae2kf ihtkt(;iptermine
(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 a4)*v;hbr dich,z9d h 8,c lkws particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by n yrjhk)/p.:xl/ il :qcombining matter and anti hkl.pxjyir l//:n)q:matter, 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 energ6v e+s1xf: sn) zir)c9 xgaba5km: id9y is greater than its rest mass:f 9ksa6)v g1nixas+9m cbd5i)x rze: $m_0c^2$ 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 p -* dwk5wo(ulv-ox5g-ph sthw de*,(can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying-v-*k(h5t shl p wwx- *d5uwdopoe,( g the pole). Can 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 hyt2. xpq7)ldd.86g nriormg: ndrogen and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in tm2)rni .rt gd: p8nd7lxqg6.ohis 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 identic5* 1nei, d jmnu(y-jpsz.z- nmal particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's ,mse (n5um1. yj-nz i-d*njzp speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures his4fk,r jzj-j0e ship tojf jr-,zj40ke be 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 away from Earth. You sc*s hp(sf*:en (0cuvk end a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the sp:c ( pschvfn(*0ek* sueed of the laser beam?

  A spaceship and its occupants ha0tzjyf2c1t t+jce w4 )ve a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away a j24t tj+wc )e1tz0cfyt a speed 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 spac//aj4de v ( 5r(rvm8pzdpf..l lizvl4eship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Comp ( rlajmvfizv44 plvp d rde.5z/(/8l.are 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 vi8c urx - ujnr 1(1hmu*9xks-oacinity of a star 6.0 light-years from Earth. Passengers on the ship wa-x*rmk 1ujur8 xhsa(9cno 1u- nt 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 ofk*6zhe2zopo 4 a spring whose spring stiffness constant4zz h o6eok2*p 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 m3 e*gkv wfdj,2xa k7u+ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.