You are in a windowlessb5waz:hz -)qmkc xmw 44v8q)r car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment yoqcxqaw r zmk) 84 :4wz5mhb-v)u 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 redfug1 r)nze7q 0 light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say)r71ef u0qgnz about absolute and relative motion?

A worker stands on top of a moving railroad car, aihme5ke1*al,3 d s ;jgnd throws a heavy ball straight up (from his sjh1 im ,e5; 3lkeag*dpoint 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 ar 0aj sgi5: e8mm9r(3grxp: emlso valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is nremi 39expm:5s0am8:(g rj rgo best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from *edw )gb.8n yza star, at what speed would the starli gen*)d8 ywbz.ght pass you?

The time dilation effect is sometimes 28htxe ndr+ 67lyqy9 qexpressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. Whahyqdyl 97te68 n2r+ qxt then does it deal with?

Does time dilation mean that time act7gsu r-f)r5d3s l+ev xually passes more slowly in moving reference framee)l gsd+7v 3x s5frru-s or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long tg,co f51hy o6oh.mj2 k r.*jyrrip. She rushes up to an old gray-haired man and in th21hm6orkfr.joo,5 h*yj.c g ye 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 chanl/5n :y m(ftk yvajk/,ge in your heartbeat? Would your mass, height, or waistline change? What would observers on /f,yj /5vlnkt:aky(m Earth using telescopes say about you?

Do time dilation and length contraction occur at ogy0:x gvg; ha+rdinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to*tr; e ielu-k+ the relativistic predictions of length contraceu-ik rle+ t;*tion and time dilation?

Discuss how our everyday lives would be different if the speed of light were obs cv,hm7-dhm3: lle5nlyd l7me b,vlhm5s-:hc3 $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used too,/e7 zx/olotl9 4dna indicate thaooa odtz / ne7llx/,49t c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tompki72(.kxfw irf wa.kic0ns, for whom the speed of li0(f2w.rwa kix7i kf.c ght is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited oj epj.lqezj 21rnl9:mdx92; to travel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? Ip:9lz j;qrj2nej1ol9 xm.e2d f not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of lightuf,e dgpwp0 0.? ----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 has0ssfb 6yyp xu1/t21ct o)jr/v more mass when compressed1x c1t2 tos/yrbj0y6)uvs fp/ than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." zabjc: *d4k w7What mustwc4:jb kz*da7 we say instead?

  Is our intuitive notion that vef l(*d c 5yhd7eq)vq 3b.f/jc b2b6ecclocities simply add, as we did in Section 3–8, completely cb6b5q3 7yfcj.h vq2) c/ dd e*lf(ebcwrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to bb 8 mar*f :p57jvrbdo3e 28.2 m. How long would it be when at rob *8bd: mr 5f7vapr3jest? $L_0$ =    m

  A certain type of elementary p dhx*,om3k bx4fj 57f2m1dzeiarticle 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 interval l:1qv(g asl49x/v+fro 8wh pks 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 aq. o7y-1j ie2y7hk g/b6pypb y09 vvzgt 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 lifetima; cxcgvs 5(+( mqp47ol tp9kte 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-ye 7smy0nxsijqg)h; a). :n1q)c s,dlmdars away. How fast would you have to trady7j1qcq lmn s xsd i.)s h)ag)m;0n,:vel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide t: qbjr 051blwa 5aduo20of1ii o travel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How ma:1fi ido1 aar5jwlb5 o 2q0u0bny 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 Eaz d8x y9)gxt5iqdd 2z1rth 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 tjk qi2s7-ae9ety .j ;khat starship Enterprise had just returned from a 5-year v7e2 qj.e-k t;jyasi k9oyage 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. How1--pjlvqf+nu long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by obserjvpl1- u+fqn-vers:
(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 0.660c. It i3 :j o;gs6tycgc;*z9fls(/uacgg*qns measured in t3gcf sy;l9;/ * gs 6gcagnuqjzco:* (your frame to be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to travel 15 m before6 kk;k;u8b++tf6 t1tuxycbi o it decays? The average lifek 6k+fb6touk1+x8;;uib c t tytime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum w 3ez)u9u5gxz*bzhw+of a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its4;+ ifovz.8f7 s tpo(vrw6a om rest mass? v =    c

  A particle of rest mas tb0iv)+rzv62*aeffx 5upr 2xs $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ay1+nrf)n0 r+rmo7 tqtr24 ha 3:zrgapt $v =0.10c$. 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 d91 km7uarhx0in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requm9 mi2zliz2)k 7kv wl9ires $4.82 \times 10^4 \, \text{J}$ 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 rh6*f7-wn r 9r tpepbx.m.d.m lest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic 6*r e7ft h.pdb-mxw.pl9r m.nenergy 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 electrond).cy:e .pmr g 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 ma.fjv+ 3bx.*sa74lap w pgwmq6ss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States ,4 l(um5epiv duotfk+8*hyb3 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 l t(3sbxcd.h(ot 1 o:afrom conversion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic ene htu:f g a1v/k2ub 6a agi5axxbt2j7(3rgy equals its rest energy? kg2fgaxbt1au6 aa(/5hutx: i7b23 jvv =    c

  At what speed will an object's kinetic energy be 25% of i)nq7r2gtposs n3 k(k-ts rest energy? v =    c

  (a) How much work is required to accelerate a proj8k)q(8sin1 u l ribv(ton from rest up to a speed of 0.997lv)kjqbs8 (8iur i1(nc? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momen9 2 3.sg/* ewrs.dl:x osppggatum 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 7 nx (m1 eofqov vcbtzuurr)r6bn74 9* wj3i4,050-MeV proton (that is, its kinetic energy is 750 MeV*,m rxrfv 14bnvo9nwt0 i)bjur(zoq 36ce47u)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by b:,mkmzq-;t yww jm,7a potential difference of 105 MV? v = y, kbmzw- ;7m,q:twjm    c

  What is the speed of an elec f0kh(p v.bvjl2l7z, gtron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron r zof2y.5wkw; just before it hits a television screen after being accelerated from rest by the 25,000 V of the pictur25 wr ywf;z.koe tube? v =    c

Two identical particles(de ibfqm3,u) 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 qh2r p2ffb)b2proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and1*aueip c40go inj 5a,qupa:ttls ,-9 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 27,000 kg is acceleraav1 b /spwfawk-.upgs2) ,5 shted 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 momentum of a p4sk zn(my2lg) roton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleusk2 w rizd.7)hw v7mo)v, $^{241}\text{Am}$, 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 kine u.i4lb eis1,ttnm,(ptic energy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with z.tl(in 4ui espm ,t1,bero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons r.o gd7a4 y5qmax1 )kpsevolving in a circle of radius 1.0 km (at, say, the Fermilab s5a mspgx.qo1 k)7ya4dynchrotron)? 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 respect to thesdey;dg:y3zo * t: 2.3es avcg Earth) observes a meteor come from behind:;2 vygc gaddet o3zss3y*.:e and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each w dea de9yr.g33ith a speed of 0.50c with respect to Eart3.39dyd eeg arh.
(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 sg6 -8 lr-rydcay9b)zqpaceship leaves the first at a speed of 0.87c with respect t)-r- laybd68rz9qy cg o the first. Calculate the speed of the second 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 an alien vessel approach at a speed of 0.60c.xa-5fw n mh5nqe3-nb8 The Enterpri8qb 5- nnex5-m w3fnhase comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escapgm+p:sf 6bd rbze;r, ln29xntf(,ut5 e pods in opposite directions. One travels at a 5r6un:fx bft;dl e,p z2gnr+ (t bs9,mspeed $v_1 =-0.60c$ 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 s1 6kyxd*vj;ab *5hzuapeed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when y vh*b*u;z d6xk 5aja1it passes A? u' =    c

  The nearest star to Earth is Proxima Centad qi9e(, ( w. pajtqetbfl(b;,uri, 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 fy(vsu p) oo9r/;(n67yeexmy3n t c(ps6 gue- laster than about 0.1c is called relativistic - i.e., for which the correction using special relativexec; 37rp )o9-plne6muv ( yyn(ugt s 6(oy/sity 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 0pnn*aw*2rvh : siaiq*9 vw9b/u/g p r$v$ 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 des4noe0 cssy4z3-2umqd troyed to run a 100-W lightbulb for 1 yea us 03 czmsn4eqo42-ydr? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagneti.oe/8 qy mo(j/ft:r yxc 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 h8oe ./y /:mojtf xr(qyas 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 coll8d f6;+ddhw g bhids3+ides head on with a positi3d6 hwf ds +dih;+d8bgve 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 electron, and a neutrino. Assj ln 5ekss1d;)ume 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 1d;5lejk )nssthree particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate ok4--ols inwpe5:jc/ i f 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 a negative charge and 8vga5wwdj8h*su 7vd xecv2 n*a*h:l0 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 nucleus into its conxazcfe cp* 096ix2tit-u9e a+stituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the totalfp+i*ez6 c9t0-iaau 9et xcx2 binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (ri .3+ afm,xmbtelativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expant3i a,m xm+f.bsion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.93k+6, jl/e:i:9v7radoq a yrnt5c in the laboratory, are moving toward each othero /6qa9rj:i7:kdetyv nar, l+. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a parmb i re:,,x -(dzo+jxtticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power b 4nc*jd4 )zn2n-awa*wye qgb,y combining matter and antimatter, achieving complete conversion of mass into energy. If the mass o*qg adzba,y 2nw4j*-cne)wn4f 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 energy is greater than 2b * rqqjdhoe4ad) :+eits rest maq b+e2rjoq* 4): eddhass $m_0c^2$ 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 phy4o +phupftsu;j5l:hx2 w*p9c8op g3 lsics believes that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (ca:2cls*l54phoxtwu9g; p 8 f o pupj+h3rrying 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 hydrogen and one mole of oxygen react to form two moles of w vc/c .yh /n-hjbqfyt) oa1x*,ater, the energy released is 484 kJ. How much does the mass of the elements decrc) y/bh1 cxv*y-/hjt.af ,n oqease 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 identie9 v zvx9kha1gt8 )w ,,r(s exqvq3/dncal 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 s9kr(a xvq,1/vvetg 8 n3 ,q)sxdwhze9peed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.7o .dxbts.i4. jzs;2h4m w(fplr3y j1a5c relative to Earth measures his ship to be 25 m long. On the ship, he eats his ls4aj. xbfp 4y2.;irsw1 hdo( z3mljt. unch 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 zjbv r (l10lx4a spaceship at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c rjvzl xl1( rb04elative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 1 v;fk7 p963s c/: 4mpdpqjlnyg50,000 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 th9fm4ygpjs3nvq;k7 6 cl/ pdp:e 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. W-4yn,.c6:n o1 aqn fsy)ebjn ehat is the spaceship's kinetic energy? Compare with the totqs) cynny e41an6f,.-:noe b jal U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship im: ;wjous 0r4ks to travel to the vicinity of a star 6.0 light-years from Earth.ows4ur mkj:0 ; 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 it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates22w/mw i/ov( s0ayw zrc)0puy on the end of a spring whose spring stiffness constant is w2cs 0awvi 2)(u 0zrypy/ow/m$k=48.7 \, \text{N/m}$. 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 masssuo fh)z7hc)) $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.