You are in a windowless car in an exceptionally smooth train moving at co,yi5y4 ig vzc-nstant velocity. Is there any physical experiment you can do in the train car to determine whether you are moving? Ex g 5-yzyciiv,4plain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of ttp)o 8iamd: c8mb1t /zhe corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pemm1iz o)b/c8a: dtpt8dal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on topvxdo3vy9te zj4ky9c5( / 2jats3ne .w of a moving railroad car, and throws a heavy ball straight up (from his point of view). Igvj9ts2ty.e(e yc3a noj3x9zv45kw / dnoring air resistance, will the ball land on the car or behind it?

Does the Earth really gowrk* q3j5ixzbt *6d )z around 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 ther*xw5zqk6b*i dj)tz 3re is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, qo 9f- i 1sycwr*1gbv/ub. 4msat what speed would thsfov /9gb.- rc is41wqum*y 1be starlight pass you?

The time dilation effect is sometnd 3td:mq/x 7djjdt5 2imes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What q: tdxd37tdj2/m j d5nthen does it deal with?

Does time dilation mean that time actually passes m;m u6sou;uvw9;r mdelh( g-5hore slowly in moving reference frames or that it only seems to p(grm oeuu lh ;d9uh6s-;v w;5mass more slowly?

A young-looking woman astronaut has just arrived home fro5;yr ex oos(e(m a long trip. She rushes up to an old gray-haired masoex( eor5; (yn and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a 4f*3p( ucj gbjchange in your heartbeat? Would your mass, height, or waistline change? What would( gjf3bj c4pu* observers on Earth using telescopes say about you?

Do time dilation and length ,z.w8shrmwby cihx254) ng h :r6. yhicontraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would hu ,n ix q:k1vadp*bf:/appen to the relativistic predia f:dxn/v*b i q:u1p,kctions of length contraction and time dilation?

Discuss how our everyday lives woulh)xtvd/j n3 n3,fg(+r 9qficyd be different if the speed of light were onlyg,t vr)h(3cy3x/+ nf ndf9jiq $25 \, \text{m/s}$.

Explain how the length contraction and time evd p0/j-v7c kdilation formulas might be used to indicate that c is the limiting kv0 ev-pdj7 /cspeed in the universe.

The drawing at the start of this Chaptsq0f sa3yso qh2h.wcr :hc* 5*er shows the street as seen by Mr Tompkins, for:o asyqch*ch w2fs05hrq3s * . whom the 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 lesa 16o9 hgyzo-j/laq0 es than c. Does this put an upper limit oaoa-qh o 0e6/gl1jy9zn the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of lighttg8v9: o- mttd? ----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 sp. m dddpmk2,t-ring has more mass when compressed than when relaxed?mk dt.p-m 2d,d ----待选择----yesno 

It is not correct to say that "matter can neither be create 9:2yzn f0+iyu 3o yvvbwpi4l,d nor destroyed." What must v9,n34bly+u20p:i yyzvo ifwwe say instead?

  Is our intuitive notion that velocities simt; cn,o0:wio hqd n gx59b9+4+oxblb uply add, as we did in Section 3–8, co 9 honbi9+lxo+4cuxoqb0 5; :wb dgnt,mpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to bekv3+y(hqhk(u, kmkfbkr(6w+;.uxvsc yq*:u 28.2 m. How long would it be when at rest suyk (cbk.kwu6q yqf((+kxr;v uvh km,3:h*+? $L_0$ =    m

  A certain type of elementary particle tr gck:m ;p/wy- 9m0xhsbavels 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 fact)1 ,esz/i.z;cem lwdfor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from Earth at a spj)vurx87gx:gii, es cvne830eed 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 ix l x;gjw5u(xx5( (fjwts average lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 8s8o-du5mej n12 light-years away. How fast would you have to travel s -undm1je5so8o that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star ,vdz9;ik njc3 85 light-years away at a speed that tells you the distance is c9n3i v;j,dkz 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 Earthyjx2c(rppa.9hx7( w(yk hta vk6nc,+ 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 returnmoy9.2z* 29p kcheny med from a 5-year voyage while traveling at 0.84c.z mmy*.99hpn ko2ecy2
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a skgmqcb+d-gz-x /(vtu g3 p03epacecraft traveling 0.960c to reach that star from Earth, as mea(3vgp k03 /xmbggue- qdz- tc+sured 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" sm,p g5h5exb i0pacecraft at a speed of 0.660c. It is meahm5 x5,ipbg 0esured 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 travel 15 m before it decays? T-qarf /z,hk:5 eokdx,he average lifetime, at rest,-q:f,5k/kax zrd eo h, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton 94d1h7 rqnbe jtraveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s r-pmlmsi:01h9 a y, mguelativistic mass be twice its rest mass? v =    c

  A particle of rest massrk+ ooge7j-q) $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels f:pqh , tthi /29nz*a p2:3wohn2gjlu 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 protovyhq69qj s twk .qn.bpk8*w03n that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction reqvuyvowo., a 93 3ugik4uires $4.82 \times 10^4 \, \text{J}$ 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 prockyd vwb5 ,w4,ur*crgc31dl6jz ik 6)jess known as fission in a nuclear reac*wg6dr 4vkk3y, rb1)j6cz 5il,w djuctor, the resulting 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 yfqz;xq-9trb kj*67san 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 prt jmw:f - ze-;7zbhr392 l c:pbloxr+toton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abou3by.clsjjlk-77pl/sv 71w/twi 8 hp ut $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 1.0 gram of mass? i*.t4c tdy +kezks8 u4    $ \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 kinetie .5 sj(gu4vcx4io.gj 4 mfj,fc energy equals its rest energy? j4.4g,s fg j.i 4(cvomfxju5ev =    c

  At what speed will an object's kinetic energy be 2cfz2p*2 )s 6bvi 6luvsn(a nd-xazs ),5% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a0 u.l yoak4+cr8pf n140jzd j o.wbu.a speed of 0.997.p04dwa 0j1fbu. oz84 oyal+rcuk.jn c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic ens -a1-6 tt+ o+w-nh1ld(ph dhx) w: +hvnavnabergy and momentum 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 kinetic energy t ek4b;81zhvsniu 33jkp;0jwis 750 MeV3 h; 34iskjjnz8epbu01v; k tw)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentia2 ;iho+esch*a l difference of 105 MV? v c +hesha* o;i2=    c

  What is the speed of an electron whose k5 :g vy4og4c5)w:b owjb(ejxp2sbod+inetic energy is 1.00 MeV? v =    c

  What is the speed of an electron j1bv p8nvh8 n9d/od; wiust before it hits a television screen after being accelerated from rest by the 25,000 V of 8no/dhnvwdp9 b1i;8 v the picture tube? v =    c

Two identical particles of reg4./ uaot+f/i spboz:st 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 pros9*-4vyu+ivt 6 w pofpton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the m y5u4b e9e11s gu6+af,irgd3ch7zb k,gfdcu , omentum 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 acceleratxl9p*e p* pzf;ed 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 ene9 q* xlnngcek, th4z;9rgy and momentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleus,lh,kew1idj j+1smf :/ $^{241}\text{Am}$, 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 ki9 us2 0la:ndfknetic energy versus momentum for (a) a particle of nonzero rest mass, and (b) :flu9d snk a02a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons 2/e 9xk,oam3dcvi9-g.yox ma revolving in a circle of radius 1.0 km (cd29egx,ov.mai ma-39xyk /o 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 trk9 no goah:ihs469z a,aveling at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a sphooa9 ig6s4,nk9 z:h aeed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in m ,jlct3w8o 1: gp,4ujupgh2 dopposite directions, each with a speed of 0.50c with resp3gtc gumwph,p:8oj ,d l2j41 uect 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 0.71c. A second spaceship leaves th hx;h:j0o 5drre first at a speed of 0.87c with respect to5xorhdr h:;j0 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 spmi4yf 1* get8 uvds3m -)vk7uueed 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 Earth. What is the relative speed of one vessel as seen by the other? uk d)i*7u-tuu8vfmv 4gy1 me3s =    c

  A spaceship in distress sends out two escape pods in opposite directions. qb,f/k/njsgc2 n5f s9 One travels sjq9n k5,b nc//sf2fg 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 xi3og i m6i6-g0.75c. At the same time, rocket B passes Earth moving 0.95c rela 3 oi6gm6giix-tive to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri5:fczb9p+ j is, 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 t6xf; ,83zdc8ej*lb8 bihhv pthan about 0.1c is called relativistic - i.e., for which the correction* z3lbj8xh 6fe,p ;vcdbtih88 using special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) ----待选择----relativistic not relativistic 

  (a) What is the speed p*hh 4um4tmv4;iw 7q -eimmq,$v$ 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 e xqerug6rj92r+ ud ,8have to be totally destroyed to run a 100-W lightbulb for 1 yea,gqred+8 r rj6x 9eu2ur? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electronvx . vad)r7;bc and a positron togethb7v);rvx da.c er? 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 speed of light colik7ax)2ij o.2/izz 7jjj wn * 3l+qomrlides head on with a positive muon traveling at 50% the speed of light. The tijoij7ijn m723.z *)xkq+jor2l/z w awo 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 otkm; rd5(5ku 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 = om; 5 kutdk5r(   MeV

  The Sun radiates energy a5s, il*m7 (fkpj+74yixkxu p+3tzly)*ayat c t 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 measured to have a negatuv ehsf+)9z ws ;cpy kgh58)j;ive 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 break5hdhq, k1x4x74pl mtm4p e sr: a helium nucleus into its constituents, two protons and two neutrons? T44 1qx7m ,xphpms:kd54rehtl he 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 total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) e w6 8nf3unkdmi.h73omass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomii uodn3efhw3.k 86 7nmal expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having,:m un vxry1a56hdes8b uz y eq(/o18g a speed of 0.935c in the laboratory, are moving toward each other. Determine (y8dzuebex m6 1: g yrvqua1s5hno,8/
(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 vy 4vjwgf -w:21p qlrcmq6v8- a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship p5gjl i) oazco* zs0-q4in87rstf. p0Enterprise obtains its power by combining matter and antimatter, achieving complete cj g0 os)0.latn45p8ii* csz-zfqorp7onversion 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 accelerad*o kh+ , )bgfsl u-:yy+fif6cted so that its kinetic energy is greater than its rest mass y ,-+gfi6uf*kcblfy+h:s)d o$m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-long poleml -.uc(vk/3ne n7xs iy 7h:rf 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 there /xkin 3um( n7.vc s-yl7h:f 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 oab9qrzw; ff x/17fw i9f oxygen react to form two moles of water, the energy released is 484 kJ. How much doe az/b7w99fifrqw1fx ;s the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling in opp*1jtjj* td n7 *y hj:vno rimk+;ks/tw a:./onosite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's dot/ ;m anj+:jtjkj17ry./nv* kn*oiw*:sht speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c ru 7ffmv 3i8:tuelative to Earth measures his ship to be 25 m long. On the ship, he eats his lunchfv83m:uiu 7tf 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 a0a3+yt43d d7bh ffevkphj:1 zt a speed of 0.85c 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 fo4fyk33dveap0 dhj f +:b7htz1r the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg.k6m+. khp.opb,e/4 hbg gy ;w 5xloxz8gtcm5. 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 changes mass directly to energy. How much mass will be converted to energy to accel 4h.k5 8p g.,toegxc+.zlyxmp/wb hm6 5b;kogerate 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 t( ,mzzzo6xi,zcks ig i 4tbw++,vg26yhe spaceship's kinetic energy? Compare with the total Ugxv+ ,i 6c z2s6ziigkbz,m+wt, y4o( z.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 vicinity ofy)ukrgsk l,, g-,whu( a star 6.0 light-years from Earth. P , ,k l(ywu)ggsk,-ruhassengers 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 oscillates on the end of *bmk rzv:)9ync/2x nj 3yfex. a spring whose spring stiffness constant iy:nx 2m.fr e9/3czk *b)nv jyxs $k=48.7 \, \text{N/m}$. 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 metftggt1j*1wp2j4 l o o;9s8gass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.