You are in a windowlmbqaq d4(r z+ 8y(8p*jzcdz1xess car in an exceptionally smooth train moving at constant velocity. Is b+azjqz 8d4z8r q m(d1y(xpc* there any physical experiment you 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 whenw:1m2lh7qoko. h b)pi , out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomplmbo wq12.ok 7phh i): 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 railroad car, and throws a heavy badkwk+ w 39uwm f8u(7nall straight up (from his point of view). Ignoring air resistance, will the ball land on the car od auwm3kfn+uw( wk78 9r behind it?

Does the Earth really go around the Sun? Or is it also valid to say1ii/ydm ij*oysyr247 that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that /1*7mro syiji4id y2ythere is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c al eb6c it .)es4zwh,j-way from a star, at what speed would the starlight pass y4lt e,ei -wb)c 6zhs.jou?

The time dilation effect is sometimes expressed as “moving v-,r3*x2eztsg8 r ch uclocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of cec* hg8sxrvu-zr 2 ,t3locks. What then does it deal with?

Does time dilation mean that time actually passes more sl 47 xqc0ffr5lqowly in moving reference frames or that it only seems to pasfx5l4fcr 07 qqs more slowly?

A young-looking woman astronaut has just arriv5tb9pli v. bx,jyf7.hed home from a long trip. She rushes up to an old gray-haired man andf7.vp 5hl.bibt9yx j, in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.50,c0vol- v upqd( wl(lc, would you notice a change in your hear ,q(u v(lll-vwcp 0o0dtbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occuvx*dvthsw0 /.w, 5 gcur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of li;qkegc7mh e6 .ght were infinite. What would happen to the relativistic predictions of length contraction and tih.m6 e7;gq kecme dilation?

Discuss how our everyday lives would be different if the speeitje0gg/ 6dv)t7 egw- oon7-id of light were onlgeo)i gj /vn0wo-7i e -tt76gdy $25 \, \text{m/s}$.

Explain how the length contwti3.gjhx5i nc9+z1 braction and time dilation formulas might be used to indicate that c isi n hx9i 3g5tjbzc1+.w the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by .sx9t hv9tp9 aMr Tompkins, for whom t9.hxsa 9 p9tvthe 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. Doesgiddfs*v ,nt7d1 q 5g: this put an upper limit on the momentum of an elect ni1:t*, gdfvg7q dds5ron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest masj(frs+wm, 3 jwyzf e*;e4qs;js attain 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, dru6oo pa 7f fj;:2:oteoes this mean that a spring has more mass when compressed r;ojf :a : op72t6feouthan when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be crecvhe5h3a h-(aated nor destroyed." What must we sayha-h35cea v h( instead?

  Is our intuitive notion that velocities simply add, as we did inj jbqjf;5b.8a*kowd4 Section 3–8, completely wrj8a .fwj5q4 * dbkbo;jong? ----待选择----yesno 

  A spaceship passes yo/qt5w4df x3 dtcam8 9sk n0qwg68t5vbu at a speed of 0.750c. You measure its length to be 28.2 m. How long would it be whec8 qwq8 x 405/gwft9smkv3ddt bt5 an6n at rest? $L_0$ =    m

  A certain type of elementary paryhs;6qo5cof+ysy9n* x,nl 1/ tafq0 kticle 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 intervals depend on the factokd:d apj nyja)tynm)*z+8 36yr $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 .l,gt3 w38mrxwvr.uf 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 kqx.s1ceo oy, 4(p)c4b5dhkt 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 82 light-years ojah5ichpp.t9m7*fw)e /u 1vaway. How fast would you have to travel so that to you the distance would be only t wa)u7oh fjh./c1e mpi9 p5*v35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-yg *x;wxk vph04ears away at a speed that tells you the distance is only 25 h0wv *k4px;xg light-years. How many years would it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the Earth i 64gh1imw/zs y6y(w yf8y7kgs)m: rob s $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

  At what speed $v$ do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.) v =    c

  Suppose a news report staqq pb879 whivdjx8 :q-ted that starship Enterprise had just returned from a 5-year voyage while trav:qqid7v 8pw-j xh9qb8eling 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 would it take a spacnr2fdv/w(*wxp v4v8*sx 7q) l u2e dtcecraft traveling 0.960c to reach that star from Earth, as mear*xfxud ( 2 /pvc4d*2ve8qv wntwsl7 )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" spacecraft at a speed of 0.6kdp.e70 p (6fxm5k dxp kfn/- tvcta8+60c. It is measured in your frame to be 4.80 m lcfk+pvn m8fdtaex(d -pxp 507 .ktk6/ong 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 i it+(ux jet3*lzg:c y7t decays? The average lifetime, at rest, islu:ez + xijcy73ttg*( $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a c sgts*,x10 h3ci+ qmnproton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass bg,uxhu3v(x 8j2( logz 2g mlvj38bx b6e twice its rest mass? v =    c

  A particle of rest masshwph mt+ yp57x( *etx4 $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travexgn(9yh v -rsh e/f 6cpj)aj-0ls 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 accelerates ej0 0m( 1dqbwt
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requireski6skl 3qrc;5 $4.82 \times 10^4 \, \text{J}$ 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 proces6jjsv;ze 3n (vs known as fission in a nuclear r;(3vz jev6nj seactor, 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 an electron in joules ed5fb7pun sgt6 1q-,z 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 proto-l,e;( lbq g-gm hgz+on in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual enee1,b8kf+ nyzg b5k6z ibrds(hs**f + xrgy consumption 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 obtaintfs7da) /- xpsed 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 particle when it;p.xtm 5yea:yq2:dc)aox1slonh a;873ngga s kinetic energy equals its rest energy? v =n:)2saalh8d:gqoyx ;om1y7 c.x n;at3 g5pea    c

  At what speed will an object's kinetic energy be 25% of its r64w(xo kbbs 7gest energy? v =    c

  (a) How much work is required to acceleratl3o c5y4a0 c alvl4im-e a proton from rest up to a speed of 0.997c?o 0 ll a3vcamy4ci-45l W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a p4y.:7 ta0 yae8cni; xfsp+ jlj;thh,rroton 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 energyw4sjd23 n, pn-bwk ;io is 750 MeV);p nw, okb-32jdni 4ws?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 10v9 fon -fcpjz p(ryt0s(8ul6 ;mwal2;5 MV? v2;-jm wu(; pfz6nl 80p r9tvfaos(lcy =    c

  What is the speed of an elz z2a 02r+wym+y,jldx ectron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television schir +4qn4z1 eqreen after being accelerated from rest by the 25,000 V of the pictu1+ihqqe4r zn4 re tube? v =    c

Two identical particles of resjv*sm t8 oxg(8t 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 plxy9+x8ud q8ujb* l.proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 of an electroncsw -- wp8+gyt ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 to 0.2xnpk2 w ni*5dn-)wbc *b- bu7q1c.
(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 +wzxm1fc ik/u2-cxn* 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 nucleu)yk sd/8w qv6g*iucomeor /x7 4 si0ph(f-v y-s, $^{241}\text{Am}$, 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 +hr82 yk/0smtpgu:p 5j gu)62jpaqluenergy versus momentum for (a) a particle of nonzero rest mass, a0rhppsjg:m g2 yuu5kapq6t )2j / 8l+und (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-c1(j fuip ocl.5z.g fb.i :v2xGeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass c fxv(1zc .f.ol25jipi:bu.gis $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [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 the Eaals2,9bci bnbdwm6 h1* e- n9wrth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to thebm96-dlb2 1b*nhwns ,i eac9 w Earth? u =    c

  Two spaceships leave Earth in opposi0 r4yjum97 .q. izphlnte directions, each with a speed of 0.50c with respect t in.pzu 4. qr7my0lhj9o 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 Eartbwom 7xc 82yp*h traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c mw2b*8 cy 7opxwith respect to 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 atma (vtw.3hq a7xads4a:i/l6(fxb g 9v 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 Earth. What is the relative s9mt : b74xgf/adsv ha3qa w.alx(v(6ipeed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite kb+;rd37d iqyfz iw:9 directions. One trr7 dbd+kyi;3f iz 9q:wavels at a speed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth at a speed of 0.75c. At the same time, rocket B passes Ear5n e(nhcbh.4gl umg(*th moving 0.95c relative to Earth in the same direction. How fabhng4mnu.l(g(* e ch 5st is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 lgf -uz x/bn0(s gstgq b tud*yl)1kt *375dvj1ight-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 c47iled -mpp ):a(vj8d 1bbb,tfdj o8k alled relativistic - i.e., for which the correction using special relativity is a silajp8 v: if 7(mkbdj)bbp41 8 o,d-etdgnificant 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 speeqpnl;p2*:(gfua. va bd $v$ 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 destroyed to run a 100-W lit+ nenho/:aa ;ghtbu;: nhaea/o+t nlb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an7au)1xs pef(had q1.)nxxv o :l )hf+xo*xn 0k electron and a positron u xx*f o1ql.vd apk01h+e:f )xxonn)h( )s7axtogether? 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 coll*tovzp16de72 yo okl5ides head on with a positive muon travelingdyt*2 6o7oozp l k15ve 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 deca- ob8 r5y pqf 6cu68bszaf1e+ky 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. Determine the total kinetic energy shared among the three particles when a n q16bs5-cef by68fz8k+au orpeutron decays at rest. KE =    MeV

  The Sun radiates energnm- .6dv(slmv( 8*dbrk rai ql*/7x qiodtm53y 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 measured to have a negative +zqe6(sv)yaz 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 nucleus insa7l;zdj d3dj l-q-yv5te/3 ato 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, and 4.00260 u. (This energy difference is called the total bindij-zl;3ldj vaeay s53qd/7-td ng energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistig wh+72fcwf(1:g zflr c) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomia:wh c7f+gfl1f 2(z grwl expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving toward pziv31- omob )each other. Det3vo-bz 1)pmioermine
(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 ua0* jfsllk jw0 75it;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 comb8ljf;wn8s:l /8eul:6ied plpv b7;qu -f h8kgining matter and antimatter, achieving complete conversion of mass into ene 8l ;g88 lufepes6hlk8u :/fiwjnd7;v:pbql-rgy. 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 kinet3.phb0g 5jrayj: *orq ic energy is greater than its rest massr.jr*:b 3p qj5g y0hoa $m_0c^2$ 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 f (5fz pnc1k(c +3mnhlkit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the bazn 3h kcp(c(fmk n51+lrn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen reacq2 tw5swlq d;,t to form two moles of water, the energy released is 484 kJ. How much does the massq2ld w;st5,qw 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 particlxu5:l5 cvg0 hjes are created, traveling in opposite directions. If the speed of each particle is 0.75c, relativ 50xcv:jl5ug he to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship tr 1lf .jk bj5jrrz(u7v;okc ap/6t6*nbaveling at 0.75c relative to Earth measures his ship to be 25 m lon6v/ fb *jjokz(a k7;ncpb .5rlr1u t6jg. 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 0.85v2 u wgfmp h,6a+t-xl6c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the +-v6laxt6mghw u pf,2Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a totpn )b)eypsx.s )x+uj9al mass of 150,000 kg. The occupants would like to travel to a star that is 25unbsp9e+js yp) )) x.x 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 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 an u2d.9 natkalxx;)qn.xa6* a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the tota6).*d2auxxqxn;la ank9t a.nl 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 vicinity of a stvmh gj3:ymi4r73 b2x yar 6.0 light-years from Earth. Passengers on the ship want the (one 7ymimjv2rh4xg3: y3b -way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffness constpt51 (0c pjvz rz6h*ooant is c tpz6zoo *5rj1pv0 h($k=48.7 \, \text{N/m}$. 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 mas ib27jgvvt3z3t, koi:s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.