You are in a windowless car in an except)sh/g m zjf2y21g ux(yionally smooth train moving at constant velocity. Is there any physical experiment you can do in the tra uy2hz g s2f/)gjx1m(yin car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light(2ey;d c y.8uh hwr3cz when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking thahryy2cwc h ; 3d.(uz8et you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a movisa+)a+ks9 rvs l zzo6.ng railroad car, and throws a heavy ball straight u os9a6 szz)rlv+as.k+ p (from his point 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 -0* 6k8xlr8eea9n7n svyjvtlfw -wv/ it also valid to say that the Sun goes around the Earth? s 79flae yrlvnkv-0 8/v*8-xw e 6njwtDiscuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship travelinqob igrw ,2-n,y6 xk7xg at 0.5c away from a star, at what speed would th,7xkwo,rb n6 2iq gxy-e starlight pass you?

The time dilation effect is someti( -tia+e49m5va3 v pied af8tsmes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning ofmtaa+8vd e3 4p fvt5as(e-ii9 clocks. What then does it deal with?

Does time dilation mean that time actually passes more slow arn)s9j/yr )aj: s8czly in moving reference frames or thaj)8: rryn/cszs9a j)at it only seems to pass more slowly?

A young-looking woman astronaub((c-6pu rw jk 0aew9lt has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensrw6jb(u(09 - calpkewuing 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 4 k f50onevb6achange in your heartbeat?ob ven k046af5 Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at obz:bq g87xn*ic+beu/rdinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. Wh58hfo pms;3ea p.up r8at would happen to the relativistic predictions of length contractione;p hua 3.f8p8 5rmosp and time dilation?

Discuss how our everyday lives would be diff/g 8h-8uk;c) zlca*l.jpfy1q/s ser 8dy0 xmlerent if the speed of light were only gly e;auc8/lsr0hm-jp *1d. cqf k/zysx 88 l)$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used to . m52fs/j7zxxrbgeb- indicateez7 m5xb2jr/- sxbg .f that c is the limiting speed in the universe.

The drawing at the start of this Cha zc. qvazu0./fpter shows the street as seen by Mr Tompkins, for whom the speed of light is uzc. a/0.zqfv$c=20 \, \text{mi/h}$. 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 tijmsw uuwg r9w zlz. q7/t7.h 56to46bhis put an upper limit on the momentum of an electron? If so, what is this upper limit? If not,7 o.w6b7uhmt wr5ls 4ujz6 ti.gzqw/9 explain. ----待选择----yesno 

  Can a particle of nonzero rest massn 1rytv)vjcud3ry4: 6 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, does this m6,xf ldc )exvl .5it-yean that a spring has more mass when compressed than when rellc .dlxix,t )6 evy5-faxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroye+mo; qsbk4 .o/uijjvfd.*a7 bd." What must we say i/+bfqk oaimbjs*vj4o.7. ; udnstead?

  Is our intuitive notion that velo j w0q,gd2;vujip )id 6w(mmy5cities simply add, as we did in Section 3–8, completely wrong?wm) jdqi05dg piw 6m(,jy;2vu ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.2 uiv.stg.* *x+cql ,gf m. Howstx g*v f+g. i*uqlc., long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a sp*2xl obn;v: wcm8xf mp,; tth5eed 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 facto0+x (ez9kes eur $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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+u8 xf3pae/ vb 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 measured to q*nxvu 5luk,s7jfck:a74 pxe emo8( lt4(u o1be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a s*4o 6ns z. myiljya x+g3vds8,tar is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years8ls i nzj,d* amvyy3+4 6sg.xo? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed that tellsl5zg 8rm mw4aj:,pnc ( you the distance is only 25 light-years. How many years would it take y(mzrn8 jml, :gpa5cw 4ou 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 isc9qbwc .gol nr1k1lt,4i z,/ (w2lkzg $11.2 \times 10^3 \, \text{m/s}$. 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 s1aq e :4chj6gx kub0f*tated that starship Enterprise had just returned from a 5-year voyage fek 1:gc4xauh0q6 bj* while traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a spacecraf74xa3 n . dulc2gl kgyw:5ygm,qe*e o*t traveling 0.960c to reach that star from Earth, as measure* wye2l37k u,ygxng.ad 5:cgqo* e ml4d 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 h4hqwl6j 7--x0 sbg s 3wq.m(eop0w afber "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 40(mlwpsawe x b 6.q3jfgso -bwq-h70m 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 b+cqip8rki+d) bcymd d(,:o:be moving to travel 15 m before it decays? The averageq( dd:rid8c k ,cpoy++mbib): lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a prt ms4yq9 e/7rioton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twicr)gtun7 oaj00 e its rest mass? v =    c

  A particle of rest mneho) dgel2s9 ;+odt;ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travet nt3is 35pt3cgqul ;)ls 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 accelc4 (og7*jms72aqidzp / ojw85ti6h xyerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reac93hy 5b7u/oogsqms;*y ijy ,ltion requires $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaks apart in 6xqd gi-d1* rd;25xqra0e n+rjxx7uwbh1, oa the process known as fission in a nuclear reactor, the resulting 15- r+7 dgxdxa,xh0;xn2ojw r 61baerq uqi*dfragments 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 and in p4bdx*;oz98 4be5zgz*rx.x by hwc *s$\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a proton ia 5r;)ybjl uydm1t 7(dn $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Saqgmy, m1 5zq5isi)3ctates is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 1.0 gram ofeomcf:t0;u i ; 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,is7;ur;u p.3udhuarn4yu8p/2 ztwb a particle when its kinetic energy equals its rest energy? v = h;rru432ws/yppuab8.idu n u7;zt,u   c

  At what speed will an object's kinetic energy be 25% of its rest ej+.c jgzkn/b,o0v sq; nergy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a h50jr er+ )0egqb,pwkspeed of 0.5k,brr)jhg0+ qewpe0997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and mos mj ajm3mu0,oa j5(e5mentum 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 pr: t6nj+1havnf 1a(f xdoton (that is, its kinetic energy is 750 MeV)?v d(xa+n1 tf16:hjafn    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accel9ffzb3dtw2gnty)kfvg 3d* :3 erated by a potential difference of 105 MV? v = 3k9 )gd f3f* n3dg2tvzfybt :w   c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? voit ssfp,u 1*2 =    c

  What is the speed of an electronp4(pfy ,qxq3v wrq7g4 just before it hits a television screen after being accelerated from rest by the 25,000 V of the pi rp(v7x4gwyq3,4pq fqcture tube? v =    c

Two identical particles obx +2q eqqb*xnja, *kj. i.pv)f 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 ofs*( bs .mn i4;nm2yqu4nvy.0hs feem0 a 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 elec ucqnt h883cwg;i -5)o2vbph atron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 0.211ya9l n,xtj37 b()muoa wjz6 qc.
(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 pai 8vkeyrc//-*h(r sw 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 nucleusdenp3qi +igs 7:0 tpa8, $^{241}\text{Am}$, 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 ve 0511s;vn(bcav jci dbrsus momentum for (a) a particle of nonzero ressb;1(51vcadbjv0 nc it mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is kk)s nq hl/3hbrg:14(vam; e yneeded to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? )gve(: 1nbqa km/h4l3kr ys;h 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 (withv(0mqm.zy jewf+ uku8 +y78xh respect to the Earth) observes a meteor come from behinu 8 m f mze+.v8k0xj7yyh+u(wqd 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 ,u o/w nd4csn pk0.7cadirections, each with a speed of 0.50c with a wc0k4n/c,u7snodp . 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 0.71c. A secondzh. dl.c ys2b )9(kgke spaceship leaves the first at a speed of 0.87c with. zdk2lg(b)9hes c k.y 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 alienejlobov 6 t37- vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed oftje67 3v-o bol one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escapebximsm*8chrp sb ,bfh7e,/6 2 pods in opposite directions. One travel,2hmf b68spx,*rb ec 7bihsm/ s 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 um lz h2/2 ach p*,wtd-hc-ve*Earth movin*c,-- m*zh2e h wu2atcvd/p lhg 0.95c relative 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 i 7:l li7rsl y+f;euo-hs Proxima 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 se*bkqc 3sp8id) ,f+k called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an)s,3psfie8qkc+ kb * d 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 z j0h/h)rok k,$v$ 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 toxyz17 mq+l-21dllvcjr 1drc4k)iw 6fn b9v7j tally destroyed to run a 100-W lightbulb yvb7idv6qfn+9mc)k1lrd j7r41 lxczlj 2w 1-for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic 77jf8.oolabo energy is needed to produce an electron and a posiofa.7j 87oolb tron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

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

  A negative muon travelic98x avfip wex-+ly :-ng at 33% the speed of light collides head on with a positive muon traveling i9-y+ -cafplwxx :e8vat 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, an2n * nw ak;j*5,mf mmzx9xxz7vd 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 thjx5m*wkz, mxv ;fx* 9mnazn2 7ree particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate onn1,lscx jr .8f 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 uar4ie )o ;1aoa 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 brea6 np oxy5yf0dpjvsa r. k82cck-7 q+d7k a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total bindidry77-ka0o.pyk+vpf6 c c jsdqx8 n25ng energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of g:n7rdf pixf-ro /. a4ogy.0*o n a.xpa car traveling 110 km/h as compared to at rest? [Hint: use x:p0pg. o.a7ofn r x4. g-ria*dyo/n fthe binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a sqrs +djbmb l- 7z5d6g.peed of 0.935c in the laboratory, are moving toward each oth dqz6gbd jrsbl7-+.m5 er. 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 particle with hen eb.,ubo cpz sut5). addaa5)2 ;h1momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains:3k.v,dk4v4ngboc j o its power by combining matter and antimatter, achieving complete conversion 4j. gbo:k3no,ck4dv vof 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 ki+8f100 izh jse/ zm 1pvtbe(irnetic energy is greater than its rest mas b(jzeh 1m/fi0r +1s pi8t0vezs $m_0c^2$ 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 yc.toqu4 y:7ahe can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carr4.7 tyu :oqcyaying 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 ret hm +rc9/vhp1act to form two moles of water, the energy released is 484 kJ. How much does thmhct +ph/9 vr1e 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, tr)80 lsto2- y(wmzg fqgaveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one)q0s 2mg(8lzyfo t-wg particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures his qh /8;py6/mgsy ms,csship to be 25 m /y/,sgp qch6m8y;ss mlong. 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 spaceshrs.hs c7+d d4er*jv i;ip at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative td7j .*c;erd ivrh4s+so you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a totappo(r j1 :cf7ml mass of 150,000 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 the spaceship changep f7r(m:jc1op s mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What is the sp ,q cxj5q)l;fo efo+a-*ci32e ogj)8ieoykc;aceship's kinetic energy?qf;coci;io) f e-,ej35g2e akjql xyooc*+8) Compare with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to trave7 qhcm lsk 0(on3e/t1pgdgw:/l to the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? l dgqc1hp/m got/3k0 ne(7w:su =    c

  A 1.68-kg mass oscillates on the end of a spring whose spriny, l/vypn r1;a f4s)u*jhu)) z meusp*g stiffness constant,apu/1us)fesu)4*yr)h ;j p vln yz*m 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 mascyy/c9)k 5u kws $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.