You are in a windowless car in an exceptionally smooth train movinzq3 m1 cva:;bzg at constant velocity. Is there any physica3 :m;vzb qca1zl 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 when, out of the corndr1leugyu ny 1(9/3t(ph-f v ytzd*n -er 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 savtdtp* ldhy1 y e3rgnzn1/( fuy-(9 u-y about absolute and relative motion?

A worker stands on top of a moving railroad car, anxhu0-bd7v,:e3 yxby vk,sk l5d throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on thlv3k: yey hb7x,x,k sb0d5v-ue car or behind it?

Does the Earth really go around the Sut1*6i,pui sndq5 pvj)n? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first princisv1 ,djq)56i*i nuptpple of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c5l-mb y i:x6o-fj oy -/uf71a opj 4rwwach4t: away from a star, at what speed would the starlight pass 4c6outf:- rjayjp4y o5 -:h f lwa-bmiow1/7xyou?

The time dilation effect is sometimes expressed as “moving clqb1 7zvg1bqd2 ocks run slowly.” Actually, this effe1zbqg1bvq 2d7ct has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passewa+xw2(1slxb zv k1i7-egbu )s more slowly in moving reference frames or that it only seems tos abz7bvw+x uikw-x l(1e)g 12 pass more slowly?

A young-looking woman astronaut has just arrived homemv 4;3l jwd5jh from a long trip. She rushes up to an old gray-haired man and in the ensuing cd;v hj4lm 5w3jonversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, woul (wh/w )cylj0sd you notice a change in your heartbeat? Would your mass, height, or waistline change? What would ljy)0wc(/hw sobservers on Earth using telescopes say about you?

Do time dilation and length coni;zi6ab,bfe5ts k 4x: (eo w;mtraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would ha*ib +euccf*j0ii2 ld6ppen to the relativistic predictions of length contraci* c 2 je6*iui+f0bdlction and time dilation?

Discuss how our everyday lives would be differenteqef5up 2: 8cr uz.hv8 if the speed of light were only.fu qzuv82eer p:c 5h8 $25 \, \text{m/s}$.

Explain how the length conq2f1 :h gds olw-i3h5straction and time dilation formulas might be used to indicate that c is the limiting speq 2gd w-fhss5 h3ol:i1ed in the universe.

The drawing at the start of this Chapter shows the street as se (.y)lwdr uoi;en by Mr Tompkins, for whom the speed of ligh.o u)r;l( yiwdt is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Does this put an up(fjrk a q24bj:per limit on the momentum of an electron? If sqbj:2fa jk 4r(o, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass2q.azf .qn qkkmd. x5. 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, mjbh (.vfrsin /3e(d +0l )tcadoes this mean that a spring has more mass when compressed than when rnfeh+jl0 mst )vad/i(c. b3 (relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor dest(l)0lsh8j5ff0 vk )m/k bf pmvroyed." What must we ff/l5v0m) pvhkbs0jl( )8kfm say instead?

  Is our intuitive notion that velocities simply add, as we did in Secm3 +4eodfw9f kdv)bn4 tion 3–8, completely wrondde+f m3b4vw9f) kn o4g? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length agon l44yo l3 tpm:z3:to be 28.2 m. How long would it be when at r pytzaogm 3 ln4::3l4oest? $L_0$ =    m

  A certain type of elementary particle travels at a speeh/v8dy 0x na0bd 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 intervj;22okp8u rk t*a2cdv ;2p uqfals 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 stgj4x-x s:h-1my o4ev tar 125 light-years from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetimj 9 (twe:m4qamv.9nw ie 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 s c;agh um(leg1o0yfv(s- ib29-p (a2mnnm(chtar is 82 light-years away. How fast would you have to travel so that to you the distance would by(1hboga( a-im (29 ccg(mufl-p v2h; mnn es0e only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 lif2ud dzi8l)cjhkt,(bxu qzw 0+y./ :cup36csght-years away at a speed that tells you the distance is only 25 light-years. How many years wouldkt+0(c,suw cbjd .c 8:yz ix 3z) q/fuu2dp6lh 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 is *f-xn(ey2oh/-+fxg 4vf o xjo$11.2 \times 10^3 \, \text{m/s}$. 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 starshipz08 v2vp +7jlutqjc2t, wvgp1 Enterprise had just returned from a 5-year voyage while pc wglvj7tz +vp2v0jq8u2,t 1 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 awaygys8v+d z69 ml. How long would it take a spacecraft traveling 0.960c to reach that star from E8 y+ dsg9mzl6varth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecrk7u, tn8 fl1u3nb ut3taft at a speed of 0.660c. It is measured in your frame to be 4.80 m lokn33u7 ul8,ubt1tf t nng 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 piofmz/)ck1.n 5.hng h gz.mv cy;n be moving to travel 15 m before it decays? The average lifetime, at rcz yc5.nf).;m/ gzvg1k mh.h nest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of ax0:xmo0syk-e+ +l fyl 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 its rest y(u *:fexk/oh4 p stua ;n9: ucfv/a7fmass? v =    c

  A particle of rest maske/fl+af:2o os $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travers t7qufl egu:i,1( a7ls 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 accelerat(qn *mt otr*ed6c8 jc8es
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical rea k bc.2zk*zo3myb,+y yction 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 the7pkhf2yhj m2i9 g3x/k process known as fission in a nuclear rea ymk9i2fpjx/ 27gh3 hkctor, 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 4acy75jn 6 m;q ymu(rvof an 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 m,nq1akxv.0 8uj.k rkuass of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consu t);bc alyi.cqy(0d 0jmption 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 obtained fromzs yz)w70 ,c:tlk rf5y 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 energyfoz hj, 2ly4ga5(dv 9l equals its rest energy? v = 2hoz4j va(5ydfllg 9,   c

  At what speed will anxr3j0a m x:v9e object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required deyr u6li -1auhmod,*.5+o zh5y wp7l)d mv-g to accelerate a proton from rest up to a speed of rhod7zo6-uleg wud y5 . a,m+5)- dpml1vhiy*0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton trau(3m ylc: pj9tveling $2.60 \times 10^8 \, \text{m/s}$.
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 is 750 vg) tcguf,ryd*c21jwg9rv (8dn5 p4 bMeV)?d v49wcf)yrrggnt * jd,c2(pg1 8v b5u    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a po7)l(vipa 5lm +ecqky h5j0ob5tential difference of 105 MV? v =me+ a5q5lhvc)ij bk05p(7yl o    c

  What is the speed of an h6f.hq6du;, -lla dl;5pdcwhelectron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just n g)k .9e5xibubefore it hits a television screen after being accelerated from rkg.9ui nbx) e5est by the 25,000 V of the picture tube? v =    c

Two identical particles of resx/ve 8q4ujv 6rt 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 oxp*/sr bp/s 6tf 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 momenvkg-fb j9dk4q(v+5i d +3bb ubtum 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 accelerated ts1x v jf5yuu02o 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 prbfh8lgf 8ljb-+cw( dq1ix2 pcv;0 o3moton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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,3ba(hnrtg 20 43e smc4 xgul)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 energy versus momentum for (a) a particle 0 u6q0znpe+sd ,uh/ow of nonzero rest mass, and (b) a particle p,6eqw 0n0+ uo/huzsd with zero rest mass.

  What magnetic field intensity is needed to keep 99 mctf5rc1y8bh.*g h:f8-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use thecyg hfmrbch*5 t.1 f:8 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 atts x0qs ekfu;o (3*.sl 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0e( *oxkss q 0ltu.;3sf.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a/ gsikei80;d u speed of 0.50c with respect to Ears/guie 8k 0id;th.
(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 travel;ig u2p:xf.6 j,wbpscing at 0.71c. A second spaceship leaves the first at a speed of 0.87c 62si:;jxpc,b.ugf w p with 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 at a speed o(khxfq0s s raie5. ;8nf 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 ;.r5kaxehn 80 sis(f qthe other? u =    c

  A spaceship in distress sends out eqpa59f;mu( um1l+deo h4 h;x two escape pods in opposite directions. One travels aap1dq ol4e(uhmu;+ 9e;fx5hm t 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 ah2-bwygitwm i.0 g3m b 55yfd99bx va: speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the y-05hibwbdy 93 5:tmf 9gim v.xagwb2same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, ipwc)d:y 2a:tk l4wjh - er7r.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 th zy x+b-7pbi0f v0x.iraveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in ai0.+ fx -bybi0z xhp7v 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 speedk0prf x8:aq w bu- :jzn4uqzv3w:8); uulw v+a $v$ 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 j-; r b4lp;/b89i2t zv, gyv+ud waaifdestroyed to run a 100-W lightbulb for 1 year? jiv-g4d8/ ;at2bupz9vl iy+a,r; fbw$m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed +m/+ -oglwily qx ow1)+otff0 to produce an electron and a positron together? A positron is a particle with the same rest mass as an electfo0 mwf-)ogiy /1+oll++ xtwqron, 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 collides head on6x4 c96,ubmpcm ucz9 a with a positive muo p9 ca4uu zbc,6cm9xm6n 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. Assum) rp;2dvmbt)yn(x2e4 e 7v (dukp6nl de the nbdlxt p en )u;m 42y(p)v7n6evkdd(r2eutrino'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 =    MeV

  The Sun radiates energy at a s(xxb+fo)d2pdz fp.0rate 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 charge aeug;r) ,dwr* end 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 constituent8iif,x, kv0t6jg 7 0l-etjuoj s, 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 diffetjf8x0k ,7t-o0 jligu ,iv6j erence is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relat-o o z8ib5 i;bjrv +;s43zftn+j8lst oivistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansion.]5lsob o3it;4jj zn-tos+bvf 8ir z;8+ $\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving towanskgq dq1q- r9 ) l-0t0x6xddurd eachdu s- t1x90qg0 - )nld6qrxkdq other. 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 pahqtp5kequ0 nq0*f8s *aik-7,(wi ybfrticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining mtof k wb9ugvm5* 02u1aatter and antimatter, achieving complete conversion of mass into energy. If the masv 5*to01w 2u9makgbuf s of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energy iws/zyg(2cyybrq. l2cqz +:*x s greater than its rest maw( s:z crx/q2 yc ybgl*z+2yq.ss $m_0c^2$ 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 physicstxpz( /st y uq5m)do-vhowx3l r:*k32 believes that he can fit 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 detailzw5 y3)tutrkvxh3 */mps 2(do oqx- l:. 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 hydroge:) odpqjr,d+a n and one mole of oxygen react to form two moles of water, the d,qr:odap ) j+energy released is 484 kJ. How much does 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 crea j.sxo:5quasau-: .j 4a ivh:p36jrglted, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle'ss5rj -:v.x j3g6.:ul phjq i:ausa4ao speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measub4t 8htji59px lhw6 7gres his ship to be 25 m long. On the shi4h i x85w bht9jp7glt6p, 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 speeh g83aqk)e8k td of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers g8)k8kt aq eh3on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The 9pp0kyy* ep2n-r9tsget ,e 0doccupants 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 accelerate the spayd9pp nk90 ,ge*2-t0ep yr etsceship 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 spe59qjo6)igloj7k -o l:a, ufiaceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual eneoif o,j9qk67ei-) jg:lou 5alrgy 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 star 6.0cn)1aq-c0qg n)ac4 w2vnx3azft 0:s r light-years from Earth. Passengers on the ship want the (one-way) trip to take no more th)a1vaatwcgfqqn)- n:s4xc20c 3 n0r z an 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 stiffnesskfq2 see5dka.-i3 nj0 constant i e3.0a5n2sji- qfk edks $k=48.7 \, \text{N/m}$. 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 ma (ai23hlepsp ,fui,1z ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.