You are in a windowless car in an exceptionally sm;b) w/h7of -keqphd x8ooth train moving at constant velocity. Is there any physical experiment you caobx8wh p / e7fq;d-h)kn do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being :i hdd+)x7 gsm :6qywrat a red light when, out of the corner of your eye, you see the car beside qgdmxiwsdh:6 +)7r y:you creep forward. Instinctively you stomp 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 y wu 4sv( ag: z2yitlk30z.t/l82sqwirailroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car ol :gak4t3/yss2uzv 8l.(wqt i 2w0iyzr behind it?

Does the Earth really go around the Sun? Or is it also valid to say/o 0to s*h6)av0bn/a tgun4d k that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explainah so b0t/*a6/t)u4gv ko0dnn.

If you were on a spaceshl nw/,j pdi9t8ip traveling at 0.5c away from a star, at what speed would the starlight pass you/w8ti9j np,dl?

The time dilation effect is sometimes expressed as “moving clocks run slowly.” An brxbk(a ql ,+19t4pxctually +npbk tq,arbxx1l (94, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving r5rq*yd f) ms9j;mi jvukebq,9o fd.. *eference frames or that it only seems to pass more slow fq*qsjkiv5 r9udm;,.f*mb jo.y )9edly?

A young-looking woman astronaut -g rdfkc:y1+fy t/kk21 f39)quua cuthas just arrived home from a long trip. She rushe 1aukf2 f c)fuc/3d1tk q-9yk :rtg+yus up to an old gray-haired man 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 change-b/i:ptfg8dh zd4st8y,9qtn in your heartbeat? Would your mg-tqsbi8yp, d:/ f tn84zth 9dass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary s t7)nil tg-/ x,p)n z,fmurcg0peeds, say $90 \, \text{km/h}$?

Suppose the speed of light wha23c.ttkzc752.kes ag9j2.kt is t r ere infinite. What would happen to the relativistic predictions of length contraction and timek3kt9 rctt2ic2jase7t.sak z. . g5h2 dilation?

Discuss how our everyday lives would bekxsv(aqk:8l3 .s-wyq different if the speed of light were only-.q xa ws:lv3 qkyk(s8 $25 \, \text{m/s}$.

Explain how the length contraction and time dilation fi- t ,r2aipo2,5wwugzormulas might be used to indicate that c is the limza twuigp w5o2r-,i,2iting speed in the universe.

The drawing at the s,oty s9gfacfah9j x5+v 711ustart of this Chapter shows the street as seen by Mr Tompkins, as1y +997g1 hjfo s5vau,tcfxfor 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 less thakv cj .lf0:o*yn c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not, explaiyv0kflj:c *.on. ----待选择----yesno 

  Can a particle of nonzero rest mass attainqgzodi n5h q i1n.gf.;t l7l:, 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 e-x 0s3a;lmk25ccmzh0-y gz t vnergy, does this mean that a spring has more mass when compressed than when relaxc-5;v3zcgz h2-ay kx0lms0m ted? ----待选择----yesno 

It is not correct to say that "matter can nei;jc.sp 99f pp5pgfpx+ ther be created nor destroyed." What mustp;9xp.5cf9j ppps+ fg we say instead?

  Is our intuitive notion that velocities simply add, as we did in ulv8.;61 u ot6-ymj)ae .xdetwdm*sdSection 3–8, completely wrong?u) wtmotxse dl-v6 ad ;6y*1m.j.d8eu ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length t50jd)v kya9mt o be 28.2 mkv09 yt5 jadm). How long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle wk (ty.o730 yu,rmiuxzt s3sc 8( q,tltravels 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 onovs*5 m yovy1.u.yqq+ the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from2sd6ctp+e k,y inr *(s 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 lifetime is mea*agy) f0:;z5yvmm 8wdr jw gozm2yj )5sured 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-year/.woofq )enw/ s away. How fast would you have to travel so that to you the distance). fwwoo/q /ne would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at0( c4b pu/h6vzlq5tzld2 d4hl a speed that tells you the cdq2dl /l6z h04 4(pltb5uzhvdistance is 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 t3*j*p xeol0vk 4 b4gxi 8rflh4he Earth 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 Entrjpq)9y )x*y* g sfl5werprise had just returned from a 5-year voyage while traveling at 0.84c.lp jys r5 y**)xq9g)fw
(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-yearsq*j6zqdj +97; e1fci(yol n (ydjna:w away. How long would it take a spacecraft traveling 0.960c to reach tf;+ln9ydq (6 qc*a:ezoj(1id7y nw j jhat star from Earth, 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" spacecraft at a speed of 0.660c. Itbsf .cdkv::5 t is measured in your frame to be 4.80 m long and 1.2d5vts :cf .b:k5 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 id/ .0l sii:idu ux8t4kt decays? The average lifeti t /4.x08kdul:usiidi me, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton cb1m:v7 dk)4*mo(7rgqk scrr traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic masszelzbz7(;vn9dc 9e7:wce5 o l be twice its rest mass? v =    c

  A particle of rest m)we8eh/ukp 4n osk9itz9m) *u.3(bdx)axgt g ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelhcx ykfg)t12g4 2bf0 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 accelerk-mv1.ns yiof1di 7 x8ates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical rrfwu h:fz6;g c+c:x;aeaction 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 rz vsegll3w.2o* jk1*a est breaks apart in the process known as fission in a nuclear reactor, the resa.jokge v z3 l1w**2lsulting 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 jouee lezm94 k2n.les 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;iwqvq.+e5b lf8kkei kbo7:, proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy cllfvyra0 0hy ; e jguxmhk6 vm1+5inzi-5a8 )6onsumption 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 from conversion of 1.0 gr2l s0 a8defdxn/;v:wpam 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 energy equals its re z2ybkxhyl x ymso(yuy8b/39ds m+407st energy? v0(xbmlm 4 37dy9byhy/xy zkyosu2 +s 8 =    c

  At what speed will an object's kinetic energy be 25% of i,p 94atv 4lfdots rest energy? v =    c

  (a) How much work is requirlwra +h0 av/9f:)f jloiw4 s6ked to accelerate a proton from rest up to a speed of 0.997c? ah skf)f aow0l:r9jwi6lv4/+W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentumx,l(e . 5qizmnq y.pw9 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 (thatgx4,asso f4 lt6s;lr: is, its kinetic energy is 750 MeV)?srlog;4 f:a xss ,t46l    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated rc n4ib3e ixzhh+(m- -4l,pwcuf zz41by a potential difference of 105 MV? v =i1ul,wfr 4+h e3zhp z(4-ix 4zmc-bcn    c

  What is the speed of an electr0x a5kh 5ciqt+on whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a s d80szklaw8- television screen after being accelerated from rest by80 8d k-lswazs the 25,000 V of the picture tube? v =    c

Two identical particles of retgnrv 2)k gjt-9:,ahxst 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 protbmblp ay)m66 *on ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electro5moh12s lbwmn0, ) oy(e*utsgn ($m=9.11 \times 10^{-31} \, \text{kg}$) 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+ u3z s 2h )tw;bepue87d+nlqj8 ek-lx 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 enp74.dz a8zfbu ergy 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, 3 +emb*r/lfynh32m.z * v a f(fip9iaj$^{241}\text{Am}$, 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 momttox // m p gj;t 1zbq1lf8zer/ pob847t9qo4fentum for (a) a particle of nonzero 1/8gt7b4ozqpp b8l1t /zfrofjo 4tqte/ x9 ;mrest mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is neja5av .3h f,yy8ycuy;eded to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativh5 y8;y.ucj3yy aaf ,vistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with respect to the Earth) ob8uncff a;o hscw 3 (aa,gzl;5*serves a meteor come from behi ;8cf; ,alznhw 3gsouf*a5(a cnd and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each lw7 q x0 ra/qqi o ,;6(mciwitz.:u8bgwith a speed of 0.50c with respect to Earth.ut6m, qa :qb8. ii/; rgclwow0qx7i(z
(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 spacaa-e+;tk 7mrse th-0meship leaves the first at a speed of 0.87c with respect to the first. Ca7 -a+;tskre0- hame tmlculate 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 a2uzi1it qum6y089p6 fbynhr3dq *)i alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the alih* a iy63f qz n)0tr 6pbu1um28d9qiyiens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out twn3 veaa5gj 1a846xv2 pn*isoco escape pods in opposite directions. One travels at a sg52vj38 e np6co4an1sxa avi*peed $v_1 =-0.60c$ 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 sp9qq -(2h qri zt9h0-f3sffzpfeed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relativpq zffs(-i 9rfzfqhq209h-3 te 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 Centauri, 4.3 light-years awa.mc085- +k5paz h1kdkqkek ym y.
(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 49)vmep ijst9than about 0.1c is called relativisticep)vj9 9ts i4m - i.e., for which the correction 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 54h8 oc1lhnje $v$ 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 , bmrc/h 11wrk+gx;.+(0tvolr axwvw to run a 100-W lightb+c+a( rwl1wrrgv/ w.kb xmxh01,;votulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electa 2 de-pu.jom1romagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest maum.o2-de 1jap ss 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% thmzkih,1q4yibe 8va(, a t2kx-8b c4wde speed of light collides head on with a positive muon traveling at 50% the speed of light. The twv4bw iqai mc8 kt8,,2bzkyxh4 d-1ea(o 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, anb ku,jou+ 8gm;q3f 5hy 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 5 gy;boqkh,3u mufj+8 particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rjo 7nl15+2gf fds( zzcate 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 h pi9kz+q2nm el/vyh5x ,64a( itt,qddave a negative 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 0a*kwpxmiggnf(-b sk:.9+maj n( v3 binto its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium3( n09g+j*bg knbvf-im wx:a.a( p ksm 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) mass of a p2xftrhhj/ u;b)o 3c( car traveling 110 km/h as compared to at resrup;cft3(/)2hb xj ho t? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the ;5l5gj(*r njyls ccq8 laboratory, are moving toward ecr5jqjcgsl ;8n(5y *lach 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 particle with momenx8k7 0d .qdagxxun4b)tum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship uzp3 44fglf2z Enterprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is apprz443plfg 2fzuoximately $5 \times 10^9 \, \text{kg}$, 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 mu1lmpne673 sso that its kinetic energy is greater than its rest massp7ulm3m 1es6n $m_0c^2$ 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 9w4ovdx5a.bsb/ ox * jfit a 15.0-m-long pole into a 12.0-m-londvwj4xox5./sb9ao* b g 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 barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form twrgkj,gcddwd8-rjiq p-01go2gkv47 1o moles of water, the energy re-2pq11drvdgw0g k8 jij,c k7or -dg 4gleased 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 created, traxkghop*h6f1wk 6* j32l h lmfmnj1-r6veling in opposite directions. If the speed of each particle is 0.75c, relativeph*k2x6wl6 *nr f-om mj 3jg1lh6kh1f to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measu)l jhe7b ):g7gdup9a4 wp*wgr7n c-oores his ship to be 25 m long):w-u7o)7gogpg7 njl r heb4apd *wc9 . 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 0.85c avo glg do;/vgo)v8 lrbx mvr4;**x9ajww /9 5dway from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observ9vvr d5x*m/gvw ro;g v ;l4b8aojx/g dl)*9woers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occupantsmcufm ad(jx:;a :01 y oiyu)d; 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 d ;ydofd;j0yu1ax :c)i:(ma um irectly 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. Wh/.fusq2 z hm,izo5u.pc+:2 )kxfync qat is the spaceship's kinetic energy? Compare with the total U.S. anuuox ks),q2f +/h2f ..qi5nz cz m:pycnual 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 star 6.0 light-ye4aa x*;wy.gb xars from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 yg. xxaa 4*by;wear. 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 i,srqfi w-83i whose spring stiffness constant isw-isfi8 ,q3i r $k=48.7 \, \text{N/m}$. 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 mass;; jjt-99ss7gcdr5;6x t+jlh gja yw t $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.