You are in a windowless car in an exo-*bgh1* gle 6;z8uq kpy r4qiceptionally smooth train moving at constant velocity. Is th -o*q*z6y ql1ikh g;geb8u4r pere 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 ligk.igs.h2h7v 8irczknj ns 2fg7x46kx ;a97dj ht when, out of the corner 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 say ai4rsxv7.sa kh6nj ki ;c 8nz k29gx7 gd.j2f7hbout absolute and relative motion?

A worker stands on top of r.uwfr wpf1rb *3c 9rt8wv yvrtm482.a moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, .3r1r28m4rwwvf t*v .bwr9 pyuf8t rcwill the ball land on the car or behind it?

Does the Earth really go a;f2s9c h ct+ysj-x7n2l gz7jkround the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (cf tl 2 2z+-g7jc7n9xyksj;h sthat there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed ol69r *v- )vl qn aya;p8q0kiawould the star8o) qi;nyva-lv9*0k a rqa lp6light pass you?

The time dilation effect is sometimes expressed as “moving clocks run seu 3u, 0e-hopblowly.” Actually, this effecte-hp,b0oeu 3 u 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 referenc+m4mmg j0.pm :i /q68vocsybze frames or that it only seems to pass more ss.ym:p+j 4ozim vb m 6c/8mqg0lowly?

A young-looking woman astronauhkj sl3 ok:i7zciq)4 +u(t9skt has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her tk:)kl9ss(j iko+ hq3uz7i4c son. How might this be possible?

If you were traveling away from Earth at speed 0rn m51lyxuhz:7i1 .ky.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about youurkl5zxyiy h 1.m:7 n1?

Do time dilation and length contraction occur az4 (nrl z;1 5ta:4.w63shjjsjk nnxnyt ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would hw1 6g(r6tgv dsappen to the relativistic predictions of legt6gvd 1w6r(s ngth contraction and time dilation?

Discuss how our ever1ejvsiu w)m;(b- 7. bntgfy*myday lives would be different if the speed of light were onlw. t17*mbimusbeg(n-;v f y j)y $25 \, \text{m/s}$.

Explain how the length contraction and ti (y:g.-dx 3t,f1 lly hhrtpjhg9:mt4 l81nqbkme dilation formulas might be used to indicate that c is the limiting speed in the universe8:.4gth hyt1xm -lf t,b3 rypl1hqjl( gn: k9d.

The drawing at the start of this Chapter shows th-8c:wxf .7 asiggh mg0e street as seen by Mr Tompkins, for whs 8.fi gg-mwc:ah x0g7om 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 than c. Does this0e; mh (qqjq-op8v( od put an upper limit on the momentum of an electron? If so, what is this upperdh-8epq(q(;0qjvoo m limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mask l9:nptb51 ilxmf8; ks 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 ed0 vx-/hpw6w 4n3v kvqnergy, does this mean that a spring has more mass when compressed than when relaww0 /k4pdxn6-vvv3 q hxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed.a-,nj3m sja 9w" What ans,93j j wa-mmust we say instead?

  Is our intuitive notion that velocities simply asf0o1wnj(vuk: /d99m .f efovdd, as we did in Section 3–8, completely wrvsn wv(mofodk19. ue:j0f9 f/ong? ----待选择----yesno 

  A spaceship passes you at a ;lyli02 gk1i,u:o;amt1pxeta2y :brspeed of 0.750c. You measure its length to be 28.2 m. 1rap1lxg0: t i;lmeu22o; a:ki , btyyHow long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a 1 a0u5y90g1ixpymh8,hms vfr 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 0k8g l0ijro0 non 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 from Earth a1 ed5apr, da7yt 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 life2czt35,b aouz8ot2z ptime 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 :h + d-ja4(j8hrhpmqd is 82 light-years away. How fast would you have to travel so that to you the distance would b8hphmdh :(rj qj4 a-+de only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away anc+i4 h61y opst a speed that tellsn4ysc6i1 o p+h you the distance 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 .yalxfuh(k8uwv)/5z v4sj j; the 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 Enti 5phixe+zfu(z 68yen1r u c,*erprise had just returned from a 5-year voyage whi(uc x6pherye,8*in 51 fizuz +le 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 wouluug) fmy)t-voz td 5./d it take a spacecraft traveling 0.960c to reach that star from Earth, as measure/5uto-m) gzy tudf)v.d 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. Ip(4- (pngqv jnps6t a+t is measured ipp4tvq na+ s-p6g(j(n n your frame to be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to travel 15 m before it decays? The ai c)m5 c,v/vbtverage lifetimc,cv vib5m )t/e, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling at mp9 4i1vjh,im l )gl r/n77yfp$v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an objea6yrzt,h5: dhhnv., o-ck1odct’s relativistic mass be twice its rest mass? v =    c

  A particle of rest massfj3eh a+6mf e4 $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels : +6xqmmd 0gjuat $v =0.10c$. 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 th*4bumf qz;,uta18 45/:qap: +nfir rti wg pceat accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reacti,g 5i. vker4 :* r0vriflx5esson 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 the process knoz d lw.b/:yi-kwn as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in thl/zwd yki:.-be process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron 1z 4m5lcjfscl(e vn-5yucn 0/ in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a proto uv: cr4h.2 ox)2zhrps1rat3c n in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Sta*:yi2bcpj vkj.x7s1 ates 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 obtain a35hpe1(ymdqed 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 whenuw2mcw ;uwjfgt:f7+) its kinetic energy equals its rest energy? v = gcj mw2tww7;)u:f fu+   c

  At what speed will an object's kineticzzxl8u0d xtkj:vx*f -f0 w (t3 energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerat9 sxs0 krbq)d0e a proton from rest up to a speed of 0.997c? 0) srb09 qsdkx W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy any5x75k qcpuykq m;) o+d momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV pr96h vit+j ;uisoton (that is, its kinetic energy is 750 MeV)jui sitv9+;h6 ?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed ofklxv*z61s 8kp8 . dp08kad8q afgqz6dg)k d 3f a proton accelerated by a potential difference of 105 MV? v g68k*kdpadf) 8adf 1q .86l3dqkgzzskx80v p =    c

  What is the speed of an electron whosevm0xj bz3* d8qa qo(co4e, b0b kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television scr gujf- zndt()z6 p94in/rpj/e ia/i 7ieen after being accelerated from rest by the 25,000 V o /(n- u zj/adgjt pi7rn ep6iz4if/i)9f the picture tube? v =    c

Two identical particles of renn-03uf jha/k r y5qr1 m*/cwust 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 ofig+ 7 md1ddcrb 8 k2d hfa20p6kdbki,7 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(so 9x)n4fz q.f9ve py 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 to 0.21c+4ttop .ga1mi8 l5 mi4ftg i,l.
(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 kineticy58bv3q*w4 ms+pcu d2s pfz1fi 3k fo9 energy 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,9jqcl pbg( *:*; kkfbl0s bjhfq5 ;gw3 $^{241}\text{Am}$, 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 vern+sw,u 7tm x/fsus momentum for (a) a particle of nonzero rest mass, and (b) a /mf xts7un,+wparticle with zero rest mass.

  What magnetic field intensityk7ayak)q/ou 0k : v4vz is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the)k/q oa7 v04yk:kavuz Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket y;u* 1t2gwv r 7fyjk qlf5ku6,traveling at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is theufl6y71wqjfr5 k kuv; y*,gt 2 meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposif) x d/n hf/lm d48tz0t+ds/sdte directions, each with a speed of 0.50c with respect to Ea 4fsmlzf//d+)dh /ddt0ns t 8xrth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A second spaceship leaves the fipte e5,+4i5mym r .bdwrst at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it ipeb y5,+mr.5 m4dw etis 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 shq dratbqv*h0-)( b q9ees an alien 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 )q0 - 9hvbbq*qdrh(atthe relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in ogwy,b8azovv)+7b5 s9 *o igcgpposite directions. One travels at a speed 89 7wbog5a+b*vg)csov z yig, $v_1 =-0.60c$ 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 pasl be5 u,yikthvb;r026k 6lq/rses Earth moving 0.95c relative to Earth in the same direction. H/rve5lukt 2y; 6lrq6b ik 0hb,ow fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth rbuag6r-o1 m p.xy2 /ois 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 callf-fg 6uze n.x* cg3nq4ed relativistic - i.e., for which the correction using special relativity is a significantg-fnf 63nezq x4c* gu. 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 zra8b ek yaawe(w7iqy c b( z+3+of(14$v$ 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 lj a2i5p n (fh/rov:44 uxu;xqaightbulb for 1 yearx o2pix;vu(jh 45nu/ra4 f:qa ? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electron(f16unpa f3 nu and a positron together? A positron is a particle with the same resn31up6fu fn(a t 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 r0 jdz uz.).l j+d;.pz bq 3xxg2aaqn6collides head on with a positive muon traveling at 50% the speed +.xz2u 6jzx a.rq.3jqlgbnd0adpz) ;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 b,lt vb8ums p y0(4w0h9e3v b dwd/lmo2sm-( yneutrino. 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 kinetic3d 8w2bm ( w0d-lsl vestov,9bh4m(0bp/ myu y energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates ener43ed: ncl c dj06y prh1hg5d:ygy 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 negativi6s-urxv- alx;; fh8xe 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 would4 he6h ;r*s mbubi7r0w be required to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and h6irm hu*b7 es4;0bwr helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a car travebp *0s+hp1 9ml xqs0eup8/h jxling 110 km/h as compared to at rest? [Hint: use the binomial expansion.jh qs0p0p uxs/8h b19m le*+px]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a 8y 2lnvf0m0c mspeed of 0.935c in the laboratory, are moving toward each8y lv0f cn0mm2 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 par7l*p;(jzxpzng f j1j /ticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combibhiv*vh41 , rj/ dwt8uztm2e 4ning matter and antimatter, achieving complete conversion t 482vth/w* emh4vzdb1jir,uof 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 kinetic energy is greata -*,gvj-qwv ter than its rest massq*, -aj-vvw gt $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-long pole into a 1moe-q9* m,hpgt3*e/rtl: xj47n k4mid b +eed2.0-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 barn looks even sho mt3xlb*hm4q9d+4k m7ete*or/g: j n ed-pi, erter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to formnz di*:dh/( rx two moles of water, the energy i*d x:d/ r(hnzreleased 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, traveling in q/n:uyrsq:r y(yd m+c)67s6rpww rl4 opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other parti l(qys:d6r :wq/ u4pc yrr)wy 7nrms6+cle? u =    c

  An astronaut on a spaceship travel)e9 q s + qhpo+r*/8okxaahg(ds ck93king at 0.75c relative to Earth measures his ship to be 25 m long. On the sh o kh+c/xaqog+asp hd 39r skq8k9)e(*ip, 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 away fromy(5 axj dx hi2t5f-s1a Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observdhtsxj5a5 f2ay i 1-x(ers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000xbzgjv 5s 8o-.2ou/yn kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, th2/-zo.gbs8n xyo5 v uje 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 a speed of 0.99c. What is the s u.mpjt2y 7q fa8o08ympaceship's kinetic energy? Compare with the total U.S. annual energy consumption 08qy8mptoja7 u2f y m.(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-yearsz(gd::-qatz,k:-idk f qe-ug frm;iis*f7g: from Earth. Passengig ; i gi-r7*kfqtsmkqde-:df ,:af:zg( :z-uers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on thr(j23* va,4h zxezaete end of a spring whose spring stiffness constant is 23( 4h,z*eerat avzxj$k=48.7 \, \text{N/m}$. 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 syxn 2b3 6tj(e)2 rjm lm,-eqo$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.