You are in a windowlesfm )ga hbeibos.h;y.n;4i(z6s car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment 6ni )b(h;gz4sh.boye.mi af ; 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 th 4z u0 ip/hd1ozn/n)cse corner of your eye, you see the car beside you creep forward. Instinct/nn14z hpsz /0udo)c iively 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 railroad car, kk2-zh1q( mor5d, gin and throws a heavy ball straight up (from his point of view). Ignoring air (2qkr-5 odi nk m,1gzhresistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also99 ygfjn3 m84gug 5pcm valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (th9 m5uc9jy8f g34nmgpgat there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c awa .ev9g5lny +kmy from a star, at what speed would the starlightyk l5evm9n+ g. pass you?

The time dilation effect is sometimes expressed as “moving clocks run slowts0:ufp9t v (ily.” Actually, this effect has nothing to do with motion affecting the f(t9vf 0us :ptiunctioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes mort. 2b i/tdk,7hcoo s3ze slowly in moving reference framek72iho tc s.bz3,t/ dos or that it only seems to pass more slowly?

A young-looking woman astrom q8k4ofea6h4naut has just arrived home from a long trip. She rushes up to an o864 fkqhoa m4eld gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling gm+ 6if0kem2d w*oz y2away from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Eiw eo yz0md2fg6m+*k2arth using telescopes say about you?

Do time dilation and length conv6 eka9y0e )rsp6wz 0oa*xhp u828x i x2bd5fttraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinqd7iyapj p,wz2-3 : jnite. What would happen to the relativistic predicti 2w:p3a d,i-jpz7yqj nons of length contraction and time dilation?

Discuss how our everyday lives would be different if the spegktnl25u -c p+ gwa;z3ed of light were only c5w3kg -tz;l p2gnau+ $25 \, \text{m/s}$.

Explain how the length contraction and time dilationmk n7wwk5gg 3: formulas might be used to indicate that c is the 7nwgwkmk g:35 limiting speed in the universe.

The drawing at the start of this Chapter shows tnmo-glam5x i+/a5.m *k.a96eehzz4, lmni a fhe street as seen by Mr Tompkins, for whom the speed of light i ixk9. /n-ga+z.5fa*zmi5e,lm hl a om46m enas $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to trave4ym) jlp zd* -hl;o:idl at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not,z4 dlod; lh-*m):ypj i explain. ----待选择----yesno 

  Can a particle of nonzero rest mas ok nad0l.8mo-s 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, doesjt q7l d7 lysym0v0p39 this mean that a spring has more mass when compresm00t3qy 7ljsv9d7 p lysed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." m :gkg9bti d;g 9rokj y;d,r77What must we oijdm7ygbtgdr;9kr; :9 7g,k say instead?

  Is our intuitive notion that velocities simply add, as we did im-zf 4-z*ih x*9dfupco , sc.pn Section 3–8, complfcp9f*s*m.c-p i4h-o zd zux,etely wrong? ----待选择----yesno 

  A spaceship passes you at a speee )a pvthl/*8bs;o4ps/t6rji 8hi+emd of 0.750c. You measure its length to be 28.2 m. How long /r)e/6 tem ;+* 8h4pl bjasiivt 8ohspwould it be when at rest? $L_0$ =    m

  A certain type of eleme;t6b;ugla0ik k me2x;ntary particle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals depend on the factor cyfcb56 j/2qcfq us78 $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 strk5a)gu w lt4ps +j1/.8bk lenar 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 lifetid7(fk/k)ypwbc0 u8 vime 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, asqr fl5vv5.m,dph6:ox zm)s9 star is 82 light-years away. How fast would you have to travel so that to you the distance m 5q 9rvzs)d.ho 5x6sm,:flp vwould be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 lixlwa mt1-n61x vj0:hr:t; g dtght-years away at a speed that tells you the :ht v:ntxa 6xdwmt110; gjrl-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 fromhz q0b1)h5w k z d1qe(yya9 p2k.)ettf3jt6mm 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 Enterprise had just returned fromh.;6: w64vy sjsek nho a 5-year voyage while traveling at 0.8sjev4 ;.h hnyk6:os w64c.
(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-year1jw06 9eyfoq/muk 8zz1k2 zdxk+c +mis away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by y xk1iz 9dw+fk+o zj m/eq28ckm01z6u 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. If;4m a)q: jzbqxr* q-qm syw);t is measured in your frame to be 4.80 m long and z fq -q)jx:amswm *q;;) qbyr41.25 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 fw-o/4 /rlosbg hj)v/b sa9 a3averaga)f lg /jhw/a3s/obvs4r ob -9e lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum o*rr2;z2g6)jmc ugc (i2d az nyf a 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 mass? v = hc. (n1cbntvgp 4k, d*   c

  A particle of rest massr v+ mw,jzm tqmn,;x2( $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travew68z+qb8e 5 sy lqcc)yls 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 cc2w n()ovr xs*c *qvi5 g(b3q ome:wn-hange in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires:4m( bx lbmno, $4.82 \times 10^4 \, \text{J}$ 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 restwouck7 yw. ,a0tr6 +e*if6fp u)aa 1fx6b 2bjc breaks apart in the process known as fission in a nuclear aj+yf*k2wfbu6o t70w6)6ai p c.bcx,ur ea f1reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an elecg:,rjar2pk6su,vv3 jf xd8 s(tron 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 masa3lx-k:fv, hp s of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumpf*zt a v- tk4r0dwwd0; ;odr4htion 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 ,;4rlqmgda dym.kyt-o- +9s tconversion 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 ener+nw (80 s jvewy)+bbddgy equals its rest energy? v =dj(b)ew nb++ds v0w8y    c

  At what speed will an object's kinetic energy be 25% of ;l2fggd/ujx(, 3 1eqi4jg g7oxib -*b.cypbjits rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a spewz/hw+w- b5hy ed of 0.997c? W bwz ww5-hhy/ +=    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and )x5f h8r j4aqmmomentum 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 w-,sd-,8n1 (-s e2ak6fog fcvxgm wfm(that is, its kinetic energy is 750 MeV)? sgg(o e,2s-m,-6n 1 wk -mx cd8fvwaff   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerav e.6syotxa5u( ka bq(29:wzm ted by a potential difference of 105 MV? v = 9ea y26(s(ot5vakzb.:mxq w u    c

  What is the speed of a,brb+sa:gjh wf* tbn87jh- t5n electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an elqve4 /d 7keb(nectron just before it hits a television screen after beingk qnve7b(e4d / accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rn o t4.3.u 4l3-rzetcjlqp- edest 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 6bna+) hfas5 x az)joqr,3*r hproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momx(odr3b:k /mm9ojwe 8entum 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 to 0ih((5(dbjzbiw* 6 x zddz :p(f/pxfd0.21c.
(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 oflgz(s +) es6x a1 2iqe ffbijs*26mu(n a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleu i b*3cmd.fg4ss, $^{241}\text{Am}$, 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 versusvp9rr5sr m2jumo 0hv*)t zo8 , momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest otz5 p j)rm80vo,su9hrm *rv2 mass.

  What magnetic field intensit1u -zsjpz:1itnt2m4u y is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, si4:j sz1uttp-1zm un2 ay, the 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 traveling at 0.50c (with respect to the Earth) observes f*k o6rb96p ega meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with resep o66k9 *gbfrpect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50c wi dk;l 23nmlfz9th respect to Earth. 2n3lm lfdzk;9
(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 0.71amy iz) e8vwo x-pz-)2c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with repezv 28 o wx-)iz)ya-mspect 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 of 0.60c. Tx+op) ,y8 tkx -ma+ 9t:ezi5dpjfwy4vhe 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 rel dyy xi4o wzm: tj)a +fep9,8tp+-k5xvative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. c*ghe- -r)w +td0rsb vOne travels at a spr*s) h0-g+bvcw-dre t eed $v_1 =-0.60c$ 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 .pvuh4+l5s :+ymaviny:p- fqof 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative tvf hl::-ip4 5++yanmy.qsp vuo A when it passes A? u' =    c

  The nearest star to Earth is Proxima C:r 5t8fkpl5/k h4b6se7v /d,lbcwapk entauri, 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 trave / --y teb -s9j;dihuytg/7ykcling faster than about 0.1c is called relativistic - i.e., for which the correction using d7i/yj;9b- -ctkhg-yuye ts/ 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 :bildujq8oldt5 7 ffj4p4+8e $v$ 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 destroyedm1lp;*e3xo6f /h uh5 tksehf2 to run a 100-W lightbulb for 1 year?*uesmf/2; t 6h 35epk1hol hxf $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromakyn vnq1t3 x6fwx(7( ognetic energy is needed to produce an electron and a positron together? A positx7nn361((qvftxy o kw ron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

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

  A negative muon traveling at 33% the speed6c-i3 -kcn wrfnnr0.z of light collides head on with a positive muon travelc-cwf6n. 0-i3 rnr kzning 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 decayo/gz-pn+ 6p 6qzzkr 3w into a proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared azp 6 zonr-6pwq+g/kz3mong the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at m1neowvf.j(1 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 3xxnxsbr od.3q1o5d. have 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 auaz m+/+g7ku*snep2p helium nucleus into its constituents, two protons annz +k2ugp se+a*7m/ pud 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 binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) man2yqb-im*wniy6)zq0ezk:kor 6 r7h) ss of a car traveling 110 km/h as compared to at res6 imiyz hey02nrn* b))qw67kzor:qk-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 laboratory, ar)osjnv8ta hd 0f zq4a4 tl66h(e moving toward each other. Determine 6t86o)4jh(4atnf ha0slv zd q
(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 particl s9(hcw(ia be)gdvl( 5 +kkol spf.1f2e 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 matter+ /,dewti ipk2aaaolls u51* 1 and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprisal2ow aik tu/1,+5 a1*ip dlsee 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 kinetiu ehth:+)tp 7 im)kjiyt)k;y)c energy is greater than its rest ma i)e:ktty)hhm+k yp7tj ;)ui)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 physics believes that hwt+7 gn6oxk0p vywc 7 .knlus7x7ia+,e 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 detail. How does this fit with the idea that when he is ruwk.oynu+tx,7wc+ni67sxp 77a k lv0g nning the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen r)8/q3 bw bngyand one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elemeqnwb8gb/yr3 ) nts 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 twok7ikck 8-wqr)(xl2qkeh3y +x identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative 7k)83ck kw lxqhkri e yqx+(2-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 relati r e)ry8vbv q-ge 1ojo;v(krde;/m+ 9lve to Earth measures his ship to be 25 m long. O;r-y)ero+d j1e qlbvrgev 8 m;9/k o(vn 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 away from Eavygm)5c:kq ;r/k nxp5ry7, sarth. You send a laser beam toward the Earth traveling at velocity c relative to you. Whax7r mvq y:p 5,)k;cgr/k5nasyt do observers 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 occu ymdr 80n2rsxqmd2d5):+rw smpants 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 m :ddmr5 qxd m)0y+2ws82srnrmass 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 spw b1jj*ea0zg90n j9ycx nww+5aceship's kinetic energy? Compa1 05*ww 0czjxjeb y9+ 9nnajgwre 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 travel to the vicinity of a star 6.0 cjh99o*ci tzw r) .2ob7, 7csitpzdg *light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much7w*i.ot7cdszc pt9 92 ih zjc,gbr*o) 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 w4zlb6 /moi,g3l9xt2p u fev-spring stiffness constant isxu i/ 2-lzm34ogb6l fve9p,tw $k=48.7 \, \text{N/m}$. 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 masxs3 u0a64 nwjss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.