You are in a windowless car in an exceptionally smooth train moving atxgh6vax, 6 h(l constant velocity. Is there any physical experiment you chvh6 lxg (xa,6an 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,2rqp4qtiu).u2 vep u 2 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 abruiuqv e.2)p42 tqp 2uout absolute and relative motion?

A worker stands on top of a mote6fh;w5n7v v ving railroad car, and throws a heavy ball straight up (from his point of view). Ignohvnf5 ;etw76vring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say th8hp0hdr31t ejk9*fu eat the Sun goes around the Earth? Discuss in view of the fhredjt 10 p9*3h ufek8irst principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0aez0 2g v0ou)p.5c away from a star, at what speed would the starli0ua2gez pv0) oght pass you?

The time dilation effect is sometimes expre qojf0-rah6a5 ssed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal withorfjaq0ah 6-5?

Does time dilation mean that time actu1tq) cs*5my zatrs;c4ally passes more slowly in moving reference frames oacmqs;5yz t4s*rtc 1) r that it only seems to pass more slowly?

A young-looking woman astronaut h7fr aqtsv+ qgy38cam2+mvc49 as 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 he4yafr+vca7c9+ m38 sqvq 2g mtr son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a change+7q/ki,vpk w d in your heartbeat? Would your mass, height, or waistline change? What would observers ok d/ wqv7ipk+,n Earth using telescopes say about you?

Do time dilation and length contraction occur at ordina0b4 .lby9+ffpk e9lg7 /mlbiary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light wel-, pms ryb*a ow7.-9m/,ed x becjwy/re infinite. What would happen to the relativistic predictions of length contraction and time dilasyj9 d-/ ,lwb7,ey /e .m*obprcamw-xtion?

Discuss how our everyday lives would be different if the speed of l :k+6jslmsyjd b5dyl9mt0m*+ ight were onlysmtbm 9+ jjlymkysdl05+*6d : $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used a8y ,imr5hs;f to indicate that c is the limiting speed in ;i58r,y samfhthe universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tof 8tt8hr dqv 5d-zrf 5a(1tqq2mpkins, for w5qdqtrv2 q z18t5ft(ah- fr8d hom 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 q p0 l9 grukz 8+4fsx,nm7ala/than c. Does this put an upper limit on thfxn k0qlzr/apasgm4 7+l98, ue momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass a1vbqpw(gs3nig ; q bi589af2yttain the speed of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does this mean that a spring has more mass : i6q) vj,da8 d2x,7y.jk s9*rttzs wsxib*o cwhen coms:j stdxb,)8zas6 wjdqv k 9xio2t,* i7yc r.*pressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neot,8 tcv *nzw.ither be created nor destroyed." What mustvw* ,zn otc8t. we say instead?

  Is our intuitive notion that vehz6,grn4f - f5)h:yviaj 9xp xlocities simply add, as we did in Section 3–8, completel xyha)rf6fg 5h p9jn4ix:z-v,y wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure ih w7u)f 9t+qn x-i.c-cbx0q lnts length to be 28.2 m. q7)t9uqnl.i-n+0cx bx - fwchHow long would it be when at rest? $L_0$ =    m

  A certain type of elementda t,mu4v4bm3c jli w2xpr ;v ):dy3p/ary 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 duse ,*w01(sshqhw: gq epend 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 star 125 light-years from Earth byz 8 5xt,d87cxwq*vqat 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 lif 4x3xcg55xk p 8lmri s*)cqn* 8+mntdfetime 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 is 82 light-years away. How fast would 9tgk wawbz83( you have to travel so that to you b3w(9 z kwtag8the distance would be only 35 light-years? v =    c

  Suppose you decide to xa1zo6z k nx7y9,3m istravel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years7yz6o19s3axx ,kniz m . 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 from8sqrqu 63s7lw 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 fr d olmcm09bvo,.p/,cuom a 5-year voyage while tr l,cdpm /0oocv9.mub,aveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a spacecraftfczx +bu lngr8k(5- /y traveling 0.960c to reach that sta 8lruzfg-k c(5 nxb/y+r 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 mu,* k8vo0 r+e lndq4q9oaqv)at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. q4 )d,lun rqo0 9* veokvqam8+
(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 )ih pj/bow hqlifv (7cr ds:,;ipp:-6 pion be moving to travel 15 m before it decays? The averahjvh7; 6p pqioi-:i)f/rwldcbs(, p:ge lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of axbcvt0lc gkj,d lr +d x7214l7 proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an obju/ e) xkl67 2derdjo+mect’s relativistic mass be twice its rest mass? v =    c

  A particle of rest massrn 3r5i ug(c5e $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ac.pst;8 ffa tfw-/;)ydwvpc +t $v =0.10c$. 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 p4ve,k0 mdsdz( roton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires cmm8p 6kw5 +kb$4.82 \times 10^4 \, \text{J}$ 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 breaksceb;8b 3nqok,lgw qo8e9 ,*cd apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinel ,cb 8e9o3 gcq,kneb *;q8wodtic 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 electronc.ylxxjjyr0ngb66 s; b+,r gt45 bzc* 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 promoca:di /gb /qrhd he0.6*ww-ton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consu1upm fp*b0rr9 q m3dh7mption 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 obta +h )/hjfa2rs3 joay*gined 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 when itb0o 7hqin) y5mx4c)bgs kinetic energy equals its rest energy? 5cbqiy)gx) m 47 0onhbv =    c

  At what speed will an obmyl* z-.8lnlu n 2n)bj9 v/ytdject's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to acceledms*uc;c2ms--fg0 )) byy wg hrate a proton from rest up to a speed of 0.997hmg)y cbc*w)0;- syfus d-g2mc? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momenf 1bd: x:p9yixtum 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 (that is, its kinetic energrh l1 0ikit+2ey is 750 MeV)?0hr12le+i ikt    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentialc;zhu9mkrtz 38ptc04 difference of 105 MV? v8m9 zkr0t;hccpt3 4uz =    c

  What is the speed of an electron whose kinetic energy is 1.00 Me2sgv;h :bb:2bzuz,rg vx gn51+ f/qvxV? v =    c

  What is the speed of an electron just 3pr w egr+4kg9before it hits a television screen after being accelerated from rest by the 25,000 V of the rgg e +w439rkppicture tube? v =    c

Two identical particles of rest e5 q/rh+4flo*chvl1 t 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 ;lmsm6bf jr2rgi s*p )6*phz0of 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 o 6mri/px8w:uy u) bzgt0 ve,d5f 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.60n(gu -icuv 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 kinetic energy and momentum of a protonzg4ki;x lb(j y,g r7c7 ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleuct+sv5,kz0 6zh9k6 xavx;uzns, $^{241}\text{Am}$, 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 par-ci rr6vt r8p+ e2j;vwk , fc-c*7mjojticle of nonzero rest mas6t-rjki8v -ec*vw7 r,2c c jrjfpm;o+ s, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV ps+ (z-jfrr/8xp 4dqjurotons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest maps(u-x rf+q jj48z/ drss 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 ny pzz+l1,5fux9j3o r/g 2jxc)f5qswrespect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How1ynsc+ qujf ),5r/zgpz xjolf295 3xw fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, eauz g1l -u i-v2gl)z:auch with a speed of 0.50c with respect to Earg- guul az- 2il)u:vz1th.
(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 Earth9 y6d9w60yrw+na npzs k *kti( traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculzkd(n +9p0atsiyk 6wry6 wn9 *ate 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 vsfzxvg 9t9w lk+*iqf m88-5jcessel 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 5 *ijx+z l8v9k- 8ts9cmg qwff0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two xo2*p-e kgx5l;oy,v dg5u5cbescape pods in opposite directions. One travels at a 5og,;lo52 5 vex*kug-cdpxby speed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth at a speed of 0.75c. At the same time, rocket B pass5 r1lvl8gdzj; es Earth moving 0.95c relative to Earth in the same direction. How fast is B ;z8l1 5vrjlgd moving relative to A when it passes A? u' =    c

  The nearest star to Eari:u(.+mb kvlk zpz( +jz*d2h lth is 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 called rela3y mv jor:v9-ftivistic - i.e., 3rv :v9m ojy-ffor 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 )ec5qsgayye3 jr5 j 79em/fx 3 zw:me0$v$ 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 sv(zxdvqf ,:4 run a 100-W lightbulb xzv,vq4( d fs:for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic eny,qljlu (/z t2ergy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conser zy t,/lquj(2lved 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 o,qhwfdi+ cj/3yk a. , 7qs6pdpz.zg0af light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of z pgpa y0z ,3qsicjda+.6wh.,k7/fd q 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 elec */ry j;zxfusscxy58j88afy obw1dkqv+ 51s8tron, 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 particles when a neo swzj5abdv8x*/y5 8k cq 8 81xf;jyfus1+sryutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of abo,bav+:y xb8 vfq 7fk uc;v+o6tut $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a negative charge and a speed ofx adr1 hliv08- tz5x7j $2.24 \times 10^8 \, \text{m/s}$. 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 nucle9 8z ;ufcc/+t y8onae/lzmx 4ndtfp 83us into its constituents, two protons and two neutrons? The rest masses of a pr/ctfaeo8 t/ mx+ 34z;zu8cfn 8ndyp9loton (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 ,)mmc :el 3jgkytagi:/7un* xthe (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial e n,i: xuacmj g/t)*k7gy 3:mlexpansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the bzio-62w t+ lxlx c,:f1 o9zlf dk4nk.laboratory, are moving toward each other. Detld 6.:9 -n i wocxbz+zf21o4,lfkkltxermine
(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 part/l8y2s-b ihsgs0ow n/8*cw zp epx9k8icle 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 and asm8 +6gktorp :7 e*bv(b5a lj49mko gyntimatter, achieving complete conversion of mass into energy. If the mass of the Ent 8 +(vkr9ot kb7g*o: 4j6pmey l5gamsberprise 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 greater thlyiu 2 hkuwt63 lh*,2zan its rest mass ilylt,2kuh h3w*z26u $m_0c^2$ 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 physics6y.bz.pf -gk,o1p+yt0sk6 obo ll x e* believes that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough 6o*-.k t, xy06poez b1polsglk+bfy . (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 mok;bi- vhev8x 4c (if/2;suer cle of oxygen react to form two moles of water, the -c;ee/v;ksc fiv i(rx hb u842energy 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 created, n 2wq:uvjmc+ y:nbs1:traveling in opposite directions. If the speed of each particle is 0.75c, +c:: y 1v juwnn2smqb:relative 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 Eartud vk)gdin: nzt)-3/h h measures his ship to be 25 m lon/vdg)ndik- hun3) : tzg. 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 spacesw9hnxi a1c1 l6hip at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on tac 1i96lwh1xnhe Earth measure for the speed of the laser beam?

  A spaceship and its occupants have axq .lswvs2;m9 total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass q;.wssml2vx 9 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 spaceshxzcpi6 h a2 h9rj-a97sip left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare a29z a -i7rh9s6hjxcp 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 light-k pmb * ih/io3xo gdm/p6fx05)years from Earth. Pp5xi6ok)/f0g hbmxpmi*/3o d assengers 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 the end of a spring whose sprin/mqm)y htw zu hb u,mr,o2z844g stiffness constant is8/4,tuwzm,oq2 ym h)u4rmzh b $k=48.7 \, \text{N/m}$. 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 )4ctc0zyj.8leofs/ z $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.