You are in a windowless car in an exceptionally smoox:9hj2 cws,zhb+ bsf3 th train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are movingw,h9 cfhbjzs 3:s+2xb ? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of the cm)or:qm8h)7vp ),qwski3ur u orner 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 about absolute and relativ mm7u))pqhi) owqk3rs,: r8uve motion?

A worker stands on top of a moving railroad car, and throws 09cie6n:a dn (w-pwc0oni:p da heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the cdn wp c0 :dniw:0- ae96io(npcar or behind it?

Does the Earth really go around the Sunvuz3t vg15)ty /tqus7h d)1i p? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first princip1g thq vu5id/sy1ptu) t)z 7v3le of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a std)n;i:7j 9bv he: wwbiar, at what speed would t)i7:hjw neb vbdw 9i:;he starlight pass you?

The time dilation effect is sometimes expressed as j,zhew1 :rzulqs33a(“moving clocks run slowly.” Actually, this effect has nothhz uz,l3swe:j3 1( raqing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean thatzt8gon7( c()f fhyl 4cnkhw s*e7 ;i(g time actually passes more slowly in moving reference k w; 4ony7 g hnci8zhs7fefl()(c gt(*frames or that it only seems to pass more slowly?

A young-looking woman astrona0ctf rn5-*go ol,jxp:ut has just arrived home from a long trip. She rushes up to an old gray-hairerp-tcg lfo:jo 0n x,5*d man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earto/ts/nz gaq9 c cgh20-h at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about yoz2c/hnct/as 0 -q9g gou?

Do time dilation and l1; 4djsergv .jength contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relativ u+45z ih/bi:tpn)fj histic predictions ofthnj+pb /f 4:hz)i u5i length contraction and time dilation?

Discuss how our everyday lives would be gy l mu( e,kw9i68fq0xdifferent if the speed of light were onlymk,0 x(6u89ewfq gyi l $25 \, \text{m/s}$.

Explain how the length contraction and time dilatio,h9:gogj.g*x. c ho7 ckmjl3p n formulas might be used to indicate that c is the limiting speed imo7 o cjcpg9*glhhkjg,:..x3 n the universe.

The drawing at the start of this Chapter shows the street ab8b y8dt4b *hys seen by Mr Tompkins, for whom the speed of light y*h8bb 4tyb8dis $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at snk,te-kqh 8-1jc0 +o ni mn//xxly/rypeeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If not, explaih0+kjnlmxqn t8/ci ok-nry /1,/ye x-n. ----待选择----yesno 

  Can a particle of nonzero restk v+gxs4 8pb7d mass 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, does this mean that a sprinwe x yq;5eq2up*,-n3sktkvt v21bf.fg has more mass when compressed than whefvqt 5q, k2swu*1n b3eetk ; -vy.xf2pn relaxed? ----待选择----yesno 

It is not correct to say that p2 7l1prvq:ofl1o7 fb "matter can neither be created nor destroyed." What must we say instead?rpfp7 ovbq7ll2: 11fo

  Is our intuitive notion that velocities simply add, as we did in 88zbb8 c7 1d,twbh7xt tr kts;Section 3–8, completely w88 c tb1wdt 7sb7t rz;th8,xkbrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You mes nxa582ks,+s bl. h8l;acc iuasure its length to be 28.2 m. How long would it be when at resixk 8sah+ c;l.ba2cu, s5s l8nt? $L_0$ =    m

  A certain type of elementary particle travels eo eg.b p:.he4+gdsz *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 t n64 3mx7rgi32phkns xpty-c 8he 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) pe-+qmcf n0i star 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 lifgih9 ck(bz: ig*1en/ betime 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 isqhrsw:kf-z d,8+8 wje 82 light-years away. How fast would you have to travel so that to you the distance would be onrq+w 8 8hdwf :zejk-,sly 35 light-years? v =    c

  Suppose you decide to travel to a star 85 lightwu6 vq4c z0qj5-years away at a speed that tells you the distance is owq5zv6 uqj0c4 nly 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 the Earth isnho -xczyuhe l9i+-2rhj 5 ,9b $11.2 \times 10^3 \, \text{m/s}$. 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 from a 5i bn 4wz2dw.(driqvoc 0+;-9 3d rqohh-yeob drn.d4wh qrhq wio9+(3id2v-cz;0ar voyage while 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 would it take a space, o-moizkbusc9 o597fjfd-y:craft traveling 0.960c to reach that s-do7:b ou-9o y,cjf9 mks fzi5tar 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 y)b7 ur6nss)gpf ) 3hgg/r(wvm ou in her "Ferrari" spacecraft at a speed of 0.660c. It is mwvbr s)(g3gr u )s)h7nfgpm/6easured in 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 rhn5/lji8p mo ,ew6g vm/cw22moving to travel 15 m before it decays? The average lie6,wrm85w2 ociv /nmjgpl/h2 fetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protoljn;08/ m9c7s t6* olfz+0 pvvosppgin traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass bewmw2sf a9zv; ,t 6iufep2;bk: twice its rest mass? v =    c

  A particle of rest mas 5fwrj:bs 7.xbs $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at :3k , wggvz;nbgbqi;6 $v =0.10c$. 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 momentumgbmdhmy 49oqa*s(( :k of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction rewqs6 v);xaf -w1mi s5yquires $4.82 \times 10^4 \, \text{J}$ 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 known as j/ pbav u)(p;vfission in a nuclear reactor, the resul) pvpa/;(b jvuting 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 joules aniupg+kab m, 1.d 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 pu1qf*e;n foq 2inepb15tqi 70roton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States iau2o :5foozg(q) l-qry::wst s about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can b8d(ikobj.( ole obtained 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 its* i 3m/gaohlj-8d x,mm kinetic energy equals its rest energy? v*8jxa l o3/-gd,imhm m =    c

  At what speed will anaf (wymfm ,54f object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelecw5d8;9wt 3 uq jnd5rfrate a proton from rest up to a speed of 0.997c? 9rq8uf5dw5n3wdt; jc W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a pr8b,) cg nd9 os(qd sy.pnapi*)oton 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 (thatn7 m+ snwt(ohmv+gm2lbbj 4/(tw 4,q5t 7ksnm is, its kinetic energy is 750 MeV)? vmg omq +w(h2nkt7snn/m 47t+bb (,wts 5jm4l    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a h gwwln0n7d,e9+jprr5n0 5 yfpotential difference of 105 MV? v = 5j nhgy fp0n9dewnw50 ,+l7rr    c

  What is the speed of an electro .4e+qcmih9 iug0j xz5n whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron j0mz re*wp3l3wv nt o46z0ais g34skf)ust before it hits a television screen after being accelerated from rest b l34esrzm3p n 40) t*wvwk3oiz6af0sgy the 25,000 V of the picture tube? v =    c

Two identical particles of rest mjiwp76 po -z.fvbxzj6 a-.4 hrass $m_0$ 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 aiwl-wp es7a(rto -35 w 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 an 2,vvqvf5y,* 2m/md bt2v oh tyelectron ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 accelerater1jrwqtu6 2j0d to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energy and momentum of a protu2hes53 x b0iq-upsrt ya 91l0on ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleusg 7sma2n:f lh+, $^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

  An electron ($m_0 =9.11 \times 10^{-31} \, \text{kg}$) is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.60 \times 10^{-14} \, \text{J}$. Determine the electron's speed $v$. v =    c

Make a graph of the kinetic energy versus momentum for (a) a particle of nonz ustp (3o4yg+gzo0k;vero rest mass, and (b)4 ; uzg 3p(tgksy+ovo0 a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV pr*d5r gigs( 2zlybk;pv wk(,d8 otons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's r5zkvd g ;wks82yir gb(,( pld*est 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 r szf,gm:(mw 91h1mx kcespect to the Earth) observes a meteor come frmmx1mk :gf,hc 1(z9 swom behind 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 leavey+k;)1 ysc5y b(ja0kcq/dq ku Earth in opposite directions, each with a speed of 0.50c with respeqc)5cs jy;k q0/da1 (buykyk +ct to Earth.
(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 0.71col -*(cdhwoiib3s za):8t feo.m x2*w. A second spaceship leaves the first tsdo :23o oi.*b 8hz*i(caewlmw- f )xat a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speed of 0.60c. The Ente7h2ct7(l;hwf4ut be y2; cb(ul47tyfet h 7whrprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out twoy5w*0/ t+mlqqo 1 mg7st zu2wk escape pods in opposite directions. One travqqu+ 1tsm0wt2m 7ky/5wg *olz els at a speed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth at a speed of 0.75c. At the steat2kl:*eml u6++ e vame time, rocket B passes Earth moving ml+t 6eeavu+l2ke*t: 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Eacq9pn .a(x do6rth 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 tha*vk 0n/py /m.ypw8; wav 9 nrfc.fqos3n about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine thk.ypfp/;cvw o.0w v9 3q 8an/*rsnmyfe 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 spee 3eo*ns)b1h e8+qs7c x(jewr qd $v$ 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 touh,/m5j0r hhmt f; gcdk:ps6in2y :f *tally destroyed to run a 100-W lightbulb for 1 yeard0tf6c* ku:njh ,ry25m/ hmgfh; :sp i? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electron a8ohpz9 5nk q8nnd a positron together? A positron is a particle with the same rest mass as an electron, but has z npo8589n qkhthe 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 colc4w7c+xv) zi elides head on with a positive muon trex+ci c)wz47vaveling at 50% the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino. Ass(5.tw6wmhwvmx zrbc8 a ;66iu ume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the tot(xw6h; 6uzbirw av. 6tm58 mwcal kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates ener1ma .p;, mch:k 5mhaccu f27ojgy 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 negative charge ande7,qd1b u hiy. a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to break a helium nucleus into its constitxvtd1ko tvq,leq 66* +uents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is callxv +qt,klt* 6voed 1q6ed the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass oft)p md- o2v( . -yd/0cxcjgevs a car traveling 110 km/h as compared to at rest? [Hint: use the bino(smv/-e.0oxg y2 j cct-vdd p)mial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are mov-lm1es 6 2iesxdm0p -ying toward each other. De0-xmm -y6s ei1ldse2ptermine
(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 parti:yrc5v jiobaz.58 nv 2cle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by cvb2-b .( z/mb m)vnp97dbzsfzombining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is 7) bmdpz v9.vsbz-bfm/ n(2b zapproximately $5 \times 10^9 \, \text{kg}$, 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 accelera8f6ras m4a-hfted so that its kinetic energy is greater than its rest mass 6 hm4 s-aa8rff$m_0c^2$ 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 ctkk-r1h4h8/ljm x +zhan 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 running the barn loh-/+kk8 jh xlz14 mrhtoks 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 two moleb 8uv.9ng*mw7 dr v7jls of water, the energy released is 484 kJ. How much does the mass of the e*v8mg79vjulbnw.7 d rlements 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 twyq6+ 4de a9dezo identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative t 9q4+azddye6eo 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 Ear )t-t8xgq(8lerj. eez th measures his ship to be 25 m long. On the ship, he eat eqe.8lzr(tgx8 je)-t s 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 spac,8jn2saic:b* 7 aa qkheship 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 h a*nsbc2aqjk8i7 , :aobservers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,09e 8h,q 2jnbus25ijk0 x 7lbpg00 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 directly to energy. How much mass will be converted to energy j9k2h2,0 5 g j7bbsxepn8lui qto 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 al9 vnpq*q bezin84c/um79bt( speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S./q*cbe p9v unbtnimq4 7 l8z9( annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship +i l(,qt9pc2 6wtceakis to travel to the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. Howcw+l2ptak,i q (6ect9 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 ssx;+j*f 8kyq:gpg4o)bz n l4 kpring whose spring stiffness constant :k*j sky ;8glfbg) 4pqno4z+ xis $k=48.7 \, \text{N/m}$. 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 /)p)i,iw zha4 deul0h$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.