You are in a windowless ca: wi t4b1bqojj3q0 ea(r in an exceptionally smooth train moving at constant velocity. Is there any physical eqtj wo4:0bqai1(e jb3 xperiment 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 g9gmxq:f/;k sof 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 about absolut ;q9/gx:kfs mge and relative motion?

A worker stands on top ofww/7 s/9insu q-rwnp9 a moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, wilsnq wrw7/ wsu9npi/-9 l the ball land on the car or behind it?

Does the Earth really gotiu6hl;3j6a+ hr w0ee around the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in vi w u63h+rijaeleth0;6 ew of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spac*kf8b22-d x,rv ,ovbifnko,x eship traveling at 0.5c away from a star, at what speed would the d22f-i,fno*,v ,rk8 k ovxxbb starlight pass you?

The time dilation effect is sometime*hic(w bssc 9;ox/ :j 0crqc,rs expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functi*hcxisc9wcc(0js: o/ r;bq r, oning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving re:(33my kqvs j2cf 3 tioyzc3u4ferencicc vy2juk (fq ysm: zt34o333e frames or that it only seems to pass more slowly?

A young-looking woman astrij,s /kz6gns ;onaut 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 son. How might this js n /z6,;kgsibe possible?

If you were travelin13v0fd ;wfvp6a5c nulg away from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observernawdvfl6;v cu013pf 5 s on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary aog8-yp+nf/3i ;lwg 3 yh*hp aspeeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. Whatsp:+ghh -p2yo would happen to the relativistic predictions of length contrg:2 p+s-pohy haction and time dilation?

Discuss how our everyday lives wouljfg8;;2 3 ,lgvw r9qwf/1aslm i kscozj;2lf/d be different if the speed of light were only;3o v1c i,j mal9wf ;lg/rzl fs8qk;f2jw gs2/ $25 \, \text{m/s}$.

Explain how the length contraction -unvihn3wybs e/1 /k-and time dilation formulas might be used to indic ev -nhiuw-yn1/ bk/s3ate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows theucm . (bvzxefs- 1a6d ou ,2ooow++g,t street as seen by Mr Tompkins, for whom the speed of light2(zw doo +6+ cxsefvau-tobm,.1, ug o 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 this put an 36t *ld jtinl1upper limit on the momentum of an electron? If so, what itlj tld*6 3ni1s this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed op(l2udl1:xr cwgy5e, f 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 po-q ik 2pif .g)7;sscmean that a spring has more mass when compressed than is7cs2kqi o -;p)gp. fwhen relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be crefbc+hd t-6rn- e* )sjtated nor destroyed." What must we say if* j) rh-e+ntsc-tdb6nstead?

  Is our intuitive notion that i 8 9tgx nk86hjkn )bybu7 orw+46ruh7velocities simply add, as we did in Section 3–8, completely wrong)r8tr4+o8nbknh u k ju9b76 x6iy g7wh? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. glhxq0 b;)v lua-lp(7 You measure its length to be 28.2 m. h;l 7 p ug)xal(vlbq0-How long would it be when at rest? $L_0$ =    m

  A certain type of elementary pa u -cyti.7tgaz w3pni96rl*0n rticle 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 interv *ifrh )0n/uqy;vx7mvals depend 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 at a s b(ri- 8td /i:lki+l.k ttvf)wpeed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of al9-trlme zh56 pion if its average lifetime 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 framemp 4k e,l2;mhe, a star is 82 light-years away. How fast would you have to travel so that to you t2e l4;m ,mepkhhe distance would be only 35 light-years? v =    c

  Suppose you decide toxcut08 i5s 7os travel to a star 85 light-years away at a speed that tells you the distance is only 25us50t7 ix o8sc 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 rsz4z /evp,0z 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 from, 5)cjd ul3b 5tjr31s qni7t:mkdtaler+k 3;y a 5-year voyage while trav,+) tdaus r1t3 b5jny tq;d33m:kkcl rljie75eling 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 me,h(d1qk3dan1 wkl4 z2 iq +nspacecraft traveling 0.960c to reach that star from Earth, as measured by obs aq kln(14 ,n2kwdzmi13 +dheqervers:
(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 ql2 b xb-fh51mof 0.660c. It is measured in you2m1b qflhb- 5xr 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?asojxw2j8c,z. bhyh g)*w,t 1 The average lifetime, at rest, i8wc*.,2ahtxhj gy1o ) b,jzsws $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling *7lru2: h puxqp9 ovjbz0;b+h at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice pkcla/q )y 7:kkv8 ji0its rest mass? v =    c

  A particle of rest m 7k ca2ysizm/)hn rv3/qr u(48qw*bctass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels .kje gy;x3u +.nd:eb gat $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in momentum of a proton that accemo vh5e;s d8t-lerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction r/:nb1lg l -lubk3u8xrequires $4.82 \times 10^4 \, \text{J}$ 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 / vfw1x97 cksalpf1 8kq)j)a0jk w;g8xnpf6dbreaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV./as97kaj8lx wfqk)j fv1dwc g 0kfnp;p618)x How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in jouggf*0x9 t:m zoles 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 protib n7wimdr: g-lo,gx *lez /3*on in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Unitee xomi( 3pqu7.r90gqcd 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 hjdym-.8ciq 8l.1r8my :bbyns kn4,j 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 dor4:iajzsnf 0gehy 7 / z-7v4its kinetic energy equals its rest energy? v = zjs ivnfro hg ez/da4y7-0:4 7   c

  At what speed will an object's kinetic energy be 25% of ith a4 w1xao5-vw(.jel ts rest energy? v =    c

  (a) How much work is required to acceler d/ dv/t2ro 5is:v)atwate a proton from rest up to a speed of 0.997c? W = st:vr5t) oidw//2 va d   GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic en vnt3m 5q l4d id -/i fr,mnr1d:sv/fbuhao)42ergy and 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 proton (that is, its kinetic energy is 750 Mez,*a5g3 yd b4 qvkn3 a8yzm/arV)?n5d 8 a,g*bkvq4/ma3zzy ayr3    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated /sn n.bf9 7vpwby a potential difference of 105 MV? v 97 v/n.bwpnf s=    c

  What is the speed of an electron whose kinetic energy is 1 p mt;trmwzcdaq,8j yf+*f3, ).00 MeV? v =    c

  What is the speed of an electron just before it hits4 6uo2ke, sse szad+/4zw7lxr a television screen after being accelerated from rest by the 25,000 V of the pictw6zk2r7/,4 a s sex+ esud4olzure tube? v =    c

Two identical particle se7dqr1)of if;-g2/n niv:ics of rest 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 /dv e73r);e.qamu 7 eii zl+kqproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electr/*e2d8*h,,epu amsx pg givc:on ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 mztq7c xan,1co0,qv bl12f 9m 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 protonpo cf8; ,zlj0e ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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,nstz8a7iq q-4 $^{241}\text{Am}$, 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 partiqq i 6 ztev:/f1rptq:/cle of nonzero rest mass, and (b) a pa/rtt :i/:6qz fp1qveqrticle with zero rest mass.

  What magnetic field intensity nvud 7ew65js9is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotdensj 7 59w6uvron)? 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 respsoea e69 r;:rp e):ndaect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respectde ) a:n6re; 9osaper: to the Earth? u =    c

  Two spaceships leave Earth in opposp,0 hwz8fyf7cite directions, each with a speed of 0.50c with respect to Earth. ch,yw7 fpz f80
(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 mhebp+u 6j35tl4 o)t0sjwf r*leaves the first at a speed of 0.87c with respect to the first. Calcul *+r ehtu 046sjf5pt )wob3lmjate 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 de:w-bgg*-a3g8e)0bfvj pu n . The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth atp evb)8nabe-0 gd :*g-fj3wu g 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 two escape pods in oppositekss1 cm9j*03jr-xe8pwk)* fvd bzl0,i bop 2k directions. One travels at a ew0kboxdibj)- p9cjp 1s8s0kkvmlf3z *2,*r 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 passwo fd584rqkma -r5r 9les Earth moving 0.95c relative to Earthr4r5 aq5-kdm9r o wf8l in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 lir/a klr;xift) *o:x+;,qvdxdd s l.s, 84qibught-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 aoe (q iek ys/ggeo3-8:bout 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydroo:-eeg ksg83o/ qi( yegen 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 7j /c7)bzy u2 s4qbthl;nmau)$v$ 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 n7sng v a0*) eys5ai h+twqcs+e(d, +h100-W lightbulb for hv snt*n7g w(5+d i+ye,ea+s0shac q )1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an eoftx jbjm 351voy ua0eo+ *i(9lectron and a positron together? m fv aoe1j9ob+tx*(0yj3 5uoiA positron 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 33zlp: u k,o6dueae s31v8lup2j1 frj;7% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The,paj :l21 esuv 18lro;763 u kuzfepdj 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.ay85c;i,ooe p Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover,cy;i po 58aoe. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates enery.9i nxc ,ac1+:ptf9qo 8p ay*bagv/2ei-ff sgy 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 ne: jo-mk1 z1:dc* mp *hvadbvf4gative 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 requp 8 sgcx83hj,nired 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 helium are, res8g3cx8 jp nsh,pectively, 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 +lfk3cei3um-ck: 8 mka car traveling 110 km/h as compared to at rest? [H 3ui8ckkle 3:-+ckmfmint: 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, are moving towar:y i8ku 4 50zvwkbc3bnd each other. Determine uk z8wk0 v534bybc:ni
(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 partic/w+v7:bd/gaaj jnlz3 le with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise o( -,i.jq omnqs lb/qf wn 1f*e1bbno::btains its power by combining matter and antimatter, achieving csbm11n q:f.oo-bl(iqj q/w bfn:en,*omplete conversion of 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 kin rf-z75b iy2d8chfgir 0x +p2-rxd5ztetic energy is greater than its rest may-27-ph zdf ctxi2f g 5irrd05x8r+z bss $m_0c^2$ 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 15.0xldbfd-e /y54m k .so-l 11+f lvds0wf-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in ws-dfm5fx+ l 10dds4vok.-fe /1blyldetail. 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 and6;dm+ e jxg4bwc)/ik.mwcg u+ one mole of oxygen react to form two moles of water, the energy releasej +uci 4e/;wdg.+bmmgx kw)c6 d 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 opposi ehx *9xd;w1tz;l ck8zte directions. If the speed of each particle is 0.75c, relative to the laboratory frame of rex x 1;8;hzkdle ztcw9*ference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at eqoap 2d8/d:*g4rd7,uly+sjg8t zo r0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in :lqr,p8 dr/ju+o7o g t4ysad 2edgz*8 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 frodyb w q5kbpnianfrx6hft-, z) (g 5f(,s8-w )tm Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers os -pni f8, 5hz(g)yrbw ,fat q)(xn tfkd-bw56n the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have9ipwt1uh kh,y 7hfbq1) s*k y( a 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 directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speedf ,w yksu *k1hq)97hybhtpi(1?    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 zes zjb y57h2,at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual ene, bzj2 7hzeys5rgy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to tray)x ):l.adxc 8whk5m rvel to the vicinity of a star 6.0 light-years from Earth. Passengers on the shl). yx) madwkx85 hcr:ip 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 ssi7 g ng t47+rmo::mrwhose spring stiffness constant is7:g47+ mitgo:mssr rn $k=48.7 \, \text{N/m}$. 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 mac0rh6/odx61dhl9 sfxss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.