You are in a windowless car in frc,(qw.ngguum 860byu. nm ;an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train .nug8y(g, fwunmb0 u6.rc ;m qcar to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red lig4xn v js3p. 7pppwp/(dht when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rp/dn vj7.s(pw34 pppxolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy3 9: 5/jh(srv4q;dwhl 6 x wcwqtwxi5c ball straight up (from his point of view). wjqwq lc5vx4i( c:/9srhw htwx3d56; Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth reall9f 8y oivbzr.5y go around the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there isy. zb85ov9 irf no best reference frame). Explain.

If you were on a spaceshiamu,8l0h a sd*wm x.x*p traveling at 0.5c away from a star, at what speed would the starldmhx. al ,u*8x*sa m0wight pass you?

The time dilation effect is sometimes expressed as “movsk 54x+4:i9ray0bw7fs;- zli mkwupming clocks run slowly.” Actuyk+4b sw-:px kas 75w m4f9mli0 uzir;ally, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowlyh8h bh5xyrn(3.cn7wd0.q,iy vp t3 bl in moving reference.30l(.w 8 n b7q3dxtir cyvyn 5,phbhh frames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She rush svu.nnky 13ov-/:, lnf*v efwes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this b1,-*:v. fe k 3nnlonvsyvwu f/e possible?

If you were traveling away from Earth at speed 0.5c, would you notice a changt:2bw/p,lgbud)vih u9-zdk( e in your heartbeat? Would your mass, height, or waistline change? What would observers b/-l(tbd,khiw9v 2u uzp ): gdon Earth using telescopes say about you?

Do time dilation and length contraction occur a6vq+or//xp 4jtj kf 6fsy yv4-t ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen thwqp1vbhe9.5; b:gn6 bt+ei uo the relativistic predictions of length contraction and tim.pvbb5:hqige+ b1;uen t96 wh e dilation?

Discuss how our ever 2/zsstgbv bb.d1f(q8yday lives would be different if the speed of light were only bst.v q8ds/2g1bz(f b $25 \, \text{m/s}$.

Explain how the length contraction and time dilz/o+lgh zhq6(ation formulas might be used to indicate that c is the limiqz holhzg6( +/ting speed in the universe.

The drawing at the start of this Chapter shows the strdv/sszk+ri8g*zd.g n6o d+ y 0eet as seen by Mr Tompkins, for whom the sd g* gz8+y0dodvik+ zs6 sr./npeed 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 afknotmy7 02 4gk-ds4nyo r7. 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, expyt70 g4.as 7dnookfy4-nk2rm lain. ----待选择----yesno 

  Can a particle of nonzero rest maxazc, n9g(h 4xg55s cjss 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 spring has more mas4 cr m.rowe,z- 9bs;kvs when compressed than when r.wo-,czkbev9;4r s rmelaxed? ----待选择----yesno 

It is not correct to say that+96c2g.qml6 jts(jz lmba jj) "matter can neither be created nor destroyed." What must we saa(bl6tl)6+j.mj2j gc 9s jq mzy instead?

  Is our intuitive notion that velocid s9bn(t/w r5mties simply add, as we did in Section 3–8, completely wrmb(9dt rs /nw5ong? ----待选择----yesno 

  A spaceship passes you at a speed obgrusc5oufg,9 h k.1 ,0t:c;9dwst brf 0.750c. You measure its length to be 28.2 m. How long would it be when at res5kb,9tr; f ur190 hcwgt osgdsuc:,b .t? $L_0$ =    m

  A certain type of elementary pz t ;cli3sp8b)n x/h0uarticle 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 d*c vry7d,6cg f6:qjggepend 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 speed ofjbd4+0 yua/t2tj9s0 y 8y;rcd(m fxdj $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

  What is the speed of a pion if its average lifetime is measured mor.1zy8e9l wto 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 fram i2x*6bv u/gixfvyib;1; tcr :e, a star is 82 light-years away. How fast would you have to travel so 6i;t /uibcy1f* ix:2xv rg ;vbthat to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a s0bh.2/ b x0q oncnqfx7 0pc4nxtar 85 light-years away at a speed that tells you the distance is only 25 light-ycnf.qb/n20hnoqx00pb 74xxc ears. 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 ie5- 5m(tvraqi 5s e qkwu1hvq)q7 gv-hl1+ 6rEarth 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 x:mbe hmgx73n. ooi4/ just returned from a 5-year voyage while travelinbnxm3oh4:./x g7i moeg 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 awx+jj+ylt ,7ck*oy d t,ay. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured b,j c xt7lyk+j,y* t+doy 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. Ifo)1r:kw 3pg h)2yg gst is measuredgw3h1k)yo p)s:f2rgg 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 moving to travel 15 m beforemva dw6de9 m:* it decays? The average lifetime,m m:d69awve*d at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a5 urx jf sa :t4ii1l(k7mnrwnb(5+*j f proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be t,is ww+gv9 fm6)92l xm/tusgtwice its rest mass? v =    c

  A particle of rest m:5wi3fsftd.x +iqwflc e;1 )kass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels i 9.(qdr fo,oyat $v =0.10c$. 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 accelerates 8mq5fj-vr tsow )b1 hn3 (u0-kx qmrq4
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction req 8h2*fx-uobff-h xuqtb(;6 0u h;geh vuires $4.82 \times 10^4 \, \text{J}$ 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 m79er0 q/otuvthe process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How t/9u0em 7vrqo much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy 0(gika;dt y+q of an electron 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 protonn9jcyy usks0-j/i m 9) in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energ(ye9 rxy27m ej *6ivc yow2 bg f7qan/9+ac6rry consumption 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 77 yyz,ir2d oki+nyd5conversion 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 energy equals i v75( ihxttjs:ts rest energy? :7(jth5 tixsvv =    c

  At what speed will a,cc; 6t hw1ipvv 9jnl5n object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a kv,77 tdidv gj*c7 -uc0pn,atb s+:rbspeed of 0.997c? W = bt+ ,7bts ijkr: v0dda7 gu7vcnc-*,p   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 prot*-g.hmttr7x( xz,jy von 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 8od+xa57hvwhis, its kinetic energy is 750 MeV)? 7 hx8dw5oa+h v   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differencevaa/d:xpg s jyps /l20/v-v7 b of 105 MV? v =avvl /2j7:xp/sa /0psydb -vg    c

  What is the speed of an electt4 oq6w v+sd i7vg1o2zron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an e (+z2b,p n,wezrqp8p/ps k s0nlectron just before it hits a television screen after being accelerated from rest by the 25,000 V of the/, s+2pk snwqz0n zrp b,epp(8 picture tube? v =    c

Two identical particles o -f 4rbljulp4*f 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 protoeibm79hurf g 8 6gn)lf,m dyv8x5k:2 in ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electron9pibnl(jkjcw6 n, 4n8qu4e q3 ($m=9.11 \times 10^{-31} \, \text{kg}$) 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. hh3 7 )f+qiklx
(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 proton (jgcr 6r v cqm(,t7( 0fe;3zpga$m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleusqn( 0f34dhji :+e yss jkgsjd:: 8xg*(lrmr2s, $^{241}\text{Am}$, 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 nozq srt.e59iq6 nzero rest mass, and (b) a parteq qi95z .s6tricle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons rev)i4q0bg9 e.wm2 .ih1lis xuieolving in a circle of radius 1.0 km (at, say, the Feri. b hm2wsiqil9)g1u 0ixe. e4milab 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 0.5xsmv(luz*y e 95b mp3 bq y,;aj*sg((f d)kp6z0c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? 6jkdm()xl p,sq vg5z*zy(pf3e9mb(asy*u ; bu =    c

  Two spaceships leave Earth in opposite directions, each d4g7 /4aynwn,ql s;dgwith a speed of 0.50c with 7ndad4 g;s 4ngy ,wq/lrespect 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 0.71c. A second spaceship leaviap11jr9b3 kvlh12 ojes the first at a speed of 0.87c with respect to the first. Calculate the speed of thb9haojp3krl112j i v1 e 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 af -qjc 5 g8wusv5o8yr02tbo5zt a speed of 0.60c. The Enterprise comes to the rescue (Fig.wo5 80bygv2jfz8s-5urc5 qot 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 distr:te gy+b (xdy+ess sends out two escape pods in opposite directions. One travels at a sp t+xyd:ybeg+(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 of 0.75c. rfjjr 22 ealwks( 3c.7gi*u4 wAt the same time, rocket B passes Earth moving 0.95c relativ *uwka2wjf(4 j. igr 3lesr72ce to Earth 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 ligha*m1o wpx/y) z4- (fcszy.h btt-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, anytrsl7+g c jkux:;+kwn0e auh,uj,-a)lhing traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. D -):lu a ew+jku 0acrkj,l+sxn;h,ug7etermine 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 speedxyfwpw:c53y 3zy+ 5 vp $v$ 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 matterydx99 2 yuu.jd would have to be totally destroyed to run a 100-W lightbulb fo 9ud9jx udy.2yr 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of eadz 0(8mtjht0q 8n 9qelectromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same resthqda0 te0m9t8q (n zj8 mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

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

  A negative muon traveling at 33% the speed of light collides head on with a posie da2ufunbny (v 8znyirsq/6)s6v v3*+fp- z1tive muon traveling at 50% t3 / fn rn2v p sbeyyizuf s(zvn)+qdu*661v-a8he 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 neutrig 6 kq2z+*(jsb.icsz zno. Assume the neutrino's rest mass is zero, and the other masses can be found in the Tabl*s6. bsg2c jzzzq(+k ie inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy )mty:uk ; a+ y5hfkyc;l4vh -oat 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 charfj.)c(uljwa 9saw)lv(5o 1u t ge 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 to4u 2n /ahsaxr2 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, respectively, 1.00783 u, 1.00867 u, and 4.002 aau4n2hrx2s/ 60 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a g)c47vge;l hdokz1q 5 car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansion.])4ec; qh7gv15zd lkgo $\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in yyozz2;+sq.cf5pi )g0y (pe hthe laboratory, are moving toward each otoy5p2f.z;q( ypy e gh0zc s+i)her. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particlq8css- yj:2k/2hx) mxnano:be 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 matteph 9*8(ha8(p ocwrtxs hsg)9ur and antimatter, achieving complete conversio (arsshg(x) cuh *ph8o8w tp99n 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 kinetic energy is greater than its rest m 9yxhssfma 1q-g(n7/p gxs/hsm 71y-n (aqp 9fass $m_0c^2$ 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 qs+ y/5n q.myr* qpqo4 ,3rmwta 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carryyoysq/mqrmr * q+p3.t45q, wn ing 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 mole of oxygen rei4 8fglhc.l3k act to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease icfi4hk 3.l8g ln 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 cdp j 2d6dht;v3reated, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other partidjhpd3dt ;6 2vcle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Ea/2b ngdlb5/ vurth measures his ship to5ub/v2 glnb /d be 25 m long. 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 spaceship atto mv g2ydl b)gnp,/j j+8-b xwj-(p9i a speed of 0.85c away from Earth. You send a laser beam toward the Ep vn9wo-gxbjg/d-l+2 p b,j)y8(imjtarth traveling at velocity c relative to you. What 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. Thk ic/p0zz9 ho31xbzu3 u aye0+ogs0t(e occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the en t9zcx(0uu3 o/3oe1 sbig+0p a 0ykzhzgine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship oa+l9vr 8y(s pb14j msleft Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare ya( ps4+89r 1lvbmosjwith 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 thejrleug7.-t m6 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. How much work must be done on the spaceship to bring it to the speed ne mjutl 6eg-r7.cessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spf.xsl pmoaf3jn21e 6 /ring whose spring stiffness constant 1ja.ol23 sf6epnxfm/is $k=48.7 \, \text{N/m}$. 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 massj s*far(/7:d+bc clvm $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.