You are in a windowless car in*q v91qfi lyi/ an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to det/iqf1 9y*ilvqermine whether you are moving? Explain. ----待选择----yesno 

You might have had t8mu. lam/2ybqr-v w:t he experience of being at a red light 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 roll-r/b8w lt 2q. vmymu:aing backward. What does this say about absolute and relative motion?

A worker stands on top of a movin-bqdq+1.vm q xg railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistanceq-d.m1xq qvb+, will the ball land on the car or behind it?

Does the Earth really go around th1gwfqnl5la)s; v. 7rhe Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss inn )lrf.;va5lw 1q7h sg view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a st aa3z8 yhs 2f/lo9f5uqhf6o1s.nm :rjar, at what speed woulu/ 1m r8la:q3.6hofhsaynzos j f59 2fd the starlight pass you?

The time dilation effect 3)(n (zeuzs s5gqhzcpwm7.ja : /e 1hsis sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functionin/q 7pn(3z1e.asgj)5zesz hhum: cw ( sg of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moviny9g .t q28bel-;qizm tg reference frames or g; ze2q ytl9m-tbqi .8that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from c z9b3z;5rivp.ao6o c a long trip. She rushes up to an old gray-ha5;3a .6ocprcbvz i9oz ired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a change ik j(( nk0 3 jv44mo6ctdy2szrqdx8-uwn your heartbeat? Would your mass, height, or waistline change? tn8j wox2m4vc6-k3urks(qd4z(dj0 yWhat would observers on Earth using telescopes say about you?

Do time dilation and length contraction occg jk*nax-. sst)v 8d.v:f xj w1(hixa+ur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light wegl/ cj:x,8m w 2jd4hpvre infinite. What would happen to the relativistic ch 4lx8:2,/wmpjjvgd predictions of length contraction and time dilation?

Discuss how our everyday lives would be differ7eoj*n (yzzzod* kl / zw-.yuz/q8fl1rbq*1l ent if the speed of light were only efyzwozdz*jozqql-l r b/l1y*/n7.8ku* (z1$25 \, \text{m/s}$.

Explain how the length contractiondvonly ) kx*cpr +sj,a:6 6r+q and time dilation formulas might be used to indicate that c is the limiting speed in the a o )v x:d+r*kc6q6rjnl ,p+syuniverse.

The drawing at the start of this Chapter shows the street as seengkj+a*ym0ysm6 zx big vf *b)vr139v 6 by Mr Tompkins ba vi 1z*)6g6fgs3 yv0ym*jr mbvk+9x, for whom 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 limitexowa ,)jr:31p6xcj w7ymo gtku53 cd,d to travel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, whato gj:drc 3 ),kpx3ju w,1wy6x cmota75 is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attaijygj(x0y i2; :d nu4arn 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 t4 b3z*mzrgnf;0bb3c; a :hu ojhat a spring has more mass when compr4z0; cnmf * bjb3;og :b3uazhressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroy*pp)r)j c,q u( dz+ux ybu4xn:ed." What must we say insteadpjpx)c+bru:,y qu*) zx(n du4 ?

  Is our intuitive notion that velocities simply add, a 9t/ vjf0ynm:qs we did in Section 3–8, completely wrong09tf vym qj/n:? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.9ie/ bpp,* qkd2 m. How long dp k,ibepq9*/ would it be when at rest? $L_0$ =    m

  A certain type of elementary a a*i zq n.,:rdq3b4gbparticle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals depend on the fam vyvn0 21op *fc+;ak cjm6n0sctor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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.;inrox qs 9w q 7of(nsdz*6l; 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 lifetime is;er7d6-tteq h 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 lightiszlie5cz9 lcp 0x 0/6-years away. How fast would you have to trave65splcxi c0el/ i9z z0l so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years awahkth2s6 8(xujgaoo:5y at a speed that tells you ta6 stu h( oh5og2:8xjkhe distance is only 25 light-years. How many years would it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the Ep dg mq4exvjc .r0+.a*+bau ; qsowu/ ;sgk19yarth 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 slc fazj02d42i tarship Enterprise had just returned from a 5-year voya4dj22ciflz 0 age 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 w1c+mkdvdp ijn(r;w15ould it take a spacecraft traveling 0.960c to reach that star frwm(1+nr icd1;p5vk jdom 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 "Ferrarij;wtv 7 p7p.r0xkjn:t" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.rv;w 7 pkxjt7tp: j0n.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to travel 15 m before it decays? The npw )e2 0d7bktv 6gnk.average lifetime,tpd g6 2 kkb.7nv)ne0w at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelphz/c2w+u dfn )5zp tsp,, q;hing at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass? v s ;s1s7d.1pzl uy2 tnj=    c

  A particle of rest ma/bl4n;1pop m hswntb 2pvilp,y;v.f m23r w, :ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels atl1.:;esjv e zq $v =0.10c$. 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 protonzy3gxi3hxqf w :242k k/q.yrt that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactiolh; :i)t8st jh7s.thbukr5 j3n requires $4.82 \times 10^4 \, \text{J}$ 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 i9y*9 dkztxx3z/g5aitn the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy oz x*i5/aztdx3 ykg99 tf 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 ineek 56l f;d3 cx,:rdzy 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 protow,70* f hkkxern in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual enerq)9g (- djmp1x /+d,2qttnb ilknxb u4gy 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 v;i7thqt5 dl 2conversion 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 p fxle3wp68mewh k)7h e65v, jsarticle when its kinetic energy equals its rest energy? v = m8e 5vl s )6fk3 xpejhe7wh6w,   c

  At what speed will an object's kinetic energy be 25% of its i;i7tylvakz h*5- j8h-,h hwc rest energy? v =    c

  (a) How much work is required to aamf 262b/py3/n ijl dmzg8l; h;kaf1pccelerate a proton from rest up to a speed of h mpfa 6kg /j8fnza2i23mllb/1y d;;p0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic enerny,j i r2vq p;d1ygsog..4x;ygy 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-Meid yhg7t2p; a2 7nom5xV proton (that is, its kinetic energy is 750 MeV)itp7a;2d25 hn x mo7gy?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differemn /yyipj.80 bnce of 105 MV? v . imbyj0 /py8n=    c

  What is the speed of an electron whose kinetic energy isr +dvbp+4e 3jo 1.00 MeV? v =    c

  What is the speed of an electron ju;gznba kh5 y88st before it hits a television screen after bein8gan8yzhb 5 k;g accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles ofm *,t:(lp i)98hjmf/vv shah 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 pr 2dh. 6b3 ekg chkc6hnzs;(a:loton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momq8vr+-.7 n/ rcou f:ahh,ij shentum of an electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft/o1nej 52 ok;+s wqstc of mass 27,000 kg is accelerated 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 momeq g7nn3 8ps0h)t zxq6r*rrmde35luu 8ntum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleu8uvf*v w-g5h-w: jxu hs, $^{241}\text{Am}$, 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 moment8pg+ hm y-d zhu.3ha:num for (a) a particle of nonzero rest mass, and (b) -yhp :n+h38g umzd ah.a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revo a;r qj(d7j1 +tozgh4z6i-kpulving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the 1(tozd;kg 467j+-aiu hjqpzr 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 t. l/.t)i ,tus-llz ,zo2pqlibraveling at 0.50c (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? u = il/squ z)lt-l.p2,oi bl.z ,t   c

  Two spaceships leave Earth in opposite directions, each with a speesp)87p9f (fponm8p cu d of 0.50c with respect npffs( o mppp c889)u7to 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 travelid9(e-qjus(kr ng at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship withksdj9 ru( e-(q 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 anj3 n.58aih6upnijbu 0 alien vessel 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 0.90c relative to Ea83ji 0aninj h6u. 5buprth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends ou/3sjdg7vx 7w pt two escape pods in opposite directions. One travels at a 7g/w3js pxvd7 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 satbvvk / ,e0yg4rr,hkz.5 vxbsx:x-7c me time, rocket B passes Earth moving 0.95c relativ7,h5 rcbxt- ,z v: y0s.gve/k4bxrkvx e 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 light-y8e+ talwa9:wj)y40 f ,gamxgdears 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 travelipd-ci+56m fx jo,q, gvng faster than about 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 ,p+ -ojc6d,mg5i qfxvhydrogen 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 n fxyx+5k l4fby.c+ :qo5tgw5$v$ 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 destrd+.8,pt 4r(b4s6pt )3k zfzt dznb oqyoyed to run a 100-W lightbulb for 1 year?zdt n4.z bo8sq4r6pfp(,btd+ )z3t yk $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount owey hbq/o),j:f electromagnetic energy 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 th/ j)e yoqbw:h,at 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% th,l,)ef fi yq1efz:1rm e speed of light collides head on with a positive muon trave lf,fm1yi,:f)e rz1eqling 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. Assume vsbu5skc.1ng ,f7 )zpthe 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 shang)v1k.su5 c7 z,pfbsred among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rvlza pg a+m:es/: f :33x.icpjate 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 meas gqpmaes 7u a0g+h1w-:ured to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be requ aiu7ao 40a* ffn)f5(i8jp*dvi ia1znired 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, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy differ5nfzj(ifo 4u *)n a i0aaav1*8piid7fence is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage incrrz n8lxi s6v-yx;x)tml0ui* a5n (2nmease in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: 2xi*)l (0yn x5l ut6rvs ;iamn-n x8zmuse 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 labo16-6u;yoc piljz 8rb bratory, are moving toward each other. Det-bru6 zl;bi6c8ojp y1ermine
(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:sk5x u gn8h*l a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains i ojd(pbj+w /18xo2ed5fftu+uts power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enf bd/1 px+tjouf5jewdu(+82 oterprise 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 re nxp n*;0cl4 gj )ryiuof6: hmg:r0a3ist mass 0aj 6:ypuix l*oghr: c0m;)n 3fr4ign$m_0c^2$ 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 15.0-m-lvevqar 0m5 *0gn+ fjx)ong 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 this0+*vqm0j g)vafe5r nx 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 react to form tw b*g*ky pbklyhk1;1iwu4 .(huo moles of water, the energh y* ukk .1 bub1*wl(hyigk;p4y 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 parti2tewu g9c7 us.cles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative tosew2 u79 tu.cg 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 hl nkn4oxx*-80.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch ohxn*84xn lk- in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a s ;f .cuamgs;.7+zre8 yyq ue*vpeed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do oaez*8.+eu yug m s7c .qvryf;;bservers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass o wy+yca7/7aueg; t(sj f 150,000 kg. The occupants would like to travel to a ys/7 + ;g(wtejuyaac7star 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 speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What is the sy809t6yflg bspaceship's kinetic energy? Compare with the total U.S. annual energy consumption9lyf0gs6t b 8y (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is t6o4-wj p cro2no travel to the vicinity of a star 6.0 light-years from Eart r-w2nojpc4o6 h. 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 necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffnes -e.eeyh fox8:a./u czs constantu.f-y.zheec xae /o: 8 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 m)+ wwm z9kfsa:r -1rrq5ocw l0 haht8(ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.