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习题练习:The Special Theory of Relativity



 作者: 王信东Wood发布日期: 2025-07-15 10:29   总分: 94分  得分: _____________

答题人: 匿名未登录  开始时间: 07月15日 10:29  切换到: 整卷模式

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1#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  You are in a windowless car in an exceptionally smooth train moving at cow+0z+40b1 z davlsi 1exd d2xenstant velocity. Is there any physical experiment you can do in the train car to determii1z21xs +4b+av0ddxd wze 0le ne whether you are moving? Explain. 

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2#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
You might have had the experience of being at a red light when, out of the cornewhrgg 8,qvt+ :7yoaj2 g :qt3rr 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 s2wo38 hg7gyrjgtrvt q,qa ::+ay about absolute and relative motion?
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3#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A worker stands on top of a moving railroad car, a ua ;4rr6xxqfdg 8:8i .ctc8bgnd throws a heavy ball straight up (from his poif.c8 c grdxt r:a8bx g46q;ui8nt of view). Ignoring air resistance, will the ball land on the car or behind it?
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4#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Does the Earth really go around the Sun? Or is it also valid b;tie(e * lfwb epchwvp 30/7hoxs(/6to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Exhbe7 sbpf/ (6p;( 3xeol/0htw*ivw ecplain.
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5#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If you were on a spaceshi6 u*s bhhec 2uetv+e79p traveling at 0.5c away from a star, at what speed would the starlight pass you?*6eusc 2h9t vb hu7+ee
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6#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The time dilation effect + 8dqd.l yf7(ybnbie/is sometimes expressed as “moving clocks run slowly.” Actually, bd7q(+dy/.by i ne8flthis effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?
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7#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Does time dilation mean that time actually passes mo,o*cghkp: .nj re slowly in moving reference frames or that it only seems to pahno g pk,*jc.:ss more slowly?
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8#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A young-looking woman astronaut has just arrived home from a long trip. She crcjn0p3cuf,lb3n 5k 96x )skrushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How mir 5 pk 3klcn bxcfns3,c)0ju69ght this be possible?
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9#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If you were traveling away from Earth at speed dr1*yutht (z; 0.5c, would you notice a change in yo ( ;dzyhr1*uttur heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?
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10#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Do time dilation and length contraction occur at ordinary s)(x ma+tymth7,xt 2u:(8evk nndlcw. peeds, say $90 \, \text{km/h}$?
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Suppose the speed of light were infinite. What would happen t ej 837p +i+rp2fnqof( jrz8akenjv-+o the relativistic predictions of length contraction and time dilatpqoafv8(z+2j jri+r+j -fkpe8n3ne 7 ion?
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12#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Discuss how our everyday lives would be different if the speed y hld5pe7;j, 9nsi 0eaof light were onl9 l;n5ih yae0s, edp7jy $25 \, \text{m/s}$.
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13#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Explain how the length cg tbmrq57*4vcontraction and time dilation formulas might be used to indicate that c is the limitirvt * cqg7b4m5ng speed in the universe.
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14#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The drawing at the start of this Chapter shows the street as s:bk r9 wcsnh)kk66 7efeen by Mr Tompkins, for whsc: 66 k9w)kbefnh kr7om the speed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.
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15#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An electron is limited to travel at speeds less than c. r4*nlilcwfc,, x. +no Does this put an upper limit on the momenxcf4ol +ilw,, *.ncnrtum of an electron? If so, what is this upper limit? If not, explain. 

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16#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Can a particle of nonzero rest mass attav +)vn .o,woejin the speed of light? 

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17#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. 

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18#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If mass is a form of energy, does this mean that a spring has more mass whee2nu oibh: 6ig2ni) h8n compressed than wheg2bo2 hn8nuh:ii 6)ien relaxed? 

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19#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
It is not correct to say that "matter can neither be c e9mngtrmdel6s26l+; reated nor destroyed." What must we say instead?2 lr;+ne6 dl9gtem6sm
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20#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Is our intuitive notion that velocities simply add, as we did6bfji.+9k24 eucttf s in Section 3–8, co4kb6 i.t cu sftef92+jmpletely wrong? 

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21#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spaceship passes you at a speed of 0.750c. You meaq a n*)xdn9)t;lnx;pj k+st8q0 ebs / hjvk1(zsure its length to be 28.2 m. n+ejzsa/kt80nsn k hq) jb)(9v1l;x;pq t*dxHow long would it be when at rest? $L_0$ =    m

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22#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A certain type of elementary particle travels at a speed o p4jxgum*x 2o(f $2.70 \times 10^8 \, \text{m/s}$. 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}$

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23#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Lengths and time intervals depend on the fac2t1scrvuln 64f /0fpp2*bhcq tor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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) $v=0.999c \;\; \beta =$  

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24#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If you were to travel to a star 125 light-yearosk1gr0 h g,; uw46rxbs from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

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25#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the speed of a pion gcj1*33sy rc1g( vwcg 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

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26#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  In an Earth reference frame, a star is 82 lightj 9 we8 eq (*.1tl/qh:gn7w.cvdqouct -years away. How fast would you have to travel so that to you the distance would be only 35 light-years7. gdhwq1wnvo*cl e je(:9 qc/.uqt8t? v =    c

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27#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose you decide to travy6v-a,a .c0gm7fptsu(aed y4 el to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make 7py-y.d 6,aat s0f4ueag(mvcthe trip? t =    y

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28#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

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29#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Escape velocity from the Eart q0iym*8,wx2g(lw j 46 b5cfl;ffrcblh 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}\%$

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30#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  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

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31#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a news report stated that starship Enterprise had just returned fro:a1 enj yz6jfo3r1+*dnd9 ekem a 5-year voyage while *3e1:a16ejdnof jd+nkr9 z e ytraveling 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

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32#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A certain star is 10.6 light-yearslh 5oph ss-r.: away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observers: hlr-hp:s.s5o
(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

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33#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A friend speeds by you in her "Ferrari" space tjf3b4o yeq2)wfg tes(8e +)jcraft at a speed of 0.660c. It is measured in your frame to be 4.80 m ej +ef(y2jg83q )s wbe4ftt)olong 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

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34#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How fast must an average pion be movj5mw* :eo (;ty ugvs4ving to travel 15 m before it decays? The average lifetime, at s(yg;w vo 5*vet jum4:rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

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35#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the momentum of a proton traveling at;d eiz*aw6h4 m $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

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36#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At what speed will an object’s relativistic mass be twice its re,)evo4sf i(ucl z(u13z* b xtsst mass? v =    c

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37#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A particle of rest mass5as9 tt-xp/ cm $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

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38#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) A particle travels apw1 g uiskc22gk64v5yt $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

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39#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the percent change in mo+djj2f)i uf.fke .3o mmentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

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40#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A certain chemical reagc;dux4a(so5scv r 4ybq2dh++go- n4 ction 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}$

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41#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When a uranium nucleus at rest qd;) -xk oz.og0x:niq breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of ax oqn z0o-;ixgdqk .:)bout 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

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42#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the rest e 7oc+ 1m;rh9ulyqhl09 s(voycnergy 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}$

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43#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the rest mass of a proton)rhwww 0b7h7sw *fb t; in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

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44#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The total annual energy consumption in i 1 f2weit +q(e4cri(zss w41nthe United States is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

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45#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How much energy can be obtained from conversion of 1.0 gram of mf2hh2p 3+ ro0i:q nziyass?    $ \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}$

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46#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the speed of a particj*-k7ynn z3kw le when its kinetic energy equals its rest energy? vw-*nk j7kyn 3z =    c

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47#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At what speed will an w6hf/ *j vt:g8adcjw,jkytk+9.bx * aobject's kinetic energy be 25% of its rest energy? v =    c

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48#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) How much work is required to accelerate a proton from rest up to a speed +zf/x 2ddjxc 7 9y p9k)cb7, iem7cidqof 0.9cp7 z+xk xd7qj9i ,/midcfcedyb 97)297c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

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49#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the kinetic ener f15qh3a rtb /*si-auigy 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}$

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50#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the momentum of a 750-MeV proton sg ypi)c)mt856b wfh7(that is, its kinetic energy is 750 MeV)c5y s6 ptmi7))h 8fwbg?    $\times 10^{-19} \, \text{kg·m/s}$

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51#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the speed of a proton accelerated by a potential difference of 1hrlij/y4*( b3n.0gki xnsb8gxk u.;m05 MV? v i.b (sb klg8.yni*xn h jx;0/g mu34kr=    c

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52#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the speed of a9-b ge5kjur p x1yx.m3n electron whose kinetic energy is 1.00 MeV? v =    c

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53#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the speed of 9gwk etpd++ r11 */ua/ iacptian electron just before it hits a television screen after being accelerated from rest by the 25,000 V ofpi*+k1u 9iwtta a/pgc/+1 der the picture tube? v =    c

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54#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Two identical particles of rest mass wz1;x4 9 p j,h,nk+mimv9zjhlxu i3/c$m_0$ 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?
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55#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the speed of a p u nx1cwa 3xf5mxileq4jk;:3- roton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

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56#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the speed and the momentumlc j(mnxp w:/. 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}$

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57#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a spacecraft of mass 27,000 kg is accelerated to 0.21c.+ czj5ls -d t90viqna,
(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?    %

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58#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the kineticx(f6ad l n9gj7 energy and momentum 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    %

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59#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The americium nucleus,w2uryl5d*o6y6cg1 h z $^{241}\text{Am}$, 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

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60#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  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

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61#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Make a graph of the kinetic energy versus momentum for (a) a particle of noyzpy8.4i5i0 y:cttum3r6ffunzero rest mass, u3 uypr y t4680zti:m5 yffc.iand (b) a particle with zero rest mass.
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62#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What magnetic field intensity is needed to keep 998-GeV prh xigy,7q qa9s.m4o2 eotons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use th xqi2.qe7go9 ms,ay4he 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

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63#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A person on a rocket traveling at 0.50c (with respect to the Earthja (.suq* lpd+4c.e z.8s grmu) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How f*ld. (4+ ausjse8c . umrpqzg.ast is the meteor moving with respect to the Earth? u =    c

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64#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two spaceships leave Earth in opposite directib2 6rg.j wnkzu-ryi:wa q(0r8 ons, each with a speed of 0.50c with respect 26. zjbyu-g(k rnww: 0aqr8ri 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

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65#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spaceship leaves Earth traveling at 0.71c. 28n 5nf pop5fgl+vdn6 A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if infp5n+gl5o826dfnv p t is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

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66#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An observer on Earth sees an alie: .1om*+tpa,d:lvk1nphs z1iq4pgt on 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 Earth. What is the relative speed of one vesspo 1ktsmv t+lih n.ao1q,g1pz:*4:dpel as seen by the other? u =    c


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67#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spaceship in distress sen;q 7e5t9 d6v lix prg,*n y:3ncyj6ksk ry4bv,ds out two escape pods in opposite directions. One travelj64i 9, 5ykne x;3,6t*kylg 7vbq: dcrvpn syrs 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

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68#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Rocket A passes Earth at a speed of 0.75c. At the same time,y:qb q; cvh1-libas,sx: 2v(v rocket B passes Earth moving 0.95c relative to Earth v(issq:vb avx lyq2c,h- b1; :in the same direction. How fast is B moving relative to A when it passes A? u' =    c

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69#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The nearest star to Earth is Pro5m k4sr+pvr hgn sc)-*vuyv43xima 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

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70#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  As a rule of thumb, anything tr/: g-ogtmcl fg( x:,utaveling faster than about 0.1c is called relativistilfg:g(: uttc/ x go,-mc - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) 

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71#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) What is the speewx9/*6 yhixa td $v$ 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

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72#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How many grams of matter would have to be t9sj3e8vgw8 c yp li(xlu5/w a-otally destroyed to run a 100-W lightbulb fora5 es/ 8(lxw-3gw 9ji 8upycvl 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

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73#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What minimum amount of electromagnejd- mp ;pit;(bke:,(zs qe:ks tic 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 j;;(,p kdsse q:kbpt ei:m-(zthe opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

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74#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  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

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75#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A negative muon traveling at 33% the speed of light collides he l zswc hlwohg8g014e/:4 l.msad on with a positive muon traveling at 50% the speed h/4e lzlw.80lo mg4:g h1cwssof 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

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76#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A free neutron can decay into a proton,1u:,zfzf/k2gk mlu3 s an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron deca,u fzufmk/ :13lk szg2ys at rest. KE =    MeV

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77#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The Sun radiates energy at a rez,76vi jgk n sk:6h;date 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}$

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78#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An unknown particle is measured to have a negative charge and a spemej qb/vmq * q6*)-ngzed 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.
 

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79#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How much energy would be required to break a heli.c1rds4sk+r43 jh lk dum nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and hr.sl+1 k sdkjr3 4hdc4elium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

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80#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the percentage increase in th9wd3* np0k;*u.z :fl fdlzd p0dt y1sge (relativistic) mass of a car traveling 110 km/h as compared to atfy pwk9t*ps 0dgdnfd1z .0ldz*l:u; 3 rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

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81#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two protons, each having a speed of 0.935c in the laboratory, are moving tow w* ic9*6 bgihnr-iq1gard each bh nrwii 9c*-*g1qi6gother. 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}$

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82#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Show analytically that a particle wi/385 hx+nv 3)r rxgkrpy. ppnf *.xjphr hl*u0th momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.
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83#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The fictional starship Enterp/o6c klt.es()oda+nh rise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is cado)th.o/ nls (k 6+eapproximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

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84#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An electron is accelerated so that its kinetic energy is eyz:5*zvia 1ggreater than its rest m5e az*1z i:gvyass $m_0c^2$ 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$)

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85#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A farm boy studying physics believes that he can fit a 15.0-m-long pole into a :xxjoh)t;zg1 8 wd9il 2cn3zo12.0-m-long barn if he runs fast enough (carrying the pole). Can z ) 83z2xhl;n9:xid 1to cwgjohe 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? 

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86#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When two moles of hydrogen and one mole of oxygen react to ) qip,s- mpeu7form two moles of water, the energy released is 484 kJ. How much doemp-p7iequs , )s 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}\%$

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87#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  In a nuclear reaction two identical particles are created, trls)min evd49 ao096x maveling in opposite directions. If the speed of each particle is 0.75c, relative to thee m9 96d0nisal4mov)x laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

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88#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An astronaut on a spaceship travelin-lw/ i/opb e,p*ov fs:g at 0.75c relative to Earth measures his ship to be 25 m long. On the /psvb p ooe l,wi/:f-*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

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89#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
You are traveling in a spaceship at a speed of 0.85c away fr 6g)oh 82yzmpeom Earth. You send a laser beam toward the Earth traveling at 2)mo6 ge8zyph velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?
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90#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spaceship and its occupants have a total mass of 150,000 kg. The occupants whfos. ffi/3, t+vpbw5 ould like to travel to a star that is 25 ligpfh/+ ,bf3sw ti.o5vfht-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

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91#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What is the s lixamqx1fp220szp3 7 r(8pcgpaceship's kinetic energy? Compare with the total U.S. anxfr l2p18agi2m7c3( spxq p z0nual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

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92#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 42,000-kg spaceship is to travel to the vicinity oq.;*lve xua (tf a star 6.0 light-years from Earth. Passe l a;equ(x*vt.ngers 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

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93#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 1.68-kg mass oscillates on the end of vkp*7c8 )ddqa a spring whose spring stiffness constantcda vk*pqd7 )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

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94#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A pi meson of rest m,7bxbhg+l9p b ,f*k yx:awlw/; go9ovass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.
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