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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 1 u4*m;kfhx2wb*zxwi smooth train moving at constant velocity. Is there any physical experiment you can do 21i 4*bwz kx*fmwuxh ;in the train car to determine 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 cor.nh9lzdr97 vq4e,k qrner 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 sar7l4.,qrqn9v e9hzdky 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, and throws a heavy ball x(740pdaglv2:dq nq37xrr fd straight up (from his point of view). I72f rr37 dxv (x0 qlq:ng4apddgnoring 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 to say that +nv+ p:)azf50(ton lcs,lef+din d a: the Sun goes around the Earth? Dist+nn ( ,: i +cpl5:naefzs+a)ddo 0vflcuss in view of the first principle of relativity (that there is no best reference frame). Explain.
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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 spaceship traveling at 0.5c away from a rfdr;lvhq* qg9k, /c 8 ow 84e1bqf6 xrjyp0j;star, at what speed would the starl;jr0 p djrhw6*qgekybf ,vcof;4 /r188qqx9 light pass you?
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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 is sometimes expressed as “mbx:b7 ,v)h dim, ddb)foving clocks run slowly.” Actually, this effect haif mxbd:)v)bd,b7 ,dhs 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 more slowly in moving refm/ 4hjuwxfm- zg .o(q9erence frames or u/j mf-(hzmw9x4qo.g that it only seems to pass 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 astroyfk+hv8 c6fl(+lxz 7lnaut 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 be possv8(l 7+yc+fzfl h6lxk ible?
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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 0.5c, would you notice a ch1oo 5, :phwexp 8cfy4ly4:s;vtb y:buange in your heartbeat? Would your mass, hei,;bs o: 4eypop14w5c vhyuy:f lx:bt 8ght, 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 contracti32lvv56aao)9ihfp djb 8kl3p on occur at ordinary speeds, 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 wo+u/-pqk q)wi 9a wkm -yz.bh*huld happen to the relativistic predictions of pz-)-i uw9qmy+h /akq*b.kwh length contraction and time dilation?
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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 of light were onlrih/s c ody:y (hbx()( kv0q.;ky,tb ay : xov k);c by(skrt0. abqhd,(h/(yiy $25 \, \text{m/s}$.
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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 contraction and time dilation formulas mightdacw5 c sfdf lz:iw*n/*)dl(/o0 o j+c be used to indicate that c is the limn*ljfzl /:*w0c ddc dao/() +f ioscw5iting 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 seen b:ar b . nsyrt9sfi;t)w.+5bfxy Mr Tompkins, for whom the nsba;rf5 f+sbiy 9r ).wx.: ttspeed 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 limittite/3 x-3g6bq6qtxu -x(mge ed to travel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this gg6/q t6b exxx3t-(-uqtie3 mupper 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 nobb(wrr 4ao7x 2nzero rest mass attain 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 morgsxdr y/g) l1,r/g4xqe mass when compressed than when ys1rxl)/xr,dg4 g/ qgrelaxed? 

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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 caatx7eksz mg2wx, /h;fi(c8q (n neither be created nor destroyed." What must we xaz8(x qt/e, (;27kmhg is wcfsay instead?
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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 did in Sectluc5 .s,tb/ bc-pvde; ion 3–8, completely wrose,cpd b.lvu ;/5tb-c ng? 

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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 sp,+jo 9wiohm *oeed of 0.750c. You measure its length to be 28.2 m. How long would it be wohoo* ij,m +9when 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 elemecm/e1pothr 0bjny1 x,nx.e32 ntary particle 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}$

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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 factor bc 0 m9z;6k k50rx km20m/xed-pp zzwp$\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 liod9 *-v 8muclgght-years from Earth at a speed of $2.50 \times 10^8 \, \text{m/s}$, what would you measure this distance to be? L =    ly

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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 if its average lifetime is measu76lxs1 ift(14yvy l nered 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 light-years away. How fast ccxjvl/7t;2hb 0oi7xwould you have to travel so that to you 7 h0xcxto; /2 vijcl7bthe distance would be only 35 light-years? 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 travel to a star 85 light-ye2cb)2/n s wd*:n 11pnrchgq g2apb,x gars away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip? t = g sdc2q) hgp1gx *21wcnab2:bn, rpn/   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 Epfc9 oqki/hfs)r8x m9 b9t63qarth 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 from6zqri *) p5/i jc :.jlxkp+kid a 5-year voyage while traq )xlkz6:k*ic j.rjpi p/i+5 dveling 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-years away. How qp2h 27s) c7qzi,u sialong would it take a spacecraft traveling7sau,ii hcq2 7z )s2pq 0.960c to reach that star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

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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" spacecraft at a speed ormh/ mfn:*)t4rukc- tf 0.660c. It is measured in your frame to be 4.80 m long and 1nt :4m*u-hck r)f /mrt.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 pioregm7mkg3.f 5 n be moving to travel 15 m before it decays? The average lifetime,g7.g 5 kmme3rf at 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 tr2fp( h*.dnwj eaveling at $v =0.85c$? 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 rest mass 1oc:zvpa* t;na 1+su1fo8jho ? 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 massn0/d d*57yxqb x oc:l9o nfa7zh*vda6 $m_0$ 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 at 60sji/sd1hr t $v =0.10c$. 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 momentum of a protoni hc8t.yu3 bo/ 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 reaction requires3-p fo7)-6exc zi sshh $4.82 \times 10^4 \, \text{J}$ 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 breaks apart i1 34gmibly2e by kgbf t0tv*v+57z a+qn the process known as fission in a nuclear reactor, the resug+b k*tb4mg3 y7+ teiavv251 q0fzylblting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

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42#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the rest energy of an electron ikw .w.qiq/ g;on 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 in ,*mbg25 jc vo cvf0l2l$\text{MeV}/c^2$. $m_0$ =    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 the United States is abjx1,(u)mj o yfout $10^{19} \, \text{J}$. 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.+kclb)mgk3-hk t ast0/ krn y-k69)s j0 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}$

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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 particlepa.r ru4pz .-jv( blq7gu2 zr: when its kinetic energy equals its rest energy? lbp zap.:(j7uqzu -vr4g.r2rv =    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 object's kinetic energy be 25% of its rest energy? v =l -c5a.dg +m5k4ry ygvu0cj 0z    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 sppnv4wl ,1+ .+i oc9tt vk*vbkbeed of 0.9 vnwcpk.o bt*1i,vtbvk++l4 9 97c? 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 energy and momentum of 2 x-ju/ ghm2mtde6qf*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 /fi)nq -iys*i .ju +dz750-MeV proton (that is, its kinetic energy is 750 MeVy.)ifuj/ iqsn d z+*-i)?    $\times 10^{-19} \, \text{kg·m/s}$

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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 buofj . tvuyt.y/t4(( ny a potential difference of 105 MV? v f. . u (jytty/vtn4uo(=    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 an electrocfju)i 7wl+p/ n 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 an electron juksx,7d *gcs3j q+b1zw st before it hits a television screen after being accelerated from rest by the 25,0s bk+gzx , c3w1sjq7d*00 V of 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 particlekx.frot zde(66hp:n 4 s 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?
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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 proto -idn)vjq85 uv+uud -xn ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 momen yau0 4v:r/9n woe h3r5abqh-58foxhftum 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.en;:o4hf;qor v(iq, q p)*d9.g taqzg21c.
(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 kinetic energy and momentum of a protoq c-w2jk qh0 6t,qxef(ts)th8n ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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,hhavv(zonv-;6ou k h6 n(nv1( $^{241}\text{Am}$, 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 nonzerygh0b8)tsoip1 uy 2a )o rest mass, and (b) a particle with zero rest mass.)ot8 hayb210 ispy ug)
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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 needed4m i5b 4)7ms8lkml :w)llff ou to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton l )ml4w4b f)8lus:mk 7miofl5'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 Earth95gk 5noly gx-) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fa5k9xngl- g 5oyst 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 directions, each with au m0ywn/5a0ha svv.)nq6 2 oc98zydcd speed of 0.50c with respect to /on9adms 5)cy 8wucqay00v n6d.zvh2 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 Ek 5 5kxk q cto5abqjwd47w)2h-arth traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Cal-oqdckk5 j4)w2 aktxh575bw qculate 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

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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 alien vessel approach at a speed of 0.60c.86 lx /+yml-dukhy +bb The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c llyyh -d+/b 86bmx+kurelative to Earth. What is the relative speed of one vessel 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 sends out two escape o9c;/ 27dj mmxsydat.pods in opposite directions. One travels at a /cmsmx 9j7a tdd .yo;2speed $v_1 =-0.60c$ 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, rocketea/sb1 ) c0ohwada8-d B passes Earth moving 0.95c relative to Earth in the same direction./dw-h oabasdc0e a)18 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 Proxima Centauri, 4.3 light-yea4 frov0z(z,*xh)f li prs 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 traveling faster than about 0.1c is called re rzzjx7 xmsy 7,-of.,e q9fl:zlativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speedfyxf- :,oz l zjrq e79zmx7s., 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 spee+ mh-o2b lneu:oks6yz;ao:g 4d $v$ 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 totally destroyed to run a 100-W li8zi3+z t ,k+1t lgiepm+p ijr-ghtbulb for 1 yearmk+gzze3 i,ptii 1j+pl r-+t 8? $m_0$ =    $ \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 electromagnetic energy is needed to p9gdvj, 8sg(hrl -f a2hq4hkq .roduce 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 that electric charge is conserved.8dvjkh( rq29 fghals ,4q-hg 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 qn-jq-a-omjt9d+ 8il 4 m;tkpsq*8(bvz z.s x collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of-vs( z *b xpmjtils.88 jqz+o kqanq9mt-;d-4 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 e cza /x.ywt5l,wper1v9 ugc +rrpg63 y:l))yinto a proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the otl eaeu lwcr ):.g)v6g1ry,yc rxz p9w 5/+3pyther masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays 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 rate of altf2dx,.f 2a vbout $4 \times 10^{26} \, \text{W}$.
(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 chargevt*;,tqn/bk p 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.
 

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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 brenuyq9gy *xu 9 gvt4;l*ak 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 difference is*tgu 4yng v9ul 9qxy*; 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 the (relativistic) mass of a cax*ders z+ 54err traveling 110 km/h as compared to at rd5 s*4xzee r+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 spe .ke*0cwvy ix;ed of 0.935c in the laboratory, are moving toward each other. Deterv*kc x wy0;ie.mine
(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 whiwi /fdh2uz5sno 2a0u7 *u*c ith 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 Enterpriyc 0b37u srpmmp762 qgse obtains its power by combining matter and antimatter, achieving complete cogm6ms7 p7pcbu2q3 0rynversion 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?    $\times 10^7 \, \text{kg}$

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84#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An electron is accelerat/8v*gt gi,rax sd9. cged so that its kinetic energy is greater than its rest mass git/gr*xs8d,9 . g vca$m_0c^2$ 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 iizj8gt6 rd-w.rj pr6zci8 ;6a 12.0-m-long barn if he runiirt8jc-6g;66r.zw jp8zri d s fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn 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 form t2fgxe/; jo )dfwo moles of water, the energy released is 484 kJ. How much does t/2;f)gxfeod jhe 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, traveling in op:en. l7 6id-n ohty1rjd 6,hlyposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relativer,-h61:eyi6l.d ty djn7hnlo 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 travelinruqmvu4o8 j*vf 5d5m6wst/2cg at 0.75c relative to Earth measures his ship uvm/r68 5touq wdsv 2*45fcjmto 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

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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 /szffcs,-r5 ,bvz9br w)2 tqdof 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to bbr2,w) 9f /sfcv-t5r zqz,sd 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 occupan 9ti+v.enb;n8,w c qzits 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 ze i;+ti8b9.vqnn,wc 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 spvfpu1l7u;bh.1 w6i ov3 bo i*aeed of 0.99c. What is the spaceship's kinetib1au h.w7i b1 v;f63pou*oivlc energy? Compare with the total U.S. annual 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 9e v kdrwm29.rto travel to the vicinity of a star 6.0 light-years from Earth. Passengers on the s9vd k2mr9.rewhip 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 a spring whose sprmch/m,mtc t lv:hj1 /2ing stiffness constant m hctvc/mtj: 1,mhl2 /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 mase/6oovn ) 0ql5vo hk6eu w1lh4s $m_\pi$ 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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