You are in a windowless cb 3rl4h.ddfn(v 0a ze8m;vyl6 ar in an exceptionally smooth train moving at constant velocity. Is there any physical experir.6 (avndb0fdey;3 h8mlv zl4ment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a rniny2 ,hxz/v69 lg u5g n/ge(jed light when, out of the corner of your eye, you see the car beside you exhjvg( 6i9 , gguyn nnz2l//5creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a hea- xns z:tsx*hzo(/j d*vy ball straight up (from his point of view). Ignoring air resxssd tzh-*z *:/n(xojistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Oz h57t 6l/lcyhr is it also valid to say that the Sun goes h ythc 6l75l/zaround the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveli,vw a 0/e g)iozch.)fsegq f8,ng at 0.5c away from a star, at what speed would the starlighw/, )g a8gqche zfo.,s efi0v)t pass you?

The time dilation effect is sometimes expressed as “moving clocks run slowlvf26h e - kkuarho/;r8y.” Actually, this effect has nothing to do with motion afu-kek v; 8/r2hf 6orhafecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actzg lbdi6 cl+(db6ghy)z9t) -mually passes more slowly in moving reference frames or that it only se-h)d g gl6)lyzzc6dtb +bi9 m(ems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long tqp e3)dbjb :2+hz yse(rip. She rushes upeyhdj+:3z) 2 p(qsbb e to an old gray-haired 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 0.5cv nv6+ . u/ll*xhh,xmx, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes s* x. u/nhvlh ,vxl6+xmay about you?

Do time dilation and length contraction occur at ordiv5ish 0yr7 sn1nary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to t(ck.v1nvdeax7a3 c(7 nzml86 e zchiu8+p-uqhe relativistic predictions of lengt-ea 3n (k(817xecd8u ln 7.pac6vcuizm qvhz+h contraction and time dilation?

Discuss how our everyday lives would be different if the spw w;)sv+(qpy2 q sz6uveed of light were only6susv ;pw qv+yw2 zq)( $25 \, \text{m/s}$.

Explain how the length contraction and time dilation forsbznc *q3s/ k l)is:h/mulas might be used to indicate that c is :)3/hsssnqlb /k* zi cthe limiting speed in the universe.

The drawing at the start of( u,c1emu/i4 oscwz tw4g 9y.c this Chapter shows the street as seen by Mr Tompkins, for whom tig uum(.z4 ow9yews 1ccc/ 4,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 limited to travelviqf2o w7;w y9 at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit?vf q; wo729iwy If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain th(xozxlv0 bpu5xxqx1b)n0-7i e 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 spra*o49zd5vk +p ,mpjd ming has more mass when compressed,pod95 mdz*pj+ k4mva than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor desbc2hoiogodsq44 s 4-1 fn;g )ttroyed." What q 4)cgsh4 o ; onb2todg1si4f-must we say instead?

  Is our intuitive notion that velocitiesv9c-(l++n ipdez- ijy simply add, as we did in Section 3–8, completely wy9--+i jizlnv+ p( dcerong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.2dc(it8 sh*, rx(jk-qsqe4 o/8x k/qyx m. How long would /khq(-xxq(je/yo8c kqtd8,i4sr *x s it be when at rest? $L_0$ =    m

  A certain type of elementary particlebq7 k+zwze8yl+5 a3we 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 intervalslw9 q fg h46g y wl+1t(:drenxwx(:y1x depend on the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from Earth am xi +i*-18iwegk -yzft 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 lxs.6w./gcb;c ksun3u om u86 lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light-years away. How ff(eaw;kh hs4 l+5uws y9e3b6 s9vg+hhast would you have to travel so that to you the distance wo++e h;9w 4s6yl(h b9ke5hs uhs3gaf vwuld be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85ioz)390 bmb,li.jtri light-years away at a speed that tells you the distance i jz)b o39mtiri,b.il0 s 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((sattvsx+ 8s1r2e i w n- lckn93n9mn the Earth 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 qqm/: dhkz ),wjf:( z3xz ti;bstarship Enterprise had just returned from a 5-year voyage while trawfqz(d)t;z 3:z ib,xq:mjhk /veling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it t6c i7 k(jn(a1 hlkmq;rake a spacecraft traveling 0.960c to reach that star ik;kc nj7qh6lr(a1( mfrom 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 "Ferrari" spacecraft at a speed of 0.660bmz:p2 6 gn1w,k:rqnx c. It is measured in your franq,kbgn2pwxz: r :m6 1me 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 beiu4jjj qp+gm; (nfau((fab )4 moving to travel 15 m before it decays? The average lifet aj mig(f(4 pbj+;)4aj f(uuqnime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelr4m 0qd yu(u73 iobb-king at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s ry7seziu8 h d+;elativistic mass be twice its rest mass? v =    c

  A particle of rest mas/)vzb4x cjapdebmig). ba8 p61 g,(.jm;gmrr s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle traveliah -q69 dx(hfs at $v =0.10c$. 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 )c9udql,paj8 j uk3f0 that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reacti st(-,iq(xnjn on 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 in*bs4:-ccl hmwqs t 4x. the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about ql .st4c: x4*wchm s-b200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules and infkd76vf. vq ,s $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of.ve isg se(zpag59s )4 a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy c4b.va8 icuzbsxsr04;pd h; h.;lfna8 onsumption 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 c: ucf5w:9 o,l -h;mvyyacq2rsonversion 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 x21vd 5+3u,xihgt,ez. c :xgrm id (wokinetic energy equals its rest energy? vdxcmo ,zitrgw,:xi( 12 3+ uxv dgh5.e =    c

  At what speed will an object's kinetic energy be 25% of its rest energy? r)hfyp4n9y 8b fg(s*6mic d.sv =    c

  (a) How much work is required to accelerate a proton from rest up to az5peg,f +ky f/ speed of 0.997c?ek , fzf5/+pgy W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and7jv1kvk *fax 5 momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetic energy is 750 MeV ehc+,r 1dre( c;(tgue)rdec, +(the ;eg 1u(rc?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differemaijk;-i / nl qg0nl)-w la*3unce of 105 MV? v = k-ai0)/nlwlju- ;g i*almn3q   c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? v =hc3qj y2 q3j6u8ei8yw;o7x3v2 aegk f    c

  What is the speed of an electrox/4)p8fjo0.,1s6)g (tekd p fifpqhd5 mxh iwn just before it hits a television screen after being accelerated from rest by the 25,000 V of the picture tubexpht e/ff 0j),xq dhi1o)fs mkp564wdgp.8(i? v =    c

Two identical particl/to7 pb8d 6 vfzx/vt/jes of rest mass $m_0$ approach each other at equal and opposite speeds $v$. The collision is completely inelastic and results in a single particle at rest. What is the rest mass of the new particle? How much energy was lost in the collision? How much kinetic energy is lost in this collision?

  Calculate the speed of a pr d6jx h jl6yl/s *melyg5x gs*wsk4473oton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentu9z vd o1x,v.p02mfsnum 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 of mass 27,000 kg is acce:twg a3n- mnx1qv j m;afj/,8ylerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energy and momentum ofm8a*l;yr icv:ybpz1:f8 e2bexs+:xn 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 nucleusds+a g z.3(lvjmb 387i5aztax , $^{241}\text{Am}$, 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 versus4mixuy.;h5si)sfd -z+p5 o na momentum for (a) a particle of nonzero rest misnuh oi+zs55y;) xamd4- .pfass, and (b) a particle with zero rest mass.

  What magnetic field intensity is neeshz mbq3 3q-(h gie2;.9ry xiuded to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? 2q3h3-heiriy xb9qu(s;.mz g Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with respect tdt (611tcx jxno the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fascjxx 1d(tnt16 t is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50c w2i t), e cheu:o a2tqv-nt/v. iqu5:hyith respect- 2 uc2ut:vehq)hv/ e ony iq,:5.itat 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 ;ptz rke hbi5- w6rf6.spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with rest6p5h6. rk iewb-z rf;pect 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 sugg8: ra g9)c(vt8uszp pzyy38 l(2dbees an 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 Earth. Wha(b:88zu dpzvr8ygu3 2y(st a9 c )lgpgt is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distressra5 ren 2 wbl8zas,c68 sends out two escape pods in opposite directions. One travels rre8a, 82snw65lba zc 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

  Rocket A passes Earth at a speed of 0. :mdd0qoc +9s(/yr z6r qk *.ncnn+gqr75c. At the same time, rocket B passes Earth moving 0.9qsc+gq okq drn+ (6nmn/r *9:dr y.zc05c relative 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-years away. kqinv lsn7yx-af a a2n.3e/esv;p9:/
(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, anythi;c * 5sv7qitmang traveling faster than about 0.1c is called relativistic - i.e., for which the correcis a7c*;v5qtm tion 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.) ----待选择----relativistic not relativistic 

  (a) What is the speed 3rfmpv1q6e4mat -d33f ec4r l$v$ 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 destro+g 4dy. s1+wchg 6whlzyed to run a 100-W lightbulb for +hydw wg+6.sz4lh c1g 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an a+dj5temt,d v,kd0 f7electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite che5at,dk+7 , d0ftdm jvarge. (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 wilr j/u/ 8nf(7f itpoq uj64yn0th a positive muon traveling at 50% the speed of light. The two mun ltfq iy0nuu/p/8ojf (6 rj47ons (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 dekzju 0ao8 (t/ycay into a proton, 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 fronu0jza(ty 8 o/kt cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of abonbx .1n) cvx2rut $4 \times 10^{26} \, \text{W}$.
(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 hav ms1 fb5s0,qytqt/) hvvpgts(0 :/srge 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 required to break a helium nucleus intoaf :6beh uxayi 4,xnr8 -p;0ws its constituents, two protons and two neutronn0 b8au,yrs iapewx6h4x; f- :s? 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 called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in)x1 m oulgss :(q cmc+9tq-wkz. q/3xe the (relativistic) mass of a car traveling 110 kmse9gq) mzl-t(3x:. owc1/ qc kumqs+x/h as compared to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laborator-jc( yjxpyf5j 3/qz2jk:z ak;y, are moving toward eaz ;k/jqp2xc fyak-j3(:5y jjz ch other. 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 particle with momentu5cpxouly hbos(92 8k xlu *7hx*r97l tm $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its tso 3bv5+ *1c oiand:;* uzrcopower by combining matter and antimatter, achieving complete conversion of mass into energy. If the massncbzivdt u *r:5cosa+o* o3;1 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 th lb h3ev/mr-4gn.)jx,mnq n ;rat its kinetic energy is greater than its rest mj 3r,rn /h4m. nlge);m-xb vqnass $m_0c^2$ 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-long+ hiar ci s,1i/jui:v/ 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 this fit with t/i 1i /vra+cshi, u:ijhe 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 gep:bdn*04 y vto form two moles of water, the energy released is 48v y g0:4*bpned4 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 partojr7 d w,aok9 q:*wnip,36 7 l8+ ux6bgdryhpkicles are created, 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 relk 7il ddpa +3*ur6 owwp6bo, x98q,kg: rynh7jative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c r m4a.gze1wrqre3l*1o elative to Earth measures his ship to be 25 m long. On the ship, he eats4r e o.a1rzw1 *3geqml 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 sp5*; ruw+vt3nvxa.dm b aceship at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laservdx.rwmvb5+ta;*u n3 beam?

  A spaceship and its occupants have a total mass of 150,000 kg. 4uaddp0jglon( ; 8hf.The occupants would like to tr.poj nfad8u d4h;gl(0avel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this 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 leftpsv-u 9u. :mc rop ;.fku hn*p.wygv45 Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (abo:vpf*uncg9u.um r4 -wp y.spv5.ok;hut $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a st/j adj5,uv:ogar 6.0 light-years from Earth. Passengers on the ship want the (on, vjj5ad/ og:ue-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 sp+ -q dwqmti tts/)4b/djm b,-dring whose spring stiffness constant im4/qjsw,qd tm/b b+t-d)d-i ts $k=48.7 \, \text{N/m}$. 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 masjx(q2 4 d)v:qkrwuu(vs $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.