You are in a windowless car in an exceptionally smooth train moving at c(ea:q9b )kbjk*qb h b7onstant velocity. Is there any physical experiment you can do in the train car to determineb qb79j:() ekbk*qbah whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when,fuh yusb):sn5(sc ,)n out of the corner of your eye, y:5 ) nhu)cf n,sbs(yusou see the car beside you creep 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,fkh2 r(:n,q1gvc8 tdv3 (lpgd and throws a heavy ball straight up (from his potlv3 (qcrgv1k2:,fd(n g hp d8int of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it af0ml;t-ng 1 inhf-w,vlso valid to say that the Sun goes around the Earth? Discuss in view of the f 0nf ng fi,-;-wmtv1hlirst principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0xcs9/ed6i3d j .5c away from a star, at what speed would the starlighid/9 d 3xjes6ct pass you?

The time dilation effect is sometimes expressed as “3yxv bx iakuxtqz85 l o5285;tmoving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functiontt5q8 lbixoavxuz3 ; 55yx8k2 ing of clocks. What then does it deal with?

Does time dilation mean that time actually passes (g*:jr k1 3bnippg4vdb6q+a*w5 hiz i more slowly in moving reference frames or that it only seems to pass mqi j+kgi6 *p(zpba5:r4 v*dwnbh1g i3ore slowly?

A young-looking woman astronaut has just arrived homer(-otpnlg07 hgmd3: 7jjgv( y from a long trip. She rushes up to an old gray-haired man and in the ensu:g0y-7jl3o7m(d ggpjrt ( hnving conversation refers to him as her son. How might this be possible?

If you were travelingvxt1r5y)bshl;2jb 5bj-d393h s rcp m away from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Eartldhrx b5c59mhj t p;)-b yrvb sj313s2h using telescopes say about you?

Do time dilation and length contractiowt. 3 -xuqnzx0w 4b93yu7gckkn occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of li/wmbf.rjv 2nn 5 8vul5ght were infinite. What would happen to the relativistic predictions of length conl5.v2 5vu/bwnnjrm8ftraction and time dilation?

Discuss how our everyday lives would be differ ttk4.0lapq, xent if the speed of light were only l,p axtt.4k0q $25 \, \text{m/s}$.

Explain how the length a zjgdiaoz;deb w 8v7:uz* s ..8xm2*ucontraction and time dilation formulas might be used to indicate that c is the limiting spez. eodz ub: 2.zw8aug*8j m*i;sav7xd ed in the universe.

The drawing at the start of this Chapter shows the street as seen by M ,b as.p8 *f8swoh/wtsr Tompkins, fo ssw f/,s p8ah*o.t8wbr 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 limited to travel at speeds less than c. Does ro1 q4fdk:y5ro,t ul3this put an upper limit on the momeq3duto:k 5 rr1l,y4ofntum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of now 887j(/ i) j6g6uyqpjxdtk innzero rest mass attain the speed of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does t q v7qx*9ek8ctm7c7umhis mean that a spring has more mass when compressec xmcq77te9vmq8 k* 7ud than when relaxed? ----待选择----yesno 

It is not correct to say that "c: lk+ob)c/kvmatter can neither be created nor destroyed." What mu+/lok vc)k c:bst we say instead?

  Is our intuitive notion that velocities simply add, as we did in Section 3–8, c.ugthqo -,(o bompletely wron -.goubqo(ht ,g? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You mefcngou (k v,stj x/;w3z0e/nh 0lfs9,asure its length to be 28.2 m. How long would it be whehgznu n fs,/09cevs0t(f ; x/kol3w,jn at rest? $L_0$ =    m

  A certain type of elementary partir npyg*u1aifh ;z42iohtm,1 27/rezh cle 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 faoydpog: :w)rxknk:; 2ctor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from Earth at a speed w5;8a( shc ty2qcref -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 lfv,p. ) fbp*qzifetime 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. Howt(2 psfb5 - urw)h8bfw fast would you have to travel so that to you the distance would be only 35 ligf( ubthfw2) wb p5s8r-ht-years? v =    c

  Suppose you decide to travel to a star 85 light-yeaf7wdx1zj8c9 nq ktv2: rs away at a speed that tells you the distance is only 25 fvztcj wn29kqd 71x: 8light-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 hy306. hjuuedthe 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 starship Ent6dwe:s2wc/ 1xkf6j0 bw/p-cvxz :u e yerprise had just returned from a 5-year voyage while traveling atcxp-xf6d/besk w 1 jy2:cwuzv 0 w/:e6 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 takey9gk1o-,h(fp zlfgvxg,at51 a spacecraft traveling 0.960c to reach that star from Earth, as measured by obsf19o ,atg5pvkgz hlx-1 g(,yfervers:
(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" sph6(j x (8:p 5nlz9tmatea *-g 3p zjplisd-0cmacecraft at a speed of 0.660c. It is measuredgs-nl mt( djpm z0:j6pl3zexah 9 iatpc8 -5(* in your frame to be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average p tox0-oi5k en:wpxuo* f5x 7d5ion be moving to travel 15 m before it decays? The average lifetime, at rest, i fp50xw o5o7x:un-td*i k xeo5s $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum i a3l(f7 pd,ofw*gyxw p k(d 91g5(oehof a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice io5jf+l rl ptjbl/k.j4 e(/2av ts rest mass? v =    c

  A particle of rest mab/1it-zzb9 v ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave 1tt)z- wrua e:zz7ri2ls 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 that acceleratx6 e in:dom01les
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi9s ehq16tn 3jnres $4.82 \times 10^4 \, \text{J}$ 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 the process know+d/jkorgf4 t2 9tewn 3n as fission in a nuclear reactor, the resulting fragments h+29e4j3 n twrdot kgf/ave a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest enes7uqnhj .63kjrgy of an electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a pr;z b+rdzuj j2/,am4jyoton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Unsbnk5nh y3-fx. 6c6kfited 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 concjl2w. nxz;:x 7 t q kvo-0oi8v,jdog+version of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic ep512qf4i4yg bz 2pkavnergy equals its rest energy? v =pfq vz24iap 4k2g5b1y    c

  At what speed will an object's kinetic energy be 2i3yhxv:y h ,l.5% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up hiy qt3ue,h n (vsug7v8b7s.8to a speed of 0.997c? W = si38u s.v8 (y qb eu7,n7vthhg   GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetildm nr e-8(vv9c energy 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-MeV protiqs*,hjk*0hl x)e ns(on (that is, its kinetic energy is 750 MeV)? qhxs 0,*l(ki)hn *esj   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MV?8un rzdian 9te-wpr(fc 98o6* v = zrfwceitn-(dnu 9p68 8r*a o 9   c

  What is the speed of an electron whose kinetic energy is 1.00 Mq;a 8q yo.jt)ljy u6 03.zorlieV? v =    c

  What is the speed of an electron justvgw+fdjikgb-+cic:o;l f w-,, +les1 before it hits a television screen after being accelerated from re;kls fcgc ,+dw-w ili:-o,g1+b+vfejst by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mass6f..l.mclv* l fdr5/cwe*p wn $m_0$ 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 q2 :+e l3sr5fzxragf6oton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum of an electron n3ggrmkvm :tl( d 1h87 vf4,sw($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 kg is accelerated to 0.21c. jlfvuft1.:a1wk96n tiq6 km/
(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 ene6w khxzadg*;4vseca 8 h+li.:rgy 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    %

  The americium nucleus, 1u :r(ogeoak4$^{241}\text{Am}$, 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 momqn3 w+:br buj dapt.o46tbg)0entum for (a) a particle of nonzero rest mass, and (b) a particle with bg0)u ttr.4 + b3 adponjqbw6:zero rest mass.

  What magnetic field *uk d3t. qnc8zg* o(x4ndrb-pintensity is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fergr b8p 3n q*.4n xddz-*koctu(milab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket trav touonup1w.g 2ti: r+8eling at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speu. i :to12rog wuptn+8ed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with -nr gwbkklpzg77( s6y05l)gm a speed of 0.50c with respect to Earg -lnr6gk0p(w7m s )g5zlb7yk th.
(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 x d8zhj,.jh /s.d,rjl 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 with respect to zr.,.8jjd,h j/xlsd h Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speew) u17*vp lnvy8g 7xlqd of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens whileq) lwyx778v 1luvn*gp moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. Oneya+3hljz ka 6c7u9p8e9 spd9md2iwg 8 travel8z+p932am h9glukje7dps ica69 dw 8y s 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 0.75c. At the same time, rocket B passzsm s,u+qv *pp.4/xvbes Earth moving 0.95c relative to Earth in thesx,4s+mppu *vv zqb/. same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima v5t mr0 mgwtz-3(y,bm 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

  As a rule of thumb, anything traveling faster than about 0.1c is callip+/gnsxfhsqy4n6m+(tf/ tef :c .7xed relativistic - i.e., for which the correction using special relativity is a significant eff/:s(4pq7 fyxt tgc6e+ /hsix+m n.nffect. 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 wfd+ (m , qtdbq) 3,igv,djre8$v$ 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 teff mm::k/8ikx e.rm nz 5ib9:o be totally destroyed to run a 100-W lightbue:n:m mx9k.me8f5ri /fz k:ib lb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an elg:zilfm nms*,t *f )n e (tnr*1(kd/geectron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charmns ifmn/ ld1*ntk,r*(fe)ze :g*t (gge. (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 : vtgfez /jmiw50 s*.2r y6lxmwith a positive muon traveling at 50% the speed of light. The two muons (eg:5zs2xti/m v6m 0e rf*jywl .ach 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 the jvhwr:f nmp5 2tw9(*bneutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine them9 fwntb*h (vr5 pjw:2 total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate o/c5vyb ji3q ao3 5(vwbf about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a negative charge and ant3/t y-1av-7duw myf 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 b kjq:9 vx+l;( )taynd8vox sj.zre-w4g(i f7to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron),nvats. 7w+)(x( 84z vjqlb9f gkyd o-x;e:rji 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 the (relativistic) mass of a car traveli2tbuedzqt5k58bz daa2 5i .bu59 ff c.ng 110 km/h as compared to at rest? [Hit2z5 5z b2f.u q8ci5u.aadf db5ketb 9nt: 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 laboratorzfek4qr 37l )b8-4z7 ,ng j6wzkz uxofy, are moving toward each other. Determine wuz)7lqo 46gze,zrjxb3k8-z 4nkf 7 f
(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 partoct+7d kv/j9d8v 8 rwxicle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter av( wivi 3y+/qtitbppys g8;ylj 6;0r )nd antimatter, achieving complete conversion of mass into energy. If the mass ofv sqi i0b/lt p+g(j y6y;3 ipw8vrt;y) 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 acceleratc .v-ljhxdx s.u0 gj+.ed so that its kinetic energy is greater than its rest ma+j0.xhv d.u.xjlc-gsss $m_0c^2$ 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 pole into a 1afl6i; bm s4y .d4aq-s2.0-m-long barn if he runs 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 look4m.4qay ; b-s6ls idafs even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of cdu6)au 5;w*qu8t mq noxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decre;c)86q u*tqmwd5aun u ase 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 -b 4lw89fpk+k+qo5a5z c g oce8eq:bftwo identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, rz-wlq5f o+b9e8oqe k :5b8c4 c +pafgkelative to 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 0.75q a1/ u-pucoo1c relative to Earth measures his ship to be 25 m long. On the ship, he eats his l -apu11 /couoqunch 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 ;jke v,99w ;7 x.sbe8r zyekhpa spaceship 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 obv;, z 9;hexpkj8.w rs7ek9yebservers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. Tyowwg;2 wrlgp (9s5bbb.: c53 pbsg:hhe occupants would lik( 5g:s2lcs ryb.:go5bw;hww3bgpp 9 be 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 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 se13(r)hvs9 *f md1ryfyh 7nt qpaceship left Earth at a speed of 0.99c. What is the spaceshipf11(*hnrqdtyrv me)3y 9s7 hf's kinetic energy? Compare with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinita(7vc 1j7zt7v:o :zpet ppr7oy of a star 6.0 light-years from Earth 7pt7 1vt:7ozp(7rpjcoae: zv. 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 th4+4o z-f- mlah1qhwite end of a spring whose spring stiffness constant tm1o4h+iqw4 z hl-af -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 mass *bh-- pyd)85y;ayxmyhw )nqa $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.