You are in a windowless ud,m.k1xauan: f* xyuju iruk0u5 5dd;,,3a hcar in an exceptionally smooth train moving at constant vel3, juur; :ka.mk*,50a 1ddx i, uhuauyfu5xdnocity. Is there any physical experiment 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 red light(1;as6 yw vbhb when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pe(;avw6 hs1ybbdal, 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 thr) g6-bsptqs8wkaxo2 x g(z2 i9f-wqb3ows a heavy ball straight up (f-9-g2awq 3s86pz(xtfi wk gox2 b)sbqrom his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Oqryj*e ido+ wu0zc./ 8*b6wppr is it also valid to say that the Sun goes around the Earth? Discuss in view of the firszr.pd / *w+*p c0qj6 yoe8wbiut principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship travefp yylivi n.rf094:8d2x .obuling at 0.5c away from a star, at what speed would the starliol92r4n.pf.fbidv:0yy 8xu ight pass you?

The time dilation effect is sometimes exp;x 0sd7p;lzvd: d /frr6uqgm9m(n n5hressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What tr f lh g6md;m5r7xnpvnqzsdu0/;: (d9hen does it deal with?

Does time dilation mean that time actually passes more slowly in moving ref9ypj;f ;hk0ph,upjd)tz; od2 erence frames or that it only seems to pass m,j yhd9;;f;j2ppt hz o)0 kdupore slowly?

A young-looking woman astronaut has just arrived home from a lo3hjwe-ht;q1v; l i* eong trip. She rushes up to an old gray-haired man and in theh3 qeo;j-hw ite*l;v 1 ensuing conversation refers to him as her son. How might this be possible?

If you were travelinv3l ty cmo,9 ;t7-/6kchbi 0 jnoltcckc)+y8 ig away from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would obser3 tiicc)ct o7ckl cl; y joby9-80ht,+vm/nk6vers on Earth using telescopes say about you?

Do time dilation and length contraction hy5 xg cqxp.3lk/hb(8occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to theq,/o2d4zg3vhd6 ixsa,sbvqqp ./e 1 p relativistic predictions of lenq2 / zp qiebs4/6.ovv1hsd,qpx3d, aggth contraction and time dilation?

Discuss how our everyday lives would be diflquja-brcm l/s6 -f+b-y 7eb )d0 nl2xferent if the speed of light were onl02 /q7l- +frn y-m-sac)bjxbbdu6elly $25 \, \text{m/s}$.

Explain how the length c*4s s;vuw5jqb-l p g2gontraction and time dilation formulas might be used to indicate that c is the li*l g vj2;5s-w sub4gpqmiting speed in the universe.

The drawing at the start of this Chapter showdi0u nbl8*h (ls the street as seen by Mr Tompkins, for whom8 (bli n*uhdl0 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 )8jsk+ayjy7j *i 1 swxtravel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is thisx*) 7j as jywsi+k81jy upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the l0d1 vboal*i,6qr2 m d m1sve*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 spring has more mass when cor gn+g a(5 .,cnmwqf/jmpressed jnq5 gc.,/rf +wag n(mthan when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neitypr yh+e eh,+x1t; g-vher be created nor destroyed." What must ,ge+1yh vr;+epx yt- hwe say instead?

  Is our intuitive notion that velocities simply add, as we did in Section 3 pe:lk. oaex94–8, completely wronkp.4 loxe:e9ag? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You s o lfz3l*a8.a*y1ynnmeasure its length to be 28.2 m. How long would it bfz*1lsyaal. * n 8y3one when at rest? $L_0$ =    m

  A certain type of elementary particle travels a bgsex(m/(wh7vo7x2e wr )3uut 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 t;zfu p0cn72nq.rf /r phe 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 lightirbysu 0grt1wwgmf9.30 ,qxz/ - -ynd 4utw m0-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

  What is the speed of a pion if its p/jlq-k8 u 5y9+t qhfxaverage 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 referenc0. shkgrwe v9(e frame, a star is 82 light-years away. How fast would you have to travel so that to you the distance would be(r .ew9vs 0ghk only 35 light-years? v =    c

  Suppose you decide to t 9a0kkex ;zq5oravel to a star 85 light-years away at a speed that tells you the distancke0x o9k;aqz5 e is only 25 light-years. How many years would it take you to make the trip? t =    y

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

  Escape velocity from the Ea sou.z oij3c*o3gabm(g 07tt 8gf05ujrth 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 Enterprise had jj(; otg k 2pk72a,6mtvt3q yqpust returned from a 5-year voyage p 3( t2;g6vot m7k2a,pkytqjqwhile traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 +taj)p n*zl6w/ 0 azsjlight-years away. How long would it take a spacecraft traveling 0.96 j0aw zl/napj*+6 szt)0c 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

  A friend speeds by you in her "Ferrari" spacecraft at a spe6co+h nw-*uos ed of 0.660c. It is measuredwc -*on6hs uo+ 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 pion be moving to trm, ukovi9:qgu)f lewc6w;1nc2o0y6q avel 15 m before it decays? The avera )e: uvk0 ig1;qo,6 fnym9wwo2lcqc u6ge lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trns( svu l0*wx(aveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass? vg su 19eau)(d g54t1sivnf,lr =    c

  A particle of rest mass qc.h:i t1p7f:pywja6 $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travellt49w y:xqmb ,s 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 accenyvm )go8x2p0xwf9 sjf-p7p5,m b7 hilerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction rel : age4o*.rdfquires $4.82 \times 10^4 \, \text{J}$ 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 a ki1h 0(68 i1sx hz48o-d)rzwl qzp 9erjzkj(apart in the process known as fission in a nuclear reactor, thew lh 1d-0re8xi(a zkj1isoh z4 (jrqz)6zp k98 resulting 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}$

  Calculate the rest energy of an electron in joul2v 1q+kwh/rq7jq*dx k. mt fb)es 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 protsv3:3t 0bbc vcon in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is about a6r,uz*i96vu. afj c3 dz8wdn $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversiitd6.i u- q //teal,w t;*efyron 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 energy eqxdi,/zpnmz. c;x*q4 puals its rest energy? v z,.;dnzp4c qmip/ *xx =    c

  At what speed will an object's kinet3jqnj ta7 (9e1l e;zt2jm e2gmic energy be 25% of its rest energy? v =    c

  (a) How much work is r1fwz6n( (cpwp+zf-h vt8 ws0qdsmn+)equired to accelerate a proton from rest up to a speed of 0.997c? wspw q8mndcf( s p+1t(f6w nz-+ z0hv)W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentu3 sp/ifz a:t yf*t vdjx;t+ *,z:kkos2m 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 i (g;podt orux3*0xv8ds, its kinetic energy is 750 MeV)p0dg 3;uv( otox*d x8r?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential diz8e9qw ., u-) nhyjdidfference of 105 MV? v =)u9 .dn,zwy ij8 dqeh-    c

  What is the speed of an electron whose kinetic en-va6r mndal3nx r 1j7al4r3k -ergy is 1.00 MeV? v =    c

  What is the speed of an dk)5f zv+pm(yhds8w : electron just before it hits a television screen after being accelerated from rest by the 2 psv) f+w z5dkhydm8(:5,000 V of the picture tube? v =    c

Two identical particle5xfwj(c6-pgc h o /r3ns 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 6litq1yzz w:* of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 ofun t8+cm pyq2ujh d1k- wvm*5, 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 is1cspa:6f vet95z 25p3vpoj g x accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

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

  Calculate the kinetic enfz-d (n-221onm0o pxrwog) zzergy 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, bhq13 fps2 vz*vy q*0fp4, esz$^{241}\text{Am}$, 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 momentum for (a) a particle of nonzero39 1bqaly8hi y rest mass, and (y1hlya3 8q9 bib) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving f8iolsvxw ) .9k;/gl win a circle of radius 1.0 km (al/8w)w.ogfv s9ikx;l t, say, the Fermilab 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 travelinbw l6sqy,z8.o g at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures 6qy. bsz l,o8was 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each w)w0lyj :+-1d cihp qxg1cnee/ ith a speed of 0.50c with resyng)xi0 /1ep1-c+ h clq:d ewjpect 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 g)vss,,ozb g:-e a)d p- qy( (z/ilfglsecond spaceship leaves the first at a speed dp, yq:slg ,v()(f -z eas/g bli)gz-oof 0.87c with respect to the first. Calculate 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

  An observer on Earth sees an alien vessel approach at a speed of 0.60c. Tas jl(ne )0e*uhe Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving dir )*aju0(lens eectly 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 oppg+k uz7c xpl(q-4lx. sosite directions. One travels at l q4cxuzkx7ps+.g-(la 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 speedi*;n, yp4vji/ pux,vd of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B movxy/ iipj,;uv d,pnv*4ing relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Cent0.r :rfu9ef6hap+7kd)os t zoauri, 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 j.vquc 8e 6wm:is called relativistic - i.e., for which the com6:8evwucj . qrrection 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 spee(c+c hi05vm sk yvc2xd gu84p,d $v$ 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 destroyed to run a 100-Wl,b:ko3oggu ;+ ptye;rl o,)0z(k qkt lightbulb for;uo:r +oqe k ko,t3)gykl;t(p0glb,z 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electrf xoe2(z 5/drr7umn2- z3 yyhhon and a positron together? A positron is a particle with the same rest mass as an elecnmyhr/r7-(hd5 of x z2yzu2e3 tron, but has the opposite charge. (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 with a posi ri:0zq(sprfdu b6eq 1.obgy2k( t+f4 tive muon traveling at 50% the speed of light. The two kbsg0zd(q ipb1+q:.624 ry utr o (ffemuons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a ,ht, d4m:ie 2impmd1q 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 decays at rest.42d:p1 mmmiqtdi, ,h e KE =    MeV

  The Sun radiates energy at a rate5b )0hxl ahm/-0roqy c6 zdre4 of about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured 6mc/j v+x)g.msuvl2dh7*yb r to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be required to break a helium nucleus into its constituenullaf2 mdc7s ce9jdy 6)9qk7q*43gp ots, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.qsa7) 9uq7 ll fdpoy34g6ckc*9d2j em00783 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)aun ucf *j2x1e6s)-h l mass of a car traveling 110 km/h as compared to ats2)u - jn *fealx1hc6u 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 labommw.o iyy. u:h52ru0g4b-l hlratory, are moving toward eamy0r h:4l5.y2b mwohlg u-.iuch 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 ao+ hbm-pb/ b7pniz- :fd r8;h8-tzucs particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise o((vcgy2ma3 o8v - i68:e mvy wazl/bnvbtains its power by combining matter and antimatter, achieving complete conversiony3vav e/6c8magz(w8lm v 2i -(obn v:y 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?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that i;q0)bai0m pcrx df 3: yfbn;4yts kinetic energy is greater than its rest mass a 0;)fxy 04by i;bmc:nprq3 fd$m_0c^2$ 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 beli wv +c,dz0qjqavr ),;5s9 dygkeves that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carry9k,dq;)zvywr +0scgq, d5 avj ing 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? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two moles of wagq 0 y5oist6ra,8gr7e ter, the energy released is 484 kJ. How much does the mass of the elements d0agg7 i86 5,seoq rtyrecrease 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 particles are cre(v;:i b-s qmhqated, 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 q; ibhv: qms-(relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relatici 3p 1h um86lxa7xeq,ve to Earth measures his ship to be 25 m apmc q,3h xux617i e8llong. 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

You are traveling in a spaceship at a speed of k9cro)h f /wwg4l86cf 0.85c away from Earth. You send a laser beam toward the Earth 6owrgk49 8/f)whcc fltraveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg,;ce(r9pt ulwop wwbs( 4e/ q3. The occupants would like to travel to a star that is 25 o lqwt,wrup/cwsp (b 3 e4;e(9light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What p70oph3ams *o is the spaceship's kinetic energy? Compare with the total U.S. annua p3 *hs0m7opoal energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to tra(lbo;jv.j*c emcii4 9vel to the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be donec bi c4*j;e j(iv9m.ol on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring zhnlch+gu 8/o5tug c3 ) )lko(stiffness constant ihut(noh)g)3cuz8lc ok+ /g5 l s $k=48.7 \, \text{N/m}$. 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 mt(/ styv,p/ cp 4cwb4jass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.