You are in a windowless car in an exceptionally smooth hp-f yu13-i njee(:fo train moving at constant velocity. Is t oepf:-n fieh(1 y3j-uhere 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 ofx+1(vk9ubuefe lz)jh9n 7 ra+ being at a red light when, out of the corner 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 thu)aj7vh ebnz r +ux(9e9+ lf1kis say about absolute and relative motion?

A worker stands on top of a moving rawk* kcb3 8 gdf,bm;;c *hyspv)ck0q 1wilroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball landmcbwcb0)hkfs gv8kqyd 1; , * p;3w*ck on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say that the Sun:oh a5xfft;i2 goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Exf;2ofi:5 t ahxplain.

If you were on a spaceship trav.q-4g; hxuz2 eo zqhn:eling at 0.5c away from a star, at what speed would the starlight paxezg:oz.q;u q4hh-n2 ss you?

The time dilation effect is sometimes expressed as “moving clocks run sl x(*6as9 nhh6tmk0vkjkrppw3e6 z6d(owly.” Actually, this effect has nothing ( 6 kpw p3vjz(s dhxeh66tr09mka6*kn to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes +x1nn jom82 9vjj;xen more slowly in moving reference framesx x8jn9;v 1m+nn 2jjeo or that it only seems to pass more slowly?

A young-looking woman astronaut has justb1a y gzydi8gns)0h4frn3u. , arrived home from a long trip. She rushes up to an ) bn30zi8y,nu 1 fr4adsgy h.gold 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 0.5c, would you no2e8ekn ;r/do/f o /qjolpyg8z4b-:i ttice a change in your heartbeat? Would your mass, height, or 4ertq od /ik-je/plg288o /z;bony:f waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speedshavb.z 0jmd0l7h 5 4zy ,cmjp+, say $90 \, \text{km/h}$?

Suppose the speed of light were ii9asy2mx jc3iu*,u n 4:klo zhvc6 8)lnfinite. What would happen to the relativistic predictions 4 iz:u8)23o9cs uih *lalmjv 6 cky,nxof length contraction and time dilation?

Discuss how our everyday lives would be different if the spenc5b wx l) zmax8d+m//ed of light were onl d//m)+ 8xlzbwmxn5cay $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be use// qss/uh/ya id to indicate that c is the limitinguq y//h s/i/as speed in the universe.

The drawing at the s+67c)v qqfu/2e n;xmm8dmom g tart of this Chapter shows the street as seen by Mr Tompkins, for gv f7/mnmo2 mdcq)8; xqu6e +mwhom 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 ;5ma0 9k nk;pav4 ue inq-cd6nless than c. Does this put an upper limit on the momentum of an electron? If so, what is thqc 9idn enn4;65vpk0 ;-uama kis upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the s4u5uj( fz* kvrrq8t v3peed 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 e ur-hxya2/,lwoco d+3nergy, does this mean that a spring has more mass when compresh 3+r,do loxywcu /-2ased than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed."*lbjkzp cty+h:ke/: 7)mdts3 What must we say instead?kph tle/ czj:mk*3 +d:)7ybts

  Is our intuitive notion that velocities simply add, as we did in Section 35rwj 3qq8,g zobac5s tsp 1r14–8, completely1wac qb5ro4j,8g51ptsrz3qs wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.tjvd-*;6 v4lvjtzs1fv qt 91 7ns5i alh*jw.y2 m. How long would it be when at resvyfl tjvjq 61avj*isld ;t.v-nwh1 zs*459 7tt? $L_0$ =    m

  A certain type of elementary pcb0+vc azmm)x4.ow bo;*p2y tarticle 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 defk2vqc*0la 9dh 3zwb /pend 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-yeary9*kydc a ;jpmety0- lxb*2/y s 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 average lifetime ipkr8;z-fug : us 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 lightd o450w z fo;vjyhs13q-years away. How fast would you have to travel so that to you the dista1q 3 ; wofso0hdvjy54znce would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years awa6btp n.,a4ab4,w w9 fzx chf+yy at a speed that tells you the distance is only 25 light-years. How many years would it take you tp9f y6h, faz+. ba,w x4b4cnwto 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 Earth is 0de x8xw1 ;8ol3ukptb $11.2 \times 10^3 \, \text{m/s}$. 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 jusq n te 4: v--zt3ufx 82xg6ht//kqubnqt returned from a 5-year voyagnx2/qxt e3fg -vk:4un 6t-bz uqtq h8/e while 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 light-years away. Ho1l z bm).ci1r u(rmh).h1aviww long would it take a spacecraft traveling 0.960c to reach that star from E bhui1).vzmrl m.awi r(1c) 1harth, 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 0.660ctx3jh l5zn:qbe;;)3o h2x n gc. It is measured in you n3o2 z)tq:;h;xch xgj 53lenbr 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 travel 15 m bedd.0wbsx)r* rrtwb 8z5 zjog,k b75 /gfore it decays? The average lifeg d*sbdt5 8w0wbr,b.xj 5gz7zr / )rkotime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton k.y ct;o*ae5rqi* f)ltraveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass b m.1eya w)oc,qe twice its rest mass? v =    c

  A particle of rest maboi:dd32 cpcmcfdacc69 +3/d ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle traveljgk xd(2j )l x )4mgaty;1vvrvb; wz4m+03jui 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 prot.k 2(sey3tjsm.jgf2mon that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction require /qt(g5e m;k8(k-*w gcqwvolos $4.82 \times 10^4 \, \text{J}$ 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 g)-9jj q2s ,tzf 2iltcat rest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the proce g 9s-j2lfz,2j)ctqt iss? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy ogtl (pua.2m- df 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 ouj-j ;b,runn, y ;t+c;fzycd8 f a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Statesy+tq,:,,l n3w.t,qkefh g wkq 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 8kb hb4qj/k s-be obtained from conversion 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 ene2-ffpb 1qxzy ,rgy equals its rest energy? v2pbq1f ,yxzf - =    c

  At what speed will an object's kinetic energy be 25% of its rest ener um81uhw;t x316/owwb t lmc9lgy? v =    c

  (a) How much work is required to accelerate a protonh qs0vz 5:9eke0g oii2 from rest up to a speed of 5 2ioqh0e9i0eks :zvg0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of ac rkw8;a v1(w.cgv6im 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 ifc z 3 pke*pg+ p0ait1i84kzy7s, its kinetic energy is 750 MeV)* 3izkg c+ipta40 kp1peyz87f?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MV?j. (eqnh-bf+j v+hj( qenf. b-j =    c

  What is the speed of an electron whose kinetic energy is 1.0ih*cf 57vfk5g-bzpl5 z/oj7 u0 MeV? v =    c

  What is the speed of an electron just before it hits a tele ;d8o6zz;awpigym(6 c vision screen after being accelerated from rest by the 25,000 V of8;(c;d6i z6opg wam yz the picture tube? v =    c

Two identical particles of repha 1p2p wt oc :g-;q61py7oflst 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 ofe8k8elj1t hy2gf i, x* 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 of a))ng.i/t*lxub , pdxqn 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 accelerated to 0.2 kia*u dpvek6djxu2 px4h:hbm/e78 471c.
(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 kinetic3r.c 9raf( mxo energy and momentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleus, :y6 bvl y5uy6a$^{241}\text{Am}$, 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 ofl6egtk29w xp+ugw:ow e. ; )idka,8cz nonzero rest mass, and (b) a particle witk9 liod ekz6e tx .,g:w+gpc aw)u;28wh zero rest mass.

  What magnetic field intensity isz6,/ns(vh p ub needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use th hb6, nszvp/(ue 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 to the Earth) observes 3flk- da6l*n va meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the lv*-f nd6ak 3lmeteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, ea8p( t.lhd ;grpj 2j+z4s 5d8nczjbea ,ch with a speed of 0.50c with respect to (4jel;8ha,c+p28rjsnzdgj5dpt. zb 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 spaceship leav9( : nbvrl ca5 n+2oequln;.zues the first an:z.9qu(52n+a;clb rel n ou vt a speed of 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 ve j/m6va:)zv, euxc t+/ c2)wauo9sohgssel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Belows 2 e9o+gzvcu)v)jamc6ota x h/w,:u /), overtaking the aliens while 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 directiga x:f /(31yl-f3qtx yd+uslsons. One travels at a speed -d y / 3ft(xqyg31slufs+lxa: $v_1 =-0.60c$ 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, rock+ e)gx)qe1pfh,x;f cwqks f 40et B passes Earth moving 0.95c relatigesf)x0 eh+4 f k;1p f,qw)xqcve 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 awao/ )idb t4j+jsy.
(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 callew5kfpgzh/i1x--, 4h*km lm tp d relativistic - i.e., for which the correction using spz*lt mh4f1 k-whgxi 5,p-p/ mkecial 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.( ciy :7rpec-zrq+c;aff t/ fd $v$ 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 mattpoz c,)crnvy9u ,qnein+h9rhh4k42 ;er would have to be totally destroyed to run a 100-W lightbulb for 1 yea p44)coeh+ ,nh2 n; vizhk9r,ycnru9qr? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to producj 9hm;q k4qc d6j:k3kd rmi 56as4y1kte an electron and a positron together? ak563t6hqs r;dk j41i4 ckjk m:yd qm9A positron is a particle with the same rest mass as an electron, 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 .ej2yo r1:y mklight collides head on with a positiveyyom.kj 1: 2er muon traveling at 50% the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, andzu;qfl pae(.xfi) (u / a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles wlxz(iq e).p/a ffu u;(hen a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate ofg2;6jsmd (3 ( nbbyboqt j/j*v 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 n64kzpf lt:xh ,egative 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 r*xki t7eirn +4equired to break a helium nucleus into its constituents, two protox4t+ei*kr7 nins 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 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 travel/thq uf1b 2o d(f,t0e j0,ncdnbpu5j(ing 110 km/h as compared to at rest? [Hint: use the binomqo0d2b, p db1(je05 un/unjfft,(chtial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each haveux(x : gm5() m9 bonpgb2n5eping a speed of 0.935c in the laboratory, are moving toward each other. Detnn (( 5m2 b)o:gm epub59gexpxermine
(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 thatm3r9h: qfr/1abfkqo3y yd 5m 2 a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obw92qi*ar 3o owfb :y5,lum je6tains its power by combining matter and antimatter, achieving complete conversion of mass into wu:5o6m 3f bwrie,lq o9*a 2jyenergy. 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 its kinetic energy is gree8 ba 5.iz6m1a5fdog/ (ui/lunl roh-ater than its rest masso l6 -dmu f(/ bziaruni5eh.o/5l8a1g $m_0c^2$ 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 phy3x pxzor ,/n,*:xojpaxytxn q5,l* 0osics believes that he can fit a 15.0-m-long 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 the idea that wpypx,3xnoatxl , :0q n/*ox5o *x,z jrhen he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen zuxa bfd9+ ib9uv0e, gm 6mb,3and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass u,dfeibavu3bg9,+0m zm x b 69of 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 particles are crebta+y5n d25lc* frk)nated, 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 speel5yan cktn db*5 rf+2)d relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Ea-af 3fves-0g*x zuha 5rth measures his ship to be 25 m lo0a5s ge-h3z a*-fvu fxng. 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 0.85c away from Eartc22ci /iqjw:)/ fja tkh. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for/ jqckf 2jia) c/:tw2i the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The oc-7 r-k u3,v8k eztwss r7mbb,zcupants would like to travel to a star that is 25 lighwrtkzmsv, -3r- kbe7,z8b7 ust-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 spack qkhj 1;7c,mm7 i vz9a4,sl:kp2fhqceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy qj,7 v:2s;mkch4 hkk1 c9alm, zi q7fpconsumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to traveln lsooj -9a.bqqf 4+o8 to the vicinity of a star 6.0 light-years from Earth. o9+. osfl4q ja nq-ob8Passengers 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 the end of a springc:q*uq(o 4gqo z9elu 7 whose spring stiffness constant is( 9qoo7q4euqc lgz :u* $k=48.7 \, \text{N/m}$. 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 mas2v;skd)d hrdj0n *fo.q-m2bxwib*o -s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.