You are in a windowless car in an exceptionally smooth train movicwqaz; (;fp 4 dqgn8)ong at constant velocity. Is there any physical expn ;owcag (;8) zdpqq4feriment 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 light9vi)g. t*,sr /b v0dkrs:osbo when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brs*0o.bs, i ktsvg /9db:ro)rvake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving enu ozin ,f pj/is(: t068r)/gmwois( ,yr*gp railroad car, and throws a heavy ball straight up (from hn/gmgfe,iu)n it,: 8pwoo/s( pjr0y siz*r6( is point 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 also valid to say t8jker xo9)z 1what the Sun goes around the Earth? Discuss w)ezjox 8r1k9 in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away fromq5.9/b) y/6n ,q5ijbvgm vuk lmad-e v a star, at what speed would the sta)g-v 6n/ m j5,bi/v.eyuqbkvl5d am9qrlight pass you?

The time dilation effectdddlp to45n+f xv hqwb) 4x+v5c(8*cl is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal witw 4dvlt+qxn54v h f58 d(clop)*+d cbxh?

Does time dilation mean that time actually passes more slowly in moving referen-q,p. cmgyox*ce frames or that c,- xgpym.*qo it only seems to pass more slowly?

A young-looking woman astronnc rh)if(j *w/aut has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to h)cwr f/h *ijn(im as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a chgt2m v 8hbfe 1z9lcljp56b .v4ange in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using vb 8vtb12.j64 fc pz9lhg5m letelescopes say about you?

Do time dilation and lenstvy8 nw3rnib9sug)0 b*t-w)gth contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. fj 8 )snlwf t-6vd/b/jWhat would happen to the relativistic predictions of f v/lwdb )8t-nsj6/jflength contraction and time dilation?

Discuss how our everyday lives would be different if the sp4;xpdydzgtxnyn * 0c518h 7r feed of light were onl 47xf zcty ryg 8;n*dp10n5xdhy $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas mi0rvnv; 20t4)s f dibtight be used to i2tsdr b ;v0it)i0 fvn4ndicate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as +3 ,q)0joktt6gpi/ 9j8 fu lthp6gideseen by Mr Tompkins, for whom the speed of lighd6g,p +tg0pjujhtoi3if)6 9t eq8l/kt 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 this put an upper l:+) 93cggq n6cmym yvva 2+yq,ry xt2ximit on the momentum of an electron? If so, what is this upper limit? If not, ea:yq,yyx trmxvq2m ncy c6g+v+ )2g39xplain. ----待选择----yesno 

  Can a particle of nonzero rest mass attaov:xqzt x w;l72e:;hj in 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 this mean that 3,e0 f oaaxxr 5+yatv;e er*z7a spring has more mass when compressed than ta3 *r e ,yxraxez aeof705;+vwhen relaxed? ----待选择----yesno 

It is not correct to say th om,,u5ld5.cvsbjz5q -bif5rat "matter can neither be created nor destroyed." What must ir,, sd5u5q ojblv5zf5-bm. cwe say instead?

  Is our intuitive notion that veloc:kf(r lv bd;v q8(.xhmities simply add, as we did in Section 3–8, completel ; fx(.b8vvrl:(dqmkhy wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure iq7 f qz1r5gi9,x9 qumxts length to be 28.2 m. How g r 75zq1,99xqxufm qilong would it be when at rest? $L_0$ =    m

  A certain type of elementary pap,mr kl3vf o:k3:r r*hrticle 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 inter/hpfwjc,92th 6yv -9 agde r1yvals 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 1hmm,/hds: st-,z6s ck25 light-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 average lifetime is n .jh6mcq778na suv (qmeasured 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 fast would .,hik1),td96* oy ip y ozoc2 ioajti,qd: n;zyou have to travel so that to you .t2ciiqz*aoi9)i o;, pd6kn,hyo jz, t yod1: the distance would be only 35 light-years? v =    c

  Suppose you decide to tro )uuzle fd-rs*(2*j qvx1c0t)y xg2savel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many yeaqs ou(*tv*)j2c xxrugs0ylz)1-f 2edrs 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 Earth imx022olr sou zxv4*w+8t*bils $11.2 \times 10^3 \, \text{m/s}$. 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 jr e9i8 /t 46g*ledj5d6bixaqx 5g6qg pust returned from a 5-year voyage while trave6x j/5a5lb4xiqi*66gdpegqr 9 gtd 8eling 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 w d2l07/kh7w bf5 kad0lchwe6 uould it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observbkhwu75/cd le6w00dkfh la27ers:
(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 "2n6mm58rnj +f , jx swdxizrooyv2 19syr:1 u.Ferrari" spacecraft at a speed of 0.660c. It is measured1x rmi.osyd:z2,2 1fv rnnjy68uws 9jxor+ m5 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 travel 15 m be)2 *7+dr1nip/ ttb.i1zvzkkp d bn.mpfore it decays? The averaz+b kni1r pnpm.vd./)z21 dpt *b7tikge lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a prot6c,63 n)nlw2dfyc( mgqeo n3jon traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its6ugpvx. oh6( g rest mass? v =    c

  A particle of rest mo7qsx2y2 kdj/7ct p.iass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave bt jgta0is0db4h-,. jls 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 acceleratem49n.xy s 6wnjr8od:us
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requireel*be 0 xlb*;ts $4.82 \times 10^4 \, \text{J}$ 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 nucleut0n.*t8 hxla us at rest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of l*8. tx ht0unaabout 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electro 9dicb 4c ewxdrm)66.cn 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 proto1roiawobsp4 9 ta-(j,n in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Sq*i 5e 0pr+7hrrgv8 ertates 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 obtk rl 5h+qv*nji -ajdods6 xe u1f60p1(ained 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 particln-n*1qenh6jnnp)v k7.hx hl2 e when its kinetic energy equals its rest energy? v n6 hn7nv1.*ehqnl 2kjh-)x n p=    c

  At what speed will an object's kinetic eners0khv h64csf3 jowu9d7 o 2;rrgy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a speed of ty*xt)li *8miz- dex+yk 8t9(:amb ypmxd *-i) ypa:* +98et8b zytmylxt( ki0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic enegi5olos59y5 l rgy 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+gw2 zz 0hqd iw 2vpv4u*(idn; a 750-MeV proton (that is, its kinetic energy is 750 MeV)? 0w zhq*gv vd4i+2p( nzi;2udw    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential dif bs6x/k* h7 q4ktbw2mt(j:cvzjtq .m- ference of 105 MV? v t* x:4q bsh t(-bzcj2q .mwmt k6v7j/k=    c

  What is the speed of an electron whoseo2i7kz dc o64skzw9h6 kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a telev; k7(xr;iy vqmision screen after being accelerated frox v ki;;7yq(mrm rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rese vnvz;;m7ybx6)g) rv -u9sgm t 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 proton h*pa0c(rrm 2d ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momen.,q ssp4h ac+ yp1lpl5tum 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 kt3a kr2ya0 wm,g is 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 enerrj;lzqors-)0l +21erjiuvd9 gy 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;8q( m6k.4ty hugxzx o, $^{241}\text{Am}$, 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 versuppnzy.kkaysq s w8lw161f ;y; vc. u78u8b4ows momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest mass..y s7pufvzk 16qo 84kl c8 a b8uwysp.1nw;yw;

  What magnetic field intensity is needed to keep:c:beblg,r uvx(-f ;0ek g0d i 998-GeV protons revolving in a circle of radius 1.0 km (at g0rf (v:gb i,dbk-0e:e;lc xu, 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 traveling at 0.50c (with respect to the Earth) ook2,k y4beowmcui 4yc.b-g6 ; bserves a meteor come from bebo uwcbciy yok m -kge;4,624.hind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in oppoz8v ij5vsu.);p dmb1nsite directions, each with a speed of 0.50c with respect im85.s)p vzjd1nv;bu 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 spaceshipp4sb2xq2dej*hk;vbab rt h; 82(p jk1 leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship q( pj21 ;bt;*v2jbh4 raeb kh8xsk2dpwith 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 0.60bbp)n 8lmjly nj7+)1z c. 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. jp )8lzly+nb)b 71mjnWhat 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.qxv xkw1el5 q bg)2r91 One traqwb15q1)xlvrek2 g9 xvels 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 s wc*w3 -jdome9ame time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B dm-w*oej 3wc 9moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 li qw7l1ohkf) ,y*1yee jght-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 f,d.f. di5tp25flyu hvnu o -g/aster than about 0.1c is called relativistic - i.e., for which the correction using specip./dohu-, tyvdf. 25g uif 5nlal 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 c-j.x0 cum2exf sa4)w$v$ 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 matterssbr r)rv)i,, q(l+xdujjzk2b +im.( would have to be totally destroyed to run a 100-W lightbul+rr msd,( lbv,2 z)sbi(j)i qj xk+ru.b for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produqlmzna rvyg pp9.(shg4w6 k1g07e.n9 ce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note z6sn. lygepkhw7a 9pq40.1(rgng9mv 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 :5gq e-rfq-gu;;e zou collides head on with a positive muon traveling at 50% the speed of lige ;f;u -z:5-rqequg goht. 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, and a neutrid*,ex,f8 3ka4q f+g /o kfeodxno. Assume the neutrino's rest mass is zero, and the other masses can be k8,+ xdg4ofeadf3qk/ *, exof found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates eneox m7vjhd bq;c8(0nrj a on(s: 5628jr l-plwtrgy at a rate 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 to have a negative r5l5;pwwng kefqp64( 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 constituemn1agv-7r q:4 k+wvjcnts, twa+gcmvv4rk7 :- nq1jwo protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage incresnra2i.hc7w: ,im n,a ase in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomian7 im cr.,,w:niahs2al expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in tf9ehztx61z b+;fk ,n yhe laboratory, are moving toward each other. Determinefzz,tk9 ;e1+ y h6nbfx
(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 wf1zgum1-e m 6m( q+ebxith momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprigc1v-ku e(+ ziy1 wo2gse obtains its power by combining matter and antimatte( yv-giu1g1k 2e+cowz r, achieving complete conversion 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 its kinetic energy is greater than itus u-t+ol :0;dmdh:fos rest mass:l udm+o-:t ;fsh duo0 $m_0c^2$ 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 15.0qhy s y)tjw1b086jb- u-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). -tywb ) q jsbh60yu18jCan 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 oxyge9pqs /b0 mgms2c/)u cyn react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements dmcu/smq s02 /9p)cybgecrease 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 identicamvr5 8 swtng6ygs,7 p9l particles are created, traveling in opposite directions. If the speed of each particle is 0.7576ss9 mwnyvpg g, t85rc, relative 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 0.75c relative to Earth measures hi3x(9.a+ k. qekafdnd.hs7 k kns ship to be ..n3dfak9q .ah+ (dnk7x kks e25 m long. On the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed5lkw ;1muo6pswbj.t6 of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. b6pjmls 5t;k6o1wwu . What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupantsy-i:d4(rpo5n ol t9jv have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speejn:oldpty i-(4o 9r5vd 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 azhyq(907onoi t a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual enehzo9y7i0no( q rgy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to trat vvz e8d/ d8ub(wup;2vel 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 done on the spacese8u2vvtp8w bd;( d uz/hip to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whohqg73.mgx a qq1b5- hose spring stiffness constant is 3h -7ga 1mh.o5gqbqq x$k=48.7 \, \text{N/m}$. 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 mj* u ccxb/xy;7r d ys8dti+h((3, yegoass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.