You are in a windowletqij c7.8+f 9j fe(i8-tgrb xjf bg-0xss car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determ xbjj r-(c-fgt.89fgi7ifx08tje q b+ine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of tho+ow2)( ypeu7bap xg3ja9 ) tke corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you areojaox kp tgb9) yu(pe)2+a7w3 rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and 0gf8oz2)pl 1ereyzo b:5a.vpthrows a heavy ball straight up (from his point of view). Igbr .gfp eyo) l8e 1pz05o:2zavnoring 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 that the a3 a;8o,m/xayg1taseSun goes around theaaxoma,38;sa /gt e1y Earth? Discuss 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 from a s k7kz 6d+gr7ihiw gs(7nv(c9jtar, at what speed would the starlightn7i6 kigh( (9 wk zsv7g7+jrdc pass you?

The time dilation effe*,px:5xa df m;ak;y lqct 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;d*a;xylfpx , a:qkm5 it deal with?

Does time dilation mean that tm;q,v7t c0dtt6zt; + b*v uxkdime actually passes more slowly in moving reference framvt d0tdu;*vtm t6 xzkb,;7+q ces or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a w vcbug9+17fx.eb .pe long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him .b.7gv+ u 9ee wcfp1xbas her son. How might this be possible?

If you were traveling away from ) 17v8ynm*ie-e y:xuosh4l urEarth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, heightx)hvouye ms7u*y - eli8 n:4r1, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeoojxo;4l71zs. n zd8zxpp7b-q-mr *f ds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. Wha9 hiw7ric3q0-xrnuf, t would happen to the relativistic predictions of length contraw ixfnqr rcu30-,7 9ihction and time dilation?

Discuss how our everyday lives 8cqly o5xd8q vj2l0s/z3jph4 would be different if the speed of light were onlq j 8lvlj/qpo d82c4zxy3 h50sy $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas mswr89l37lqpi q: x6sx4ko0vl pxkly7 vpa8 (, ight be used to indop8a03 vswrxk,97pxqls7 (8 lqpyxvkl 4li 6: icate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mra)w+9vud bi ;.orr ,jq.ybz +q Tompkins, for whom th oru;+,dywq i)zqbbra+jv.9 . e 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 this put as: 7gt g3z lp5f24tqxin upper limit on the motz:g4t 5 fil7x2q3spg mentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonze w (vxik,kazr9db0fw 4; .ue,sro 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 this meansqoru02aru)m r6t 1h4 r:zu w+ that a spring has more mass when compressed tha2 trh)umzr uo64aur01rw+q :sn when relaxed? ----待选择----yesno 

It is not correct to sa 8lg(k+1lr- hc3 nefb*loyxf4y that "matter can neither be created nor destroyed." What must we1 ylnl4g3hbo kf+r-lxef*( 8c say instead?

  Is our intuitive notion that velocities simply add, as we did in Section 3–8, cfbie 2 j0rll+)ompletel le+ijlf) 2r0by wrong? ----待选择----yesno 

  A spaceship passes you e5,*r nhsy u1xrl9i rdu07hd-- g dc:lat a speed of 0.750c. You measure its length to be 28.2 m.*dg: ylh 9rs 7id0hce -n, -u5xrrldu1 How long would it be when at rest? $L_0$ =    m

  A certain type of elementary partip,rvy z. pyrngv :/f72ch( :nvh)v2tecle 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 th,1ahafd9*y d l1lss rd 068blwe factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from Earth at a speedlnz wiv(2u/.t5:gk iypra9 r + 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 ii2tzq,tzn 9k6j hpo,m+e4v (n8l : zkrxbw v:0s measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light-years away. How fast n/7.ig8+nfho5 2hze umoa* lpwould you have to travel so that to you the distance would be only i 5f ph8a/zo h*n+egm7u n2.lo35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years a9eqpytp +tbk z6 p7;(vway at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the kt6+;ze7 yvpqpb(pt9trip? 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 Eari9 m-b(: tgp0fbv;serd z2* pmth 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 t*hda0lda )fz wzh227 kz /d2zrhat starship Enterprise had just returned from a 5-year voyage while traveling ath z2l0zdwh*2 ar7dd/ 2fzk)az 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 id;5fan 7*81 zunm )ubfjhvw2st take a spacecraft traveling 0.960c to reasz af8;71u dj25whu) n*nbmfvch 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 inq51w0/8 5vcvb 1ak1/5o kgtu pcalchi her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. cvic1vg1w 5tqupl 0k8 /a5b c5hako/1
(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 before it fbc7*y-ygqqt ;cvy8r-d2 5q j e05 cx)*upind decays? The averaggy;0u*cy-qcb i7 d dj5)8- q2ytpqce5 xrf*n ve lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trau35uaj --xdd-ds l1 yqveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twlk di7mtnk.q)seq 9v7(g n7-uice its rest mass? v =    c

  A particle of rest mass n9934wpg * tqcjqtr jhlq3(d*$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at 1 k )scbo nsf6*q0su+i c((gx/omhi s($v =0.10c$. 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 accele7:kv(e-37a lg xhaasr rates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction re rfzz,og n/ :ynbr+ :chhm02v89re-yb quires $4.82 \times 10^4 \, \text{J}$ 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 b;dzp2/fq3egf2)rv c known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of abouczdbe )ffvg/ 3 2r;qp2t 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electr;zq kv 6v;*:ecp 4npp1eq;apih )/zmlon 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 protc53cyct+) q zxon in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is af8 x7; qzhx(t4 wxq,iobout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversionlv4hj8inyu+y0eur 07 x8re 3j 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 equals its r w16 xkmtix x.j7s3 p*v(hn(i9it mah8ca7fz5est energy? 5.i(tz (hx 87jin7 1h3* vxf6pxkwa maitcsm 9v =    c

  At what speed will an object's k;9 : xcklkap3iinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a .-qz;fy m xt cwu9srqhf5gaf v897+eee+ zi04 proton from rest up to a speed of 0.997c? W7g;+ 5qfeiq0yzv 9hf9x. mf4e - tzr8ewuas c+ =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy an i1l i/xyc55tfd 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 p yllhds se03w8l758qqroton (that is, its kinetic energy is 750 MeV8l3 qlqle ss7hd80yw5)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proto6fpi szpel h2*jjg2 ;-n accelerated by a potential difference of 105 MV? v e2pfzij*h s-plj2;6g=    c

  What is the speed of an electron whoseq;9uev3:ppxivru/ ,,km yy y1 kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just befo5mnmg8 8crxxi5o7 ze/re it hits a television screen after being accelerated from rest by the 25,000 V of the picture tube? v nx5emiz78/ xc8 5mgor =    c

Two identical particles o +ts7bkg9si v2f 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 pm*c 4po,,n/umtls sn9x m6xvg9gi*c l+-s *lof 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 ydy3rsc/,.(ekh6xcel ::sf 9 tijn )lan 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 mcfibk 1m/ 5j/cass 27,000 kg 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 energy and momentumf 6 :eurtb3r5q 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 nucleu:i3 s3cta i+g/br2ul jiik:6qs, $^{241}\text{Am}$, 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 particledzbxytg-598 n of nonzero rest mass, and (b) a patxbdy8 -5 9zgnrticle with zero rest mass.

  What magnetic field intensity is needed to keep 67vh4daqvsv u9 ayabqq)0(l 9 998-GeV protons revolving in a c6 ya 0q4qva) dhul9b7a9svvq (ircle of radius 1.0 km (at, 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) observ,uv5jl f)n x3g (cmhmql ,x+.2wyun:ees a meteor come xf:mjgm+u,vl)( nl,3nxy5hu 2cw.e qfrom behind 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 npg/,rnj0ybb) j)mjx4/mp/d Earth in opposite directions, each with a speed of 0.50c with xm)) d bpmnjbgjjp/r// 04y,nrespect 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 sxr otui.:t.e (3qc.anpaceship leaves the first at a sp n:.3ur(t.qa .eitcxoeed 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 vessel approach at a speed of 0.60c. Theuj4iblcg a z634kg4w ::h)n mb Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. Whatbh6 4ic : z4 bj:ulgmgw4na3)k is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress seznlysnmj ip;c(-+d)2z 7j k ;inds out two escape pods in opposite directions. One travels-dni2 lj;(p);+z msj7c ynzik 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 timewuw835 g qtanf ki*2a:, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relatu:t3 f85kwa i 2awgq*nive to A when it passes A? u' =    c

  The nearest star to Earthbhs cm6 02x1nvu /yfnfp 47)it is Proxima 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 abouw s,utad2ct)ozo-lh8b mqx.0c -nj *4t 0.1c is called relativistic - 4d- c.*8z)o-wlnjx,2aqs c utoh0 tmbi.e., for which the correction 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 speep yafuc k-o d a0uz3..9g46xcyd $v$ 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 vcr:x.. itjt v547srs 100-W lightbt5rc. x sir .:v4sjvt7ulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is neede/2- zts8suige v0bik (heij).d to produce 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 that electric charge is conservedgei viu8h e sb2 j.-stz/i)(k0 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 speed29zvo 6dtj i q,c;9tmu of light collides head on with a positive muon traveling at 50% the speed of light. Tttzji69 m2o; , vuqd9che 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 proton2wvx0g- akv 4rb4*jxt, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared abg jxv2 wrv-40 x4ta*kmong the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of aboutss ;wg( + ;,pwzgxc*j( mtwuq,k(v w-d $4 \times 10^{26} \, \text{W}$.
(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 a speevntfr ,xu1ih8 ic.f*xif hh3vd;g:0;d 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 nucla8x 3kk* ) scimj cmfyp91p,b8eus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respb1m)k amjk s, 89*8 cp3cfipxyectively, 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) m:x,wu;mt kq8 hass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial k;:u,8x w htmqexpansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving toward w0 p 3(m84z bbzji::ym at;seyeach other. Demeyw(8stzb0pzb:m34 ia : ;yjtermine
(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 q(9kbksia: a 7a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its -fgt n9kts 7,hc8x*d bpower by combining matter and antimatter, nxtg dst k78 ,h-*fbc9achieving 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 thanopsk t nsq96-8 its rest mass 9psqt n-6k8o s$m_0c^2$ 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 poymwr85+ /)nkfgxu: g1zz8awl le into a 12.0-m-long barn if he runs fast enough (carrying mfg 1 )+ nyw/l rkax5:8zgw8uzthe 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 p6 5yld7dme7my(;g yfmoles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this rea7y ypm;g675(lm ydfd ection?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
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 created, traveling h* lx)ln (1xhbin opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative thlnb*1x xh ()lo the other particle? u =    c

  An astronaut on a spaceship traveling hg6ht0kb( f 3paivo;8at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch i tv6h( 0aib8f pk;go3hn 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 Earth.(n8am /)7osj- x5ld ue/kvrhf You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on )avl 5/-omjrhdxs (kfn8e/ 7 uthe Earth measure for the speed of the laser beam?

  A spaceship and its ocnkg;xpq e1h9u - 5oa5ccupants have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away atqo;-xk95h5u1ne pgca 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 is the spac )2x0+/gyq qhg mu 5;hqnfy 4,9yqhleneship's kinetic energy? Compare with ;9uyy)n2gh gqn h meyxq0,qh4/lf +5 qthe 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 vici :qk 6oxa f7ejbgq4v*3nity of a star 6.0 light-years from Eav:*7oaqfg4k3 6jqexb rth. 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 the enq2lj 0buo3 8vbf a2y8yd of a spring whose spring stiffness constant30jyufl88y 22 aboqbv 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 masq3 z3 :1lx5gp bj7oaiivf/,lds $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.