You are in a windowless card7h1)-x1wq7 cun2h q vc1xzrj in an exceptionally smooth train moving at constant velocity. Is there any physical 12c1 djv)xnqhxcqr17 7u hz-w 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 when, out of the co9kx mht3+wdx2v,0j5z fakr w6 rner of your eye, you see the car beside you creep forward. Ikxz 0 mt3x29j kv,wh rwdfa56+nstinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a0ja(cu. hc5eo/i qr y/ heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or beh qu.o5yarc/(j0e ihc /ind it?

Does the Earth really go around the Sun? Or is it also valid1g9fd+8mfv zi3z 6hz:c2zdln to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best rl9zvcdmf6n z82dzh3z g1+fi:eference frame). Explain.

If you were on a spac/2+ p,3.ffhc6 dlr0fg 5jyi oxv3bendeship traveling at 0.5c away from a star, at what speed would the g.di6fhonx0y+rdjb3p 3 l c5vf,/2f estarlight pass you?

The time dilation effect is sometimes expressed as “movibgm;pa xwme;ds mpzt;q6 vf8yw97, )6ng clocks run slowly.” Actually, this effect has nothing to do with motion affecting the )6zm9yf x,; b 7wqv;gm;8peawmtpsd 6functioning of clocks. What then does it deal with?

Does time dilation mean that time actuag t5s n3cf /jffq1 e-lil,m2(olly passes more slowly in moving reference frames ncq1,ff- /s3 imfl5g jlto2( eor that it only seems to pass more slowly?

A young-looking woman astronaut hf9-lu 7 d ci1x(vx5zevas just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this bul95c(vdef -z7 xiv1x e possible?

If you were traveling away fr. fa ejxzoha.a2.gz q/ f4)e-zn 80bcqom Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earthzzqe.nfa 2 /a8ez0-fc jqhg. )ob.xa4 using telescopes say about you?

Do time dilation and l2bhgp70j7 p m*x6bmtj; 0ucajength contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the reqd5 jo2c*q d+0nq0kajlativistic predictio aj5qnoq*q +2kd0 cjd0ns of length contraction and time dilation?

Discuss how our everyday lives would be different i,6bfg *s+tsc70b*oxj.vtwqp8)qhnr f the speed of light were onlyj0bf6 vt+,)soh8.sc bwq gq nr*t*7px $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be usul u-(jw.h1iz1h 2kbf 3/oahced to indicate that c is tzhl(fcw2.i/ uu ah1b3khj1o-he limiting speed in the universe.

The drawing at the start of this Chapter shows the street as q14bu+h zmf.p seen by Mr Tompkins, mqfz+4u.bh1 pfor whom the speed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Does this put an uppw hawldac tz9 k-./ wakl291u)er limit on the momentum of anclk9wh w2t9a)ak / 1.zl wu-da electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of light?tb+,fz(.2qq eh )1jxh mng3zh ----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 thise0uyfn *b,8mgirk3.p mean that a spring has more mass when compressed thuipen f*myb,r 8 3g.0kan when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destrob, qaz0r,-atzyed." What must we say instert- zaa ,z0b,qad?

  Is our intuitive notion that velocities simply add, as we did in Sek.nj 5 7 um a2aqnyrh.ydn:-w-ction 3–8, compley -n75r:wn dya.akqj.u2-mh n tely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to bm*q: 5eb+gjpubmw-lx 9wvv1 9e 28.2 m. How long w9w g51 :+eljpmubx-*v9 wqmbvould it be when at rest? $L_0$ =    m

  A certain type of elementary pa 0vm0qnoe924lk;jh gdrticle 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 intfmz5pjo5)fo; ervals 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 125 light-yearsiudx 7hil u*hvp7.n e+*27dh, r-ri gz 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 gc471cfk ff(zdqo f4/ a pion if its average 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 reference frame, a qwax l 3mf(v7ju5kq gfk+5 2d/star is 82 light-years away. How fast would you have to travel so that fu 257kkf xaq (3+djgwv/lm5qto you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years a 0 ijjk5o94tj- m8kxky3qu+i fway at a speed that tells you the distance is only 25 light-years. How many years wouldj 3ii 5tmjfkukq08xj9+yko4 - 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 tl4 8hr ;:nhmk h(3bepbhe Earth is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

  At what speed $v$ do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.) v =    c

  Suppose a news report stated that starsxz.qvc g i7 9l7vf;+xuhip Enterprise had just returned from a 5-year voyage while traveling at 0x7.uf7; i9q gvl z+vcx.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a m3rvaz(e4sz t .*p8 vxspacecraft traveling 0.960c to reach that star 83zvt(4ap vm. xzsre*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 speed of 0 nud5vaex9cv, s7z-8n .660c. It is measu8d5n9uxcza7e - vn,s vred 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 before it decays? The 9/u reod8 2g(f zy-solc5: hep8r h.cgj74svqaverage lifetime, at rest, is.-scoy8qe( og8vcpz/uhf: l 9d h27 gerj5r s4 $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling a ef:x63o*mbon t $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an obje95v oy / 1q0f/g9avj*akhupq rct’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mass -7 j)qumk9d2 jely .1k edpi2q$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at qp3 cdkjs 5q1c5t- bm), xbci/$v =0.10c$. 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 yhcc)-byb )(cof a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiregy5 8w hasthwa)7)5 mdwlws-*s $4.82 \times 10^4 \, \text{J}$ 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 rea50 g fdw+ pw43:lieeyst breaks apart in the process known as fission in a nuclear reactor, the resulting fragme pl53a4:fdyw g0ee+ wints 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 wbp.igvf;; if74hyl , electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a proton i dijxlzr.)5 z7;/nwnq n $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Statqm)rivg 7+;a les is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained ,epj zc)au u-.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 eneg*f.kyi 3ki9bj0m4hn dso,. hrgy equals its rest energy? obk ki94sihm,.ny 0h3j*f d.gv =    c

  At what speed will an o* 4gwk(*gv:didq9 ouf bject's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from resxd m- hgfupx.5 8nq6h68zfbpjayh;1 (t up to a speed of 0.997cpbnq-p x 1.f6h(fyah 6xdz58um ;hj8 g? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momen1wpeudnr / ezx-o m:6tid1 a;7tum 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 ofbar scu b*-/ n8y73piegp67gq a 750-MeV proton (that is, its kinetic energy is 750 MeVcu rs y87ag/- 6qpep3n7*igbb)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated bye.:6s7-cxs8vkfkr lb a potential difference of 105 MV? v kcxrvsse68 fb.-k:7l =    c

  What is the speed of an electron whose kinetic energy is 1.00 MeVi *0.kskzq sfmar8l70 ? v =    c

  What is the speed of an electron :.:+0wquv4kch ,rnwh ( ej9ie+m jdfojust before it hits a television screen after being accelerated from rest by the 25,0(vw +k:9cmi.jh+ho,qd nuj ef:0e rw400 V of the picture tube? v =    c

Two identical particleysde0(po4 l d),hb .v6 pjrr0v.hyse;s 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 of a proton y2vvyu*f 34suat z j a4nxh/)/($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the mom( c68am7d,tjy.zlj cy entum 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 kg is accelerated tqyvc )c te.o +qj(72iytd.yv: o 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 e*ue-/a-qeddu d v8x e)fp;e+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, s b.z;z3 s+-db 1ar)4mk naeo3:mmdor$^{241}\text{Am}$, 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 pa.*mq ik71yvh l1v3 ywtrticle of nonzero wt.7* 3y q lmyvk1vi1hrest mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 9d7zx* nx.az.yqaq .w)qg itq v8i+ (f(98-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The pro iwngy+dti q)z xxa. 8.va*z(7q(qqf. ton'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 ,rtx uniz . we87k79fla meteor come from behind and pass her at a speed she measures as 0.50c. How fast is thernlutxk9z 8,e7w.fi 7 meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite dire)us t jit4(f0edw9fw (ctions, each with a speed of 0.50c with respecttww4s9() 0dje ff( uti 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 spaceship leatex/:o1vpkgp7,hz. cs e f8b;v , 8swgves the first at a sp/e8kgtshz :bpfso 8,x7p ewc .gv,1v;eed 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 1e( l ;tqobzroa;8v;y a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a spebvoelr1;;8 o ;(yat zqed 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 div wkk)emg1 ld4*- m-kfrections. One trlem-)k1w4-m*f gkv dk avels 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 0.75crl)457jxm51t ayj vuu. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction.t5uy )7 5xm1avlurj j4 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 tf+ttsr5)/r(pt5vap 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.ujh5w,lgh4or zm11 y*;-pyu6* ogfi g 1c is called relativistic - i.e., for which the correction using special relativityjwy 1u*igfu;z5h* m ,rgp4logo1 h6y- 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 spee2h r;jh2qya w*-vz2 1 kxj 82mqvxmc72z3kpxvd $v$ 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 rubcdb+o/t; qfcs .6tx znjt)4 6n a 100-W lightbuld )t6f. qc6;cst4nxozj+/btb b for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to prod;u6ysh07md *c:eaqv euce 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 cocv ehqs 7*yum;6:0deanserved 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 collid 96,2tj*v/;kq ,cd y1jws x9bpgy. azhosv4ares head on with a positive muon traveling at 50% the speed of light. The two muons (each of rej629ts1c,9,.gwavy vpskb/ y*zr; ax o qd hj4st 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 .syph nvux*g 1pk reis ,46hgq,k(k9.a neutrino. Assume the neutrino's rest mass is zero, and the other masser1h(iqukg 96,p.x,. y s4 hnkp g*kvses 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. KE =    MeV

  The Sun radiates ener4 35hwf69x;sid h2td;uke,zldu w+h8y6 g hbogy 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 7jjk x,b3hdb lxp59l r2cyu:occ; (7va 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 nc/gsdm jk8g um4s6qu)ev0 85lucleus into its constituents, two 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 differesce sk m4l8vuj)uq 06m8/ggd5 nce is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage iw+r:qcexr:nd d 8,/ggk *ef7x09r hnnncrease in the (relativistic) mass of a car traveling 110 kmx8 nn+r x,:rnd7h c*/eke : fwrg9g0dq/h as compared to at 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 laboratory, are emgn ):i, ujb:moving toward each other. :ej ,b g:umni)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 a particle with momentu4 t83b y+tn sq83qp/cfs5ozqmi g3 tq6m $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its ycw xi /dz*:0o ljx);wpower by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is apx) lwjx:iczy*/ ;0wodproximately $5 \times 10^9 \, \text{kg}$, 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 kine 54nf.9sujk nz fxaq,66zsh7fh7tm9etic energy is greater than its rest mah., sz9s6ft6hq7a4fnmu 9n7jx fz ke5ss $m_0c^2$ 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 i34q do:6 qqfsbelieves 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)q s 36qoi:qfd4. 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 osp; sih9p;g+w iq5ii +f oxygen react to form two moles of water, the energy released is 484 kJ. How muchpis;i;sqp+ + h 5i9iwg does the mass of 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 created, travelingvr8f isk3p99 utn k/-a in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory k sfp /i 9at38nku-r9vframe 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 measuredo02s e e 1b90;jpu*yx+fdnh ks his ship to be 25 m long. On the shi0subky;2fnee0*d jhp +o 1x9 dp, 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 spaceshh 7anneq -ikvp 2w2xr +qop0-r;q i)e/ip at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c r x;qvewqirpn)2-7i0hrp-o/+eq 2kn aelative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occup6k8yr0m: vmo rants 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 speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted tm y08or:6mrkv o 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 zup-b8pcqzu s715l7;t 7uzkc left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare z-c87z1;z pul7 cus75 uqpbktwith the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a star 6.0 l72dryks0 l /.tkm3ggh ight-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 0sh.k3ykg/t d 7 rg2mlspaceship 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 stiffness,qu kp 1/hjpv+i1ly1 u constant is1jpp 1y v/u klh+i,q1u $k=48.7 \, \text{N/m}$. 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 ma,8ver*bx yw t80m) tyjss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.