You are in a windowless car in an e5ygoeayfd l , rxw6y)4;cd-hj2 p+tv ,xceptionally smooth train moving at constant velocity. Is,- ct l;vy6 japx5h, +fdgye2r4wody) there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experz8mcb:a c8gf:7j)iy p ,olhw-ience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Insy):8mpla,z-igjwbf h c:c7o 8tinctively 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 a heavy ball snopvl 4v+mf* 04my,jhe ;zzb,traight up (from his point of view)jv,vbf+,ym404*m lz e;h oz pn. 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 that the Sunj - c :yiee63sk1cx vtb4858efy bl1uw goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame).xcyj64 8kfbi lb tcu 3-s511:eew8y ev Explain.

If you were on a spaceship traveling at 0.5c away fromlsrk4 rrq-uii,g7yspeon9 *o*)b z0, a star, at what speed would the starlight pass you? bi*u,s9rskgyez*l o,pro q 07 -4n)ir

The time dilation effect is sometimes expressed as qvd4r(qo +a96iu fpq h0)jqus br:h/ef3j1 u ;“moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does u1o 49/ru0(ehavuqfr)ij:qf3 +s 6 p ;qdhjqb it deal with?

Does time dilation mean noj:i*xo; i n;that time actually passes more slowly in moving reference frames or that it only seems to pass mor;ij;o:*ixnno e slowly?

A young-looking woman astronaut has just as4xt 4jmv6/fj )nihmd r04+j srrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing co4j)/vrs44fmjjn0+xhmsd t6 inversation refers to him as her son. How might this be possible?

If you were traveling aw mqnn20mp1q3gbyv ).wg. nky 5*3c pclay from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes k*g2 5n3n0vlgqm.m pwqcbypy 3) n.c1say about you?

Do time dilation and length c2 xv abw8 5k9k52pwu hizvd4l1d8jes ,ontraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. ih5e* ltoh4okqawy 8341 )j1jj k u/jnWhat would happen to the relativistic predictions of length contraction and time diaw *n4t5ei4oh q) u1 j8ljy ojk/h31jklation?

Discuss how our everyday lives would be different if the speed of light werfl ,krn7l76 r yob)gzqazqrarjz155n+3 / ,ef e onl 6f1zq5ln7or )af qegrjr5n bkzz+7rl, y 3,/ay $25 \, \text{m/s}$.

Explain how the length contraction and 6ns*x2 fs wqob3v(pzr d 5,vh7time dilation formulas might be used to indicate that c is the limiting speed75h6f,vv r poq(d*zsb3sxnw2 in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tj4 xjj3al-tr/c nxu.kw,dfk)dh2)/sompkins, for whom the sj))x/ dl4ru/afn hjks, tx-w j .2kd3cpeed 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 atn yqmb2b02jop pm.0jfd(- vn/ speeds less than c. Does this put an upper limit on th2m p(0d 2n v.q-/jf0mpbybnoje momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass at; 9mxinnopw5.gas 7e,tain 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 thism(o61 xl jji,e .42y en9 31 w/rgbrxvyrqrj*x mean that a spring has more mass when compresse6ei ryx*w j1x9e(ln 3jqorj yr/rbx2vg, m4 1.d than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." Wgdx- 7xn(cdpjp ae3j:,;tyk+ hat must we say ins+a:dj3 ndjyt ,p xpcx7(-g;ketead?

  Is our intuitive notion that velocities simply add, as we did i1wosjjicoj( s7t3c/a r+ ru).n Section 3–8, complete 7. ( 1awj)t+ur3 sjosc/icjroly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its j -w/h*q5ldg wsq;*jnlength to be 28.2 m. How long w*w*sd5n-qjl; wgqh/j ould it be when at rest? $L_0$ =    m

  A certain type of elementary particle/qn16sr 4ja camp tdog( ),6wn 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 iv.xdsq)5szn(z vod9fk q5 62hdy 6b 4on 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-yenzy2:ke f dez, 3foq/:ars 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 measu5pa3;,dld*yz*dde u 7xzd/ o ored 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 lightbv/felo 6,*l u-years away. How fast would you have to travel so that to you the distance would lol,6v eu b/*fbe only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a s):6aa rjl1ps rsj(vk8peed that tells you the distance is only 25 light-years8l6ka)aj :spr ( vs1jr. How many years would it take you to make the trip? t =    y

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

  Escape velocity from ti k .k*qac4gm (c6wdyggs28re52 i/s ahe 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 sta3 5wf)5 +w*6zcy2upnxy qrdau rship Enterprise had just returned from a 5-year voyage+w 2y 5uu5wdzy3 fpxn6cr qa*) 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. 3tp/j 4ofu8h :d2.q6kc arvbbuq y ,x;How long would it take a spacecraft traveling 0.960c to reach bo axtyuc k6q42,ju f8b.r; dh/:qp3vthat star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecraft at r4 2+.q9(y*ep xm*kble jkxj qxx6ke2( uyfd2a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.yx+uex mek2(.jyqqfek 2 2l br*p*6 x(4dxj9k25 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 1cl2 yeing m8m+h4kw,8gmv74k g; nj6 a5 m before it decays? The averag kn+vm 84mhyw 8 aelm6cgjig47nk,;2ge lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a tk6 kt71uov; 2 ;hlgrx0fl5:oivqf ( fproton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will anh yt(5 + avyp gykix;qlv/;72h object’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mass 7 ik2fbr,4cp.uyowuk-9m8 je $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels i18 gq2:o fxj/gbgy6a 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 protr:t0tgz ji(edi 32w3 7p6o kma su.h(ton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires+9(eww pd9m 85 *fchq0fszehb $4.82 \times 10^4 \, \text{J}$ 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 tn.jzupox,f3sag+gm) p3is i,- t42: 4vwkn t breaks apart in the process known as fission in a ij k,smo g4:wg) vpn a.4zstif3u+nt x23-t,pnuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electrob 8cy-jp2x.d8ur:bnfn 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 xe7grp6 s57 sp3 q1euva proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy c;nc h76a47gyfmbr ;yi onsumption in the United States 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 fromi74.due8yuakfi8hf-hw .ss qf 0k .+k 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 energy equals its respvqy-w-jb w*s:(j (u ct energy? vp jy(b:qju(v* -csww- =    c

  At what speed will an object'urqg:o-vm )chx,c )t:cq2sv (s kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest u3a;us9 :m7eoc-ch y lmp to a speed of 0.997c? W = yc:hlauc -79;es3 mo m   GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic en1hs*qzm9 i q(sergy 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 a 750-MeV proton (that is, its kinetic energqqh3jr9jy91hp29 x( : lvpo oey is 750 MeV l r op1v29j3y 9oeqx:hjphq9()?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differenc( r (glcf/(mwoe of 105 MV? v (w( r /lm(gfoc=    c

  What is the speed of an electron whose kinetic energyg19yap mxvql/ 78 w5ip is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen after bu5ws(a7t tv c :wd.cchg82 xu:einug:tccau(c 87t:wwxd2hv .5sg accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of restej8,i .xb8xnt 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 p 0k (f,(muoyu5t;e zo0aztw) froton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momenkt* u, txv:y:ltum 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 27md q f0ao+6b,z*tnl w-,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 momw v2b xp8z6us,entum 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,k*qkwrs. qk9: $^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

  An electron ($m_0 =9.11 \times 10^{-31} \, \text{kg}$) is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.60 \times 10^{-14} \, \text{J}$. Determine the electron's speed $v$. v =    c

Make a graph of the kinetic energy versus momentum for (a) a particle of nonzevp+ 2d6esd.e zro rest mass, and (bp6see.z 2vd+d) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolvi+ 07w jz0ydp5dgibxc7ng in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's res705w7xz gjdpyci0 +bd t 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 Ejogb1 nvx2qgo j9u,9: arth) observes a meteor come from behind and pass her at a speed she measures as 0.5:2 uo bqvg,j1jgxon99 0c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speedp h-zthopt/z0fu+:b)eeng ,ka 57 k x:o r/w-d of 0.50c with respect to Earth hnp xd egu5z foea0tpk:7k,-t - o/zh+r/)b:w.
(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 ,ranpz1 *c;jcrad o3;0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the r3 a ;p,a;1co*zcnrjd 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 ali(x*2 jqjf /lamen vessel approach at a speed of 0.60c. 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. /(m*qaflx2j j 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 direwkyihb6c;-yx ;v p ,e+ctions. One trb6kxw;ypv,+ ei;h -ycavels 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 time, rockg huiv5z9)z7 get B passes Earth moving 0.9gz95i7uv)gh z 5c relative 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 Proximagilf wit6n k ud 9djrks:d8m7r:g+gg..v77 6f 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 about 0.1c is called relao+or8 9lpdwg:00xdef tivistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of a980xpgl wdrod fo:0+en 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 speedl p3vjw25dtno2 ;5g cxhr5* xy $v$ 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 havwm 3hs* i/ 1;t2l)qcaix8mrade to be totally destroyed to run a 100-W lightbulb for 1 year?laimqs w* cdam/)hi81;rtx3 2 $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an elecwpr rw( ,qxnk.. p25eitron 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 xw5.ek( pqp .rr,win2charge 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 co (tmx2r n6w.bvllides head on with a positive muon traveling at 50% the speed of2.(n6wv t xmbr 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-yf 1fsew8 ew4, and a neutrino. Assume the neutrino'f-f1ewys48 ews rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate m g0qp(gf*btnm5+n0h 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 charge and a s0dhu, 1it u468ubchiuj0bk b; peed 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 he5o2yx.x, bgukp .qyt5lium nucleus into its constituents, two protons and two neutrons? The rest masses of a protuxoqby5.tpy .,xkg25 on (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 travellc yl .5krw65ujf/6yz ing 110 l/ 6rkfj.yz ulc55 6ywkm/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 laborato.:j,fmr45)ivxteengh x 1 8xjry, are moving toward each other4t5 mnxjfrjx e8xe).hv1i :g,. 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,ogiafw+)47yj s4i xe a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtaac))mte0cbp) ins its power by combining matter and antimatter, achieving complete conversion of mass into )))p0te mb cacenergy. 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 its ,g.m/zl6 1l2a b morjwxck.f 2rest massj .xafm b26mz 2gwl1o/c, lk.r $m_0c^2$ 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-ma 2ku* r2th i,5 8c-y(rtmvdwd-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 when he is running the barn looks eveny2r,*-hc5 a8d2tui(mwt k drv 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 mo ieru4,)trkxqf/3 ff 3les of water, the energy released is 484 kJ. How much does the mass of the element, e3 rfuk)ft 3/ir4qfxs 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 qh;wwo* b 8l. )d/yweqcreated, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, wha 8o .hwd/b;q wwy)l*eqt is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measureib3l a:nx2ym168wk;gr*ozkgs his ship to be 25 m long. On the ship, he eats 6n1rx3i2 zgygwbaokk8l ;:*m 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 t*z05 zvhxk2pa speed of 0.85c away from Earth. You send a laser beam towt2hx zp*50vzk ard the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The ocsftq e9jr5y,51xpwp,bfjv )s2 1d.rz cupants 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 to energy to accelerate the spaceship to 1jxjy swpp9,r efbv1)d5s.r5tf2zq ,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 spac(xlnxmngo/ 98 eship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.l9 8x/ nxonm(gS. 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 6.0znd+c3 zjevfuci2 )2 + light-years from Earth. Passengers on the ship want the (one-way) trip to take no more th2 f+cu3j czv dz+ni2)ean 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 onplh 5s5vh6eh qe q9g4, the end of a spring whose spring stiffness constant 9 eh 4evhsq55qp6,hglis $k=48.7 \, \text{N/m}$. 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 m 3 (ux)f6 g iqls;kni rjy*wb/bqr94/cass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.