You are in a windowless car in an exceptio6x4y+vi4x-s q l hud9do9ha/bnally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are moving4l4hhus 9a bvyx6x9+ d/-id qo? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of k1b0 yv 1a u,(ezevsq*the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking e,zbq1e* 1vus0y(kva that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of q ;vba m0.xvu1 ezy(2z 91btbfqn2d;p a moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance,e( my;vp 2fnvz2z;u0qx1b 1.a 9qbbdt will the ball land on the car or behind it?

Does the Earth really go around the Sun?krsku4rn 5o,6 Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explror,k5n64ks uain.

If you were on a spaceship traveling at 0.5c away from a star, at whaw w1kqacrx89tj i 49x7t speed would the starlight passa i7 wrqkj1x98 c4xt9w you?

The time dilation effect is sometimes expressemlr,bsj:fx 3 irp5u1 8d as “moving clocks run slowly.” Actually, this effect has nothing ,x:rs8mj1fpur 35il bto do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passl arjrk:nq layfu21;37:t4 pfes more slowly in moving reference fr rq;42t1jp7ll krfun3a yf: a:ames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home fromzyrpv w5ezn 3+uy(f)6 a long trip. She rushes up to an old gray-haired man and in the ensuing conversavz+upz)6r(5wy ny f e3tion refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a change io i16eu/ zf-9;j uftc*yb1frjn your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using tuy1- ctjr/ ozef fifbj;9*u16 elescopes say about you?

Do time dilation and length contraction occur a6j +8l bni-dwc.n yz1yl7l h.nt ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happg ztk)7sbs3(sw-x )lten to the relativistic predictions of length 3swsl7ztbs)-)k (xt gcontraction and time dilation?

Discuss how our everyday lives would be different if1w mk)w0h be:dbmu /u9 the speed of light were onl9b u:mwkb)/huw0ed 1 my $25 \, \text{m/s}$.

Explain how the length contraction and p3jc f yd.nuxx 1/rx872-sjbk time dilation formulas might be used to indicate that c is the limitingjcf- byu 2xr p7.3snkjd/81x x speed in the universe.

The drawing at the start of this Chapter shows ky2 :ep/s+; +tkf*iav:bgfc g3ty(gv the street as seen by Mr Tompkins, for whom the speed of /k ty* b+veyfg t:3f+g2va(pcski: ;glight 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 cb4 (* 0w5qulk7iuwj nc. Does this put an upper limit on the momentum of an electron? If so, k* 4u l0bwuc n7ijw(q5what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of ld8z4iznm c04 ai*wnn yn/v0s 9ight? ----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, doe8g u /,nqs6zvls this mean that a spring has more mass when compressed thang8n/qsz l 6,uv when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." Wh zf/d4m5j 4k5j venxkr7.xsf, at must we sayvfd4fx/m7k jks j 5nz. e4,rx5 instead?

  Is our intuitive notion that velocities simpl e;0 a9sc7tf;zcuow .wm+zf6hy add, as we did in Section 3–8, comp;hcew 76w;zzauf+o 0. c 9mstfletely wrong? ----待选择----yesno 

  A spaceship passes you at anw)p o1/ k9k 2vcfvlf, speed of 0.750c. You measure its length to be 28.2 m. How long would it be when at rekvpo12wc 9)fk/n ,lfv st? $L_0$ =    m

  A certain type of eleme9wla t0,m(;mj m+k lmu i4j-ji5llz -dntary particle 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 q ax +ptu;lb;w(bv 39pthe 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 sp y zqb8*8lq7n4+ mt*zkzc+aspeed 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 itim o26rs tak s:;vc,od:9o a1us 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 star is 82 light-years away. How fast woux4/t cz 3gqnrz9se33c ld you have to traqznc9 e333ztx 4sr/cgvel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speu37yhsu2h fq:n,tdo, ed that tells you the distance is only 25 light-years. How2no,u 3:q7ft,hshud y 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 the Earth is 8rsa 7yt-e2cb$11.2 \times 10^3 \, \text{m/s}$. 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 just returned fro *gkc7 7u9dxzs4pv58bq pjl4.q-xti d m a 5-year voyage while traveling at 0.848vj si uq4b cp7g qd t*l.px5k4x79-zdc.
(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 t bk 4ko9p1tf)fcxm :e*m-:fuwould it take a spacecraft traveling 0.960c to reach that star from Earth, asb1 koe tf9f)4xp :*-fcmum :tk 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 ; y8pgfc+fsz5"Ferrari" spacecraft at a speed of 0.660c. It is measured inpg f58zy; cs+f 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 thp8k19n ;;8fp ay lhrbe moving to travel 15 m before it decays? The average lifetime, at rest, ikt ;y;hrhnpp98 fla 18s $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of rzt f.1,hf w.da proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic massz )ldbrpb 7n ac,ze ph,,e--/j be twice its rest mass? v =    c

  A particle of rest mass qadcr8 7w6rq4gkwm-d -/fz o6$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels qpn ob(bp q7:4at $v =0.10c$. 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 thm*e ,/rd ,.zs1 dfj 1frt0cth9gepk:lat accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical rea5k wq15 k2y69gjkm (djgk:kthction requires $4.82 \times 10^4 \, \text{J}$ 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 .5xmdyydsx/ 3fvoqvj p66 i*e6+y i c3process known as fission in a nuclear reactor, the resulting +6. x6 dicp3yyvio3xf/v65q*meyjdsfragments 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 o gsj(oya371 jyf an electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mas-klm q104vpjko5qp fl:up/+f s of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Statza3g9k.qhuig- e7j*xes 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 froz9 em76- kdbbom 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 enertwq jkf qk7d7/l )6hiy9-vwr2gy equals its rest energy? v = d2thqw9fr-)kyj w6/k 7vl iq7    c

  At what speed will an object's kinetic energd.-thb y d0(e) d8rspq5tks.zy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a spec:y j)j eij5mk :60eumi 7qjgjj;(.cc b)b8ybed of 0.997c? W)mib5: (. ij j8)j 7jc:becjyegmyq6; jc0kbu =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a protonatsx,z, +vmxn bjfdl,9 05m:k 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 energy is 750q9okj 4qi;n8,digp 1l MeV)gdp;4j,8qik n1oi lq 9?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differencez+*5 /l uwd9afsrer2 q of 105 MV? v = 5*zwfurqdsr2a/+9el   c

  What is the speed of an electron whose kineai77 h8fs7*ub m-p1l k/cufgrtic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it 1 dj ,dkva(-a3jc1hvd2hm .xlhits a television screen after being accelerated from rest by the 25,000 V of td kj-.cd(1advh3,2 1 mh vjlxahe picture tube? v =    c

Two identical particles of rest masf q *bv5(cgpfvl8pe 7,s $m_0$ 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 (6f9sze(aev )je4yh3 y$m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 af.p7qyx dpc,9qikf*l(l4 k-zn 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 acceleratedmh ul:a-/ /qzo8hbfe, 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 momentum of a y5k isco-d- -::cwxjeproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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, l 0rs4fbg8sqacaiy)*/ud;h , $^{241}\text{Am}$, 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 pu 0 3kqo1k pxa(heqokw7- i7byp9 3f.narticle of nonzero rest mass, and (b) a parobfyxw(70n.q3hku1oe7 -pi 9qa kp3kticle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV peu6v7 nc.t4sp rotons revolving in a circle o 4e n6tvsp7.cuf 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)a,xrc6vlli.n 3gs,n (wvnfjc u; 1)o8 observes a meteor come from behind and pass;.u(nx n 6a8rl,) nfl sic,vwgvo31jc 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 opposite dir qbr7b nh3-g ak 0+)qwxwr*bi-ections, each with a speed of 0.50c with respect to E gbaqnbkwr7b3qw h+ -i-0 *rx)arth.
(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 secocoy 5ww,-kr vkmed56:u lj83gnd spaceship leaves the first at a speed of 0.87c with respect to the first. C5y 6jkcumrl8 w3-kd5wogev :, alculate 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 x w, vht6cc-jd3k 6fc, 3wkv lk+;1ambspeed of 0.60c. The Enterprise comes to mjtd 3k ,ck;f63 cxv6aw1k -bv,c+whlthe rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out tw6gefg d5l* ck.kb0/ ef0q1utno escape pods in opposite directions. One travels a6gfgd bke5 0n/qt *ck.0ufl1 et 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. Ath x1yeec p/e+- the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B movi1hc- e/ e+peyxng relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 ,s :kwyb9brg3light-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)25 x5:gryycwad.j hqaster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogew)ryxa gq:.c5h jd25yn 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 , qp -wbz+ ,w jpcm,x:itrxw +9/g(hp3lcq 0yq$v$ 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 matb:gzbkv3mfm 95l , 8s3nu/dd k.b9jnu ter would have to be totally destroyed to run a 100-W lightbulb fork58msj n: du3zl93udb.f ,vgbmkbn9/ 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an elect-4ax x u2b/nnpf:v eq8ron 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 conserved in this process.)afp2:xu /nqxve-bn48 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 collidupfpm1q2j-c94 7 f lw+8f rqy)5sxoy+ eja *ktes head on with a positive muon traveling at 50% thexypaf9f2ep4kuw+*85l1m7 cqjo)y r-t+ q j sf speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a protosk46.bq 3ad szlds3*wn, 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 among the three particles when a neutron decaydzq3.bkl s4*6 dss3was at rest. KE =    MeV

  The Sun radiates energy at a rate of apwdf4i.) o u(azq3,3 xwk -sq1oysr*sbout $4 \times 10^{26} \, \text{W}$.
(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 h ebxc+yy*i8-vave a 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 e wah: *+axvv8wj; g*d d: 2tfus7xvl8nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, wsvl:;82 t dgeuv +:8da7* fjxhva*wxrespectively, 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,g c xhw jzn0bmq7.wz 4ny .5/q6usu7u of a car traveling 110 km/h as compared to at rest? [Hint: use th4jzh7u z/w05q,unxu cgsn 6wb .mq .7ye binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each havink9cced +sb((a, ee8sk/ix ;pvg a speed of 0.935c in the laboratory, are moving toward each other. Determivki( c( d;bs,/ pex9ce8a+ eskne
(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. *fkit /2xehcqn*j-:to1p9a 3vru hg with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprisx,wbz g6f:rg/e obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise f:gwrzgb,x6/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 accelet b5qxdd03r 93mkpqm.rated so that its kinetic energy is greater than its rest ma30tqxmbdq r.9dp 35mkss $m_0c^2$ 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 beli ys 8-g)t14 /pcd9 ztlzaclpv;eves that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fipg d-l zt;st)1pay /8zc4vcl9t 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 pow/a)2y24 mhj n-fuzakd3 q )of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this reacj4 k2 hqa/ 32)wnamo)z -fyduption?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
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, tra f6yl ;m4ty2jv2uot u*veling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, whatm utt2* yl v2yu6f4oj; is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measuresd0 uu,82 hf2 q.yjyuwc his ship to be 25 mdu f.jycu0 w hq,2u82y 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 l-3 ywgn: 8nqbak;+pxspeed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. Whn :yk;l nq3a w-p8bx+gat do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupan0owz* v gy* 9yimu1cpazhz 8//md 0fr.ts have a total mass of 150,000 kg. The occupants would like to travel to /9hd c0i*ur/mfpym*zv.gzwoza8 y 10 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 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 st37rf4.drtp 2 78qcempqi u. is the spaceship's kinetic energy? Compare wtqq 7u t.r7mf8.ppsc2die r 34ith 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 z52hb2hzy; h7 fz53vza4n ldzlight-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 h;z2 zlzdh57znfzh235vya4 b spaceship 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 stiffh441/ki h tyk6vdpbk:ness constantk1:4vp bkkhhytdi/46 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 mask qypfo+j+p b8yv ylfa qx6-/q67e4 a7s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.