You are in a windowlesr(q: rf)t qi3*lmjy 2: zmcatozv 4b6)s car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determibtz) va:zfc6 ro)ri4t3 :m* ( qlyq2jmne 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 oripw.t ,1bp lx(3 e;tcorner of your eye, you see the car beside y1wolprp tx(ie;t,3b.ou creep forward. Instinctively 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 thi9mu/n2s7:g kxtjfcu -u 6ep:rows a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the cagix:met u-976up2: s /cnku jfr or behind it?

Does the Earth really go around the Sun? Or isb ,kjiiu 2x0*78u4dccfhpz 7y it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of repic4b jhf i72z7k *dc80x,y uulativity (that there is no best reference frame). Explain.

If you were on a spaceship tfa2 lc-pnq7e,v .2iza raveling at 0.5c away from a star, at what speed would the starlighfz,7av a2 qc2lne-i. pt pass you?

The time dilation effect is sometimes expressed as “moving clock,ltwa9 qlr tv5z;x. 4rs run slowly.” Actually, this effect has nothing to do with motion affecting the funza54tw; lr ,xt 9.qlvrctioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving refereq0l wau ,(rvd4nce frames or that it only seew r ,4ad(luv0qms to pass more slowly?

A young-looking woman astronaut has just arrived home from a lo+ agl)e)5 k cztwj-tb6(ou9 tdng trip. She rushes up (te9otaw6)kzbj )-du+tgl c5 to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you noticeonb2bu/mel56/j g *j t a change in your heartbeat?eu2j/ ob5/gtljbmn*6 Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occum5e54 fcx)4 91m dicpzo t0zscr at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of;rok*h -ybr 4x light were infinite. What would happen to the relativistic h-* r ork4xy;bpredictions of length contraction and time dilation?

Discuss how our everyday lives would be differeng6 g6e x-ezv5g3q3dret if the speed of light were only d3 z6reegeg5qv6x3- g$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formuts/ mokvldv3;lue ;v;6(n +tp las might be used to indiukv +;63vts om vntldl;p/(;ecate that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as : ygzdv ba2m5y6 6pa8/hclae,seen by Mr Tompkins, for whyyc,p6z :85v la2ab am6g ehd/om 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 spe)/lqy2eywf r p0fpg 4:eds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limfw) 2p g/qlp f:yyr40eit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of ligh8imskbc97du1 u4 ;qkbt? ----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 th+b68mk ,msc*e 0o3fxqrrr ok 6is mean that a spring has more mass when compre e6rk mq oxcs0 ,rf6o+m*3rk8bssed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be crea ov4n70cz )-cvd 8xxceted nor destroyed." What must we 8 cenvx)7 vcxcd0-4zo say instead?

  Is our intuitive notion y0zpqbs j rya -7a-74zthat velocities simply add, as we did in Section 3–8, completely wrona7-z q4s7-p zrby0ajyg? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be ;ovju;z .8s4afs:bp/rrw 4 aco/gaz3 28.2 m. How long wo aobvzg8r u:p; j;fc.o4saw z/ s3r4/auld it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed of 4v. g6 zaf)agha3f0,r5li7s kt z2hod $2.70 \times 10^8 \, \text{m/s}$. 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 the factt6ssmr7l)a02ld qwh q3crf80*(xipj or $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 Eh5 tkiv7k6p49zpckh g:s;4kz arth 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 lifex pc,t3)l),pjkv0,ppg 4q wz m9 y4wvwtime 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 lightg*n :8glqpt t4t:u lo3q: ;non-years away. How fast would you have to travel so that to you the distance would be only 353t:8u q n:gq: ;ln4opngtt o*l light-years? v =    c

  Suppose you decide to travel to a star 85 light-years 7 0g)hxf3z pckaway at a speed that tells you the distance is only 25 li)fz 0 7gpchxk3ght-years. 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 the Earth ia ;,fswf 1*j ;fw/tnl ebtd8;us $11.2 \times 10^3 \, \text{m/s}$. 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 reetz5k ;u4na pep7x c4rek,n fr(n+ 5i5turned from a 5-year voyage wh5xa(7, eepn4e f rpnr4kz5 i+t;cn k5uile 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-year b ky3h4u5cnw 09bxe2es away. How long would it take a spacecraft traveling 0.960c to reach that0 x3w b49u5kehbney2c 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 "Ferf0t2uqwa q9z2 sod:+ hky0s5jrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m 0a:udw9jhyot2s+ k5sz2 q0 qf 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 aver.x6fbqm;rbtnq:un 2( cj2a*a age pion be moving to travel 15 m before it decays? The average lifetime, bq62na*qu r2ncta b:mjf(;x.at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travel34vwoi)ajxx 0p2ms( n :-v p,gtdsgm2ing at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass? v =2z bbu-gd*ma,s x:n ild;j3;u    c

  A particle of rest masj:x2.9xv*egzy)(xwz 9 xfqc os $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelsrgqtw0v7bj-: xi7a-u 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 ihhef-bc2h6z s f(s n+jh,u7 s2n momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactiozuxl- yw b)hc0 oor j+i7e4q4*n 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 apartv ucafn oe:7- m9fw 0+mna3*pz in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process *n3 mf-c w:ou+ev9anp7 amfz0? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest eyg3v19 jdzv de3+alh10zam/ y nergy of 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 mass of a prov1uy d t*2c 5b(gn8cr0j1z zkxton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abosb/;fn*noxju b 9 )cy-ut $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 1.0 gram of mass? 8peozdomkn fn50l* gk36f+f*    $ \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 lp /c03f )mg/zyk 3*s7 eqsteyits kinetic energy equals its rest energy? vss0 /z*y/g fpelqcyme)3t7 3k =    c

  At what speed will an object's kinetic energy be 25% of its res4q v) m/e awk5:j2tmeot energy? v =    c

  (a) How much work is required to accelerate a proton from resf8 3/ y*y -qcx(uhvfplt up to a speed of 0.9 uqyv3fl ( p8xf-cyh*/97c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic enerb)xa11rvhwr *gy 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 j*qdh7xq ;9m3ejf9o n energy is 750 MeV)? eo7qjq9; hmn*jfdx93    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differw3y7w/srij 8 jence of 105 MV? v = 78 wwjysj/ir3    c

  What is the speed of an electron whose kinetic energy is ft0c3 ixs7iu a,5dz7z1.00 MeV? v =    c

  What is the speed of an electron just before it hits a televia;)8b pmw p:vbez4nm 9sion screen after being accelerated from rest by thew;nmmp ):4vze9b8 apb 25,000 V of the picture tube? v =    c

Two identical particles of reazph b,- t5m*xtm.ym 9yxy0v 0st 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 sx v.p3bdd/n (($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 an electronu/9as 9ptp5*oyn3m jp ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 accel*qz /k(gnvov5erated 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 momentum3aellryr 5n-( 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,ny 2b kim tdiq.,nu(-i6u s5f;5cs.gd $^{241}\text{Am}$, 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 kineti(k i7ru/ 0zca2c 4gpvgc energy versus momentum for (a) a particle of nonzero rest mass,z4c2p(/0g7r ia kvugc and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in a cxuf;jtgrqw*e2g hp2 ,w8*1 xnircle of radius 1.0 km (at, say, the Fermilab f 2wu,ggn12; r e*txj8hxp wq*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 (wito67 +8xb syzga3cte( ih respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u xey8(a b+gz36 t7cois=    c

  Two spaceships leave Earth in opposite directions, each with a speed 3o8ha ijw 1n 9ekd6lj-6ouiy*of 0.50c with respect to Earth. 8wyjuo3dl 9*hk6a1 - 6jni oei
(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 btf/*z+gix s8ryg: z(v9iv y1spaceship leaves the first at a spee + y1ixgzf:8ys zi*g(b t9v/vrd 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 any t/cr iq 3a 1z2itfnd-i9(:-t-b18x qrrvftl alien vessel approach at a speed of 0.60c. The Enterprise comq9(fr-ti3nif1:rdiztc r2 vl t/t b8-a-xy1 qes to the 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 distresyjml7)kw:8nwy6v8 ys b/qk- g s sends out two escape pods in opposite directions. One travels g v6yk-lm/bq)k y7:y swn 8jw8at 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,-r dyk q1qxxj8 mf/97c rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B xk c79q81yjd-fxq /mrmoving relative to A when it passes A? u' =    c

  The nearest star to Earty3 knlgtqu::( f-nhmri *bj ):h 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 about 0.1c is called ref-rwbp)f/q 4 plativistic - i.e., for which the correction using special relativity is a significant effect. Deterfppq4r/ b-wf)mine the speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) ----待选择----relativistic not relativistic 

  (a) What is the speed /rr k3* t 4gu,ffvzzz5$v$ 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 totaljvk// b sgk9xei 7/lhalm5v,) ramw8s (, o,cfly destroyed to run a 100-W lightbulb for kg95, vw 7h f8a,jl ,/cl(/vms/keoxi bms)ra1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to *o620ll i7 0vvdfotiz 882zm7;onwcc2 azcghproduce 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 conserved in this process.) E =coi6icz*2t0lvng 82h7fv0l ozo8z 7 aw mc2d;    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 collides head on with a posq6w(zyikgy.k 5q*v e:itive muon travelikg(w 6.qe :yq*vyi5zk ng at 50% the 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 proton, an electron, and a neutrino. Ass 7:d zpx7 qzes6m1bdg vg o.pji/90lh0zf ::ztume 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 decay vzjpdg0pz 0lz/:h7s f7id: .xmq:tg oezb169s at rest. KE =    MeV

  The Sun radiates energy afr0yk7 nw e1d6t 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 -k 39/unbvx : 38wmao+dyzwt.q x o-sjhave 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 reqrx-.ug*11xvk ryri 1 lv z8;npuired to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, rer1y8 ril*r p -ukx1vx;1.zgn vspectively, 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 1 -(0b8ebb)k r4 gq4nejcqgxuthe (relativistic) mass of a car traveling 110 km/h as compa1qgnbe84ck(jber u xb)4gq -0red 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 th,-n(ka10 ;ws so1yj* ilf shptpr56wxe laboratory, are moving toward each other. po6s*nwr1 sx5-,sw iltfjk1 ;0ya(hp 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 (8nidh1r8o)ons )c jy with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enn6f he*x2+.lg ushd-gterprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Ent6 fd*hu-xn2h lse.gg+erprise 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 kin7mdlj 2 sx+j;qetic energy is greater than its rest mas sxj +ml;qjd72s $m_0c^2$ 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 1.lcxdf9vrxu/kj-mo q ;2r)l;5.0-m-long pole into a 12.0-m-longxj oq .)x2ckufrlmv -9/r;l;d 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 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 *+afy- :p5. 8ve4scamufk aj ymoles of water, the energy released is 484 kJ. How much does the mass of the kfm+ap*s 4f c-5v yju:a 8ay.eelements 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 crea90 v +ll-lonnco4g/qmted, traveling in opposite /0+ cl9l nqgov4-oml ndirections. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures hif0qpjk; u q9fa5i.6vz iomynfm3* )u2s ship to be 25 m long. On the ship, he eats his lunch in 23 min.*u.oymmi0pu6;2 z nkqqf9v)f5 3 ifaj
(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 s1ed-qqr-c cn- peed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of c1- d qrqen-c-the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The) 4dcn-v8 om:mpgdl-b occupants would like to travel to a star th8mdc:- -pdv)b4o ngm lat 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 spj6 50 lcc7tobvaceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with thec50otclv7b 6 j 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 light-yearsmr*3/mtvmef3qg phjs *1mhu d4.xe79 from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How mu1 mmpmqet7g3h**mfd 9vuhsr43 x j.e /ch 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 end of a spring wh8xrbp -gns. 4zs lkw4l w4-z+fjgf.o:ose spring stiffness constant issfwb+gfnozz4r48.sl k g.:pjwx- 4- l $k=48.7 \, \text{N/m}$. 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 mau gb/v-;gr7 grss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.