You are in a windowless car -*19 g kc7lfqxbk8yeuin an exceptionally smooth train moving at constant veloc k-kyqx91b* glfceu78ity. Is 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 experience of being at a red light when, out of the corndir( muv;x 7q*km.bq o87cxx)er of your eye, you see the car beside you creep forward. Instinctively you stomp on the brakeqo*xu dvr()cx q;bi87.mxkm7 pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of:9vd4 1a4pjmmkg2k.dt wz .uc a moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air re mcud1v4t 4g9a kdzp:k2 wj.m.sistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? id osg 1xq+8ip9g 5:zkOr is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (thg8dq pis i15ko9zg: x+at there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at 91n r r jykdfy079ftf/what speed would the starlight pass yo/9tdf7nfrr yjk09yf 1u?

The time dilation effect is sometimes expressed as “momnenv4vns8-gq 9c 4o7 ving clocks run slowly.” Actually, this effect has nno q 9 8v-cnvs7e4g4nmothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually pas,ib5c 6+em 1- huark/lp iru2uses more slowly in moving reference frames or that it only seems to pass more +r1u rliamu6hp,u2 / -kc5beislowly?

A young-looking woman astronaut has just arrived ht rwg48 d/(qnni 3hp:tome 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 be pos8pqt(w ndti3:nr 4/h gsible?

If you were traveling away from Earth at speed 0.5c0fg ubvfwd)34, would you notice a change in your heartbeat? Would)d g3b0 fvfu4w your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speed i 4fr +xmiv*aucm:f2:s, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would ha 7f;n9sx6rd9 ag8sjm*( 1enf ob8blc pppen to the relativistic predictions m c9 sep8 7asn;*ff(9 bojrblgx6d1n 8of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light were bc 6n3 u6;jpm3eptzg)+y h-zyonly ty; 3pyhzzcbjmg 6eu 6pn)-+3 $25 \, \text{m/s}$.

Explain how the length contraction and time dilationxw:mm8si75p.l-e dbj 8 q)zxu formulas might be used to indicate that c is th8 7)l-ji: 8xd.mqz eswu5xbpm e limiting speed in the universe.

The drawing at the start of this Chapter shows the str opa9 69jn6 x8rz*nezbr(rw :yeet as seen by Mr Tompkins, for whom the 6rrz8(* 9ay6 bnowerx:p9znjspeed 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 .8 nhsz kslsk ,k/.my;c. Does this put an upper limit on the momentum of mh.s;lk8y,kzss nk. /an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero reie9 7) y fita1yr0i;mtst mass attain the speed of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does this meae*8jv. w1-r-6 (vj;a gi qwe8jpzotd3 vq. svan that a spring has more mass when compressed than when relaxedaew jtqv.(p1j8-zqej8*-6v.vgi dvs ra w3o;? ----待选择----yesno 

It is not correct to say that "matt(s;grxrn 1g9be 0b)o mer can neither be created nor destroyed." What mus1bx9n(rb )g0 sroe ;mgt we say instead?

  Is our intuitive notion that velocities simply wxwra mo8nhd3ux ) esx* 84o*5add, as we did in Section 3–8, completelon)8 s*xw8*5weo3 rxhm4uxd ay wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 7 ,lk/g4v fp0o yiyw9o0.750c. You measure its length to be 28.2 m. How long would it be when at rest?poifyy o/gwk749 ,v0l $L_0$ =    m

  A certain type of elementary particle travels at q+m pw6r00 w2zoww3zga 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 de)pnm+7 ovj94(oum qhhpend 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 h)hkg de: )g2u: 9tfvvstar 125 light-years 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 measu rd3 ;rycirb1;z9mh7 lred 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.5xoj dz* 3gfy2 sy1bb away. How fast would you have to travel so that to you the distance would be only 35 light-yeagj3xd*z b5f . obsyy12rs? v =    c

  Suppose you decide to travel to a star 85 light-years awaykbo-mr52zs7t0zjm y f7b ;gwj g/+:cy at a speed that tells you the distance is only 25 light-years. How many years w7b;+ y0 c2kz5 ggfr/ yojs-mb7wzmjt:ould 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 +q r(sgc8b bv;bq*02r eakhwt+1oq;b $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

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

  Suppose a news report stated t r+7 vxdes3yv1vaw 3;khat starship Enterprise had just returned from a 5-year vy 3 d;1v7+3skewvvraxoyage 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- h n/y guxqxx)5qi42e5years away. How long would it take a spacecraft traveling 0.960 4xgnq5huy2/x 5qex )ic to reach that star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecqr 9qf( (hczx3e:h2wj(g blt2raft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and htzb 2q 2wj:3 gc(lf 9q(hx(re1.25 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 befohhcb-v 6wn)prz a;t94re it decays? The averavha; p9rt h bw4zc)n-6ge lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling fl:d*4*ksul0ue 4c cbat $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an objgcuo.rk6 t g n(tez c6g;32th-ect’s relativistic mass be twice its rest mass? v =    c

  A particle of rest m+e7 ,w6pk*ctum3:.c j.dg0f chyv phlass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at9wlo*wmac , q)kq-h.v $v =0.10c$. By what percentage will a calculation of its momentum be wrong if you use the classical formula?    %
(b) Repeat for $v=0.90c$.    %

  What is the percent change in momentum of a proton that acceleratj* tt aucwbu(wk*b4c(;pjh 97es
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reagcmj s5,wy ov o(v.0st 54m6elction 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 process known as fission in;m n xdwd-u.m4 a nuclear reactor, the resulting fragments have a tota-wxdmn m; d4u.l 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 * ijy5ry.qa+1e)bte1 w )yc to43yrbl 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 pi+ p2y ej,w-eqroton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abo1, oe/3 f7qf6m/9bbdky o-4w jpfg9m/hpky afut $10^{19} \, \text{J}$. 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 mas m0dedrkb//e, r j12fps?    $ \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 rest e lne5 yf 3ko4pwdm1d1gj1w0p .nergy? v jmf 101k1odwdl 5ppwy.eg 34n =    c

  At what speed will an o e0xi1/fqa0mm : 1/mjx7g)lf5nkcbb jbject's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a sp)esv jqs/3wo -pm6fe4 eed of 0.99-e6/ vswsp3ej)mo4 q f7c? W =    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 proton travelingxkbq0-c5o y q/ $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (thenl(q jzaqfp.ya88.h0p zi 8+u g8dz -at is, its kinetic energy is 750 MeV)? h.ez .- 8jfqz zplygd(a8a+0 n8pqui8   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accev rbh glkc9662lerated by a potential difference of 105 MV? v = ghcr9vkl66 b2   c

  What is the speed of an elec:::kdj ;lcf yxtron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a telep,z8i fjgkkaml ,0m89 dy.4 iuvision screen after bei kiuml.80a4 jmy i8zgfkp,,9 dng accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of5n ajfp/j r vrd)r6w2+ 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 pz;obi tfzg:v*re9*q. t 0 n pwc*cj;7nroton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and thld-urat .4lz- 7nb 2bt42rqeoe momentum 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 27,3 zk)hi3rn j+pt wjj50000 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 encfw8knr5fgu;l4p,;w ergy and 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 nucleusyy x+0*s m h )ou/sa5p*6wzxru, $^{241}\text{Am}$, 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 nonzero8jjxf1 yx:g9 p4e i;rqrxl :;h rest mass, and (b) a paeg1yf :9xx j rhr4l8; ;jxp:iqrticle with zero rest mass.

  What magnetic field intensity is needed 9vam, bp/*brp b5lnewec6v2s08 tlk2 to keep 998-GeV protons revolving in a cir2 vbc / pk *9vbb emletl502wpr8a6s,ncle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with respect to the Earth) 34yz1h uxtmz/lt1nd (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 Ea3zt 4nymh l1 /xdut1(zrth? u =    c

  Two spaceships leave Earth in opposite directions, eachm ;oyw5opnc/) with a speed of 0.50c with respe;npow 5 o/m)cyct 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 spaceshiugl0w m-*,vx(h h*d unp leaves the first at a speed of 0.87c with respect to the first.hu- hw*( n,ldmug 0*vx Calculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speed of 0.60c. T0jo/09, d/ c9y u/rwccafowznb4uy6d he Enterprise comes to the rescue (Fig. ona9fz 0cuwc 60/r y/d/w94ub , jcoydBelow), 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 two esca tp )o4l a z/am4wdhe8s46laa2pe pods in opposite directions. One travels atm dwohapata/ a8e s6l244 )4lz 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 my0bj7 s9ge :b0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B movig:s9emy 7bb0j ng relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years aw:;lqurr 1e o r sc/w-2a,jj+x1ffu3fpay.
(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 calledfg(p, mp bau0 3aj:niv1( 8yjv relativistic - i.e., for which the correction using special relativity is a significanyp j:uava(m,(gn381fjpibv 0 t 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 speedox gx t;jyd)g1khm337 $v$ 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 havybec-j(qb l fd *q88.ve to be totally destroyed to run a 100-W lightbjq-8fdv.y(8bc l qe* bulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount oi x.zan*6ijw2u stl.7l. ox ur mp4n)/syp ;h+f electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this pu hw xy.7m r. /p;642n)usl+ aj.ozipnxs* itlrocess.) 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%,4+yabn gdllt8 o51pi the speed of light collides head on with a positive muon traveling at 50% 1olp+ n5b,tdl4y8i g athe 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 prot)zc3ykr( )qljv g71dyon, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the othed)kylgv 3r1j zqy ()7cr 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 of uievx+ 75bs-kn.an.h0 scw a ko6(o8fabout $4 \times 10^{26} \, \text{W}$.
(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 chafaac(7zvyj f6 ef+khvy 74j;0 rge 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 nucleus invtz3p y7 -zzb-6 eo+hdto its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectv-hzto7ep6 b-z+3dyz ively, 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 w.bid n azc4.)j*vt*hcar traveling 110 km/h as compared to at rest? [Hint: .*4va.j) id*bzcntw h use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c)m-nirgkch 1--: hb we in the laboratory, are moving toward each) ngi :-ewhk--brm1c h other. 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 partiadt/:t1w qrp+gpl-) xcle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter and antaan cgau/t5 91* *eejx;hucc:2u :d ziimatter, achieving complete conversion uud*5z e:a 9geta1c *h;icn 2u:j/xcaof mass into energy. If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic enea+skv,6bq5jx rgy is greater than its rest masssxa v6+jbqk,5 $m_0c^2$ 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 go2xx.p 7/2 n*ijjajdcan fit a 15.0-m-long pole into a 12.0-m-loa2i* .djn7j xx oj2/pgng 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 fs pe*iv )aub .eznq7:*orm two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this reaeev7*. bsa) zipq*n:u ction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two ident.nq w :mj*l/ddvm2t+ wical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame:m.qvw* tn j lwd+/m2d of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship tra78c ( zvzdgok3h*uy9cveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship,h(cy*kv c3 z7o9 uzdg8 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 spacesd8dtoav0i q6vpn 4) r3hip at a speed of 0.85c away from Earth. You send a laser bea)nd 3qp6v0 dotr8vi4am toward 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 1* q) j1p)obhoe20qnfl -1 2sbhs fyjiq39 hwv)50,000 kg. The occupants would like to travel to a star t*2qbf2qhnw )h 0o3 91-jbj fi1oq)vs hpsly e)hat 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 Eatjbkwi pq4l*b c51t2. rth at a speed of 0.99c. What is the spaceship's kin 5p2bkt.c*qj1t4ibwl etic energy? Compare with 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 light-yearsqpu*3mu /oq, )fek 6fc from Earth. Passengers on the ship want themqqf,f)/6 eup * co3uk (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spmrpybd,;f4:efz sefd7j8j hu:/ 5r ;kring stiffness constant i7r,jf esur:d;fb4 ;pyhez :8 md/jk5fs $k=48.7 \, \text{N/m}$. 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 masd/47hspcv6 nss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.