You are in a windowless car in an exceptionally smooth train moving at constantnx9x0,jx1* ppy5* gs;w 32wdu vzpzxw velocity. Is there any physical experiment you can do inx31;2 xyx*u0 d j*z9s,zxppw 5wngwpv the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experiencjjym-+6w :zxy e of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this sxy6wjj yzm +:-ay about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy jb jc,zk2) .kuxvo4d +ball straight up (from his point of view). Ignoring air resistance, will the ball land on th2jk4 v,c uz.dx bjk)+oe car or behind it?

Does the Earth reall bg,(.md+y 1 subbe3amy go around the Sun? 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 fm3,bgbed1+y.( uabms rame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed wodmegp dz yi,a24,jcaj20 gk 0ood /5j/uld taiay, dgjg,o kd0/o2 j 4edm2/pz0cj5he starlight pass you?

The time dilation effect i.h u) okf)gy:is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothi.)) gko yhf:uing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in mo w wz2jwljdx1/p0x.t 0 /kqol:ving reference frames or that it o 2x01.jozdx0wt lq:pjw/l w k/nly seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She rus-f9 ie:d5 zqsrhes up to an old gray-haired man and in the ensuing conversation refers tdfer:s9-zi5q o him as her son. How might this be possible?

If you were traveling away from Earth at speed e0)1 1ralx t.lm 8bkam0.5c, would you notice a change in your heartbeat? Would your massa1)l1trkm ablem0 x. 8, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary8-8p*tvnpz sb nu59ty speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were qsygu8d3,/ x/e ar6qsinfinite. What would happen to the relativistic predic8ud 6/rayqq3/g s,sxe tions of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light n /kh-nm/ *apiwere only -p* nmh/an/ki $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be usedox* 4fk5vvtr vcj-s9i doy)3*c +yb4 r to indicarbc*y v- )vdytos4kxci*ro5v39 4j f +te that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mrnq8 x5rq10 c- rcp+xk.oju xq0 9bbe2w Tompkins, for whom the rn.- qj+2 ck qoxb0 1re 5xc9ubxq8p0wspeed 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(b*svwp e3*nd 1i ra8e speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limite e n1sdb 8par*(w*iv3? If not, explain. ----待选择----yesno 

  Can a particle of nonzerold rh enx+03 * otu-yd.of)7mj rest 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, doucq/ ohq j3 u-my wd;z069/kudh+cuk5es this mean that a spring has more mass when compressed than when rkku-05 /c36z h q9yu;ho+jd/wc mduu qelaxed? ----待选择----yesno 

It is not correct to say that "maozx 01,j q 4mmmt-2y di.kug7btter can neither be created nor destroyed." What must we say instead?dot27giu,b 0z -4xym1 km.qm j

  Is our intuitive notion that velocities simply add, as we did in z lgq)b2v8eexx hb ,9z ci5tmd:n /b)5Section 3–8, completely c ei5x evb b)mg:5txl82/zb,qn) dh z9wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.h ae9bc3c9u4k2 m.ehkccbu 9a9 34 How long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travc *cz;f-m0exm p2h; wcels 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 intxp7mwh6r/db0 4qn 0 gnervals depend on the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 li/1z /x5yd)i +ikosm haght-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 /w6c3lyit6zu;yn0 ms its average lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, vtn nlw3s61j1a star is 82 light-years away. How fast would you have to travel so ntvn 6js3 w11lthat to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years awao1i 7fa0w zfnag1 v+d(y at a speed that tells you the distance is only 251io 7 d+fzwg1(fav0an light-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 z0) cifi5k:mvthe 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 qx-uyx 3hr8us vyqd8 e-1g :ng+iu,v ;starship Enterprise had just returned from a 5-year voyage while traveling at 0.81eq 8;uxu-nyqs3h v+vix:, g-ur8 yd g4c.
(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. z. p.qtx:;8 urou:ez. mc3ysw How long would it take a spacecraft tra8: .oeru zwq .:c ysux.3t;zpmveling 0.960c 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" spacecraft at a:;gvfo(g gc 8kvyfoh /nf-60q2ane0 3,y grel speed of 0.660c. It is measured in your frame to8g g-h,o0n; er vfa36flqny f0gy :2ek(/cgvo be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be movi/x49utn 5nll7k tah /ong to travel 15 m before it decays? The average lifetimeh97n xan5lot//4l kut, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelinm dh1s pdoa)9(g at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic(zv5wgjcj 8fo-b a0 z- mass be twice its rest mass? v =    c

  A particle of rest maa3ex9s (z+yjz 2q7wmz ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelgzurt-h/-s p9o 5gmg8t ea-z;s 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 proton that a3 k+oz4:vun/mvg9m gk ccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requir7,4 pio 8;ukmfnd5d zzex 50kqes $4.82 \times 10^4 \, \text{J}$ 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 vkz2cs7+r*, x5hoio xapart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic 7k+2zrocihxs,ov* 5x energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest e)7+x jtpntqax cs xvdo7411i7nergy 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 protone* dxyf98q cp n nxi9refp :v2o1z:+.z in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is about ;tjp eyup)lo(f )w gc,h; 5)yq:ta-so7tcs n;$10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained fnc7b)/p c qpcq5ho; )zrom 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 reauxm ji6ju+*5co 2j0y,4jt yzst energy? v = ,oujm+azyy54 0jjtu6*c i 2xj    c

  At what speed will an object's kinetic energy be 25% of its rest energy? gp yqlm.-.v3 pv =    c

  (a) How much work is required to accelerate a proton from rest up to a s )f8r:/cz yszitd-sr1peed of 0.997c? W 1tiyczr/r )dz-:sf8s =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momsm5r/)hut) b/b (zy4q8,*gd, k p c yqit+mizuentum 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 proto(d j e r ykd4uk5*r51vu4vvbeb,rrn2 +n (that is, its kinetic energy is 750 MeV v1(,ed 2v55bk4nu k+ j4* vbyurrdrer)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential dif cp-;:t9hae0rl. ;*kjtzhbw bh4u.tjference of 105 MV? vb4:jzu *0-9thw.bt;a .prl;ejht ckh =    c

  What is the speed of an electron whose kinetic energy ilncq 8dfb8:z6 yob;p)ht.z phl9 y8 2ss 1.00 MeV? v =    c

  What is the speed of an sq7) az3,dsk:o k4o6jjtw . wf iw:f7zelectron just before it hits a television screen after being accel:4wk i67fwwds7ajzkj)foz3s t , q.o:erated from rest by the 25,000 V of the picture tube? v =    c

Two identical particlerj t,rj ,:oumoqu-njt+x.3 3 bs of rest mass $m_0$ approach each other at equal and opposite speeds $v$. The collision is completely inelastic and results in a single particle at rest. What is the rest mass of the new particle? How much energy was lost in the collision? How much kinetic energy is lost in this collision?

  Calculate the speed 0pei(ujtoo: - ww1h,bof a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the mk.p 3xkt5p,yeomentum of an electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 kg in2 ze4j; q9eyjs 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 momentum of a z.mrm(0zu/qw 9i vx,lproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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, in2 tawu/1n 9drcql28 $^{241}\text{Am}$, 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 ver3,br:ds :78 age w zm w5c8(dl5wkqfbusus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest b:(d fral8c zww :5s75,w3ugqekdbm8mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in-(.qb 90k00f lf q.qtdtvdvba a circle of rad 0q (9fvldtqq0.afb tvkb0.- dius 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.rl/g31dr i:py s n-w-1rynzl.50c (with 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 r.1ygp- zr:nwynr3l 1d l-is/=    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0p0; qzj(a7 kld.50c with respect to Earth. 0 zqalj;(pd 7k
(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 s*45ggcdj l axml :t.z(econd spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the g*a.gljt(5zmd 4xlc :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. Thyl.ry;y: *b* u2 t*kb.p teti,yv2sdae Enterprise comes to the rescue (Fig.p2 .y.sy,ytru2** bb a*lt:iyt;e kvd 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 two escape pods in opposite dire fod8 29jgwz.gctions. One travels at a speed fjdz 2 gw9.8go$v_1 =-0.60c$ 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. :z+ve s,pg 3hvAt the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast izh e3p:s,+ vvgs B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 f1 hhe3c( fmh-vj9lr7light-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 rel/(x*)7 tqklfl-brquy /djup,ativi f*lky/ -ulx7j, ) qprtd(qb/ustic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) ----待选择----relativistic not relativistic 

  (a) What is the speed z*uzn5/*x rf*7 iyd8oo5jjsw$v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter would have to be totally du/d ++ t9j b z elhwu-km.1ip1lq8va.) *xqfueestroyed to run a 100-W light em ev+tkiu.au)bhq. +f pl-x 11l/jq dz8w*9ubulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed0 j m/rp8,+/a ehsdbwi1lge/ y to produce an electron and a positron together? A positron is a particle with the same rest mass as an elm0p j/ e e+r/shlw,i 1ba/8gdyectron, but has the opposite charge. (Note that electric charge 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 collides head on with akb:h(pw; v1fq -w zya a5p8a*i positive muon travelin*a;aka-p(bw1: iqpzywfh5 8 vg 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 dei6kv p+w 1hg-acay into a proton, 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 neutrov pi+k1aw6g-h n decays at rest. KE =    MeV

  The Sun radiates energy at a rate of aboutmx:y 1 :oi buim2o2fw8 $4 \times 10^{26} \, \text{W}$.
(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 measur4 nh-ify,gr2 8ue*l;st m,9*qugnwpj ed to have 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 g q.gya3oq; .2to k2wpa helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and heli.2;go .qpay 2t3kqogwum 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 (relativistcm /g 5 mw d9rod;0(rox3hd.eric) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binom;9(hcod/wm 5r0 rdd3m gex.orial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a saf+j,*-a9c qi exjx)e peed of 0.935c in the laboratory, are moving toward each other. Determine 9q)ejf-xia,jxc a +*e
(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 partic yw)w1-jss83*kl8r jfg5yvauv0c s:gle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtainsmgqrv (si b/190jmb/b its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approxim1b jbqmv( i0g r/msb9/ately $5 \times 10^9 \, \text{kg}$, 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 thagbb( ahdq:dzd:mw9 jc3 8r 5-un its rest mud(amc:zd-bqr jdg3wb 5: 9 h8ass $m_0c^2$ 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 belieqq q3ivaq(+ clq z8i-2ves 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. Hoq8q- zq 3ca(qil2i+qvw 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 tl pqf:s49m3atx5h1dk obf( 6fo form two moles of water, the energy relpqx4msh 96l3 fo (b:f5 ftd1akeased is 484 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling iopqr;szi9:grbhq)2j 9ua1m4 n opposite directions. If the speed of each particle is 0.75c, relative1)zojaumsgr9b9 :;qr2 pi4qh 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 0.7m) yi+a2ianztvjbgz; :mc2cu3 :ha7 95c relative to Earth measures his ship to be 25 m long. On the ship, he eaa9;2 iucha ng )mjyaz:z7+mi :3 cb2tvts 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 cmle*c(nk 4 vz*z8 (6z6gqqpespeed of 0.85c away from Earth. You send a laser beam toward the Earth me g6 kl( c*qz6*cnzpzqv4(e8traveling 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 h aovw)n2ivff / k*izbo*8 0kclr*dt j;.g es:(ave a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, tfn2(r v)tlkv zb icw.o:e*id8ofjks 0* /*ga;he 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 spaceshipos ron* 2:ec/i left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? i r/cso*o:e 2nCompare 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 travelzb rwjl631kgmx+1)iaf 7 6 pml to the vicinity of a star 6.0 light-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 spaceship t ira)xlkfm6jw3 gm+ 1lzb76 1po bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose sprin3q ah-xotq0 l7g stiffness constant ixqq7la 0oh- t3s $k=48.7 \, \text{N/m}$. If this system is in a spaceship moving past Earth at 0.900c, what is its period of oscillation according to
(a) observers on the ship, T =    s
(b) observers on Earth? $T_{earth}$ =    s

A pi meson of rest ma vovg:ti66osx 6r).d lrad5r2ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.