You are in a windowless car in an exceptionally smooth train moving 9nd91okl/egf / us 8mpat constant velocity. Is there any physical expergfm1kue/9o9s8 /pldniment 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, qd70,x , rm:qjhfdjq 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 rollinf0, md rjhx,dq:qqj7,g backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad cart2s;5 1f.c /5:5.znjqmiaknf, gryv8ij sk gc, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or gc/;1 5tsq acy: ,j.jnkr2v f85f z.5si imkngbehind it?

Does the Earth really go around the Sun? Or is it also valid to say thxe g0zhzu 7x:8at the Sun goes around xg zh80ezu:7xthe Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship trav 0) f/xwr-hp1roxr. zu e+tr-+dr kbf*eling at 0.5c away from a star, at what speed would the z.o/-1*xud +tprkfr- b f)rxh0wer +rstarlight pass you?

The time dilation effect is sometimes expre m45m4gvm twzue6d qcrfb f8so04p8x y6d::n 1ssed as “moving clocks run slowly.” Actually, this effectpn 1vdq u6mxz:mg 6:ftr4sm5oc08 8f4byewd 4 has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actuac-r+l1d wdkq,lly passes more slowly in moving referencr1 w-l+ddcqk,e frames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home1 5uxib f n8hgwwc.7trou 0i7a7dd3v( from a long trip. She rushes up31i8u07u hf7n.( gc7drv xw5 bwdo tia 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 Eaf1x:/ksefwfq15oav)l ; kv3 ) /jr fyyrth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height,5 rfof a:y3))qevjf y //fw11kv;xkls or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length con/pvl v0o eny52be 3yd7traction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relativit+x0m(7fktr ln h 4r (b6m1z5 xeb9mnystic predekh6nt (5f9 z 1(bxnmyl0+74rtrbmx mictions of length contraction and time dilation?

Discuss how our everyday lives would be different if thh2vbd. twcb ;v-k2kx/e speed of light were onlydxkk/bt;bv- h .2w c2v $25 \, \text{m/s}$.

Explain how the length contraction and timeeq zmz9,j/;aa dilation formulas might be used to indicate that c is the limiting speed i e9qamjz/;, zan the universe.

The drawing at the start of this Chapter2r06h xp e6vvfj ya0*m shows the street as seen by Mr Tompkins, for whom the 6ymvj* a02 xhfr0 pe6vspeed 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 trqpe1(mzq ffv xe)7:q2 ls8:vp avel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is thipfzqp2v 7 vsfe qm8(x1)eq:l:s upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass atta /*mmnm* ypd:sin 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, does3lvi20 ip kj* (a fr1x;esxt+t this mean that a spring has more mass when compressed thaxrf+t2kei3 j1asvx; tlp 0( i*n when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created ztdvt bj26t+ pilu y*67yi7u* nor destroyed." What m*+tytu pi7i6zly vud*b2j 7t6ust we say instead?

  Is our intuitive notl u6wyo c/:cjo04aeoax 6g;i.ion that velocities simply add, as we did in Section 3–8, comple oy6/c;a :wac.oiou x e6lgj04tely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28w:s, )nd+c.ihrl vmc2.2 m. How l +.crm :vi )2d,wslnhcong would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at *psfmam(i /udj0za7fba m. 98a 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 thh;zh6)b,u wnve 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 b0ha)daetre.1h:aopnr lcr*582c k) 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 yr-k(lyz:3 re 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 referencek z /(p5afdj+m frame, a star is 82 light-years away. How fast would you have to travel so that to you the jm+pdkf(a z/5distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a shffqkw pqi5;px :xf+ ;ax;43c peed that tells you the distance is only 25 light-years. How many years would it take you to make the tri5f;;pcqaqpx4+hkfi fxx w:;3p? 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 osfb7tai5b4 14zo usf +4m1(: kudtr i$11.2 \times 10^3 \, \text{m/s}$. 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 ju a:w/z ex5dg2b eq1z5jst returned from a 5-yedeb: q 2zex1gwz/5ja5ar voyage while traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. Hoq u,r,ja3 fg4uw long would it take a spacecraft traveling 0.960c to 4ufja,r, u 3gqreach 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 id7vk l2 8( m5v5ufk9bng6yx fmn her "Ferrari" spacecraft at a speed of 0.660c. It is meafk6 xgkn8l fyv 7mvmb d925u5(sured in 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 be moving to travel 15 m 2ar ag jc,na:q8)gdp.before it decays? The average lifetimedrg)8 ac2,a:.jpqa gn, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protof 0gh :ia lgusu 2e)j1kqm0j8/n traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice1 p*mc2cf+rw(tg sxz vv; xso(zj5 66sn6cw t/ its rest mass? v =    c

  A particle of rest mass5 9jd:a9h4b z9cfsdfx $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave(c 7+q)wqagc wls 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 mz/fbr; j68l;e q d6fzs* sk6tt0s6cxu omentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires :g h+9a* cx4sucwf1nl$4.82 \times 10^4 \, \text{J}$ 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 vzc9i vkn)-7din 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 procv)ki zv7d9 -ncess? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron k:r 6m an 45coltp 7lqr-s0qfsz j)jc2;fs:m8in 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 pro len w)*es*xan;it.y1 ton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is aboutm 4pq4tl s4/ns $10^{19} \, \text{J}$. 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 g7bmpak4 ; f zak/jtyflq) (j3;ram 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 ene(zw, du*goxs. d /nsl2rgy equals its rest energy? v = uo.zn dds /gw*l,s2(x   c

  At what speed will an object's kinetic energy be 25% of s5a0y oh2jb 4yits rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a spgl:cdfgtlckfeyh gb (g -w/*v3r)s( +c* :qf:eed of 0. :k )dg/-l*c(f3 qg(: :gr+ceyf*gwlvsfhtbc997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentjx+o2u* k pj,sum 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 (thaufjv-v +6a9 iwt is, its kinetic energy is 750 MeV)?- avvw +u96ijf    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton acce0 zq*wf (qpt7mlerated by a potential difference of 105 MV? v = t qz(*p7w 0qmf   c

  What is the speed of an electron whose kinetic w;kl23 d e+)nnitjk+j8pl k/jenergy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen after bt:vkuavh 7 v ,y+.quh,p*hb 0qeing ac qvah,vp7hk0 qh.b, uu:t vy*+celerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles ofox,dpj;*sl. ery0cr5 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 .df1p/ve; 3fh3blr +jp q+r m 4yiy5rfproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentun vp9 -qi*q6zbm 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 is accele0+dwaq *yq) gmrated 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 oj(rms0 h3/9( fndj tj-+ fetdenergy 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 nucleu l ex2*g,trkg*;je+9g0qjgol s, $^{241}\text{Am}$, 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+ri.h.q ,mz qg+; diddc energy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero re. igmd+hqd,; +.r idqzst mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in a vz; pnttx *;r0circle ofpvnx* r ;;tzt0 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 atgeog:e42v(* +oacvx c 0.50c (with respect to the Earth) observes a meteor come from behindv4c: ge*goo e(x2v+ca and pass 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 directions, each with a speed of t;h sgmvm+)e;9(imxu0.50c with respect to Earth+gmhe;;x)sim9mv( t u .
(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 h8ynuv:s,d p)0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate uhy),sdnv p8: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. The Ent/ sa)urxm9ucz.eo* g2 erprise comes to the rescue (Fig. Below), overtaking the aliens while moving direcs x)/uc*2z eramog9u.tly 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 directions. One trgnxd 7 23 g;h;0rok;ru2zx,aw7ja t ok a, huo rr xa27o;73d2g;w;kkgnz 0txjavels at a speed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth at a speed of 0.75c. At the same time, rocd 7bvoob n;j xej6+n(u8fg/a4d;+le9hm. xf cket B passes Earth moving 0.95c relative tac9d x ne/hfbvo7+m jnd+ befo(6x4u;l; jg8 .o Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 ly cd9ih7x.we* u,-qhhde 0tm:ight-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 thanpcq) 73ocy bza* 8wg:q about 0.1c is called relativistic - i.e., for which the correction using specwq738p)*ag : zcqbcyo ial 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 jf k:r8q7wgkkj+v24k $v$ 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 totallxubw e0/;mz; iy destroyed to run a 100-W lightbulb for 1 year? ;0ix;z umbew/$m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to r 1 07zjrs3bcwy r95-0ebfhdoy l*( adproduce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite chy rojd1l7cb(b9f0*errda y0 3zs w5-h arge. (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% tpkbu2j* c*p-hc d/qr;79nx q8u lkmu:he speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of l:8u*u pq*j/; qpnd -kcc2b79kxhmurrest 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, uv.n)3v)xm;d yzqr3 q yznv:h95tag3an 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 y azz q5yuvvxg3tnd.9 nqh3 m)) v:;r3shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of about zxhznj a2 / 2n5 xwm0 2ncn.ck8er9e9j$4 \times 10^{26} \, \text{W}$.
(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 wuv gr7y4lnzy8v t./ ,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 nucleus into its constitue9)wev/ln-p9x6l6g ikqjn.(g kmhvd ( nts, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference idv6)n (.-exm99 6vl wlk jn(/gqpkihgs called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increas f,*s(nci -5k irip*uze in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the,*pck*ifz-n ir5 i( us binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are mb9 sz+mxp /cb.oving toward each otherb9+xzc. s b/mp. 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 thatx v/iuvf0 l9ulwhd8-r mwqmo: c b80:2 a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powerw vrnkg 7a5wj5 8ojg5x:xf .o2 by combining matter and antimatter, achieving complete conve.vogr5an o :xgjj 2wx5w kf758rsion of 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 thatalfzhbytz6 5 w8e cc8) 5h/*oa its kinetic energy is greater than its rest mass8b5a*f lhat5z)ycwh/8 z eo6c $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-long pole ifbnr pfm;w h)8u 79rh3nto a 12.0-m-long bfhfrnp r8;w)mh937u 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 twmz s3zsu 442f;qjhns av;sblg:8w 3x7o moles of water, the energj smwqxuasg3z3:hnl8 v74f42 z;b;s sy released 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* (mf-r l*gtz0yaba 1k two identical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one p(la1 b0 -rfk yt**mazgarticle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to E+:: zog5x 6y mrbt:eizsmqnz - +p+pq,arth measures his ship eqq -xg 5bppnyzr +mot+m:,6:: zs+izto be 25 m 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 speed of 0.85c away from Earth. tm8l95f/ 5a sqjz2c1zukom67b xv mb/ You send a laser beam toward the Eartflms5/ btkza mj25z 6bx9vmq1o c7u8/h 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 occupann g vtdt g2bz570sdpzv3v8mzx;p 31v*ts have 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, the env 253p x;v v zbt3zdpz701gn8vm*ts gdgine 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 of8 ytjkuj3gz ;(mrgo *7 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual e 3jgt8( y ;*um7zrgjkonergy 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-year0p i;yie pv86ws from Earth. Passengers on th;0y w8iipev6pe ship want the (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 spring stiffnq:jq;b-rf4i7 i(hui(f (zfkn7 2xuj oq4y8eiess constant u( bqxf ;qri7(j:f-i4u iin2qh(4kyj78ez of 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 masst3bmmre3vepm.)) c- *euf8 gx $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.