You are in a windowless car in an exceptionally smooe5 l foxrxit*.r7 0m5qth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are moving? Explainm 7xt*xolriq.0e55r f . ----待选择----yesno 

You might have had the exe1qyso 2yv *:/ eldjz/perience 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 bryqey :/1jl 2od* /vsezake 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 throws a heavy ball s2v ke0hhche:;oh8ov c22fd r1traight up (from his point of view). Ignoring air resisr8vo c hhhv0ekdo21f :22h;e ctance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also g a)o4:qoo n4g l9sqt;valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explainn g44o9q:s;o)qag otl.

If you were on a spaceship traveling at 0.5c away fromwl*yqbu m5 cc 168tux 8l8shxeu1x7u 4 a star, at what speed would the starligh48cl68qx1u5b18 xeuuc hsmxtl7 * uwyt pass you?

The time dilation effect is sometimes ex.y ( ho.rusfg hwn1;1ppressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it 11hy p..o; n(uswfgrh deal with?

Does time dilation mean that time actually passes more slowly in moving refe4)gj s6 q;(y embit-qbrence frames or that it only se)yj(-si et 4b mq6gq;bems to pass more slowly?

A young-looking woman astronaut has just arrived h46-nga5nxn 3m 8hhl q ax1(dihome from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation3hh(i8 5gqx4-n dl mn1n ahax6 refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, d(2lkjqjjfu yw 1/h )2would you notice a change in your heartbeat? Would your mass, heightjwjh2l2jkuyd fq/ 1(), or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction 94mj8 qxl5chu:bh;nm occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would o u 01ef7ot-jbhappen to the relativistic predictions of lenfb1oj0-ute 7ogth contraction and time dilation?

Discuss how our everydai ;ld(zk+8d mxy lives would be different if the speed of light were only ( zkimld 8d;x+$25 \, \text{m/s}$.

Explain how the length contrac lm bkvb;72qlmnf wg*-35d* ection and time dilation formulas might be used to indicatvle lmqb c7n*fb;k dm*g-32w 5e that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows then p/(n 77br.obeaf,g8 jh*hb mir4r: k street as seen by Mr Tompkins, for whom the speed of lightprf:rk7hj. oea(n n8/bim bh7r4*gb, 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 c. Does this put an upperk,re5nlk* d ,woq8i-u limit on the momek*5rd lk ne q,-wou,8intum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of lip2mf5bt 7j oww6 2qnz1ght? ----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 mean that a spring has more ftfoi:r bd7 -4mass when compressed than when relt4 :f7 iorf-dbaxed? ----待选择----yesno 

It is not correct to say that "matter can wp w gxglhypgv,*; -);neither be created nor destroyed." What must we whp v-;gl ypg *w)x;g,say instead?

  Is our intuitive notion that velocities simply add, as we did in Section 3–8, cg:*9x :oxkr riompletelr*9goki : r:xxy wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measmoo5w2by h is/0j/ ;j1stik k.ure its length to be 28.2 m. How long would it be when at rest? 1o0k jktojm.bw;/52iyi ssh/ $L_0$ =    m

  A certain type of elementary particle travels at a afk- r8(t *9b6t gkyb4uh/ :2lqlectq 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 s -4n m9wr8bqnlw*nm1pend 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 light-)yg :lidpm eu3d:e;. +p p*unwyears 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 measured to bgk qz( ;7),mf.k7xt vhfo 5b)ykjvi- ge $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 lightn:qn4u /q,- b,uf ftf.r)knii -years away. How fast would you have to travel so that to you the distance would be only 35 lightfkt.un ,f,n/qnib) f-qi r:u4 -years? v =    c

  Suppose you decide to travel to a star 85 light-years :eov s j/-6teebh8yqb :da. 4a6enx3y)awq(jaway at a speed that tells you x(aeb ad v6 )o b43.qtwsaqhyye/-:: 8ejjn6 ethe distance is only 25 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 tlrw /4bajzxb7k 1m.ha4:t ym*he 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 starship Enterprise had just returned fri emgc 6)90awoom a 5-year voyage while t wcm0e6o ag)i9raveling 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. How long would it take a spacecraft traora)5 cz7a6/(l* g ru f:nbfkhveling 0.960c to reach that star from Earth, as measured by obslu/6b*ro (anf7)g c5zkh fr: aervers:
(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" spacecraftlq84 xaek3ji hy;nx/ 3 at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25;3hkn 3xa xq84 jily/e 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 before87vich(*l4n ,bmaaxn it decays? The average lifetime, at rest, isvb7c nm 4x* lih(8aan, $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trave vuqoho9h;6 7 hm4jmb3ling 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 = /xw 72kvgrd:k 6y .gy1oouwa)   c

  A particle of rest mas;m d/;lhzmo(8kpa*c j s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels h;cb )aaca3-ecis7qap g) ;i, 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 momentuhh 7ol1xmn3w:y+4qr *vfo/o1bdorm+m of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requ7o ttuhrd80(kkgke+ *ires $4.82 \times 10^4 \, \text{J}$ 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 pr3;mysutu2h j9j* r151cbagr+s)z r sj ocess known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 2;9c1susz3t )u yjhrgb15m2+ ajrrsj*00 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron i94kvswn6fpwamb*(d:ab::hyn) g st / n 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 protzsd*6hpc+cr-b el:x3 vrppr(j t t:(0on in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States h 7xf wmh79w(dis about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of aruhf/ w;0i. + ,7huw5asofbv 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 p t4ys6u*q;pq karticle when its kinetic energy equals its rest energy? vpyut*;4 sqq6 k =    c

  At what speed will a7 )mzpk9m z0rwn object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to acche*s+jnwnkwso 2tz a 0nxn-3s 3 //q;helerate a proton from rest up to a speed of 0.997c? W tw+q whsz0/aes/xh3 nj2 s;n nk*o3-n =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic hmf+m5vs( r d)energy 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 pb1u ( 6yseg,zh4hg kli8hy*3mroton (that is, its kinetic energy is 750 MeV)l 4u*618k3ymzyh,bsgghhie(?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potent as;x:ivq axka h,v,,2ial difference of 105 MV? v aa,q ,a:svv k xih;,x2=    c

  What is the speed of an electron w. v,yeay t,.dhfj r7o.hose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a televi0-q.cl 8sw* ;6x.8jkxuo nq6 bducb su)8ybpwsion screen after being accelerated from r0-woxc wb.8l 8)u6cpby*n8 jud6;uksqs xbq.est by the 25,000 V of the picture tube? v =    c

Two identical particles obqh.k-.21 yd khxmxj2 rb;b l1 bwa7x0f 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 /ej38n, z h5kk0kydzz of 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 momentumzh*hf k24tytk-. omo g:kl87o 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 acceleratehx,juxqaa7 6g2 e3 7fhd 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 oftkgqk52+u6 / n :onvcn 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+4lfbe qwxa/-:58e fjjm3ix o, $^{241}\text{Am}$, 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 k4 4 jgrohch ke8;ec37vinetic energy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero h74e3 c4e8ro;hc kvjgrest mass.

  What magnetic field intensity is needed to keep 998-GeV protons rev(efq,s +7xkt *pbt yuv.u,j ;lolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic massp,.kbxvt fj (q7* ,ltuesu;y+. 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 qiz v3 81ynvv.traveling at 0.50c (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 ivvzq .38vn1y respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed 4o zv.cr0 f. 22ptfdbwof 0.50c with respect to Ear2 t4f.2czvdf .oprb w0th.
(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:*(7 gx (imkr/hhxtkx spaceship leaves the first at a speed of 0.87c with respect to the firsxgik:t rh7*(/xmx (h kt. 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 sp.4 9fpa h6ubdeeed of 0.60c. The Enterprise coh9dpua46.feb mes 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 distress 3wy 2 x-7gl(mibduwj, sends out two escape pods in opposite directions. One travels at a3yl(dm gi,jwu7w- xb2 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 samu jmdux : 4mrm)ad62flxi.n+2;hs. rqe time, rocket B passes Earth moving 0.95c r du l.+i) nfsmh mdu;jxa42rr2m xq:.6elative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earthcor3bbv6t8 shr0)n y4 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 fastemxolx8nv ,l h+kk.9t) ;ikdk2 r than about 0.1c is called relativistic -v .ko 82hitdkk x, lx;lk+n)9m 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 twkx(uj*3aqtd,vqj 1zljbqu ;13+ p)$v$ 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 wp2pzi72*ua 6wd,i+gn3 wjuvnv)mi p+ould have to be totally destroyed to run a 100-W lightbulb fnz uw2m2j+vw,p+)i vapun i *g367dpior 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of 65x-splpdi+ )etn) t 8an7rtj/c.n rjelectromagnetic 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 process.) j+ p5- x6r.lann)/ 8d pcetsj)7rtitnE =    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 6 gw a,pell-b5 qmah)6of light collides head on with a positive muon traveling at 50% the speed ofbl m ahle6g),qw-6a5 p 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, 3al;f 5oxr nkq4-u8 vpand a neutrino. Assume the neutrino's rest mass is zero, and the other mqk vr upnlf54;3 ao-x8asses 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 4lq)2szui((is)ti vl at 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 have a negative charge and a speedpy iy*9 .0juyo )gu(yi 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 i* /qxr*a*nys1y p,nvsj/h+pe nto its constituents, 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 4ern q h*p+n*vj1y,xy/ps a*s/.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 car travelin(f 3k9dlft)ztb )a.gj ,efhk6l-h r3zg 110 km/h as compared to at rest? [Hint: u ka lzfbl(e,f-)j hhz3dk 3r6t t)gf9.se the 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, ard:*;*p 2 b 35pxhqza guj-flnde moving toward each oth3ph;*dl b:xf g *uzpad2-nq j5er. 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 partium-sr ylae-9 o/mj42 icle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains (w)q oz-z::v :grmxovits power by combining matter and antimatter, achieving corowqxovg:v zzm(:-: )mplete conversion 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 that its kinetic energy is greater than its rest5zsvo 6v dsjp:/*l0 of mao *zo 6p/:djslsv5f0v ss $m_0c^2$ 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-f5;t1 ta yqz5h8)q lk6b4lxbvlong pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea tx6l ; 5aqk4 q8v1z5)fbt htlybhat 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 ofl4.7kz,q hxzzw )w4x x oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the ele. 4zhwx)z4kz q,lw7x xments 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 reactio3mg9ia fjkemf w2b06) n 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 particle's speed relative to the otkw0 mg3 mf6f )bea92ijher particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures apc7q63 9i slrte9d6y his ship to be 25 m long. On the ship, he eats his lunch in 23 min.pcyql3 6ria t6d97es 9
(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.6;nb8j a erqh2xpd9hbvi; d1x;ul t.+ You send a laser beam toward the Earth9 jdbl8 p.u vh1anhx6qei; d;xtr+ b;2 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 150,000 kg.ir(zwu st,s;)dp43k a The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the ars; t3p) dk4,(z swuispaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. W dv1lxs/v6isd 4(iv ,qjs v8*qufh0- what is the spaceship's kinetic energy? Compare with tx61 d(dvs 4w/* 0sv,8 s-vf luvqiqhijhe 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-ylwh4m-3 n 06dbh)hhyde5-l jjears from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.e40h bl yl hndj6j3) h-d-hmw50 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 thi*gfh p4l 8xwdn0z:pxz5l i24sk k8ib.s *mw-e end of a spring whose spring stiffness constant is 5sp8:l xk-g0.*wkmp ibn44whi*xzsz 2 i 8fld$k=48.7 \, \text{N/m}$. 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 mas3ew 7mmrhyaoz l(i7 2kg v;9+pj93 iabs $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.