You are in a windowless car in an excl)9zu5 i d5khq4o zux co;k4*neptionally smooth train moving at constant velocity. kku5 zn xoc)d5u4z9h;lo4qi* 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 beingx6cs9eogv 5wwm (*7cam d)y.k 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 p m6.ge 5sod )mk( 79*wccvwyxaedal, 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, l * yeu8jhlf,4)xdbc(and throws a heavy ball straight up (from his point of view). Ignoring air j x8b*y, hcl()elufd4 resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? 6tu7q ;ip *nkp,s1nnc Or is it also valid to say that the Sun goes around the Earth?sq;,c nnt 6iu71k *npp Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speabecui,x1 vshvx8t90+8*wic ed would the starlight pass yoc09i+xu8hi,vbat x1v e* 8 swcu?

The time dilation effect is sometimes expressed as “moving clocks rtd b;0 4-,nudyn2mysa.gmcou: , m2f .xwr8wmun slowly.” Actually, this effect has nothing to do with m.w gymyorcd2 w n0dab,s4 m2ux,: .mtm ;un8-fotion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving referen wh9ke xrvo0/s 04td/s/dny(s ce frames or that it only seems tovhr/(st9dwd/k n eoxy0/ 0 4ss pass more slowly?

A young-looking woman astronaut has just arrivetdtcda;;a3 )ye7iu 7 gd home from a long trip. She rushes up toy7t7uea)3 ac d;d;tg i an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth am95,qaywt /sf t speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? W sat/ qmf95,ywhat would observers on Earth using telescopes say about you?

Do time dilation and leng rh/ysjll io/ah;y: w; 2k-zon5jzeg+3, yo3ith contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were inmujtl,bzo2 35.i:kjq j 6k4u nfinite. What would happen to the relativistic predictions i 5k jq:63tmb,kujuz4jol. 2n of length contraction and time dilation?

Discuss how our everyday lives would lkit xfx325e5jr1-iy be different if the speed of light were only xf5ii 3ej1rl25 txk-y $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas mighv9ny;kcf,)flk.mww/wp i :9a t be used to i).w vkyfw;cm:ki99 /fn w ,aplndicate that c is the limiting speed in the universe.

The drawing at the start of tgrlf d6njg -5*)-u ayl8.uxrxhis Chapter shows the street as seen by Mr Tompkins, for whom t r8l)*ua gnrxyu56d.gl -fxj- he speed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speaflr-v.ggi a g;6f39hfk7 r*e eds less than c. Does this put an upper limit on thfv7lar* ;. akehfi63 ggr9 g-fe momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mas8*0xwr:dt o uh36rskg s 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 mean that a spring has more(l0e-31 zwrcc e qlw.r mass when compressed than wheq0c(rc1 -3w e .elwlzrn relaxed? ----待选择----yesno 

It is not correct to say that "matter can neitrilk. nq*hw 1+her be created nor destroyed." What must we sanhilr *w.1k +qy instead?

  Is our intuitive notion that velocities simply add,uua r(0nm xrg.hh)88 zjaomos7)9sb 7e0 p7hl as we did in Section 3–8, completely ogas7)78h .9uhz( r0 j8s lnmoupe)xa 7brm0 hwrong? ----待选择----yesno 

  A spaceship passes you at a speed ofej*agk t: -5urs0a3 bq 0.750c. You measure its length to be 28.2 m. How long would i5* 3e-q0sa rktagu :bjt be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at )zpjrzb*- o9 8:ajdkya 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 intervalsig:yepa59 y73x;kj nt 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- l)e*updz g,rlrgd.k ,wg.a 8 star 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 aao/gi;p kgxh j-1n4hwl)gf 90verage 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, a star is 82 light-years awayl . dbaj38by7cs ,xhc5. How fast would you have to travlsj, b3 .8hxb5d7cyacel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-y9 a6f-xsmlzw8rfit/6 ears away at a speed that tells you the distance is only 25 light-years. How ma fsfwm6zit6xlr9 a /-8ny 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 th8y* p p6-cmlche 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 m5gzba;5t6ay 92bvkx from a 5-year voyage while tram5t5 kab;y 6bz2g 9xvaveling 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-9: h u5;t pdj fnwro6s3kvyy51years away. How long would it take a spacecraft traveling 0.960co3u:dyrn;95 tk5fjh1 syp wv6 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 speed onn tlc4;qo;(wh f(j/ ef 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m higw to((;;ln/h4nf qejc h.
(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 mo*ul ;vki9wx z-ving to travel 15 m before it decays? The average lifetimezluw;vi*-k x9 , at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travlp.8bx8-p 96t ajydf jeling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistid y5ck k6f8,daso(1i g ud.k;oc mass be twice its rest mass? v =    c

  A particle of rest m7w(j;cslin ej1j/7- hylwfp o+n+b u(ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travell;xn o3f:. v75ba09dxkvx le ps 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 cha4r5vxr-kurlxq w .24w nge in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactiok2t8i*el w h*6no 8jkcn 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 ps7 acqx(+0 (noz87gozwz en ks-h0o1apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lo 7o zse ng(c1a qox 0-0(7ok8hws+znpzst in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an elec89a8cd 8pglzrb0emt6 u5 sa(htron 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 p. rzdovj3 s(8uroton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption n7zf07zpt r ynf45qm;in the United States is 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 1.0 gramda * mx2 4gtu,gvh/2ud0jk id9 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 resb fx 9yxkn *w.anyv2pgh 2(14dt energy? bhda .yxyvwk(*2 4xpnn2gf19v =    c

  At what speed will an object's p45,klwukbjj p2s6v6 kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is requiredcfs8i:7y t y7y to accelerate a proton from rest up to a speed of 0.99y 7 t:s7fyyic87c? 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 pai0 dd,ragfe5;u +i: aroton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinezysq+l0,dy fszo;m iq4 r9e4yw2n:8u tic energy is 750 MeV)di80onqe4u; , yys4s mywr :92+lqzzf?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentia0q e 3jcklt5cq9 6ao-fl difference of 105 MV? v =toaql j q kc5-9f0c6e3    c

  What is the speed of an electron whose kinetic energy is 1.0f9 *bq,3 sjc22yl3d h;vygnpz.6ilsu0 MeV? v =    c

  What is the speed of an electron just before it hits a televisimo;0po5/ 5b i4mf .zy2tuep avon screen after being accelerated from rest by the 25,000 V of the picture tube? vymp uao o;v5t4z0 mbi2.5fp /e =    c

Two identical partic7yx759;9i mo-do njsym jo;c yd9l4 7hiuf5kfles 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 of a prot ym ut0wv my:f3oa/9f/0jv *lton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentum of an yw4cc, w 5gtt)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 accelerated tb-6dar8ey -invr 4r )so 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 :obiq4wlxxrnw 0i/8p/(uq0p 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 nucleus, pcqoe 67(0yp-br8nwl $^{241}\text{Am}$, 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 ng 6,(+(h a0andur5urcln*yp kinetic energy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero +ln*udh(n yuag56,a n0r(cpr rest mass.

  What magnetic field intensit909tohol ise *y is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass isite9hol90o*s $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [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 Earth7hcuxzaxl6b :s)gp,qd + 4ef5 ) 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 thu+lz7as6dpq:x, )h c xefg 5b4e Earth? u =    c

  Two spaceships leave Ea ,d*tl a n-j+4ifbxqr/rth in opposite directions, each with a speed of 0.50c with fj*4tldrxq-,a/ n+ ibrespect 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 trav9jh(+ua gq 8nfle;f)xeling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the x8ffah;l9+ ) uejgnq (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 alie(. o4zr+0/oyiad0j;(byqqha-m asjc n vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What i/zo0qj4ayhcm ;d(aj o-sy.bq0+ i a(rs 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. j5o)i xez-c84- gx mdypys:-h One travels - gey 8o)yh:xdsp-z4im j-xc5at 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 cg5)b0g(xt ooyj /,h ptime, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it pas)(x,g0 yopbcjt5o /g hses A? u' =    c

  The nearest star to Earth is Proxima Centaufce1r3 az7e9 rri, 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 tx+z;salooam 4 (ly(o7raveling faster than about 0.1c is called relativisml4xl oao o((zys;7 +atic - 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 spee) nmd1mfctt624co t-w6 )nds8rhae 9fd $v$ 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 destroyed to r(bhrfy:blxrr7;- )tv:ac 7x run a 100-W lightbulb for xbbltr;yxa r 7vr h)c7:r:f- (1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is o7 irdd3,p93fsyh,dsj e ,0qrneeded 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 proc 3,dd ,r,70f q3dsesorph9yjiess.) 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 yuiqv,l7ik:a 2d33g v head on with a positive muon traveling at 50% the speed3ay l u,i3gq2v kv:id7 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;we)r+k5l z dson, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in )z w+s k5re;ldthe 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 bf-z jcq(t .u-dmgd n0r-,vd6 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 q,fq 9+inku l(o( zgk8g8k0:i if ivs*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 aok j+zi1b,4un helium nucleus into its constituents, two prnkju z+,b14 oiotons 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 is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the v2mv5.bp8k+b1;cc;jd zor )ksnukl *9y,jy l (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expc vk2b5l d1;)rp 9;v,*n.zm uk8j+ ocksylb yjansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the luf3xdc 0,k g) sv2vp,xaboratory, are moving toward each other. Dvsxd 3)kfv ,g x2pu,c0etermine
(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 paa0;p) lwqp tmdo s,c092p;xoyrticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combininjr .5* 3 k. afy-rsmtrihnq)+vg matter and antimatter, achieving complete conversion of mass intoy+. m rj if5-q*vr knras3)h.t 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 kinet;wp s(o -blh1pdzr3t7k5n kg/ ic energy is greater than its rest mass w1 rk7-bd/ (poghk;nt3 z5lps$m_0c^2$ 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 t,a.fr z(w yn5bhat 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 detawza y,5f .(rnbil. 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 /7em 9b6nslnxof oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements dees/nb 6 7xnml9crease 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, travg ufkln+;;hol v b9l/:ao +eb(eling in opposite directions. If the speed of each particle is 0.75c, relative to the luonl+ ea bk;l:fg+;l9o/bv( haboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship eta ./j:7a ;upcz nu.straveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his luncap tj7c zsuu.a:;n e/.h 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 )s-se2k)tw pxeuh6 k8 Earth. You send a laser beaske6p2s 8)xkue h-t)wm 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 or(ereey5 co (-ccupants 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 engine of the spaceship changre(eo5( -ryec es 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 of 0.99c. What is the spac,f9 3umktrrn w2repuc64lq9 6 eship's kinetic energy? Compare with the total U.S. annual energy consumption (qc6umrn 92ruepr,wl 3 tk9f64about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a 88mvv y+b1i kjn6yuv cyt9)p3.uq ojlu(.q(q 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 to bring it to the speed necessary for t( vuqnovu. ijb k).yl8(3yjvpy q+8uq c96m t1his trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffness :i(+kgqjzzp s7m*q,s constantz+m(, s: jk*sigqzqp7 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 mapz *l*pp xqwdj r-3a1 or7e38fss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.