You are in a windowless car in an exceptionally0kwu**5 cqep tg2ug) ool5am3 smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you areg*ku*c5o0wq)25mup o 3 tleag moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red lighttg;q)qo1mv80uxjjn , 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 thi,vnoj ;u)tj1 qxq0m8 gs say about absolute and relative motion?

A worker stands on top of a moving dsm rh+ik39e vy)5delp8g 2a, railroad car, and throws a heavy ball straight)y p+e ash 28m3rke5dv, idlg9 up (from his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say that theo)q cdkva3c02 y95)dwh*+w9-ocikrozn gvm ( Sun goes around the Earth? Discuss in view of the first principle of relativity (that the o(59 2 qkv-a)k hrz io*wco+0cdymcg9wv3 n)dre is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at wh:04 mg rc 2e5ya8fhfs,qwsg2iat speed would the starligh,q2:hyefgw 802rsfi4g5sa mct pass you?

The time dilation effect is sometimes exp,mj i3*tr56,xke+ fu4ov r* jmf / )g;vwpuvkpressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then dmuj5/w xu rjovfk4 *)rm pe+v3g;v6tik,fp, *oes it deal with?

Does time dilation mean that time actually passes more slowly in m9n 0800 nibos vgrmne5oving reference frames or that it only seems to 9nm00vbsg 8nneo05ri pass more slowly?

A young-looking woman astronaut has just arrived home from a l xtyw mik/d ,sds5ah,((l*0y pong trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be (sy,lxdh0dkp*w5a /(t ,mi sypossible?

If you were traveling away from Earth at speed 0.5c, would you notice a chang uxjvr.c4(dfd t(q9nyy.;;vre in(q rx;jyv(n;vfr tuyc49. d.d your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occk,;.xnhxt n0ke1 e 4t2cj*sc hur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinit*u.c-1db*q z; (se+j7( ecg2/dkrtv z okuqlne. What would happen to the relativistic preb/-cug . (+*r(oqs lj7ue qc ezk2tn;kd*vzd1dictions of length contraction and time dilation?

Discuss how our everyday lives would be differcbj28; exsqi; ent if the speed of light were only x8s;ce ijq;b2 $25 \, \text{m/s}$.

Explain how the length contraction and time di7 j/nwruhladps 0n/4*or q /e/lation formulas might be used to indicate that c is the limiti0 7/enud/rlp h4o/q* nawj/sr ng speed in the universe.

The drawing at the start of this Chapter shows uz t-ato*s7/j; o hwln4w7ck0 the street as seen by Mr Tompkins, /t4l 7 czanw ;7-u0ok* hwjtsofor whom the 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 tr*cflh -eks*jk v.1e bf +h6gw*avel at speeds less than c. Does this put an upper limit on the momentum of an elect.f-+*ck *gv *s kjlh1wfh6eebron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speeb9*e1c8 zazs a5 m1dq- m;vhlid 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 w+aa p 0-;f-.rn lau kje)hunr30ige .has more mass when compressed than wh;i)0 h- a na+jr0ue.gek. np -uflrwa3en relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destrow7y*btvz hs +71 r+pctyed." What must we say instesc z1+b rt ptw+v7y7h*ad?

  Is our intuitive notion that velocities simply add, as we did in Sech g83; kg8plnntion 3–8, completehn8;kg8p3 gl nly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length , 4 fq5+eon)5ehnaxlsii(; -0wfh cmlto be 28.2 m. How long would it b w5ae,l(s)4 fhf+iqmnch;oi nl5- x0ee when at rest? $L_0$ =    m

  A certain type of elementary particle treedmji i(n).u81,gfy avels 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 intervals de )fden) /ie0tat5( rgadm-i6upend 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-ye dktvs8s.w2 iuub+7w( ars 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 92bufvkbj/ -erpc rc f12hn -9a pion if 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, a star is 82 light-/dv j zzmr9x et2r/00hoc9e v:years away. How fast would you have to travel so that to you the distance would be only 35 light-yejrehr z2x0ze90 /vt9:v/mocd ars? v =    c

  Suppose you decide to -do 3 hi a mfgik902+mn*brwr(travel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years 0 rmairn* k+2-gbi9f d3o(mhw. 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 th,)2pb mmg m6oke 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 ot7dfygom 3ck// re:1just returned from a 5-year voyage while traveli3ef /ydo tmrgo/c:1k 7ng 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 wvo*q gc8vun17ould it take a spacecraft traveling17nu*cogvq 8v 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 speedouj- * sph-u--ti)qkn of 0.660c. It is me-ui--t)*sku hn-oqj pasured 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 h ;m;p,x7fyvg uji)w7be moving to travel 15 m before it decays? The average lifetfp7viuxhy )gj7, ;m;w ime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton5o s01icsbt4d traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice ez ;w6c)ljc5* d+jmmwits rest mass? v =    c

  A particle of rest madc8oxfyk)50 hlx/ 1x ih-v;hzss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelr1c1-ox s i)tts 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 kjqtumim e.ys9( +/3.zq z nb:of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reacteq e-4 as)rvl;d(ya9 gion requires $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaks apart in the process known rkq8g*j c4 2dref.bud)pn4 lzq*5l*pas fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass q)2r 8fl r*4bpz d4 nl. jkpegc**d5quwas lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron ipitm i.r5 z g1klh5*t3n 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 r . q+n:y:tenx+0xes la proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Unitnnz uy7 jvv1,9fix,f3 ed 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 y.hdyii 5lcic85 m46dconversion 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 kinet7 )lp:q v/ tl xm6iuhhm17ub5eic energy equals its rest energy? v77thux b /hmllpq1iue):5 vm6 =    c

  At what speed will an object's kinetic jl ;xa*l /b0d h0lfxf5x(z)jwenergy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a speu z-( w:ndv6u)kehc8ued of 0.9 udcvkhw-ez :n6 u8u()97c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton traveling b s:hsbt+uwm: vh ,j)+$2.60 \times 10^8 \, \text{m/s}$.
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 kin/:eo(ul yl)hkz (b/zi etic energy is 750 MeV)?/)h ke b((olz i:/lzuy    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accele5zmv:mn1m-; wt um-f krated by a potential difference of 105 MV? v =- wvtzumn :kfm- mm51;    c

  What is the speed of an electron whose*j )mvq nn+t3hz4j s3u kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it o, :uq n8i1b ;ih.l5 squxn8behits a television screen after being asl. b;b8no8 ih eqq:n,xu51 uiccelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of 42 95 9eycqdgzchfu+xrest 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 proton ta*8z .sh.,tzx;nwv5 wcdrt-($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 hwl72ain/ +yzaqg6i 3an 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 acctqs ) /1ah,py(e g*ueymn2,u celerated 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 proton( 9-hffrus tqzxcys0( *u2uv9 ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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, m):pv,i ha6o9fgh30czvt - mt $^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

  An electron ($m_0 =9.11 \times 10^{-31} \, \text{kg}$) is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.60 \times 10^{-14} \, \text{J}$. Determine the electron's speed $v$. v =    c

Make a graph of the kinetic energy versus momentum for9sd ommoayi (at(ef3.(5hcb - (a) a particle of nonzero rest m((5sech d9bm3ay otio(-.f a mass, and (b) a particle with zero rest mass.

  What magnetic field intensity isg( ohi,n8 -nyo needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab sync8g-nh,i o(y nohrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (w woqnei; fwc6,e/g;1 jith 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? ui/oqwg1 e6nf ;w,ce; j =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50c d9r1 kv,umggs9z3e5pwith respect to Earth. 91z9,dke3rmu gv5pgs
(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 spaceship leaves the firstte5.0 wz-ajtf)y yt9x at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with ew.yzf-tx9 5 )y0jatt 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 approachldv3td /n vwik3agqt/c ,ne 3af+w7,3 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 nv3dq +a/gvwn t3akwide7, 3lc/ ,t3fof 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 oppo)kis4 6d j/3mw i*6jy*vbi rjwsite directions. One travels at a speedid4/w* k viij6jy6mrw) s*3bj $v_1 =-0.60c$ 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 then0vv zxn3i+vgi +qge(78i-mx same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B mom +g ne i0i3-iz(qxvn8g+v7x vving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years awjxs5/y46rsoc(r 7l yy ay.
(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 ibv7i7jhjo27 5rh .re8c x(m xfs called relativistic - i.e., for whico8 e(r7rc x5j2bxjv7.hfi mh7h 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 speepz,gbhka5 y7pl89t9px0kh/fz b: h 0qd $v$ 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 totpz0u k(fje l127firp* ally destroyed to run a 100-W lightbulb for 1i 0j 2e lpu*pkf(rz17f year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an el;xe f7a8kmz (giv7y3c ectron and a positron together? A positrona c 87;x7m3yvi ekgzf( 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.) 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 kap4x8 gd6b5 kpf1k e6with a positive muon traveling at 50% the speed of light. The two muons (each of rest mass 16 k6kfpkgpad 84eb5x $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and;)g3wq hw pw*;6 zjaoa 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 neutron decays w)*63j g;oa zwq;ahwpat rest. KE =    MeV

  The Sun radiates energy at m4fnn 7q 1xxb(fllfws).l(2u 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 ayi*k0(4hl, i,r-0vdqe yym iqnd 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 breaksc,q. sai2*mqurt n2 , a helium nucleus into its constituents, two pro,.2 sc 2qua ,nir*qstmtons 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 percentageh2cj64d p npr67uaga- increase in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: usa-dhrc 2u 7 6gnpaj64pe the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a spwf8d0j 6u zq8reed of 0.935c in the laboratory, are moving toward each orf0 8w6dz8ju qther. 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 particle with momentum-qlwz .,wa ur. $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power+hd4)bhjkosse- 7 9 ba by combining matter and antimatter, achieving complete conversion of mass into energy. If td+jk- hs47 bo9as)beh he 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 accelehc nu(/q/jggzu7o1e ;rated so that its kinetic energy is greater than its rest masguqeojn z//c 7g;(u 1hs $m_0c^2$ 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 belihr(, + rdtdr7xeves 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. How does this fit +xrdrt 7 ,(drhwith 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 on*/o a6 8k ikdfaypd2r.vilf+1 e mole of oxygen react to form two moles of watea8/l2.dvykk6ia pd f rio*1f+r, the energy 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 two identical particles are created, traveling ix)q/d76u hhtfo qwg(+fb;rmwht3(t 7n opposite directions. If the speed of each particle is 0.75c, relative to the laboratory fram )q fq hh(thrgtdt(u7o7x6wbf3+/w; me of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative i 0gw(j1 yw,haqk,eo,on x53oto Earth measures his ship to be 25 m long. On the ship, he ew(gnjey3 qaoih0o5 ,w ,,oxk1 ats 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 awc-) yv4nbh3pn4( geatay from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the s-)4e cpt3by a( h4vnngpeed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The oc5mo7,jdt 5 jr61ymb dlfuqw2 3cupants would like6f,j bm2ly1o5q57 u r jdmt3dw 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 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 spzfdwj)kd42k6 eed of 0.99c. What is the spaceship's kinetic energy? Compare with t2d64 k zkjw)dfhe 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-y9 tz ).ct,-zr8qe dzujears from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work )zc.ut d-r zj9zt,qe8must 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 p s5zeq: 5t9tzwhose spring stiffness constantz ez p:qt5ts59 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 m nrx00kl6ir;bass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.