You are in a windowless car in an excepnanog mbx *(p5c2w62m tionally smooth train moving at constant gmc6x(5p a w2nn2mo *bvelocity. 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 being at a red light when, out of the cuf 99 zmcnj39forner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking9 f9z9ucm 3jfn that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a mt37wh qse:byge7us+b c fh9.k2f ;s.g oving railroad car, and throws a heavy ball straight up (from his q gtssuf 2fb.3;yk79 7he ew+ghc:.sbpoint of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really g/.ft gmde xy5:r -)sdvo around the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of r:mxy-ev gt dds /5)f.the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c awsulyy /bf n -wr841d)id.mhb,ay from a star, at what speed would the starlight ndml1hdb4ru /sy,fb 8.)w-yi pass you?

The time dilation effect is sometimes expressed as “moving clof1e c)t.0jbc iq(gg p)cks run slowly.” Actually, this ef pc(g10q )j.f) etcgibfect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that tim73sitsx7:5ng+te+o twlnh k:e actually passes more slowly in moving reference frames or+ nt s:7 :e+t3tnlhxgwk57soi that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. l(8bk63wnaz9klw g- d She rushes up to an old gray-haired man and in the enalw(z3w b- k 98k6dlngsuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you qqp :i7 e thz1l.nr;;dnotice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about yo;nperhq. 1 :dz;iqlt7 u?

Do time dilation and length )khzbn 2ehs:1 contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What wf1*wa )ctuub bvi t473ould happen to the relativistic predictions of length contraction and t w7*v c4iu3bf)1buattime dilation?

Discuss how our everyday lives would be different if the speed of lightg9 (h f0l+p.2jr4bvne9f 6l -daegzt k were only l24 pav96zfr tbn- lkfeedh ( .+g0jg9$25 \, \text{m/s}$.

Explain how the length contraction and ti(j kx1g)p0 bmaq+x( dwlm6b, fme dilation formulas might be used to indicate that c is the 16+bm m(bxgqdw ka0lj)f, xp( limiting speed in the universe.

The drawing at the start of this Chapter shows the streg5.dw euekeeml(0 2x3pbl f:; et as seen by Mr Tompkins, for whbl.f 3mge2;dxk: u eewe5(0lpom 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 travel at speeds less t1(9 ykdzdd9i1mbt9ff a.c 3kehan c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If n b1 fdtze9dfkk1(idy9.9ca3m ot, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the specrs5ri:me u3,ed 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, does47n m x3;y zfn 2uns-jj3o :gz+gekt*j this mean that a spring has more mass when compressedz *jg-n e7+4som3 yg zuj 3n:kn2tx;jf than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed." Whvwsdz)c;19mu72lx ,gk cyht( at must we say intv c;w ,hk) u2gcl9 (7dz1myxsstead?

  Is our intuitive notion that velocities simply add, af qqxdw(ujw *p47;6cos we did in Section 3–8, completely w7 q*u p(4fcxdq6wjo w;rong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You mea23exn ehs(vnaj pk()h: 6hux;sure its length to be 28.2 m. How long exn;he(3)n(hjx ahu2sk :v6 pwould it be when at rest? $L_0$ =    m

  A certain type of elementary particjf 1ti5gafx542 mdw 9ule travels 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 i5z */awgo2 eodepend 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-years from Earth at a )h :jy.+cv-seiivtc on6 i(6rr .t;igspeed 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 p l1xj quw(;2uits 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-yearg2erh2p pd8(z s away. How fast would you have to travel so that to you the distance would be only 35 ligh pgh(2p8rdze 2t-years? v =    c

  Suppose you decide to travel to a star 85 light-years awayygmh ao (i/y qy82.zuo27) bho at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the tripaoom . yozhy/biuq 2g8)y(h72 ? 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 Eartw.cet wm4ot 75h 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 5pe5. 8u1t b-qzdewj ;hgl 7ubjust returned from a 5-year voyage while traveling at 0u8 ephu b5wl51jz7e ;g-qbtd ..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 vf**q9 zfx jtfkd8okb35 w*p: away. How long would it take a spacecraft traveling 0.960c to reach d9tjxf* kk 3*8ffw * v:5qbzopthat 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 of )eq 7x q.1jtcan-e*ba,)j g*fb9o htw0.660c. It is measured in your frame to be 4.80 m long atgae *1jte .o*q bjh7nbx wacq,)-)f9nd 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 b9btmx3/ r9 ygte moving to travel 15 m before it decays? The average lifetime, at rexgmtb99 t r/y3st, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of owfvl)g2vuewv1 p):7a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its2pw r wmf*nt;wuc 1z(, rest mass? v =    c

  A particle of rest mass k+3 hq:mke+c v$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travew:cd 3hpse2 m+ls 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 momentu6r( fi yi:yvu*7fxyn7w8zh,u m of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical react 2p5tazr:ja5v i:izi9ns3 .od ion 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 proc(q:;ry v7s4qwy sdf pxpy2 ,(k8jqra 1ess known as fission in a nuclear84 1r,day ( s r(kxqpfv72s :;yjwqypq reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of mvd442rlwx9gevsdi 9 wq8j34an electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of0 2j;er:tz l-y at;fvu a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumptn45 hl) h/udfiion 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 b;: m+if yr*ymu:d ,vufr/ia+ve obtained from conversion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic energy equal,9xv5 txifo/br oavd5pcn (f,q ( 4(nls its rest energy? v (q(45oivpn(,arffn bvo,x9d /c x5lt=    c

  At what speed will an objecjwj(.mxm (-r+eii-yxca ( j+4 bvy+pxt's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a )hhev b:2k,jssx 6z8nspeed of 0.997c? be628xhh vzs:,nkjs )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 - nry2tab53 e dw4(gvatraveling $2.60 \times 10^8 \, \text{m/s}$.
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, it0bwy2e 5 35hrm 5(apmim:qojwu/1l nhs kinetic energy is 750 MeV)? 3qm0eji mobhumw2w5yl 5hrn5(p/1a :   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerm3c 1w6mf dsjr2s 1y.lated by a potential difference of 105 MV? v y mcj r 16s1m2.3fwlsd=    c

  What is the speed of an electron whose kinetic energy i rnb)2(e,zdx) v n( xbpy/afr8s 1.00 MeV? v =    c

  What is the speed of an elect*p z2;8 qaou rv7iosp8ron just before it hits a television screen after being accelerated from rest op2 7ro;iu sqv*8z8ap by the 25,000 V of the picture tube? v =    c

Two identical particles o,d l-xc zim4(ef 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 prnru xv58, rqhnbcd :/0q(a y/moton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momebt*sv l 3 pa 4*ejh:brdk.:dlu8i:x ;rntum 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 isz)7p )c5k2hklvkovs g5, d ms :j:u8ov accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energy andq0sokuv1x m-y 4h):rjev/z8d 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, 4f6yhoj(wodfg7z+ w.$^{241}\text{Am}$, 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 mom 4t5lil 71m;wpfcbw+rentum for (a) a particle of nonzero rest mass, and (b) a particle with zero 1im74cp5l bw+ftw ;rlrest mass.

  What magnetic field intensity is needed to keep 998-GeV8qh) olkp -l;zrr -pqg07.5rd 0rttk i protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Uslrt rgko);td08 qi-prq5r hz-p.l07ke 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 (with resp5q*krvta +;g wect 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 r;q +tgv k*5wato the Earth? u =    c

  Two spaceships leave Earth in opposite directlmk+ -o fk2,,xp k-yfb4ozr8rions, each with a speed of 0.50c with respect to Earthrz, l-opkofmk4fx+b r8k2-, y.
(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. e4row 3/ m7irza, mh+cA second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to E/4errz,miwc m 3a h7o+arth 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. Thstun v9v(4uwi919 m p,xx0w tle 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 is the re(9 v0u4t9inx w, tvmx91lspw ulative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. One cbrpoo wi9es2 ojuc0-2)n x1,travelsc- u2xp1c)j o0 ,ob2wrson9ie 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 -+t48lkm2jh(m v la2qfuc pzz g.5w3e the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast ilm5awlg+ cv8-z.3m (f hkpzjt2qeu 24 s B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Pr lgwp*,u zhny;/v0a5 ooxima 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 faster than about 0.1c is called relmi czd zf7,o77ativistic - i.e., for which the correction using special relativitydcz7 ofmi77z, 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 +y *wl9ai aro+$v$ 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 8t ,ccy 7h,pdltotally destroyed to run a 100-W lightbc c8d,hy7,tp lulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagneticu 08zn wfagf;7 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 tfnwf8ugz7a;0 his 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 oiy3.eo /* uq90v 7gk3w m )ghvjstwv+of light collides head on with a positive muon traveling a y.uo3g9e/+w7ji)o 0 q vgsh3* mvvkwtt 50% the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a protol(twhw;coo - 5c0 gyhc1bk:5uto6wgz .j4 cs.n, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles wt.(ltw; jc.g:g ho ccz05ywco51u4k6shb- o when a neutron decays at rest. KE =    MeV

  The Sun radiates energ71rt4anbg o y*y 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 anwd/sq08qki(p1 tvj ,kd 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 iv7akcx dyj*yr5( 9v nwpx8 *z)nto its constituents, two protons and two neut*yz*79y(vcn5a kv jd )8wxpx rrons? 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 (relativistic) j 9xre,ac 0ymqkm. d-4mass of a car traveling 110 km/h as comparmxmjqd4,e9yc ra.- 0ked to at rest? [Hint: use 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, are moving t*3xxi ( om4/6lz o+ii:kbcqlx oward each other. ll:c3*k/imz ( 6b4io+xxix oq 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 pw f+w1( mh8 hv:qcs0ogm;)nl uarticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powa4ojn*cv4,*5eh cak jsu, .eyer by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is ap j45*cjecou e,vk4.* nay, hsaproximately $5 \times 10^9 \, \text{kg}$, 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 accelbex)wi94 n z/ .xlnfg6erated so that its kinetic energy is greater than its rest ma zfb x6le/g49x n)ni.wss $m_0c^2$ 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 into a 19 g-qs .x:oseb2.0-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 t:q.g-xs9s eb ohat 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 andh/iaif 8swpil80 u40 e one mole of oxygen react to form two moles of water, the energy released is 484 ke8li0a sp4ii0huw/ f8J. 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 sd9pa ,su(2l4 wb f5krin 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 tu(f,29s kspd54lrab wo the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative tkc 1f-ggj/ci;g.br; xxee 2)jo Earth measures his ship to be 25 m fcg xb;j).eg;c -ri/gxk21 jelong. 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 0.85: 7t9zypwhmp5c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative t 75my:pwtzp 9ho 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 150,9s tpui jf18c(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 changes mass directly to ene if1j9uspt(c8 rgy. 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 sperg0 ;zpxh/ *pped of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energrg;php* z 0x/py 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-year3cpunqo6 g8( ps from Earth. Passengers on the ship want the (one-way) trip to takeoucn 6p8pq3g ( 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 en7jxe y u ygv1s3ui045nd of a spring whose spring stiffness constant is ujy5 0 7 ueigys341xnv$k=48.7 \, \text{N/m}$. 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 mass 5etoikc,v)cm.+ yl l7$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.