You are in a windowless car in an exceptio x(zs1 sszl39t 4m2)6tvsdcdj nally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to dds9lvj3zs1c26 4dt )(tx ss mzetermine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out ocb2slkm0() )t p eh)azf 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. )ehac2zpms0l)bt ) k( What does this say about absolute and relative motion?

A worker stands on top of a moving railroadiyt9yew/ u/jc :/es 5o car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, wil 9o:wj i/ scy/ete/yu5l the ball land on the car or behind it?

Does the Earth really go arosmn5nm z3of9* und the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no bo s*n5n9fm 3zmest reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at wu-m7g6 8p, q*pgwgq jihat speed would thm7pqju,86- gpqg *gi we starlight pass you?

The time dilation effect is sometimesm-)vi6fw pl6z mob:-g expressed as “moving clocks run slowly.” Actually, this effect has nothing to do wmop:v6- )l6izbf-mgwith motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in mpe hsdcn,)q;* am:)e w:qak6j m5/wyuoving reference frames or that it only seems to pasw a)mkq5u,c qp:ny awse6*h)dme/:j;s more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She ru mr0g*yj3gs6t p +8bydshes up to an old gray-haired man and in the ensuing conversation refers to him as hers6dm 3+gy *yt08jgprb son. How might this be possible?

If you were traveling away from Earth at spf7:qkikic t() eed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observ7(kkf:iq t) icers on Earth using telescopes say about you?

Do time dilation and0jhod p5-7grf length contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were inf t+tvfp;ag (pb6wdy; 0inite. What would happen to the relativistic predictions of length contraction a0( gwtf;d tp+p;6 vaybnd time dilation?

Discuss how our everyday lives would be different ifm6hk.j9w:dvny h a- 2y the speed of light were onl.- kvhy:h yanjm92 dw6y $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be use7f0bwsr1; oja yet(ox3(es5n dupy :,d to indicate that c:bses3dforxao p,(0 n u ;1eyyw75jt ( is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as s bp:tvu8xh77y een by Mr Tompkins, for whom the by 78ht: xv7puspeed 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 traauv 0oazh-i4fa :d 0u:vel at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, whz-a:ah 0f4:vuaodi0uat is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonfus1,x x t;8tqdr4we.), pwzw8/ s noszero rest mass 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 mass when ci-4 qqpgl)o. 7gm0gv eompressed than when ). lo gieqvpgg4m7q-0 relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither b +ha jvm,w 6gtr rcdw*/f.y20ye created nor destroyed." What must y yv2t.rwc0h/f grmj wd6*+,awe say instead?

  Is our intuitive notion that v(ynpj ga 0;.chab n1.xelocities simply add, as we did in Section 3–8, completely wrong?hxba .1.jng ;c0p(yan ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 21(l/fmr5 tx1rnw *ukx 8.2 m. How long wofr/ (l wmktxu*115 rnxuld it be when at rest? $L_0$ =    m

  A certain type of el id806dtf 4)qpouyr 3vementary particle 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 depend on the fkh 2 v9bvenfk8eqd8rffs6-( 6actor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 aork *1/iii esz4d;frqz x75c * 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 lifetime6zq8o+)h r3.(o iuxggly+fvn 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 ligkqfd/2f5 n .nlht-years away. How fast would you have to travel so that to you the distance would be only 3dnf. k/2lf5q n5 light-years? v =    c

  Suppose you decide to travelrvs)uc b/)m+ uva4co0 to a star 85 light-years away at a speed that tells uc rcb/+0)vuv ms4a o)you the 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 the Earth i+pk g0/a 6oi9dqv;dc os $11.2 \times 10^3 \, \text{m/s}$. 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 Enterpmydkf0 31k ipk l7nmn2+ yc lq-bl*ycjc8,)- lrise had just returned from a 5-yea7,-cyk )2jyicl qp3-+m0y nc l1f8 lk*md nlkbr voyage while traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10j0sg,nqbkck)xx j7n 21yg j3 5.6 light-years away. How long would it take a spacecraft traveling 0.960c to re0gn1gbq,y)knj xcj 5ksx3j7 2ach 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 n;ix f 9r;kz7xqmp:9 l )/sflfa speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m hi)7lfmpf xl;/insz9qf; 9xk r:gh.
(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 aver07ra:t* mdnuiage pion be moving to travel 15 m before it decays? The average lifetimad 07rui n:*tme, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelingjndslt 8/e8 08y) zgpz 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 maz az vp36dpzvc+uw i53t,:jo1 ss? v =    c

  A particle of rest m5 1 b,ejar4,z jap4saeass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ahdc d -7;sq2oet $v =0.10c$. 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 inc) ;57gb9 hah l9utneh momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi zznwl9.b cvgjbj 8ts 3m/;2d pv7u ,sv:lx;a(res $4.82 \times 10^4 \, \text{J}$ 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 as fission in a *j29ywhbaj 3k nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass wasjyab wj 2h*9k3 lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules and in 4 pc*qg8;dzax $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a prlvmfpnkaz4 eji/ 6.;31 t;tfjhxz 6k2oton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Strli*)mgt ulo mmik,-v;+-b8rates 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 va c j,d;yyauwd1,c+0be 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 eq74 u ayrs8peknx8d;se28 unq2p2 e7 sfuals its rest energy? v = er7 8panxq22kuees4u2ysd8 8f; p7n s   c

  At what speed will an objeir9 2xq1tbmjkcdjjth -9.6m :ct's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a protkyj ;yi r df5f8r7 f5:-g7jbhuon from rest up to a speed of 0.997c? W = 7iyjudfgh rk:frjb ;f y5 7-58   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 j 2c6uaphqp0(7xj i.z ivl7(ktraveling $2.60 \times 10^8 \, \text{m/s}$.
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, mua*q-tb 3etl-kn7jr4 s8 *fkv*r6jr,h8ec pits kinetic energy is 750 MeV)-ku,*lesnhmt 7fr3 aetrc8 8 4 r*j6b*-pqkvj?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed off.cy c 8*afk/heo8v /t a proton accelerated by a potential difference of 105 MV? v .vt /cffe/ 88oy *ckah=    c

  What is the speed of an electron whose kinetic energy is 1.00 Mej7k2t0gx6yc qn qys+qrmt264V? v =    c

  What is the speed of an electron just before it hits a television screenp w4gjw)v-du* after being accelerated from rest by th*4w)jdu w- pgve 25,000 V of the picture tube? v =    c

Two identical particles of rest mass*)/usjefx g7 h $m_0$ 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 ygn 1 gz.72rkzh v+wc3proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentumznpvdfoae0 u6,+ ov( q(jn ju/p- 7:zn 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 mar 5wgl-3wrl)u4:ber qss 27,000 kg is 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 and momentum of a pri6 ohrx(nebw3d7 mre f84xr 8;oton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 /o;y dkj5ni mi6cim2., $^{241}\text{Am}$, 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 e t,5af /kie26htje7n tnergy versus momentum for (a) a particle of nonzero r/2tefje6tkin5 h 7,taest mass, and (b) a particle with zero rest mass.

  What magnetic field ina iewk q:0(ztsdqnjqjl4,19 .tensity is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron) qw ldk,n :.0q9(isetjjaq14z? 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 (with respect to the Evwao mh -4czt -a 8-.s33evtve4 m9ja(ai kck2arth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respea4t-4kz(ek .v3v2iv- ojwth3ce 8- aa9m cmasct to the Earth? u =    c

  Two spaceships leave Earth i:;r,mzy (r l0khe )9 dblmzhj*n opposite directions, each with a speed of 0.50c with :z 0h,y dlz(r mr;bhl9)*kmejrespect 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 traveling at 0.71c. A second spaceship le) oz.:*qnbx olaves the first at a lb*:.ox qn zo)speed of 0.87c with respect to the first. 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 speed of 0.ueo;n-vngwe 4-1u 5kj60c. 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 is the relative nu-egw14ek5-jun ov ; speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods k0r wu,3k w6xgin opposite directions. One travel 0k k6u3x,wwrgs 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 tq09i nyy9: cgzhe same time, rocket B passes Earth moving 0.95c relative to Eartnz0y gi9q:y9ch in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-yearsg (e38v8 dhrh 3pdou/p 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 c3s u v w,*w 5xjn7qzeoyj(f9jg*)yvy 3alled relativistic - i.e., for which the correction using special relativity is a significant effect. Determine t53, 7ne(y zf9qgosywyjv j*uxwjv)*3 he 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 -w*lt/sbyyl9c sk 6f7 $v$ 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 totallb9lrbc):qwv 0cq f6 /sy destroyed to run a 100-W lightbulb forl9bqv6rc0w: bs)/ f qc 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of elecp 7bs) pxrod.u: mfixzm:1m:,tromagnetic 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 mm)xmx p:d r.:ozf,b :p17usihas 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 ip6oof/, 5 ol2g gyf8 ks0nk*bat 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest mass lg6s 0kofoy p /5o82n, bkif*g$m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino. Ashpvze 9qwqb : gnvutra )/)1v9/g3 o)usume the neutrino's rest mass is zero, and the other masses can be found in the3vu) u p)t z: abq1g vr9ghw)/vn9/qeo 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 ab uw5wzas+kmr3f p85 gmi1y j81out $4 \times 10^{26} \, \text{W}$.
(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 mea2k: tt.v9d03xhyvvysf ,mzb ;sured to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be requfwarc 5l n .a06pe: o*gr1fj6dired to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an ele1* ff .d6nejpacr0 6arg5l:w octron), 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 increasecok1 i,zas6( -lmu:xw in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the bka:xoiuc,slwzm1-( 6 inomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the9lu n0vbipg2* laboratory, are moving toward each other. Detebvip *l2u9ng 0rmine
(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 particltap- uy4u:7eij o.buj 4d gqez x(05z1x. ite0e with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its pow vxnp/ztrpi, ov 6*n7/er by combining matter and antimatter, achieving complete conversion of mass into ener/rx6o inp7vt, nzv*p/gy. 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 kinet6pqci/ 0qwhz+ ic energy is greater than its rest masqc6+wi pz/qh0s $m_0c^2$ 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/7na *53a: p0elw kxmq i;cpro 12.0-m-long barn if he runs fast enough (ce a/:7 wncm5plioqka03 p;xr*arrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two moles of wz/ qef;f/y w-h)4: ueehlvv 6aater, the energy released is 484 kJ. How much does the mass of the elements decrease in this e) y a//h;l4eu6qvfzh :-ewfvreaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two ide4;c ku;7p-ytbiwr(1nj h -ab-dp zrx/ntical particles are created, traveling in opposite directions. If the s7u4w(yrphdat;c- xb jrb;1kn -/-pizpeed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0k)nb2of7 g vw+og3 xu2wx lj;9.75c relative to Earth measures his ship to9 )2+7wuxf3ox;g2 bvo lknjgw be 25 m long. On the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away bcjr.kz,j1 ew;ab/d3/ ptk n;from Earth. You send a laser beam toward the Earth trav1 bn.p, kwejbtrz k/c;jd;a /3eling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its ogy3f,3 a8s ay1a 8zgjpccupants 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 changes mass directag jg81asfap zyy833,ly 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. az8 ehp:3alms.wg j0o zn,-8rWhat is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption spzm j zlr38ganea.o,-: 8w0h(about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vic0vwv 2krc1b6xmw9 uyc ,( he+hinity of a 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 v6+uw c( c90 vmhkrh21eywx,bwork must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring d5(y 3 o6v j0fyhfpnq8whose spring stiffness constantn yf 38h5 q(doj0pfyv6 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 mamny ic0piz(;.l(v n 5sss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.