You are in a windowless cx-d wwnm9w.q1wb(+(yaor :iq ar in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determind+ a.rx(nobw9(:wmi qy wq1w-e 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 coi c(k3e u*6hlurner of your eye, you see the car beside you creep forward. Instinctively you stomp on eu*(cul 6i3kh the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and umn wb4k pem/*zr8 c5ia90e:e throws a heavy ball straight up (from his po5r0ikun m4wm:b9z8pe c* ea /eint 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 tg m)93flqxcvs kub64 (he Sun gb(x 4ukqmls6) g93cf voes around the Earth? 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 na145j( rsjyya3 rzo,away from a star, at what speed would the starligrn (j 4zor3 ajy1ays5,ht pass you?

The time dilation efa u b1c5p(c6bdfect is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal wita p(bb1ucdc65h?

Does time dilation mean that timk2 9 ihv5hv6nbjw2cj0e actually passes more slowly in moving reference frames or that it only seems to pass more slowly9k0bvv5n2 2ichjjh w6 ?

A young-looking woman astronaut has just arrived home from a lo akze6uxjfrjkqs4c 4,.ew e(hu1 ;+ rl(tdn4.ng trip. She rushes up to an old d .lh(4c,kr.nxfet4+e(sru z6k4 ej q wau;1j gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away fromx9o0 gv tm*pzfa47sp8 Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about vsgx f4 0t*mz9pao87 pyou?

Do time dilation and length contraction occur at ordinary speeds, sayoa3ww6 3k fkfwka48t - $90 \, \text{km/h}$?

Suppose the speed of light were infiniteaji8pr7 8 gc7;lf6qe8(lgs ws. What would happen to the relativistic predictions of length contraction and time w ijl88cle7a8s g(7rs q;pf6gdilation?

Discuss how our everyday lives would be different if the speed of link1vmvgm8 m pk,; o*z8ght were onlnzvm ,okv m18pk*8; mgy $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used zq3o eny)m6 v5to indicate that c is the limitinv q6nzmo)35ye g speed in the universe.

The drawing at the start of this Chapter thq6(v.,ui jib+9ve*aor /kx shows the street as seen by Mr Tompkins, for whom the speed of ligh9ev .6xjv/*t ahkiqbuo,( ri+t is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Does this put an u3ssgk z 3e2:rspper limit on the momentum of an electron? If so, what is this upper limit? If not, explai3 : keszg3ss2rn. ----待选择----yesno 

  Can a particle of nonzero8drth3k-m bq7 wb+5xq 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 t-*rzzf,1fgx a spring has more mass when compress1tgrx zz,*f-fed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyedci56au mzpe2x,m u.2 t." What must we samuu2 ec itx ,m52p.z6ay instead?

  Is our intuitive notion that velocities simply add, as, c iga7*u(f+okuda n8 we did in Section 3–8, completely wrong?7(kf,dgnuo8+ *ciu aa  ----待选择----yesno 

  A spaceship passes you at a spwo0 pja:;7 5x njr;c9 .jeefvneed of 0.750c. You measure its length to be 28.2 m. How long would it be when at resceafrej5v7:0 9;.pxj;nwj n ot? $L_0$ =    m

  A certain type of elemwt (2fl3mx4q yentary 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 intervalql:ny ;6 tz+ rn9gwu7ms 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 star 125 light-years from Eart,l ;6i )0na nq(jkjwbua8 sq.qq4wqg4h 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 avx vn 3.k bbhev65u4ja.erage 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 away./2zxkswks.ddy s 0qnl+qr(4b /qygqs70 +6 ge How fast would you have to travel so that to you the distance would be only 35 4nzbdyqsyds q 0s(0gg6l2ke /++7w q/sxqr k.light-years? v =    c

  Suppose you decide to travela;;u18xgx)mn. g)ile+p cley ih;e7x to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the tre;.a gulienhp;;m 8 gcex+7)i)1 xy xlip? 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 t-agk a)d b/xom9 +jdl1he 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 sts lcx)im.(lg2 3c yyvn(+l y9zarship Enterprise had just returned from a 5-year voyage y9(czl+n.ivx3 gc )ym l lsy2(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 10.6 light-years away. How/8qcdf)5h oudqh5 c 7 5l;jnxt long would it take a spacecraft traveling 0.960c to reach that star from Earth, ac duf)q/do;l 5nch8hx7jtq5 5 s 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 sh6 r.0xuilbb.i l n:u6;(cfrwpeed of 0.660c. It is measured in your frame to be 4.80 m long a( lniu:6hrxc0b; rbf6.i w .ulnd 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 be moving to travel 15 m before ixm2vazw 79uu6l ai2x 3t decays? The average lifetime, at resw 2m2u xi6v93zxa 7alut, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protz lqsq, jalo20bc-)l qx w5z++on traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an obi.pd,)tv wchw;0 ejo1 ject’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mas 1xhzly57+;ksr;h m yjs $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at4ozikgv/0e m* s e;/m2wmswl, $v =0.10c$. 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 of a proton that accelerates p*/ sq+d4iuiaj/ 4jxa
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical react(kdpnut)k s9,obbw:u1se. g3b3 dj x3ion 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 as fi t rr1aw1(xi3fssion in a nuclear reactor, the resulting fragments have a total kinetic energrw1 1 fxr3ia(ty of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energuc1doe6pmu)* y of an 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 of a proto;;td twbx h:waj(bny -d, 6d9wn in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consump:s)u nr 0/kuvbwiu+au/qz0( wtion 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 h* 1eicl fs (6.r8mbqu:n2z5s zmov5q 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 kineti50 n. was*yr8l*vne avc energy equals its rest energy? v = * le05av. w 8svnr*nay   c

  At what speed will an object's ki u6l3qi sb3s7nydg)2 9o;mrbznetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a speed ofb.u myjr9/kz12 d4 zeb7dxv2z9,m h*,tctjdo 0.9jt,d1 o/dtzc hb zmbdvk9. x2z 29,je u7y4*rm97c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy-5;6.mie sd7vnxwtkj1o5mlw id- s ,t and momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is,k o61d; ft;psav .zz9c its kinetic energy is 750 MeV;p.6 vdf kc1tsz9 azo;)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated b)q/31hcr /t2wea ijxly a potential difference of 105 MV? v 1 xltq2cire) j3ha/w /=    c

  What is the speed of an electron whose kinetic energy lmxd7gl ;,h+6jran c7is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen aft o0),0o w txehr5qy/lfhk7o+yer being accelerated from restxf5koh,er07hy0t q wo)o+y/l by the 25,000 V of the picture tube? v =    c

Two identical particles of rest m:19hrd6 qk-exuqj ey9ass $m_0$ 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 p zaf 6qvo mcny*:xor10j14hn 1roton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electronec20ggeo+ y z( ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of ms8 8h c2u0ecwb hsk4g w)7bf3nv3q7efass 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 y--6tj un 0hkdsn p:3ka 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,gvifs1 v +rg4.or+zp: $^{241}\text{Am}$, 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 for (a) a particle of nonxzeaj2r1 i0g/ws/1 mnzero rest mass, and (b) arx2izseng /0 w11j m/a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV prozl5omd 5u3bf 9tons revolving in a circle of raof lmd35zu95 bdius 1.0 km (at, say, the Fermilab synchrotron)? 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 n; 1igm fhgm4es-7p*sthe Earth) observes a meteor come feh;sm*gsp -m7n 4 ifg1rom behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with t 3md1lsk5srxli 1 x6(a speed of 0.50c with respect to Eartm xxlr(s 51 i1d3tlsk6h.
(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 ,p7 sk/ a p7ag(ap,nunspaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired 7 s(/gup,a7, kn npapa
(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 appccy2p-qjo/.n(/ e(g( mc.qph b 3jfglroach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below(.nq/clo. my( q 3g pgj2f/(cechp-jb ), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape podsbt:qnaza 8gr5q wery (eo3:3 . in opposite directions. One tr85r:t3 aye( go zr.e3nqwaqb:avels 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 the same timeg n2h8 jli0qb3, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when08l nb2ih3jqg it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years qb+* equ5 :sadaway.
(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, anythi2)2d hsnhpn k4ng traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of dnh)22s hpkn4 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 spee3 ffm3w(r8f/b nr6abdd $v$ 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 totallylwbs o 1 b lfwmj+7n412cet8k2 destroyed to run a 100-W lightbulbcbefkmlww7o8t11 42s lj2 n+b for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic k( v+xk9zj.l,mj byu,energy is needed to produce an electron and a positron together? A positron is a particle with the same rest,klm9( zjybxk ,vju+. 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 3dd55p uaw4 fq((ha48mfkyol9 3% the speed of light collides head on with a positive muon tra muaq958h (wod4 a(4pf5yd flkveling at 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 proton,*+car/gl8 x ak an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the T*+8kxr/g cla aable 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 85 ssbhf y,(d,)p5 : ,uydkxcw7ulrbwrate 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 chajg+ 8dby8 ij0 z/v3 qacecqq62rge 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 required to break a helium nucleus into it x0u8(p odkdtcoz . 5/0uxmu)qs constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260dxtou )u0/qkpm ou.z58cx0(d u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass of a c,inljc 0mtb/66qj*o3dw 5rc car traveling 110 km/h as compared to at rest? [Hinwt o0iqc6 *65,j lc mdjb/nrc3t: 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, are2y;a puikmh didy 5035 moving toward each 5 idy3dp2h 0ka;m5uyiother. 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 moment(j e8 ldgp2taxbwf4v7:iom:6um $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterpzjbqnaqe*mkf 85.o om0 (z/c +rise obtains its power by combining matter and antimat/.aozkbqe z(moc +f5 8m*0nj qter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is acceleybu33l caj70jrated so that its kinetic energy is greater than its rest mass30bj acuj73ly $m_0c^2$ 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 1fny4jo*9-pkah4 o +pnn+2wd 2s2 ed bp2.0-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 that when he is running the barn looks even shorter to him9wok+ fnhdp+d -n24anbs2 peypj4o*2 than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogend5nbdqirsf e9 xuy1au5w/p27y/)q h+ and one mole of oxygen react to form two moles of water, the enerdqb1/w5d7a+f )hy u y9/ unxe2 rspi5qgy 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 createk ))d: (a4ej b z3nvb8:hawprmd, traveling in opposite directions. If the speed of each particle is 0.75c, relative tov:e(ah nm)wz)apb4:j8k d 3br the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling atkq0up2.od*,bx5 wy rh 0.75c relative to Earth measures his ship to be 25 m long. On the shibyo *.5qd02 hru pw,kxp, 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 ofd(1egozbwqyh;x 4s e/x6 5,ca 0.85c away from Earth. You send a laser beam toward the Ezg(1s6xy;ho5 a, ce/x4dbweqarth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a to:pjics t g46*ytz ah63tal 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 directly to energy. How much mass will be converted to energy to accelerate the spaces:p c 6t6i*agsz3j4hy thip 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 y-dgv43nb 1i vsc6a .iof 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy con bc v6av31sg-y.4n idisumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to nn15i 1gr mzq:the vicinity 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 work must be done on1i:qgn1zm5n r 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 sd(z6lx5 k-h2(n o( v rw0ye5fz+cldyypring whose spring stiffness constant h+(lz(k vxwf6o(ddy5y l- rnczy5e20 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 , m)rkhukaq8go 7 *4njsaik5.xw4ay 1ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.