You are in a windowless car in an exceptionally *stu(g:g e-bqsmooth train moving at constant velocity. Is there any physical experims:g* (guqbe- tent you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the exp s;gvd4) .uazjerience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative s)dagv. u; zj4motion?

A worker stands on top of a moving railroad car, and throws axeui np7j5m-, f:oh-k heavy ball straight up (from his point of view). Ignoring air resistance, will :mkxh,f 7-n uo 5eipj-the ball land on the car or behind it?

Does the Earth really go around the Sun? Orbpv lq+x*5 :od is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of :od*x+ vpl5qbrelativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c awa4a l9pe:9aevcy from a star, at what speed would the starlight pass :l9 vpecaae94 you?

The time dilation effect is sometimes expressed as “moving clocks run0 ed(4bui bxc5 slowly.” Actually, this effect has nothing to do with motion affectinbud b5(0ixe4 cg the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more s6 y9s+xt vl-,wx- hqzplowly in moving reference frames or that it only sez,p-9vqs+x 6w-x yhtlems to pass more slowly?

A young-looking woma *u+pzo3puf,6yu yk6in astronaut has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refer6okpyu*f3u iyup+ 6, zs to him as her son. How might this be possible?

If you were traveling away 4gk su* : q hd2asydkvw5 j*vy2v2/q4qfrom Earth at speed 0.5c, would you notice a change in yourvqhaqs y2s54 2 ud 2g:jyd4v wk/v*qk* heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at or53g1wu5 l k7a)ionx;fhs o e(tdinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What 83c( f fyblxd;d3e-yolx 9/sh would happen to the relativistic predictions 38 sxd(d boef x/l;fyc lh3-9yof length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of lighugc h32-r0b hht were onlyr hc 2bg0-3hhu $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used to inu/vd uc o,5w/b/ogji-p z7j 8-itm6tndicate that c is the limiting/7jtm- wcuovj5 pzu8igo i/dt/n,b6 - speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mer v *ec8 :vcx3rim9u*r Tompkins, for whv :rr*iu8e* mv9cxc 3eom 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 than c. Does this put an uppery fl*,xx rt.(k3odom8 limit on the momentum of an electron? If so, what is this upper limit? If not, expyx8kdo xltm .rf*(3,olain. ----待选择----yesno 

  Can a particle of nonzero rest masg :ndg3gjs 90 z)o0mvzs 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, dn8p zwi,u o1+qoes this mean that a spring has more mass when compressed than when relaxed?8u, opiwzq1n+  ----待选择----yesno 

It is not correct to s:5 x4 zu kksu4y iqsi(zi+bich; e29i5ay that "matter can neither be created nor destroyed." What must we say inq5u9ic(skiiz+s z4xiiyb :eh5u 4 ;2 kstead?

  Is our intuitive notion that velocities simply add, as we did in Sectisv;qo +l rzf*z :8vy)uqtb4: ia-5afdon 3–8, completey*lf tzfb;r q5v:d8s+:azua-4 o)v iqly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You meabtav7uf v/;q3p 9m(*umh. hczuvl u( 1sure its length to be 28.2 m. How long would it be * b 9v(ul1 qzmh7m3 uuuvh(p/tf.vca;when at rest? $L_0$ =    m

  A certain type of elementary particle trjh l vy)ojq5*: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 d9yh8l b8 s wv)cub(wx5epend 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 vx5iq/ks av*e;2s5irzsa5h ( 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 ae-bxc vzd58 m1verage 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 framex p2xr9;bb 7yw6 ke-sn, a star is 82 light-years away. How fast would you have to travel xynrs9kp- wbe7bx6;2so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed that t-law4pav8l s )3g vm1xells yo xlm-av 8asl43gwp1) vu 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 hu,1b uvk)lbit:m vq:h246pjis $11.2 \times 10^3 \, \text{m/s}$. 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 st,w.(wkb kjky8 ated that starship Enterprise had just returned from a 5w(, 8kkybwjk. -year 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 10o m240gu f0 qesyvny.p a.te1 xk*(rs*.6 light-years away. How long would it take a spacecraft traveling 0.960cmr av2fgs. e1sy. *kn 4q( ytopuxe00* 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 you2y2p37ulb c i2k1cmbu in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. 22 cly1 up3c7m2bi bku
(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 behv8,83r)fennb e6pqe2 4uww j fore it decays? The average lifetim 8vfrjw ,h34)w ueneneqb8p26e, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of kbxu9,uat9 d7a 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 ixn6o(g;z0fst ts rest mass? v =    c

  A particle of rest magp 1)nc *oqqc(;w2 oqxb;nb h8ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels ati9a2g9ktj :y4 k8avh*w 8qqkz k/cwq; $v =0.10c$. 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 chupgv6y 8 p.if1ange in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactis zn4 br0gd qp; 2x)mwxh1rw88d7qm1eon 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 procesj 0z5/rgn,fpw s known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process5pg/rjwz,0f n ? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in jou/zc(* qn :tx* rzpyhv0les 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 proton inph5g7 nlf(1p e $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United dneb*e(. rgxzk 741da States is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion:24k jsrokqa: 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 j-x3kbm66n gn0 yva)rwhen its kinetic energy equals its rest energy? v = xm yg3-b6 an)r jnvk06   c

  At what speed will an object's kinetickmnil;-z3/ wf energy be 25% of its rest energy? v =    c

  (a) How much work is r- x.( +7ffimz/ miqqscwf:3zw equired to accelerate a proton from rest up to a speed of 0.997c? W izqs(/f7 w+zcq3ff. x mwm: i-=    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and mo4+7dkl3f lrliy 8 jv9mmentum 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 y n2y2xpl,o (:lef vgtgq5) 5xy /7dzkof a 750-MeV proton (that is, its kinetic energy is 750 MeV xx(f2dykoly z,nl:v 2g)5gq py7/5et)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a b.iih+f :2z1h , dnjjmpotential difference of 105 MV? v =+zjh i hmb2d 1.,ni:fj    c

  What is the speed of an electron whose kinetic kzkxtvjwdun,)//2r q1 n 8enrj :)c;qenergy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a televisioek6oa6vu03 v1d *cvr yn screen after being accelerated from cu0vr1*y6 v vd3keao6 rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest*owy d.udy -l: 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 protcm8s k8/h,esg on ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed an.w +r 8 fh(okx7jhpb,0w9fu eyd the momentum 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 m+2 wh./v+1ym jc y7h*jplcqcmass 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 anpf6- +jg4osog0 wy2 ljd 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 nucleur+b22sp bmyg ,p ybi3h **ie7es, $^{241}\text{Am}$, 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 8 .ruz o71 dmmvj8uee7momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest mass.7.r1o d8z7vju 8memu e

  What magnetic field intensity is needed to keep 998-GeV pe 6x;lr hew.:j0fnd7qrotons revolving in a circle of radius 1.0 km (aq 0l hwxr.:6nefdje 7;t, 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 x.)u7v,y nfzfx, b)jgto the Earth) observes a meteor come froufnxgy.7)x,fb j vz), m 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 a speed of 0.50c wif hu(6)4koxremhc:-./ p8bkds, si alth respect to a/.l ,h sh(i dxkc 6kr)m8ue-fspo:4b 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 0.71ox4cx ful3 si: r6z7,) +xtlvh 1cg7xic. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the spe7ctu7lx gr: 3 4,1sih vlcio6xx+x)zfed 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 0.60c.i:ii,u1ke 7*5 kyqyg k The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c* iiek17g k,kiq 5uy:y 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 op70ydat6urpkp, *pf0 w b .dan:posite directions. One travels at a spa d*a0:0k nfdyru,. ptp7b6wpeed $v_1 =-0.60c$ 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 amwfy7onha*u z 34k48s speed of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fayauh4ow z4f8 k 3*mn7sst is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima C 9x pbx(yiap; .mg.wr4entauri, 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 call0 4(nd nte2ie-vwho83)bu ysged relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an elecwn2h-nie0(uys)vb 8 3oetgd4tron 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(;ferom7kxu ( $v$ 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 ma;( dl/u*5yzmy .drgtw tter would have to be totally destroyed to run a 100-W light yy m*gu;5z/dld(t.wrbulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy iyqgos- +/*bn.s8me gl s 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 cslm+q oby -g.s*/ge8nharge. (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 atcr; ktmk/;ar/ yjq:uhbqp .35 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons r5pm;.a:y/qk;b/t rj k3h u cq(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, an electron, and a neutrino. Afo ,n:,d,y)x /eg/1mnbyuqigssume 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 ene :ui ,xb)e,odggm1 ,y/qy/nfn rgy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at h3h slme-0z l (xh7hi+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 icc/ h:b 6f5nkce*g ztga 9t8p8s measured 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 required tt0q2ff+5tng brb2; h qo break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (in ft2t+;5 bhgqqbf 2r0ncluding 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) )fgq+ slskf -4mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansioqg k)s-slf +f4n.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the labo fc3ah5raidje9m7 hw) -65 nliratory, are moving toward eac mhj c)-7 ifanlei9da55rh3 w6h other. 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 momeu:rzxy-; 7y l qbrwg1salg3 09ntum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power bysw1 g rw/chn: 7h*+j0i rujdp. combining matter and antimatter, achieving complete conversion of mass into energy. If the mass jw*7:nu.prd jg/hr+10s iwhc 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 kinetic kfk g(uz,e7b.energy is greater than its rest massze (u7. fkkbg, $m_0c^2$ 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 ca(h + ou0mzn;d/; k.b)3 ujg.ufsluwrl n fit a 15.0-m-long pole into a 12.0-m-long barn if he runs flh) g.; ufzo.u musw u(rnl/b0 ;jd+k3ast 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 him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react tou3 w 3x5 lrkrvp(i)tcyj1m: k. form two moles of water, the energy released is 484 kJ. How much does the mass of the elements1kiwrx3tu( pjc. v k53lm)ry: 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 in opo8;y coyf/5d *2 urqoyposite directions. If the speed of each particle is 0.75c, relatiy;2/uf dr* o8yqo5cyove 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 0.75c .*l.oy x/tp6nk1r: cel8mendrelative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in 23 mink:x der 1/ylpteon.6m8n* l .c.
(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 5fvb)v2 -;* 4qrkq8*sj7orickrx dkpspaceship at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at q ks cd52o-; krkq fvjbv*84rri)*px7velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants hax fg)ertr0pi5(m 8+ bl2wo0np ve 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 directly to energy. How much mass will be converm0 b rpite( 8n02gfx rowp+)5lted 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 spaceshipcdd8+*u v03yb/fnbv p left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with vucnpdvf3by08 + d/b*the 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-yearsftws 09yfce .(5lb*o e from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to thofy0*9.tebels(f c w 5e speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a sprin unn/-yzbse1xf mv)u*y,/q e- g whose spring stiffness constanteq )-bsnn,*f xe yvu-zu y1/m/ 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 mass , bxhp2,w rfb,.rg vy3$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.