You are in a windowless car inh44iyo+ j)4um sezx .bje ,tr mr(+y,-lr/ aep an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in t4x-,4mp , zi e +(r)y j/eomsthe.ylrrba4+uj he 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 wl6s x.1,ww ugahen, out of the corner of your eye, you see the as uwx1 l6g,.wcar 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 motion?

A worker stands on top of a moving railroad c+uvs 2s1v:tlnar, and throws a heavy ball straight up (from his point of view). Ignoring air resisvs2+t s:v1lu ntance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it gv)huzrasx t n)8v:;;also valid to say that the Sun z ;vug: rtash)x)8nv ;goes 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 away from a star, at what speed lqy )rzg9)uk2 +,tgx mwould the starlight p +m q)l9)zr g2kxt,uygass you?

The time dilation effect is sometizk 0d r(p6ea.c(tes8w o(- h9aqkz9tomes expressed as “moving clocks run slowly.” Actually, this effect has noth tq-(kwdtr(9szac( .kp86oze0 oha9eing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes w g9x. k ald ;nx)/lk2p9x8bmtmore slowly in moving reference f;t99kpw)8xdbxm x lnag. kl/2rames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived ho33m4p r2qm*sfzj ;zd bme from a long trip. She rushes up to an old g*jq4233zrm;z m sfdbpray-haired man and in the ensuing 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 noti* ae bfkoj;o23 30sjq -rt.oiice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Eaqf*te3oobks ao;ij.j - 03ir 2rth using telescopes say about you?

Do time dilation and length contraction ocfpu cl2md2/r 7cur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light wex fp*k8o ,((lw1fbseimp1ut ;re infinite. What would happen to the relativistic predictions of leng fpl1(ew8xim ,o1(* usbktp; fth contraction and time dilation?

Discuss how our everyday lives would be different if the speed8bmj ud0 vc1w( of light were onlj uvc(1bdm0w8y $25 \, \text{m/s}$.

Explain how the length contraction and time diu2xndu5dh n )ng 0+ub0lation formulas might be used to indicate that c is the limiting s0 n0gnxndudu2 5+)hbupeed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr To rlx8 ;2nzl b ege072.uuj-yf80mpbex mpkins, for8x02zx.l27uee8ugy0 n r-fje m;lpbb whom the speed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at sa3ke*o:r( qnvt f+w)tsa5;xkpeeds less than c. Does this put an upper limit on the momentum of an electron?w)k(tt;oq+ aafre* k :nvs 53x If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonnb v *km/(ddq.zero 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 h(q y.)ru-r1lz -ol) 1mxdfsl das more mass when compressed ()fmrlyo dduz.1s1lq r-lx) -than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyyox.*p 8x*awqk/ o+p jml9yh-x0q+ fued." What must we say ifm x0ka- *+/oy*.p8 ol x+uxjy9wh pqqnstead?

  Is our intuitive notion that velocities simply azu -wl /no.e/zdd, as we did in Section 3–8, completely wronu/oz/e.- wzln g? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure618f ysgpg+bz;z2s fa its length to be 28.2 m. How lyag8 psf2g;z1+ fs b6zong would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed oac,ow; mc er ,f,lc0no6 cic66f $2.70 \times 10^8 \, \text{m/s}$. 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 facto7nc c ctr8p)kso7u4 n)r $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 E6gxdafqx1 ( je/oxr3: arth 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 ebwi u kay4 ,+j9na.;bits 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-years away. How fast would y.m54hdaeoa2sftw6g :ou have to travel so that to you the distance would be only 35 light-years?f.so62heag4 tmd5 : wa v =    c

  Suppose you decide to travel to a star 85 ligquq,g ic-2d1 x5nbt ,mkj9vj3 ht-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make jdxvk,uq,3gtj-n 21 c5 qbim9the 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*glnur u+w 9j6 the 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 sn4wzhn ,y*o 7uj ps-;qtated that starship Enterprise had just returned from a 5-year voyage while n*q;y74wz, h j nup-sotraveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a spacecraf1 ,/o /jjzpyktl yw60zt traveling 0.960c to reach that s wy6ztj,j1zkyo 0/l/ ptar 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 0.660c. It0h sf0e+v k rqgm0-ri4hh 8l(e is measured in your frame to be 4.80 m lon-em0q0 4hr gfv 0ihk+r8l (hseg and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to travel 15 m before it decays? xc;a saw z *vkvn3v;t oopy35/9r)nc8The average lifetime, at rest,xoy apn339;;* 8zvcavtc/sovk 5w r)n is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentumdxvp(h80 9 7qykh+s ae of a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an2rek3p8t0nez object’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mev. bo7.pp/ luass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave rqp6g u5-b2x.7zhnnenh*sfw wj7*h; 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 momentum of a0vdliu u0gl7ot:+.mvd)z+ a; tf3 vxg proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requira 9znb( cp9m9aq,hj o)es $4.82 \times 10^4 \, \text{J}$ 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 as6j 0:syyafe ,s fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 :y0j6a s,sefyMeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules an5w a0 z:8daprfd 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 oeepc/zzx -:m /f a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United 5q)/: hfmtzk - rm oxg+omd.3cStates 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 convermo/x:bop -v- nd0j3zb .t+nli sion 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 -0wcd08 jcm pzits kinetic energy equals its rest energy? v = w z0-pjm8d0cc   c

  At what speed will an object's kinetic energy be 25% of its rest energy? 8v 4;p1(q vewu- cyv3gvmmdvb k80+ky v =    c

  (a) How much work is required to accelerackxoevjkd4xe9b(t )9sr8- +pte a proton from rest up to a speed of t()eorck9pd4kb8x9 s e+ v -jx0.997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentyad-s;4i(9 ilrqb7 f kr.sn)c um 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, its kinetic energy i)o5 d +*jlg q2l6tqqgis 750 MeV)? 5gt 6iq+l olq)d2jqg *   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a pfsk2q7i 2 8echh9ke;rotential difference of 105 MV? v r2 cee97qh k8;2fhik s=    c

  What is the speed of an electron whoseg742z7f oac uh kinetic energy is 1.00 MeV? v =    c

  What is the speed of af)9my. l) 7kekbr*bl un electron just before it hits a television screen after being accelerated from f er)*)7 ymlkblb9k.u rest by the 25,000 V of the picture tube? v =    c

Two identical particles q gnd4h ;zos1a 8qn36hof 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 proton jhmgn g 1i 4.euoj.:d2($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed andqz/n1 4gyp/e(b/ rmgf 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 mass 27,hoaqw4v1q cp r4 fyh3p(+x+m/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 ando1m ofi dt:b92.st4leokv 4:s 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, 3+7u2pl exn ou$^{241}\text{Am}$, 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 h2n2ylcz(8x r.tvy5o of nonzero rest mass, and (b) a particle with zero resth(n8tzyyr x52 c2lv .o mass.

  What magnetic field intensity is needed to keirm37d zf l81eep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)?fdr13zl 7 m8ei 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 (withph7i.s r1*cl 5sx8rlr8d1pnct03 jla respect to the Earth) observes a mn7c1 jad rx8rl1 lh0cp8p s s3lri.5t*eteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in oppositej st:uvnxq/o+0 ;6 3asm 0frqk directions, each with a speed of 0.50c with reskoq:ntqv0sf6asux+ r/j 0;m 3pect 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 spaceshian 0.geac.s 5qp 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 isaa.0qn ges.c5 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 seeieqk +8w ri4w+s an alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vesselir4ww e k8+q+i as seen by the other? u =    c

  A spaceship in distress sends out two escape;(/d vee,* b:okmavsh pods in opposite directions. One travels at a speedbe ;km , /d(vhsv:*oea $v_1 =-0.60c$ 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 0.7t9:3gr.i 1s 1i epwvdb5c. At the same time, rocket B passes Earth moving 0.95c relative tot.9: e1sviwdp g1i3 rb Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth 2xirgst .a0nn1l 4nreua n)18oqxq7 / is Proxima 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 aboutstg;tx.vt4 y4 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine 4tv. s 4ygtxt;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 speedmj)cz x ct21qu;b00vaof +kc 9 $v$ 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 totallygypm5 ty/xw ,2 destroyed to run a 100-W lightbulb y5wg2/pmytx, for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electrom)to31;3odn x.lfy lumagnetic 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 el 3uo1mxl)oly. n;3 dtfectric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collides hea:gs1cir4bv gr7s* ;0 ar8 wcotd on with a positive muon traveling at 50% the speed of light. The two muons (each of resr17wirtg :*s8ccbgra0o; 4 vst 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. .dygju 82d4v9 q+hneaAssume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine th+e2hdv4ad 9.8ugyjqne total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energ wo,rmgbktpo :)o,h4hi44m *my 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 measu h5pg +1g9(sprle -o bunot;w9*kdr60gj*k jqred 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 to break a helium nucleus into iy,(i p sx0yxy1/ tygne1b)o m:ts 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,y(x m xygionye:/sb1) yp ,0t1 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) mass of a car t1 mh( zq1e*9wl+ 4 cwhyqip5hsraveling 110 km/h a(e 4hq1 1+cph5iwyzqs h9lwm* s compared 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 toward xl lk27uwr9pgj45 ;ulh ;rq-aeach oqrk xpwhrjl ul5-4g;a7;u 2l9ther. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle with momentum v/. b s-fvm*ifm-qr8k$p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its vl d6xce-/bl 6 (soou3power by combining matter and antimatter, achieving complete conversion of mass into xv(3l/6sclo-o ud b6e 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 accelerated so that its kinetic energy is greatervfte2bz9x0j6;5 ey7 n 5qzhpcte9 +a k than its rest mas6;27kx0z9 yp5 qfn e ze9tah+ j5vtcbes $m_0c^2$ 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 bem--mm,)s0zm d* sskt ulieves that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter -susm- mts,z*0dkmm)to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to nk+s 0cx tk;h9l7mlf9l h(gv ,form two moles of water, the energy released is 484 kJ. How much does the mass of the elements dxl;7tvfshc90,h g+n (9lk k lmecrease 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 iden.pjjj e8rj+h 3tical particles are created, traveling in oppositej rj+p8ej h.3j directions. If the speed 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 0.75c relative tk )rj.)(isezg 6g8r gzo Earth measures his ship to be 25 m long. k8).( gjs 6z)rrigeg zOn 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 stx v8ah55f6 p ojjrd02peed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam6pdjox ah8 t0jv5 2f5r?

  A spaceship and its occupants have b3yq*cb1q)5lyy h 7cxa 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 converted to eneryxc*yqb5b 73q )hl1cygy 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 spaceshe+j g+p ogfu+ 8z79fifip left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with o98+fjpu+f7 f +iz ggethe 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-years fro *m+ i/wjtvip,m 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 the speei+pt mwi *v/,jd necessary for this trip? u =    c

  A 1.68-kg mass oscillal+;ppaw qt/e*tes on the end of a spring whose spring stiffness constant ist+a*/w q;l ppe $k=48.7 \, \text{N/m}$. 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 mcx+x+bmj;n. na yy,ey1a 8z;fass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.