You are in a windowless car in an exceptio447m jgi8sgxf .73nd b+mr nhjnally smooth train moving at constant velocity. Isd jnmsn. 8rg4 if7j x47+gmb3h there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of:co 4x*)(lq tn yrv;pb the corner of your eye, you see the car beside you creep forward. Insop l(v;*q :rxyc )bnt4tinctively 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 car, and throws a heavy ball strrtkfix;oagsl ,*16v b/z 9e km-b gz88aight up (from his point of view). Ignori9m6xs krgv/bizof eb, -z8; a*1ktl8gng air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it alske(uf.xq-j qc f9g(s .f.hip*u ,hj/jo valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best referencej.kc j-.egf( *q(huxusj,/q9. pfhf i frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star,g,kmm czj,(rr jg-9:g 7u8m0 buq0ldx at what speed would the starlighu0 gq:jm ,d0cux(lg9gj rbm,-7kzr m8t pass you?

The time dilation effect is some) ynxew ,g*vsy-:4w wytimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioniywxe- :vw, sng4yy*w)ng of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in mor zbweo; r j8:;rc+jf6*w(czcving reference frames or thatw zc:bcor*( j8;j6;w fre czr+ it only seems to pass more slowly?

A young-looking woman astronaut has juskv9o ere.l1+mt arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing .9kv+meo1rel conversation refers to him as her son. How might this be possible?

If you were traveling away from Ears38;vde:*gv8 wxy/5bibw viv th at speed 0.5c, would you notice a change in your heartbeat? Would your yvd s*g/bww 8ei3:;x vb58ivv mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length co i(ncude mi1r (8.- way1*qtuontraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infiniybp.zwfmsum:w x)f xh5a5fg;m6cga 85u* ,*u te. What would happen to the relativistic predictions of length contraction and time dil ;5ugcw, um:baum5wx)fa pf5 f*xg*sm.y68zhation?

Discuss how our everyday lives would be different if the speed o 3*tr*geao m co;+,juef light were only ,euj* a;eo+c3 r*mgo t$25 \, \text{m/s}$.

Explain how the length ymj4 *itp+1 jocontraction and time dilation formulas might be used to indicate that c is the limiting speed in the universeo*t pij4 +yj1m.

The drawing at the start of this Chapter shows the street as seen by Mr To;yp:jsw4rl6si db 9b 3sf4,uvmpkins, for whom the;wvul:bsps94,sd i6bfy3j 4r 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 upp.u;l +sw .rgz.py xrk4er limit on yu g4 krlsz;.+r ..xpwthe momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the sfta/5c( tonsk0n0 f6 fpeed 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 hasb/8pf)yp ) fsg more mass when compressed /fg8pp)y) sbf than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed."fh7m.caoa b2: What must we say inao 27fb .h:mcastead?

  Is our intuitive notion that velocities simply add, as we did in Sect *g2/e fs7pgv24nfvwpion 3–8, completelypegfg wsf*22 4n/p v7v wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be9dbi2n4sz4( vk o h/gu 28.2 m. Hovhi ng4z/so4k2(ub d9 w long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travee z42uq;0scughc6 av(ls 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 o un03qn0* l vvrkrzv4wz6ll( (n 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-rv 68d 7jz3o+ ikz:hvpse7i :hyears from Earth 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 itju dmq 51ni08ixy9 4was 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 fip*j4y*gb. yjs 0-kq tast would you have to travel so that t bjqikt-0pyy*s *j.g4o you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at te8mhga dw 14 wvgaae:n1851fa speed that tells you the distance is only 25 light-years. How many years would it take you to makg1n a:vte4 fd1w8eag wm58h 1ae 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 tb8y8 z4yfma1mhe 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 starship Enterprise had just retn -vook.:u.aqurned from a 5-year voyage while travelquv.o : ok.n-aing 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. H4;o6x; 9d+ uohipky ogow long would it take a spacecraft travelko6 4gi du y9;x;hoo+ping 0.960c 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 you (9zwvbmj(w qfkg /b 1u/rns3z7,nju+in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to n(s3 7zm(/bqbuv gnu wj,zw rf+k9/1 jbe 4.80 m long 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 bx51 c8mlm0 vgje moving to travel 15 m before it decays? The average lifetime, at5l j1x mvc0m8g rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proqmpp 83v j,emw,i6:m gton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its:bni 9lx s86ct rest mass? v =    c

  A particle of rest mass ;xxvazyjq- f5b0/ z5d $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travel milj1-fo):vss 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(x1iq-1vk neeti kq .v4o62cf of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiregeswxlmockk; s: l jc,1fh/. 9zg,n2: s $4.82 \times 10^4 \, \text{J}$ 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 knowbx/ d6eg)5gmaj5ro79 *nmb c tn as fission in a nuclear reactor, the resulting fragments have a total kinetic ene6gj )5/9m7br*tc5 n dgmbeox argy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in jou5al :xxmy.p/c g,6 pdfles 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 *w:qe9wk1jj 26 klq ue:1t6chmiysi4 in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is au+nq8us((he k4 m4ycb o jo;e7bout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from cop3/b u sz q-vdre2ibu*uyy995nversion 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 w ih n lnj37*i;lnks9v*hen its kinetic energy equals its rest energy? v =vn 7k3hi *9 ln;*insjl    c

  At what speed will ans k2m r* j0fevk03ob1h object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a protoe, kr0d :jey,fik7 mc.n from rest up to a speed of 0.997c? W rfie7kkej. yd0 ,,:c m=    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic enk,yt +gu 5ds6rergy 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 750rj cbn;+d z.hzdjt 7.bu g:y04-MeV proton (that is, its kinetic energy is 750 MeV)? rz0d:u4 b. c ;njgtd hj+.zyb7   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentiald o; ;79xvhkeo difference of 105 MV? v =;doehv7x k9;o    c

  What is the speed of:f,s5 q(tj bcvklr e(o0y7m jw20atp+ an electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron ju0-f1l9kfyl fl st before it hits a television screen after being accelerated from rest by thyll9f lf 1k0f-e 25,000 V of the picture tube? v =    c

Two identical particles of r.)uh0eowtt28 s )cq npest 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 proto+m5( lg;q. zj d vpak.e+5tgjln ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and thegzf;nim 59g(o 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 27,000 kg e;ky3hx n2 lu8is 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 kineticjalk gdaz1r j,p65: * ivy;u*x energy and 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,c00 rzzh6t ng+ $^{241}\text{Am}$, 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 ver1z xm67j9*xn8l kc jbh.sfy )tsus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero restj s)8 h tl7m*9cx xjkz.n6fby1 mass.

  What magnetic field intensity is needed to l5 (o pc- fef1*x(zocjkeep 998-GeV protons revolving in a circle of radiuo co1( - *ljpfc(fe5zxs 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 the gd em9rk:ya -3Earth) observes a meteor come from behind and pass her at 3kemy :d9gra- 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 d1c 3: wz(y,b l yclqiak(uxxczd,3*4hirections, each with a speed of 0.50c with respect to (cb3,h (:yk* acyu xlix1l4cwz,3d q zEarth.
(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 E ,ko))bty8 prdarth traveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired ) 8ykdtp),rbo
(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 stc bn-kkx52.tjop)f9xd0 0 pjpeed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving direct0bp5o)k.0x d-nx cjj2 pk9ft tly 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 pods in opposite le 2*. 0sbk*e;bv-obmz(i cqydirections. One trai 2(0yek- v*.bqomz; bbc*lesvels 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 t7w iv3u q1-1wexlcpa5-2 nsfgime, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relat1nu 2xqc iwe37 5afv1wg-sl-pive to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years awh0 6ja7uwv7reyr y.9p ay.
(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 0.1csw.e b83bpiw0c2wp1v is called relativistic - i.e., for which the correction uswp8w0bbp1ec si3w2v . ing special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) ----待选择----relativistic not relativistic 

  (a) What is the speed 4dm wnkg ;j5*i1 izww0$v$ 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 totally desrc: f-jgohux/.-2x o qtroyed to run a 100-W lightbulb for 1 o/g.qr- :hxjxu 2-f ocyear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to producg w).b*x cc2ofnrnn -wbmt9 :3e an electron and a positron together? A positron is a particle with 3cf bcg.xmwn9 rn t):2*o bn-wthe same rest 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 33% the speed of light collidwq)mj.nz36ukjbd8s 0 xh 2;r ces head on with a positive muon traveling at 5)xk n0hqm3jw;rdz8u. s2 c6bj 0% 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 y.ec m6+-mds lh8mcs.a proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles wheesm8 m.- c6h. ydcmls+n a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of abfe.(*1ce g;e .uj iuzzout $4 \times 10^{26} \, \text{W}$.
(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 hpy/ n5bn+ijgb1/6 vois 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 to bu4;ksy(bi guca :a +li:k)/ic 6 k;yrwreak a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, ii: /4ccu;(k bw6+a;lur)yg :isaykk 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) mass izy7ur:ng ,d1of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expaug,iyn 7dr:z1 nsion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving towarhh8 x19c26w *gmzfrofd each om1h9rg zc8h*fo6w2 f xther. 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 -+rtbj2vo y54nud+ut8k7y ei um $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powqxeb g4lnj+ )./uf a0yer by combining matter and antimatter, achieving complete conversion /q) .lux ye 4n0bgfa+jof 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 accelerated so that itl 5eyukyh51s *s kinetic energy is greater than its rest m15h yek 5yls*uass $m_0c^2$ 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 wgtg6a. f3(f3 tyeud9a 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 whenu3g69 f(e waft y3dt.g 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 mol. 4j xdxk+ b)6lkitz)xdp, *xies of water, the energy released isjidki 4* bkxx)x6px +tz.d), l 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 creat3 ;8hazcipwa p5u(t42 2bu ooved, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =c38uv hz2b(u 5opa pw2 iat4;o    c

  An astronaut on a spaceship traveling at 0.75c relative to Evha.le ;co6zc/vc )z9arth measures his ship to be 25 m long. On th)c ec9vha .6lozvc; /ze 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 0x+dls-5p duu7p x v n9w7wgx6).85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. Whgu)5w7s6p +uxxpwnlv d7d9 x-at do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 f+ y be t,txugi49e:f4kg. 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 acuefbyitg4 x 4:t f9+e,celerate 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 spee dk jsuwi5d,3,d of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S ,5,iwdksdju3. 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 6.0w2(+tg kz6 mzo light-years from Earth. Passengers on the ship want the (one-way) trip to take no mozo62 k+( twgzmre than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stif. so6t, c6wbylfness constant is6 lyoc,. wtbs6 $k=48.7 \, \text{N/m}$. 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 ma:x 8afj) y 7ij9juq7xsss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.