You are in a windowless car in an exceptionally smooth train moving at constantqb/h l*2ugxe(tr.b x/ velocity. Is there any phy/ xxb.(2lu b*htqg/r esical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the ex9yj 3j7eql z-operience of being at a red light when, out of the corner 7 yjq9lz3joe- 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 motion?

A worker stands on top of a moving railroad car, and throws a heavy ball straig4+mpzlv 6tlpso:ktt(ows. 7 byd h-81ht up (from his point(o d8kl4ly 7hb. v swsp:tzpt-+o 16mt 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 t bamg)u82(wr ebur5 v2o say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no b )2gma2r vw(u8b5rebu est reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from cnl(nn/ h 4 :*l2 wcao+bd1be0hp:lcha star, at what speed would the starlight pass yacc:+hnebnlcwln 2olh0 :(h p4d* 1/b ou?

The time dilation effect iso-k b*haspwn ,,a/)ak sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning ofa,k kohnp-a)s/ ,wa*b clocks. What then does it deal with?

Does time dilation mean that timeol4 4q2znv 3e4dosg3f actually passes more slowly in moving reference frames or that it only seems to pvol 3nd2zg4 4oqf43esass more slowly?

A young-looking woman astronaut has just arrived home from a long umxhm/ --,3u fmirsl:trip. She rushes up to an old gray-haired man and in the ensuing conversation rm-3lhm xrfim s,u :-/uefers to him as her son. How might this be possible?

If you were traveling away from Earth at s2z.2s:huk m(bv qxn c)peed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistbcvz)kq x2 (hn2s.: muline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinart6 gpn-t u7:ohy speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen toy jgj6 5mdhm8b5f*js2 the relativistic predictions of length contraction an jm52dyjfj 6bs m8g*h5d time dilation?

Discuss how our everyday lives would be different if the speed of li;1why pr6p+.:h rfhvd ght were only p.h r1v+ry: hd;h pw6f$25 \, \text{m/s}$.

Explain how the length contraction and time dilati:yov3m 7zf .j*jnym;3pxyk 4u3-qhxoon formulas might be used to indicate tha*qmz x hkj3 p-3m y:nu3y;.fvjy47o oxt c is the limiting speed in the universe.

The drawing at the start of thisca f2tym8pnl/re d; 2ljt.fmw0 /ew :/ Chapter shows the street as seen by Mr Tompkins, fom/nmw fred28jyllp20 t;awc: t/.e /f r 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 speeds less than c. Does this put anhmabo6i-ha- + upper limit on the momentum of an electron? If so, what is this upper limit? If not, explam +h 6a--haobiin. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed obu3;ij5v9 eyuy9l i+kf 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, dr wy jph:rq8+6oes this mean that a spring has more mass when compressed than when relw+r6qyhpjr8 : axed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed.xjonur2g k7vs1 o+4r 3" What mnxvr+s 43o12g7u rjokust we say instead?

  Is our intuitive notion that velocities simply ku /f4kyl9 g:1i:-cr s:de uahadd, as we did in Section 3–8, compa/1 :-rc9euks: fd yu:i4lk hgletely wrong? ----待选择----yesno 

  A spaceship passes you at a 2;k jt (n, bzb2giv)s xufa0-fspeed of 0.750c. You measure its length to be 28.2 m. How s0n;fa(bu)2 zj2v,i xtf gk b-long would it be when at rest? $L_0$ =    m

  A certain type of elemz;nf-u3r nx/i entary particle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals dependcwgt9x eb:y o usufki8hqr36 (2r 9vg1u4z)t5 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-yet54sxh xz( bgfv)r8j 7ars 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 its averajlrk +4mm(ld1h*+ umoge 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 fa1 b1vs; bxe:tmst would you have to travel ;:1ebv1t sbm xso 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 t:yxu:6 qrv;s:;ssm, zzexzf*wx9i -ghat tells you the distance is only 25 ligzr *; ssxqw96:uy:i zgvex z,sxm;:f-ht-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 E7ar*7ek/an r (plimy1 f65bw+fujci 3 arth 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 Enterpri2ml80mv bdl*bj vbx7 3z4td6 ise had just returned from a 5-year voyage while traveling at 0.84c. v z4m2l*6djb7 vd3iml bt8b0x
(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 spacec+hmr-,,/ry hy l4crpi raft traveling 0.960yyr+,cm, - irh/4r plhc 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 in her "Fe r2cqkx 49n-yfrrari" spacecraft at a speed of 0.660c. It is measurexy49cn 2-fqrkd in your frame to be 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 pion1c-qtm d s7-wb be moving to travel 15 m before it decays? The average lifetime, a1 - dmb7swqtc-t rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelind,s9x,zp ku*rg at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an objectotp+i+pgi+ m10gi q m3’s relativistic mass be twice its rest mass? v =    c

  A particle of rest masg d5 /:u4xvtdjs $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a(p r*k0cpet0h0:fl t) i.gfr ct $v =0.10c$. 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 anpx d/*2fw:vt yc qr9ef68,xu proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reacv iqelf.z ix)7.2 )eeution 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 procek,2bx1xmr 6nbss known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of abk,mn1b6rbxx 2out 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electr+hfpwht+jerr3 /*9o / 8ul)rq0 bvmlnon 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 pr3 ,3hzmy9yyzx oton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energyx jy9a+h-6fqdv+ gtw7 consumption 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 kejw2glw(0 0 hobtained 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 parqr*. 5+ezej( fk oqp;mdu:* vkticle when its kinetic energy equals its rest energy? v =;+*(q f5ed. kq kr*peuoz:mjv    c

  At what speed will an object's kinetic energy be 25% of its rest,zopd qq9rgrcd 61q) 8 y/dnquy((td 6 energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a ssg++ k8zif8a dpeed of 0.997c8da gk++sifz 8? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentumf/ . egvl b1fca9s(.qz 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 kinetinhe4*1 qm pp,lpb53b6b /v qrdc energy is 750 MeV)hp1epp54vbbqrq 3,bmn/* 6 dl?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potentiap+) tt7 lypbs (rqv.g6l difference of 105 MV? v lp+ q6rpvt7y)bs( gt.=    c

  What is the speed of an electron whose kinetic energy df 71d;zgf9aat s9 e8n 8imss- so89oyis 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen 1 r-varql7y)c, gewd ivj;e16after being accelerated from rest by the 1v)iq vc;,da- wy r7e1glj r6e25,000 V of the picture tube? v =    c

Two identical particles of rest mass abwxt8 73kylk.igv8/ o .l ,fma/se d6$m_0$ 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 o.:5 o/sbewvwj /lqx1oc.p 0lsf a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 electrvq3h6 z196pgu ajlo lob0.3f,oba 8kg on ($m=9.11 \times 10^{-31} \, \text{kg}$) 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 is accelerated to 0.e*qzd(:i -i 08apxl h a3g+-oqn1okxezzqr+ 6 21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energy and momentum of a proto r7xds q4bog1-3 dd3kwn ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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,t/q2relzd* czt w p9;) m-rjd1 $^{241}\text{Am}$, 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) a9dh+dv cmd0 c t) ku0iau lqr70.jt:8h particle of nonzero rest cmut hd0dctakh ilq.j7u0:)89vd0 +rmass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protxw 1+6jcb, uhrons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrox6jhw1,+cr ub tron)? 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 Earth) observes a u7sr . :cm j -huy2kh)h/eni6ameteor come from behind and pass her at a speed she measures as 0.50c.:chk6- ij7h. um /esuar2)ynh How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, eacv8)a aftwnb12, h :jzfh with a speed of 0.50c with respect to Earth.) wnjf8v2:abfh, zta1
(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 Ea4ohhkg0 :-buirth 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 fire- khh b40go:uid
(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. Thl-ui a(qf d8 *xxyq: wk*9c-qae 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-i9 a*:(q ucaqxqlwdkx*fy8- one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in o1plpvmdk.erq5x; w9(oi 9 i (ypposite directions. One travels at a sp xv.9wde9pyoq1p5 r kil;i(m(eed $v_1 =-0.60c$ 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 time, rocket B px( rfb- 55mytzasses Earth moving 0.95c relative to Earth in the same direction. How fast iszx(mbytf 55r - B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is P3x8o um83 rcskroxima 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 ti1rq*bb)d1ba8ry x 8 uraveling faster than about 0.1c is called relativistic - i.e., b1 ryb*uqi 8d 1x8b)rafor which the correction using 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 spee, m3 rz 3ehf,)xuhlw3sd $v$ 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 destroyed to run a 100-W lighf t9+z*bksot) tbutk 9tbzo+) fs*lb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagne( vxxue,d-*i ctic energy is needed to produce an electron and av-*u,(ie xx dc positron together? A positron is a particle with the 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 l*bsg(1y6v- kcpeb ogl ;(a gu9ight collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest m e -ysobl1( ukggav96cpb(g;* ass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an.o9hivdwdslog ( ;*p4 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 when a nph.odl( ;*vg49s i owdeutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate o2d*4nwezd-zp f 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 charge and a speed ofi0cp ijwd9ony ,d64y* $2.24 \times 10^8 \, \text{m/s}$. 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 f/4af e hf52pss9bcmv+dv (+z helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783m f(cb+z+/9 vh4e f2 5psfvsad 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 percentafa a4 21f 8ksknie,- j6gjoc8ve h:w2ege increase in the (relativistic) mass of a car traveling 110 km/h av1en62jef, 2 8 f 4-ekkaws8iag:j ochs 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 1hs ;(bboh:nuw. : wuyin the laboratory, are moving toward each otbuw;h.u(o1b :ns hy: wher. 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 momentpq23n(nu2v33 2aiwa wh pt mb4um $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprisef0 * z+kcxrxk7 obtains its power by combining matter and antimatter,0 7xkr*fz kx+c 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 accelerated so that its kinetic enere iu7iwonr:38 29jaef m: ena;v;ayk7gy is greater than its rest mafekj;aa7r::2we m97ei3;u no8nviy ass $m_0c^2$ 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 physism/ *i- 1vdmamv 5.vaics believes 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 sh a- m*vimm.isvd5a /1vorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of o6g ts1e0 qgmm12fzz1o xygen react to form two moles of water, the energy released is 484 kJ. How much dmg1g0z6qf11 semz t2ooes 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 created vjw4 :kse/l c0xqk3+k, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of refc0k 43/k:vlxqesk+ jwerence, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relativegx0m70u pwe+ 5xg ll8d to Earth measures his ship to be 25 m long. On the ship, he eats h5ugex0m8lwdxl p 70g+is 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 spacm eewaw 2l /2u(upy-: nfglj).eship at a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do obs/ ue(f)yp -.elwg2nw :2amljuervers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total masxa3g(7 )m2:c wa1afk w. aliars of 150,000 kg. The occupants would al23 cmwa fark1x:(.aa g7w)ilike 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 spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. What is the spy36c *gyr6iv3ntpsgu u/6b i0v rr t(1aceship's kinetic energy? Compare with the total U.S6/nr*gsug 6r1y (yittp0 3rvu3c bi6v. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to tu8tfam 9/4w l 6ydrw) dox,bl6he 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 on the spaceship to bring it to the speed necessary for this trip? u = 4droyt am,xd6l6w)/fl8 wbu9    c

  A 1.68-kg mass oscillates on the end of a spring whose spri.c1y -od3ej;;. orisb;c*vanl6 qcusng stiffness constant i onsrue3-o ;;16jc;* bqcs.dc i.ylvas $k=48.7 \, \text{N/m}$. 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 mcpzqpbkz*( 9 5kjhh5bef12 1x5tqq:i ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.