You are in a windowless car in an exce ouh*:t8c3nbmcn u349i z p1doptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether buc4p*n8 unz:iodh3c 9om3t1you are moving? Explain. ----待选择----yesno 

You might have had the experience 52px- -on xsqix(muh *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 thq5puni( h2s -xm-*xxoe 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 ballgrh)w-/7+o hjtejvz 5 straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behi vrw+ h/tz oh5j)g-7jend it?

Does the Earth really go around th7kh 1dd psq+n8e Sun? Or is it also valid to say that the Sun goes around the Earth?hsd7pk qd n81+ 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 speedl 79(5hipv .h8yd 3 mjrqxxs4h would th9.yspimqjvhh3d 547r 8l h x(xe starlight pass you?

The time dilation effecte* / vigi8g(kn is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What(n8giivk /g*e then does it deal with?

Does time dilation mean that time actually g9 :js 2pv9sn.rm snn.ll;q*f passes more slowly in moving reference fml nqn2 sp;rn lj.gsv*9.fs:9 rames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home2 i;b.3 dkarp *ubr,wmtc+ac. from a long trip. She rushes up to an old gray-haired mu* iptaw.ca2 bm3;,k.c rbr+dan 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 notice 5y+zmrf diy-)m 4wnr( a change in your ynf d(y5+4rmwm iz)-rheartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and l,cxg l4wt4b2fength contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to tiw:m,8 ,dp gb,u 0mkgfhe relativistic predictions0mpkgf,8u, wb ,g md:i of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light d o3dg8fdxp() 4dxm,8cx l/vg:naem) were onllc4d)a() 83fxgx m x:d, p/gdem8 dnovy $25 \, \text{m/s}$.

Explain how the length contract ;shq.rk5g 7p ;8egriaion and time dilation formulas might be used to indicate that c is the limiting igs7kgh8p ;qae5. ;rr speed in the universe.

The drawing at the start of this Chapter shows the street as seegi+cry2fzc 0x oo/3vy s )g-l+n by Mr Tompkins, for wogo lg32++y)/xyzv fr0 cs- ichom 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 atmfc 8n(6lj6xb speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this up nxm(l6b6jf8c per limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest ma gjk.tiy9y6e jdd0sre*- +4lcss 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 has mo+;g,7i 1 *xy dit2vakbsrtbc0re mass when compressed than when relaxed2tb s+*b ir7xt0 ;,d vgak1yci? ----待选择----yesno 

It is not correct to say that "matter can neither be created norabzn q8a :y9k/ b53sxc destroyed." What must we say insteyx nz:c3bs8a q/b9 5akad?

  Is our intuitive notion that velocities simply add, as we did in Sectio ;/06ropqyvx3k s/ ii4. o+wmj9xcyno n 3–8, completely wron/y34.im /vpwn +xor0 x qooyj9;s6i ckg? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28.an r,+x/5gx in2 m. How long would it be when at rest? 5+nrixa, gnx/$L_0$ =    m

  A certain type of elementary particle travels nl1p ;qmle8p/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 on the faccbj l1mvf9*/c6q iq : r t2*bv;s9s)hn,fjlextor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 frompo2ct.vc +o.wqag7 z u1mt)j9 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 average lifetime eb;1g so/u*ha qusj/:o*ol u (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,ogw)k ba89 na you have to travel so that to you the distance would aw)n oga,k98bbe only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed thljux w,/3)z sq : ei,nes s5mlc,8t5u9bdk:jjat tells you the distance is onlyl5 w8j,jqis3c5k stx:ne bj,l:d /m9 esu z,u) 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 theln g aqj25jlfm/.f-3lpm4l s+ 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 Enterprisgcay+np/hh jy 2(fn. .gke8 :oe had just returned from a 5-year voyage while traveling at nkj. ny/ hgh:a .82peoy c+(fg0.84c.
(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 l 8 l84y /3sl9gt5ztiaqu g*mxsight-years away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as me3tt8q/ zim *sg4x sl9a8luy5gasured 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" spacp fewpq)0 fujv4j344 xlz6r/y ecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m 6)pe v r4 z34j4 ywp0/ljfqufxhigh.
(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 be-rsjzl+)xn m-b o,q 3ifore it decays? The averagemzq n lo+)3sx j-i,r-b lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of atzes50;dia ab 8;0ep a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twicet- 3y nr1qyn1hlr05 im its rest mass? v =    c

  A particle of rest masegip nvo)7 d)15jc*a rs $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a*phj 2)9cn 7hu;pd/ -tncf rnit $v =0.10c$. 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 c1 wgl2f 4+( :xecbtzne3a0oi bhange in momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction x c1w ye8t1ve9lh0k-g 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 procesriy*pu 8 xb-.+u8kkbjs known as fission in a nuclear reactor, the resulting fragments have a total kinetukxri+* pjb88y uk -b.ic energy 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 joules and tfqkh qy,w/ji3g;0f- 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 ofofl7fg/ (90io :ndnip a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is aenwb2 rym8viz:-b8: fbout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conjer jm0n5syh8* -kye p*9b6cyversion of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic energy equaltq);r(i9f ydqs its rest energy? v = 9d) ;ifq(rtqy   c

  At what speed will an object's kinetic pf-7 hnuez a2xg1ym) /energy be 25% of its rest energy? v =    c

  (a) How much work is required to acce siv1+ *q80kqhg6npln lerate a proton from rest up to a speed of 0.997c? W =vksh +8q1qnn i*p0l6g    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic 2pdms6eu . 2sfenergy and momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetiq /z8vqaew i;k5 97upcc energy is 750 MeV)? cw/z vai eq;9 8pu75kq   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differenma8h*e.i ,h7 p yqcbp+ol)( ehce of 105 MV? v =i 7eahceqp 8lp*(,mbh. +oh )y    c

  What is the speed of an electron whose kinetic enec)4+fh*swj yargy is 1.00 MeV? v =    c

  What is the speed of an ele k21(ak) kexlqctron just before it hits a television screen after being accelerated from rest by the 2e2xlakq(k k) 15,000 V of the picture tube? v =    c

Two identical particle xhogh0:pal1 d56cy5 xs of 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 protodexu g2a1 .*x . +ylv,gw1n;ku9de yuon ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 e fscdfs g2qm4o2 5 84 8,due-;brbygoxlectron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 0wqxb1s6ki z* z2 ,sgl3o /pna27,000 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 e19:sbpyx9g/s 7a qxm xx rfh-3nergy 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 nucleuvyas6) tjuq 2.jt*vf3s, $^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

  An electron ($m_0 =9.11 \times 10^{-31} \, \text{kg}$) is accelerated from rest to speed $v$ by a conservative force. In this process, its potential energy decreases by $6.60 \times 10^{-14} \, \text{J}$. Determine the electron's speed $v$. v =    c

Make a graph of the kinetic energy versus momentum for (a) a particle of nojqz x 1.se51b aq5hfz5nzero rest mass, and (b) a particl s5 q.bzzae1f 1x5hqj5e with zero rest mass.

  What magnetic field intena//kw)av esocx5gf00 sity is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The protosxow 5eak00cgvf )/a/n'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 tykvde 3(+eppnalz6 :-o the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with r(-ad+ppk6 ln e3v e:yzespect to the Earth? u =    c

  Two spaceships leave Earth in opposite direction f( x-99:4,nl vq5xjyfa q/zdveul l(ts, each with a speed of 0.50c with respect to Earth4q( y ll9xf fu9 5v(,dqx:vteaj/n z-l.
(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 lg r huj7:n7:xg1s i9h)ny h1x0.71c. 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 respei :y9hg)s jh:rln7h7gnx 11 xuct 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. The Eal *azocr8sr .b)bfaf6rz:( :nterprise comes to the rescue (Fig.r)z cbsfa8fb:a r(:l *r6z.oa 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 vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directi68sgukxz *v-xe6 -mz)/cbua nons. One travels ag6sbuu z-x)v c-mxz */ kn86aet 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. uux)bx12ypxl ,:1abqAt the same time, rocket B passes Earth moving 0.95c relative to Earth in the same dily2,pb) 1xbx1:u qxuarection. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is P diz)r y2w4gr/roxima 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 about 0.1c is call02m3obs k 8mry43 wrjeed relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speeo3wrm3rs 0 4ekyjm8b 2d 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 speep;tsc eyw*c;;a .:wqzd $v$ 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 toti;wb.g*k 7+t bd1rut ually destroyed to run a 100-W lightbulb for 1 year? *urgub+iwt7. k1b;td $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy i2qtyy*5i+h mvrza oa,u(,o1y 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 azqoh25y r,ia1v y*+(oumty , 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% tq46.gk,y)q lkd+cl pvdi7eykpm.13zn d+9 fehe speed of light collides head on with a positive muon traveling at pkvqq+emy zk,g .+f7idll 6 p9ey.)c4d3k d1n50% the speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino. Assume thap7 /t(j3cp*wyli 4uge neutrino's rest mass is zero, and the other masses can be fountigjc3wp(/p *y4 l a7ud in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of abou4ilu uw(8y ibt(/yy* rt $4 \times 10^{26} \, \text{W}$.
(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 measuredwwa 0r*evgr(htc+g3nr +2ny 6 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 nuclfj bppi02;nc 9eus into its constituents, two protons an0 fc;2ib9ppnjd two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase ou 5shfib0r d25+nol/it,k4vin the (relativistic) mass of a car traveling 110 km/h as compared to at fd 5unr li,h54s2ov oit /b+k0rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each havins(oli:75 xya cg a speed of 0.935c in the laboratory, are moving toward each other.i 5o 7sycl(:ax 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 /ge/ 4jroohj 0;u)gdsum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining mat6jj ke 8 k/k4nf5y(anu) e.kddter and antimatter, achieving complete conversion of mass int6/f4ked 58djy k).kjk n (enauo 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 enepz 8 tady/x-s9/ ,/5vrat9xup 3u foxergy is greater than its rest mau,dupoxfvrs z3 /- 5pxa 99/axyt8e/ tss $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-long pole iw;rz,ke e*00lggn d 3;fbsbw a6tw7j,f;f4bb nto 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 runnibz0 3*f,gbb70w,t;b4ewedkn slgw;6 ff rj ; ang the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one moievwmdx+ ( u*s l.8 -w8w6imrlle of oxygen react to form two moles of water,llx-6 *wu(i wv8rem8m id.+w s the energy released is 484 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are crearh8dm,b* hr; bted, 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 p,rhdb 8r mb*;harticle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative ttulhs/ t, u1p1o Earth measures his ship to be 25 m long. On1p /1lt sht,uu 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 spaceshn +r3kxk6 kh/(b h:pxuip 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 xhk6u :hkpn+r3b/kx( observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a totd)zq7 ;y jay+dal 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 engiddy7yq)z+a j ;ne 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 ish-t 7h/:sivbkx1t;ae the spaceship's kinetxe;hst -i b1kah/v:7t ic energy? Compare with 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 lhnkim7..+ 5dyqp 9kfhj2+qpqight-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 sph+5d kpm.yk .qn q i+h9jpq2f7aceship 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 stiffness consta-3cmgts gw. i5r x9bf;nt i 3ifbr9g5tcw.gms -;xs $k=48.7 \, \text{N/m}$. 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 massw cemr4k6 ) v:xnntu*;g2u u+x $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.