You are in a windowless car in an o+u.3.me lc gfdfifv;:: b g/ip;g8 npexceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in t;d; p ff g+.o:bvmg:ii 8l gc.un3/pfehe train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the / u : vs,;d+qpjfe1wpqzt554yxr0mez experience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brvpe f/pt5su+d50 m ;wzrqxj,q e1zy4:ake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of c9i x;htd m0k3a moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball laht0cxm 9 dki;3nd on the car or behind it?

Does the Earth really gov-m ;f8q1 gnzc around the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss-z1fmq8n ;cgv 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 stark mwe5 ttq3dtfx5k84*lm5j )i, at what speed would the starf53*e4t l58ixq kmt )jktwdm5light pass you?

The time dilation effect is sometimes expressed as “mo blvd-n/c eivyh-74 p8ving clocks run slowly.” Actually, this effect has nothingvph8v/n- e lci4b -7dy to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more sxhksd .y8al/ rluvn m568be+3lowly in moving reference fram 8hd3y6nu/ +rse8. v5llbxmkaes or that it only seems to pass more slowly?

A young-looking woman astronaut s 83 u :s4ulctk*cxof,has just arrived home from a long trip. She rushes up to an ulcs, 8f cox4u3t:sk*old gray-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 s in)vl a6,kyjal/7( kwpeed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using tel ),a 7(kl/nyi6 vjkwlaescopes say about you?

Do time dilation and length contract, tc )i8rmd*auion occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of l9a.uhyi *n,zjf) h--gaxci/ f ight were infinite. What would happen to the relativistic predictions of length contih9nu.j g,cz/-*)fa f -xiyha raction and time dilation?

Discuss how our everyday lives would 7hk9q8,rjvwts20e v s be different if the speed of light were onl9vtsqvjreh, w0 7k82s y $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be usevkvzm ,4 p/rln/x90csd to indicate that c is the limiting speed in the unknrvc4 pm0//xv 9lzs,iverse.

The drawing at the start of this Chapter shows the street as skp 4t1w dnysh.84w 3n7sk2 qj uyk/di6een by Mr Tompkins, 3 1 i 4kd28pyyuj q4.sn hwnt7kkw6ds/for 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*l )xfrk(+/+ypws) gcg/o ao5 mkjfbu4+s1oc this put an upper limit on the momentum of an electron? Ifo gf/wbg +ckk omrs s 1 yo++5pja(/l*uc)x)4f so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonze pwi x oz3;hr /.qah6:;d1zuocro 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 has more ma249gpe 2cbs c-qlw(vn ss when compressed than w2 -sec24w9v g(cblpnq hen relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destvw ua-untx/ete:+ b ovdvuq+ 771f-.h royed." What must we s-++7na.hx vfv/1evtu udut w-7 b:oeq ay instead?

  Is our intuitive notion that velocities simply /s 1v1fej 6daiadd, as we did in Section 3–8, comple6aej sif/ dv11tely wrong? ----待选择----yesno 

  A spaceship passes you at ah ;u-)ioajnn .-qfyv-k */rro speed of 0.750c. You measure its length to be 28.2 m. How long would o na nj-k iovfu;-*/-h).rryq it be when at rest? $L_0$ =    m

  A certain type of elementadl4ewn429 1s,ivxau s ry 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 depend on the fa/9jyyl qa 0yu ls 70q7h-qau5fbz,ld3ctor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from Earth at 9nbq e + rsac5v17yj)qa 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 is measured jor85ko n7m2ac m it54.erak: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 framla3 wt0ya ,u.iy 8li(s/.n etsm,ny-ae, a star is 82 light-years away. How fast would you have to i n /0i( -ty.myyauatnse a8 .,wls,3ltravel so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years an);2lsj m -mj.b.mappo sn 45cway at a speed that tells you the dista 5snc) lj.42.oas -pm ;mmnbjpnce is only 25 light-years. How many years would it take you to make the trip? t =    y

  At what speed $v$ will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)? v =    c

  Escape velocity from the Ear y55j,wq0m(b/nn+bc 0qn5 ly wlzb-noth 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 s5 43pd*rnpsnEnterprise had just returned from a 5-year voyage while traveling at 0.84c.5rnsn3 4d *spp
(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 loonar,cmv+ +.q:e6zdlr n4u ,cng would it take a spacecraft traveling 0.960c to reach nv+ .4+6,zod nr:qcrlmuec ,athat 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 v8oqt +n+g x;gqvo3c .in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. ct + og3 +xov8qqgn.;v
(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 doqdoubwy62 l94y 85p/a n4baaecays? The average lifetime, at ro5yp4qy aa4wo6banl9b28 u d/est, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton toj+ p4b:+wg7ovnx 8yaraveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s rel dmbrbl-amh) y u152 tfizm*06 zah/-gativistic mass be twice its rest mass? v =    c

  A particle of rest mas9xiw+t(kmlz;8u,t5 me y k t.ts $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travefq2p7boe0,*l/kuc v wls 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 a proton that acceler5nmad2 5ar7f iates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction re9)fn(.ny tk x,2lludkquires $4.82 \times 10^4 \, \text{J}$ 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 kn alv1y992t0syudw 1 f au6,:obabz/zoown as fission in a nuclear reacto w9/0yyf1 vzabubsaua l d61ot,:29 ozr, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy oflxs3zdq:xo t r-hc+)g i hk+9ui3o 04x+qlmt- an electron 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 ojj9 1syh uw7p)l5 t4tqf a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is jr6*spjxzv j++t.2 1y;b cr vpabout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 1.0 gram of mass? +z ap.x85ql ge9k:bft2um 9veg5i ac 6    $ \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 equals its rest enhc( xyh-r, v0z5v wly:ergy? v (:,ryvh0 h vcw5-zyxl =    c

  At what speed will an object's k7yood imh/1tc2 rrj*)+l b5cie ;i d/ninetic energy be 25% of its rest energy? v =    c

  (a) How much work is requyys we )y-eu4ijt 6/vdk7/9isyv3k2yired to accelerate a proton from rest up to a speed of 0.997cy9j kd/-yv4yi2 v/t) wssyey i3k76ue? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a protjlq9 9i0ima3 h2a9sjd on 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 kiiz/ xr t0pnj-gu r0l0txn55je++i6 slefg(0inetic energy is 750 MeV)? xz s ru60ei0elj5+gi5/ ri-gn0 jl (xntt 0p+f   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton :* v 8 lrepm-hktcs:6caccelerated by a potential difference of 105 MV? v = :rs*8tl c:vp-k emc6h    c

  What is the speed ofo5ded te)/ tz; an electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hsf,h6:g e f.qtits a television screen after being accelerated fromtqe:,g .fh6 fs rest by the 25,000 V of the picture tube? v =    c

Two identical particles of rest mar 7lek a/il 26r8ejyt+ss $m_0$ 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 (qom4(h7((mnlbe o lj.$m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed andjy(us2s: zvu / vg5uz8:pg*ha 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 27,000 kg is accelerated to 0.21c.:jyacdnie ,hm8)3e(6*bji u x
(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 andho 9ujjg87pt +5dw7ti 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 nucleu,7c2pxrg2 o 7/rqgn wss, $^{241}\text{Am}$, 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 k,b;sji(ry; + unuyh:) a particle of nonzero restn ;ujri+u ksb;hy:(,y mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-G2 u3 tvwkogt68eV protons revolving in a circle of radius 1.0 km (at, say, the Fe3 gv t6ku8owt2rmilab 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 Ear 2o;8fwfa:8d)n a vkfpth) observes a meteor come from behind and pass her at a speed she measures ff 2odp8na)8 ;wv:kfa as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Eats8 ,w4bxpy l)rth in opposite directions, each with a speed of 0.50c with respect to Earth.lp,x byt)8sw 4
(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 0.71cm8d b/ki2j2lsps9 (cc. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship m 8bcj dp2k9s/c li(s2with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speed of 0.6gh6e*/nm j9i:nvc4e b 0c. The Enterprise comes to gv/eijm4n 9chne*b6: 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 vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opp j*x mk8.e2xetosite directions. One travels at aee8xt*x. jk m2 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 time, rocket B pass n((9sqkcu;p f/bl6y wes Earth movin/(96 fps(uw qbcl; kyng 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth0z00psy kdyl : 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, anythi7eg /qmxkavq5md6b+ ytlj .0h2m+4oing traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativih2d5l6y.g mbq 0 + a4tj+xq 7vmimoe/kty 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 ev;c vy1qsgp9,f 254lq f* kmv$v$ 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 gk2qnpj s;.a3dyi )h( be totally destroyed to run a 100-W light.k)s3a2yqnd jh (; gpibulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagne baj*49c3 etysr x4ph1tic 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 electric chargh4*3b9x4rc 1jpte yase 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 kbgl b t0 r(4-)qac.6raqc rw433% the speed of light collides head on with a positive muon traveling at 50% the-64kaqbaqrcl 0c.bw 4(rtrg) 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, a(e nmc3)7fhkeg94yotg x,5qkl 6v: e an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masseso:k9eakh6 4 )gvyft5qcgm (,nxe7le3 can be found 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 i*3y6nzolv; e 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 measured to have a negative charge and a speed y s*kpu24y5 nnof $2.24 \times 10^8 \, \text{m/s}$. 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 tj9eh yxicx c.6s 1* 2+w+utzvwo break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutr yxx9*w1+ t 2.uwi zvecsjc+6hon, 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 of a car tm ;8 3hrheau u1g/+yizraobv3 kk;7k*raveling 110 km/h as compared to at rest? [Hint: use the binomial u+ z *ge8imoyhab/3hv;7 kur;1 3 akrkexpansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 01 ;o*8ki4sky wwtbp5 l.935c in the laboratory, are moving toward eactblp1wwo s58 k;ki 4*yh other. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically thegrld5n i7 *;gabeu-9at a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combi /jo+e;dfgeq7s 68jguning matter and antimatter, achieving complete conversion of masg uqgee6j /+ jf8;osd7s 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 accelerkub ah+5zsz2iz- bp8 m se*x5;m1;v rmated so that its kinetic energy is greater than its rest msm-k2r i1vxz55m*eaz zps; m;ubb +h8ass $m_0c^2$ 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 canx *nvfeh0z2g ) 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 wh)f0ex 2zhg*vn en 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 oxy/cql3f ;tpzr5sw: lay:+jak5 gen react to form two moles of water, the energy released is 484 kJ. How much does the masss3 l ylawtp/a5zjq::k+ r5c ;f 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 crea.enhe- -u7z9mn5gsceted, 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 other5m cnen-zseg.9eh 7u- particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth meas w4l 8 4tb7)8l 3vwzzlo.lzhgsures his ship to be 25 m long. On the ship, hezs wlt88 b43)lvzg h. w4z7llo 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 0.85c awayoou:tf dw( -i1 from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Ea f-uo1t:i d(owrth measure for the speed of the laser beam?

  A spaceship and its occupants eb51s 7 hy sjonsk+a:vh /:o*yhave a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of thsnjbh 7*yy h: s/ao+:5oek1vs e 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 spee)pwut7:v;lh a5dt ew*cqz * rp,(ujv9d of 0.99c. What is the spaceship's kinetic energy? Compare with the totarhwp :dtp7q9ewuju)*,vv5at(l c; *zl U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel toe btf+3josgfbl45 ;p gjfk6+: the vicinity of a star 6.0 light-years from Earth. Passbsg +6:p+e 5j fofljg34;fbktengers 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 =    c

  A 1.68-kg mass oscillates :jiy,kqzq k g. i5lv-b2a7i-kon the end of a spring whose spring stiffness constant iyilbvg:7i-z,q- 5ik. a2k kj qs $k=48.7 \, \text{N/m}$. 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 mjbsix33q,a2o.bawl 3 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.