You are in a windowless car in an exceptionally smoo-rx o4y6bc9mz th train moving at constant velocity. Is there any physical experiment you can do in the train car to determine wr9zx-bo6 m y4chether you are moving? Explain. ----待选择----yesno 

You might have had the experience of beinmo83 ;run 9)col2i9 j e(e htg+q;jwg1nzxyv;g at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on vt ynqh i;gox99mer 2 j oc(8gwun +z);j;1le3the 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 b8-wo;6(xx 1w vq +que;oyohgball straight up (from his point of view). Ignoring air resistanc; o8v xq-6ewo(g ;ouwy1qxh+be, will the ball land on the car or behind it?

Does the Earth really go aroun ab7rdb;m2l, yp,r ng9d the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in vid,b;b,rpa 7 2ylg9 nrmew of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship trr( pqqqf.p i y f2)y4b3a-w7vfaveling at 0.5c away from a star, at what speed would the f - aqb.p7(r qpq4 2iyvf)w3yfstarlight pass you?

The time dilation effect is sometimes expresfl5j.r.ybv/ s sd-xc; i ws/2xsed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then does ;vwl jdf/x.is5ycb2s . -rx/ sit deal with?

Does time dilation mean that time actually passes mc (kr b5g+wc ki3:ake1ore slowly in moving reference fram:ac e1wk k5bc+ik3(gres or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a loiyznbm,j5cfot) :.fq, a6y1dls58 p ing trip. She rushes up to fdbt1i n8pmjasz5,o5.6 ilq,yf:y )can 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 Earwfldp*tm767kd 1rko t6xf7 :/ .lc7hfvwjgv4 th at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observfxlp7 l 1 g7*ttdkcw77fdow 4hfvm v/:.r6j 6kers on Earth using telescopes say about you?

Do time dilation and length contraction occul62l njhkt ziqpda clx5257 y2t*0)obr at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of ligq3kd xcx:l-a *ht were infinite. What would happen to the relativistic predictions of length contr-aq* l xx:cdk3action and time dilation?

Discuss how our everyday lives would be different il7nto + z;lu qtb9i9f4 kzyl*/f the speed of light were onlyylt/ *uli9z z f 7bnk9+4;loqt $25 \, \text{m/s}$.

Explain how the length contraction a-8 i*i p* rmbk1c+3jybxep3nfnd time dilation formulas might be used to indicate that c is the limiting speedb*b8c epx3knp3i1f+*ir - jym in the universe.

The drawing at the start of this Char(g6ghf a *i .(obog22 lyxsz.pter shows the street as seen by Mr Tompkins, for whom the sbyf6(g2oa*.ogri(gzxhl s 2.peed 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 ugp :8 xsmh0s/gpper limit on the momentum of an electron? If so, what is this upper limit? If m:hs 08 gg/pxsnot, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of l c hkil7l77 ;p;w7 x0p0vk,hrltlf:l right? ----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 this0 nav*/r 86bkayuydu / mean that a spring has more mass when compressed than wb/ydrkuna6v/a *8yu0hen relaxed? ----待选择----yesno 

It is not correct to say that "matter i8:e5 2n1 plcss arzw-mx*nf1 can neither be created nor destroyed." What must we say zfs-e n :a1ixpcl8w1r25 m* nsinstead?

  Is our intuitive notion that velocities simply add, as we di+khv litf h jv+-(:t3dd in Section 3–8, completely3kvh+d ifj+v-tlth:( wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.75ptj v(d uz+d s( yr9fr4:s.p,m0c. You measure its length to be 28.2 m. How long would it (pp rsdvm,d(t :fr zsuj4 y9.+be when at rest? $L_0$ =    m

  A certain type of elementary pab tz +z t.u:e8ldli-/zrticle 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 interva0j:grdxs ;gk/jkhh / o6s0m07tydx *els depend 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-years from Earth at 0*3 cbejye2ve ynkn:5a 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 measj-q +gf ac0mch8aweu zxw. 228ured 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.zwb xsy:9/z2,qtgc2k How fast would you have to travel so that to you the distance would s/y x2b t k9zwg:,cz2qbe only 35 light-years? v =    c

  Suppose you decide to tr ub6ug-x0,y rmavel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip? t x,b uuy6g-r0m =    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 Earth 7wa mua:92zbj 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 returned fry./su t.71l ;d y7x 29 sofohzabwn;)shc4o kdom a 5-year voyage while traveling atc oy. nsfbw9d;;soolh7 41hy.u/ks)x 2 a7dtz 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 li(4ohqffr v,t zgr.*2wght-years away. How long would it take a spacecraft traveling 0.960c tow*tfrfoqzhgv,4r.(2 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 yo:5 huz) zssqic9899 epozlw)tu in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m loilz8)cspq9wt: z59e h )ozus 9ng 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 ave xl2 *yef:pl e7 .x/vxtts6r)trage pion be moving to travel 15 m before it decays? The average lifetime, at rest, is l p x e/:e6xvxryt.*)27fttls$2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentumak ;wexlr,to- ) un)0x of a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an ob/; lxa7 hd)re5md*wo eject’s relativistic mass be twice its rest mass? v =    c

  A particle of rest ma;(sats1h3 tk+tv 6f)amj(w h wss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels 7 a-e9o /bqj6iqrjc u32 j.g ri3f4udmat $v =0.10c$. 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 chan nzfg9, b g:ak-bmxx*,ge 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 requirenpvff)0b ;pl1ee3by0 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 qi v:h;dv; n 2q9yifg4apart in the process known as fission in a nuclear reactor, the resulting fragdn9h vi:qfiq2;g4; yvments 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 of an electron in jouleng.7+ byep5r ys 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 nahxgp.zg8d*)2 cqm +a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumpt:1 )l9 gflttecion 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 obtained from conversion of 1.0 grp d;n /2kffxuah1t0s 6am 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 equals its rest ent*fu qp4vf4,g7mq2lzq+0 sldergy? +f7 qtpuvsgzf2ml * l44dq,q0v =    c

  At what speed will an object's kinetic energy be 25% of i l5y9l/fm fclm),s cl9 uj(7rwts rest energy? v =    c

  (a) How much work is required to accelerate a pjgugbvb ( tx:6) +eo,0k erdr1roton from rest up to a speed of 0.997c? W g t0)bdx(rue6r1 +j:gkv boe, =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic ene+3 jcz.h(u2h xogozl2n e)tc7z: 0gm srgy 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 pro2yv)*b4nxp;7n,di kfw-.n tfuz niz 5 ton (that is, its kinetic energy is 750 MeV)?vi ,n.4z nxnwd;ty2k- *p )7inbuzf5f    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differencr j(gto6/c4rkvx*q 0de of 105 MV? v =v4rqc xj o d6*r/kg(t0    c

  What is the speed of an ele.hl5k qjd t/:2 peh0uxctron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just zy7h ox5 f/h,zdnl9t ;before it hits a television screen after being accelerated from rest /zy;,ztf7xh lhodn95 by the 25,000 V of the picture tube? v =    c

Two identical particles 3q/kxgu uwk,18w,nhq 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 8o3v0qma. *k); pd pi*zfeip kproton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 /g) cb c*ugo+ian 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 * nlv(- jkx; cq7)ry(fgc df5sto 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

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

  Calculate the kinetic energy wtufw:;ro1pkg x 1./hand 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,)trtnce:uv m uoh*)8/ $^{241}\text{Am}$, 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)q2pc) rbrn d-9 wwm:5/n4tvpqo kp(8t a particle of nonzero rest pd k4r(:8m/r95npwt)p v to2-cbwnqqmass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protonsvyqw: 7p-wqota)iw9x m 7h*h8 revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. T- ti: a7h9v7w hq*ow xm)wqp8yhe 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 (mk3xv .s.:o pswith respect to 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 respect to the Earth?.. ssk3xpo:vm u =    c

  Two spaceships leave Earth in opposite directions, eacheyhrlo)8rvcz b(p- ; / with a speed of 0.50c with respec-;obhe yvp /r()rl 8zct to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth traveling at 0.71c. A second spacesh9.hh:q r1h 0kz1kwemzip leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respec1m. qk0 h:zw1h rzh9ket 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 a6v q f92/eglm+y/lsil ;z:ugupproach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one ve z; u2ielf+g:q //9ly6mlg vusssel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. Olu7gt 6/i8a axz5zbr4ne travels at a speel 4gauzzbitr/58x7a6 d $v_1 =-0.60c$ 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 cadp4 k0x7ku; :cc 1b4 pr2g)ymgl f)ysame time, rocket B passes Earth moving 0.95c relative to Earth in t) d1ku a2cyc4 g7;fyrp)x40g m cp:blkhe same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is P8 kyebz9z-ign1 ;;90h fmxk qkroxima 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 trave0akyq8sx+l5 + f,+:g k ftbmnrling faster than about 0.1c is called relativistic - i.e., for which the correction using special re+tyam+5b f + kgfn80sqx,klr:lativity 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;zk-, l+iiqn cd $v$ 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 totally24(ht wsw3juf.iahz vy wlwt6 w*x9:+ destroyed to run a 100-W lightbulb for 1 y2ww*hhu f6.+ w:w43ty sl9 (tvjwx iazear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electron a. 3z1frfszt+m 94k nw sa8r)dlnd a 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 +8r )f4anm.s z1 s dktrflzw39=    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 trave05 f7lld tuyk5ling at 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons 5ykftll 7u0d 5(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 prow+8 ( ia2 dgq+r)aua a38jbtyxton, 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 when a neutron decays at rest.x8+ aaj8 +2yt3aridga(q)wbu KE =    MeV

  The Sun radiates energy at a rate d:6/17::jqbuonw*hha )x ztyyxvtm)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 measuri j7ipj :d;ns8ed 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 6bpx 2;ugo o7f8q oqr4nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutr xfu7ob6q8gpq;2oor4 on, 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 op9boak5b /bqi61y rz7fm6 k8ww bt*1of a car traveling 110 km/h as compar7iq581 fb b *barwwokt66k9mz bpy1/oed to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laborfwu(.l)7aib urh b9q)atory, are moving toward each other. Dehbwrliq( )u u)9f .ba7termine
(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 ( pe:n z)d6cj)chm+xm particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship h3beczl, ty )/Enterprise obtains its power by combining matter and antimatter, achieving complete cyt/lz3,eh b)c onversion 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 acceledj 5k lxvdqc/je0732lrated so that its kinetic energy is greater than its rest mass ld kjq d 5703e2ljxc/v$m_0c^2$ 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 zc ,4ih0+fv0 xdp(i x cleh(;acan 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 tha0x(elchp;4avf + zi(c hx0di,t when 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 ofc 1sa1 w1 f.jz8fid.nj oxygen react to form two moles of water, the energy released is 484 kJ. How mf.1 i8 1f .dj1wjsazcnuch 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 s 6buvujhrvq+ 7uk q+v).n it,+0k7hpmt4nm3 created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, whatv.+u m7ruptkjiv+7) k4 m6n 3s qhbu+tnh,0vq is one particle's speed relative to the other particle? u =    c

  An astronaut on a space+s;5 fm tpz6ek lze+i8ship traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in 23 + e lmt5pzefsz+ ki;68min.
(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 s tdohx5l9 hm5:paceship at a speed of 0.85c away from Earth. You send a laser beam t5hlo: xh9 5dtmoward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total 9 w.dujrr-fp *mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converf 9- *rpw.jdurted 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 ofhitth3d1tzs2;2 is* f 0.99c. What is the spaceshii2 h3s;tttd2f i*szh1p's kinetic 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 light-years fru9gd/ymqs1qj5ak:b (om Earth. Passengers on the shipq:15u sgm/ b(yq9adkj 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 on the end of as/g no :5emtn. spring whose spring stiffness constant n tsne/omg5:.is $k=48.7 \, \text{N/m}$. 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/ j1mtf1s25 s mvmie8uss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.