You are in a windowless car in an exceptionally smooth t19rc5 pk, vrx j27wgryrain moving at constant velocitv29c1xrk,yrw5r7 jgp y. Is there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had th t*ty/m0gj3y,n q(xotvu0 x;ch ,zqz6e experience of being at a red light when, out of the corner of your eye, you see the car beside you creep forwa x,v/zg0c tyn(ty ;jou h,zm 3t0qx6*qrd. 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 throwq6 izjpbcb v/ 0;1,g+y vw(utys a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or be1gvi pc+v;zt,b0yj( /w6u bqyhind it?

Does the Earth really go around the Sun? Or ig9 h1jxrlz);vs it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativityr l1 x;9vzjg)h (that there is no best reference frame). Explain.

If you were on a spaceship trave(ej/+w f1u ewr1v;6kcw*pcjv b px gr2c9ge.(ling at 0.5c away from a star, at what speed would the starlight papuj ecb9ej fwg12rcv*p/ k;.g+((r wecv 1x6wss you?

The time dilation effect is sometimes expressed as “moving clocks run sw qz4vqs6c4 b1lowly.” Actually, this effect has nothing to do with motion affecting the functioning ofqwcz 14qsv 4b6 clocks. What then does it deal with?

Does time dilation mean that timq ltkkz 7dz62fb8fp48 e actually passes more slowly in moving reference framesq4pl z6878 b dz2fkkft or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long tritnt4(b un 37ejp. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as h4eutn 7jtb 3(ner son. How might this be possible?

If you were traveling away from Earth at speed 0 h,q 8zxet63mt.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth usin x63tzeth8,qm g telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, say oewj6:wb q /qf:uy 09p ig7o1y$90 \, \text{km/h}$?

Suppose the speed of light ;vcf5vt1kqn14mx3 tp- 0ihbc were infinite. What would happen to the relativistic predictions of length contraction axt0phvt;bc43 if 5c 1nv1 q-mknd time dilation?

Discuss how our everyday lives would be different if the speed of light werse q3t.twcmz n3hun .z:vda:d 3p6*s2e onl2m 6d.dzsvqa cwps3.en3t z: uht*:n3y $25 \, \text{m/s}$.

Explain how the length co 8)aab) :k ogiil 5)nl s+/iipr;1ziqlntraction and time dilation formulas might be used to indicate that c is the limiting/a8rpa1; +ilg 5):libkli oz ) isiq)n speed in the universe.

The drawing at the start of this Cjiuww z ou8bg6c904v j hz(z*a(z9a 2yhapter shows the street as seen by Mr Tompkins, for whom the speedu8v99zjzabac 0 o6(hz4u2 y*i(zg wjw 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 thkm:kles +kznfj-6+ z3an c. Does this put an upper limit on the momentum of an electron? If so, what is t+:nk-6z3mfl jk ks+zehis upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest (rk, 5sojxk(u 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 mor2mv p)s4)sqyj e mass when compressed than when relax )q)vpm4 yss2jed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroy2hutr 9jwyu8q7 w5 0ried." What mutrr0qhwu259y w87 iuj st we say instead?

  Is our intuitive notion that velocities ffkb1( b;s;26umi.bj e 5wxxq simply add, as we did in Section 3–8, compbbq ie6f.(j2;5sbw x x;1mfu kletely wrong? ----待选择----yesno 

  A spaceship passes y* 5lnb owby,q7ou at a speed of 0.750c. You measure its length to be 28.2 ml5oyqn,w7b b *. How long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed of4cu.eb)3 ht g,t j/3gnx gnne9 $2.70 \times 10^8 \, \text{m/s}$. 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+iq5: yb3l g*w:qsafg 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 to41tt*s us x7gpdvvg6 ff*zx)2 a star 125 light-years 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 average lifetime is measurgpmxr d0/x.c*)ukrcmc g t 4f.xsr56 1ed 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 86b sb y)+czbk7hrwp-ltk ) 1f(2 light-years away. How fast would you have to travel so that to you the distance wzp6w ybc rbk-1l hb)f)t+ sk7(ould be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed that ;+9x 2 omfsu 0djjxph2tells you the do 0 2+9xf2p;mjsuhxjdistance 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 th.uikaoz td7t)9 8et 2ie 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 t mp(u..k qo9ecruh(owin y691 hat starship Enterprise had just returned from a 5wr9o 9euyi1(u(mnq. pokch6.-year voyage while traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would ik 1num r62:tabt take a spacecraft traveling 0.960c t6na tbm2k :ru1o 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 ;9/hv (sjhjd)y w8owl9fw.rurrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m lhou; v(fhwl9jr9 .)/wsd 8ywjong and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to travel 15 m before it decayssh .gtuss7uqr9j.) (fs)( zbs ? The avers (hgzsu9)btrj( suq s. fs.)7age lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelu223mw d08k taxos6) q0hd zzling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’sn naespir0 179 relativistic mass be twice its rest mass? v =    c

  A particle of rest mn9jgz we . xf-nhy608 j;mc6zyass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at r6l4f4*j(g lsen/wh-/ ntlk a $v =0.10c$. 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 accelerhor*ndvv09 6m hkj4z. d i*myw:; 1rytates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires i d3.g/z 0)d.mjjpusf$4.82 \times 10^4 \, \text{J}$ 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 breakctk ix+/ix-,bs apart in the process known as fission in a nuclear reb+ i k/cx,ti-xactor, 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 enedno4a t ; r,zoyzy)5zcs*g+-j rgy of 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 of gf s22kqn9k;,e esbf7fp9 jh7a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Statesk5l+fp4)ze x dksc jjch 0c+v) da2/b7 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 oaatie 9l.lg37ub/1n0:zcf mt8 mwl( cbtained 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 particle f z/9*yqbbzo,when its kinetic energy equals its rest energy? v b/9zb fyoz,q*=    c

  At what speed will an object's kinetic energy be 25% of itsnnyp*iiq4e0uw/ w9 g 2 rest energy? v =    c

  (a) How much work is required to accelerate a proton from44br rfj0qc2 a5 skkjtlf1 v.+ rest up to a speed of 0.997c? Wff1kqkrs5v l a.c4jb 0 trj+42 =    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 proton travelingjiog*3ra6+9g )(xu(qlyzy at $2.60 \times 10^8 \, \text{m/s}$.
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 kinetic energiqhannwc/mt06ot + j8yo6 d s/2bo):nw;k u6iy is 750 MeVsakow+nnt 66jim n2w tuh)y i08oq ;6d/b:c/o)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MV? vymgj9a1j g,rq iu12 7iryi1gj j9ma ug7q,i 21 =    c

  What is the speed of an electron whos8hs/f bqdd7jk 3a o22oe kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron justz5k fa9 /aqjvm)-6e hc before it hits a television screen after being accelerated frh)69 jfaka5vcq/-m e zom rest by the 25,000 V of the picture tube? v =    c

Two identical particlz x7m+w mur 232z( fv40khswzkes 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 1h 5fd-wxj4vlof 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 momm z3) r-xyovhtc0/y 6kentum 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 accelerzunqr9ltc5 x.h u:ew t91 ne/+ated 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 energy and mn 7:(,4fyvxsokeoo 0d omentum 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,x8rw y 5+ujthddg;(3b $^{241}\text{Am}$, 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 morr gson :zrhwc;;74 8nmentum for (a) a particle of nonzero rwgsr8hn r z7;4c;n:or est mass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in azwgoi b 0jb0:9x(cm8f circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is gbco0wb:90 ifm8x( zj $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [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 tnm.9xubsowb +1 .dkic 2u+:ol he 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.+ndw ums29o+. 1uxko il:cb b respect to the Earth? u =    c

  Two spaceships leave Earth in opposite direz7jvymr9vq2jxw dr/u:* mpqve, / 22m ctions, each with a speed of 0.50c with respect to Earth. qpm q2e,mvyu m29z: /*r2wvx/r7vj jd
(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 atuq:v1c6vfq+hfyv7dv + xx:.zm .c4o g 0.71c. A second spaceship leaves the first at a speed of 0.87c with resp6vh147vx qyq:++.v.fmg ufd vc:zxocect to the first. Calculate the speed of the second ship with 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 0.60c. The Ente7kfuqmi*7i hulb24t1rprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative 77 bukq* ihl f4mti1u2to 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 directions. One trfq .gfk0tpzge.db(wa;*px 6yd l0 1z9avels a;x ypz1b.(l 06 dt.gez0d qfk9gaf*wpt 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 an p6fi 602iziz;5r gxof 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u'6x2gpi 5z n06iazf ;ir =    c

  The nearest star to Earth is Proxima Centaurian v -6+pqt *ocaq7mcer6us(c;(wlm:, 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 fariuohtc,d,4.kbwef9 c2rc 6.ster than about 0.1c is called relativistic - i.e b2eic..,wd6 otc9krfruhc,4., for 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 speed w rhjj-/y3* o-v erz7tzd;zh9 $v$ 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 wouldk+ h(fo uxz3f.8tzf( opm*3qj have to be totally destroyed to run a 100-W lightbulb for 1 yptmkhzo8uoj.3x(q3 f +( ff *zear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an elecvz262eru.c;ntr;yh+zh/ f4 lnjv-q:hx wc 1o tron and a positron together? A positron is a par 4: j zq.xch+ rowzcn;lynre2 -uvv2h6hft 1;/ticle 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 6,m gsffypdv-d:o 0mat5n76 l of light collides head on with a positive muon traveling at 50% ttvsnd:lad5 y07 ,-m66pmfgf ohe 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 eledhw f- 7vn.p/sctron, 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. Deter7/nvhp-wsf d.mine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a g 6w,pj ym6ja3yv(;rvrate 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 3gma+2 iev,wpllbp/ 3have 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 nucleus into(ma, l/-hj fbwqpz65 p its constituents, two protons and 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. (-l(bapm wqp/,zj5hf6This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage inckken 8rhe*cms;euk:6 q09io co3 / rz)rease in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binok36h)kcnkqueoz9/e*8: ci s ore;0mrmial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the mcf y;qv6o a fgv:/u)a a5fk. j1c3l8elaboratory, are moving toward eag8 cfv ;6)yc31eafa5a.:fm/ jlk vuoqch 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 that a particle w)1 po)p uwh3gvq7.b siith momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter and a8l zcrgd:o u:)ntimatter, achieving complete conversion of mass into energy. If the mass of thzo u:rgc)8d l:e 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 energy is greater than its res p:/xu.zewy7 tt mass z 7pt: /uy.wxe$m_0c^2$ 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 29kpo a p3k*v;hz7 l*pibbh 1n15.0-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 shorter to him thkvp9pp713zo;n*lh a*b2 kb ihan 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole ofk)ek0 kriyqdhs)1u(* oxygen react to form two moles of water, the energy released is 484 kJ. How muqr*yk 1ks)e0dh ) (uikch 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 created, travx27yzoez81 *pr n o.t(d tlzq)eling in opposite directions. If n 8(1qo2tzdx)* e7ypt. olzzrthe speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship travdjo3m+ cr*x a0eling at 0.75c relative to Earth measures his ship to be 25 m long. On jx 0om a+rdc*3the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. You sea1+(oky,z 3w ri) ofhvnd a laser beam toward the owf (vzri) ,hk1y3o+aEarth 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 mass of 150,000 kg.dca f:c/ gj63l3 vw 8q*u2esfa The occupants woul*3e qdw3c ff 6aac28vs :/ljugd like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to 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 p- 7ae2 gy.td+(w3nq 7z6z eey:jl pejleft Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare wi( jzppw73ealy en-gq7dt.+e26:y ez jth 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 ( vgqi-u ks18hthe 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 b(hk-1vsi8gu qe 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 ab- /vbz9fb( ,pdf g6rof a spring whose spring stiffness constant isgbrb(bzva 9 ,/6fpd-f $k=48.7 \, \text{N/m}$. 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 mass (r;v1*hdfizd $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.