You are in a windowless car in an exceptionally smooth trainwm m3nl/6 7vri moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are moving? Explain.vn7mml 6/w3ri ----待选择----yesno 

You might have had the experience of being at ae(t8n.vz81as vi vw1j8 7t rpn red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thin8izw7vtp vv8aen j8n1(s r.1tking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on tstam8vv3k5e8 h r *ke5op of a moving railroad car, and throws a heavy ball straight up (from his point ohkav35kmr5se v e8t8*f view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it alsotb)+em9joo pztq3(uq -m lz8* valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that therq o e9jtzmolt3qzm )(p-*ub8+e is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c awyx:s7;k9 o vdburk8, iay from a star, at what speed would the starlight pass you?bd y9s rv7,xkoi: ;8uk

The time dilation effectrtr5qh mq 7 .g, *kr8y mmb-1,e(mtgkt is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with mh(5r,b7m8 myg.m rtk,rqk1t *- tqge motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in movinf*ex5k) dp1rz:fwb+ s r*4s9je ihsj7g reference framesw7+*f *4xj es1prb hrsk) d9s:j5 ezif or that it only seems to pass more slowly?

A young-looking woman astronaut has just ar: 8x4k 7h*p:mhspvqoc rived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversatio h:h pv48pk cxq*7:somn refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, woyz8;w7lud1ym lbr b;(g2n +oh uld you notice a change in your heartbeat? Would your mass, height, or waistline change? W2(z r+g lydu omn7w y1hb8;lb;hat would observers on Earth using telescopes say about you?

Do time dilation and lengt oprn4 .nma;p1h contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the relatiqcltwu+unt6(:6 hzv 3q g;ir0vistic predictions of length+ 6v zru3h:w qt(n60tqgul c;i contraction and time dilation?

Discuss how our everef/g15ko4gne( s rfm 5yday lives would be different if the speed of light were only(4nrg5e/1 k gs5oe ffm $25 \, \text{m/s}$.

Explain how the length contraction andz.w v,y d1ry.b time dilation formulas might be used to indicate that c is the limiting speed in tvb z1,.dyw. yrhe universe.

The drawing at the start of:xq-x vi/4 xsm this Chapter shows the street as seen by Mr Tompkins, for whom the speed of-sqx 4/m: xvxi 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 thanjidi(b,) fxyf- aa t:*fqd i9:l-pu j, c. Does this put an upper limi:i)tfyb(a,q ,iaf jj*fu9 pd l-xi -:dt on the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the 3jju jf xe (;tq.ir8vvp+5c. jspeed 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 massga58 x7 (m r6)wg ,a:n+j rakxudy*euy when compress7 xd(u x,m gygn*5y:eaaw ua86rj)kr+ed than when relaxed? ----待选择----yesno 

It is not correct to i7ykm56f 5 (zgxesw5usay that "matter can neither be created nor destroyed." What mx(egwmzf 5s 6yu k5i75ust we say instead?

  Is our intuitive notion that velocities simply add, as we did inom8db ,aesqozmjr 9y (a;1h /+ Section 3–8, complet,+mz/ j aaq ;9 y1m8drooehb(sely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measurif3xkm,:2 a/un6 gsuo5dog f *e its length to be 28.2 m. How long would it be when at rest?,f3nm/d6:fugxi 25sokau*o g $L_0$ =    m

  A certain type of elementary p ( e86nd-n rb)xf -eft j9pnr -/nw55elme)xrearticle 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 interv+ri uul, 9xceeu(6mu)als 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 a spemtp+z)*6deg m ed 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 agpy/ ftw t4 w;+c2kcz3verage lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference fra op9 rt)0kaqif+;8v erme, a star is 82 light-years away. How fast would you have to travel so that to y;f08tvre+a 9 qrkipo)ou the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at ab8dvr- ws om 07 9fxm*vlb7t7h9fmgt2 speed that tells you the distvd 0* gm-rwh7 t 79bmsf92bt8xmolfv7ance 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 Earth i8 h ui 8o3hdzyicos,4 2y0*bbqs $11.2 \times 10^3 \, \text{m/s}$. 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 r.t/ np/,sng8u otmmja :j7o;a*va y7starship Enterprise had just returned from a 5-year voyage while traveling at 0.g7 7v*ay/uso,ma mjonjrp ;:tt .a/8n84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it tak/)l )pfzmch-(e l*ogje a spacecraft traveling 0.960c to reach that star from Earth, as meash) oplge*c)f(/lzj- mured 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" spacecraft at a speed of 0.660c. It i .m.umc;sgcq+ /ua:ras measured in your ua/. q.;c+mrcm u :sgaframe to be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an averaskzk8 2vsk l 5*r5 eh/97:qt c(unxlyvge pion be moving to travel 15 m before it decays? The averq vskt8(*:nuvsxe9ycl kr7zk2 5l5 h/ age lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a prf5 +4hbxs *ruuoton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass bwm8 80 sre s e;kuhvy e057b8lj6p+sxce twice its rest mass? v =    c

  A particle of rest masstzarq.: pg als(yr7j6j2 u12v $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle traveqt (,r( +hiweqzrl.6w*u+m.bqy3o gc ls 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 a-)bmu9cqe b8v ccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi+i,+ k7sl vdqxres $4.82 \times 10^4 \, \text{J}$ 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 breake;4cbb3hep x .vu -re99bems5s:zbt. s apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in 35z..ebv9xebb4mpuc9 e:r-b st es; hthe process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules an.a3* f)ydap-x d8s ytod in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a prafd+s p)6q1kb oton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States i+jhigp0das m4 y :1zm/gmqz*6 s 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 a 4g-1jv q rcxrhpq41/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 wheogbt;;b m.k))xs q .lwn its kinetic energy equals its rest energy? v =)ts.okb q )bw;.;lmxg    c

  At what speed will an object's kinetic energy be j2/w0ov y-v51pyutqq 25% of its rest energy? v =    c

  (a) How much work is required to accelerate as+i*tii./ztohpjs:i h2k* kn4d ex* 8 proton from rest up to a speed of 0.997c? p*:s/ 4*k.t 2+iis* jni eozxhh8kti dW =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum)klr/c 7/b1bau4a msw 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, itsj2jt +wred25c fezgos3 2 xk44;(mpzj kinetic energy is 750 MeVe( 2jwkjd fc2 5p x;4eszrg4 o+z3m2tj)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential differenc+f*rsd di m,:w xvkg3:e of 105 MV? v xf+gk rw:d:smi v3, d*=    c

  What is the speed of an electron whose kinetic energy is 1.00+9 /t jumnqq rt83r1wy MeV? v =    c

  What is the speed of an electron just before it p5 4xea tsi62rhits a television screen after being accelerated from rest by the 25,s er2i64atp5 x000 V of the picture tube? v =    c

Two identical particleaa + jvoyo2f sx06v7+uvvp5*ss 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 proton p0; q;ej1xsng /elog0 ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed anb 1ad0r:w ex*z lx*(nld 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 2wh5q jyrkb-: 3vj*-jbgw p96x7,000 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 energy anms56zcycw)5mi/ g z-ld 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 nucleuzu)9z+ +2ayxiopdxc3dk u )8b s, $^{241}\text{Am}$, 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 zs u- ;ybhvz;5z;ab6l (a) a particle of nonzero rest mass, and (b) a particle with z z6azsyul -;b; 5vhb;zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV proton uq/ c k*v4z.fai w7xk::sa(xzs revolving in a circle of radius 1.0 km (atkkvc*z 4:aw:az s/q(7i.xf x u, say, the Fermilab 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 Earth) ob0 lph:;2f20uq45d agbe h kydv dg*;giserves a meteor come from behind and pass her at a speed she measure2vh *a;0gup ddy 4 ;5gq:lh2k0 fibdegs as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave h yn85q4egta)pnj4 ki+pgy .5Earth in opposite directions, each with a speed of 0.50c with respecy 4tygan qki8p).55g ehn+4pjt 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 t9hn qehm:(ao3rdt1 e 0raveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with d103to9e:e hr( haqnm respect 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 0.608zfdu * xrx3(9ct6dgm,a svw 0c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directlysav ,xdt6 30x*z(89du frm wgc 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 distresyd.n8 xwa0bj*s sends out two escape pods in opposite directions. One trxy.d ajn*0 b8wavels at 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. At the s,peln 0v o uiw7drzthx--7()s(pvsi/ame time, rocket B passes Earth moving 0.95c relative to Earth in the sp-ox/iv )ws- p(l0h ( v,nd7izsuer7tame direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centaur( d r7a)eheza6i, 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 fasy 6 hx8m80yml9sbcgb 2ter than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the s2bs hgby 9l80cm6xm8ypeed 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 shpjg ctnb-z 70nv,236m;e jq$v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter would have to be totally destroyed to run a 100-W- nq)n*sx v/or lightbulb for oqnr/ nv-x )s*1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromav4t(1s7zjxew f 9dja 6gnetic 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 charge is conserves1 jdv6x74eat(jfz w 9d in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collr,+rk l8+ mso,jwx/srides head on with a positive muon traveling at 50% the speed of light. The two muons (each of r+j,oxrmks+l, /s w8rrest 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, an z0u p ;rgrl,pwhs,(msjzw):2d a neutrino. Assume the neutrino's rest mass is zero, and the oth zsuw0,mp:pj);(2hs,wgrz lrer 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. KE =    MeV

  The Sun radiates energy at a rate of ah 2b2pl 1cw)e(t+nmakbout $4 \times 10^{26} \, \text{W}$.
(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 charg +yi*oo cz,fp 4us43ybe 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 nu m f53fl9re:(tgi )(fjpv;lba p *eyk;6ahj *vcleus into 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, andpk;69*5bt m: ;j3avv*(yg r ehl)fiflafe p(j 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 carypbib85jh e (- traveling 110 km/h as compared to at rest? [Hint: use the binomib hpb (iey-85jal expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935cy,j) bkt;d vkqw8 2hh4 in the laboratory, are moving toward each other. Determinv ),djhbt hykw24q;8ke
(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 mo o6 /:ozwzh7xrmentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its powenrr, 0vg 6yrihwyd6 vb,mx849r by combining matter and antimatter, achieving complete conversion of mass into energy. If the m0grw vrr6i 6,n48 dmvhxyb9y,ass 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 energy is greater than its rex tlkm3 osd qs6180l, hnso22vst masslm 3sd x6v01 olhk, 8ts22oqsn $m_0c^2$ 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 belieh0d3rraa q 07gves that he can fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the po 7ard0q0gr 3ahle). 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 than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form x97c 5 nnrpvn7hh- qb 1wt.d9stwo moles of water, the energy released ixdhq5t9 71 9 np w.rv7-bnsnhcs 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 par* tgyo*4-5 ercv .qehsticles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to e4 oce *y.tv*hs-g5 rqthe laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a sp-p0d.ozs,pdw*pzy o l f tt,,xcn+s*)aceship traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship,,,p,zd .0ysocs d f)pn zot -t+w**xpl 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. cx91. b 2mylrpYou send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on lr. xy9bpmc 21the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The oc1lngb pkodec30 3z.(p cupants would like to travel to a star that is 25 light-years aw g o0d1 (nkpe3zlpcb3.ay 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 sp; ydy6-hur fe vjr)7 zc2k,9cvaceship left Earth at a speed of 0.99c. What is the spaceship's kvy e2 cv9,c-dfhr6u7y) k;zjrinetic 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 trav p+t8 qk+y2-bc gmtf,qel to the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no+q2bfckg - ,tmp +q8yt 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 a spring whose sprivgnmc o:u,xpcqe u4mr2,6. m0ng stiffness constant imemogucp :6,4v0cq .,rmn2 xus $k=48.7 \, \text{N/m}$. 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 mzv4 sfhq)w 1*bzsnm8jz/ty8c6 pr7 h* 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.