You are in a windowless car in an exceptionally smooth train moving at constant 6.(jpym2sm q ex:.x1o c taryv;a7zl3velocity. Is there any physical experiment you can do in the train car to determine whether you are movxc1axz.y.6(2yreo7smj m :l tp;q a3ving? Explain. ----待选择----yesno 

You might have had the experience d 7prn+y zmb+5of 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 brake pedal, thinking that you are rolling backwa ybd++75 pmnrzrd. What does this say about absolute and relative motion?

A worker stands on top of ao(8mcq f d.q7d moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behind it(qfo8md. 7 qdc?

Does the Earth really go around the Sun? Or is it also valid to s,ufq,jv w xc40xz/ k.lay that the Sun goes around the Earth? Discuss in view of the first principle of r0,xqj u4l fw/v xkzc,.elativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a sta(x .ejgno c.8idtt6mdlu e(0(r, at what speed would the starlight pass you?e(tjig. l c(du.o6ndemxt80 (

The time dilation effect is sometimes expressed 73 y6/s pxurf4pl1a zlas “moving clocks run slowly.” Actually, this effect has nothing to do with motionz/1paf6s3lp7 yxu4 rl affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in movxybc;l4+tz gb 8: u7wuing reference frames or ;w+u7x4zbyb u8l cg:tthat it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trq*promp2,f- *kl.zpb v e+jk,ip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How r2koq+,m b *ezl,kp-*. fpp jvmight this be possible?

If you were traveling away from Earth at speed 0 p,.mwypz (g0mmqxbla ,z f:09.5c, would you notice a change in your heartbeat? Wouldm lya :pb,zpw,mmzg .9 qx0f0( your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occutkcx 8wk :0h8cz: gy6dr at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. n9tr q*:y u5hkWhat would happen to the relativistic predictions of lengt y*:r knuth5q9h contraction and time dilation?

Discuss how our everyday lives would be di-eyzoop0: 7 kfe0c/8g jcwco3vnx:9qfferent if the speed of light were only -pcwojzcke0 :ox8ny q: 7vo0e g9c/3f$25 \, \text{m/s}$.

Explain how the length contractioso0 ho e5b/qj7n and time dilation formulas might be used to indicate that c is the lim7o h0 jsqo/b5eiting speed in the universe.

The drawing at the start of thi2i/cx9++4e2p pqe fd j.t kyoqd-ht( js Chapter shows the street as seen by Mr Tompkins, for whom the speed of lighd2 c+jq4h -yptefx i.teo2qjd9/( kp+t 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 travelo wqy92y v9f*u at speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? If notuof w*29vq9yy, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speju(- ltioh j, edbsh99x)lg-,f)rr5 yed 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 tha74ctxo jzq21: y;gl du(x;(qa r s af-ij8v+vet a spring has more mass when compartxq(-;efdv qg7 +l(u81 y:j 4z2c;sioxvjaressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor destroyed.v )9vrfn t*f+ycmz1* y ws kuws.9al*0" What must wstvvu0zkflw *s.1rmy )n*9f* y9 wac+e say instead?

  Is our intuitive notion that velocities simply add, as we did in Sed)0p8am+vxrnjfxr u5 0:z+bm ction 3–8, completely wrond+5:f80m br umar)+ jvx0zp xng? ----待选择----yesno 

  A spaceship passes you at a sperv *wkp2ba/o/ ;1y sgmed of 0.750c. You measure its length to be 28.2 m. How long woup r*/ vkm;oa2wy b1g/sld it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels am5h p 3wn)u/jmo,p(shud6aw(kwm(: o t 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 o(qf5cd1v8b a bn 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 lighttrnn z)lcg op,8,a b-8qpjzt3:x sc4) -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 mxsbs r z.284j*q/ahqieasured 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 fr dh .hb1d9evv2ame, a star is 82 light-years away. How fast would you have to 1he bdvd2 .hv9travel 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 away at a speed w5 ddfd;c/eu u2pcs,h 7j 34iothat tells you the dist 4hcds juwocp2d75i/;e 3,udfance 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 i o9pad cp:mqquwy r*qn84ps. /28+ ofgs $11.2 \times 10^3 \, \text{m/s}$. 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 from -8/i+pduti:rca tfy12p e ldrbgd3 63;wcbc4a 5-year voyage while t i2gbfrl33:ytbp;dc p1-+ catd4/iwudr c6 8 eraveling 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 0 d5jo-)n 9inpu- akrwwould it take a spacecraft traveling 0.960c to reach that star fromu k-0w-5nnapij)r od 9 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 "Ferrari" spacecraft at a speed of 0.660c. It is b y./w j2 9 b7ol9gmbv)sy6pldmeasured dybo b 6pb9sy 2wm )/97lljvg.in your frame 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 average pion be moving to travel 15 m before it decays? a7jm;:jsh ik ;)ck1kn The average l ka:i;c 7kknjs)m;hj1ifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a nx/d) q .zddjq 8 /zwy.c);tyxproton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its 7:x4q rddvmm h0uyh3/rest mass? v =    c

  A particle of rest masvp 1(cfqph69pc 77ot xs $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels . cpxdiys2b.r +j)zc7r w+gt9at $v =0.10c$. 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 bds6oa65 cwzvtm i,7 5momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiressh3l,e tr8s n9xq4ka ne+s +v( $4.82 \times 10^4 \, \text{J}$ 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 a+)o) lqqqo60 t ze)idvt rest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of abz +qi0o)v))6oeldqqt out 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron inza+ztxc1;4 t n 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 a pr8ihrh(sq :e 9qoton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in thv)9rw)lzqh* 3 z k js+sa.pr1me 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.dxuue2mh 9 b,78b mzm pvd/u700 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetic 7gb + agpxp l4 tdde,wd:cfkzc8.w+- /energy equals its rest energy? :w e4b +a+7/xgd.cfc,g- td8p dwlz pkv =    c

  At what speed will an object's kinetic energy be yas80ccjv ;v iz(;ejq s4,*z y25% of its rest energy? v =    c

  (a) How much work is rec k .bt9o*ns.v;n +aysquired to accelerate a proton from rest up to a speed of 0.997c? sv9* con; ybk.t .asn+ W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic ewo6 v:pf9sejwly fv2-5 qt4b0nergy and momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that p0 p6cg 0*-tsen6hynu is, its kinetic energy is 750 MeV)6-u c *tpng0eyp0sh6n?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 10zbnvar(ow r hbpf+ka +.kf5 x44:,du/5 MV? v.,a4(df k r: xbw5k+a4h/npvobfur +z =    c

  What is the speed of an elect. sr94odblx l,ron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of m*uhe rf ddfw2:7f)dh2l 8kj( an electron just before it hits a television screen after being accelerated from rest by the lr7 2:82mf*fdhf hjd()kwde u 25,000 V of the picture tube? v =    c

Two identical particles of rest 0(xr3f8d1 kibor 7ukxmass $m_0$ 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 cqfwiuh ,fpd-zq8 4t x 2wf7)*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 the9e,rd : twsi7n 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.j* tk m2cm,fot(g6p i: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 momentum of a proton)dkayavh4to y+ / 7g0g ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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, q t8oh6azn ;qd/egg1( $^{241}\text{Am}$, decays to a neptunium nucleus, $^{237}\text{Np}$, by emitting an alpha particle of mass 4.00260 u and kinetic energy 5.5 MeV. Estimate the mass of the neptunium nucleus, ignoring its recoil, given that the americium mass is 241.05682 u. $m_{Np}$ =    u

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

Make a graph of the kinetic energy versus momentum for (a) a particle of noj/q-f+ mw xik:hx; a-rnzero rest mass, and (b) a mkw r/ja x +-x;qih-:fparticle with zero rest mass.

  What magnetic field intensity is needed to ke;-1 kzm cwtru,ep 998-GeV protons revolving in a circle of radiw1zmrt u; ck-,us 1.0 km (at, 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 Earthq-w wzn:j:bvm528n it) observes a meteor come from behind awiw qm5 v-2 :j:tbn8znnd pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directiotr;- q *wz90xxv09 p 8zikpnmons, each with a speed of 0.50c with respect to Earp;v*x-9wim9zk0r0 x8zqt on pth.
(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 spaceship leaves i fqyod+d -zk7lle 88yh (j-6xthe first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it i- oydej88i( lky-zl6fhxd7 +qs 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 vesshq 0/ar3e g3lxel approach 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 relatqh0 g xl3/r3aeive speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in oppo 3l 2mpxavr:r,.wqbe mpox, 1n6p5j;zsite directions. One travels at a spxe.6j,mp2; aopz b1n: x,v3rrqmwlp5 eed $v_1 =-0.60c$ 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 passessty(a ne8l)q9k5+fvu Earth moving 0.95c relative to Earth in u5)ve8ans yf +9lqtk( the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is f l )xkdc+cm/,rs;:uhProxima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faster than jgt:*b4jl7ah:k / tqy about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significah b /j4j::t klt*qyg7ant 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 spee3w2 timin4l .nd $v$ 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 woqmgt* bg /w9p*qls t1:uld have to be totally destroyed to run a 100-W lightbul*9gb*qtsqw:l tp1m/gb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount ssr hy.8u2+oqx qhb 3+of electromagnetic energy is needed to produce an electron and a positron togr2 xb+hsuo8s .y+qq h3ether? 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 =    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 collides head oy ze3c.o7qeljnx4t1 :n with a positive muon traveling at 50% the speed of light. The 7jyl43xoqc eet1n: z.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 electrg2- hqep x *kl9 abt5f0zxcje g h3t)-gel/3g:on, 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. b3he0 eg la-xz5l xet:/gj3*k2-f )pghg9q c tDetermine 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 abwj3-7 h8l3m cd ifzanp z6fq+6out $4 \times 10^{26} \, \text{W}$.
(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 an;7j/4t) cejazhj auyi* ynn.)d 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 its con )n: agi9k8cil oa5j/zf5 3cnbstituents, 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. (This energy difference is called the total binding eneng5 :3alc9a c 5fi8ikb j)/zonrgy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mash jz-;hzx-go+t ojqv i. ;3sf7lf/)lcs of a car traveling 110 km/h as compared to at res j /h zg3+c)s7lf-h ; ivtojfzxl.;oq-t? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having aay+03 faljws9 . kafz) speed of 0.935c in the laboratory, are moving toward each other. Determine 9) f az. 3+0kyfaswlja
(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 particle0qkvtz;t3; yp with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining mattthwe uod*u -z)8mqrle f,nb:-3fkgad7-: ) s yer and antimatter, achieving complete conversion of mass into energy. If themwe-r8: -ouh 3lt*ds:y7qezu -f f abnk,))gd mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energy is gfmhr7- /a4m/s)qimvm u4i6imuf9c r0reater than its rest mauii) / sfm6rmmmi44v /q07 -9ufhcmrass $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-f 9ynvbkz4)6(ad: kga )4a,htjz c9ndlong pole into a 12.0-m-long barn if he runs fast enough (carrying the pozbv:)ah9 cdf ya 4an6j( z)dtk, g94knle). 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 mc: db1t5uqs2 7ps/av/vk lf x,sa5d2 vole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elementb//2kv x, 7qsdplcs1a2d5: vv5u tfsas 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, traveling in op m7the5,v/2g-f(nn a8 bnnhrmposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what m7e/fvtnnn8g mhan,r h-2b5(is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measureo/cd2*akiu t6 s his ship to btiou 2/dc a6k*e 25 m long. On the ship, he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Eart9s)g7m)qv8 zcq p e:3hai t)7l/bybmv h. You send a laser beam)7 98v t)h qcmgzbv/:7qim3ely pb) sa toward 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 mass of 150,0q (5q 7p ,9ckr-g7rjorpetle, 00 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.g 9te-lpr,7 kqj7o qcr5,( rpe60c. 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 lefpbup 4fi5 s9u/t Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy cibpf/ s9 54puuonsumption (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 lin4d73b gqybv, 29ymp0qep .nlght-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How muc4by g7ypvb3l29,0qq n .md pneh 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 +zjo3 a a,ate(a spring whose spring stiffness constant is a (j3+,zatoae$k=48.7 \, \text{N/m}$. 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 masxwsa2 u0.d nt4s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.