You are in a windowl/4 jbf;k8n vsyqbxr)r l.8d/iess car in an exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine irxy/)bd8 vs 4kj/;.l qnr bf8whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red l.km)i)qzp o.q ight when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the bzk qq.pm.o i))rake 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 siq27.g1 kkjz heavy ball straight up (from hisj 17.kzgqk 2is point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around thg+y l otk37x/de Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no beslt/k+7y3o dg xt reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at wh9,-b9nnck4upa k 6dbsaan8f ; xxh akei;3q:(at speed would ah ak8b4i ku:x9(; nk93xpqfdabn;a,ns-6e c the starlight pass you?

The time dilation effect is sometimes e 8rxpy+4+6qh3e j 3vzmlu ot)pxpressed as “moving clocks run slowly.” Actually, this effect has noteu o )t3zvpm4 6 +j3ph+y8xlrqhing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean thpg c(l9m2g7t4fbq;i pat time actually passes more slowly in moving reference framb974i2flq (ppmgct ;ges or that it only seems to pass more slowly?

A young-looking woman astronaut has 62dd-h x sl pqaec;+h4just arrived home from a long trip. She rushes up to an old grayadc+4 s;d62hlp- eqxh-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notic9 v(leef5p39 kseykdx p5+ t9lbdg1 r2e a change in your heartbeat? Would your mass, height, or waistline1v9lldxkb +td erpke2p993ys 5g( e5f change? What would observers on Earth using telescopes say about you?

Do time dilation and len;gqucz )iwk duq/8p *1gth contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light we kur;s3b39tgu )w59ob ifz ho/re infinite. What would happen to the relativistic predictios/ 5 gfo9khu9w;3o btru bzi3)ns of length contraction and time dilation?

Discuss how our everyday lives would b + ksptv.:3+scuusqe( e different if the speed of light were onl.s3 ptc +(e:v kssuu+qy $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might bn)u,-4v2tfjcheih x*e used to indicate that c is the limiting speed in t uichjx,-nt* h2e)vf4he universe.

The drawing at the start of this Chapter shows the street as x0vvg maz-r jm.gm)44seen by Mr Tompkins,gvr4jgvzm-ma)m 04. x for whom the speed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Does this put ay+5oy fm qlsz8.u d dovp)47rw, 0c*wxn upper limit on the momentum of an electron? If so, what is this upper limit? If not78+clmvo oy5dw *w)rpfuqz., 4d 0 xys, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speedkfs(2f pi+fbn 1ni3 c2v (3wuu 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 nq. g2pzwa7f-s5mzl(that a spring has more mass when compresse7m (s p 2la.f5qnz-zwgd than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor de)znq 0l7fnv 5q ie4+ e0wlok6lstroyed." What nfl eq5)z 0l7ek4l wvo60iq+nmust we say instead?

  Is our intuitive notion that velocities simply add, as we did in Sectionrqkflent50/6*vdqfa/f5 / gx 3–8, completely wro/5r akefnvgd q l0fx/6qt/f5*ng? ----待选择----yesno 

  A spaceship passes you at a speed u3s y0n )taiz 7luf z;q+qs92zof 0.750c. You measure its length to be 28.2 m. How long would it be when at sizq; 2y+ zs z0fu7unlqa)93t rest? $L_0$ =    m

  A certain type of elem0u7xvae e3toax y:1 2gentary particle travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals depend on thexp m/g e op js5r+p 2j2bqng7efhh/41ree7k-; 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 a4 0f.qaaty8mgh4f*k,xl v .+ k gm/yls ref,;v 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:7r znw p(rtg/4e w6f,6sat0 p;ymo; wtdhmj6 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 frame, a vq-,be 8h9osn2 vu3e fstar is 82 light-years away. How fast would you have to travel so that to yo2qn-e 3vefso89v u b,hu the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 8v1 o31s; j(p5thvxgfl5 light-years away at a speed that tells you the distance is only 25 light-years. H(ogfv; tx35hsp1l jv1ow 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 is q:uf9td53 x,lk ++bjf :cogti $11.2 \times 10^3 \, \text{m/s}$. 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 a 5 nxt igypmx+ 92,-:rwzgk2be6-year voxxgeyr gi,nw:bpm 6229zk-+t yage 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 it take a spack mbcs,t+r2c7 a0h x-xecraft traveling 0.960c to reach that star from Earth, asa+b xh m kt0xrc,-27cs 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" s3:/v dn9q vsypwumq4o 4ed1*zpacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. q ndp/m3yu 4 w:vse*o1dq4 v9z
(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 15nq:b:ya3 j b-m m before it decays? The average lifetime, at b:q y3m:j-nbarest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum oopj+v:w2 ig6 jf a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an obj a7ot urcrm0 3+ t,s)at*vbwf1ect’s relativistic mass be twice its rest mass? v =    c

  A particle of rest mdp(dj ipr0 )ofbdmq43 ;flk8/ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels atqsj 4nx)37vgc7tir/d $v =0.10c$. 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 protc+ u ndfh 7ay91m4h3dzh;v.yo on that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction require.zf8x l:z wbcejen*5lss*w 6, k9l.r48parwx 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 apart in the procesi gg og r+a5(0n0xj9ess known as fission in a nuclear reactor, the resulting fragments have a 0ige0a+ jrn( gxgo95stotal 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 (mhi jcdw;++7.ray :5 x) qwwe5ckjgh 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 mauofm aq)2/eey(.0 p abss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption i sx/,b)q-adaj w0ep5)bdp,7 c*ey ddvn 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 ofo2 jlwg(5(vybjj: n* i 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 particle4hk6iwz; :zqs when its kinetic energy equals its rest energy? v6khqw: 4 ziz;s =    c

  At what speed will an objectvp irkkc663wp+*- gcg 's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is requswqoys j0pl(3: )az,5 aq7pyaired to accelerate a proton from rest up to a speed of 0.997c? ayqyl, q5wjp(70azs) :oa 3ps W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a pryz/(hj)ii h l.oton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetic energy is 750 8f w(/9x j6-k(fwwn afvnav:eMeV)?ew( 9/6-xkawffv n8jf:(a v wn    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a protfsn 8id) 1c.uqon accelerated by a potential difference of 105 MV? v =cf.sui)1q nd 8    c

  What is the speed of an electron whose kinetic energy is 1.00nze5kc r.zu 86d1o ,re MeV? v =    c

  What is the speed of an electron just before it hits a tek(p n8r.54sbtucn7 du s(/g qclevision screen after being accelerated from rest by 4 nc uubt(sp/nc7sgq8d5r k(.the 25,000 V of the picture tube? v =    c

Two identical particles of rest mncpcppcr(w :42 x8cn+ass $m_0$ 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 proqxa0a-rug *w4 ton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 :s h57l4)wh2b9mjuwiefzh)q + z+vx uan 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 acceleratedh3 c-c4h;t--rxo7x hb ccw7kc 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 momentum of amqve p y6ue*x6 kf.d07 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, mi*3b;t ee(m g$^{241}\text{Am}$, 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 vd y 7r,4cp ffrzvot::2ersus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest mass.7:rczd2fpyro t :,v 4f

  What magnetic field intensity is neede9yqcg( i5iwr/s,* c aud to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)?i9(ga siqy/cr, 5u*wc 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)lunkx/pk)x i6cmg9 f e2:g*a; 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:n ec9akg lmf*g pux6x)k2i;/ Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a syg;uxpt 2fx1lo 7 st(lf 7 esn9i;+ny6peed of 0.50c with respec6l ig (+2 ouet;;xs7lpyf91yxsn f7ntt 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 spaceship leis80j c fh6jj0aves the first at a speed of 0.87c with respect to the first. Calculate the speed j0ji jsh6cf08 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 h8kn8il6.mg tvessel approach at a speed of 0.60c. The Enterprise comes to the re8i6k8t nl mhg.scue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress )f5bz c h33k.fxbb db9sends out two escape pods in opposite directions. One travels at a specxhbf3)bz b k9b3.f 5ded $v_1 =-0.60c$ 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. Accm+olankd1-h./ 4)u m;wqc ut the same time, rocket B passes Earth/ udc.-ma4c 1n+omuclw kq;h ) moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-ll*wh/c1k.m 36+p3d o h knviiyears 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 about xf o,aee3 .;bzxt d:9p0.1c is called relativistic - i.e., for which the correction using special rel,: edpzt .x39oefbx ;aativity 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 i9x3:1 klp.vckgb0;/ yne,mtfy7p yj$v$ 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 mawo7m /l3 nec qsbm.0*utter would have to be totally destroyed to run a 100-W lightbulb/s.bloe m*c0 uw7nm 3q for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to pgbqy.-s/peb np,dlfxq )s69 )roduce 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 conse6f,-yx. bp q/) qp)eb9lsdgns rved 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 on with a lmd5ewfi c.q0/5f: uepositive muon traveling at 50% the speed of light. The tw/:fde5euwi fcl q 0.5mo 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 electron, and a neutri w l r5jwlnds 4ow8k)k73dp3;eno. 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 pa w8pd owj53w lks3)den4 7krl;rticles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate oz7-tvf.iucx- zz,p*/vhir* o f about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a negativem3psk .h+v sx4bn5zh2m9 z;o d 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 its constitul y1 +o-vnvu,uents, 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 differenu on u+-vl1,vyce is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass wqa (tlqg:b5 0 doyr ls1);q*bof a car traveling 110 km/h as compared to at rest? [lwbs:1r qd(g0ya ql5)q t ;*obHint: 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 th /2m4xfup/wr 0zoa+ mje laboratory, are moving toward each other.x/ um0a4zo2r/wjmf+p 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 with momentum,g sd*di) + -tp)h)r a3lphpgf $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combinqsn9);djk4 pak ,/tv;y 0u wboing matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise i0 ak4y,; vk)q/s9ndt bjouw;ps 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 em3gs:m )05q9l(hm 9or 8x *wdpaotrlits kinetic energy is greater than its rest mas93:l8 wr 0hp) osdxlmgt*5mae9m r(qos $m_0c^2$ 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-long pole 5f1lr vp dwq*h :tt1c0into 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 bar:wt*d h5t 1qrf10p clvn 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 t. v z082z g md4xo*e1btzqmab-wo moles of water, the energy released is 484 kJ. Hom-dm0ta24e 8z*bgzzqo. b 1v xw 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 identicaztkc0 /pcvh*kk(3,htm ; n tpoo (-g;ol particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to thn,v -zthk0c k3ptcgmt(*p ;;o(h oo k/e laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth mx7s ) +w.ewtjmeasures his ship to be 25 m long. On the ship, he eats his lunch in 23 ws7.t)e x+mjwmin.
(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,: u2 ayx* fqf)+yecom. You send a laser beam toward the Earth mef, ya+f*2yoq): xu ctraveling 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 hav8y,a0 (l5lr2dp0v bso1uqi jhe a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-ds0bo021lqljva, p ( hui85yryears 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 left Earth at a speed of 0.99c. What is the (3 4g3ctq m97yu: erxo 9bozrl5kll:jspaceship's kinetic energy? Compare q:35: zot9l cry7l ( r 9lbumgek43jxowith 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 frlt(:kk)r k:xetpkf 0 r qtz9)/om Earth. Passengers on the shi:)lrf/):9t0 tp( rkkezq kxktp 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 axpjk)q se;-v - spring whose spring stiffness constant is;vp)sqej- k- x $k=48.7 \, \text{N/m}$. 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 m77j4zaga5 etw 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.