You are in a windowless car in an exceptionally smooth traxi1ri s;h h:yf*iv -f9in moving at constant velocity. Is there any physical experiment you can dix ry ih v;9f-s*1hf:io in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red a-,dqfkqy ya+s ba5 5+ujb6b, 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 backward. Wb+,y j-kybqua+q d 6afs b5,5ahat does this say about absolute and relative motion?

A worker stands on top of a moving railroaw4wih * wbek50vh3*q jd car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, 35bhw*4ijv * wewq 0khwill the ball land on the car or behind it?

Does the Earth really go around the Sun? O- - hlb3oq3 skv*tt+frr is it also valid to say that the Sun goes around the Earth? Discussq vb-o h3-sk+*tft l3r in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5ceel 0nw(6vw7h;lz71*).iia btl dnbc away from a star, at what speed would the starlight pass you.(wia l0 wtldz;vinb1c7l6 e*hn7 e)b?

The time dilation effect is sometimes expressed as “moving clock q71ltbg 7l c+4pvni:is run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clp4cg+v nti1q :7l 7lbiocks. What then does it deal with?

Does time dilation mean thh6lwe 0*z s mwal.r5k(at time actually passes more slowly in moving reference frames or that kmwr6hs.(*al e 50lzw it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a agb8p p/5 hbg)long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to hibgapgbp 5 )h/8m as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a 95 6cgfwqz812bj kxkn sfy1l/ change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopesxkf1ly1wq/29j6b g5s8nk f c z say about you?

Do time dilation and length contraction occur at ordinary spe b4*qnuc60t 9zdavr2beds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. Whfy , r29s4 9dqoqog*maxcs*4 bat would happen to the relativistic predictions of length contraction and som**4o9fs9,ybrdx q4 g q2 actime dilation?

Discuss how our everyday lives would be different if the spe)fje9jky7)/xg r7a i ged of light were only 79f)j/k y)jgxigr ae7$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formuv4ajv;jfz lb 5d 82fc5las might be used to indic;jc 4jf z82lab55f vdvate that c is the limiting speed in the universe.

The drawing at the start of this Chapter ; de-7e qi)quegrtsj +ynrrb/ 9sx 4 mz39c.7zshows the street as seen by Mr Tompkins, for whom e rr4;zq7s dicy7esrq9tz/ -3xn).+jgm9 eubthe 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 an upper aba(94y i8 xcwu xy.0 :i(kf1mo9 fyjllimit on the momentum of an electron? If so, what is this upper limit? If no8yyki. l: ci( 9(04aw91bjy mox fxufat, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass kzjugg8a :s1 7 ymh+s(hb 6yv0attain 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 energ:w+iarfmn:d9 y, does this mean that a spring has more mass when comprr:+i:9nmad fwessed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter ca wpdq 7:hjxg:j,m8bx1n neither be created nor destroyed." What must we say insd,:jxp7gbmwj qx:18htead?

  Is our intuitive notion: p9bvzns)g* qb93rcw that velocities simply add, as we did in Section 3–8, completelyr:9ng wzb* q p)bv3c9s wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure itsr7o tz2obwb u 7s5 2w2hr3w;cp length to be 28.2 m. How long would it beo2b2775hw2r pru s;ob3tc wwz when at rest? $L_0$ =    m

  A certain type of elementaryh+)r/twb ggr - 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) g:xy72v qcki 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-yea3-fcj9w0a;t m8qz pt: cv vtmzs01b+urs 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 measured hitpgpx )s+;+pp 24; dpjhab3 *hcj.s 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 star2g9 f, ,5dw4sokdq ww)iodq5f is 82 light-years away. How fast would you have to travel so that to you the distance would be only 3o,fw o qdw5qsg9)2 ,kf diwd455 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed that tejk7i2wyf/ 8 tblls you the distance is only 25 light-years. How many years would it t/f27t8 bwkyi jake 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 Eartsn1 ghpd7;(g zh is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

  At what speed $v$ do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.) v =    c

  Suppose a news report stated that starship Enterprise had just returned 4mr+v ;q ak3fofrom a 5-year voyage while 3voka+m 4;rqftraveling 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 wg,; h3cd2 qinfsn 0*aiould it take a spacecraft traveling 0.960c to reach that star from Earth, as measure 3hia; d*n fcq,nisg02d 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 "Ferrar/ 1o hdpsq 1+:hhhbeww-w0f ,go ie-7pi" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m- 7wgoeohpp,h + 1 :b si-d/e0qhww1fh 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? x;82g()e vw1 o1v+6kfvv w0q8rndrpeifihr 7 The ave f0r(2h7xir68 1o+ v8i1wqkeven;p d)r wfgvv rage lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton t4wq;o6xoox9 j raveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relavlu*h1.bswjp .b njm)z /n,x3tivistic mass be twice its rest mass? v =    c

  A particle of rest m+4ajuyjm)ce- j1t*ksm y8j l/5 1jcxtass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelso r2faotb(n:7 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 inq9vk01)e/cg., wtq:gnk uc i9ycu: rs momentum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reacticn zv3skhwx j,*aj:2/on requires $4.82 \times 10^4 \, \text{J}$ 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 process known as fission i-luwu. ufodzbc0z8r o 2gnxb/-j c92-n a nuclear reactor, the rer2 n0fjlo9-w--zzcxbug8odc.bu/ u 2sulting 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 energy oa 3mmi+ b4* ebqjcu9;hf 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 6rixrl8bny :b30d hvg*ea-j: a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is abpu) pq4:jc oh6out $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion o8bgcy2miwf) l,)m8gh2 ii+v*qgx:3 lu gw/xcf 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 when its kinetic energy equals its rest energybi(3w(*b n n+ q5nvjgb? vwbi gnqn n+(3b5*(bjv =    c

  At what speed will an object's kinetic energy be 25% of its rest ener9tx3s-p/s-ajvlt- zz 71 jisi gy? v =    c

  (a) How much work is required to acce.mvhkx i5ga;eae; 8 ;zlerate a proton from rest up to a speed of 0.997c?imgxe;k;ah z 8v a5e.; 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 proton tracp93g d4oh/iy veling $2.60 \times 10^8 \, \text{m/s}$.
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,h0a)*pl3 gbu urd*i6 x its kinetic energy is 750 MeV)?d)* la6xgbipuu h3r*0    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105( n2i2jaqn 1rm MV? vmnja2q( r i12n =    c

  What is the speed of an electron whose kinetic,9 t)y/xcha;fd syc 8ya.*mp2zowgn4 +ctr 6v energy is 1.00 MeV? v =    c

  What is the speed of an electron just before i1koouzh p (q66t hits a television screen after being accelerated from rest by the o(p k66zuoq1h 25,000 V of the picture tube? v =    c

Two identical particle8k iy/ (5 pklq/rhf:g:nan f4is 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 (c 76lsg9 kqw.;wzw7y7gdlf, s $m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and/ cso8ygpn)osn ; 2lf5 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 27,000 kg is accelerwqp:)6wk *.m weh1zd nated 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 n m*b5/ug wgg :mfdld 0z5;ab7of 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 nucleusvx4t. et ,vr06fu1u ewtp(ks ), $^{241}\text{Am}$, 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 xecgt(w- p4 :mfor (a) a particle of nonzero rest mass, and (b) a particle with ( xcp-ge 4w:tmzero rest mass.

  What magnetic field intensity is needed to c1 g gaw..hg2bkeep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilah c w.1ggba2g.b 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 olikqpxb 6emtj zp0)9p*;g8 -to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with respec b9k;*8 6 jptp0peqzl gom-x)it to the Earth? u =    c

  Two spaceships leave Earth in opposite direct+m cj6uf s,4eekr0m9q53gj p dn0er;f ions, each with a speed of 0.50c with respect to Earth. fr g +5k90e;d4mpujmfrsn,e qce0j63
(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 secoe+ uy8-dt wj(wnd spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of th8j +eut-(dwwy e 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 vess)c*7hgado t), (c vnzzel approach at a speed of 0.60c. The Enterprise comes to the rdvg*c)nho, (a 7ztz)c escue (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 sends out two escape pods in opposite dp m rq4;v *-nch0z+)ouvup9pry3od :k3ml mm;irections. One travels at a speed r c3)l; * u :hd0ppm;4 o rm+pkoqmzy9umvn-3v$v_1 =-0.60c$ 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 . 9aovmwqvsn.3+ube1/y qkh*of 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? m bw*qqev.v9 ahou.k/3+1nsyu' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years .d 3c y,udqcwatei56+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 wv) it3vorh;. kpy *3f0.1c is called relativistic - i.e., for which the correction usiwf);vyh 3tr ikp3*.ovng 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 b /(jg,vvb:y/9uwxpz5r0phh $v$ 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+ 7-vd ax;f:1hpchphb-W lightbulb fodpcxavfbh7 hh;1+-p :r 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needea k g b7:lsqhg(xb00l(o +ewj-d 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. (Notek(aqh- eb lwl0:s( g0+g7jbx o 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 collidesv9lg)ote9vy ()mcyb 6bt uy.h2hx)(y head on with a positive muon traveling at 50% the speed of light. The two muons (ev (b9e)hy h bg)y) 6tyuylov9 x(mtc.2ach 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 ;:rvbi9 px u e)68cly *go,g3f2 pddrja neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kincu2begil*)3,9f rjpdd68:o r;vpxyg etic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of apl)o-x k xph45bout $4 \times 10^{26} \, \text{W}$.
(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 measf xjdry9zgwmn+ b 1r+t.7 49ueured to have a negative charge and a speed of $2.24 \times 10^8 \, \text{m/s}$. Its momentum is determined to be $1.07 \times 10^{-22} \, \text{kg·m/s}$. Identify the particle by finding its rest mass.
 ----待选择----electronpositron 

  How much energy would be lyrc-s54j . +q-se;rb1 ri bkyrequired to break a helium nucleus into its constituents- ljs bc;rsiey1 5rq- .br+4ky, 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 energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativistic) mass.x6 ;ik+ kssyt of a car traveling 110 km/h as compareds;sy6tk+ix. k to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are 0bpwl2rp5qzrld,p )i 868 d k+ l4qiokmoving toward each other. kwdp 0i q4268 bi+dp )olpq5,rz k8llrDetermine
(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 m r,vt,ysttxsd5 :0 0vdomentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combininyi)/hv/aw t4 ug matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approximatelw4hayvuti )//y $5 \times 10^9 \, \text{kg}$, 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 gryacp8rgz-t63m -.lozh j6*t c eater than its rest mazyo-6.h -jpczc6ral*m t t83g ss $m_0c^2$ 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,m3, ;0g8kqrpqfa q xi(lt*:b4klmvk -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(kkx8m4:t , api l3;qqr fm0qkgl,vb* barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen qvn en+xf2h22 and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the qx22vennf+h2 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 identi f.2zi2a *lnm 8ln-dnwcal particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the labora wf*dznla28. -l ninm2tory 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 measut 9vg7 bypb 5eldtc85;vk(5add* m c+tres his ship to be 25 m long. On the ship, he ea *ba ldp v5dgcv9;tye5m 5+td(ckb 8t7ts 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 8dcpp*+e4nu aa speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to yp4ec 8a pudn+*ou. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000absjsvjiv whhi.9)88:,*m7s2z c cov kg. The occupants would like to travel to a star that is 25 light-years aw .m,a8z svv)cwjb svj9hi82o7i:c sh*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 spaceship left Earth at a speed of 0.99c. What is the spa,jogt n8tm:yae2s; 2zceship's kinetic energy? Compare with the total U.S. annual energy consumta2n; s8 ,meg oytj:2zption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel lui jjb-+2jl 6xg (xk7mtjhi/q/ 4j0y to the vicinity of a star 6.0 light-years from Ear/x42t 7jj(6mblk uljq-+0y ghxiji j/ th. Passengers on the ship 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 c1o.6wij 2/ydaw m73umb ogh3 end of a spring whose spring stiffness constant is 3judm gcyiabw63 7. o/1mwo2h$k=48.7 \, \text{N/m}$. 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 mas/9/ ox3uzs1z(du guwv s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.