You are in a windowless car in an excepw rvl4oc r(f)8ms4 (hrtionally smooth train moving at constant velocis(fh8 rr(c )wvlr 4om4ty. Is there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out of the cn*3b .0p u/gd(e.mt o w/kcac (gzayb/orner of yo /e(*.//p wakdmy c(b ca0tbg zonu3g.ur eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a hg92lw /v k1o;8zdsic heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behin81zgo9d /;sikhl vwc2d it?

Does the Earth really go a jacc.eh78 *vmn yl-f,round the 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 best reference frame). Exh-*ae.7jvfcc8 ,lynm plain.

If you were on a spaceship traveling a26j*jaq6 d*lydo .vv rcun2gw2coc5, t 0.5c away from a star, at what speed would t jv6w.*6a,c5 * qrd2n2dy2loovgc u cjhe starlight pass you?

The time dilation effect is sometimes expressed asu xw0a(s mwz8( “moving clocks run slowly.” Actually, 8(z(uwax ws0mthis effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving r7yxtf/ or+fz2rhw7 0s eference frames or that it only seems to pass more slorh7+ /zryf7fotwx20s wly?

A young-looking woman astronaut has just arrived home from a long trip. She rusmkyr psy) i(4 qoe..k4hes up to an old gray-haired man and in the ensuing conversation refers to him as h)(ykosemp qi.y44 . krer son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a ch9 b5hhzm3xsm:ange in your heartbeat? Would your mass, heighh9hm:zms5 b3 xt, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length cont+qpmh4 s9+;/ yi,cqr pd iikl,raction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to t7+nlr -h r*uf t okmrbi;u,2z4he relativistic predictions of length contr+-,4irlz7of2n bum;kh r utr*action and time dilation?

Discuss how our everyday lives would be different 3j ybea1h ru:)6dglfabvq29z /( dbb6if the speed of light were only f 2 9/bg qabvd:u6)a1bzbj dhe(3l6 ry$25 \, \text{m/s}$.

Explain how the lengn4 qm94/cgep aio z1y1th contraction and time dilation formulas might be used to indi1qn y1i/gmae4 ocp9z4cate that c is the limiting speed in the universe.

The drawing at the start of this Chapter sh+dfk:t.9eo( 0 lm qlfd u.,5glcc gy;oows the street as seen by Mr Tompkins, for whom the speeddcl,: .c;omgt +9(5fk0yuo e.g l qfdl 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 aner p;9 eik;ed* upper limit on the momentum of an electron? If so, what is te*9edkirpe ;; his upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzejtn ow)ff6 (eidn w82(9d)gk.x2t quero rest mass attain the speed of light? ----待选择----yesno 

  Does the equation $E=mc^2$ conflict with the conservation of energy principle? Explain. ----待选择----yesno 

  If mass is a form of energy, does this mean that a spring has morp g pii2s07-w-czkg 8ye mass when compresszii0spc 8gp-wk7yg- 2ed than when relaxed? ----待选择----yesno 

It is not correct to +2cxbsyi p9 y*say that "matter can neither be created nor destroyed." What must we say csb+iyx 2 *p9yinstead?

  Is our intuitive notion that velocities simply add, as we did inz i7xsrn8.hy0qdj9q; Section 3–8, completely wrongd7qr .h sq;njxz0 y89i? ----待选择----yesno 

  A spaceship passes you at a speed of 0a 2,+0hyqokgq9hka(w.750c. You measure its length to be 28.2 m. How lon,qokyq2 9aa 0hkwh (+gg would it be when at rest? $L_0$ =    m

  A certain type of elementary part(wyg18 ydo 7 henvbe36icle 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 depl(c+rf c0b7 *i ddq7slend 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 speed ,/bv1ypp i*,e+eokkb 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 lif9lq w9usi(8j , a(msgqetime 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 star is 82 l-xvo*ydkl-,6j 6 hyt.lljau* hdx (j:ight-years away. How fast would you have to travel so that to you the distance would be only 35 light-years? v hh(:y.o,d*l-ly uxtdklav* -xjjj6 6 =    c

  Suppose you decide to travel to a star 85 light-years away at a speed 0gxwmk+by5k *n u4 *ujthat tells y u+n *k*u4mgkbyx 50wjou the distance 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 Earthk-j* yn9za+rz 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 Enterprisuup6yq2 epj0v06 vhd,e had just returned from a 5-year voyage whilqueu0pp j0 6vv6y2,dh e 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. q n-pm due5)kao6pl,2 How long would it take a spacecraft traveling 0.960c to reach that star from Elo,)5 q- 2ekp6pdamu narth, 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) mv+s ;v (7iyjhktz3uuc nqk 5hp:5x5 in her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. uq5)v(mu;3pjx57cthkv ih5s yzk n+:
(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? The at81bm75gv 9q9s z(d-k vpk 7x ykrc9yasv3pn;verage lifetidspq9 xk7atk9cm yg3v 8zprnbv9-s ;7 k1v(y5 me, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proto 6oge1d 3aq v0l k;jquk6v.na*n traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’ nkb ;ry6jo9c2;7e m*m 4egxfe;fzm1 fs relativistic mass be twice its rest mass? v =    c

  A particle of rest m/ ,cmr*s+jm(bsnzlc+ ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave+h)2d8g qnvdttc 5g*g 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 1hgdcti fm9 aj*8nxe( u,/j6 r(bw4 ncaccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requir6u91 -*k2mz)d)sxpj //jvgr njs mcb: clew6nes $4.82 \times 10^4 \, \text{J}$ 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 g fp ns; es3 fm-no:ba0moe27.fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in them7 se30a2m- on.epbfn ;os:gf process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in jouw +;heul;ns;y2k p 5wt4pu7rules 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 gd93pz;t.h i 97pcwuo 9den1kof a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption ox55 8w;nqp1s;ir x sc foze19in 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 conversio 1l y+2;hv0kk9ps ,s,c4d8vea yjlk arn of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle mko exp8wn/1p- z07 *0 bcmkujwhen its kinetic energy equals its rest energy? p -x 0bn8wjzkompmc*1k/u0e7 v =    c

  At what speed will an object's kinetioqel0(6 l,5 l761ecuk ionxr1ug/cx) bxok .kc energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton ffpyn +.2l0 psgrom rest up to a speed of 0.90+ p2fgl p.nys97c? 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 trasf.7 shgu:.(o qp ya+hveling $2.60 \times 10^8 \, \text{m/s}$.
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 kinetickovw- 3k6*fwr energy is 750 MeV)?*rwvf3o 6k-k w    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated9v1hv6f96+(uxws raxe4hkwv by a potential difference of 105 MV? v =+fvhw1(kxu w6a96vx hvs94r e    c

  What is the speed of an electron whos+x7g2k0ejf c2q ud5ez e kinetic energy is 1.00 MeV? v =    c

  What is the speed ofev3 *a6wdvz3 2va lb)f an electron just before it hits a television screen after being accelerated from rest by thefl zv23 b) wa3v6ed*av 25,000 V of the picture tube? v =    c

Two identical particles of rest mass :fafle/c9znlm :xb5o3 ,9 grc $m_0$ 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 prwato)7d fx)(f ,3j osaoton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentue /c:gzy 7d vdczo-zj5lwi5 -2m 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 kg6 -y/s8awe j18fvbtna 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 and momentum of arox 7r 3nrd,g a.9uhwt+s3 8wm 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,cxa1 b*-uw: xgi-*czz $^{241}\text{Am}$, 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 momeng0-hz q((lmim tum for (a) a particle of nonzero rest mass, and (b) a particle with zero res g0(m-iz ql(mht mass.

  What magnetic field int3q4+4:co+c jar f rvfe7 m1b-0jg tjmmensity is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (a 4:3+ tgcjmejv7a1 0 -rmjb+mf4focqr t, 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 Easn:s0y 8hk9rxrth) 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 Earthkr ssn 8yx0h:9? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50cgm a0sbz/ghwh 9,a -1l wit1-9g,0 szblagamh wh/h respect 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 atd r*594rosui( r3kjr u 0.71c. A second spaceship leaves the first at a speed of3 9 4*do usij(rr5ukrr 0.87c with 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 apby29; r4gxxy b.:y dpt a speed of 0.60c. The Enterprise comes to the red;ypy42x b. rbp9 :xygscue (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 opposd)j,bz/5pw e0;as3 a)ajuse wite directions. One travels at a speeejuap3de)s5 ;ab)0jaz/ ,ws wd $v_1 =-0.60c$ 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 7l8s gwf:*7xhcv;f zyof 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*7fx7s 8;gcy :lwzvf h when it passes A? u' =    c

  The nearest star to Earth is Proxima Cdmj tp(n/,9 wamm- q0hentauri, 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 about 0.1yq3jkp7oh 1f p q*vn56c is called relativistic - i.e., for which the correction using special relativity is k1jhn6 5y qpof*7q v3pa 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 spee*hfxy4hm,2 kz2(-/; jl hioayr zz vs1d $v$ 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 8uh(66qi zvqqa acpca:afv28 9gqrq 7g7+id .totally destroyed to run a 100-W lightbulb for 1 8g 678976v a.ra zhqu d(ac:i+2qaqvgfpq iqcyear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is . s6vc9l zp iv*u7r9xkneeded 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 thazv.9s9x kc pr*iuv76lt 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 olq/8 6fc syk:7f,lk5 8c txfrdn with a positive muon traveling at 50% the speed of light7fx5f r: 8ts86 / ylkkcqc,fld. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a proton, an electron, and a neutrino. Assume the 025zm 27:p.myhi hp qpm2j8nr tyopf9neutrino's rest mass is zero, and the other masses can be found in the Th.z 922ypypf:m0 r82h5pti qpomm7j nable 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 ener*r.(r ie6pr mfgy at a rate of about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a negative charge and 53x+md t*a: l+ko.urmwd-loc 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 pd1n38, h4;rhnfvk nj required to break a helium nucleus into its constituents, two protons and two neutrons? The rest 1 v4p,dkjr3n8 ;hhn nfmasses 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 (relativistize:45y+n m m yzk7cza,c) mass of a car traveling 110 km/h as compared to at rest? [Hint: usenzcyzz:my, m754a e k+ the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 7d5oc 2sji 8q0to 7pze0.935c in the laboratory, are moving toward each othqdtozj7c7 pse5o8i 20 er. 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 thatpsn31x o8gdqf1 z9sf :n1iu0c a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by cji :0et2 a7kncombining matter and antima2cjn et 7:kia0tter, achieving complete conversion of mass into energy. If the 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 energyr*(e oq3xtt c-/mnbf10ouc a; is greater than its rest mmaot -/0b*q31f tenco(;u x crass $m_0c^2$ 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 po3vv y5ynf tymm7/x 7,qle 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 runxtv 5,q7 m f/y7vy3ymnning 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 two mo,zr,+ gn((vwyp8o0ej qri f6n les of water0 8 vp (jiw6fyro,,znr(qn+eg, the energy released is 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 identica +e zcd.a2 iaa*v1wmo0l particles are created, traveling in opposite directions. If the speed of each particled o.zae* v +w1a2mca0i is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earthr2mp)/ ey9krp measures his ship to be 25 m long. On the ship, er9py2k/)mp r he eats his lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. You ayom jrx df4vk+ n.w3a0 w0*7vsend a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for thew v3.d ko ay0nmjwx*07ra 4+fv speed of the laser beam?

  A spaceship and its occ i, zhrn 2f*g4b0;efvuq* nda8upants have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be convertediefhngd, n;2 vq8rz **4b0fua 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 ia s* gb7s0: pbqhqrf8-s the spaceshiph gsrqpabf07-*q :8sb 's kinetic 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 travel qt.*9 +fixrzm to the vicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to t*+ txfzq9 rmi.he speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the 8homh h,fhxw/ f; t5cl:kz1 5nc bdq,+end of a spring whose spring stiffness constant is f5 8, ztkb+5o wlc/ncx hhhf1d;,q hm:$k=48.7 \, \text{N/m}$. If this system is in a spaceship moving past Earth at 0.900c, what is its period of oscillation according to
(a) observers on the ship, T =    s
(b) observers on Earth? $T_{earth}$ =    s

A pi meson of rest mass 7*aw/ qb4kip 1sx(m mi$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.