You are in a windowless car in an exceptionally smooth train movingb (i7tj a 5ir :dfs3hz0.s;wtb at constant velocit7sis3wj.r haib;( tf t:dz05by. 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, l bw14lw-9l bjout 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 back jlbb1lwl-w4 9ward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy )2dppk;f 6 yjxball straight up (from his point of view). Id2py k) p;jx6fgnoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say that the Su0++r 0d(cams:/6q 9* +e ua dfxpb wuv,dzruobn goes around the Earth? Discuss in view of the first principle of relativity (thuvd +a (a6d,mqfd :r+9u+eowb0ub z*0sx/rp cat there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed j7tyfp271crx+dd + nu would the starlight pass youxy 7+j1d+f ptr 2cund7?

The time dilation effect i1ezie5ta*p d.8i6z ;qcgq g7as sometimes expressed as “moving clocks run slowly.” Act gzeqcag ezp7iqda1t6i;.5* 8 ually, this 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 ret6.8ll b v8jskference frames or that it only seems tostl8j.v6 kb8 l pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip.zdyb 50;w ,vr 6 zmht/gzdy*/w She rushes up to an old gray-haired man and in the ensuing conversation refers yw 5my;zvhtz0/*r/wd zg6,b dto him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, 2z g;t 9w jhh(ev-dkt-would you notice a change in your heartbeat? Would your mass, height, or waistline change? Wht-w g(hjvkt dz ;29-ehat would observers on Earth using telescopes say about you?

Do time dilation and length contraction occurt l*a8ea3oa n7 at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of lioo8swh4x b3 r80-lrozii(c )dght were infinite. What would happen to the relativistic predictions of length con8b xziis0o w-8)h(d3 r c4olrotraction and time dilation?

Discuss how our everyda d2ua:ln)f 8/owe1puny lives would be different if the speed of light were only)fe82ou nnw a1:u/pld $25 \, \text{m/s}$.

Explain how the length contw9/o onw)2 x wa-sgzj:cdev6b,a +)nx raction and time dilation formulas might be used to indicat:o)o/6x9g daj+ swx ,nc2wwb v-a)ez ne that c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr T. a rxfdtoatt2me/; 3,ompkins, 2m o 3rxaa,ed t;tf/.tfor 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. D qi1brg4p :tlswl/,6,gj rp+ noes this put an upper limit on the momentum of an electron? I,6qpb1/i,+gtjrw n:l srpgl4f so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzer1:hc0 :qyuuv xo 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 ensqdsgo1 hs6/6ergy, does this mean that a spring has more mass when compressed than wh odsqs g6sh/16en relaxed? ----待选择----yesno 

It is not correct to-y; ))ntuz eue- oe7hh say that "matter can neither be created nor destroyed." What must we say inu eehy7 )zo)n; h--teustead?

  Is our intuitive notion that velocities simply add, as we di91hc8 ed.cdh4 w gdsw .7ay1pad in Section 3–8, completecghh.yaed d9p7.18 d4acs1w wly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measu *ug3w73wa iwbre its length to be 28.2 m. How long would it be when a wa3biuw*g 37wt rest? $L_0$ =    m

  A certain type of elementary particle travels at/,asnx.fjl,oo7s9l 4 nxa8fj 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 tvj2824q bcvws he 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 liggl2b(b gu-k )vff4d*jf4ta ;rht-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 is4bui6:1ua ;gjb23kchm /x wc/zthgy qs6/ol+ 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 light-years away. Hd-avs6- ih l72.cbjqxow fast would you have tcq 7s6i a.jh-lvx-2dbo travel 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 5w.v l- tc4uxcat a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip?vxw4 ct. l5u-c 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 Earthq;.povk8xvi3a w+-b hi: ko o( 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 th )ydgb/qns) 4/1nzslf4c b-unat starship Enterprise had just returned from a 5-year voyage while trav-cyubnnd 4/)s4fqlgs 1n ) /zbeling 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-yeag 6 ,i mz(plq0d2pgsm4rs away. How long would it take a spacecraft traveling 0.960c to reazgs p(dml,6q p 0g24mich that star from 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 ad/ 1en8gi0+svrx:x g dt a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1/d+ge dgxrxnv8si: 01.25 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 11kwc7k 5wse ntzrn s2d i15*q0y/-nni5 m before it decays? The average lifetime, anweds1*yk c-7 iwr nq zn5s 051n2k/itt rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton t 8kyoubkvnn ux.) iif;(y,(.puo ql7 :raveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twicip /i: o1t ypkpz0*axtkn 38/q p1pw1ze its rest mass? v =    c

  A particle of rest mashwr9nz x /ul9v:gm 3f;s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travenys76dz6a.0utdaq g56 j iz l9ls 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 ajbjqr;/8wg8 (5gr xqvccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires j61odg(r7gtn i 2 :esj$4.82 \times 10^4 \, \text{J}$ 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 tha3um8 f,j n2yweu/.xg e process known as fission in a nuclear reactor, the w j.afgy 83x2u /ne,umresulting 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 of an electron in joules and inoi: a(rvjsr : 0y1z6ei $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a proton in v (yg3j 6xzk6 hpf-o;gc:u2iz$\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is aboccb shq dl4 j4qy/g56ywbdyl 8t3 1e;;ut $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion5r)7qtl4m rmg;c d(jbu(d fcp- js54q 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 ofecob ,hd- ckt6o6 )-z5dfbho5 a particle when its kinetic energy equals its rest energy? v oh)to d,b655 c zhkbcodfe-6-=    c

  At what speed will an object's kinetic energy be 25% of its rest energy? w*dt dw bt54 w0k6/audv =    c

  (a) How much work is requi5 cc0lcs 0gwr(red to accelerate a proton from rest up to a speed of 0.99(csc0l50w rgc7c? 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 o*e5iq)kloex;7ncsl 0 jsyu -+f a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, 4 26vqhrymj.d, wmva;its kinetic energy is 750 MeV)v qah6v;rwj4y ,mm2d .?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated byty gbsgi 1y 2r0g7p5c/ a potential difference of 105 MV? v = g ygy57tpb2grc1s /i0    c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? 3(0g.*sggr p3cs(corkhrh6k v =    c

  What is the speed of an electron just before iok 1hhvce8 j9l9mr:sg,1/ 5kq.coxbwt hits a television screen after being acceqe 1ox5wgh18cv9k /.km jr9s,:oblc hlerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of f/ bq0auv:.f0efnp1d),e w zu 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 kkj1jsg-:k q*x0h tus knu-hf1 5v(0 oa 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 the momentum of ay ne*j h;swxw;hk7) )fn 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 iy44g2e1*o(jya. qap d po j9wgs 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 energzwa 9v69dekv (d4w2bhsst9 t0 y and momentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleus, a gsl:f,-9hd l$^{241}\text{Am}$, 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 fo vkg0 ,x)m.ndtr (a) a particle of nonzero rest mass, and (b) a particle with zero rektv mdx g),n0.st mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving qupcb:.4 z)idin a circle of radius 1.0 km (at,d .c) 4pi:bqzu 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 respen :rrx6* x 2r19x).yeow ggieict 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 resrwr2 yggx9 x.niox:6i e*r1 e)pect to the Earth? u =    c

  Two spaceships leave Earth in oppm9 (zeej2vc) f gm*;lu,0/u fgoz. vidosite directions, each with a speed of 0.50c with respect to j*md ,lizfe/z) 2 fevmcu9o(vu ;gg.0Earth.
(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 theuc3a5uz(s7 8 dp noxl4p-8lr.mduy- m first at a speed of 0.87c with respect to the first. Calculate the speed oolrcyuunm( p l-73a5 -u xdd48ms8p.z f the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a speedv4+n) un yvg))vgmy(pxw-yj( of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking thm(gj y u)4ywnv+vpx-ygnv )()e 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 set h,vyf*7a5vd+ b1 9vm h:wt 4j9tsqeynds out two escape pods in opposite directions. One travelt1vh jsdb ve9ah,y: w5mf7ty +9 *qv4ts at a speed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth at a speed kmw 1lk7y(-oe,9rwy)fqq yq ,of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast wqk -fy9lq1ryk q, (),me7w yois B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima.p e;tn(ih 8d*3yjo :k3i ym2l krtgk-f z(i0u 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, anyponvw 9( -qme10ssu,kthing traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine th1koem,v0(sn s9p q- uwe 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 y4hcfq:x.w1 r$v$ 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 matte1p.ezx (u,yler would have to be totally destroyed to run a 100-W lightlp ,eue .z1yx(bulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electron a e 8bgg3;ajsi7nd a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite chare3sggijb8 7a;ge. (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 hei +tt(z:i ad39ze8ooe2dk2 cfad on with a positive muon traveling at 50% the tz+f:(2ok iiteeado3c2 d9z 8 speed of light. 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.v,9 * 3nsitn p1uwndj. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table i n3u9n1 ,.jvsdtinpw*nside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at av6:5a ouom ,/b /s)a ealhzg8 t7u7byp 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 measurxvi kogc3h()6 w,g,yned 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 required to break a helium nucleus into iti.wk6dj f3-s/c iyve0 5ih;jys constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (T6ch3 v.yekfsiiy/j-5id;j 0 whis energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relatqqhr-ws;b-lun.e0t *b ,nw hcjs076fivistic) mass of a car traveling 110 km/h as compared to at rs-qj f*c.7;sqnu6t-0 l h enwwb,hbr0est? [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 laboryhw)+t/5(. sr pm1nu.z df wixatory, are moving toward each otherwsd/pf+y m(). zt1nwhiurx .5. 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 parti hb.dne53y+bq, vbr+icle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains 11m,a1qq5r db1xcv is1; ns 7pfpw)xsits power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Entervip5c1q71ns1;wqpsx a 11s rmb,)fd x prise 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 kineticp0+edlzbf446m4u u;,t d nm hb6*nukx energy is greater than its rest m4pz felud40b,k m4* 6uxun nhmt;d+6bass $m_0c^2$ 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) j57/i6dd4teu; (dy k iqjhns fit a 15.0-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 i es) 7;dn(h4t5uq6jdyijdk /with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react ;;(;)mtj76vfcooj vo 7mfbfkto form two moles of water, the energy released is 48fkvbjfjtf;om); 6o7mvoc 7(; 4 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling (4 r 1e29qve7+lr hsefll ra6rin opposite directions. If the speed of each particle is 0.75cr 94 lesqe67+ aev1 2(lrhlfrr, 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 travelink ac:za 3p7lba 0mq0tq-ck88q g at 0.75c relative to Earth measures his ship to be 25 m long. Onz ka qbqk0a:qatc l mc8-08p73 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 atuzb* q4esv ,;v qe/jtd.vfy5)qa*ri - a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for thefvb .5aqzj-vyqtu*s; eivd rq, /)*e4 speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occupants is:.6q :z4glwn yj2xx would like to traveln:.:xsjgyilw x6 2z 4q 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 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 sp8h fax5hzoun-0c*im; aceship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare* mz5fh0-hcu ia8 ;xon 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 to the vicinity of a star 6.0 light-years fro i9q,n9nhezv+m Earth. Passeng9n+9qn, zievh ers 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 end of a spring whose spring stiffness constancl 9 3ymaxa7t(t x9 mca3alyt( 7is $k=48.7 \, \text{N/m}$. 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 masshm 1cdj6uuj,ci1 30yi $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.