You are in a windowless car in an exceptionally smooth train moving at consts9ucdh k -kyd ;kb e,e4u(kq 8a3v+ha,ant velocity. Is there any physical experiment you can do in theey4hkev,hd9d3k- aska u (cq 8;k,u+b train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the expev54v; fyp1nryrem 24zh f*0pvi/,u lt rience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that you are rolling backward. What does this say about absolute and relative motio4 ymr;iu2/rtpp4* 0zh v,f1y5nevl vfn?

A worker stands on top of a)vlx *57v9 ;xruk,d-amdyvh d moving railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, w) u7dk* vxdxvvha-9,ld5y mr;ill 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 thef)zm n6 r-9fnk Sun goes around the Earth? Discuss in view of the first principle of relativity (that themz6)fn9f nr-k re is no best reference frame). Explain.

If you were on a spaceship fng4*:)1wqgm.:t b-jzsn ig f traveling at 0.5c away from a star, at what speed would the starljfn mi-s g.nwq 1t:4gbfzg)*:ight pass you?

The time dilation effect is sometimes expressed as “moving clocks i2j1c(s2ntq arun slowly.” Actually, tnq212i a jt(cshis 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 sl;e it4re-8cjbyx3 er6oqy09 ox89s sfowly in moving referency8q y r3orcj 6see;stbxf 49xe o980-ie frames or that it only seems to pass more slowly?

A young-looking woman astronaut has just m lrcx,cae*,.ph p;8x4 zm)te arrived home from a long trip. She rushes up to an o e;th.pex,)m4,zacr l xmpc8 *ld gray-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 notice a csx 8do .g;fhh993 l ij/m2c(, vbqwghfhange in your heartbeat? Would your mass, height, or.8/qhmb;9gvf9 x hojg ,lcd3w(i2 hsf waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occurh5xnoek zerv 78md;,+ at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the rnp uiw+(v *3kfelativistic pruf*in+pv (k3w edictions of length contraction and time dilation?

Discuss how our everyday lives would be diuatu7- i qvu2b 9d1a6nfferent if the speed of light were only uv71 a92ib-6duqantu $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be uslmlk18yl0 ;vged to indicate that c is the limitinykg8lll1; 0v mg speed in the universe.

The drawing at the start of this Chapter shows the stm 1/x0n.fea2np9m upwreet as seen by Mr Tompkins, for whom the speed of light ip20 wu m9m/npe.x afn1s $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at tcop*b7l o3 hw,zl63 qspeeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit?qwo3 ,l*6 bptoc7 zhl3 If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the 5ocqi-+l 3pdnspeed 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 more4g6cz 7rt pjc: mass when compressed than r:7p ctzc4gj 6when relaxed? ----待选择----yesno 

It is not correct to say that "mattetp;c n. licbql l4453wr can neither be created nor destroyed." What must we ll.bc4nclt4pqw ;53i say instead?

  Is our intuitive notion that veloc4a8v60h1rtoc5a dmzpities simply add, as we did in Section 3–8, completely5hac8oprz 6 a 10mvt4d wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750cxnzd d:nxqd,q82 sn q872ke+n . You measure its length to be 28.2 m. How long would it be whene q,n8dz+:d2q2dnn n7xsk q8x at rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed ofmq47a-oer nbd*e 1hy: $2.70 \times 10^8 \, \text{m/s}$. 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 the fa +zc a-3cblzow),cv ( f7pi-flctor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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-ytou)p-8zgg4dhy6 o k 7ears 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 mea5;fyw )w1vw-n,xekop sured 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. How fpl7 d gwkuv c9o57i*bxdh: :)sast would you have to travels*lk)p bcdvh io9u7wxd5g::7 so that to you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a 7- kllppkcw ,9star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it -p 7llcp9 k,kwtake 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 E s*a1h2 twpkz1iv-a7 warth 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 Enterpriss)az m7b,ncdi d1vqf /+5vlg 7e had just returned from a 5-year voyage while tra1m)7q i fcvn/+va, 5dzbds7g lveling 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-yea,xoer*6 .)w(x) 1g.wnmd lhmqcakh j;rs away. How long would it take a spacecraft traveling 0.960c t)1 g nahmqwkw;lj cx, hd6 x..ome)(r*o reach 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 at nu9)q-kd;)n esn*z/ngs rk-wa speed of 0.660c. It is measured in your frame to be 4.80 m long and *n) d)9/-ksnq ekws-r u znn;g1.25 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 pioa:t/;gd 0pn tv;okz-ay u-sg5n be moving to travel 15 m before it decays? The averagk ya; -sd;0:-tztopgva ng/5ue lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentumyugjfj u9y xwvumy7,9td+ +y):;8cfv of a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest mass? v wtt)c9 s w1j88lknxj hfa5 b5.=    c

  A particle of rest mass , glxt7lh9+qvs .vr ;h$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travel,h4 6g idb82( 5ti q nl4npccocbwb:c:s 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 zr3c3.gvco, *l d*p2+uk rckbthat accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical r4sywmpyh* + uz5*n8 o epb.u(ieaction 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 brm*z7l+ld lma) xbk*:qx u5jv*eaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinm* x5+ jv7)ud*x*l: kbz laqmletic 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 dpfh1 1t,gtx6ea2 nu.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. g0vd,atet+vnyv0 .h a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is / :0yv;bl* 6*p2b jp:uu3aodb lbfvjtabout $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtainelul)fc+ :/wdqx6dq 2ed from conversion 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 when its kinetic energy equals its rest ene hlydoh*n rbl- q:9zgz(n6c 2,rgy? v = g62b qrhz9lo nyz-l,cd hn(*:   c

  At what speed will an object's kinetic energy beysyij+l d;;5en/e o2z ( lu.m zwbk+soao62c. 25% of its rest energy? v =    c

  (a) How much work is required to acceleh.s8hx* 0v2ltmz.s c krate a proton from rest up to a speed of 0.997c? Wvz. hx* tshcms2k.l08 =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic enei2)3rl 25l 8lqgbpatx rgy and momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetic energysd4e9m-iakhg;/+is ) ovnol+ .ghme ) is 750 MeV)k; l/iam) +4dhmie vo 9eh+-.gosgns)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proto2,fmd9hpt 77 dpgz4ysn accelerated by a potential difference of 105 MV? v =gdpp7 27m y9hs,fdzt4    c

  What is the speed of an electron whose kinetic energy is 1.00 Mee64onllfyf m x5g8jgxi5mq(3* f hh1 (V? v =    c

  What is the speed of an electron just before it hits a television * 7+wl :)scves agktru7p-2 byscreen after being accelerated from rest by the 25,000 V of the picture tube? v = y7wpb )s: *2vg rtkel-a7 uc+s   c

Two identical particles of zqtq u *um.op(1ma-h p i;7pk)d:+sssrest 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 tl;y9 jhgzt v(e467*ifs,rm51 tev wj ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momen5vq dr ,*bgxz f8h /lp;q*zvi8tum 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 n(/e7w/3k vf;qwrzcjj 3+q ujof mass 27,000 kg 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 m,ta/ cjtue-em ,- op 54fntdk1omentum 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,v qpdi9(jbe3ht37i n 0di,ft6s o 14df $^{241}\text{Am}$, 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 en lj2 m8zy*gdg.ergy versus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zer8.gj 2 yz*glmdo rest mass.

  What magnetic field m9pln 79 m1e cu7t xwd0fe))c/ot3ap iintensity is needed to keep 998-GeV protons revolving in a circle of radius 1dm a970pcn /lu9wt7ftm)ei e 3xcop)1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket trav;o(atb .2lpej :vyp4zeling at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she meas;boe pt y(z pj:l4.av2ures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each w m.mfega-ce41ru t 7+i p,;rtbith a speed of 0.50c with respect to Earth.er7-e4p r, .b;mtc1m+f taui g
(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 traviv k,v19azb6 weling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Ckva6 9b,z1w vialculate 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 ali ubl 4vyxa /*7hi: dkv5etd2;sen vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overekb7a/ txly;udi vs d2v :4h*5taking 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 se1 p5ed6n dzyk924mz. *u cjjnynds out two escape pods in opposite directions. One travels at pe.yu4 m *jdk9z5jyz6dn21cna 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 ,y yytr80+h xbof 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How faryh y8+0by xt,st is B moving relative to A when it passes A? u' =    c

  The nearest star to Eart:x o8 f- yor1- dnr28vqwuhhd g6npu(cc:k82th is Proxima 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, anc .*efb9 r0 )pdeq:gtuything traveling faster than about 0.1c is called relativistic - i.e., for which tr*9u bfg .t:0edcq ep)he correction using 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 speedv ds 9veo:p6x- $v$ 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 to:mcdsv; 2 s(i b))srxqtally destroyed to run a 100-W lightbulb for 1 mbsc i(:vssq2x r;)) dyear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needc:fdd)2 gsan2aa:o 5rqxv 6l.ed 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 that electric charge is conserved in this procnxldv6qacr2 sadf 2 :go)a:5. ess.) 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 hexqy6l;8 0iwvve , ob- *q7pfscad on with a positive muon traveling at 50% the speed of light. The two muons (each of rest mass 7p06- q v;ebosiqyw8lv*f, x c$m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a z4jo jz ;ajp.:proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table i j j.a4;pzzo:jnside 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 a rate/rsfdlx8 6y9ksu b5o* 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 a speed 7p)x;l)i1zy;;gj dvtcsrx; yof $2.24 \times 10^8 \, \text{m/s}$. 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 constitu 60nw.r+ek(lw1 ozdk pents, 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 enerzp lr+. e6wo( wd1nk0kgy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in themon(jseshnoi2q t) o45s e)-y6my h2 8 (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: use the binomial expansion.seh84)i( 2noq) 2n5s htoeyoymjm6s- ]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c 8d49ryyvfnpg-a(ga +in the laboratory, are moving toward each oth4df gpv8(-9ayr a gyn+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 that a pao3z2a sb l1-i- 7aswmurticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter an,* 5o(ccfqh(8 liczfu d antimatter, achieving complete conversion of mass into energy. If uczcqlf( 5f(hi oc* ,8the 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 somu (;vtjp5v pf+e.fhbkuw-/9 that its kinetic energy is greater than its rest mass ub +wvv/pmjt( 9f;k5 u- fhp.e$m_0c^2$ 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 polv*l63bx t. g1xubmlve) hy:0ae 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 vm*bvx )l6geb 3x1.:al0 tuhyis 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 to fo r4urfhk;j.73o ne)v9pe r ih(rm two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this reaction? 4 f .)pv9eh;3h(rjunrio7rek
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical paozw 5t86cmk+ articles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory f kat+w86m czo5rame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling tb1 i-u xpum z99w14rqat 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eaxpwuqr 1 uz9 t-9i4m1bts 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. Yob) vt( byfj46pu send a laser beam toward the Earth traveling at velocity c relative to you. Wpv )6j4b(tb fyhat do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occupantsi spek *3acx/5knm+2 d 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 converted tdksk +icnx*a5 3ep/2m o 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 a50in;iim 2;gju jog:6 ftp7hp speed of 0.99c. What is the spaceship'sg5i 7;hgt mj2 ijip6opu;:n0f 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 to the vicinity of a 1*sd :ar /q.ksjhu:1j opvz 4cstar 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to 1 q* a1pzj o4kvdsucj.s:/:rhtake 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 6ip4mv mq1 k*t(nx p*vof a spring whose spring stiffness constantv vpmp(4n* m*t 6iq1kx is $k=48.7 \, \text{N/m}$. 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 r4n5c.rw6t o1 ozz 5gq1+ dgry$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.