You are in a windowless car in an exceptionally smooth traidgiy ,; h-wm:p:p lum1n moving at constant velocity. Is there any phpw1mm- iu;p:d ,hl :gyysical 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 whenp ure3u/c;j 9v, out of the corner of you;93ruce j pv/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 uf.wnok u; 7l.railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car 7nu.wuk; olf.or behind it?

Does the Earth really go a vxls2qw gp(-8lwjt w 5mi8ty.6)k;turound the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the pj -.ugl v5 l6wmkwtw (i)2tstqx88;yfirst principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away;x o qu()qo09pzyzy4.wuh le1 from a star, at what speed would the starlight pass yo9lwopyq .;x yuq04oh)ze ( 1zuu?

The time dilation effect is sometimes expressed as “moving clock,ecx ppg1+gwj7o7bl -s run slowly.” Actually, this effect has nothing to do with motion affecting the functig-bxwj 1 77gep,lcp o+oning of clocks. What then does it deal with?

Does time dilation mean that time actu.x:tut*bk6;/f mpc v jally passes more slowly in moving reference frames or that it only seems to pass mor6.jtvc:fk*u xp ;m/tb e slowly?

A young-looking woman astronaut has just arrived home from a long trip. She ruhdngl;/d,hh(p,8 ;z.an p ydgshes up to an old gray-haired man and in the ensuing conversation y/gddpn g h n,zpahd8,h;.(;lrefers to him as her son. How might this be possible?

If you were traveling au vi8lrc( 9:ysxb7j 0kway from Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or w x09:bvry ics(u7jl8 kaistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinarh x n5rkvg*vo2aw9 32xy speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would py0 :iaz+,suohappen to the relativistic pres pau+0ozy,i :dictions of length contraction and time dilation?

Discuss how our everyday lives would be different if the speev xy4p f), +9kog5rjwyd of light were only gp+fy9r x4 5y )ovjkw,$25 \, \text{m/s}$.

Explain how the length contrac*h+co 70lh if(kqc jv(a;8vswtion and time dilation formulas might be used to in h0;qvci(jlw(v *fsh7 oc+8a kdicate that c is the limiting speed in the universe.

The drawing at the start of this Chaptut, 8yewun /; hcq 0c4zv7i9qxer shows the street as seen by Mr Tompkins, for whom the speed of lq;nqeit94/0, uwzyx hu7v8 ccight 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 speedj/ycs)l:(wti.-6 3s j et sseks less than c. Does this put an upper limit ons(ec/)iy3kt .tls e j 6:swsj- the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain th;lys*2 q1 vikge 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 ftj/ mj o4u)x-spring has more mass when compressed than whenx4 f-u)jm toj/ relaxed? ----待选择----yesno 

It is not correct to say that "matteki*hn6w/o1pq xz 1 v2xr can neither be created nor destroyed." What *1xx/ nkvo1pi 6hzqw2 must we say instead?

  Is our intuitive notion that velocities simply add, as we did in Section p8s0symh;nx5l3scu 23–8, complete3xu0n 5s2y;hp8lsc ms ly wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to bb ,z6rdm6u dyt g)r6n)e 28.2 m. How long w6udb gr6dy),z 6t)r mnould it be when at rest? $L_0$ =    m

  A certain type of elementaryxvb4u-6bynw v+( t5u,ck g8gk 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 the facjkw l 8m65otp-y3hn(ztor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 l nmg)d +sr-b.omus/ gy yg/+(ww1 qp4a star 125 light-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 averagecfaq *j4j; q(u*xbc/p lifetime 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 light-years away. How fa1 ,rgmnv)wc +ap:/phb st would you have to travel so that to you the distance woul n1ac+rw:)vb/gp, mhpd be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 l 9svi.mtd-w -r 6 cj;xr09 -uzo)oeucvight-years away at a speed that tells you thcu zj cvv-u.o sorwm9i6d;0r)-x9e -te 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 Earth6uxdc e7v pn;2 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 from a 5- kp3 8iqpiv y6i2z0yp-year voyage while tivqi82p-ykpiz03p y 6raveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How long would it take a spacecraft tn 3 ax3/8a(silh6i(bgi;d fbp raveling 0.960c to reach that star frxlaf psi3nda / (;h3ib(8b6 giom 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 "Fer-ab 0+)yreoa rrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 ma) 0eby+ -roar 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 beqzgh9 a+8nh yq/yny5ernnn20r;k 1l :fore it decays? The average lifetigq kran9 yynlyh1z;qh25 0+rn :ne8n/me, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a protont cfi. ksg3o )ga*;jf* 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 maslv 8p7 e7thp ;q+8uudrs? v =    c

  A particle of rest maxrxph0; zr;oj90 /wv fzcan 87ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelgq0uvf1;j c + *js3-lza1gdnr 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 pr0nt aj-bk3ysx mc(0v, oton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requigst0z m::3 a58ku wyuz5 o8exores $4.82 \times 10^4 \, \text{J}$ 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 knowwpe;ny6h01im/2mco j1csz m qx5q0;b n as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in pb; ;cxqq6mw/1hzmj 52 yionecs1m00 the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an elecbtgt ds )ufn;d-*y( 1ctron 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 ma-k 5cuibs/,5 xmmmlw4ss of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energyqx2v sqh:d)+5y3cjd q consumption in the United States is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion ofs:h xu8l/)p fm 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 energy7fo65 av:j/z 9j6 gnffnrpsr w.poa-: equals its rest energy? nj: f.:5vj a9/p apro6zg7-nffwro6sv =    c

  At what speed will an object's kinetic energy be 25% of ie0fx)t2av 0s t/y7ljs ts rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a lh.eg-ltc * .si*pc7xspeed of *g7pxhl.tlec .* -cs i0.997c? 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 travelij m* ay p e p8a/d2sq)clp.o9pyd;-ao6ng $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (thatgp c8l1eu+rx5 me.bn 8 is, its kinetic energy is 750 MeV)eb8e.p mx5ruc ln+8g 1?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton a (6oxvyzk0gk q4shgj / qx+jp*8yyv51ccelerated by a potential difference of 105 MV? v5+ys1zyp8xjvx* 0 g6 kqoqkgj yvh4(/ =    c

  What is the speed ofv-0x9 6 p3wpsiwunou5 an electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just bera50+m i6and*- sju+k gdc0k)pi*xj afore it hits a television screen after being accelerated from rest b0 jauid+ gacr)pns kx+m*i6a5d-* kj0y the 25,000 V of the picture tube? v =    c

Two identical particw( yf52u)m yo4b/rwdm les 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 protonj,4jpp1ks 7unj l wa aeoe;w*kos;+5mjrq86 , ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 an ,qtjes.fwayi. h on58. d mt2/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 maf. tbwlyx(k 42(,yur ass 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 anfd.j aexr(q ixk,wdt7 g:.6l ;d 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,i t 0trk4ejf8: $^{241}\text{Am}$, 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 for (a) a partpwv 752y hc*-k gcsu9iicle of nonzero rest mass, and (b) a particle with 5- *cw9i2hcgp7svy kuzero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protonsxr/zlz. ynd.c9 cge +/ revolving in a circle of radiuzerc/9.ldg.y/c n+zx s 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 traveling at 0.50c (with respect to th er8z( i0q75xd/m aaprw3l/fre Earth) observes a meteor come from behind adz38/m (a7r5e/lp xwq irar f0nd pass her at a speed she measures as 0.50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speer g x,b84s*6:cuei jred of 0.50c with respect to Earte:,cxe*sg brr8uji 4 6h.
(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 the,l ftt(x vxf6ok+miq j*.q+-t gx1z/l first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth+xfqv.gl + qt/-fi jlt*xmx16t zko(, 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 a;3y9mvnypw/q ruin * nj q7(p+aw1 9gspeed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking th wn aj9 p9u;m1rpqiyq(n/+y7 na *w3gve 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 direct+ka mlt buxw*r1 53u ch+rd ::ut98mvnh dha-9ions. One travels at a + -culx b:8umhah9a *+u5tn91dvmkwr:d 3r ht 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 of 0.75c. At the same time, rl;ufj 5z)a t4aocket 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? u' =; z t)al4ujf5a    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-ye vie a vqvwh;044cm-i3ars 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, anyic+r g-4.y vte p+i) zr4h*eqwthing traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity ite-.qi*r+)4w h ivz ecrp 4+ygs 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 vm x;g7b/c qr0d:e/*vh mr:gk$v$ 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 -fp)c2ueu)x zbe totally destroyed to run a 100-W lightbulb for 1 year) upufzc2x)-e? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of el)v zjopn1 6) uv-(vnxbectromagnetic energy is needed to produce an electron and a positron together? A positron is a particle wi nzvpv j u6(-o)v)xn1bth the same rest mass as an electron, but has the opposite charge. (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 h,v6 n clhp p8fnxri6p2nh. mffol.2+3ead on with a positive muon tlr.hf+ px32 mn2, .phivnp 6lf o6cn8fraveling at 50% the 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 dez+w )li ffhi 7tv8ab0*,(j1wks jj4wycay into a proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front coverfwtlw k4* +,fv(zbw7h ji)ay j8s10ji. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at7y4vx1sf 1bkc 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 a speezqu/scz 0. d2/jtabu 8w9o:q pd 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 uq k3 nqy3,*wj)6cqd tf6vjx+helium nucleus into its constituents, two protons afqdyktj3 6qq3*x c+ )vuj,wn6nd 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 of :q d 2.g7wpguaa car traveling 110 km/h d2agg7pu . w:qas compared to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having kdo.7ap -fjue40pi+y a speed of 0.935c in the laboratory, are moving toward efa47ppjo y 0-eu.+dkiach other. 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 pk1k5bu: ou9m3nt;bbm article with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtai; k.5n o;baabkns its power by combining matter and antimatter, achieving complete conversion kaan.5;b;bo k 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 energy is greater thanb1p-4hhyicv15ht h*w its rest ma 1wy5b-4ithp hv* hh1css $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-long pole into a ,8xq*g/t9cnfmjmhw o53 k-dd12.0-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 barn looks even shorter to him thj3fh/qg5mddom c98xn-*t k w,an 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and ongl -fu2fzba, b9ln*0we mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much doe-g2az,f 0llb*n9b f wus 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 1a0q+ v,x,ve6; c 8sj 0mp miozjwfhn;particles are created, traveling in opposite directions. If the0pmj, o ;v6v;w180m+fhzj, xnsce aq i speed of each particle 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 travelinwz+6h2ag* dzvg at 0.75c relative to Earth measures his ship to be 25 m long. dhv+z w2ag*z6On 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 at a spee 0thdwykavk g(9-,hc.d of 0.85c away from Earth. You send a laser beam toward the Ec(wt0ky-g hvdakh9 ,.arth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 15;i wo. 2br2plc0,000 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 converte wcil22r .;obpd 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 acq9xpi k.z r)p,mq to2id,7;s speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (aboudq i 2tzsxmo)7p,q;ick,.9pr t $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity xxplk +ag2.d ambdbw 4 x9fy4g ca9h+.-*jo.b of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.f-* +x94 2 xm ybp9gdk a doxch+gl.4.abajb.w0 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 constav, k s/xr+;a /kqkzq0znt iz/za/0 rkksq;q +v,k xs $k=48.7 \, \text{N/m}$. 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 mc7m1 f(-x 7bm a(upjrytk8q4oc (wfo j:v;k.uass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.