You are in a windowless car in an exceptionally smo8bxs+kk ies ,3t*:zus1 w(brs oth train moving at constant velocity. Is there anys 83kesxz:*u( rk1istsw,+ bb 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 t 6v3f z-fw dzc8(j6rmzxbc;y+he corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal,xdz6 f yw(8jr; f cb3vz+-mc6z thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a mov8d n-si,9cnb b+ fl6kning railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on tnbnbdk8- + 96cflisn,he car or behind it?

Does the Earth really go around the Sun? Or is it also valid to sazuk8 : -b6kg n3ge,)rmxkkf1 ;jlyy5xy that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explaikz-mub:yfe3g5j1,gn8r6x;k)l ykk x n.

If you were on a spaceship traveling at 0.5c awa) q( k7d f4uk49bfm8, qwpq1lxznqjt6 y from a star, at what speed would the starlightfk4)ztx1(p w l7d,89 unq6bqkq 4fmqj pass you?

The time dilation effect is sometimes expressed as * egl )y16+ne7(1 *kh qnjkxcobty:d i“moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then d1:c* 6lb gq1+)xontdhi* 7kneek(jyyoes it deal with?

Does time dilation mean xbtx4h 1h2qa 2that time actually passes more slowly in moving reference frames or2hh 4xxqab21 t that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived homes 3sc;wqy5ce1a9 ,gg j from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to w1s9j cc;y3 gsg5a ,qehim as her son. How might this be possible?

If you were traveling away fje;h+c0w5t y drom Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would obed50+yjc th ;wservers on Earth using telescopes say about you?

Do time dilation and length contraction occur atonqs.pr,,(u c ae97d y ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What wouls ,v 9zr0ry8ifd happen to the relativistic predictions of r0ryvs i98z ,flength contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light were onlam9rki p v+*i0ai+k 9mrpv*i0y $25 \, \text{m/s}$.

Explain how the length contraction and time dilation for7fymwfkv0+zws( opw k2+;/n s mulas might be used to indicate that c is the limiting speed izmysf wv/+n pkf 0o+(sw2;7kwn the universe.

The drawing at the stalfilj9 *lpnx 4ql7a,ml*y 7rn7e4xo:rt of this Chapter shows the street as seen by Mr Tompkins, for * 77omep:njnyl,q*ll i4al79lrf4x xwhom 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 : ps8j /dn c9c7n+n wrd6ka,8rhfgo/v travel at speeds less than c. Does this put an upper limit on the momentu8fc nrdad,n 97nr6:ksh v/ 8/ j+wpcgom of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest4cvw s p-4qbozbcu/4ksykab 9x .6*1m 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 enesnnujv pfmdv/m j*8:8p .ew 3;rgy, does this mean that a spring has more mass when compresse 8m nm/f8pjwd: p.vnu *;esj3vd than when relaxed? ----待选择----yesno 

It is not correct to say that "m dja2yoa1(zy ogu70i-r73cxd atter can neither be created nor destroyed." What must we sagd0 u73i(y1do7aora2 xyz-c jy instead?

  Is our intuitive notion that velocities simplyh:yebk o2 pf+4 add, as we did in Section 3–8, compl+:p by kfo24heetely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length to be 28)dh6yfdug4h30 hj8t(sn( hl y .2 m. How long would it )h (nyh6yhf3 0ghj(l4 dudst8be when at rest? $L_0$ =    m

  A certain type of elementary particla3,bm09lfi kb e 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 facvi1 2qles:g, 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 a star 125 light-years from Earth a ty b9n+kxf)17abwot cl 90u8it 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 bp g+l3ru)i5 qf,c l,khbe8k (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 adq 6q t3q ;q(acrpj 0)banh:9rway. How fast would you h3anq :rc a0bhq( )6;qjrt 9pqdave to 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 at a spep8 q.1ly u4h yhbx+2xued that tells you the distance is only 25 light-years. How many years would it ta8uy 12xhq.hp u+4lby xke 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 the8 vu*ul 2l;zla Earth 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 hayj bi5b +qf5;xd just returned from a 5-year voyage while traveling at 0.84c.+i;bbq jy 55xf
(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 jcm d zh-qld-r1/q-u) take a spacecraft traveling 0.960c to reach that star from Earth, as measured by om -j-)r-dqd/l1qc z uhbservers:
(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" ss5y 95ddcwc ywr/nv4fn:; i, gpacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m 4cv5w/ n sf9: cn5i wd;y,gyrdhigh.
(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 average5hk urx3 tavtt+frdd 8-12; e2eq yi,x pion be moving to travel 15 m before it decays? The average lifetime, at restiudte a3yhq+ d-k e2r2xr,t5t8 1vf;x, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton xje5j g9c x/u- 8 dfwg.0 x*oyz75yslatraveling 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 m-o 26zc1y8yufnuy/k h cxp:1bnb4t0 mass? v =    c

  A particle of rest mass wafo b90x1 .lf6+lkgq $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels qjo jqi(38madv:vk9 ,d e-hy; 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 4t53ovrtq 9 c-ppc5kxaccelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction q89 y1mopotblx9u;g7j 9a +kq 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 resta hi)pm- 1ub6vdp n0*s breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy 1 *bmuh ad6n)pp0-vs iof about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of a)2p7dm z lrqd)tt49wiy 2z7mmn electron in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass o2 h0q3)o wztjn z5n9jzf a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Unitnlr8cr. 2;z)pw 8x-q jlxa3vx()r b uged 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 beu1o-/vs +b.km1kxxp j obtained 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 rgd7 l(nxtwb3 3bg;8zbest energy? vz;t(db gg3x8 b 7b3lwn =    c

  At what speed will an object's kinetic energy be 25% of its rest enemw5 otg.o85c (w sx(dnrgy? v =    c

  (a) How much work is required to af,;j;7s x(zr jsjbb1d *ff9py acem4. ccelerate a proton from rest up to a speed of y s9smc;f41 bdj7a erfzj,;bp(f j*.x 0.997c? 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 travo .luw7o-h1zweling $2.60 \times 10^8 \, \text{m/s}$.
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 k ltifn+6 t9a/wy,pf+r.x9 fnpinetic energy is 750 MeV)? ffyp lnani t 9t+f,rx9w.6 /p+   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 jo4 mf3 x;3wiv aj)b0nu1mrny: gun e6:a6 k:dMV? v : minwj nx3)aary;mb634u 1jo u6 dgvk ne:f:0=    c

  What is the speed of an electron whose kinetic energyyqo3zq9gwxa2 *rg + +g np+1us is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television sn wfmky a4qqc5+;4e: vcreen after being accelerated from rest by the 2kwvfe 4 :q+4cn;qya5m5,000 V of the picture tube? v =    c

Two identical particles oecw./bil5 m t- k3dxl8f 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 pzoiw-ed yq9(9 roton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the motu4h8t g))ha zmentum of an electron ($m=9.11 \times 10^{-31} \, \text{kg}$) whose kinetic energy equals its rest energy?
v =    c
p =    $ \times 10^{-22} \, \text{kg·m/s}$

  Suppose a spacecraft of mass 27,000 kg is accele2teb: 4rr/oserated 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 mome- )pd/hl ordlxx* 5sj4ntum 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 nucleusexubt( k1.fftixr h 3.) s:+sj, $^{241}\text{Am}$, 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 mol.hi0aa ;(2 dbjgrb6e mentum for (a) a particle of nonzero rest mass, and (b) a particle with zero resthr;(ad ie.2b 0balj g6 mass.

  What magnetic field intensity ijsnd*u. n9 .b4jsr 5hys needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's res.j s5 n.h4s*rjn9 udybt 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 h/y2n+/ aez d is(.qnyrespect to the Earth) observes a meteor come from behind and pass+esy2nd/.a zn( qyh/ i 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 speerqkb j1e 6p8hm4vz c70d of 0.50c with respect to Ea vp8ke670q1 mbr jcz4hrth.
(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 0.71csg;ot vs 4u:l:. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Eartovt4;gsl: :su h 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 seeskjfh 1 *l6bb /lqx*, .eez(byn an alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), k fbe*.nblj bel*yq/, xh 1z6(overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite dirtz s(0uctt*y.. ihrg9ections. One travels at a9u..c*tizth0 r (ytg s 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, rocket B pas,nr l.u8bma4sun)lj )ilu8 (l:dk q g.ses Earth moving 0.95n.8lqaudu .(rg)4isl ,bj: )8lulnkmc relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proximaz.xdgd7 bem/, 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, anything traveling faster than about 0.1c is calledcp nnd,-)lu68mgg-* mt7. i8v ofbbrg relativistic - i.e-bgb *i-orl gn)76t.v8 8,nmgumcd pf ., for which the 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 speed btbklrbwpsw -;,/ ce-(x7ik;oe;c2m $v$ of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference $c - v$. Such speeds are reached in the Stanford Linear Accelerator, SLAC.    m/s less than c
(b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]L =    cm

  How many grams of matter would have to be totally destroyed to run a 100,u anu;+p7rhx-W lightbruh;xu ,+7npaulb for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce h9l s giv-5l;ban electron and a positron together? A positron is5s9lhl;i bg- v a particle with 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 1js x0lt zvzj(il)/e( at 33% the speed of light collides head on with a positive muon traveling at 50% the speed of light. The twsxz) /jelt( zv1 0jli(o 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 neutrin-l*p xu*w7rl4;ml kmho. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at reu4*wm7hpx- lr lm ;lk*st. KE =    MeV

  The Sun radiates energy at a rate oft l6*whnn ojfb53k2 ;c 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 spm/zii .t.;qbtp : 7itsqe eoyk-6 s)g6eed 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 b h+z5yt o70bpuj 8mkr:fn5 1vvreak a helium nucleus into its 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. (This energy difference is called the total binding k1fvhzp ro+:umv8 5y5j 0btn7energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage iwmj :x lwb51oeseliew+2 8f d4f 1pyj-c8y1/yncrease in the (relativistic) mass of a car traveling 110 km/h as comparedw owed1c/yy +im8e-j21pj lx8s1bef w4f :5y l to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in the laboratory, are moving towardqw/- 2,qd;l;zfkdt2q:jk ya g each other. Determin2gk ,ft:2a y ;dk dzlq;-qj/qwe
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a particle with momenp f2a jd h,405wdf.wfytum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterpri9 snw0/sa+cvmu/cpe7se obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is app9sm/w7cec vun/ 0p as+roximately $5 \times 10^9 \, \text{kg}$, 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 kinw,etj e5s*, dta(l uh4 ;pph9detic energy is greater than its rest maseh(t l9 p5t4djhupd,es,*aw;s $m_0c^2$ 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 phy,hwr r -ou7v/fsics believes that he can 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 doeshurwf/ 7r v,-o this fit 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 to form twoavdeatu*be q5w07 /s6 kp5/k y moles of water, the energy released is 484 kJ. How much does the mass of the elements de5q v6t0ye/kb w5 kuea sd/a7p*crease 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 identicaxgfu i7v/z-ym4cm+yq+zj;zbe s9,:5on y 4phl particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's oh4;9zzq+-my yefu p jzigm7,vbnsc45:y x +/speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75ilxd5; hwi8.quoav* l074a gjurs ,i 6c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in 23 min 6ux ;hq.r *0w giid7lsi lv,a8jua54o.
(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 Ey9p+r,m a1y-y( exnoh arth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the sperp 1x,e-nya +ohyy (m9ed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occupan+ t i olrgo0x.qto(--nts would like to travel to a star that is 25 light-years away at 0or-x .(otiq+otgln- a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.w4 jchtm9idktm2v7dh 89o5 e199c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (abjid2hm 49c8e5 k 9d7tw1mhotvout $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinity of a st7rhuoyoi2-x,p-. oyw ar 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than - o-xw2.oy7,rpyouih 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 stih q e8pnd1rb5+ 1ei1sgffness constant i5ibe81sr +ngp1d1e hqs $k=48.7 \, \text{N/m}$. 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 mar8nhve h2j; q3qdk6c. ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.