You are in a windowless car in an exceptionacgdx iq1y) k:i ((hd7 kufs9s1rm,i;elly smooth train moving at constant velocity. Is there any physical experyq1i7kd ,1; i):9cg (iduxesf( hkmsriment 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 a ont vdgz.:/ *bb+qr/mt a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp ovrqong*.bt+zd:mb / /n 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 movinpokwr ms ci8o vq+/t- 2-. bru(0.oajjg railroad car, and throws a heavy ball straight up (from his point of view). Ignoring air resisc8 or br.u mitso.ap vwok0q/+2(j--jtance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to sa 1s(yhfhbq(h2 y that the Sun goes around the1h(h q(hsby 2f Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a sywo8 hx)4ha2)(j kda star, at what speed would the starlight pass (w)84kasx 2yao)d hjhyou?

The time dilation effect is sometimes expressed as “moving clocks run slowly.; xi2yyp.1 o3kq yid2b” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then do2 i.ybq i1;p dx32yykoes it deal with?

Does time dilation mean tpd5b :r ; oano/7/zbsnhat time actually passes more slowly in moving reference frames or: 5/zsob d 7n;rbon/ap that it only seems to pass more slowly?

A young-looking woman astronaut has just ar +z)6tzrs-f uhe )ct8erived home from a long trip. She rushes up to an old gray-hai8 es6ucfhz)e- z)tr+t red 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 p+ o/l)roqx; dspeed 0.5c, would you notice a change in your heartbeat? Would your; opxdo/)q +rl mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occuucp.fqhro0 -;r at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happenf i2 df0zzle0) to the relativistic predictionsff0dz )0le2zi of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of light wer+b 3t h;pbfi y2u:mnr7e only r tmby +iu37 ;hfb2pn:$25 \, \text{m/s}$.

Explain how the length conc0d3bf hm0 mso e4kgjbf9,-d0traction and time dilation formulas might be used to indicate that c is the limiting speed in thc jmb-dkohsdb0f 03,e 0 g9fm4e universe.

The drawing at the start of this Chapter shows the street as sc;q+y n4r(ah oeen by Mr Tompkins, for whom the speed of light ir(nqha4 ; cy+os $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Does this puvfv-u8j(sj6 mt an upper limit on the momentum of an electron? If so, wju(vj-msfv 68hat is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass mq-k q2yxder:w;9 )ocattain the speed of light? ----待选择----yesno 

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

  If mass is a form of energy, doe ix;2 r9xtg/ql(m aku)gr3n ;ps this mean that a spring has more mass when compr p/k9unim3at(lg);r2r;gx xqessed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created-zur(hlz0fz, y-aa . c nor destroyed." What must we say instel ry-fu0-za(zcz. a ,had?

  Is our intuitive notion that velocities simply add(bj r2p yh*4 :bh1pmjk, as we did in Section 3–8, completely wbjp 1*(hh 42pybjmk:r rong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. Youepul;p+aiiq- ykn01 2 measure its length to be 28.2 m. Hu; p-epkq iln 1yi02a+ow long would it be when at rest? $L_0$ =    m

  A certain type of elementary pafjhjf;;r( n*e 2vxgu0, )lxlg rticle 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 theluy67 fz6 mmi) 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 temy xat8go q2 b ol:q3/k*h/m7o a 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 average lifetime is v(x1fbha(a y)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 fast woul rawf 2 xjr -jjqi5k0e*t- :dr+kn82ncd you have to travel so that to you the distance would be only 35 light-years+*jer t2x nqjikdw n:r2 0c 8faj5kr--? v =    c

  Suppose you decide to travel to a star 85 light-yean**s3s m orr5nrs away at a speed that tells you the distance is onl **3onr smrns5y 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 Eart3w -.1tnknlilq;-sxu+ins 9 rh 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 j86kjqec u )fv )v1w48jydi/sydhp : d:ust returned from a 5-year voyage whcyd8 )vq 1k)jsf u e/wpyj84d:dhiv:6ile traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. How )k0usmtnvb6n-i8 2vhv4ndy,6izh 5 klong would it take a spacecraft traveling 0.960c to reach that stkndmu-i)ihh 6n,0v bvyzks245t 86vnar 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 a speed of 0.660c. It is y-:hivb +fy *o9c (dgcmeasured in your frafdcgivy y(:b* o+c- h9me to be 4.80 m 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 before it decays? T/l ad,x4c 7ekzv8f;f rhe average lifetime, afce fvlxdr4;a,zk8 7/t rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travtgd0m w55w.6qu+ jcwuo6)zim eling 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 mass7w qw4:a)fs pt? v =    c

  A particle of rest mr vrs/48-p+ f; iscqgtass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave/o959y ls+u aacm i;ivls 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 acceler,9 fnu.pl,mcxlkzt3. ates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction re( y ds/k3 ui1wya/tg3oquires $4.82 \times 10^4 \, \text{J}$ 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 a:*p(ow vzs-w lt rest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments ha:ovw( z pslw*-ve 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 inf2ki(0ufsph *fyxsg/h7j: r1 $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a o4.03 )g k5fstimn njkproton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consu;7aprrjm9 q2bqt q 4q.mption 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 obtaine*4 u/(ii k(pmt blx0jud 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 res yzt84 nfzi2njxfcd *4h 2oo87k+sdj3t energy? v dfjy kn jxt847 zo*i4+d8csfzo223h n=    c

  At what speed will an object's kinetic energy bj54 zqva8fygxc ) v7t:e 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest ul 7.vvhqt(x;uw9l( y jp to a speed of 0.997c? .l; u7xwv (vj(hlt qy9W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and/zc3b p4z( +5.m fzrz6s yfsod 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 wggi .c4m5cv- is, its kinetic energy is 750 MeV)? w.c5ggcv4-im   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MV? x(vx1:vxjz c)v v )x c(1vx:xjz=    c

  What is the speed of.hz/gv;41rdxft y(n4 dpr0u c an electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television sc* -a*gwtw(vhr1wd (1b)i webb reen after being accelerated from rest by the 25,000 wt-h*wg i1be*w dw( v)(bb 1arV of the picture tube? v =    c

Two identical particles of rest v.ne(zs:f w/b5dz m;g7xty4t 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 prp821dj y7rjgv/d qkw*oton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentc*8:xr,qb dsuum 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,hrjd9trt gsp s 5m2o1-bs8p5(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 fqa9zi 6tb,y7)xec7l.; hf yn8zyvh 1 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, e 1qniz +w/6e j;ph0ls$^{241}\text{Am}$, 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 kinetid ,0v h.kr(we7 k6wtm*,26wu ejgpv hlc energy versus momentum for (a) a particle of nonzero rest mass, and (b) k,whtpl6*.vr dh(6uw2we 0 7kge j,mva particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving inrv1by/o:ehd + t/ s1qn a circle of radius 1.0 km (at, say, the Fermilae s1/ :bvdqt1y onh+r/b 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. y-dmt7-ibp4d50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. Ho4-7myddtib p -w fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each whq /fs, o7mit(/b5y ckith a speed of 0.50c with respect fohc/ibk s5/y (tq7m,to Earth.
(a) What is the velocity of spaceship 1 relative to spaceship 2? u =    c
(b) What is the velocity of spaceship 2 relative to spaceship 1?u =    c

  A spaceship leaves Earth travelin v6n +u9 z2qoh,-u ;w0pzcjgwcg at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calc,9wg2jv qzz;c0uu n6h +owcp -ulate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approach at a s9,ytul) (wzc5up h/b .ee9bfjpeed of 0.60c. The Enterprise comes to the r (l tbpj9 be.9u/fw),ech5zy uescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite directions. One trx03 v2e3yol/. ak li6-ktxtqoavels at a sp t xk.-x 3lo3ye/alot v0ik6q2eed $v_1 =-0.60c$ 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 aau/)jvmlqp 1( speed of 0.75c. At the same time, rocket B passes Earth movinmap u/lqj)1v( g 0.95c 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 Proxima Centauri, 4.3 light-yea ::v1qieckxx 6rs 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, anythin))b jg uh2( xwl3aec8vg traveling faster than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant l3 2wx)h8u jge bvc()aeffect. 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 jm36z-(uwrpb $v$ 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 h 0/id(dqc) xciave to be totally destroyed to run a 100-W lightbulb for 1 yea0d)icx (icd/qr? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is n f7. i .g2lre1(tbhcsn +xxlb.eeded 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 els (1 r+.l itglbxxe7.fbc .2nhectric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collides head on wi /kx4xguga9 oo70e5vjth a positive muon traveling at 50% the speed of light. The9kv 0g4x aj5gox/7uoe 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 electroxa). ahr6fhn q 8saj ,ey(3db8n, and a neutrino. Assume the neutrino's rest mass is zero, and the y 3x6(hjas)fadb 8,qaen. h 8rother 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 rest. KE =    MeV

  The Sun radiates energ . hcgdf)do2 (3rvtx)vy at a rate of about $4 \times 10^{26} \, \text{W}$.
(a) At what rate is the Sun's mass decreasing?$\frac{\Delta m}{\Delta t}$ =    $ \times 10^9 \, \text{kg/s}$
(b) How long does it take for the Sun to lose a mass equal to that of Earth?$\Delta t$ =    $ \times 10^{15} \, \text{s}$
(c) Estimate how long the Sun could last if it radiated constantly at this rate.$\Delta t$ =    $ \times 10^9 \, \text{yr}$

  An unknown particle is measured to have a negative char/*mxl+bwp )ap f:aapo tv8 49kge 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 nuclaq+ fat9sr ;r/eus into its constituents, two protons and two neutrons? 9tar;+ r fsq/aThe 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 a car traveling 1qcql*,nc n f7gx 9s -tc3bd+1j10 km/h as compare t*+1xlc cq3sfqcdnbn-9j7 g, d 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 laboratg v;qr6ye a(w3;ntf) ,yrio5jory, are moving toward each ot iro,5t w3aj fy;g(rq)y6env;her. 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 particle with momenm.z 6 ,k7sx3lno k4gattum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combiningis 4bc cadc;/; matter and antimatter, achieving complete conversion of mass into energy. If the mass oab4 /sdcci c;;f 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 itsuyxdr e;,ho; 2r-k3v u6xxk, t kinetic energy is greater than its rest m vde; hr62k ,xkx;ru3 toyu-,xass $m_0c^2$ 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 azeclblz 5fu;2d x(9 :g 15.0-m-long pole into a 12.0-m-long barn if he runs(f2z9 : eg;z5lxudcbl 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 than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two moles of wag + der(g*cg8eter, the energy released is 484 kJ. How much does the mass of the*8rgggde+ (e c 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 tc(n8 zn qx2/brdv xjtr6-48z)euhp6pd d,r9awo identical 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 speed relativect2xpz,89 r addb8rxv-)r6jz( u / n6 ndhepq4 to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth mea m; kt sre-8m17oyyyv tw77sf1sures his ship to be 25 m long. On the ship, he eats hismrfywo k-yt; m1te187sy 77 vs lunch in 23 min.
(a) What length is the spaceship according to observers on Earth? L =    m
(b) How long does the astronaut's lunch take to eat according to observers on Earth? $\Delta t$ =    min

You are traveling in a spaceship at a speed of 0.85c away from Earth. You send le vm++g+imv)a laser beam toward the Earth traveling at velocity c relative to you. What do observer+l iv)egmm +v+s on the Earth measure for the speed of the laser beam?

  A spaceship and its occupanu*b ,9nguzrm:ts have a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to energy. How much mass will be converted to brug ,z:9nm *uenergy 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 spacayn8/js . qq-lv/::yqcf oot, u+2rqleship left Earth at a speed of 0.99c. What is the spaceship's:oyqaq/l,yo.2l-nqv+/8 f u:q ctjrs 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 star 6.0 ppdw1 e;23ns mlight-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? mne 3d;1 psp2wu =    c

  A 1.68-kg mass oscillates on the envq y,f6;4vw36-vqfo (memuund of a spring whose spring stiffness constant is q6eqm;3fuuv-vn wv ,m yf4o6( $k=48.7 \, \text{N/m}$. 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 ma8y xu4y.mra5hr+h u0q 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.