You are in a windowless car in an exceptionally smooth train moving at constant )x 1apaojz0u)g /g8pz velocity. Is there any physical experiment you can do in the tra8pzg z u/0og a1)xj)pain car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the k*linwvv4h8;;j 9 l0rcghti i z64e:x experience 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, thinkili8htv z r:lnigej*c;w49x6kh4 vi 0;ng that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy ball striumq9 .wmxgqb* : -ur.1ajxd)aight up (from his point of -* 9q x1xdr)g : mwub..auqjimview). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go arw0o,sj b+ qa6, 6 socean ew4lx+gg05zound the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view j0 4eb+gqwaw66gnooa0 x,l+5zs,cs eof 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 star, at whq;etn 3a 2 9*mvkf(dm-ko 0bexat speed woulnvk e9* -fdx0ko3 ;ma2(qe tmbd the starlight pass you?

The time dilation effect is sometimes expressed as “moving 6ef- ac6)xp8n4w ixpqc3 rfl xn 759anclocks run slowly.” Actually, this effecan8r 9w7p6nf l)p43n6efiacxxx q-c5 t has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually evyhx5z+3kttb;0g ym:p ,q,2q*r ngnpasses more slowly in moving reference frames or that it only seems to pass more2tqz, gyyt ,g3;p5q0k +xrhm n:vn eb* slowly?

A young-looking woman astronaut has just arrived home f )r,eb(vae bk* 5xh j(vfknu76rom a long trip. She rushes up to an old gray-haired man and in the ensuing fbjx,)vb au*5h7e( 6(krke nvconversation refers to him as her son. How might this be possible?

If you were traveling wzz3)ieyet(/ twn 87e away from Earth at speed 0.5c, would you notice a change in your heartbtie 3z/e7(8wtz) newyeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at orddheg-5z d 1.sqinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would ha:+ -3- j(lc0tw t2laops ihbqcppen to the relativistic predictions of:w il-tjp 3l -q0cc+hb2toas( length contraction and time dilation?

Discuss how our everyday lives w :ip bm3xi3nu0ould be different if the speed of light were only bux3nm0ii 3p:$25 \, \text{m/s}$.

Explain how the length swq -1f7r-t8nj7y zpvcontraction and time dilation formulas might be used to indicate that c is the limr1f-8vtyzw 7-np j s7qiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen baz2m8lh(5k psw. */s pp jwov-y Mr Tompkins, for whom the s( s /z p.p8k jow5l-m2wp*havspeed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Doesatq9tg -1 b+s -oze.fzybay8. this put an upper limit on the momentum of an el9 8y so.-ea+-zyq1gt f b.ztbaectron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass aq2pxv1cud bve( b23 qik4cv 7m*8hd q)ttain 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 s8u :fmt2iy9*qw m9 p/tu-bvnenergy, does this mean that a spring has more mass when compressed than when relaxup:/n-99mwib tsv2 uy* fmq8 ted? ----待选择----yesno 

It is not correct to say that "matter can neitherwal0 v1g4pt v nymi689 be created nor destroyed." What must we sig amwyp16v4 9t80 nlvay instead?

  Is our intuitive notion that velocities simplrx+nwr /u* xemtk)r)zx ((lw:y add, as we did in Section 3–8, comx:)*r(/nwr zux wm r e)x+t(lkpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its lenlfa3 gw kt,17ugth to be 28.2 m. How long would iaf317wlk , ugtt be when at rest? $L_0$ =    m

  A certain type of elementary particle travels at a s 7 *07jbf er99nccgacopeed 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 depe s :7pjg--h*p gmve:jw0a1mn7n)gfvdnd on the factor $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ according to the theory of relativity. Evaluate this factor $\beta$ for speeds of:
(a) $v = 20000 \, \text{m/s}$ (typical speed of a satellite); $\beta =$  
(b) $v=0.10c \;\; \beta =$  
(c) $v=0.20c \;\; \beta =$  
(d) $v=0.95c \;\; \beta =$  
(e) $v=0.98c \;\; \beta =$  
(f) $v=0.999c \;\; \beta =$  

  If you were to travel to a star 125 light-years from fc7f;ru zkj*a1er -:dEarth 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 measured to b r :/ tdk37sa,yyepgt)e $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 lisw0ogu9zx /)y8c;am gght-years away. How fast would you have to travel so that to you the distanceo8axw; 9zgm)/c suy0g would be only 35 light-years? v =    c

  Suppose you decide to travel to v9:vki os)- 00zzjp uw3,jdkra star 85 light-years away at a speed that tells you the distance is only 250j)-s zw9 ok,0j zv:pid v3ukr 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 froma t;;y2 g/w)hw7lm hba the 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 i)p ewq*e8n9skoy1 )tvd8/jo had just returned from a 5-year voya9 /ek)y*d nvi18o wj8qot se)pge while 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 aeopebm 9)85 saway. How long would it take a spacecraft traveling 0.960c9aep) oesmb8 5 to 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 a speed of 0.660c. Izlyc91 mo 9f8ct is measured in your frame to be 4.80 m long and 1.25 m high.y zc9l1c89fm o
(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? The a8mjn58bm yk(n verage lifetime, at rest, ijbny5n 8m(m8k s $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum xc:rf p4gy3hb z8 wv am;m*t9;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 i4ua ed1br(s c3b pa-6y z+9xvcts rest mass? v =    c

  A particle of rest m4m-hbcy .(h14fdqxnps5oq2 pt5 ro -wass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelwlengsv ; 0/x/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 that ac;hjm we2- dlbd./v,xzcelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction reqv6voi7u0/6jpvdo d 7 puires $4.82 \times 10^4 \, \text{J}$ 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 known as fission ial(y4ohfg ( :rtww,9d n a nuclear reactor, the resulting fragments have a tot4wtf y agh9d:,rw o(l(al 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 inxu.ern) sd:zib)rgh f*c3k9 - 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 of a proton in r xu nxyi)+dmr: /)dw*$\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the )c7,8jfbpgrgUnited 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 conv4m d;+r .m90ffjy +tb7xxgzzeersion 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 rm q27iuz61 q/dxy ze-(nr)fs gest energy? v dq 1 gn(qe7s - uyf6)zx/rzm2i=    c

  At what speed will an object's kinetic energy be 25% of its rest en/q0xg bkgg,5 6bod5sdergy? v =    c

  (a) How much work is 9jlg/ d9ihy gu -zh+uv*2a ng*required to accelerate a proton from rest up to a speed of 0.997c? -9av/y* jun hlgg d*guh2+9ziW =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and/ujlrn.p :t8 -h *lvvp 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 (thotrp no3x uda6l+i71 azi+: p.at is, its kinetic energy is 750 MeV)?lno++.:xi16zir a dp 73ou pat    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potenti8(cujz* qp jl7sfg/q .9c:vvnal difference of 105 MV? v :s78jc/f.pqcnvjgvz*(q9u l =    c

  What is the speed of an electron whose kinetic energy is z 904g,c .y r3nzzp+z2yq att(r;sjzm1.00 MeV? v =    c

  What is the speed of an electron just before it hbt;i:q e1j y1jits a television screen after being accelerated from rest by the 25,000 V of tqi1bt :y ej;1jhe picture tube? v =    c

Two identical particles gr/cfi2,ga(qen/, o kz a/fx4of 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 aagfk:zj4br6 h zdk4)srxgep 7,ld6q,b4 )v2 y proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed an0w4yzr0 fy 2v*zjpc i 4n8vp +(*vvzmpd the momentum 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 accele e9) jynr :at:n5cgddlp(kc77rated 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 a4m(d r- *xhabwg wbyk+9 xa*;qnd 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 nucleu*g7 dvh4ech o4ra+7bl 06ay lis, $^{241}\text{Am}$, 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 mom ;xq(s.hteo;gesgh-ot(8e ) d entum for (a) a particle of nonzero rest mass, and (b) a particle sx;d8 (hhqes e)o g;(ot-tge .with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolvi-wh e le*wp95td(/qnyng in a circle of rhqp9 d -n( wl5ey*t/ewadius 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 the Earth) observe:3 :4litnbwef56t njl s a meteor come from behind and passeblt:j63nw 5li f4tn: 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 .*glki3u-q bs ma7y 7cwith a speed of 0.50c with resps 73lmkbuaqc.-igy* 7ect 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 traveling at 0.71c. A seco*)fd btff /;kand spaceship leaves the first at a speed of 0.87c with respect to the first. Calcula*t) /d fb;kfafte 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 a0z-lkpb(1z tc+ota eo*/jc/.fd-m yipproach at a speed of 0.60c. The Enterprise comes to the rescue (Fig+ m-ozlyibo 1(t-cpet / c*af.k/0jdz. 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 bd* 8 k/u)a.pro c7nlar.gi:q directions. One travels at a spa i)qo7rb 8.* .n/dgkacp:rlu eed $v_1 =-0.60c$ 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 0.75c9r h/e l1dpbaah-x bki rdz 7*q2+0.zw. At the same time, rocket 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' a7 a92/kbq0bhz*dwh xp-izl.r er+d1=    c

  The nearest star to Earth ik,.nm,i shgxn5gj5 wpg73 /ufs 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, anything traveling faster thay.;9u;n 1cnh 2aqokgs n about 0.1c is called relativistic - h.2unosn1g9qay; ck;i.e., 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 a 6 j6 hpij8dpmfkjul;7n)v- )hje*w1 $v$ 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 wmic, r4l4xd+ would have to be totally destroyed to run a 100-W lightbulb f ,dx+44wrlicmor 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount opm+-i gf gq(m*f electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass a+fm(p gi*q-g ms 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 traved80x9jqjut,pb bd k).ling at 33% the speed of light collides head on with a positive muon traveling at ,p9 t d)du0bjx8bjq.k 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 decay into a proton, an electron, and a neutrm 4iys*2kho3s l+tzy .ino. Assume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determinem3 tssky.zi+*oyhl24 the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy atpfd6n62 l/pfe 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 cid30an- bm,w wharge 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 tov7)-wilq xvv;e : b;nt break 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 callednvv-e:wx vbi;)7q t ;l the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the sy2 / wxzn22nyb5bz/jmaq*5 b (relativistic) mass of a car traveling 112/22qjyy/snb5 zx n5*b bw amz0 km/h as compared 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 0.93 ttn, uiv8(7(zs+o rbz5c in the laboratory, are moving toward each other. Determine (z7rbvn soi, t(z8+tu
(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 wiv6q-ut8i esb9*wi r .g+jtww9 th momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power b xow+72i9nih sy combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the9in+ iwsoh2 x7 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 k+bmbo/w ya.; dinetic energy is greater than its rest mass .o;bm ydw/a+ b$m_0c^2$ 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 cgi 42j sqke2hx .(+hr7evi0fvan fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the ba f.724+(kixv jhh2gei0 rqes vrn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydp;l9kwxnk ./p gl.1l:mce ,bzrogen and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass ofz1;c e.lk g.:9wp,kmb /lnlxp the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are created, traveling in opposite pt 3m)jea*d+yp5b np-lqt)f8 directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particl-+tpppjty)*5nf 8qeal b3)dm e? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earte+nt8a uxi.gde.ux ( 4ataj,4h measures his ship tttae.ngai(a4+ x eud,4u8jx .o be 25 m long. On 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 speed of 0.85u7v exswg 01jhp7i61z4o (n0s wu dj.szxi5: kc away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser zh1vux 6x:o1gs sj5 w izd0e.7u4 sw7nip(0kj beam?

  A spaceship and its occupaievg0 v.9pwn-pm0 rwwk8jw28 nts 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 engir 2gem0pn8p.w8 k-9 w0w jvwivne 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 0.99c. What is the spa) vy(u(3vo)yvdyj:k oceship's kio j)y(duv)vk (o:v3 yynetic 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 trge hmaw i *.5.p:m03ocdf- prxavel to the vicinity of a star 6.0 light-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 bwi-:h0 e. *amc .3pmdoprgx5fring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillat)e3wm f1w. sgpks9x) des on the end of a spring whose spring stiffness constant is me9. w)xkgfd13sw) ps$k=48.7 \, \text{N/m}$. 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 mao,r ia 8z d2f0spz rbhjc9(-/wss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.