You are in a windowless car in an exceptionally smooth train moving at-ggk;kr3/ll 6mhbtk (w-q- x s constant velocity. Is there any physical experiment you can do in the trbh;-3g 6lt(- sqk m krxlk/-gwain car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light whe2tia53 qvs en9n, out of the corner of your enaiqt3 v9s 5e2ye, 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 railroad car, and tadbgw 1a zs4cqa;2lr.lspi*qf/ df.lro/ 5; 9hrows a heavy ball straight u5 s.dblsaf4 l*;r d lqapwq.;o f92c/1g zai/rp (from his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to say that tfbei ph.0k+1qhe Sun goes around the Earth? Discuss in view of the first principle of relativity (that theree0kq1. b h+pif is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a star, at what speed h:ar ru bq0fn7j66k9s would ther0hjru 6 :fqs67kan9b starlight pass you?

The time dilation effect is somo ,drwdxedhnm229cd :/-d. tr etimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motio,c.:rdtdd 2rm9owdd xhn2- /en affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving re2- shuwy-l4nof1lxs8 ference y-s2 4flh-1o lu8ns xwframes or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a lm) o ,m4u vk5)kt9hodqong trip. She rushes up to an ol9ov m 4)5 tqokmuk)dh,d gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice a chzi ik-sxbjd nbq8g*+6r .(k)d ange in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about yzi-rb8n s dg )*xi(qbk6j+dk.ou?

Do time dilation and length contract9a:7 g k/ed+jhy(a uinion occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happe5ltd -hu94x ygev4 ab:n to the relativistic predicthty4xv-4: 9g a bled5uions of length contraction and time dilation?

Discuss how our everyday lives would be dif24cszxko0u9b nw;t 4 :5 olfwiferent if the speed of light were only w4:0unf4 kz2sxow 9lbco;i5t $25 \, \text{m/s}$.

Explain how the length contraction and taa2 zu 8ylqsp5v)iop-5r0oz 4ime dilation formulas might be used to indicate that c is thez 85 o0q2oa4)y- alzipprs5vu limiting speed in the universe.

The drawing at the startr, kb1a7; )(ooi db5xnv0v bjx of this Chapter shows the street as seen by Mr Tompkins, for whom the speed o, x57oxa )b 01bk;ibonj rdvv(f 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. Does thi;)sp )ox.d hjjp 0bs6ys put an upper limit on the momentum of an electron? If so, what6x phb0. dyo;ps )sj)j is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of no(qv3tstthfo qheo:9/ - z9, )do 1swicnzero rest 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 energy, does this mean that a spring has mty 1vf(x;06o on4u gh3y rn/zmore mass when compresseyfy m4;/nu ot0n1ox gz(r3hv6d than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nkep2o(b 6dm(wyj20k fxt8 -zyor destroyed." What musyyz0 ep2-d6k2t (km 8f(bwo jxt we say instead?

  Is our intuitive notion that velocities simply add, as we dru86;nch 5/z(t 1 lc lzzvq4yjid in Section 3–8, completelyzhj/yv46 ;(llcrz5 ctz1 8qn u wrong? ----待选择----yesno 

  A spaceship passes you at a sp xq(i,z5v sb ( )7ggpjzrav6:leed of 0.750c. You measure its length to be 28.2 m. How long would it be qrzg z7g s():i(bv5jlvxa6p, when at rest? $L_0$ =    m

  A certain type of elementary particlnhr*mip7,oa3buxm4 4 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 factorc9vxtf5z.sb k1mp79h $\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 5rd9uheol2 c*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 life tr, 0zz)1f0lrbdwf-h time 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, 2h4e3u c.- bu *fyk a9zmerif1a star is 82 light-years away. How fast would you have to travel sozemf f. yk2eu9rh1b3*icu- 4a 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 speed thatv 6,fo8 jpka31tq ze9y tells you the distance is only 25 light-years. How many years would it take yot 91e fpjvo6kyz8a,q3u 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 t/n4vqz zh 1cp0he 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 had just retu/mvr t(9+l9no ub,pjp(b lr.zrned from a 5-yearmb/ r,jt 9vlzp.lnupo((9b +r voyage 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 away. How long would it take a spacecr4nu4jyg7)wr gaft traveling 0.960c to reach that star from Earth, as measured by obser74 grngywju 4)vers:
(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 4awfn1,ihddt9( +fgu "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frameh+ 9ad(u1nfd gi,w4f t 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 tfhz0qw +) bftg2 ici8u(-s 1tvravel 15 m before it decays? The average lifetime, 8g 1z0+cbtiiqtfu f-h )(w2vsat rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling atl9rz;amm :0d w $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice its rest q yhq*9lp, y*tmass? v =    c

  A particle of rest mass to3q m 0omjx(0$m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travel zkmci-v+dacz f:(* -rs 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 t: ja4fa1 ,p(fzwt asp4hat accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction rvjz+t28cn idgx8xoa; 9hhky /)0r(umequires $4.82 \times 10^4 \, \text{J}$ 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 proc9oz,h;n 1-nb ervwnh8 q a5os0ess known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the ph1-8 0nevw aqons; r,nho bz95rocess? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an e7lhhuc4;94zez3ayx 6m0 u (m exryh*blectron 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 of apzwz7dzn .:4b proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the0ilsu9we d-2a6p;fev1d7bise p 7p- e 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 of *x oz6m/dl p ;5un c;kktd6nh31.0 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 r4jw2-ho dkzxeqv5c370vbd du.la83rest energy? v d-jbe xuv o4dc2v3h.03zldqw87k ra 5=    c

  At what speed will a; .d .x6nsjn8vz 2pybzn object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up tguc*.iw dg0c*a ve 08do a speed of 0.99c.g* ve0dcug8da0 *w i7c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy andg 9kfdt2nmhd9g 2b0vn.n6c)x momentum of a proton traveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that is, its kinetic energy is g + ath4) gmfy.a*jl,v750 MeV)) h,ag j.yl4mvtf*g a+?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a protocwai5m)r6u/qv+0g *pgtt5y f :u+ex5o a6oye n accelerated by a potential difference of 105 MV? v = futq+ *r5u /)yieg+5ta eap56o0x g vwmy :6oc   c

  What is the speed of an elec/0t qhsl 2lph6tron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screedmklobfyz* 6 +kyt1/-n after being accelerated from rest by the 251o -b+kytf/lz*ym6k d ,000 V of the picture tube? v =    c

Two identical particles epu/6h unatq1e)x8oi0id: - r 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 proto+mdhwsy a.rch dp.(b1g j*l2eifm v6 r*/i+ (qn ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momhn1 l8 e1sj4./d tvedyentum 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 accelera +a;chzu2fg q5. oxb:lted 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 a5qde 8.rej us1nd 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/ gtcishuo ;n7f o0yi/559 onzs, $^{241}\text{Am}$, 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 o alsbd6 ogst1)8 x,6efor (a) a particle of nonzero rest mass, and (b) al s6bs o6at81xg,deo ) particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV (p+onvh a mu2i/5xlq xb48- bkprotons revolving in a circle of radius 1aq uib (ob/xnkv58+ lx42mp-h .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 (wib b4ozax2c0d5d8v7we th respect to the Earth) observes a meteor come from behind and pass her a 5d0bzvde2 4ow7 xc8bat 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 oppou cdgz1;4,q4v1.anrmv6-gw jt5tfi wsite directions, each with a speed of 0.50c with respect to Earth. frg.qtgcm a 1 nwv54ud;,vt6 w-iz41j
(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 trave*u m8c,(dpj yqling at 0.71c. 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 Earth if it is f8qcd(up m *,yjired
(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 an0cx3-xcky)*0wz 93ptbeoyz b alien vessel approach at a speed of 0.60c. The Enterpriseyybwp30 z tobx) 3ckxc9z0 -e* comes to the rescue (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.3l)am gqe /dw7 One travels at a awq/3g d7lm)espeed $v_1 =-0.60c$ 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.7l)oqunsb+e xz1v /z passes Earth moving 0.95c . 7xzns)qzl+ /uve1obrelative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Epuy7m*t i 7.tvarth is Proxima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling fa90;fu hgdkt+:,u ghjw -d. gjbster than about 0.1c is called relativistic - i.e., for which the correction using special reladkh9wut.hfu:j0gg; +bd -j g,tivity 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 speedq; jb)xj 6xdv* $v$ 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 yepzhed*y0 fp;p8x2 +3fygw + totally destroyed to run a 100-W lightbulb for 1 yffhy8+ p+3p zpe0d ewyx2 ;y*gear? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagrxl(qh*s1 ) xunetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, b x* xs1hlqr()uut 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 head on witif lbmp79 -rc)w5kwy /h a positive muon traveling at 50% the speed of light. The two muons (eachfy9-l5 wc/r7i)mkpb w 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,5rcl 5 kqbtl+ 4mks4d,/b(9cr-oj vi k 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 cover. Determine the total kinetic energy shared among th/r ,dlq +9kc tk5so - (4c5bjvibkrl4me three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate /tx/lb zp9ythb, 5,tu 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 and1h( kyanss9jyra* ik 57f4o8l 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 nuy-ng(c 9q yhhn4/e z6jcleus 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,-y(jgc yzn 6 hqhn4/e9 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 (relativist4gqv/eovq ) xfv934sfic) mass of a car traveling 110 km/h as compared to at rest? [Hivxq vq4fs )/eo 34g9fvnt: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.9x78.j ji5,z5rioy8ro)6pb evoj 1 awo35c in the laboratory, are moving toward each other. Dz j1ya6vrwr5xoeo8.ii o p 5o8,)jb7jetermine
(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 ukv.vif6 -mj gi//8 bdparticle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterpqm)qf7zb *kt0 rise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise i0f*mk qt b7q)zs 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 en.vl:ckrgrl 8 7qx :t1yergy is greater than its rest mass vq 8: 7rltyk1rxclg: .$m_0c^2$ 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 fitf1r/gd )q) bpm 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 runnin)bm1rpg)q df/ g the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydroge9r. .bxc5 kwbpn and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in this reactiockwb bpr 5.9.xn?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
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 ib - 4r/b8srpmcn opposite 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 prmrbc 4/-b8 psarticle? u =    c

  An astronaut on a spaceship traveling at 0.7 1tdf5r+go7ljmg,u biel9i5 (5c relative to Earth measures his ship to be 25 m lll,5g 9+f5ug(d1ioeb mi7trjong. 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 0.85c away from E6ognro.07/tn pc ly 0tt:,dyrnu.3tfarth. You send a laser beam toward the Earth traveling at velocity c relative to yo.r 0tytt3.c7n o rn tl0dpf:n6/yguo, u. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,00ys(kse,hzx*qz8l. 5 h .uxn s(0 kg. The occupants would like to travel to a star that is 25 liy8l* ,h q.uz5xkszexs .n(sh(ght-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 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 82f+tom/ emcdspaces2tf oc8ed+/ mmhip's 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 vici30k3skkb9dj6( i ty y/nqrfi5 nity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more th/0k yd(j5sqrkybf 3ni9kti 36an 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 uc.3r2d( ppw: dmb o6sstiffness constant is bdpc: wrm (pos6d2. u3$k=48.7 \, \text{N/m}$. If this system is in a spaceship moving past Earth at 0.900c, what is its period of oscillation according to
(a) observers on the ship, T =    s
(b) observers on Earth? $T_{earth}$ =    s

A pi meson of rest mass 7,iidss5,-l jphn r 4f0qnc a6$m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.