You are in a windowless car in a a jp1dom7vgftbk; +tw t+;ppm )mbb61a37s; qn exceptionally smooth train moving at constant velocity. Is there any physical experiment you can do vjt;t;wa7g 1p )m7a;m +m1tk +bobpsf3 6 dpqbin the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a redinvjw+81 vzi8 light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake pedal, thinking that yoj81inw8zvi +v u are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of s1 z rplok1ajtf,10u. a moving railroad car, and throws a heavy ball straight u.u1kstor1l j fz1 0,pap (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 the Su)ilgy 2eahgj1 w:21avh2l 6(s jel0ywn goes around the Earg2 e yas1 hj(1lewh220lj)lwgai:yv6th? Discuss in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship tra/xhvy*;q3 itp 4t,g+3 csrzrkveling at 0.5c away from a star, at what speed would the starlight pass yo4rq zt hik /tp,+3;3grsc *vxyu?

The time dilation effenhky c7qz fp9z20zv69/g.qu jct is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of clocks. What then 2fcnyzv zp/ u g0kqz.96q7h9jdoes it deal with?

Does time dilation mean tbwj s0f ;9bae o0no*q/on 7ky4hat time actually passes more slowly in moving reference frames or that it only seems a7oy*4owejbof/n; 090 qbk ns to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. She 4 1 re:r1jrzt,n ,wdx xpa8/2kdto/qd rushes up to an old gray-haired man and in the ensuing conversatio//1rx4 z1or:qnk,j awttxdp2d ,8rden 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 change t uchpu/2 *3t6-erm;ho kly 2rin youpto ym/2u;-6t* hecurk3l2hr r heartbeat? 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 ordinar5ocut r4q9)g ky speeds, say $90 \, \text{km/h}$?

Suppose the speed of9ll5d ezz+ c2er +yxj* light were infinite. What would happen to the relativistic predictioe+dxz * l9y +5rzelc2jns of length contraction and time dilation?

Discuss how our everyday lives would uxm7qvp 1/icfix* 5hn3ogz 0y8* pqc,be different if the speed of light were onlyfu5ixopqvqghn780 /31 cp*i czy m* x, $25 \, \text{m/s}$.

Explain how the length contraction and time dilatie 2f+: 9qbwcjldew: s5on formulas might be used to indicate thajww:c 5bed9f+ l2:eq st c is the limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tompkkv2i:(ze drc 1ins, for whom the s zeivrd1k:(c 2peed 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 ab s 70( doeh7(8ismtppt speeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper lim (p e(8itds 7b7hmosp0it? If not, explain. ----待选择----yesno 

  Can a particle of nonz8ids1-oak dq5/ p(3e rpu:nmwero 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 spr4:m4v wnt k(bsdy 3.lfing has more mass when compressed than whentkdm.vsl3(bf w44y :n relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither bg lu 7efwc.voj;j.,i;e created nor destroyed." What must we say incwj.;flg o7ie, ;v.u jstead?

  Is our intuitive notion that velocities simply a4h60f,qadpe,l +r zj jd; x5padd, as we did in Section 3–8, cofjed+j d,ax h;046pp ra5z,l qmpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure itas+: pvu8zpt*r 8ww. ms length to be 28.2 m. How long woua8 mw8 s pz+:*rvw.utpld it be when at rest? $L_0$ =    m

  A certain type of elementary n hjo71p r,bg7:bzzsm17g8zcparticle 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 bd; 9vb whnp7k3rq(+x 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-82r. utfsji )yyears 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 pi7c6hd9 0nl;uebd*t nn on if its average lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, q my*ssqtchqe*b1 )1/ a star is 82 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years *tsqq1q1c sbey)m *h/? v =    c

  Suppose you decide to travel to a star 85 light-years away at a speed thatn 9bn qkq,z*:ug9k5dey8vd (n tells you the distance is only 25uney 5,kb8q* n(kd ndzg q9v9: 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 theva 1)xl;6t4w2f cvdys 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 )4zwdco4e3jws* ni a0rned from a 5-year voyage while traveling atn e44aj0 cw *o)3wiszd 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 m4*t1)jdppz fspacecraft traveling4zpd p)j1f* mt 0.960c 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 inm4gdu7km/p-orm p 6oug bn0( h3j xf:: her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your f6n-fbpr:xgm(/ mj4d7o gu03uokhm p :rame 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 q8j(q;q if hc5before it decays? The average lifetime, at rest, ic (qqhq8i5;fj s $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton traveling45.:k-h lwq oxebmp8q 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/vvlm;+ f pz/n mass? v =    c

  A particle of rest maclfyb x :2:/opss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a +rfhrt,. 1ljb/xv0q1tg: 0 :rdqf- dgzb8zgxt $v =0.10c$. 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;kcrs, 8h ej)r of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction rec7 7(.vc ,dkxwf h3sfhquires $4.82 \times 10^4 \, \text{J}$ 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 processu m*fk5)kq3lnk8xb e3 known as fission in a nuclear reactor, the resulting fragments have a total kinn5kkx3) 3*mbuqf8 kleetic 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 (mffblai6j+ / 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 of a proton in d,tf0i5r6t.x klcff 6nr 50xt$\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is aboutf0ak/ u .xwaf3 $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can b yks9- );7kf45xvth2y 5ntk a8jjscfte 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 rest enddmqy- 9(l+1 ky .j hspt6:i :2gsautmergy? v d hjy.i:tk2m p1gad(:utl s9qs6+- ym=    c

  At what speed will an object's kinetic energy be 25% of its rest eiin9439se ag mnergy? v =    c

  (a) How much work is required to accelerate a proton from rest up to jgi;m3*zfzqh lew w-0oa 0.z-a speed of 0jwh.00q3gz *; wflzmoia-ze- .997c? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energyq db;c 16t5ag; p*dgn:3edhsa and 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 enerqx: 7 (ucsas.a qoz ;iujb/9+pgy is 750 MeV)? abji a pxusz o/c7:sq(+uq9.;   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MV 8ve ty(;i0veg? v = ti; 8ve0eg(vy    c

  What is the speed of an electron whz g4((lb qdy0zdme e68v;a ta.ose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an4zb nn;ch.hu , electron just before it hits a television screen after being accelerated from res4 ;.z nuhb,hnct by the 25,000 V of the picture tube? v =    c

Two identical particles o ;cl+c.cde7u 1/odig dq3ts,j f 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 propvu n+ .ev cz8b f7(kso*xo7-lton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the m2pa3a-8fn*faxldx /zf*ig: s omentum 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 spacecraftqxcdfxg) 6abcgn( 830;b q;8ajnw1db of mass 27,000 kg is accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?    %

  Calculate the kinetic energy and momentum of a9pd j r*wtmc;*4 cq57ez)w)mtr oah7f 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, )fxyc+,kr8l4ddp3r h j5 a+nu$^{241}\text{Am}$, 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 momhshbil3hm+9/2hxcjbw(+j2jm h (e n/ .yyrl ,entum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest ih9yjyn2.leh mb2s/h + (wj xm,j+l h(c hr/b3mass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in a oqe9 3 qyi.nq at3n*b*lw; 9zlcircle of radius 1.0 km (at, say, the Fen*aeq .q l3nbz ;3*tqli9 o9wyrmilab 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 travelin+nrmc *9n2h3xa6n nm +ux3jr1zqe/ h bg at 0.50c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor c 6u1 /nhb 2a* m++xenrznnrmjq 33h9xmoving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, e0+mr(f (euml lach with a speed of 0.50c with r( (ue l+rml0fmespect 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 second spaceship leaves the f,mftzn ;tgk 59irst at a speed of 0.87c with respect to then 9tgtkz5,m;f first. Calculate 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 speed of 0.60c. Thez lk03tc4 j)(lov2:rj xd4mxd Enterprise comes to the rescue (Fig. Below), overtakt4 djzjx4k3:0 2colmvrd l(x)ing 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 p g .serk3x.3ztods in opposite directions. One trkx e.zts33g. ravels at a 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+mvs jan 00z*0 u3ymtz. At the same time, rocket B passes Earth moving 0.95c rely mn0ajsuz0v *0tm+z3ative 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-yesxd pzk+k -,riz294wmpj- o/kars 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 thany4m )hd694l;vn ap zna about 0.1c is called relativistic - yp h; naa4v9z6nd)4mli.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 6cm .c.sv r4mms7v,bb$v$ 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-W lig8b 16 c n2lwxetzj,)wlhtbulb for 1 )wb1znj2,lc texw8l 6year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produ ju:4;we9dz2e94k. ea2xqaufon)f ;hvkx l( rce an electron and a poswq u:xx 99v2d a4juzfee)2;erlno (h 4akkf;.itron together? A positron is 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 at 33% the speed of p2xmzuz92h0 7vhmv3r-.jazl light collides head on with a positive muon traveling at 50% the speed uz v0- ax2z7 mh2rhjm39v lzp.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 neutrino. ui ;whf:di 86pm4 dx:rAssume the neutd himu:64p8 r xiwd;f:rino'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 rest. KE =    MeV

  The Sun radiates enerk0ye e,sfdq*r+xci8-zcu 8-ygy 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 i3vtbnmj g9v)d a b542have a negative charge 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 nucleus into its const z 5hyftp)-j72olw-oiituents, 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 pi- j -th5loy72wfz)ou. (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) masniek.p17dmx80sy 1pgmd y /t (s of a car traveling 110 km/h as compared to at rest? [Hint: use the b7tg yd1y(emnps 1./i08k mx pdinomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c in thev5 . /f-hw g1jryprtvj/h4n* l laboratory, are moving toward each other. Determine -j5vng1rp.h rl/4jfthv y/ w*
(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 3t5knkp 9n ,l+xf r31l-u2 yvwt. rbvcmomentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its pow g5henn0.l,tb er by combining matter and antimatter, achieving complete cont.el n b0hn,g5version of mass into energy. If the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energy is grea ir+1 d5+gu;i,(e3 hebxrwcgiter than its rest m3(r1xw ;g+u,hdieic +ebri5 gass $m_0c^2$ by a factor of
(a) 5.00, v =    c
(b) 999. What is the speed of the electron in each case?v =(1 -    $ \times 10^{-7}c$)

  A farm boy studying physics believes that he can fit a 15.0-m-l9b1j;p1qjievszpac 35vy i.+ong pole into a 12.0- .1pej1s+;z93qv ybijapcv5 im-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two mole5s*7xrfsu37nn5yv w v s of water, the energy released ius55f7sv7 * 3vxrnywns 484 kJ. How much does the mass of the elements decrease in this reaction?
$\Delta m$ =    $\times 10^{-12} \, \text{kg}$
What % of the total original mass of the system does this mass change represent?    $ \times 10^{-8}\%$

  In a nuclear reaction two identical particles are crean nl*xx (ef l 9hpcra-d4-m e1-cd5vy2ted, traveling in opposite directions. If the speed of each p9c4hxnpc fnma-r(de2 dx5v*el - 1yl-article is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling aigs-st5tsc 8t6; yk a5t 0.75c relative to Earth measures his ship to be 25 m long. On thtt68 5 5yssts -gka;ice 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 at6xxxjo,a,h9z d+/nhrvq):lk a speed of 0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Eax6jh +),d:xv9 h qlr,xna k/zorth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occupa8b pr/ qnj04g kx3g+-v)gmr c+qgxguh3d u3v;nts would like to travel to a star that3 g -ng)gdxq j/+ rh3u;+mr3v4q gvp8g0kbcu x 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 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 ss,)w;am iv 1sbpeed of 0.99c. What is the spaceship's kinetic energy? Comparews i1,;s)bvma 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 jm2ubw8twmd:)+mh xzi 6suf e8 c68.bvicinity of a star 6.0 light-years from Earth. Passengers on the ship want the (one-way) trip to take no moz ib6mdx .w2m+bm f :c8)esw6 8uh8ujtre than 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 oscillatihhj5ex4r2u :.yj *b jes on the end of a spring whose spring stiffness constant is r5j be2xj* .i4huhj y:$k=48.7 \, \text{N/m}$. 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 mas8qwdsu8c. rp0xvz dl6y7lz .5s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.