You are in a windowless car in an exceptionally smooth train mo* kfdat /feo)2tf3qok s2ma)l*l53u vving at constant velociltt lf2 me3k)uvsaq* o)/k3fo*f2d5aty. Is there any physical experiment you can do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of beinoet+6l*cqzwft* .sljx/ lr - +g at a red light when, out of the corner of your eye, you see the car bee* fl o+tst-/cq j6z .lr*+wlxside 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 throws a heavy ball straigo3w q 9x-m4*v2phzdxlvf 5/xp9 5s.w fn:dfds ht up (from his point of view). Ignoring air resistance, wdp*fx/vh:s5-3xf2dflm9s opw4 w z 5qx.ndv9ill 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 Sund*ovep.h:pm qy v 8azvy;,d(8q 5fb+m goes aro v+faqm om *y,5b;8p d8vqpz:ey .vhd(und the 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 s7n9ou yrq5ao; ;)u hsgtar, at what speed would ty7uqon5hu; sa;r 9o g)he starlight pass you?

The time dilation effect is sometimes expressed as “movint ;yywfhkp8.(ys2xxahj : e 1/g clocks run slowly.” Actually, this effect has nothing to do with motion affectingyyk2f :1(t8;s hjp .exyaxh /w the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes m*90s-b8tqeovx: / ndnei7 m psore slowly in moving reference frames ip:x/t sn0o7vd*nee - 8mb9qs or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home fry p fn+c6)ow-2 *rcbwu*nul6gom a long trip. She rushes up to an old gray-haired man and in the ensuing conversati ubg6n - *ww l+*6ycnp2crf)uoon refers to him as her son. How might this be possible?

If you were traveling away from Earth ads. 6es 4lkm5(vyss(wt speed 0.5c, would you notice a change in your heartbeat? Would your mass, heightdys s4(5swe6.vkm(sl , or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length.ze zyo/qlnn oj9 2h,, contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What wq +fwi b1rp6:* nfcb24ni:cs5 y alfp0ould happen to the relativistic predictions of le:sqpl6 cr2na:0 b1i 5b+wnp*4 fycfi fngth contraction and time dilation?

Discuss how our everyday lives wouu a9ft s 8*vb5pb ;.+fjis3ag:h7 nquyld be different if the speed of light were onljp5nvbi;s3 tf uy afu 98*.h:asgb+7q y $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might br.x9mj8uh 4bmq5vtsz4xi . 0de used to indicate that c is qvt ji5m8hm4 x. 40z 9rsxb.udthe limiting speed in the universe.

The drawing at the start of this Cb, o;,kv ykd.fhapter shows the street as seen by Mr Tompkins, fo fd;yok.vk,b ,r whom the speed of light is $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less th2z(s4 bij gt.gan c. Does this put an upper limit on the momentum of an electron? If so, whatzt4 g (jbgi2.s is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of light?i2n x e-xmg o 87j)ab.wki)i7h ----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 more mass whe:ne7ki o z6jpz(s3t a)n compressed than znsj)iae3o7 k6 :p(tzwhen relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created no eu8hh 4xfuv2ur z;,y(r destroyed." What must we say2 ; r fuhuxuh4(zevy8, instead?

  Is our intuitive notion that vf: yifn;-)p blhrdq4 /elocities simply add, as we did in Section 3–8, compb/h r iyl):pq;fd-4n fletely wrong? ----待选择----yesno 

  A spaceship passes you at a f) c, -r-gjk-eyg;ly bspeed of 0.750c. You measure its length to be 28.2 m. -kb;- y-g)g yl,rjf ceHow long would it be when at rest? $L_0$ =    m

  A certain type of elementl)tuc5 - g gx-s(vca,cary particle 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 83+ alu ;pa9ri tk)xiion 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 Earthj2v ,g6)p onu,5sxz0f /htnq l 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 measurel;s)c jjc4 f+gjj zvl 3,;m;nhd 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 lig3w;ar( 2fz3,f aq nbczht-years away. How fast would you have to travel so that to you the distanceanqbfcw;3fza,( z2 3r would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-y*xt4 z b,bvfk.ears away at a speed that tells you the distance is only 25 light-yea*.vkxbz, 4ftb rs. 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 Earth47uj nlmh6c4 -o gkak: 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 retuj g21zg92x8) a hs ow9eul0eabrned from a 5-year voyage while ao1 sgx 9 bw8haz2le0eg2)u9j 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 spape*6x7ei,y ndcecraft traveling 0.960c to reach that star from Earth, as measured * yxe,idpn76e 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 herfj3d z+okc*1+ e5wduc "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.2o ++5e dc*fk3dwuj1cz5 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 befo65l7 /-lhw z 3crdara6f7nx drre it decays? The avera3f wl ardrxalc6-6 /z7d7r5nhge lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum o)po5 w uvu(2azf a proton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will ans oqx d*ax)s16)zu2qz object’s relativistic mass be twice its rest mass? v =    c

  A particle of rest masdbtjx h9y1)qj 0jm l,cub16-a s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at e)pa4,xnrwa) $v =0.10c$. 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 of2aihgu2: : oe inl/bq+ a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires kw4e*rxte2aai,a/ 9d $4.82 \times 10^4 \, \text{J}$ 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 fio *sz6 ,oprs:5e8nck gssion in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. :gozk 6cprnoe, 58*ssHow much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of wx4m68mtt ki(an 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 ox upkfx4lhqp6 +tv818 f a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is about *s:*:f6ntm lhes:0z ocf 5dzb $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversi h -zgzcw-s4*con 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 0, 0m(f gzhwz1 24taxr+o2o kmbs+mf aa particle when its kinetic energy equals its rest energy? v = h0g z4 m ,zkt(ra+ ofam021b+swmfxo2   c

  At what speed will an object's kinetic e)q3kr-4gp:ezv rnb w82cnp t(nergy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a speed ot k ;e 2irm1ukye3*cv-f 0.997c? cke ; t1imu3e-*vky2rW =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton trava4q )5mkyvoj3v(g 0kvr5hew-eling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV proton (that mr bmm czba g del:i3-6995h8tis, its kinetic energy is 750 MeVmaimdmr8hc 93t9be 6g l:z-5b)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of *u9cz57slmn sr9 x:jw 105 MV? v rsjs99luzm57nw :xc * =    c

  What is the speed of e4qvq*+g 6dzy an electron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron juwkt:: tr:ho7z( ju)l/k -ftqzst before it hits a television screen after being accelerated from r( u t7)j:fh lqwztk/ -rko::ztest by the 25,000 V of the picture tube? v =    c

Two identical particvl8xmt a6(y7vbnpn / (les 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 pbsxjid7tu+t 4-le0*o roton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed andjs gf31tcp:uq*b8 i-y0j. unx 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 3ki3 ijt f2dj4p;bvc;ja ) f/laccelerated 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 a protonady6 ,ju,9 * hc83 lccfqosi4m ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) 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 nucleusf i.8 ) cnih(.r:ffe6;qk bbuu, $^{241}\text{Am}$, 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 for (a) a particle o5)sc3 4qi6b pwizpw/ ui* l0vwf nonzero rest mass, and (b) a particle with zero rest m)6wiqz c0 wpb5lw3iu*vip /s4ass.

  What magnetic field intensite4 ul :j4s/ yztbsf+y-ze++e iy is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the:-leysizyf4/4 se jb+t+u+ ez 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 oezc:i6 txm2idbl*( : to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.dbt2e c( zm io*l:x:6i50c. How fast is the meteor moving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.kdc z7chld( n/6ef s c m79fvxfj*mki6+df);250c with respe( hkd66ndivmfkm *dfjf +l2s7fc ;c)e/9cz7xct 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 nd o/xlk hnviu* kj.+n 5)v(3uthe first at a speed of 0.87c wnk l 5v.uodxuh/ (i+3jn*nvk) ith respect to the 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 xfnwj;1hsertoz- 9 2jl5 i.2tan alien vessel approach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. Whatoittjw n x.r; fz95-2sh2jle1 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 dire+yr)ri t.5pq vctions. One travels at a speet y ivrq)r5.+pd $v_1 =-0.60c$ 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. Atbhcp-) o:pwv 5 the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B mvch)w o pp-5b:oving relative to A when it passes A? u' =    c

  The nearest star to Earth is Pr:r6yujh4 9tn fz1b hu;oxima Centauri, 4.3 light-years away.
(a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?    c
(b) How long does the trip take according to Earth observers?$t_{Earth}$ =    yr

  As a rule of thumb, anything traveling faster than about 0.1c is called. y *yptasnug/( kb;j+ relativistic - i.e., fo pnu(;tajy.s k+yb/ *gr 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 spee5k,r1 0li: xqabj) ng6 z1hcuje ph:-jd $v$ 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 tota1ul;q4zllrhi9jyo0r0 ) 9 c+bi)rekx lly destroyed to run a 100-W lightbulb for + y erlch0)90j9q)zr kiil 1x;r lbuo41 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is ne )wt.wb7t9 +lkaqbsq /eded 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 tb.9s)b7/wqltq+wat k hat 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 el;0zjc6cm.bz + :blvcollides head on with a positive muon traveling at 50% the speed of light. The two c bvel .0zc:+m6blz;j 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. A0jr s-qb td 4acawea (7a4wj d3g08kr4ssume the neutrino's rest mass is zero, and the other masses can be found in the Table inside the43t47 w-rswaek0qc d arj0jaga d8b(4 front cover. Determine the total kinetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates enera/bl ,p. *e-2bmowqn ogy 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 l.5xceu- m).,*4l pxor ys- x*tolamwnegative 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 n *djqj9aij q2.nzi; b1ucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respectively, 1bin1 q; .i9d jjz*jq2a.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 cag)goav)b y: z2r traveling 110 kmga o2)zyvg: b)/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 0.935c in the laboratory, are movimgv:t 7z/nr-u ng toward each o/r :n-vg 7ztumther. 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 ,fc)(b5qzgv a particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise oaqbdg)crvc d7 t1vt,(+l 8zk 2btains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the E b8 kc)ct v,+gra1v7qddlt2z(nterprise 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 kine. f,,ye)h qxpitic energy is greater than its rest mass fpih qx.)e ,y,$m_0c^2$ 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-long pop8oy(;h y ql9wle 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 barn looks even qyh(8 o;wl9pyshorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydro; s8v5(odgti+jyfvc km s88k0gen and one mole of oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of vj8 tif s 8 cd;moks08(v+g5ykthe 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 idobd - h/r bf/*(ow5kzzentical particles are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reb bwo z d-zr(fo/5/hk*ference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship trak:n bf/q0 a *( wzhoy6k*o+b 7-idfctje x+s0uveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his l0 nau*c/ y +b: fb+tox*-6ksde 0ozfq(k7jh iwunch 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 ab+p zmc;w nl6ks cb5,zde f3.0e2xc wnugy172t 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 Earth measur6+gk3xcc z;w . nsn7 feb0m 1y2wp2d,bezulc5e for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 150,000 kg. The occupants wou/m3cu,:r4 u 2d7z 0ozjrgjmmsld like to travel to a star that is 25 light-years away at a speed of 0.60c. To accel3crm /4 o:zmruzd7u02 jgs,jmerate, 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 wvqkbvatebq0b,j 8 n51-qk7 uwq n/(.is the spaceship's kinetic energy? Compare with the total U.S. annual ew7.0b1( 8q kjev wqb kqan -5,qtunvb/nergy 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 liqxy +yqyet6.vhf/ ei/gu5hs90h1 .qdght-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 trivt/yqhx g.+hyy /df901ehiuq5 . seq6 p? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffness constan 1avn 88f2uasxfp.l8ot n.v 8a1lf p8sf82oaxu is $k=48.7 \, \text{N/m}$. 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, q kspim 5er /uot,en/6+m6ra $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.