You are in a windowless car in an exceptionally smooth train movich*/yej5px, ttlg1z: w z.j0dng at constant velocity. Is there any physical experiment you can do /,cg5hj0zxpdtwlje.y:t *1 zin the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the e2(z eire2w 7iqjgf*.c xperience 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, thinking .e jczwri2 f*(2iq 7egthat 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 h-waaxu z; ba kegd0*p5f00gf1 1ov(fceavy ball straight up (from his point of view). Ignoring air resistance, will the ball land on the car or behind axa0cdup1;-wff*f 5bv0z(e k ogg1a 0it?

Does the Earth really go around the Sun? Or is it also valid to say tycslu+ ,h :vk3hat the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best reference frame). Explaiv+h ks:3y l,ucn.

If you were on a spaceship traveling at 0.5c away from a star, at what ww2t rqzjl (.:ou3few5 c/n6lspeed would the starligwo w:j.l(e2cf5zun/tq6wl r3 ht pass you?

The time dilation effect is sometimes expressed as “moving clocksttm8 hpy.wq1qxbv4 gt n7)j8- run slowly.” Actually, this effect has nothing to do with motion affecting the f).y 7n818pgt twtvhq-x q4mj bunctioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving ref ;9/x/;bg9viczh isiwerence frames or that it only seems to pass icsw9b/ zig /;x9ihv; more slowly?

A young-looking woman astronaut has just arrived home from a lxrb,vn p4d9h 2ong trip. She rushes up to an old gray-haired man andb2x vp, 9rd4hn in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away f . 6v 4dl l9tiw.hlsc;gqw7k4fa/9hltrom Earth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopesd.vl/til7hshg 46q;.ll w9w f aktc94 say about you?

Do time dilation and length cr cyx*y38( -y xsseca )ak9(zrontraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What o05ae bh1 hzj6ss+-jg would happen to the relativistic predictions of length caez6j0 g+ 5hs-ohb1sj ontraction and time dilation?

Discuss how our everyday lives wc1:-i3pk qnil l.g7-+ ooi geyould be different if the speed of light were onll3- nilicg7:qog yikp+ .-1oey $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas mighthr*o4-nhxixzg*zpo9 /ib f/ ( be used to indicate that c is the limiting speed in oh*przf/(gxiibxh -o9 n/4*z the universe.

The drawing at the start s9o v4vv g*e:xyx o:a2of this Chapter shows the street as seen by Mr Tompkins, for whom the speed of light is vvosego y4x29 :a:v x*$c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less than c. Does this put al ek *.9tt ls6,0gegrkn upper li06.tre,elgt l*gks9 kmit on the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed of ligstzqc/vr z90fg-;5,ltp;5 r .jnvs jpht? ----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 mefk4n) gm72)p ( wkske,ngz8b nan that a spring has more mass when compresse8 g zgs w)k4 ),nempbkkn2f7(nd than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created ymb/m;(d ;5w) ,qmttib8d xzjnor destroyed." What / ) dmtbt wq8m,bzyjm(d ;;x5imust we say instead?

  Is our intuitive notion that velf.ns j: dyrqtji 5-9*yocities simply add, as we did in Section 3–8, completely wron.9*jdty -sf i:rnyq5j g? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. 9jbkymo/f-wgp9 zj.- You measure its length to be 28.2 m. How long would it be when at rest? /w-kzym jjg99o .pf-b$L_0$ =    m

  A certain type of elementary on0)h6oz3rbkp-qnj cj(any)n,/i )n 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 interva*,q5kzd3b e ty;j6ev q4avuj3ls depend 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 w b mbk+02beinzbh9 o:p,i;0u125 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 lifeti;pu j;nxj-8e6ygj48z,cjgs *ao+xzi me 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, a star is 82 light-years away. How fast would kl61t :zz6y+m nihl- cyou have to travel so that t l1 z-6n ly6kz:i+cmtho you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years atfm8s/ghefs87h xw( +i;4xg zway at a speed that tells you the distance is only 25 light-years. How many years would it take you t 8t8sxhfw4xzghi;/e7(mgfs + o 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 fromoaxk7 7.,foee vx-qgy nh-* :r 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 yyhj5:y jo / qb7bejt*nay.((vc3z a)Enterprise had just returned from a 5-year voyage while traveling at 0.84c:.beanv*a73 (yyzyo5 yj) (c jj/tbqh .
(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 ix l2pqcmyl: r g/zx. apgg4)q(04h-qkt take a spacecraft traveling 0.960c to reach that star from Earth, as measurl2ql q/ qgx ygam:g- x(k.h0c4 zrpp)4ed 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 "venb. njeq69a14bwm.v//mkm2an v ;qFerrari" spacecraft at a speed of 0.660c. It is measured j9vkn./m qm ;w 1mn6abe4n /2bqav. vein your frame 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 piogh*b5wqj3/ adn be moving to travel 15 m before it decays? The average lifetime, at restdq5 *jbgw /h3a, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trav e9h and0* .l 8fac0fqnn9zf-jeling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass be twice itg lxe;r9/m q)euk a*c;s rest mass? v =    c

  A particle of rest masn/ub lmj/tl1 7y(sb . kv0.yjp smy(h5s $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle trave kx i4;qsbyg +mwv+:c+ls 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 accelerat*af )ck7mzq.a es
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reac(vl/lsep8x,es(v 2z;3gfhgf tion requires $4.82 \times 10^4 \, \text{J}$ 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 attcqpo.v 6edlu 9s07pw c 5-jkxj m/9u- rest breaks apart in the process known as fission in a nuclear reactor, the sm.plke60t j o 5w/j quv79xdu--9 pccresulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules bnn06 ug/p8hp2.wniw 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 17duz ,o + 5put,;y) uyvv3gajcwmj.lproton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in tm6pt ;4v,vu d68 p.-ivqqxnibhe 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 ov nd8 .tv0 6wn-astn1gf 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 equali:y rawfe8,5+- q gnybs its rest energy? v5 - +biqywrfgy,:n ea8 =    c

  At what speed will an object's kinetic energy be (zq bmx+x l-ze7pqs: .25% of its rest energy? v =    c

  (a) How much work is required to accefo8h:7bx h i s,4afl.id0vmh) s7o7t slerate a proton from rest up to a speed of 0.997c?hd7vs ho 0aos 4: 8ls)7i7 tb,.fxhfim W =    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 pkyi bz3uf jeqjs, 5p 260sj8jepd/, zi86ag/aroton 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 (thath79x5:a,4kjqa k . wqwuhc/ujl9(g nh is, its kinetic energy is 750 MeVuw /97qqljh cu:9( kaxg5,n 4 khjwah.)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MV? tn m)qzv. 6jpm g8-uo0v um0njmq) t zp-6ov8g.=    c

  What is the speed of an electron whose kinetic energy is 1.00 MeV? vo3:b(org (w 7npuu +18bfnr3e p9wogi =    c

  What is the speed of an electron just before it hits a television screen after j/ z1ndnyfs xi5zmdb)is 4*z3lb s 825being accelerated from rest by the 25,000 V of the pzb3 zsxzif)n 45 8d* jd1/inlm2byss5icture tube? v =    c

Two identical particles oe jhtj. 8g4dyr4i14c,w6n,h(vmmt f vf 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 f4zp pw0 l..lko szd40a 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 and the momsb8771t txqeb entum 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 w0lcbu2 iu6 7p-dg k*hy4pek(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 momr p2knlyz.1 vj fpet9elm 4eu/-9p(z q4iw,9 xentum of a proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) traveling $7.35 \times 10^7 \, \text{m/s}$. By what percentages would your calculations have been in error if you had used classical formulas?
KE =    $ \text{MeV} \, $ with an error of    %
p =    $ \times 10^{-19} \, \text{kg·m/s}$ with an error of    %

  The americium nucleus, g9i bb6phh8+s $^{241}\text{Am}$, 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 energ)ry wloant52 y/ zm3y6y versus momentum for (a) a particle of nonzero rest mawr3om z) 6 /lyy2nyt5ass, and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998pvhd,xyob pi02s,g6 1o/0nc v-GeV protons revolving in a circle of radius 1.0 km (at, say, tgxh1ip6cy2n ovs vo/pb,0 d,0he 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 t 5a.t1wfj;mtw(o+fd(:i nmb *eb tla*he Earth) observes a meteor come from behind and p:mt*(eofal bj*wdf(.m5+ ta b;w1 tinass 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 directionigix 0c+;2i/ )k-3d*cgxeiagov(t k ks, each with a speed of 0.50c wigt i3c+k2g(ik ie/)dvg*c ;kxoi0a-xth respect 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 l ioy+44ns) vmleaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth )+ vlni4moy4sif 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 bpw)-v9j ua76lcr p-v l .n7rbat 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. What is the rel 7b j)6-l9vr-rpwlcbv7a up.n ative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out two er.,,ixgesz x pjmjk838 jm5r 9uq k,x6scape pods in opposite directions. One travels at u sxkq jpzm8j,.,j9r,53mek gxxi86 ra 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. At the same time, rocket B passevrn3fhguw37ghw99a-mkup.eu /eps6 ,k 0 ef ; s Earth moving 0.95c relative to Earth in the same direction. How fast is B;v. h 9u3-eusk30 w7epg,/hfkr mn 6fueg9awp moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-yg6a +p)h1axg9x2, wjhmape g7qej2g8 ears 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 fasterxtpj/0i4n 0yx than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a spx xynt ij/040ignificant 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 spee b10vy9)gwkvl d $v$ 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 ;msvxa ,7v ;ld100-W lightbulb for;xs vl,7mdva; 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of-) 0kzylbl;ud sfe jvg)7kw/+ electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in /bls-k;k+d) gzl)f0wj7euyvthis 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 q 5zs1qq )1gdgvcc*xw;oy4 3i) enl 3twith a positive muon traveling at 50% the spc43*o3 c xvg) 1t5sw;deq lyz)g 1iqnqeed 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 decbibw6o j 32fp+/5xtpi4 vgc j+ay into a proton, 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 kineticfjpv2b4xj wp3ti+i g/+c o56b energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of 7n4 2azwxp a(2h 1han w9.ptcdabout $4 \times 10^{26} \, \text{W}$.
(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 measu ( 03yncvbmsf,red to have 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 breakl, i4bcx:)0f8iowt9qk h37 gq bi)ukj a helium nucleus into its constituents, two protons and two neutrons? The rest massesoqi h0:k )fik3t9 gq ilx87)wjbcb u4, of a proton (including an electron), a neutron, and helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the (relativ9b7 w ylrw5ax93x 0lrb*kg ,s; kgdp(oistic) mass of a car traveling 110 km/h as compared tg,pbkg rdwox0 93(sa 5yb;l*wrk 7xl9o 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 la 5*q7xp4rm bq; gat0taboratory, are moving toward each other. 0xr5 qpq t ;g7atmb*4aDetermine
(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 aq)w3hom 0eg4,iu xsg -6o*eu f particle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Entsw60*iw fbg jw q4dh8 :pp.1zqerprise obtains its power by combining matter and antimatter, achieving complete conversion of mass i db6qg4w0*p.81fph ws w:z iqjnto 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 accelerath w;yt8/,avmg ed so that its kinetic energy is greater than its rest mm 8y;w/havgt,ass $m_0c^2$ 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 belduk hw*(o:*am* n,fifm9y 6r lieves that he can 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 barn looks even shorter to him than 1kw6m m*,ofydn9(ral *ih:f *u2.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygen react to form two moles of xst+ lj/ .zwsc9(d ds;waterl/dw +s.t(sz j 9xdsc;, the energy released is 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 created, tx f/2jy7o::ixc+ksduz p 6dm *raveling in opposite directions. If the speed of each particle is 0.75c, relative to the la /ddoc m6xu2:k xsyp*:i7fz+jboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling0sc2;s l.hn dp at 0.75c relative to Earth measures his ship to be 25 m long. On thecs n.0 dlhs2;p 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 Earth. You send tdc o1(i*d-4n aa hth (fxqr+7a laser beam toward the Earth t-n 7 a td+odcq*h((14trahifxraveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass v.ecm+ fe ta b42tr62jof 150,000 kg. The occupants would like to travel to a star that is 25 light-years away at a speed of 0.60c. To accelerate, the engine of the spaceship changes mass directly to ene+brmttc 2 e2e64.fvjargy. 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 Eapdj+ .hh4iys+r) /pys rth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual ened prjypi)s/+.hs4h+y rgy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is tor(bdr-am lyq -m:*ueiy.tkm:na0 d:+ travel 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 1.0l--dqe r(:m aryt ybi:.u:k +*0n mdam 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-eh+jcz1by*4. jssw b stiffness constant.ycs1sj- +whb z4j *eb 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 muaur0n:o x x-/ass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.