You are in a windowless car in an exce7n6 3 yovpigr hc/k( w*37anocptionally smooth train moving at constant velocity. Is there any physical experiment you can do in the train car to determine whether you are moving? 7yn/ oacwr kch(vgn7 6op 3i3*Explain. ----待选择----yesno 

You might have had the experience of being at h0 */-b:)4s kxzeu ian8kpaeya red light when, out of the corner of your eye, you sy -e)akx*h azpknusb4ie08: /ee 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, rwf d ppg5)52)hj8v 6.b woclpand throws a heavy ball straight up (from his point of view). Ignoring air resistance,)ppp2wr6o djw v5b.h5fl 8)gc 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/ 5+w5tqw ganb the Sun goes around the Earth? Discuss in view of the first principle of relqtwn wb+/5a5 gativity (that there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a k;)ij)54d1qy 6wi yz2,+raxrai*o hymstw .f star, at what speed would the starlight pass yout,qzki)o )dm;y y5yf s a 4i*1. hxjarr26+wwi?

The time dilation effect is sometimes expressed as “ms.+) xqv) fzw0y ai(or4- qtjaoving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning of c )tyvx-jia40rwz) aqs.+ q(folocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving refe +0f6u:a+mepise *drw rence fra r:*esa+ 0+pm6 fiuwdemes or that it only seems to pass more slowly?

A young-looking woman astronaut h gmxw i-s7xxt6jngks( e h/ .8rqrbv)1 ev)3q;as just arrived home from a long trip. She rushes up to an old gray jr / veq;ksvx3 .6s(ggnxwe 7r8)1q-b hx)tim-haired man and in the ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Eaha5 dup u jnw75 qd:o4+/jnqi.rth at speed 0.5c, would you notice a change in your heartbeat? Would your mass, hdu/no4 auhq q:.jw+5pijdn 57eight, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speedsnw 9 l3s54u j q9r8xfe)ivh-wh, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen tog;8x :ou3p ydo the relativistic predictions of lenx8ouygpd3:o ; gth contraction and time dilation?

Discuss how our everyday lives would be different if the s;nl 7)uwtmd0( jhv tkj354p0 s7usupnpeed of light were only j( j n;)p3hl077swdu ut5tmk4pnv su0 $25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might be used to *vfw 2g+u tp4oindicate that c is the limiting speed in the v ut*+w f2g4pouniverse.

The drawing at the start of this Chapter shows the street as xe k5,vwx9w62 h ftsrma.k9)nseen by Mr Tompkins, for whom the speed of light i)tarx65ew 29s .knfv9, khwxm s $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at sn) lv*acu-ub az4cvl 7p:y toy57 y1e3peeds less than c. Does this put an upper limit on the momentum of an electron? If so, what is this upper limit? 75o:3e*cylz7n b up4y yv-av )c1a ultIf not, explain. ----待选择----yesno 

  Can a particle of nonzero rest matii8l .x*zg3tg6 mmo,i c, c8bss 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 m*;7vdgavg5ej5 g7 u xmean that a spring has more mass when compressed thanem755gj 7vxvgg da;u * when relaxed? ----待选择----yesno 

It is not correct to sb yz -x*7,lw8zp 4k;y (vhvwryay that "matter can neither be created nor destroyed." What must we say insyzl ,ww7vz( hp4-kr;yv8* bxy tead?

  Is our intuitive notion that veloci,n gnnr u-5)fwf4zd 0hties simply add, as we did in Section 3–8, completnr40hz ,ff5- wnnud)gely wrong? ----待选择----yesno 

  A spaceship passes you at oer g.y6e74kza speed of 0.750c. You measure its length to be 28.2 m. How long would it be when at rest6ek7 orzg.4ye ? $L_0$ =    m

  A certain type of elementary particle travels at a ok q6kh)xy47,ri s; adspeed 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 factor f+bet+ knkr4v 9xq92x$\beta = \frac{1}{\sqrt{1 - v^2/c^2}}$ 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 travea6jiy efq. csq7 mhh3,3 ab-j),o- cpsl to a 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 ckrrb-t a6;68s ur;8)mfu4 p eqnm6ovits 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, a star is 82 light-years away. How fast would yoe:v c o mb5.;9pxyl8xou have to travel so that to you the distance would be only 35 light-ybm oe5ly c o.;xxvp8:9ears? v =    c

  Suppose you decide to travel to a u6pu2hk:wn; lk)yfm/f kr* z ,n)8wuhstar 85 light-years away at a speed that tells you the distance is onu*r)kl;kn:yf,f n uh8uwm 6 pwkz)2/hly 25 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 the Earth is azp ,9oa7covwn(ha) x;vo5d o7+y/o i$11.2 \times 10^3 \, \text{m/s}$. 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 j a10;ct dwbk j;bri3b(ust returned from a 5-year voyage while travel;;bbwjr dt10a3icb k(ing 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 longnq5n 8rf; 7qrl would it take a spacecraft traveling 0.960c to reach thrr5n nf7q8;l qat star from Earth, as measured by observers:
(a) on Earth, $t_{earth}$ =    yr
(b) on the spacecraft? $\bigtriangleup t_0$ =    yr
(c) What is the distance traveled according to observers on the spacecraft? L =    ly
(d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? v =    c

  A friend speeds by you in her "Ferrari" spacecs (9 ,vhct((e:p frldlraft at a speed of 0.660c. It is measured in your frame to (( tdc f p9vleh(sr,l: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 m4g pu9hjsw:kv 8fjf;3oving to travel 15 m before it decays? The average lifetime, at restfu j9;hjsf:3 kv8g4wp , is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton travelingc:nmgnx 0wy2ziw 6+,g 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 mass*gaew03 3pn bw? v =    c

  A particle of rest masxslm +q)/k xr451ekku.:zfz ds $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels a1idc+u; ln5 lat $v =0.10c$. 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 accelerates vl8v5ykiy g))
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requiq m;3 s uopnlclw72): nvkja3fc/1aj9tt )xv4 res $4.82 \times 10^4 \, \text{J}$ 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 re7b9vz2yu g:z. el1wq hst breaks apart in the process known as fission in a nuclear reactor, the resulting fragmen.7h vbl ywgq9z e12u:zts 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 g- r zss2lhn xlwh c;9-(0mdyu2 b)(qzin 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 protolt8e rka6njx86p: a:3 yc dc-*7sb bign in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy co43uqxy2 yalry.g(a1s nsumption in the 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 fst)jo)* p2z0)fr)fy fb c8krsrom 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 490asbbeh vw40yql7 (b:fxhs energy? v = s(s 4wel: yha07qb4 bbf09xvh   c

  At what speed will an object's kinetic energy be 25% of ite+m+6 frbtt a0s rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up tawph00fx8,s.,buqxw o a speed of 0.997c? sx.pqxah,fbw,w08u 0 W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy anwg (y/y7 p zbn:t51zagd 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 kineu5qz4/u7 xfw x (mytu 3qi6sp.tic energy is 750 MeV)t3s i67 fq5uyu.wxum/ xz4qp(?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential diff0 ,2t)zsnmkjs 4ts njzb;7d*fo. uut5erence of 105 MV? v = .tdt2st 0m)n zs*jbsu jno5,fuk 74 z;   c

  What is the speed of an electron whose kinetic ene )vd+wcz19st krgy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a television screen afhy8+ d x zk:5ah+4pdw vt8ilg7ter being accelerated from rest by tapzl48i dgyxwd+k8h v5+7h: the 25,000 V of the picture tube? v =    c

Two identical particles of hvd 5t) mbb+b,n n;1bvrest 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 proton en .*9+izn oq4tqzo-u($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and th(;orr 7)fn.p ,kdr2ich2 nm sye 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 accelerated to 0.2)jc2 n6l; *soe1l0r 8rfaombe1c.
(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 momentumw.d*z*km 4 lbm 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 nucleukmxmd,l/m3 w,r*lm + hs, $^{241}\text{Am}$, 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)jdwn/0c a7zy . a particle of nonzero rest mass, and (b) a particle wj7. cyda0 nz/with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV protons tvtbx:c; c6p.bbh3k8 revolving in a cic vk3bc b.; x:ht86ptbrcle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket travkn:yd *eb* 20fy+xzx,q e:fjueling 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 moving with+ j:,xuy*ey:*b dkfqe xz0nf2 respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directions, each with a speed of 0.50c wi6 ue8whnee 1:ocz r,j-uzisob.) 1o2rthun uzse,re1c:62 h1-ozj ore8)ob w i. 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 travjl 4 srcb7y8f-++y(t(ddwk1ojh h l*n eling 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 -jod7h 1kc(ht8jyl+( w fldrbys 4*n+ 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 ofi:brsim e7 .jvctx++*g( j9kz 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 Eijg*+.e zvm( :r +ic7btxjks9 arth. 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 o gk l)skji6;0y whv1 woof+ku0n+8za: pposite directions. One travels at a spj v8kza6hl0+k w1:k+io wf)us;ng 0 oyeed $v_1 =-0.60c$ 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, rockety h7f 8hid-lomvm9, 6d B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u'8-v7h9ddi,oy6 mfm h l =    c

  The nearest star to Earth is Proxima Centauri, 44gpt+wub 3gwn l49tv 6.3 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 call, ld nzf9o/gvnt+sz: .ed relativistic - i.e., for which the correction using special relativity is a significant effect. Determidz:lgtvnn z,s9o/f +.ne 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 ..h3j apc)75igpg hwv$v$ 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 aznix .8tze52b uogqx w0.vb20rp 8/rk 100-W lightbulb for 12 rn 2bzgt v 0bio8w08p./xzrkeqx.u5 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electr++( e a yqyel:wvn*v7:wqms *lon and a positron together? A positron is a particle with the same rest mass as an electron, but has tl my:(q7 *nqvl++:w ase *wyvehe 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 lr4dn (la ,e3wbight collides head on with a positive muon traveling at 50% the speed of light. Tnblwad,r (e 34he 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 .8h 9jbw;qae1xp 1;t6 7l:gltt gwbdn 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 kinetic energy shared wbe 1 6x78:. g tlgh;p1n;ajw qttbd9lamong the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate(; j7puudmd (o 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 and od5i; gf1l8g9vnz1i i s) 2wdga 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 requiqtvrv o3q s0rzdy6/a en4 ((9dred to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a ns04d rnt6e / 93v qzv(adqro(yeutron, 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 tt30wc;tmo iy ,oj+w;u 7bha*w6 )tkzghe (relativistic) mass of a car traveling 110 km/0gk6 ;ttjc7,wz io hbw +*mt)aow u3;yh 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, argn1 zhz2g3o3f w(m .jse moving toward eas.3gfm1 h(wn j go3zz2ch other. 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 partijrn;(hvcg..;s;mpeqn+ l ,hf cle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matter k j:o,3ta3gdr sgy,*zj;vgfvf) v9r:and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is appro,, g 9zgosa v fvrjy3*vk):jd;t:grf3ximately $5 \times 10^9 \, \text{kg}$, 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 ::jh4 a5yd/i u32v:cycvc kmyy4 e:psis greater than its rest msyh:c4 : 5:dvc2yvekmi acy 4yp3/:juass $m_0c^2$ 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 thamx kmeox/ w/ tyh46:+-p3gqyxt he can fit a 15.0-m-long pole into a 12.0-m-long barn ifohx/+:4 eq6t kpm3wg-/x mxy y 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 r6 tri6 b,ta xyh5rl+j5jjg (n5eact to form two moles of water, the enera+5 5 ,jnhjx 6(rliy6t5rgbtjgy 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 zvv)h8ms2t3 xc,woc 7 are created, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of ref hcvsxv) o 38zcwt27m,erence, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to E f 0k(he c*msp/bykygh9)f): )ttiq w3arth measures his ship to be 25 m l weyf ci3)( tk0mthk)bqs ygh9:/* pf)ong. 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 keh8wef3 fq65zsdfx5x5 :h9d of 0.85c away from Earth. You send a laser beam towa s 8qhe6xk93h:w55 fff zdxd5erd the Earth traveling 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 of 150,000 kg. The occupan t.81/gt:.g, mikcrh3lulm unts would like to travel to a star that is 25 light-years amtt13kcu.m lrilu.nh:gg/ 8, way 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 speb3ijl jkb4(x9x.h ot )ed of 0.99c. What is the spaceship's kinetic energy? Compare with the tot.j)okbbtih xl9 j(34 xal 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 vicinity of a star 6.0 light-yea( x pm,3*:xsycmql/3 t pglbb)rs 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 speex ,lb q/*c)yspbxmgp (3: mtl3d necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose spring stiffness cln6)n o )qbu**,dbj (v+zro/i/idlufonstant iuul/ d)n,* +o6bz*jni v() /qfirlbod s $k=48.7 \, \text{N/m}$. 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 mass4k v2(9qh9 k3)nf (ot.ae 2bb/ sbpkgm -hqabd $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.