You are in a windowless car 1q +tes e(9zst,j.wrbv6,0d olotzq7in an exceptionally smooth train moving at constant velocity. Idt,zrw1 eoqjzetssl+ 67o bqv( 9.0,ts 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 exp1,c5 eenayd9i erience 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 that you are rolling backward. What ndaice 591y e,does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy ball strai hi/+ku-kwpjz 0 zk+:sght up (from his point of view). Ignoring air resistance, will the ball land on the car oi-jk:usz+/z 0p+ kw hkr behind it?

Does the Earth really go around the Sun? Or is it also valid.in m/h/g v rkpkth; zy0mqrmo(69w2- to say that the Sun goes around the Earth? Discuss in view of z6k0./h vh2 9m/wqrrnoy-(p;t mgik mthe 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 stasw qr45p;c-/p9a tqyh r, at what speed would the rpasqw;h-t q/p y94c5starlight pass you?

The time dilation effect is sometimes expressed as “movingk5 . iu/qf-dyyarfd0 + clocks run slowly.” Actually, th yu d5dq0y+-/k .fiafris effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation meana/il4ea e 8 -mr6*vmxj that time actually passes more slowly in moving reference frames or that it on 6 -v4ei*lj/rmmaae8 xly seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip aibof -wrhrzx 65(.o-lo:0 fb. She rushes up to an old gray-haired man and in the eabz.x5-ir(-w:ol ff r boo0h6nsuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, wypz 7g5;v r5tz/np.tmould you notice a change in your heartbeat? Wtrpt ngv;z57/z p.ym 5ould your mass, height, or waistline change? What would observers on Earth using telescopes say about you?

Do time dilation and length contractoos fuy(/9lv ;xfqzw r1i 2d/gkrh )5-ion occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of v ko/,.2tb4nit7 poa w) ugb2vj:yn/:yuxl,rlight were infinite. What would happen to the relativistic predictions of lengthkb,2/o. n/ybg)vntpl,o:ri uxj47:w a2yu vt contraction and time dilation?

Discuss how our everyday lives would be different if the speed of ;* *j+v e+thhwlcv+whlight were only ;+vt+w w*vhhc h+*jle$25 \, \text{m/s}$.

Explain how the length contraction and time dilation formulas might.dm 4r 0qz0m,eo:af1 s,7xdbkpby(w ;k ox 1uo be used to indicate that c is the limiting spe o m.,q:(,ys7dxdkeb1pu 0xoo f0zmr kb4;aw1 ed in the universe.

The drawing at the stdz4) ,r+ x, xhj75r u)gi7czudj suu;xart of this Chapter shows the street as seen by Mr Tompkins, for whom the speed of light is ,xh5gd) sx, durz ); +x74zu irjj7cuu$c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds 8 /tw4ez zd+g mlidn.r;m zt88less than c. Does this put an upper limit on the momentum of an .ni8 dltmm/wgz4zt8 rzd+e;8electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speeq(y n2jx5ph( rd 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 s :acsmm1+ t8tmpring has more mass when compres t 8ct+m:ma1mssed than when relaxed? ----待选择----yesno 

It is not correct to say that "mlddv,e c cdyf1ves*4gt5-w8 t+bxu,e/d kp 2+atter can neither be created nor destroyed." Whateed eyxddk*u+,cc-1 4 t2 w/,dg fpt+bvlv58s must we say instead?

  Is our intuitive notion that velocities simply add, as we did in Section 3–8o(os(xpu 9d ck/h32pa p0h1s a)sxm q*, completely wron 1k 0hq/udcxso3op 29a sma)p (hps*(xg? ----待选择----yesno 

  A spaceship passes you atq.i:c. la ead. kc2*hwsjf t88 a speed of 0.750c. You measure its length to be 28.2 m.8s :ac *j8f2qah.w. dke.tlc i How long would it be when at rest? $L_0$ =    m

  A certain type of elementary particle travels atb,j5nl1trms-ox2* y d 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 int4. rb/hjq3a6x zi7lhgdv.id4ervals 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 125 light-years fvjron fs6q; (9b5ezklnu; * 4grom 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 lifetimef.ao 1:k ,jlxe1i q,, /2rjyoghsw v:e 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 idvq6i 1mp6,wiull2pi l2f3i ,s 82 light-years away. How fast would you have to travel so t,3ip16 d i,pv lqluml f6i2wi2hat to you the distance would be only 35 light-years? v =    c

  Suppose you decide to trag /b 6hheq-2ecvel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make th/ceh26bqeh -ge 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 isptb 0(b/,ws2i(p pd d9(v ulpt $11.2 \times 10^3 \, \text{m/s}$. 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 starshi d 0n*r 65kn+n dj:olwebus.f 616upyup Enterprise had just returned from a 5-year voyaged66*nljby + ue10 usd6wnkuop.:n5r f while traveling at 0.84c.
(a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? $\Delta t_0$ =    yr
(b) If the report meant 5.0 years of ship time, how much time passed on Earth? $\Delta t$ =    yr

  A certain star is 10.6 light-years away. Horbu-l-p 8+.-(chs1 oi mp 3qrm5 sjkajw long would it take a spacecraft travelijo 5s upr1cpjbm a.-si-rq (3-+k8hmlng 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 in her "Ferx vt8..m injs;rari" spacecraft at a speed of 0.660c. It is measured in yourjm iv.s;x8n.t 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 pion be moving to tlqf gv(ob-nvl,** lq )ravel 15 m before it decays? The average lifetime, at rest, is qngl bl),qov*v- f(l*$2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a p. e ieif62l w2w7,u0z0lzwngdroton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativistic mass5 c)r7cre e3ueacm u80c cvte2**f4zz be twice its rest mass? v =    c

  A particle of rest masskk(b x)nnf5vb))mj: w8l .a ou4v1fge $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels atuultik1d+h9s ),p- wtvqlmz54,i9qo $v =0.10c$. 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 acceleratesxv3jt-dcn7e rs/tksw;z 32g)
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reactionbl p6w 53sxmo9 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 at rest breaks apart in th4xc)ma9 ltvip.q xf*+e process known as fission in a nuclear reactor, the resuli xmp+4q*xcv9 . ta)flting 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 and in wtluju++1by5 80y s v+upnay7)x vbi2$\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a protonl 4 (uk7uzi0cy9lw+lu in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the : ftvja/zjx3,s,n (ouUnited States is about $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained from conversion of 1.0 gram of massz9 8esbr )fu vqi00j ox ;dp6be y99x0f;wre8s?    $ \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 whm(jkmc5l8ybrvqs :sk f3qk. e h230z1 en its kinetic energy equals its rest energy? qr( k3vk:3m.8ejf1 hs5bmc z2y0klsq v =    c

  At what speed will a2 a .8ww4/qrpzkpxg+ sn object's kinetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest up to a spe*q5+jk/t zkfp)7 ulg/ 5jgihged of 0.997c? W = hgpk 7/g5t+jfglu/5 ijz q)*k   GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and (, 8qswg p0w*wz*foea 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-M nhcak09ga4nbophc+eodtp) : 39b f41eV proton (that is, its kinetic energy is 750 MeV)n p4op0 bhtaa+ dcnefk)1hbc g9 943:o?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton acceb5k4fe 83m.-ze;jiwyz e /dzalerated by a potential difference of 105 MV? vead3m5j;ey-wz/ zez k 84 if.b =    c

  What is the speed of an electron whose kinetic energy isol isa8.yh w07 1.00 MeV? v =    c

  What is the speed of an electron just before it hits/ji g .zu13akp a television screen after being accelerated from rest by the g1ika3pu /zj .25,000 V of the picture tube? v =    c

Two identical particles of r6q 90)ls, oxfey ne,o,dy.w tcbs7z3qest 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 a8a:ju we w/3oju.w la+ 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 momentum bc9bc-4oxc /w26y ze lt3ut+oof 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 accelerateaa7faeu-:w.8 o zmo7-r7 orksd 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 momentumllii( m pk30 3tf4uu8c 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,xcgq m/2xh ,8 f. 1ir-hyr1dvs $^{241}\text{Am}$, 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 oyf.w77-ex b,v hrw:puf nonzero rest mass, and (b) a particle with zero rest: uhv7.rwbfy,w-7xpe mass.

  What magnetic field intensity is needed to keep 998-GeV protons resj) a6kjc +et xtl.98wvolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotro )tc+w8tl9j.xa k6 esjn)? 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 the rvg p:hq2q::d Earth) observes a meteor come from behind and pr2: g: :pvdhqqass 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 directions, each with a speed of 0.50cg9d hw4nk7.h l8jtae - with respk8wd -et4 gln9ajh 7h.ect 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. ezlg7s0 w,3sq61nq efA second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed o nqw seg01z,lfes 7q36f 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 0.60 c .u,w4p1*jv eqpt1as8/ttzpmf26g fc. 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 relative speed of one 2p4tt8* sz1 etjf uf qm61pwp cv,/.gavessel as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opakqy. yy5m.g; posite directions. One travels .yky;aq.5ygm 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 im;bgtbu3 f 2htlx 26,of 0.75c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relatxlm2u 2bbt6 ih 3;,ftgive to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3,.f.y ys)nl ug4xj qe5im-d+q 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 thu )uy9zjs2wesle o4 13an about 0.1c is called relativistic - i.e., for which the correction ueuysel9 jz3u 2o4 s)w1sing 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 spee(scnj* u+fq1 n v/d(mgd $v$ 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 rl+n *yb2hteoj6q4 v* dzzys1(un a 100-W lightbulb for 1 year?+tsdqe1nvb hzy(o y **4j62zl $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed ffx3v4/, :nvasv*s tm 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 a ms/xfn:s*,v43 fvv tcharge. (Note that electric charge is conserved in this process.) E =    MeV

  An electron ($m=9.11 \times 10^{-31} \, \text{kg}$) enters a uniform magnetic field $B=1.8 \, \text{T}$, and moves perpendicular to the field lines with a speed $v=2.5 \times 10^7 \, \text{m/s}$. What is the radius of curvature of its path? r =    mm

  A negative muon traveling at 33% the speed of light collidefwc gv.zk;kp5k r3 1s8g2/wxxh. y2zes head on with a positive muon traveling at 50% the speed of light. Thef w3r/yk85xg.s;zk1px. 2hcek z2wgv 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 ro9du3* (s6pucpg: 91n r7cyke s tz+iproton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and then*pgsszidt6p+( o 31 u9yck 7rcu:r9e 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 energy at a rate of about v)4m u;83wsjl ;qj bx w3uu*tu$4 \times 10^{26} \, \text{W}$.
(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 negatdh3u18 unl e;zive 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 iy zfolj):/hypnsr i;r 5,.lp j(g, fi;ts constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and helium are, respeciih,ps; r; ,oyngj/ rzfl j (y.:f5l)ptively, 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 (relativistic) mass of a car traveling e+ep+4o kjxgx7u1r;n 110 km/h as compared to uxr; nojxg1 p +e4k+e7at 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 moving towar*5h lh)-7m* vb3t cr/towl 6uhublrr. d each othe6m b)h rvur ro53.l/c*h*ll-t w7ubhtr. 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 thc*.d(b z-w aeoat a particle 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 mattekj5odzc *kn;3c sk+ v6r and antimatter, achieving complete coczk+sd; ncv*j6 3 5koknversion 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 ;-cr y,zr/,je4 n/(qw c gkanygreater than its rest m, qrwy/yrk,;n4 c zjc/gena-( 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 believes that he cak 5qsfb)cjt3:n fit a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can heq5tbck:s j3)f 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( pvofu st: a*xj9ui9m(cbua9; ye l7+ two moles of water, the energy released is 484 kJ. How much does the mass of the elements desxcjl(+97p:uao imu u ; 9(9fy*beavtcrease 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 creat;o ;-eytx.( jfav jk9bed, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of refer- fxe;.(kobjjv; a9 ytence, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship trave 6;s,p *m gq).lszo;11pzvfhkg- e xbg 7mc5ylling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats h,5-)xfbklgm1 g;*py ;m zh7go csz6vel1 q sp.is 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 sp3u -h*)72+ilj9 t(wbxfyw abaa km t.waceship at 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 observw7(x2 bwa* ju3 y9 fml ).-tkbwita+ahers on the Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total massfhnfy z (d3ko: :k:4la.gj 0rk of 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, kjg:hkfd:3y 4 nz ( r0lao.:fkthe 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 lef9wpl p .mygg,,t Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.mwp, yggp.,9lS. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel to the vicinityd03-phidiv3-luy6 d 98nz jh x; csfx3 of a star 6.0 light-years from Earth. Passengers on the ship ws9-d0d6xj x l zpn8u-d3ch;i3y vi3fhant 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 trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whosegpsw1x0dk; ,1ec ;*9eed zltb spring stiffness constant id1;w0tzc bs,* eeld9xkp g;e1s $k=48.7 \, \text{N/m}$. 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 massz-g csw h5xd kw75lq-q-onud,vc/6e 4 $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.