You are in a windowless car in an exceptionally smooth train +3 *9fc eco)-jdq watzatb3,smoving at constant velocity. Is there any physical experiment you can do in the train car tozt3-q*jabd wo),fe cc 3+a9 st determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red ligzml7q4. ikzf7ht when, out of the corne7il74zq .z mkfr 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 does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws3o9 1 hn +u4b-f;ui,nlumjewh a heavy ball straight wi h f3 n14lm;9,jone+ uhb-uuup (from his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go aroun8j*sc1el;s rg59v ,n h9mwovhd the Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best rj,9v o;ns 1hhvms58 c9lew*greference frame). Explain.

If you were on a spaceship traveling at 0.5c away from a staom4wj5ri13rhhy o0 ulc8c n 7:r, at what speed would the starlight pass4n1lmjwo0u 8 rc: 5oi7chhy3 r you?

The time dilation effect is sometimes expressed as “moving clocks run sloeaxx+n2pm e;0yqw j*.i pr5+gwly.” Actual n qg +*.w axie;jp2+0m5repyxly, this effect has nothing to do with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving refe8mz;sxil(be* 0hyl uu*i) q(srence frames or that it only seems to pass more slowlil*y (m 0u;e)hxbss * lquiz(8y?

A young-looking woman;nh- x9y 8 ise4l6u*:rnnovyd astronaut has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might : -n lo yhvnu9xn8rsi*ye6d 4;this be possible?

If you were traveling away from Earth at speed 0.5c, would you notice ay ;-9mo dncjz+0g4b ed change in your heartbeat? Would your mass, height, or waistline change? What woulg4 m+c90ndjo-zby;de d observers on Earth using telescopes say about you?

Do time dilation and length contraction i* n1qpj*jo-w occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen to the + jkke * +ecqa)+n2hozawbu pe0qu-) 3relativistic predictions of length contraction and time dilat*hea ea)w+ bkp qz-n0e ) 2+k+ujou3qcion?

Discuss how our everyday lives would be different if the speed of light wees co4lw2j /8bi(ys/ire only b s8 icl4ywo(//s2jie$25 \, \text{m/s}$.

Explain how the length contraction and timw2fnfn2 d1t1j :rm /ehe dilation formulas might be used to indicate that c is th121 t:jndhfn/2rfme we limiting speed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tomn.nyr0+,naz e pkins, for whom the speed of+yz0,ennan .r 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 than c. Does this put an uppei nu kn yc*z:fla,e7oor3. 2;hr limit on the momentum of an electron? If so, what is this upper limit? If nf*e7n o uc.y k2zl:inh3o;,arot, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain the speed cchnw7*q zf7a33-lc ms)j: zxof 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 t bqd (0fh80y*u 4ppu*.qqj+x du3ieshhat a spring has more mass when compuqepybij8 0h+ 4 phsd.f(3*q0qd * uuxressed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter can ,,2of2zczie*hlccnt+,* dm/updv-c neither be created nor destroyed." Whatd,f ci-nol/d2e, cch2*m*uz tcvpz,+ must we say instead?

  Is our intuitive notion that vezap-mo9 s498sckd e9,dx r jz:locities simply add, as we did in Section 3–8, completel xocz,9r edp sk:adms 9-9zj84y wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750fj8ez6 - 1xcpak:v 2:8tpxwn wjis(.wc. You measure its length to be 28.2 m. How long would ike8p c jp:z8w.aj6 w2v(i nxw: s1t-fxt be when at rest? $L_0$ =    m

  A certain type of elemewd7ryjf1x*oq+vo 9e nl196kx ntary 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 interva1ni,ek uo8fpcfac : )/ls 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 t qxptq +d/kjub2 +2c*uo 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 its ave5q-v : fvz ma*kx6++:r:li zjpxolq r6rage 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 sj x(t-by.)enqqq56dutar is 82 light-years away. How fast would you have to travel so that to you the distance wou-qqy5t (u.ne6q) j xbdld be only 35 light-years? v =    c

  Suppose you decide to traveln +s -6lg1xldlza d(8x to a star 85 light-years away at a speed that tells you the distancn 8zdg-xd(+axll l1 6se is only 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 isd wbc7u/;q-r-mpg i*a $11.2 \times 10^3 \, \text{m/s}$. 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 ptvqo,)*4py wr- ieg; stated that starship Enterprise had just returned from a 5-year vo ;y-gqppe r4w,v*)i toyage 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. How long would it take a spacecraft nse7g8 im,2 kd(;xyoo traveling 0.960c to reach that sta7m;xe y,(o8 ns2gido kr 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" spacecraft at a speed sp,:,.(kt rmo *d3 o3jriofbylpy y:; of 0.660c. It is measured in your frame to(;oy, s.bfoj: ,*mo3lyr p 3r:ptkid y be 4.80 m long and 1.25 m high.
(a) What will be its length and height at rest?
$L_0$ =    m
the rest height is    m
(b) How many seconds would you say elapsed on your friend's watch when 20.0 s passed on yours? $\bigtriangleup t_0$ =    s
(c) How fast did you appear to be traveling according to your friend?    c
(d) How many seconds would she say elapsed on your watch when she saw 20.0 s pass on hers?   s

  How fast must an average pion be moving to travel 15 m before ik5:s0q ze i(uvt decays? The average lifetime, at rs5(0z iku eq:vest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum :8(z-in5ax4 yd6 crtlwkoa *vof a proton traveling 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 mas;p zeq7mb i;a /solbuz:hx:yc 85d-e8s? v =    c

  A particle of rest ma.zyzt ,pisan uv*2ts) h/;+df ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels y+c u qey56tu +xk z9afwi(i45k9(d vbat $v =0.10c$. 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 (sc07s6b2qi 0i0nmchsk( nr a of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requm 0e*zh /mmrjwb1cn43 ires $4.82 \times 10^4 \, \text{J}$ 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 brk o1ndtxw( wj-n/:s6neaks apart in the process known as fission in a nuclear reactjkw1t:( dow/-6 nsnnxor, the resulting 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 jg5;b c76kr mfyoules 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 protolvi70 a,yy ikz vds0dw/q/**wn in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consump bj( q nhtw13d vc+rru-+8c3nqtion 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 from conversion of 1.0 gram ofh+8745kd5j yk dg enbb 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 itxvbsq:fmfy7 :9w 8:ap:eg i+ qs kinetic energy equals its rest energy? v = gmv:y+qsqpifw 7:9 : 8fxab e:   c

  At what speed will an object's kinetic energy be 25% of its rest energy? v: vvlsq an k,y14vz6xtr x)s96 s*l3ms =    c

  (a) How much work is required to accelerate a proton from rest up to a speed4g6gc h 1c:vsup+ *evrjo*/y x of 0.997c? :4/cs+jgg x1ov y cv*eh*6urp W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and moment ik-3 hkxds7kb;p1 0tvum 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 protonlxw meey-t- ;xj)x0r; (that is, its kinetic energy is 750 MeV)?r x)e0-ewt-y x ml;;xj    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential d,p(ew8eub5sf ifference of 105 MV? v 5,e8uw pfbse(=    c

  What is the speed of an electron whose kinetic energyody)uv gv0eh/;d c4 n. is 1.00 MeV? v =    c

  What is the speed of an electron just before it : b ph4hkfqz7 *dc77ckhits a television screen after being h 74 bzf7*k:dhpcc7kq accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles7civ k1yziqalwd.ih 2;;d 0- +zgc +jp 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 px0yhy k; 7q kepu*nw(: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 and the momentum of an 9ja n50s-axfdop, fy4 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 27,00 rj wk b3q31z)uel:hf/0 kg is accelerated to 0.21c.
(a) How much kinetic energy would it have? KE =    $ \times 10^{19} \, \text{J}$

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

  Calculate the kinetic energy and momentum of awaxdy88 8zrndfj n7k9o:qx7raa+ i3, 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 nucleu*ln4 ii*bzs3y: o+iwws, $^{241}\text{Am}$, 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 momeh2om6m,yevb 6 ntum for (a) a particle of nonzero rest massv,6 by h6meom2, and (b) a particle with zero rest mass.

  What magnetic field intensity is needede*jbu5*(o ofivx x )rx*w(95oe5 sjwh to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Usex5ji5**wju v(5e*sx(9 o o ox whbref) 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 t5zrb 8h,xap -uraveling 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 mp,h- az 8rub5xoving with respect to the Earth? u =    c

  Two spaceships leave Earth in opposite directioz3r j40dzsy;jf3r (+;y xmotrns, each with a speed of 0.50c with respe mzj;rzj3 rtofr3sx0 4(ydy+;ct 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 tvyrf i c1u1u*(raveling at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Ca( v1ucu 1iryf*lculate the speed of the second ship with respect to Earth if it is fired
(a) in the same direction the first spaceship is already moving, u =    c
(b) directly backward toward Earth.u =    c

  An observer on Earth sees an alien vessel approtk z+hv4: pjq5e8n( e3huffs+8q v8ahach at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a e+j5(t z+8 hh8qsh afv4fkv8qpn 3e:u speed of 0.90c relative to Earth. What is the relative speed of one vessel as seen by the other? u =    c

  A spaceship in distress sends out td:nvz h 3nvdgg9ho2, 3lnq 8:swo escape pods in opposite directions. One travels at a spee n:h2vl:g3ohzsv n98,dg3qndd $v_1 =-0.60c$ 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, onmbt g8 :)j0rrocket B passes Earth moving 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it pabrmj n)0 t:8ogsses A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.3 light-years away. t*vz9ovwsoqipl / 3av6s-06h
(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 ck o h)0z omp0p*qyrc)1alled relativistic - i.e., for which the correction using special relativity is a significant effect. Dey k1c)z0qo0pohmpr) *termine 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 speederl2g x0 np5r0uru (4wgg(ej: $v$ 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 desteh 3,chu7j*vx royed to run a 100-W lightbulb for 1vjuh37h *ex,c year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electron a z2okae,43uz 6s ewf6euew1o7nd a positron together? A positron is a fu2ee 4 6ws3, e uzokoea1zw67particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.) E =    MeV

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

  A negative muon travelingd-slm5n9ok6 6g u56tj8ytul mxm p6t8 at 33% the speed of light collides head on with a positive muon traveling at 50% the 8k9j olmuxt-ys6g56 68mu5t lp nm6td speed of light. The two muons (each of rest mass $m_\mu = 105.7 \, \text{MeV}/c^2$) annihilate, and produce how much electromagnetic energy?E =    MeV

  A free neutron can decay into a p jyek03t ;tstptjt6q*;ywy-+ roton, 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 enep*;t w6 yt;tse3yy tkjtq-+j0 rgy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a x),vh5as,psk ar+ x78,1ngc mcc:np s 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 negative chargek1bm s up+v-3cd(qj ut(5h//i (hmykx 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 in( ioh-wh 3w4tch8bg j/to its constituents, two protons and two neutrons? The rest masses of a3 whh gtiw/4h8c(ob-j 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 (relativistic) mass onp6u kkm f-0-p*olkc1 f a car traveling 110 km/h as comparedn--p1 kk u*lf0k6p ocm to at rest? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a sef4zn; 2xlw72je lw0qe 9ue f k0krm/(peed of 0.935c in the laboratory, are moving toward each other. 0kenrlekwm4 7uw/ ze2xe;f q0(2f9ljDetermine
(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 partzq-e +9* ws-wqw.skvk;n+jayicle with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains f7r wq3y p9rj hc3ei*e3lep ;0its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprisei0l3 ee*rp7pwrqy9c 3feh3j; 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 so3 e9rftv yg9 n*oxv/avs9.h1 q that its kinetic energy is greater than its rest m9he9 nxa g3fto 9v*1yvsr/vq.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 can fit a 15.0-m-long pole into zc99 ff82sieb a 12.0-m-long barbsf z9 89eifc2n if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter to him than 12.0 m? ----待选择----possiblenot possible 

  When two moles of hydrogen and one mole of oxygde34x gqd81 dbytb /n sexk 3z07r6v+gen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elezd+yebg163 xqvs7k nr83b/t0xd d4egments 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, traveling in oppsje4iq)v 86 ymosite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle? u js 8qi v6)mye4=    c

  An astronaut on a spaceship trave odxarwbmy-*y *dik .q/z3t54ling at 0.75c relative to Earth measures his ship to be 25 m lrd yq/ oim.t*dax4 wyz -5bk*3ong. 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 of o.td+g,tmv7q bk+w1 w0.85c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?gk+v,w1+.7wd t om qbt

  A spaceship and its occupants have a total mass of 150,000 kg. The c*zj9hll e /x /(xqx9voccupants 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 energy. How much mass will be converted to energy to accelerate the spaceship to/9hj xqxlc(l*x /9e zv 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 sd8w 3eeky pk-;vw m7y9peed of 0.99c. What is the spaceship's kinetic energy? Compare with t y39m7wpedvy ;8kek-whe total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship n wmg.*00ey1nkulds w/so b25is to 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 1.0 year. How much work mus120g w/osmn yl kbe uwn*5sd0.t be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscilla,ta, yane4e aycs ll/.;3ss 4ctes on the end of a spring whose spring stiffness constant i4 cs3sa;,le,tnals/ y4.a ecys $k=48.7 \, \text{N/m}$. 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 m0v(, /liuaxq dass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.