You are in a windowless car in an exceptionally smooth train moving at constanvykx2j k: d5y8t velocity. Is there any physical experiment you ca8k:y kd25vy xjn do in the train car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a w7)e5 kz9zxw ared 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 rolw5 z7zw)kxe a9ling backward. What does this say about absolute and relative motion?

A worker stands on top of a moving railroad car, and throws a heavy ball s s q+ip jegdy88,3lx.straight up (ps g, ylq8j3dxsie+8.from his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around tht4arcejm 5b+z ; )x)vqe Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss +btq4 x) 5;jzacremv)in view of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship tw)qnu:dt2/ i.l jcov6raveling at 0.5c away from a star, at what speed would the starlight pass youw /:u.6 n)dqicvloj2 t?

The time dilation effect is sometimes expresseyyk+n (g.emcn) z,lw-d as “moving clocks run slowly.” Actually, this effect has nothing to do with motion affecting the functioning ne-mn)w( +glyzk,y.cof clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving referotu 3l 7q cd7bd (ut*swwv,94uence frames or that it only seems to pass q ld 3wt9uc*77vuts4du,bw (omore slowly?

A young-looking woman astronaut has just arrived home from a long trip. cbl v+xf+.6 *uzqklq4 She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How q ++qcb zk6vx4 lu.f*lmight this be possible?

If you were traveling away from Earth at speed 0.5c, would you noti8t8tr;n 7.1x iaxpt exce a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about y7p;1.tn8txr8 ai xe txou?

Do time dilation and length contraction(4)u /h ooze i(thqdn6 occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light were infinite. What would happen tv 5svmq*1;6j wko q*sjo the relativistic predictjk *vq*65 mo1;vws jsqions of length contraction and time dilation?

Discuss how our everyday lives would be different if the speed of lightv8wso/ve 61rh were only8rwo6v1eh vs/ $25 \, \text{m/s}$.

Explain how the lengthux5i9jgyfum4q z*bb 57,fr l 9 contraction and time dilation formulas might be used to indicate that c4fiblbu9y zf5 q* xrg7 5m,9uj is the limiting speed in the universe.

The drawing at the start of this Chapter showsr sdm3)yu/1 e(dntn:x the street as seen by Mr Tompkins, for whom the speed of light edud m (tnnx)s:y 3/r1is $c=20 \, \text{mi/h}$. 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 tn:n l+u.tl tx7his put an upper limit on the momentu. :7xnl+ttlunm of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzerey(e 6n mg:lp1o rest mass 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 mean that a spring has m: iuac bd(y(oh9j xk9v.0nk.uore mass when compressed than whenc9d(vxhyko:.j0k i nbuau. 9( relaxed? ----待选择----yesno 

It is not correct to say tha1jfv e*-4cjrot "matter can neither be created nor destroyed." What must we say i f1oec4jvr* -jnstead?

  Is our intuitive notion that velocities simply add, as we did in 7 ntfnny gx0txft7m:7/w2 /oySection 3–8, comp2x7f7/fxg yw mnyn0 t /o:7tntletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its leng;5fifo8p:a5, 6lrcnb xeeks ,th to be 28.2 m.pbf:er,koa f56cs le ,i85nx ; How long would it be when at rest? $L_0$ =    m

  A certain type of elementary ph. )wa14:qfkyt,smcw7s b, ffhxt s7(article travels at a speed of $2.70 \times 10^8 \, \text{m/s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \, \text{s}$. What is the particle's lifetime at rest?
$\Delta t$ =    $ \times 10^{-6} \, \text{s}$

  Lengths and time intervals de:,v-zj zue*p3lg;zhq-f qev+pend 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 4hnt *xq ebk18star 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 average lifethwk/9e p49es time 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 qn.zn1ayte(.* ucfd3/jvq 0 e82 light-years away. How fast would you have to travel so that to you the distaj n13 dqq*y0zvc.e(f atu.en/nce would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years lcotr9 99wat-v(g+r eb3p5yb away at a speed that tells you the distance is only 25 light-years. How many years would it take you to mak3bve tr5l9-9(cy +tw9a orb pge 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 is7(5sz geljl r;/y1b l+xnh-uo $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

  At what speed $v$ do the relativistic formulas for (a) length and (b) time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to do relativistic calculations rather than classical.) v =    c

  Suppose a news report stated that starship Enterprise had just returned from a o53szre23i; mim3foi5-year voyage while traveling at 0.i o 33mm325zoefri is;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 t77y9nzyf8 j97ib vib away. How long would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observv79yftjb78ibiy n9z7 ers:
(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" space ncw.5g f,qo7rcraft at a speed of 0.660c. It is measured 5,.g f7nqocwr in 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 pion be moving to travel 15 m before it decays? pcv +cyuj.+it vk526b The average lifetime, at re+bi v ycv+ p6tj5k.uc2st, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trz6sv:7: fj( r *r-zv iy7vtzwaaveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an object’s relativi)nl m*qbnhd:yi9y.) 2mp9w rtstic mass be twice its rest mass? v =    c

  A particle of rest mass t/(ql5ny7hx*mn2en w $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travele trec da aov2/4/b7j2s 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 acceler1*- rp(zzj wzpates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requi b:e 2zm9mh7jares $4.82 \times 10^4 \, \text{J}$ of energy input for it to go. What is the increase in mass of the products over the reactants?$\bigtriangleup m$ =    $ \times 10^{-13} \, \text{kg}$

  When a uranium nucleus at rest breaks apart in the process known as fissi, yz,-*vivdmcon in a nuclearv,-,mvz *cydi reactor, 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 electroxuxms *k wdoh:9o msqp2+ o,18n in joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass ofwh+1 ;m a)ovos a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the Unu,hprr5 qb5f 4ited 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 gramo36s i i/335c3 xfvba*zpn wfx 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 e4r1v2 hnt9y*dfa , u* x:flcha particle when its kinetic energy equals its rest energy? v = chdext9vn4f a:*fyl2r,h 1u*    c

  At what speed will an object's kis +5art3r 0bsfxxn.m;vz u 3)fnetic energy be 25% of its rest energy? v =    c

  (a) How much work is required to accelerate a proton from rest u1c: xl,eb( /x;hwpkd;zh o5eyp to a speed of 0.997cce(op,yxh; ;b x:lhed/1k 5 zw? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic eji(cc4w 5ro +,kvp ze*4llt1p nergy and 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 k, mu5cst8 cd6a(kkuxdk; 8mphjg +m1(inetic energy is 750 MeV)? ccj d6(k pku8 xu(+m;k8ms15mha, gtd   $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed ofkn/ka-c -k9db a proton accelerated by a potential difference of 105 MV? v /9bakkdc-k- n=    c

  What is the speed of an elect*(7ev+ixdxq x ron whose kinetic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before l * uz3akdd0:9jz s(wl7:r7c ezygji* it hits a television screen after being acceleratkwzz7a l3gds:ij:7rd0l (9c** yuez jed from rest by the 25,000 V of the picture tube? v =    c

Two identical particm/do8zc3 r2ttles 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 proton 0re* h(qlq an)($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momihw.0qv rx, )oentum 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 acceleratedr w4 ;bu 0l+:a-ztpjgd 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)rllmhp66qmu sgx9(c +3 zzvpew. v4i*7iil - and momentum 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,b; czj m-n-5zcodtr.x,*chr3 $^{241}\text{Am}$, 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)d-y9-iwgt s)x xqp 7lc5yghru9;s; 4uf+tv 7w a particle of nonzero rest mass, and (b) a particle with zero sv4ywd ;w 7gq 9 7tlfr-;u)sx c -y9g+i5uhxtprest mass.

  What magnetic field intensity/q7x8rk c0;x ejre8jb 9 gzn8m is needed to keep 998-GeV protons revolving in a circle of radius 1.0 km (at, say, the;7x0jc8 z9n 8xjgqr8er/ mbek 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 the Earth) observes ayp081oqw -:l9hk1bpwc w lg z2 meteor come from w:2h ll0b9yqk8c-gw 1z opp1wbehind and pass 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 wit tyh;l.o s5h* verf6so3pv.cj5t5g1y h a speed of 0.50c withetght 5sp5ylro* v.5yc . 36v j1f;osh 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 leavmb 5u-n* -odunes the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it -om*udn-5 bunis 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 approacflz2ev: g) dc3d/ji p7h at a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at a speed of 0.90c relative to Earth. What is the relative speed of one vessel azdp)evi:fl3 7g2jc/ d s seen by the other? u =    c

  A spaceship in distress sends out two escape p+az 7gkm00a zmx6k3vw ods in opposite directions. One travels0za+6k gwza37vmxm k0 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 spurgt35mavc-m4:x q tlde rm8; i5o 9e4eed of 0.75c. At the same time, rocket B passes Earth movingmdie-8urc9m 4:r l5 5m;qox gav3et4t 0.95c relative to Earth in the same direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centauri, 4.u;*ouiyl 2 qhr58ypy, 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, anythinw ggj155 d(0daa s*dcof:x:o lg traveling faster than about 0.1c is called relativistic - i.e., for which theo5j :lgaw*xdc:ag d( dso105f correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom ($v \approx 2.2 \times 10^6 \, \text{m/s}$) and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.) ----待选择----relativistic not relativistic 

  (a) What is the speede mqk4 uv;/,8vtmp5uu 8o ot6b $v$ 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 100-W lims*0u2owri -cq4vb x:ghtbulb for 1 year? 4 :*-msvcixrwbuo02 q$m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed toqlasx ,4lhws) j -m94 s:botl5 produce an electron and a positrq l,b-xs4ow)5l4sj st9m al h:on 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 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 c yud,p5 . qr1ouku7t3dollides head on with a positive muon traveling at 50% the speed of light. The tuk13yt u. ddp7oqr5u, wo 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 in* 74z.ha uew(6 8iz81yce) mhvzxoual1slm 4m to a proton, an electron, and a neutrino. Assume the neutrino's rest mass is zero, and ti)h6em8lzs yv ueuh*a1 xlz(71mca mo4z8.4whe 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 0pbdtu6 (s5bujw8q w et;)3 tsof 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 negati2k )oge)ybp,do.1tb.wy0j ii ve 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 nv 1.01qu+zsloy razp5ucleus into its constituents, twoy. us1av1 oz +z5rl0qp protons and two neutrons? The rest masses 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 (relativistic) mass of a car tr aw8lp ;5neht /85wkf w 0vhmc 0*ayfp,noe5n1aveling 110 km/h as compared to at rest? [Hint: use the binft55nwv/8p0man ;0 5e wfekcwp nh1ah yol*8,omial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0.935c inq*uuz2u 8fp( u the laboratory, are moving toward each other. Determfz *(qpuu2uu8 ine
(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 particle with momejvfnyc3b9-3(xf0)rtb:tz ycs+x a .yntum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its power by combining matta yrusc+.7s3mt.r*ab er and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approxima 3rm+.byars7c u*.ats tely $5 \times 10^9 \, \text{kg}$, 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 acceleratedinsc z6i7z/he2o od62 so that its kinetic energy is greater than its rest massoi/s6do h7zie22n c 6z $m_0c^2$ 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-28dw v2olew3rlong 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 l3 2d82rolwvew ooks 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 two molesg,hwb+rnfm (2 of wate(rm2g,+h bnfw r, 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 crij0 yl7t- nl1ueated, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the u7iljln0-1yt laboratory frame of reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship tr) i+jyf/vde8 qaveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats yi)d/+8fq evjhis 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. Your38+kht(y rf6ll,ecd h*f he0 send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth ,rhc3hfe0h+(6le*f l tkrd8y measure for the speed of the laser beam?

  A spaceship and its occupants ha8f k g20 ww*i iox/-rvojs(0cqve a total mass of 150,000 kg. The occupants would like to travel to a star that is 25 light-year i0*isqrwx co2f-v80ogwk(/ j s 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 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 les8be(ahxc x0,+1 bxgn ft Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumptio+n 1hxbcx(gba e8x0s,n (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceshibg io ).n(o+7gw*eup kx i)tm,p is 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 must be do)tg* kpmogb)ou(,7i.neiw + xne 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 sprinn1.0fba v8plvg whose spring stiffness constant isv. blnva fp801 $k=48.7 \, \text{N/m}$. 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 m 08/go .c:n9f n utxwr*fcu.fjass $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.