You are in a windowless carcuv / +0fqx0etxh z 8z*yaqi-* in an exceptionally smooth train moving at constant velocity. Izt xfy0- xc8 qae*i/qzv0h*+u s 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;0dos, bf1pap;5w cjw experience of being at a red light when, out of the corner of your eye, you see the car beside you creep forward. Instinctively b1ac5jwpfpow d,s0;;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 throws a heav*ir (o1j nbwmubcc3g7+ 2no yvzo9/w+y ball straight up (from his point of view). Ignoring air resistance,mj1+7rb 9 cw+b2wui c *nvo(/o g3oynz 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 thyssuv) z9 g sr+yw aaskx;()1-at the Sun goes around the Earth? Discuss in view+a-xaw(zk)g s y s 9usv)ysr;1 of the first principle of relativity (that there is no best reference frame). Explain.

If you were on a spaceship tvx8 y+wb rdgvm4m0d9 (s z;(ovraveling at 0.5c away from a star, at what speed would the starlights+ x08 v v(yrv49ddmwogbz;( m pass you?

The time dilation effect is sometimes expressed as “moving clocks r)il6emjn6q r,( yur.l-jn7i tun slowly.” Actually, this effect has nothing to do with motion affec )utlqjrnii,y j .6n(m -erl67ting the functioning of clocks. What then does it deal with?

Does time dilation mean that time actually passes more slowly in moving referefb0e)* jfsk-n nce fr-jfesfkb*) n0ames or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a long trip. fd0xxv bygb*xs8/ cyn, wz(+9She rushes up to an old gray-haired man and in thw+b f,b*0xnv(cz s/yxgx 8 dy9e ensuing conversation refers to him as her son. How might this be possible?

If you were traveling away from Earth at speed 0.5c, would yoi qg4p-8+ zsmgo2lsu mb )q1m7u notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telescopes say about y4su gz7 )1bq+l2m-isg pm qom8ou?

Do time dilation and length contraction occur at ordinary sp55j g+oxfm 5o6c. ogln+.x zddeeds, say $90 \, \text{km/h}$?

Suppose the speed of light 1,hm:wnt j; jvwere infinite. What would happen to the relativistic predictions of nvjw; jth:m,1 length contraction and time dilation?

Discuss how our everyday lives wou ze:g8dv bdj::ld be different if the speed of light were onlzgddb:e j8 ::vy $25 \, \text{m/s}$.

Explain how the length contraction and time dilat2 qorx x.m5 sbw w(l,sdu0y.hp:0m:do ion formulas might be used to indicate that c is the limiting spexw(.q.umw 2ro,h b p m5ysol0dsxd ::0ed in the universe.

The drawing at the start of this Chapter shows the street as seen by Mr Tomsl1.damfmx5jj,+nk 6pkins6,jxksa .1mf+l nd m5j, for whom the speed of 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 uzzd3, (id qoru6tw.2upper limit on the moment do d,(ir zz6quuw2.3tum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass attain thogq/t0nr94v r y,oh q6: jrge5q+aa9o e 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 l/ )*j+tym0 lzpfck (xi+kd6 vmean that a spring has more mass when compresk/ cpzyfmi+d+ (vkxtj ll*6)0sed than when relaxed? ----待选择----yesno 

It is not correct to say that "matter clyw 1uafg 8j+qgs,qr l1 1rv);an neither be created nor destroyed." Whaulqgyw81lgrfv aj+r;,1 )1 qst must we say instead?

  Is our intuitive notion f+f/ygcq4rll8g j j6(that velocities simply add, as we did in Section 3–8, completely wj/fjl6+8y4 (gr cfgqlrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.7p.rr++gd3co6 j kydgsmp-r*.50c. You measure its length to be 28.2 m. How long would it be when r.g.6+opg my d-sr+c k*pd3rjat rest? $L_0$ =    m

  A certain type of elementary particle travels at a speed of 7x, kmk/3 r)9kx ,qk fc4pdglfy+b *an$2.70 \times 10^8 \, \text{m/s}$. 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 intervaf;b;w6tjym*uje u6k , 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 to a star 125 lignku 8yr1 gw.7cht-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 life1igxc ;p;zng 1time 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 fr*qj17g.af uqgo zp+a2 ame, a star is 82 light-years away. How fast would you have to travel so that to quf*j2 o7ggaz+p.aq 1you the distance would be only 35 light-years? v =    c

  Suppose you decide to travel to a star 85 light-years away atdyfdo9yxgp8x bq7668 q s31vc a speed that tells you the distance is only 25 light-years. How many years would it take you to 6do8x76cb3yp d 8v fyxq9g q1smake 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 thez , u8utmucqrc*l )(l,0m*j zufu ;:um Earth is $11.2 \times 10^3 \, \text{m/s}$. What would be the percent decrease in length of a 95.2-m-long spacecraft traveling at that speed? L =    $ \times 10^{-8}\%$

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

  Suppose a news report stated that starship Enterprise had just retumnxsx+l, ;) xgt3md-wrned from a 5-year voyage while travel 3swm -xx,l;gd+tmx )ning 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 wou0y9pl 68mk4a lr9eutnld it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by l eu9yark6m90n t p8l4observers:
(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 "Ferrj *yx6n0 vl*:vl(cidr ari" spacecraft at a speed of 0.660c. It is measured in your frame ydcx0*v6*v:nj rl(l ito 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 q 4mbx5w jk(t4m before it decays? The average lifeti(kq4t 4j b5mxwme, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a p o 1v+wqbeq*(rroton traveling at $v =0.85c$? p =    $ \times 10^{-19} \, \text{kg·m/s}$

  At what speed will an obj en uy(ci50vt s9/w:hyk58z+ qefzj2rect’s relativistic mass be twice its rest mass? v =    c

  A particle of rest myat/0 5k3 fzxx 6,d6jcfsnom7ass $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelsez1i1 v m7zo8tn15 pq.glwvc7 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 ac.ii3tfw la3ndc8n+ /s gqs 4epofs9)9celerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical rea.,k6c0m-i pk oks)wyaction 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 nucleusdz4 7(w u5pndlyrl/l) at rest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost i dldrpw )5(nyul/7lz4 n the process? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an ( jbd ur*7 i7*toxnm+0fvy6hxr (d-wgelectron 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 my 48j6g,hgxqtf3err +ass of a proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United Sta1 kh3anv5t5wck 4b4x 5pz5fistes 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 mabm)v( msn1p0 iss?    $ \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 kinet cr ;f r:je)(x1r(ta6/oso0d hmp :ya.szf-vxic energy equals its rest energy? v = 6zsmt/-x (;pfjcahr ofvay:e o(rs.0d r1):x   c

  At what speed will an object's kinetic energy be 25% of its rest end(y gx4tz 0/c-c94twq1czzzqergy? v =    c

  (a) How much work is required to accelerate a p+jm)zxal it::roton from rest up to a speed of 0.997z )m:alt:+x ijc? W =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum of a proton trvmf 90ayq9 i4su5jwa uah2 r4k7*qxa*aveling $2.60 \times 10^8 \, \text{m/s}$.
KE =    $ \times 10^{-10} \, \text{J}$
p =    $ \times 10^{-18} \, \text{kg·m/s}$

  What is the momentum of a 750-MeV py;sqou ;, abd;2ft zs;lq) 4curoton (that is, its kinetic energy is 750 MeV)?t2u4cl u,;;)badfsq q ;oys;z    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a p(: leh8d:uarh roton accelerated by a potential difference of 105 MV? v = 8euha: l rh(:d   c

  What is the speed of an electron whose kinetic energy is 1.0n)5x /igw 2qft9 tkr n(d4u6ro0 MeV? v =    c

  What is the speed of an electron just before it hits a t: ,q v hdzo0no(ln u9fbu qx19g2xog;7elevision screen after being accelerated from rest by thefogu0 h :ob,(q92qv ;1nzxxdlnuo9 g7 25,000 V of the picture tube? v =    c

Two identical particy83 8ag6fuvc:px 9 yogles 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 projo2xd wwfr+sach) w2 c-56(t tton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and theve cm(9.6grlw 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 accelekfy-- 5kk vekt)ie;pbd+z :o; rated 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 amw:d4aqxoac)oa/b +4 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, p2n wxn21 xd zmm2mte)f1u6i ab e7q5/y7m7 uf$^{241}\text{Am}$, 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 ver ubi), blh h*;;bfhee+sus momentum for (a) a particle of nonzero rest mass, and (b) a particle with zero rest f;b; bebhuhi,lh )*+emass.

  What magnetic field intensity is needed to keep 998-GeV protons revolving in a cfjul+ 1(5 vztyircle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The pro v+yu1jf5zt (lton'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 Eaaent 9u jlmo8qnu4o*21u31l2h yl t n.rth) observes a meteor come from behind a2tt e41u yn* lu39.8lnauolmhj1onq2 nd 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 with a speed of h +0 pe*jry1px: l)xvm0.50c with respect to Ea 1v e *0)pr+hxp:ymxljrth.
(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 leaves the fibgv34jatm( dg /pvua9vugi 64b8 4 o1mrst at a speed of6bvt4mo3j1b d a( 49gvmi/vgua48 pgu 0.87c with respect to the first. Calculate 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 approach at a speed of 0.60c. Theb( 8voz8 l(mcsj5z* he Enterprise comes to the rescue (Fig. Below), overtaking the aliens while moving directly toward Earth at azh8o8 mb lszjv*e5 ((c 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 two escape pods il(+v2xj )pkb9mram7 z n opposite directions. One travels at mjx9z)l+2k 7v mpr(baa speed $v_1 =-0.60c$ in one direction, and the other travels at a speed $v_2 =+0.70c$ in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod? u =    c

  Rocket A passes Earth at a speed of 0.75c. At the same time, rocket B passebw sb 6;/+bwdes Earth moving 0.95c relative to Earth in the same direction. How fast is B mov;e bbw d/b+ws6ing relative to A when it passes A? u' =    c

  The nearest star to Earth is Proxima Centjgh0:y 4f bw)hn)yhjw ca.2+vauri, 4.3 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 called reqfbj ;rj*toglk dp31 wg3q/ *7lativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an elf ;g7/pd 3rgbq* *ol q1kwtjj3ectron 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 l n(.,f5tyn czk2 n)1/qouedh$v$ 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 tota48x1g /)c;hsj pd n krlue)h,z*i,ck e)5 ctpblly destroyed to run a 100-W lightbulbz)gc ,8;e)e45jp*k,htcp dl rhb nc) kixs/1u for 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnet:rc5 l u auk0+cbk0vj+ic energy is needed to produce an electron and a positron together? A positron is a p0uc+vbjk: ru5ak +c 0larticle 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- r35*/vb 2t 4gt+rjrdd 6xeo;xhjizu collides head on with a positive muon trav x6j e+-rr drtx;b/ 4voguidz5jt3h2*eling at 50% the 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 proton, an electron, and a neutrino. Assu- eb7 vzkzqd9(- nh7s dzueji m(,6fh/me the neutrino's rest mass is zero, and the other masses can be found in the Table inside the front cover. Determine the total kineth-(9/nv7u (qb,ze 6zz smieh7d-dj kfic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a rate of ajv1e ) ll*9r1uf7w ufr4tba4tbout $4 \times 10^{26} \, \text{W}$.
(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 n( aanbg8v,3 u.kk/nlp egative 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 t3280upj ahlj to break a helium nucleus into its constituents, two 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 bipu2jha tj0l38 nding energy of the $^4\text{He}$ nucleus.) KE =    MeV

  What is the percentage increase in the r ye 4td)x:4v,xk0ys2psf+al(relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hint: usdsv yerlfx y0, spak42t:4)x+e 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 labo7hfjf7p3en zgzn t *9(ratory, are moving toward each other. Determinefh7f79ntg zj (z3ep n*
(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 p yio*7mww;0ape0 v2 dsa 5g4qwith momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Ent2 ql:jp s4eky2erprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of:pelk y2jsq2 4 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 kinetf91foa8n,9 wodqaah ),u *b biic energy is greater than its rest m), dbi*h, bf f1wa9uqa 9nooa8ass $m_0c^2$ 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 fit5hnp.idv g: +fy xl.;fpr28 qh a 15.0-m-long pole into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How does this fit with the id g:ip hfrqyfx58nd.h 2;pvl.+ea 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 of25+)jje l+pj)joi hir oxygen react to form two moles of water, the energy released is 484 kJ. How much does the mass of the elements decrease in e5ij+jip)rl+2o hj) jthis 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 createsz7d m/od*8 ov.ydiuzq 4jq32d, traveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame d2y4 3zq8od/i.sj od*mv7zuqof reference, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relativettkxf+jq7hu4r4zq8 .9 l 3 yth to Earth measures his ship to be 25 m long. On thk l3qttj8 +z7yu .9qhxf4th4r e 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 sp:;tuk y +o r28pke4umjeed of 0.85c 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 th4je82u ; +umkrtkopy :e speed of the laser beam?

  A spaceship and its occupantqu,o*djac -u 2s have a total mass 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, the engine of the spaceship changes ouu2 ,jd-qa* cmass 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 space i9z s2o6t7avrvg6r j.ship left Earth at a speed of 0.99c. What is the spaceship's kinetic energy? Compa9tzr 6.a2rjg 7visvo 6re with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceshipu0)lhvzam q5; 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. Hlua; mz) q5v0how 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 spr ,j uu51s8* gj4v 2dutx0khynming whose spring stiffness constantyujt*4k u0s, 15mhjdgn2 v8x u is $k=48.7 \, \text{N/m}$. If this system is in a spaceship moving past Earth at 0.900c, what is its period of oscillation according to
(a) observers on the ship, T =    s
(b) observers on Earth? $T_{earth}$ =    s

A pi meson of rest maqh8cs) gm(f3s0r mkf h- tr,+*pnmze 6ss $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.