You are in a windowless car in an exceptionally smooth train movi0opx8zotc8a (ng at constant velocity. Is there any physical experiment you can do in the traot p8a0( x8zocin car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a redsm( srbwy*rcrm 6 )n.4 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 does this say about absolute and r(mcy sw)ns*m b r4r6.relative motion?

A worker stands on top of a moving railroa2or ):h/nuh qed car, and throws a heavy ball straight up (from his point of view). Ignoring air resistance, will the ball landhh2:nueq)/r o on the car or behind it?

Does the Earth really go around ths: slii* 4)mpee Sun? Or is it also valid to say that the Sun goes around the Earth? Discuss in view of the first principle of relativity (th4 ml*sisepi ):at there is no best reference frame). Explain.

If you were on a spaceship traveling at 0.5c away(cq vsav( l kz+ol8c,; from a star, at what speed would the s o(s(zv;8 ,lla+cc vkqtarlight pass you?

The time dilation effect072w ybtz+a zd is sometimes expressed as “moving clocks run slowly.” Actually, this effect has nothing to do wbzyt a27+zd0with motion affecting the functioning of clocks. What then does it deal with?

Does time dilation mean th)pdts3y9 coi+ pw).izvc5 kd*e22 dxz at time actually passes more slowly in moving reference framc.vo)p)22w xdd+idi zkz cs t3e y*5p9es or that it only seems to pass more slowly?

A young-looking womahi eie)q7*k :8mf ok5on 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)f5 k7k8qoee:io* mhi as her son. How might this be possible?

If you were traveling away from Earth at hwl2ob 5+ t:yaspeed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? W+bth w52: yloahat would observers on Earth using telescopes say about you?

Do time dilation and length contraction occur at ordinary speeds, d3w t2v u0poe9say $90 \, \text{km/h}$?

Suppose the speed of ao j3a1v2(aa h*wr2qe light were infinite. What would happen to the relativistic predictions of lenwaa 2v *3(a1erajq oh2gth contraction and time dilation?

Discuss how our everyday lives would be different if.n*avqcb3d za-( d*;k56m1l3wd+ hnecgi vhc the speed of light were onlbiclc;1* 3c3v*v.kg5dz(wmeqna d6nh h +ad- y $25 \, \text{m/s}$.

Explain how the length contraction ac* aex.tvg( )knd time dilation formulas might be used to indicate that c is the limiting speed in the uni t k)(gecv.x*averse.

The drawing at the start of this Chapter shows the street as seen by Mr Tws,b0,g ljc /tzl2t+oompkins, for whom the speed of light iwc0,l2ot,s+bgj/l zt s $c=20 \, \text{mi/h}$. What does Mr Tompkins look like to the people standing on the street? Explain.

  An electron is limited to travel at speeds less thanqd3 wir8a(anvb6f ;y 1 c. Does this put an upper limit on the mn y1rv3 ; wba8q(fi6adomentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonzero rest mass2 x2qyfk3w q-a 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 more mass whene*6vrmo m*5z z compressed than when relrv oz5 *6e*mzmaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be created nor dw nls:::b je9r r6mk-oestroyed." What mustmbo sl:kwrrj:9 e6n-: we say instead?

  Is our intuitive notion that velocities simply add, as we did in Sectiou2 e96rnz fk1sn 3–8, completely wronzs kue1n f9r62g? ----待选择----yesno 

  A spaceship passes y-fqmv ,91 yegsg4t8j,i es tx.ou at a speed of 0.750c. You measure its length to be 28.2 m. How lo1m iyt . ,gse48esgtx9, vf-jqng would it be when at rest? $L_0$ =    m

  A certain type of elementary particle .+xs(il, ogr lcm/r*ctravels 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 6bqrdm): w 9yldepend 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 from Earth zq;-tka0t z95wma-torrd;(h4t2rfu 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 6 fz (m**uczlk+ds;jxpion if its average lifetime is measured to be $4.10 \times 10^{-8} \, \text{s}$? At rest, its average lifetime is $2.60 \times 10^{-8} \, \text{s}$. v =    c

  In an Earth reference frame, a star is 82 light-years away. How fast woulgb*x ,c31bim1wdf3lc d you have to travel so thad 3b 3w,g cmxcl11i*bft to you the distance would be only 35 light-years? v =    c

  Suppose you decide toar whj /t)y*g(+)spsu 9rc zia hl8):q travel to a star 85 light-years away at a speed that tells you the distance is only 25 light-years. How many uc)ai(+*/ th9)q:js a h)g 8lrrwpzysyears 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 th+s- sq mn b0frt5;(zlme 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 Entev3uwcpimg r)o/:g 9h;u 2i8ht rprise had just returned from a 5-year voyage while traveling at 0.84c.hp igvt) 93h rmu2gci;w:8u/ o
(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 takkn,+*jysb7oq( z,vu le a spacecraft traveling 0.960c to reach that star from Earth, as measured by observlyq ,o7j u,(svzbn*k+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" spacecraft at a speed of 0.660c. c( rsrwg5 1am)It is measured in your frame to be 4.80 m long and 1.25 ms gr 1r(c)5wma 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? The 81 7dvggpiwvtn 3j *.b-b 0te,v mkgb)average lifeti 3ggji1p .,kdvn b)*btg 0-b7tvv8emwme, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum o/0jid)-0un+e kiy9lc jtqa: i f 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 massd jv3gx: d(-t a.r81xemd5k)fvv) un8 kwo.uf ? v =    c

  A particle of rest masn16 abfe* 5owos7jy ,is $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travelsx;-f9n r4 txmw 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 moment6wj 5qz )eqw1 hv4,bqtum of a proton that accelerates
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical re -5wmtzqo *kp ,1f-ucraction 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 the process k kbi959jvbqoqgj8+jv, iw 9w q2+0thsnown as fission in a nuclear reactor, the++q9 5 9bb2 sj8jg k,j9 wq0iiqvwhotv 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 ine :oiha9d y4mmz:6+of joules and in $\text{MeV}$ ($1 \, \text{MeV} =1.60 \times 10^{-13} \, \text{J}$).E =    $ \times 10^{-14} \, \text{J} = 0.511 \, \text{MeV}$

  Calculate the rest mass of a prou )f4g q t6s2jrc*t9yzton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumoi/fm yxv 2+w:ption 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 conversio+j(kj ai :df:f ei(c2m1jslw4n of 1.0 gram of mass?    $ \times 10^{13} \, \text{J}$How much mass could this energy raise to a height of 0.25 km above the Earth's surface?   $ \times 10^7 \, \text{kg}$

  What is the speed of a particle when its kinetil yu0+i,v7d v(vowup 3c energy equals its rest energy? y ov3wu(uip,7l 0+dvvv =    c

  At what speed will an object's kinetic energy be 25% of its rehi d+1tq 6wqyhd .8-qvst energy? v =    c

  (a) How much work is required to accelerate a proton from rest ua-.xkou b;j9 tdxv1h0 p to a speed of 0.997c? W9 u - dxt.ka1v0h;bxoj =    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and mth/mogriyee5/ t +)2l2lya4vb, bk -em0pbt.omentum 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 ozy)v;c/ uz+ff8 hyyqkvucr. e pa6 /,-f a 750-MeV proton (that is, its kinetic energy is 750 MeV)?/+fh8/.yy,c ;z6 )kuqvarvcup-e y zf    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proto7o(3 j5rx b6 yhhj5ru0q/wqi bn accelerated by a potential difference of 105 MV? v hr6qq 5brw7xy j3h(oj/5u0 ib=    c

  What is the speed of an electron whose kin7rr*jpon 0-kc+ rb3tx qc2 6oketic energy is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits ad5 l45fx.knyzker+g 5 television screen after b5l g4d. nyk5z5ke r+xfeing accelerated from rest by the 25,000 V of the picture tube? v =    c

Two identical particles of res o*s1vd8iqmpd *w,g8t )umw x;t 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 pr-+yids+sqi. sr*x2t q827 oop k1 xqhdoton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentul ;m)(jm 2to)cc :rqbj+*qtj qm 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 27,000x9.h3 byp uw7p 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 a c1 ni *f0x7/v x(u4 bcyrt(ty5mqv3ybnd 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) xq6z(puh9sih2inxj4n gx*1 , $^{241}\text{Am}$, 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 of noyn0vdt*z.ha j,r0y t2 nzero rest mass, and (bh.nz yar*0 tt0 v,yj2d) a particle with zero rest mass.

  What magnetic field intensity is3sg1v ujxk x i/qm13m- needed to keep 998-GeV protons revolving in a circle of radius 3uqki x mgmjx1v 1-3s/1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is $0.938 \, \text{GeV}/c^2$ ($1 \, \text{GeV} =10^9 \, \text{eV}$). [Hint: in relativity, it is still true that $\frac{mv^2}{r}=qvB$ in a magnetic field.] B =    T

  A person on a rocket traveling at 0.50c (with respect to the Earth) obl0)(;h n,qe2/pxzylz:v hsit 7t +l enserves a meteor come from behind and pass her at a speed she measures as 0.50c. How fast is the meteor moving with res20,tl+z q7:yzp(s hxen ll;h/t n)v iepect to the Earth? u =    c

  Two spaceships leave Earth in opposite dixh h xsev:yya 0.kbmmd8743/ yrections, each with a speed of 0.50c with0:yx/mhya dk4 38hxb v7e.y ms 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 travelinfa4virxe30 5uto+y 9 cg at 0.71c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Ea+ir3 9aux 4tyc fv05eorth 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 d p 4).v7*czpdinw09svx :s2wia6na, lvqo8jat a speed of 0.60c. The Enterprise comes to the rescue (Fig. Below), overtaking the aliens while pnnda6 8xd :4c*i v v0wj9a ,ivsz7sqol p2w).moving directly toward Earth at a 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 in oppositek,j,cu0c+gqe. stz q/uew q)5 directions. One travels at a sp /qesju w ,+g,t5qzqc0u).ckeeed $v_1 =-0.60c$ 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, roc+*)aw zi)npqr ket B passes Earth moving 0.95c relative to Earth in the same dn*a +qzr) wp)iirection. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is ol,)whs; c p9,(4hobe mrak w5Proxima Centauri, 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 fastetwv ) pi6,org(r than about 0.1c is called relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the speed of an elec)wg,ti (o rvp6tron 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 lgwsfiu5 oe ,-,e; 5st$v$ 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 total,c3ehk moz1. w, eofu9jf56f ely destroyed to run a 100-W lightbulb foowh6fok15f3ez. e,c eum9 ,fjr 1 year? $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnetic energy is needed to produce an electrowjx;b ;1x 8fwin and a positron together? A positron is a particle xj 8i;1fww; bxwith 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 collides head on with a dm +7; j mp8k8bqut)kppositive muon trap+q pjmu8)b7k tk ;8mdveling 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 wqx6 7;(hbnkpelectron, 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 ki h(w6qb7pnk;xnetic energy shared among the three particles when a neutron decays at rest. KE =    MeV

  The Sun radiates energy at a 71 a5milv(mwy 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 charge andcbv/p; ba su2ot q-)/e 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 its constituf, :)km v uy+k s;z-1nwasdk3tents, two protons and two neutrons? The rest masses of a proton (includis z:wfkk1 y) -tuv+ sda,nkm3;ng 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 o6vq wq, zqf28in the (relativistic) mass of a car traveling 110 km/h as compared to at rest? [Hiov2f6qw8,q q znt: 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 i4a px*2cs 6qct/e(dz toward each other. Determinea/ct (p2s6i *x edqcz4
(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 wizh8g5j 7y6b cmth momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Enterprise obtains its pc :p0b iefgm8,0b9nwe cuaw5 5ower by combining matter and antimatter, achieving complete conversion of mass into energy. If ma0b:5 cpwegwc9e 0fb8ni u5,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 energ8 e qn9ag2xx7zchp*2hy is greater than its rest mass hzxq8ncex 22g*p7 h9a $m_0c^2$ 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 polz;2pw(u +tc++cz s(8 pq gyszoe into a 12.0-m-long barn if he runs fast enough (carrying the pole). Can he do it? Explain in detail. How d+qpzo2 w+sz+c(ct(s8ugz y;poes 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 two moles ml,akq ddii:.z :e;*nof water, the energy released iim, n::*e l;k.dziaqd s 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 cyq k s0 igqi23:s)cbe/reated, traveling in opposite 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? sc2 3yqe0:iksbi )/gq u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures hi lb / 7jwi)x(br5gdkv8s ship to be 25 m long. On 8 vgxbk7r w5d/(bji)l 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 dpt* lhzx30+t m :d ljh2f,7u0vjh)zqspaceship 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 observers on th0dz jhvtz2lhdp ),7 t *j03fu hm:+xlqe Earth measure for the speed of the laser beam?

  A spaceship and its occupants have a total mass of 141 q/ 2 +,dzt*e 0j clr0mvesvk,btapf50,000 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 mass directly to energy. How much mass will bvtmq,v 0 10prkd*4cs2jt l zea ef,b+/e converted to energy to accelerate the spaceship to this speed?    kg
Assume the acceleration is rapid, so the speed for the entire trip can be taken to be 0.60c, and ignore decrease in total mass for the calculation. How long will the trip take according to the astronauts on board?$\Delta t_0$ =   y

  Suppose a 12,500-kg spaceship left Earth at a speed of 0.99c. W ba- roi5kd ue:)d1 w4bw3icf4hat is the spaceship's kinebi4ufbc-i wdae d4k13o) 5rw:tic energy? Compare with the total U.S. annual energy consumption (about $10^{19} \, \text{J}$). KE =    $ \times 10^{20} \, \text{J}$

  A 42,000-kg spaceship is to travel ticd 41kb-kqo8 o the vicinity of a star 6.0 light-years from Earth. Passengers on the sh b4o8cd- qkk1iip want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the end of a spring whose sl968urq ;qttv pring stiffness constant is 6qqtru ;9t8 lv$k=48.7 \, \text{N/m}$. 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 masfv7mmh5, 1rgsv8cl4l0hf( ds s $m_\pi$ 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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.