You are in a windowless car in an exceptionally smqiw3qj7ozh 0fs ;zpqo n 93x+:j+yt1iooth train moving at constant velocity. Is there any physical experiment you can do in the thzq+pw +qyo9i0s;tni q 3j7fj3x1zo:rain car to determine whether you are moving? Explain. ----待选择----yesno 

You might have had the experience of being at a red light when, out o)3kvr2 an ce,sf the corner of your eye, you see the car beside you creep forward. Instinctively you stomp on the brake3) r2kanv c,se pedal, thinking that you are rolling backward. What does this say about absolute and relative motion?

A worker stands on top of a m6 nx(eyt*9s9wu fk/leoving railroad car, and throws a heavy ball straight up ( x tnkeyf9e6s(/l9*u wfrom his point of view). Ignoring air resistance, will the ball land on the car or behind it?

Does the Earth really go around the Sun? Or is it also valid to savsw 28,r ibbs.kplnf)f4sz 9 1y that the Sun goes around the Earth? Discuss in view of the first principle of relativity (that there is no best refl .4b8 rk 9fbn1,2swi)vp szfserence frame). Explain.

If you were on a spaceship t; l4s;m 3-34xdcgikjc plq*n eraveling at 0.5c away from a star, at what speed would the starlight pass youd pjc;ics*4q nk 3-3g;mxlle4?

The time dilation effect is sometimes et u8r55qb 6d6p2 cvduxxpressed as “moving clocks run slowly.” Actual 5u6d rd568t bvpquc2xly, 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 m ymr-/au+g *g*iv2ljjc; ngy;(x ylu7oving reference frames m;rl; gl-uv 2ya*y *i /u7gjy+gjxcn(or that it only seems to pass more slowly?

A young-looking woman astronaut has just arrived home from a 6yam4to 8d. pvlong trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possimv6p8atd 4.y oble?

If you were traveling away from Earth 6nykzjot cqyu +3 qyyfw sy (4.tp2.8)at speed 0.5c, would you notice a change in your heartbeat? Would your mass, height, or waistline change? What would observers on Earth using telet3jp(yu).tk+ysz y n y8w q.6o2cqy4fscopes say about you?

Do time dilation and uhm7hnr cb u98vr, uet/.khr)xm* )prka/0 o .length contraction occur at ordinary speeds, say $90 \, \text{km/h}$?

Suppose the speed of light y +r)/v(zspyb were infinite. What would happen to the relativistic predictions of length contraction and ti) (r+yby vszp/me dilation?

Discuss how our everyday lives would be differfdyz-ogm2 mvrt8o48ayz 1 p/r.b,y .qent if the speed of light were only q o-rzyy1f do4.ymrb/p8gmat ,v82 . z$25 \, \text{m/s}$.

Explain how the length contraction and time dilatiorccogo-s2/2+ fge q ,nn formulas might be used to indicate that c is the limiting speed in the uni/o2f og+rscqnec,g -2 verse.

The drawing at the start of this Chapter shows the street as sez3*l yay7 ,sneen by Mr Tompkins, for whom the speed y es,n*y73lza 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 y j79qvu8. asei3 p*mbthan c. Does this put an upper limiv*by. qsu pi e8a37jm9t on the momentum of an electron? If so, what is this upper limit? If not, explain. ----待选择----yesno 

  Can a particle of nonze zll05o)l 1lvljw9t8oro 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 morehu:a5: ch *yib mass when compressed than ichab*huy: 5 :when relaxed? ----待选择----yesno 

It is not correct to say that "matter can neither be creat n98jkk(z gf8d(1xxmx ed nor destroyed." What must jd8kfxx8x1m (k9 zng(we say instead?

  Is our intuitive notion that velocitifscu)tg7 +-mxy2;jk,. 1q diehyh*kzes simply add, as we did in Section 3–8, com.zh7yy kct2h,di j) -+*gfk1mxu;e s qpletely wrong? ----待选择----yesno 

  A spaceship passes you at a speed of 0.750c. You measure its length too k:*) 0ec .fit *mu4rhxg-mny be 28.2 m. How fne c m. *mugoh:k y-*ixr0t4)long would it be when at rest? $L_0$ =    m

  A certain type of elementar ke6; sqg(gpl+y 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 interi7e 6tlh)a.wy*rf3j.i xh+js vals 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 st3zr(/gq0 ml (hsdfa u7ar 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 lifetime is me g/ohbtxkcakt m-l4(r0ikl6+3md,+jasured 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 would 0v(. uyx, n (qnpqmh0myou have to travel so that to you the distance would be only 35 light-years? v =x mqu (mqn0.y( v,pn0h    c

  Suppose you decide to travel to a star 85 light-years aw30yqlmrvae; x+v9ln6 ay at a speed that tells you the distance is only 25 la+rx qlv63v9;ln 0e myight-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 hp pseiqnbl 5a; q+)y;o.ysu-h6jl 29is $11.2 \times 10^3 \, \text{m/s}$. 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 jby k+wee4 )rbs38)cvicf 2b /wust returned from a 5-year voyage while travek3e4cwb/c 8vwe ir+s2 ))fbyb ling 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)5pgvur(j1 u;upx3 qo spacecraft traveling 0.960c to reach that star from Earth, as mq3u( jpuov5pu 1;rx )geasured 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 iw9 oobdrz md *70sv:i+n her "Ferrari" spacecraft at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m highdi +zsv0omd:7r bw9*o .
(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 wzx2/ sd3*vaxq a2e3vxd 0p o.average ax3zxs* .av/v 2dq3opw0 d2ex lifetime, at rest, is $2.6 \times 10^{-8} \, \text{s}$. v =    c

  What is the momentum of a proton trave: g4ugq;++onotpiw( mling 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 k a5qvb 02,bxkmass? v =    c

  A particle of rest mac+.f. x6sc jfeu w;pqc lh15k7ss $m_0$ travels at a speed $v =0.20c$. At what speed will its momentum be doubled? v =    c

  (a) A particle travels at -c9x,zdmnq6 +o fq)nk3s9p cf $v =0.10c$. 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 accelerates 3 e2zvrnc hrw;l9g /l+yexb4, x 6:qxm
(a) from 0.45c to 0.90c,    %
(b) from 0.90c to 0.98c?   %

  A certain chemical reaction requires * aashb0e8;uy$4.82 \times 10^4 \, \text{J}$ 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 fissio0umo iu3al5 p9n in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the proc0i5 m3puua9lo ess? $\bigtriangleup m$ =    $ \times 10^{-28} \, \text{kg}$

  Calculate the rest energy of an electron in joules ani5.nc2ob:scffer oq7 r/4 o+gd 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 .c4 z fz) i1tbyfowv/1proton in $\text{MeV}/c^2$. $m_0$ =    Mev/$c^2$

  The total annual energy consumption in the United States is about0u64tlnhwc c err uxm/ys(ys/x0.2e8 $10^{19} \, \text{J}$. How much mass would have to be converted to energy to fuel this need?    kg

  How much energy can be obtained*af(b* via dd3 from conversion 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 kinetic ei. 4 bvdt +rrqwjva,gu085 :zbnergy equals its rest energy? v v+qtb0rr,:bj 4 vga8.du w 5iz=    c

  At what speed will an object's kinetic energy be 25% of its rest energy? n:;42mry 1sww8jycbrn 6nx /qv =    c

  (a) How much work is required to acqb397kfq,na ddl:9 6tjas,k fcelerate a proton from rest up to a speed of 0.997c? W ak7sd,qk ,9q 6fatbf3 9n:djl=    GeV
(b) What would be the momentum of this proton?p =    $ \times 10^{-18} \, \text{kg·m/s}$

  Calculate the kinetic energy and momentum ok) 3ef1xxx i *lpr-5in5xqn-zf 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, .tiw56t9or;wl5, q kxcx olq.its kinetic energy is 750 MeV 5xqoot 9crklw.5.w; , i6lqtx)?    $\times 10^{-19} \, \text{kg·m/s}$

  What is the speed of a proton accelerated by a potential difference of 105 MVe/p kucbo nur2;v3 38do8z, hr? v =/;euor8docn pz3hru8,k2 b 3v    c

  What is the speed of an electron whose kinetic energy p:mqolp6ba;j( 6vps5 is 1.00 MeV? v =    c

  What is the speed of an electron just before it hits a tvi4 0w0j, bsx2ayjx0uelevision screen after being accelerated froa j s0 ,20ijwbxvu4xy0m rest by the 25,000 V of the picture tube? v =    c

Two identical particles of r 0voig5ptl (s78d2 umzest 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 l68hk9yrlpc: pzl;ngd +r,n 7proton ($m_0 =1.67 \times 10^{-27} \, \text{kg}$) whose kinetic energy is exactly half
(a) its total energy, v =    c
(b) its rest energy.v =    c

  What is the speed and the momentu up gjs;wf.1: m2(kxs;,ewj*kb4m rdwm 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 acceleratebzli .g,n oxz*1kze* z/ 2eq1qd 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 lepx k se so3t,h1k0f* 3vh6i7a 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-ga d:2hw9dy5a* hfwvg9fhm 5, $^{241}\text{Am}$, 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 momentujr65c;6s v uocm for (a) a particle of nonzero rest mass, 6;juoc6svcr5 and (b) a particle with zero rest mass.

  What magnetic field intensity is needed to keep 998-GeV pro4qhxm xr;(jy;/au, us tons revolving in a circle of radius 1.0 km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The;( suh/mq,y ajxu4r ;x 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 )1rjpnx5 z),sys:c/iwc7yt8 2u wjvcthe Earth) observes a meteor co7iw z)1 rs8p5 xu ,vyy2wjc:s nc)j/tcme from behind 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 oppo:01qkgbre i 0rsite directions, each with a speed of 0.50c with respect to Earth. rb0rg q k:01ie
(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 bbu1yx)0y kq0g+8qle second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the spee+k0 xgy1 q8lebyq0u)b d 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 appz2r y1tc-,-lvvd ci z,roach at a speed of 0.60c. The Enterp,cyv t i21--vrd lz,czrise 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 as seen by the other? u =    c

  A spaceship in distress sends out two escape pods in opposite direx, k4pty4 :y hldhbv;hokl06)ctions. One travels at a60tx4hlh o4y,lbk y:k;hd pv) 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 passdz2y4. xj7qj fes Earth moving 0.95c relative to Earth in the same7dyfjx zq.4j2 direction. How fast is B moving relative to A when it passes A? u' =    c

  The nearest star to Earth is Proximi)do43q z4l- skfq8 7pyog4pca 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 faster than about 0.1c is calledv1 n1pvk 7r)n.djwyg, relativistic - i.e., for which the correction using special relativity is a significant effect. Determine the .gr)n nj 1wyk,7dp 1vvspeed 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 speed -wquyerdc.u vap.3+p n6 *: kn$v$ 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 tt-h ) kye)ek 1ndxa)2mo be totally destroyed to run a 100-W lightbulb for 1 year? ke)tdm2k )n)ey1-xha $m_0$ =    $ \times 10^{-8} \, \text{kg}$

  What minimum amount of electromagnts 9u6 nb 0e1dyzbw7q8etic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge. (Note that electric charge i9e6 t wdnz1qb7 yb0s8us 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 collidestulatqd-a/ btd n/.(). 9ui*m9kgwa k head on with a positive muon traveling atuu t/tdmkg 9.qaw(nlbi- )t.9/a*dak 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. Assume uzo2 dqro0 b lj.g,h-6the neutrino's rest mass is zero, and the other ml.r0u,bh6 zgjq-doo2 asses 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 rzf )tlvnx zh*w,)w4l3 ate 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 and a qd/ y k pico9x:j-9i-aspeed 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 0t zk)drao(7gf zwq(fo ri; (1constituents, two 0 (;1fzaq(t7 kfoi)z(ogr d rwprotons 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 (relativ+fsxtuo+1 7fem*d-yq istic) mass of a car traveling 110 km/h as compared to at rest*-7 qm+ sx1fudyfe t+o? [Hint: use the binomial expansion.]$\frac{\left(m-m_0\right)}{m_0}$ =    $\times 10^{-11}\%$

  Two protons, each having a speed of 0o q,2yz98i vjryf ijxi9, oy-.+lvw kajl,5 w;.935c in the laboratory, are moving toward each other8,olkqy9xwo-rl jw i;z9v ivj5i j.y+fy2,a ,. Determine
(a) the momentum of each proton in the laboratory, u =    $ \times 10^{-18} \, \text{kg·m/s}$
(b) the total momentum of the two protons in the laboratory,   
(c) the momentum of one proton as seen by the other proton.p =    $ \times 10^{-18} \, \text{kg·m/s}$

Show analytically that a puyd k*zwuzhc8 d*qu6 ld,0o42article with momentum $p$ and energy $E$ has a speed given by $v = \frac{pc^2}{E}$.

  The fictional starship Entepgl o8jkdv(0v3lh8z4 rprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. I jo8zpv lv dkglh(4830f the mass of the Enterprise is approximately $5 \times 10^9 \, \text{kg}$, how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?    $\times 10^7 \, \text{kg}$

  An electron is accelerated so that its kinetic energy is greater than its 1*mesyeoxh k:6ks 8213pty n erest m e1ns8xhp3 k: eyt1omskye26*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 physiccy)bks 0o2p k3s believes that he can fit 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 idea that when he is ru0)scybo 32kkp nning 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 2 v:m;lh jlyngr0l4dwl7 if85two moles of water, the energy released is 484 kJ. How much does the mass of the elej28lr gi:w7 dlv;y50llnfhm4ments 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, t fs/b0czphxr9():2o znrh.d hraveling in opposite directions. If the speed of each particle is 0.75c, relative to the laboratory frame of refsrrpo2.hdbxfhn : z/9c) z( h0erence, what is one particle's speed relative to the other particle? u =    c

  An astronaut on a spaceship traveling at 0.75c relative to Earth measures hisn8qs 2n5x mm7c ship to be 25 m long. On the ship, he eats his lunch nm8x2 sn7 cm5qin 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 spaces bjei9f-wh3zx6g ( xf(hip 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 the Earth m igh(e-fjzb6w9 x3 fx(easure for the speed of the laser beam?

  A spaceship and its occupants have a tj+ 4i*(trjvzjotal 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 mass directly to energy. How much mass will be j+tz*(jri4j v 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 acmp 3lq*wn) +t d(vhz6t a speed of 0.99c. What is the spaceship's kinet*pwqvtmhc6 3 ldz(n+ )ic 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 to the vicinity of a star 6.h0uqnn(0l 3 hx0 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 done on the spaceship to bring it to the spenh03uln( 0hqx ed necessary for this trip? u =    c

  A 1.68-kg mass oscillates on the en: uqwdu3/ni1:ue) dznd of a spring whose spring stiffness constant /3zunwqd e)unid :u1: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 mas-y9neyg 0oz* f.dnsqx6lt9 qesc,y(: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 $KE_\mu = \frac{(m_\pi - m_\mu)^2 c^2}{2m_\pi}$.