Is it possible for an object moving with a constant spee6)fs 3 n+dxq3cgwb 1sed to accelerate? Explainfc gxenwq1b+sds3 6 3).

  Consider a particle moving with constantrp4,yst m+ c 3m+ev6zc speed such that its acceleration of cons czmvmp3 6,t 4eyr+sc+tant magnitude is always perpendicular to its velocity.

  An object moves in a circular pa .0ndysp /ly: lmwmw 64s9nvpm/- ov,qth at a constant speed. Compare the direction of the object's velocitsnn46-. :,/syyw 0mo9p /lvqlpvwmmdy and acceleration vectors.

  When an object experiences uniform cir *r; av9i qsjrmun51n4cular motion, the direction of the accelera1i 9nus*j amnqrr;v54tion is

  Consider a particle moving ikt02ly kr si:3fb;g9 d7leo*with constant speed such that its acceleration of constant magn;9dlo byslf rkektiig 0* 237:itude is always perpendicular to its velocity.

  What type of acceleratijuz g+ b-sz6;lon does an object moving with constant speed in a circular path experienc6-zulgjs; +zb e?

  What force is needed to make an object mgteg:c50* obfg.d r9bbna5b -ove in a circle?

  When an object experiences uniform ci3ze 5gdzj+,l m1 cxw edx4*7xircular motion, the direction of the net forcex m1+ 5zxlz73i4,ewxc* edd gj is

  A roller coaster car is on a track that forms a circular loop in the vok6 bsj-9,s)r te*yvvertical plane. If the car is to just maintain contact with track at the top of the loopss )6ek,9yjtvvor*-b , what is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) isy2pdwy5egpd n e+zq8 1y1ai); on a track that forms a circular loop (radius = r) in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what is the e1p zg8 +1;)qwda25p nye yyidminimum value for its speed at that point?

  A pilot executes a vertical dive thd 7li :pei;*dn/cdo b6en follows a semi-circular arc until it is going straight up. Just as the plane is at its lowest point, the force on hi lbp7 don*d;/id:6c eim is

  A coin of mass $m$ rests on a turntable a distance $r$ from the axis of rotation. The turntable rotates with a frequency of $f$. What is the minimum coefficient of static friction between the turntable and the coin if the coin is not to slip?

  A car goes around a curve of radiuswk9xp-1xqss . $r$ at a constant speed $v$. What is the direction of the net force on the car?

  A car goes around a curve of radius r at a constant speed v. Then it goes arou7buam)xk o2-uf tsx,2nd the same curve 2k27xmfu )sbx a,t -uoat half of the original speed. What is the centripetal force on the car as it goes around the curve for the second time, compared to the first time?

  A car goes around a curve of radius r at a co0os;cdw dob3366mvo3or +zj (s2edcl nstant speed v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compare; 3o(dbwloez od3 m6s j32c6rsov0cd+ d to the first?

  A car of mass m goes around a banked curve of radius r with speed v. If the v3i qn zxe i*:5ove0 ;36xwjmbroad is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the normal force on the car from the road is equal in m;*0j eenw5v3zxq 36io:ixvbm agnitude to

  Two horizontal curves on a bobsled run aramuf) m j08ij1e banked at the same angle, but one has twice the rja1m uf8i jm)0adius of the other. The safe speed (no friction needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger radius curve?

  The banking angle in a turn on the Oly6mr8f72 (.ypu;dfim*ldc5 7ec n1 u1o fpekfampic bobsled track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "climb the wall," thm dfo fr l f.pk*u7(dc1 f7m1u6eypn ;a5cei28en go lower coming out of the turn. Why do they do this?

  Is it possible for an object moving around a e(uknoa oe cjr4m/d /v0ud mp u/6(j61circular path to have both centripetal and tangential accelerationem poc4av /uk/due/odnj0m166 j r((u ?

  The gravitational force between twg;takgflu o 1 b+cz) ;ih821z*vj5c gwo objects is proportional to

  The gravitational force between two objects is inverseupwa r2qc 7ovg32 6lx022 ninely proportional to

  Two objects attract each other gravitationally.,c 2dmx.li mn; If the distance between their centers is cut in halim. mxcln2d;,f, the gravitational force

  Two objects, with massesrr3b ehxs3q00 $m_{1}$ and $m_{2}$, are originally a distance r apart. The gravitational force between them has magnitude F. The second object has its mass changed to 2$m_{2}$, and the distance is changed to r/4. What is the magnitude of the new gravitational force?

  Two objects, with ma zu -lqqc+5xl )mwyls1 p7jw38xpz7e(sses $m_{1}$ and $m_{2}$, are originally a distance r apart. The magnitude of the gravitational force between them is F. The masses are changed to 2$m_{1}$ and 2$m_{2}$, and the distance is changed to 4r. What is the magnitude of the new gravitational force?

State Newton's law of universal gr:mw uq8q8ru 3 6hf-nkiavitation.

  Compared to its mass on qh)r991x6xqr:-5pvg g zqb wl the Earth, the mass of an object on the Moon is

  The acceleration of gravity on the Mooj 1dzq7:8q, rt*(iojc;q jcxr n is one-sixth what it is on Earth. An object 1qqi,dj:o xz78*c( q rtrcjj ;of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's sut h87 i,lhb,nxrface, the rocket's weight

  A spaceship is traveling to the Moon. At what point ipdbhq1ga2++p7)lb cbs it beyond the pull of Earth's gravitg1+7pbbhldq p2 +)bc ay?

  Suppose a satellite were orbiting the Earth just above the su8 wgm66m0 rqpev gbnak47bt 0/rface. What is its centripetabv 6knm4g0g 6 mbwerpq7 /08tal acceleration?

  A hypothetical planet has a mass of half that z *2pf2e z1pbqdc:m/ fof the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in ter2 fzqe*mzp/2pc: d1b fms of g, the acceleration due to gravity at the Earth?

  The acceleration of gravity on the Moon issr*1wf k.5t5.k)h siau5g9 m z)bot lj one-sixth what it is on Earth. The radius of the Moon is onej o. 9z.h)mgb*s5i)5u5 t1awstklrk f-fourth that of the Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gravity, but planet B iuz-7 bi606m oucgd3o* feil6has twice the radius of planet A. If planet 6i ugbzi7-om36 icfoe0ul6d* A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, b( i:o e1ulbvv7ut planet B has twice the mass of pl7o: ( vulevib1anet A. If planet A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a circuq;teyizv v3x+. txg9w0)d3f olar orbit (radius r) about a spherical planet (mass M). Which expression gives this sate +ixqw3t3 zx)v.tg0 vd 9fo;yellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and rotat*ksr0mqx s h/7f- nfx)es in the same orbit. Compare the two satks m) ffsqrn* x70x/-hellite's speeds.

  A person is standing o m.kxwjb ww*,;k(( nihn a scale in an elevator accelerating downward. Compare the reading on the scale to .xj wk *h (i,;n(mwbwkthe person's true weight.

  Who was the first pers0o9 jf ca1*lx w iygoqcoz9;6he68 )aaon to realize that the planets move in elliptical paths aro0c 96h eiq1 o6 *x89;gcoaw)yzla oajfund the Sun?

  The speed of Halley's Comet, while traveling in its ellik4+wv. a, dzrqptical orbit around the Sun4+ .wrk,zqv da,

  Let the average orbital radius of a planet be R. Let the orbital period be T.*mpxdc y/efz a81 13y;uypql -4+ cttd What quantity is constant for all planets orbiting the/u; 4tcxte dy zl1y*q3 -8+fpacp1mdy Sun?

  A planet is discovered to orbit aroundkf0h5s(epvs( .c /qju r lmc7. a star in the galaxy Andromeda, with the same orbital diameter as the Earth around our Sun. If that star has 4 times the mass of our Sun, what will the period of revolution of that new planet be, compared to s7c0m /prk fluec.q5h.(j(vs the Earth's orbital period?

  The average distance from the Earth to the Suy* mv. buad))uod*l9x)m nkf;n is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is fu*y) nbl .;)ukxa) *vdodm9mthe asteroid's average distance from the Sun?

State Kepler's laws. ,f -tmm+993vusc)0czdlp 5 hhprq 5ip

  List the four fundamental fornr4 v8rqs1)ugces in nature.

  An object moves with a constant speed of 30 m/s on a circular track of rad)n3 l1k7:fam1taue /hi u; yrfius 150 m. What is the accf / 7he 3 auky1mrta;nlfu1)i:eleration of the object?

  The maximum speed around a level curve is 30.0 km/h. What is the maximum/dfv (reo eo: hj*-2uuq.l6 kc speed around a curve with twice the radius? (Assume all otherjfor-o 6 *eque/2c:d(khu.v l factors remain unchanged.)

  What is the centripetal acceleration of a point on m b*k2 4;zk rx*:lr8oypyunz(/e,mtithe perimeter of a bicycle wheel of diameter 70 cmz rtko4nbiu z yyl2*8/pemk*:m;rx,( when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located zm4bw17ko 5mc 0.200 m from the axis. What is the centripetal acceleraom5kzb4mc w1 7tion?

  How many revolutions per minute must a circular, r9jsmy/bj3.bb u ig hr zf8n:zg1,6b6rotating space station of radius 1000 m rotate to produce an artificial gravit 61 j/3,b8b.zgfyz69sbib: jr n grmuhy of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn i m4c6cd 2n-dhat 96.5 khin d- dc4m26cm/h. What is the centripetal force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m string. The system is whirled :3s1bmq yn,su e mrw tu)ygi;q73d 0tth83r0win a horizontal circular path. If the maximum tension r)tduq3 sm0,w0;i:qwe muy73ytrh s nb183 gtthat the string can withstand is 350 N. What is the maximum speed of the mass if the string is not to break?

  A stone, of mass m, is attacheb,stp v n/j nhgk 27(p2.p/hmtd to a strong string and whirled in a vertical circle of rad7h2 bnntg/p./hs jp2,tv (mpkius r. At the exact top of the path the tension in the string is 3 times the stone's weight. The stone's speed at this point is given by

  A stone, of mass m, is attaclt-v 55 ;(efu(j hl3 p er,xv;io3onpmhed to a strong string and whirled in a vertical circle of radip-; h;5tjvei f53lxu,vo ml3(pon e(rus r. At the exact bottom of the path the tension in the string is 3 times the stone's weight. The stone's speed at this point is given by

  A jet plane flying 600 m/s experiences an acceleration of 4g when pulling ocxi 7jv nisoac*01k;d .yy;i8ut of the dive. What is the radius of 1k;vo 7iy.n0x syicai 8*;jcdcurvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which the center of the loop idy m+dcu67h.9 j d 90wxp7jrhts beneath him) of radius 3200 m. At the top of his loop he is pushpjd+y7mjh d0.7rx9tuw c9d 6hing down on his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven times his weju n3: o5ojv1qight. What is the miqu:n o13jvj5o nimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/svqym;hvuds2nb -bf*o n 368 f) rounds an 80-m radius horizontal curve with the tires on the verge of slipping. How fast can this car round a second curve of radiu2 fqbo vsh3y*f 6-v)mnd8 n;bus 320 m? (Assume the same coefficient of friction between the car's tires and each road surface.)

  A car is negotiating iby 7e4/)abev a flat curve of radius 50 m with a speed of 20 m/s. The centripetal force provided by friction iaie)v y/b74ebs $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve of radihk*qovr5n++5saea t;isn(u0s.x m y ;us 50 m at a speed of 14 m/s. What must be the minimum coefficient of friction between the tires ;s res5k+;s0(oa* qnm5.h+ytnai xuv and the road for the car to make the turn?

  A car is moving with a constant speenah: ;o3 lcvrrssusvvd24ax3e 3,b 27n /h0n id v around a level curve. The coefficient of friction between the tires and the road is 0.40. What is the minimum radius of the curve if the car issnivcdravv 0;42h:lu,en 2/r7 ox3bn ah ss33 to stay on the road?

  What minimum banking angle is required for aqd4. 9pi/frj7k;dt a 3jp5a axn Olympic bobsled to negotiate a 100-m radius turn at d5.dfx 3j rpa;ka/ip7t 4aq9j35 m/s without skidding? (Ignore friction.)

  A horizontal curve on a bobsled rurtj)z, 5i gl.a rcm6n(n is banked at a $45^{\circ}$ angle. When a bobsled rounds this curve at the curve's safe speed (no friction needed to stay on the run), what is its centripetal acceleration?

  A frictionless curve of radius 1znix6sg61-rg 00 m, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bank;+tuj1 u-pq*eb la hb(ed at $45^{\circ}$. Suppose that an ice storm hits, and the curve is effectively frictionless. What is the safe speed with which to take the curve without either sliding up or down?

  A 175-kg ball on the end of a string is revolving uniformly in a horiwq-y8n9z )kc;d5sne)2y u fzt zontal circl 2)9n)u zkqytwdecf-;z ny8 5se of radius 0.500
m. The ball makes 2.00 revolutions in a second. (only fill in numerial value in the blanks)
(a) Determine the speed of the ball.    $m/s$
(b) Determine the ball's centripetal acceleration.    $m/s^2$
(c) Determine the force a person must exert on opposite end of the string.    $N$

  Starting from rest in t9h7ly .n fug0k;gp .qfhe pit area, a race car accelerates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular try7 g n .0lfukfq;p9hg.ack of radius 500 m. (only fill in numerical value in the blanks)
(a) Calculate the tangential acceleration.    $m/s^2$
(b) Calculate the radial acceleration when the instantaneous speed is equal to 30 m/s.    $m/s^2$

  The hydrogen atom consists of a proton of masse)g zq/k p*d g w,-;l0of.h /rp6ovkxh $1.67 \times 10^{-27} \; kg$ and an orbiting electron of mass $9.11 \times 10^{-31} \; kg$. In one of its orbits, the electron is $5.3 \times 10^{-11} \; m$ from the proton. What is the mutual attractive force between the electron and proton?

  What is the gravitational force on a 70-kg person73 98z (y pdzrhj yo6uoun,1 b:rvtso9 standing on the Earth, due to the Moon? The mass of the Moo1t8(psy6z ojvr9, 7z:ondry hu o3b9 un is $7.36 \times 10^{22} \; kg$ and the distance to the Moon is $3.82 \times 10^{8} \; m$.

  The gravitational attractivenr/q 2p1qjm5+t/(nis w ckcz: force between two masses is F. If the masses are moved to half of their initial distance, what is the gravitational attraczt(1kw +ipcq 2nq:jn rc/ 5sm/tive force?

  For a spacecraft going from the Earth toward the Sun, at what distance from the2i*p5xyc63xw6 dep 31zgq :kla h. oxe Earez6e p36:*xg5p3.2ikl wdxqcahy ox1th will the gravitational forces due to the Sun and the Earth cancel?
Earth's mass: Me = $5.98 \times 10^{24} \; kg$ the Sun's mass: Ms = $1.99 \times 10^{30} \; kg$
Earth-Sun distance: r = $1.50 \times 10^{11} \; m$

  The mass of the Moon idvc* pa f74pzi +*5 rh+rutu(vs $7.4 \times 10^{22} \; kg$ and its mean radius is $1.75 \times 10^{3} \; km$. What is the acceleration due to gravity at the surface of the Moon?

  An astronaut goes out for a "space-walk" at a dist0hiz/-4qs+iiqu :v y i 4tag)qance above the Earth equal to the radius of th-s/ + aq gi:0 yq)44ziviutqhie Earth. What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance above the Earth's mqr . pzk/(1cfg 1lldufrxc:s )zl-(; surface will the acceleration of grpf;1rd 1rqzk ul/ls. -zgm xlc: ()(fcavity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its surface equal (ei6 qbktpr88w,pkk7 (o m;em to 3 times the radius of Mars. The acceleration of gravity of the satellit; pm(wb ek8 6k kr8m,7t(opqiee, as compared to the acceleration of gravity on the surface of Mars, is

  At a distance of 14000 km from some planet's center, the acceleratio iwe * (q5w*knc mxydrtq,s3f+ji5,9qq r 75rhn of gravity rh 7mq*qi3,tk nq xwrs,qcy9i5fd(ew j5*+r5is $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on thep)qv4.)(g qtx/nps,jg sfv (o surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface4.vf)nggq (pxvj)qs t(, /sop , what is its weight?

  By how many newtons does 3: htkinzid8 mpe6) t92 /tbnsv16a jgthe weight of a 100-kg person change when he goes from sea level to an altitude of 501hs96tbtaki z )n36 :j/28m pdie tgnv00 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite ofsdl 9pyqy6(gv u zi.;2 mass 100 kg is at a point 3r above the Earthvy 69.qs(pdlyuzg; i 2's surface. What is the satellite's weight?

  A spherically symmetric planet izq((fz 1e;kln-wt b 8has four times the Earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earthqzi-twf (z l81 b(ke;n, how much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lie on the syzx 0fkae*w0 ,m:ml8m ame line, with the Earth between the Moon and the Sun. The Moon has a mass of 80zw:l am k,0*ymmxfe$7.36 \times 10^{22} \; kg$; the Earth has a mass of $5.98 \times 10^{24} \; kg$; and the Sun has a mass of $1.99 \times 10^{30} \; kg$. The separation between the Moon and the Earth is given by $3.84 \times 10^{8} \; m$; the separation between the Earth and the Sun is given by $1.496 \times 10^{11} \; m$.
(a) Calculate the force exerted on the Earth by the Moon, its magnitude is    $\times 10^{20} \; N$, its direction is  ----待选择----towardsaway from  the moon.
(b) Calculate the force exerted on the Earth by the Sun, its magnitude is    $\times 10^{22} \; N$, its direction is  ----待选择----towardsaway from  the Sun.
(c) Calculate the net force exerted on the Earth by the Moon and the Sun, its magnitude is    $\times 10^{22} \; N$, its direction is  ----待选择----towardsaway from  the Sun.

  A 2.10-kg brass ball is transp fj(68(vvi9ksyzjp9tuacd 4+orted to the Moon.
(a) Calculate the acceleration due to gravity on the Moon.    $m/s^2$ (The radius of the Moon is $1.74 \times 10^{6} \; m$ and the mass of the Moon is $7.35 \times 10^{22} \; kg$)
(b) Determine the mass of the brass ball on the Earth    $kg$ and on the Moon    $kg$
(c) Determine the weight of the brass ball on the Earth    $N$
(d) Determine the weight of the brass ball on the Moon    $N$

  A satellite is in a low circular orbit about.q/rbt6rfctnsa-w ;e/ 5xji 1 the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radius of thei 6 .r/jn5fc-wrbet1 sq/ta;x Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about the 9 x6 1p0uqzkvw7 lzm3yEarth (i.e., it just skims the surface of the Earth). How long does it take to make one revolutio37 w ky0vlqxu9p6zmz1n around the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 k. -9/ikkd( syqdi/o9+wlk gh nm above the surface of the Earth. It is observed to have a period of 89 min. What is the mass of the Ea-h9k.ligqy /kn(9/ wsdk di +orth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has a++ o-l j( tbdast1y/unn orbital diameter of $1.34 \times 10^{9} \; m$, and a period of 3.55 days. What is the mass of Jupiter?

  The innermost moon of Jupiter orbits the planet with a radius ;wa;-mys0 2tv0osoaubb nty 3f*3i9 wof $422 \times 10^{3} \; km$ and a period of
1.77 days. What is the mass of Jupiter?

  Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius ;gem6mkyyat -5 );7o ovbj78b mjr.g kr, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbimjg5y8;a-;rogk) 7k mj6e.7tb bo mvyt. How long does it take moon B to complete an orbit?

  The planet Jupiter iszbzlh.y -m*g 1 $7.78 \times 10^{11} \; m$ from the Sun. How long does it take for Jupiter to orbit once about the Sun? (The distance from the Earth to the Sun is $1.50 \times 10^{11} \; m$.)

  It takes the planet Jupiter 12 years to orbit the Sun once. Wha: ht taab5rm2.kvp*j(t is the average distance from Japha:tb jk*t(m 2vr.5 upiter to the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)