Is it possible for an object moving with a constant speed tojz5jp ux6m2+ dx 2i kk)4ou;au accelerate? Explain. 6xkzak2 jdmp5ou;)+ui2x 4ju

  Consider a particle moving with constant spyvc2y59n u :lceed such that its acceleration of constant magnitude is always perpen cucl2 9:yyv5ndicular to its velocity.

  An object moves in a circular path at a con( qsumem1 y,q7stant speed. Compare the direction of the object's velocity and acceleratiyum(e1, qm7sq on vectors.

  When an object experiences un3hiy63,chjn2y3 o s pj6 rbzzve.y55 t-c-hcfiform circular motion, the direction of the accelerati5fshbepnvzcoh y, j c 62ti6--3 hy33cyj5.rzon is

  Consider a particle moving with constant speed sj2;ewi:bdz0 om-j4 dtuch that its acceleration of constant magnitude is always perpeno i;dzw2e4tbjm j -d0:dicular to its velocity.

  What type of accelera 4p/mb2rnc m: vaep*9ntion does an object moving with constant speed in a circula*9ermp4/pncn: m2a vbr path experience?

  What force is needed to make an obxo cb 0ufhbsv4)a) /e2ject move in a circle?

  When an object experiences uniform circular5nd+.j ql:pdn motion, the direction of the net force dp +j n.dn5lq:is

  A roller coaster car is on a track that forms a circular lbi13t:n3c t)p5z ooe0s bp8evrgo +8.k+cpnloop in the vertical plane. If the car is to just maintain contact with track at the top of the loop, what is the minimum value for its centripetal acceleration at ttz05enpiolp c eno1gc +p.k 8+b8 )tv:br o33shis point?

  A roller coaster car (mass = M) is on a track that fora, ffrk4z 9p0ams a circular loop (radius = r) in the vertical plane. If the car is to just maintain contact with the track at the top of tkz,fpaf0 9ar4 he loop, what is the minimum value for its speed at that point?

  A pilot executes a vertical dive then fkoz;h.c ;yh.sow s( u;ollows a semi-circular arc until it is going straigh.hhowkoz ; c.sy(s;;u t up. Just as the plane is at its lowest point, the force on him 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 s.6,m pz(l3+lpjqty yzb o m0u o),p8xcurve of radius $r$ 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 g5ze yoczwh-t82e*s :g sr*;zroes around the same curve at 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 fir;s-5rgzwcr*to:8e*ehs zzy2st time?

  A car goes around a curve of radius r soci. +vptl/ r/)bx 8ez8af 7rat a constant speed v. Then it goes around a curve otxplrr avsz o. 8eb/f +ic8)/7f radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compared to the first?

  A car of mass m goes arou 6feev7azp2a2 nd a banked curve of radius r with speed v. If the road is frictionless due to ice, the car can still neg7fae azve226 potiate the curve if the horizontal component of the normal force on the car from the road is equal in magnitude to

  Two horizontal curves on a bobsled ruc)3zc 6o;wybhwh7*jno5z9kb z ei*4 on are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction needed to stay on th6*j n) 4 3 zc*zkbeo 9w5obhiyzw7;hoce 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 Olympic bobsled track is n/ sfbactu).be9g 1yj +j5/kjiot constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "climb the wall," then go lowejj/y5sk e 9.+/c bt1uj abg)fir coming out of the turn. Why do they do this?

  Is it possible for an object moving around a circular path to have box4eb qsts: nbt ,d/m ,za8:p-ath centripetal and tange 4nbqpbs-a8z,tmad es :/t,x :ntial acceleration?

  The gravitational force between two objects is proportionalo23) f;cyxlaj eorjiaz :4) o s6xd9m( to

  The gravitational force between two objects is inversely proportion o v*+*s qsqj4(v(k4yw)jbsdhal to

  Two objects attract each other gr ( nxw144ncwq0xa9 2bdoi3 h,xtz j*hoi4lze,avitationally. If the distance between their centej d1w34 0 *w 4 ltqzcbhex( 2zi4o9i,xhanxn,ors is cut in half, the gravitational force

  Two objects, with mass r1dui9 u 5itrk.o/mu5z0rc-zes $m_{1}$ 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 maa.3lo*ry dzz2ffp9u +7nqj*ji mze 3, 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 univ1*hczlp, nu *persal gravitation.

  Compared to its mass on the Earth, the mass of an obje3s992 c8ploi mo.wt+z4 hxydh ct on the Moon is

  The acceleration of gravitgg(3ji,ugv. ry on the Moon is one-sixth what it is on Earth. An obgr gguj,3v.i (ject of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Eart cor/gy--(q m4 g5zzcwh's surface, the rocket's weight

  A spaceship is travelinmobw3,qwqpe e0 ub5..kw1j-u g to the Moon. At what point is it beyond the pull of Earth's gravityuj 3wqo- p5bm w.e0k.buw1q,e?

  Suppose a satellite were orbitinvv emos-q56h 0dyk9gsu .8)2wvy hj -rg the Earth just above the surface. What is its centripetal acy958)j-h srmykvv eoqwd26gvuh.s 0-celeration?

  A hypothetical planet has a mass odmy-tk8aq8+o, txol /zk f9s6 rxf 4:)zmgbl-f half that of the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration d-9txm8f b6odtyz :), f 4mk+q8sloz -gkaxr/lue to gravity at the Earth?

  The acceleration of gravity on the Moon is one-sixth what it is on Eng dy( 5j*sc6c7+sn5:jghq fearth. The radius of the Moon 5 6f+5sd:7q(gyhsjeng nccj* is one-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 has twice the radius of v 7amu+ s4ls2fplanet A. If planet A has mass m, what is the mass sl2m7+ 4asfvu of planet B?

  Two planets have the same surface gravity, but planet B has tw, 2fo l 1s -k/xky(yulmjpp:0nice the mass of planet Akfp1ku pns -20/xy(lm l:jyo ,. If planet A has radius r, what is the radius of planet B?

  Consider a small satellite moving ineh(79a + ntf0ckld0nu a circular orbit (radius r) about a spherical planet 0at+0d (cknl f9un eh7(mass M). Which expression gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite 0q3hr yv,va)*- ky 50btiffovB, and rotates in the same orbit. Compare the two svqybv3 ia f-0ro0yh), 5v*ftkatellite's speeds.

  A person is standing on a scale in an elevator acceleraytfllnu-7x z7io0h1* ting downward. Compare the reading on the scale to the per lxhin-*71tfl uz 7oy0son's true weight.

  Who was the first persokq*7m29snyaj h1de t. n to realize that the planets move in elliptical paths around the Su hs2d7e n* my.k9aqt1jn?

  The speed of Halley's Comet, while traveling in its elliptical cu3rl/l1x.l forbit around the Sun, l3 lxr/1.cufl

  Let the average orbital radius of a planet be R. Let the orbital period be T. of8.-a7 xd* ul-osd os What quantity is constant for all planets loxs- 87a-odf.*o usdorbiting the Sun?

  A planet is discovered mu-t ca(heq uj4j82xk35mc9p to orbit around 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 nc9tcqp x jmjma hk2eu85-(u43 ew planet be, compared to the Earth's orbital period?

  The average distance from the Earth to the Sun is defin3j u. sde g;0mqf49f;-l4c xujhxk:kaed as one "astronomical unit" (AU). An asteroid orbits the Sun fja4kc-: uj;l 9h4m ks3d;0qg ex u.fxin one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.j2+- gdnwpi vl kt -dkbf4*1/k

  List the four fundamental forces in natujf csyfo,6(cmssr1yp3 : / x0zre.

  An object moves with a constant speed of 3qj ra i-(:v8l.jvqem5pvt y 5gx)b9. r0 m/s on a circular track of radius 150 m. vv.i (rx.jp5-l9rb q a tmvegqyj5):8What is the acceleration of the object?

  The maximum speed around a level curve is n2t/a.0: wqfu6yokq3 b laj5x30.0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all other fa yt6qnwb5j :ka/ uao.02l3q xfctors remain unchanged.)

  What is the centripetal acceleration of a pointv /hitr e7p*o3 on the perimeter of a bicycle wheel of diameter 70 cm when *pih/7ot ve3r the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s 6k:enm ef mnofi.)p78 is located 0.200 m from the axis. Whato.m 8fen pm6n kef:7)i is the centripetal acceleration?

  How many revolutions per minute must a circular vp9mq m 6l9x;ptv6z5q, rotating space station of radius 1000 m rotate to produce an ar mqp59lm9vpt6 qz6;xvtificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turxa3i4ocvd +o y -s)8wcn at 96.5 km/h. What is the centripetal force on the motorcyccds34x-+vwo ac8 yoi)le?

  A 0.50-kg mass is attached to the end of a 1.0clq p9)y/6ai63 zebti-m string. The system is whirled in a horizontal circular path. If the maximum tension that the string can withstand is 350 N. What is the maximum speed of the mass if tha9ie c6p/t)i6lyqz3be string is not to break?

  A stone, of mass m, is attached to a strong string and whirled gy:ti19m g,/o2eoo(wo ci)iblmh vpm1y:,3xin a vertical circle of radius r. At thm3 w hygo9om/i:t )g1,x:v1b2co e (,miypi ole 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 attached to a strong string au*ji/lxrz -669j wgcand whirled in a vertical circle of radius 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 jj/i*clw 9r6 zx-au6ggiven by

  A jet plane flying 600 m/s experiences an acceleration of 4g when pulli05mx yolpa,4buvu + o-r44ft ang out of the dive. What is the radius of curvature of the loop in 0, r4-4fopyxaol 5 utv +4maubwhich the plane is flying?

  A pilot makes an outside vertical loop (in which the center of the loop is benenz7 s,( s oaw;/pipdjs823sow ath him) of radius 3200 m. At the top of his loop he isz;a/sdnw ,popo7i3s (2sw js8 pushing down on his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pilot canca -k01 v;dzzvb cee7s irnx6()yw8;t stand is about seven times his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling out- 6n 1evzz;dbcx8tvic(7rkaysew)0 ; of a vertical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/s pu q,s .(nhn0a8rwzw4 rounds an 80-m radius horizontal curve with the tires on the vergq(n80.h,nr szua4 w pwe of slipping. How fast can this car round a second curve of radius 320 m? (Assume the same coefficient of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 50 m with *i;buvrl. c p7a speed of 20 m/s. The centripel7cbui ;.v *rptal force provided by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve of .;xgfy (leaf xw7 e,(wradius 50 m at a speed of 14 m/s. What must be the minimum coefficient of frictil.ew;a(e x(g7ffw, y xon between the tires and the road for the car to make the turn?

  A car is moving with a constant speed v around a level curv b,73rw, vqeq.wzz k:se. The coefficient of frictior7,vqz w be3z .:q,swkn between the tires and the road is 0.40. What is the minimum radius of the curve if the car is to stay on the road?

  What minimum banking angle is required for an Olympictvz4on9 k: 7iwhux4w6um w., p bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? (Ignore friction.,up i o x4w:kmwzw.67nuv 4t9h)

  A horizontal curve on a bobsled b:hanre;b4j; run 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 100 t za;lbb (r04f:n q+fqm, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80s3 m23yg 7b )t/jr vpern2rs(w m is banked 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 ue(s h nrs5)046rpzivwq *j i*zniformly in a horizontal circle (zpver4i*iznq6srw5 j *hs0 ) 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 the pit area, a racehm0 t/fd: oj-m car accelerates at a uniform rate to a speed ot /f-dm j:h0omf 45 m/s in 15 s, moving on a circular track 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 consis 5* s,bogfgk2r5fsn :tts of a proton of mass $1.67 \times 10^{-27} \; kg$ 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 fxlup 2 ts2jd-x4-*ne jorce on a 70-kg person standing on the Earth, due to the Moon?du2s2xjex4 * -j ltp-n The mass of the Moon is $7.36 \times 10^{22} \; kg$ and the distance to the Moon is $3.82 \times 10^{8} \; m$.

  The gravitational attractive force between two masses is F. If thyw*a t ,wn67fcc5 9kvl;sej a2e masses are moved to half of their initial distance, what is the gravitational attractivejst e2 5c9 ;7lcaw* fnvwk6ya, force?

  For a spacecraft going from the Earth toward the Sun, at what dobe/gpex3 /q .v l0or 9iy.js.istance from the Earth will the gravitational forces due to the Sun and the Earth cancel gjoirpq3.sv/ 9ybo e0 xe./l.?
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 is fk62u ;la(suy $7.4 \times 10^{22} \; kg$ 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 dis oa2e4masn5 )vtance above the Earth equal to the radius of the Earth. What is her acceleration due to n) 4 as2maoev5gravity?

  The radius of the Earth is R. At what distanboa-e f u 4*etl2p,(6)rpogiua xz+ i;ce above the Earth's surface will the acceleration of gravrpz(ixl+uf)og it u 4epe2*6oaa;,b -ity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its sur5cse 9nwx2 brf05f,5o1rw kk,ra5lszface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surfaconkzf r1s l,cwrr5 x2f5,bkwsa9e55 0e of Mars, is

  At a distance of 14000 km from some planet's centhh7sg65 *cv ln4y/i6el9humser, the acceleration of gravity is ics9llhs6m 7he4n6g5u /h*yv$32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on the spe1xh6- c9u1,tms dnxurface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what is itsme1snxp-9x6ut c1 d,h weight?

  By how many newtons does d9bk7.6 eh/6ngnbutbxt5 2 d xthe weight of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radius of t/ x7652gxnth.9 dbbe ukbnd6the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is at a point n4jyie;u .j6u3r above the Earth's surface. What is the satellite's weighi. e uj;46nuyjt?

  A spherically symmetric planet has four times the Earth's mass and twice p 1m9nl k/ .j:3iuq-v4xnnghqits radius. If a jar of peanut butter weighs 12 N on the supqq4vl:1 j3nnn-./ hixgk mu9 rface of the Earth, how much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lie on the same rqny + bj4fivw )*(ltflib10a-,4mn xline, with the E+ -wby 041mrl*n lf,4av( jix nbfi)tqarth between the Moon and the Sun. The Moon has a mass of $7.36 \times 10^{22} \; kg$; 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 trank 2d6x;/cy0tyj7jvzam dbq* s; fs:y;sported 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 the Ear jkv8ikvo49.yth (i.e., it just skims the surfac .o48j kyvivk9e of the Earth). What is the speed of the satellite? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a lotwn529na yo+m)4fj l*lsjcu -h9zd 6gw circular orbit about the Earth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution aroun)2d9lmw* uyfjh snc+56 tgl-94zjnoa d the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 km above the surface of the Earth. Ite il;s+s 6d5bb is observed to have a period of 89 min. What is the mass of the Earth? (The mean radius of the Earth6b d 5esb+lsi; is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an 9z.rwovu7a:0pp ve h c7y:mn8 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 o*w;j yel xh4ecq,pm*) *lny6:fc2kn rrbits the planet with a radius of $422 \times 10^{3} \; km$ and a period of
1.77 days. What is the mass of Jupiter?

  Two moons orbit a planet in nearly circuladbqu /0+ezuihs + rjra sj3y8w))g.p. r orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to ce0rhj)r)gaj. i bqu3wps+z8d.sy/ u+omplete an orbit?

  The planet Jupiter isy1) nrsv7c:b a $7.78 \times 10^{11} \; m$ 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 Jupite+)ps4goie z ,3vdsoc .. k(roar 12 years to orbit the Sun once. What is the average distance from opo)3dcz. gor,ksv+ se 4i(.a Jupiter to the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)