Is it possible for an object moving with a constant speed to accelerh.14jywxoe),3ya wsvate? Explaio 3j as e1xvw.,)yyh4wn.

  Consider a particle moving with constant speed such that its acceleration o d,id/ ytlrw-3f constant magnitude is always perpendicular to its velocid/ dyi w,r3-ltty.

  An object moves in a circulars),)tb,c0 l.)nz n qc u/glggu path at a constant speed. Compare the direction of the object's velocity and acceleratiog0) ,.lnt u)/csczq lg u)n,gbn vectors.

  When an object experiences uniform circular mot.qw;und+b, d.rnlam4 ion, the direction of the accelerati4 ,dl.dr a; mb.nq+nuwon is

  Consider a particle moving with constant speed such that its acc6bcu-si21s cu /9rbu/ vql1g leleration of constant magnitude is always perpendicular toll1 1 2svcu bbgus- i/u96qrc/ its velocity.

  What type of acceleration does y qlgue25ynq/ 4fpiqfz++, h1an object moving with constant speed in a circular path 2 5 ue+flyqg4y,p1/nqf+ zh iqexperience?

  What force is needed to make an object move in a circle?zp.x y*p6dq g;(j2 gvi

  When an object experiences uniform circular motion, the di2w ppya/gb0x4 kc+5vfrection of the net force25av4/+kbpypcxf w g 0 is

  A roller coaster car is on a trackpjfgnd-pi 1 p5vn-:f6o 6 hsd1 that forms a circular loop 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 accef1 n6hpdovjp- isg5:6fdp n1-leration at this point?

  A roller coaster car (mass = M) ia+-b nq6vu qxt d8 zu3.gdy;9es 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 tu. -;ydx8 q+tgnub6a9eqd3 zvhe minimum value for its speed at that point?

  A pilot executes a vertical dive then follows a semi-circr jnqbr )j*gg3w7/av1 ular arc until it is going straight up. Just as the g3 *7a1rjvqgwj )rb n/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 cqi mybc-vu :5(5+rpxhn8s e; zurve 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 sjzfjv(o fau93r)s5 +kpeed v. Then it goes around the same curve at half of the original speed. What is the centripetal force on th3 jzf vs(kajruo95f)+ e 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 constant speed v. Then it goe b5 at;il -iya8tg5qs gv:tyd l:z)/ad x6(7bns around a curve of radius 2r at speed 2v. What is the c i 5bi:sx a-q6ya)tgndzdtt8vy7 ba(ll5; :/ gentripetal force on the car as it goes around the second curve, compared to the first?

  A car of mass m goes around a banked c/j7zfgy, xox*0xj2 iourve of radius r with speed v. If the road 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 magniz7 x0x f ,yoijogj2x/*tude to

  Two horizontal curves on a bobsled run are banked at the same anglhzvy0 6rhc/qo h xx8f,/mjs)q8w e3 (fe, but one has twice the radius 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 lwjohr8 8m q s,/xhf)ehc/0qf(6vy zx3arger radius curve?

  The banking angle in a turn on the Olympic bobsled track is not constand7qy 4(npo4sm7)k/4nkszp i f t, but increases upward)4m qzp 7f74s4inn/pkd (oyks from the horizontal. Coming around a turn, the bobsled team will intentionally "climb the wall," then go lower coming out of the turn. Why do they do this?

  Is it possible for an object moving around a circulzakji: qhbra m-099zo18ql/4i kagjhun 2q+7ar path to have both centripetal and tangential accelk na 7j9q:r20l k9ob q1mi -h8ua4j/izhzqg+aeration?

  The gravitational force between two objects i)v5, xl wc1lnp/w eby4s proportional to

  The gravitational force between two objects is inven3):udmde2 u krsely proportional to

  Two objects attract each other gravitationally. If the distance between theb;du1o nsfl x 5+kf0*hfq4+kyir centers o fd sly1ku+*;q04b h5kf+xfnis cut in half, the gravitational force

  Two objects, with masse7-smtuaa8n ky3)zu w +qd4k9jhy;r 2 xs $m_{1}$ 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 mass9kew dxv50d.zm /a7 ujes $m_{1}$ 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 univers f) tuwo)5gy4zal gravitation.

  Compared to its mass on the Earth, the mass of an object on0 6 d3gmpmo+pxbf vf;h4u88 ds the Moon is

  The acceleration of gravity oned5 nb .zq(; 7,remsgi the Moon is one-sixth what it is on Earth. An ob5,eb im qg;e(rd7szn. ject of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surfaces 5i:0 5/ hdfvsqg;ri p3ixuf9, the rocket's weight

  A spaceship is traveling to the Moon. At what point is ith qd a.+le hthh,56gq8 beyond the pull of Earth'sqhladh8hht5,.+6q e g gravity?

  Suppose a satellite wers 30u nk67 wqamgo6/qre orbiting the Earth just above the surface. What is its centripetal aqus qa0/ m g6r6ow7kn3cceleration?

  A hypothetical planet has a bd-k; ,nf4itv 3l9ju cmass of 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 accelerat -ltdv9buij; fc4k3,nion due to gravity at the Earth?

  The acceleration of gravity on the Moon is one-sixth yxlq5ok; ,wc;pqxg 7 9what it is on Earth. The radius of the M975w qocpl;kx;y, gx qoon is one-fourth that of the Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gr aoninqf*.9a; avity, but planet B has twice the radius of plannniqa. *af; o9et A. If planet A has mass m, what is the mass of planet B?

  Two planets have the same surfag-:xvgru4 v7ace gravity, but planet B has twice the mass of plan7xvg4r-gav u:et A. If planet A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (rad t,8 c2l-cvhmjdoxc+ ,ius r) about a spherical planet (mass M). Which expression gives this sat,,+j lc8ohxm2c d- vctellite's orbital velocity?

  Satellite A has twice the mass of satellite B, at ; a)r5c2z;91ke mf x)dchynend rotates in the same orbit. Compare the95t ;n2kc d); )zhr xcy1amfee two satellite's speeds.

  A person is standing on a scale in an elevator accelerating down5,hzvsq 38c vgward. Compare the reading on the scaqshcv,5z v 83gle to the person's true weight.

  Who was the first person t:hk8 w4; sb,m vua:bqno realize that the planets move in elliptical paths ar;84:m bs ,nbakvu:h qwound the Sun?

  The speed of Halley's ip5scav)x n8m+k ptn2q-f0 +r Comet, while traveling in its elliptical orbit around the Sunq n+ck2r5si-n8mvft)0 +paxp,

  Let the average orbital radius of a planet be R. Let th 2/us8d,mzmjk5afg -s e orbital period be T. What quantity is constant for all planets orbitin,/g ka 5s8fum2s j-mdzg the Sun?

  A planet is discovered to orbit around a star in the galaxy Andro2lmei/g0, bsp meda, with the same orbital diam b, ipsm0e/l2geter 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 the Earth's orbital period?

  The average distance from the Earth to the Sun is defined as onegdynvg)q 8o mg kid.7h1, nxvir++0d* "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from t n +gh.gmnx ,0rg+*7yq vidv8 d1oi)kdhe Sun?

State Kepler's laws.y+ cgksp91q *v k9ggm)

  List the four fundamental forces (9.*y6f 0-pnjuu tz)cw xuwpxin nature.

  An object moves with a constant spee0 .h5 :3eg gkuc*(gnwl * bnfx3-rhvvgd of 30 m/s on a circular track of radius 150 m. What is the acceleration of tgv.knb 3-rg:0hef3 5wv*gh(xg n * cluhe object?

  The maximum speed around a level curve is 30.0 km/h. What is the maximum speed 4ze)t+/c w/zn4kqvvxd6wo r-around a curve with twice the radius? (Assume all other factors remain unch-zvwx6en/z v4qr t4+ o)wdkc/ anged.)

  What is the centripetald+66y3apuro a acceleration of a point on the perimeter of a bicycle wheel of diameter 70 cm when the bike is moving 86aua +rp dy63o.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located tp oq1 0kbs ,8vaqb7u)0.200 m from the axis. What is the centripetal accelerq usv,0q )otp7bka18b ation?

  How many revolutions per minuty3 ; /;t7qz/rejtueike must a circular, rotating space station of radius 1000 m rotate to produce an artiyee3; u/tq ;/zrj7tk ificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius tur tztt70ljdren)5,mpy*(yhq)o3lj- o3agw r+n at 96.5 km/h. What is the centd7 l zje3 w)y 3aqjgn(ryt) orl-tmth,op* 05+ripetal force on the motorcycle?

  A 0.50-kg mass is attached to t5 f79d)iz;zs(s+ aekdx bav ;hhe end of a 1.0-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 skhv e7xad; izd(a5 )b9s fsz+;peed of the mass if the string is not to break?

  A stone, of mass m, is attached to a stroq/*q j:+5kdjj so hbvo*elp./ng string and whirled in a vertical circle of radius r. At the exact top of the path the tension in the string is 3 times thj:eo*ol5.k/qb jpsj+v*/ h dqe stone's weight. The stone's speed at this point is given by

  A stone, of mass m, is at:4eir ; js f zst5oian/.x,b/ctached to a strong string and 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'sji:/ssf;, exo zr b/5t. an4ic speed at this point is given by

  A jet plane flying 600 m/s expe k8p) oqxkd,b1riences an acceleration of 4g when pulling out of the dive. What is the radius of curvature of the loo k8kp,)xdbqo1p in which the plane is flying?

  A pilot makes an outside vertical loop (in wh. icz)b3 *vqxkba( 8nfich the center of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down on his seat with only one-half of his nfkqixzab *.8(vnc3b )ormal weight. How fast is he going?

  The maximum force a pilot can stand is about seven times his weight. Wfw2v38cu3 j6wza t1 sgz a(5hshat is the minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, h 326atuz wc3v8wag(zf s5j1scan tolerate at a speed of 250 m/s?

  A car traveling 20 m/s rounds an 80-m radius horizonbw i r80rw+fz31d 1;alt:kp bgtal curve with the tires on the verge 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 eac;rl b1 wwg +3zif80rb:1 takpdh road surface.)

  A car is negotiating a flat curve of radius 50 m with wof*pi -3ay six92t u-a speed of 20 m/s. The centr i32xyi*-at-op wf9s uipetal 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 radiutu7p*mmoi: ++h;bsm 4vm 7a tms 50 m at a speed of 14 m/s. What must be the minimum+: m 4mtb*v o sm7mt;amihup+7 coefficient of friction 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 curve. Thj1m )fwt/uxm, 0ei 9bce coefficient of friction between the tires and the road is 0.40. What is the minimum radius of the curve if th mef mbj)ut,x9i/c1w0e car is to stay on the road?

  What minimum banking angle is required for an Olympic bobsled to negotiatot *0t k 8d t6c56aik5.nfzlsi6d 6c 2rxj*qhte a 100-m radiun5t2 ditrtfh olt660.6ixk k8aj cdz*6 *csq5s turn at 35 m/s without skidding? (Ignore friction.)

  A horizontal curve on a bobsled run is banked at fa hubw6z*u+ w-*um3la $45^{\circ}$ 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 m, banked at an anu g asr-putzv. 7m;2+rgle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is banked fil-: 4 tgzfs)zg;)g0 bduq ;qat $45^{\circ}$. 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 stzrao(9u)pb. t )tez.zt ( zkv:ring is revolving uniformly in a horizontal circle of rabtvtz.e r9z t)a (:(k.ozp u)zdius 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 race car accelerates at a unif v aws q-7;d,a:wl+yyhorm rate to a speed of 45 m/s in 15 s, moving on a ci ;wy,- ahad+lw: s7yvqrcular 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 consists of a pduo-;hhn /r2aroton 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 force dp0 * g f28fpx6h f)aduwc)8hoon a 70-kg person standing on the Earth, due to thed)8 f da wu2)fph6xcpgoh8f 0* Moon? 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 x fbx1 d/5/-n9lgnq(: r rssexmasses is F. If the masses are moved to half of their initial distance, what i-9(s15/xnbxdrlx g r/ enfsq: s the gravitational attractive force?

  For a spacecraft going from the Earth towaciws k-wtbt8t w49gb / /3se5ard the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the Earth cancel?b st 4t9w/ 8w wag-iecktbs35/
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 ihv zds0;o rw gsblx;i88r1 u9;s $7.4 \times 10^{22} \; kg$ 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 fz,te)v txf6e 9 88tu2adad3 fcor a "space-walk" at a distance above the Earth equal to the radius of the Earth. What is her acceleration du8)8uf3acet f,za9vx2d6dt e te to gravity?

  The radius of the Earth is R. At what distance above the Earth's surfacqj: x(3u8(qjn wc c4:q;wt taoe will the acceleration unq4x;t8(3q c(q joajw::w c tof gravity be $4.9 \; m/s^2$?

  A satellite encircles k+y 6w ald(rf)Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the sul6r fw+ad()ky rface of Mars, is

  At a distance of 14000 km from some pla5 2*iv6f+b7o oix2h.a k40yfxz hgyvgnet's center, the acceleration of gravity 42a 2y6v0yfh7ohovixfk5*gzig. b x +is $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 .psl2fby8 9)dmr 27irkeq +oqN on the surface of the Earth. The Earth has radius r. If qmb s8)+o 2irfp.er7 y2lk9d qthe object is raised to a height of 3r above the Earth's surface, what is its weight?

  By how many newtons does the weight of a 100-kg person change when he goes hxsj s*ab(zu wo2 pif3,+ugn/8f+5du from sea level to an altitpn/ uhb3f+assgz,u +j5o8iud*( w fx 2ude of 5000 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass )kndri.w9 j1 w100 kg is at a point 3r above the Earth's kj1ndwrwi.9)surface. What is the satellite's weight?

  A spherically symmetric planet has fourd(upke ,v o x k-/ pyp+0ev(fz6dli.3o times the Earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planeip3ev,(p-d+ . 06xp fe/ dyzukvoo( klt?

  During a lunar eclipse, the Moon, Earth, and Sj ) .at lnqfy8lvj)(;cr9hi )cun all lie on the same line, with the Earth between the Moon and the Sun. The Moon has 9;lq tcla8ni rf ))( .vycjj)ha 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 tra ays 789vbn(tf,j7hpknsported 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 Earth (i.e., it ) d d/3fwy urai k++v-i.cin/njust skims the surface of theni +-+vyrfi /un/3 i)ka cdd.w 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 low circular orbit about the Earth (i.e.,m8t x uuy t;8mz11vjwq5t-1jkn;t,a k it just skims the surface of the Earth). How long does it take to make onnk51 w;ax1t ,jkv8;u-1 m8zmutqyt jt e revolution around the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular rn8k,x,w(r xn1u w/mvorbit 230 km above the surface of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (Thew(nnk mv81 ,/r r,wuxx mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiternq8b n3so ;osvld4d01s( gfpi77e lp+ , has an 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 pn/ng3 2mm)uz alanet 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 circular orbits. Moon A has orbital vjj3 kit.ju6376 fkv mk4ak ;dradius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How4i7ka3jj 3dfkmu. ;t k6vk j6v long does it take moon B to complete an orbit?

  The planet Jupiter is l5yd) r 3uy2h.gzl*ncf t4q 8p$7.78 \times 10^{11} \; m$ 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. What is t/l 6;aec:vsj8w k2fk bhe average distance from Jupiter to the Sun? (The distance from the Eart;2bva:68 cfklswek/ jh to the Sun is $1.5 \times 10^{11} \; m$.)