Is it possible for an object moving with a constant speed to acch zy ta :gae40k* (69fadlnvv6elerate? Explain.kv6 v0alfd6g: za4n (eay *9th

  Consider a particle moving with constant speed 10qxw,b+vuj i such that its acceleration of constant magnitude is always pix b,+ qwuv0j1erpendicular to its velocity.

  An object moves in a circular path at a constant speed. Compare t k8+ rc nbwdb(7zmnl*90as fi4he direction of the object'zisbd9fc( *k0ra8wn+ n4l m7 bs velocity and acceleration vectors.

  When an object experiences uniform circular motion, t. m +6zxjnv8hehe direction of the acceleration xmj8+6.zvhneis

  Consider a particle moving with constant speed such that its acceleration ag(zjpy1o 0 i+of constant magnitude is always perpendicular to its velo(aoj0 pyg iz1+city.

  What type of acceleratiova zqd: bv0rz. 2ya8v7n does an object moving with constant speed in a circular y.vdab2:v 8a 0zz r7vqpath experience?

  What force is neededr ttj( *toe.kig bt:b1w)v86 /dk ycd) to make an object move in a circle?

  When an object experiences uniform circular motion, the directioizj y dm.-/ h7gqy/ .yna +vhwlzs2;,on of the net forcev /.7qj2+y .zy/g-miwln ;hzod,yh sa is

  A roller coaster car is on a track that forms a bjsqjzwe ,6 20circular loop in the vertical plane. If the car is to just maintain wjb6,s2qzej 0 contact with track at the top of the loop, what is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass5 ubutfa:p: d9 = M) is 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 minimum value for its spbp 5d:fu:9ua teed at that point?

  A pilot executes a vertical dive then follows a semi-circular arc untilh:nez,. q+ lk:-mg mvc it is going straight up. Just as the plh nkqe-v+ zcg,::.ml mane 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 curve of zl 6v*)xu7grdo p48fwm s fy4a( 0bnpgutk1)9radius $r$ at a constant speed $v$. What is the direction of the net force on the car?

  A car goes around a curved15qeo f.fvo 2 of radius r at a constant speed v. Then it goes 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 tod1oo2 5 q.vffe the first time?

  A car goes around a curve of radius r at a constant speed v. Then it t;1fu,z4e+ hi*yrmd dgoes around a curve of radius 2r at speed 2v. What is the centripetal force on the u ; ,zd4ti+yd1mefhr*car as it goes around the second curve, compared to the first?

  A car of mass m goes around a banked curve of radiup;e.u-1bh t bgs r with speed v. If the road is frictionless due to ice, the car ch up 1tb.bg;e-an still negotiate the curve if the horizontal component of the normal force on the car from the road is equal in magnitude to

  Two horizontal curves cbt 6rml.*4rkon a bobsled run are banked at the same angle, 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. Whbrtrc *.l4k6m at is the safe speed on the larger radius curve?

  The banking angle in a turn on the zm ssiy :o4i5e*m2hc. Olympic bobsled track is not constant, but increases upward 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 doi2 hmm zc .e*iss45:yo this?

  Is it possible for an object moving around a circular path to have both centrink -a 9q0bpy+apetal and tangential accelera-b yk+apnq0a9 tion?

  The gravitational foeykd y e24r45srce between two objects is proportional to

  The gravitational force between two objects is jjm4;gf6gdw3 inversely proportional to

  Two objects attract each other gravi/1v (ogfs e4zwgsb1-atationally. If the distance between their centef o1bzs -g4s(1/ vgwaers is cut in half, the gravitational force

  Two objects, with masses 9bi1 aex a+b3o$m_{1}$ 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 mav9ym up4qf:r (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 gravitatp6c7pm/ tj-) s)d uuppion.

  Compared to its mass on the Earth, the mass of an object on the Moonjr 0z )xb9,ha rfj-4kg9lh;xu is

  The acceleration of grq)b47rsn8x sdb 0h(7btj+oucavity on the Moon is one-sixth what it is on Earth. An obju7n0bds8s +o b(4qh x t)7jbrcect of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, th .e kvp/ytqzhou *jmvy)u232j4g1js:e rocket's weight

  A spaceship is traveling to the Moon. At what point is it beyond the a.re(/+8l3 *:dif gfxdjjf sbpull of Earth's gravit ff:3.8fdgj s*db+ jrexl/ ai(y?

  Suppose a satellite were orbiting the Earth just abog3i(gfey /- il k)i,8o +wlj-+eom rxgve the surface. What is its centripetml g o 3j i)i8-eo-gyikfr+/l(xegw +,al acceleration?

  A hypothetical planet has a mass of half that of the Earth 4srfv(v)dhk+nt 0 ua d)ulkh*5pxn:8 and a radius of twice that of the Earth. What is the acceleration due to gravity ona0u +)4x rth(k*nddhpvu)8nf sl 5k:v the planet in terms of g, the acceleration due to gravity at the Earth?

  The acceleration of gravity on the Moon is one-sixth what it is on Earth. The r*vi4 dgk c,4s)dxm8 zkdlds4;adius of the Moon is one-fourth that of the Earth. What is the Moon's mass c4 * vxk4,cd mdsgsk)4 l;i8ddzompared to the Earth's?

  Two planets have the same surface graxz3ntb ( 5o y0r1n45xhgif,lsvity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mon(h1y43 zf ibs0 xlgn,5x5 trass of planet B?

  Two planets have the same surface gravity, but planet B xx-yi2dy7k81r )yf lr has twice the mass of planet A. If planet A has radius r, what is theidx)1ly-y f82rkryx7 radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) about a sghy8i( );0y1 jahn 3us9aptfwpherical planet (mass M). Which expression gives this satellite's orbs8)ainh0y9(g;3 yp1 tfhau j wital velocity?

  Satellite A has twice the mass of satellite B, + * ,qj;cqckpdj*(krc5j.zwb and rotates in the same orbit. Compare the kcj+q5b*q(dprcck.z*jj, ;w two satellite's speeds.

  A person is standing on a scale in an elevator accelerating downward. ;r343kqgj ic8p 6bvl 9o:jjfhCompare the reading on the scale to the person's o:pj gcv 4hb8;r 33qj9jkli6ftrue weight.

  Who was the first person to realize that the planets move in elliptical4b4nre dh 9 hts12zlu3y)eq6e paths around the Sune41de) 4uq 623z9h tbnlsrehy?

  The speed of Halley's Comet, while trnmkwmed mh0:wub g)88/ 3p y7uaveling in its elliptical orbit around the e/mgwwk:n3hm0 u) bdm8u7y 8pSun,

  Let the average orbital radius of a w-hcg;yc-ws i1 8sdqej7wy8hy: ju xy:g1(;mplanet be R. Let the orbital period be T. What quanc qscij1:e w;d8w8;s-(hymgu yx yhwj-71yg:tity is constant for all planets orbiting the Sun?

  A planet is discovered to orbit aro1au;p 9dbl 1m q(iw0ycund 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 the Earth's i( wqbca pmy0l91u;d1orbital period?

  The average distance from the Eaip i:*,w 6uef6.icxlo i)hu f.rth to the Sun is defined as one "astronomical uohxuwufl)6i6pfii . ,:ci *.enit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.5 c,;zeizgdt:/h ykw 7

  List the four fundamental forc w tw1+ kuhx97fyeosktpp(;57es in nature.

  An object moves with a const-dx( aixf2f.s,:zpe jant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration,i( xse-x .zdapffj 2: of the object?

  The maximum speed around p/b3j.vrg g+ ja level curve is 30.0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all other b p +j.rgvgj/3factors remain unchanged.)

  What is the centripetal acceleration of a point on the perimeter omv rnv(:ma4 gf+3du(b * .prqlf a bicycle wheel of diameter 70 c vrdu3v.npqb: 4(f*rg( a+m lmm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.2096vf3 ryr1p yc7 5nxldr3gn (f0 m from the axis. What is the centripetal acf3yn v cd6nrfrp 1xglr 5y97(3celeration?

  How many revolutions per minute must a circular, rotahk*/v/t o(d pqting space station of radius 1000 m rotate to prodk*/dqov / ph(tuce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn at 96.2c zrb)dy.7vd5 km/h. What is the centripetal force .vy72bc)rd zdon the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m string. The system i6 fcsf o4kpaw f.e/.o0s whirled in a horizontal circular path. I.k4ec6afp /s 0foowf.f the maximum tension that 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 attached to a strong string and whirlemxjbd25 r/0 led in a vertical circle of radius 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 j5l meb2x0rd/given by

  A stone, of mass m, is aai -m//6f (gxjhk3f bwttached 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 weighk/bw6x/mja- h(3f gif t. The stone's speed at this point is given by

  A jet plane flying 600 m/s experiences an acceleration ova pf- se0ex(f vh223expnc1. f 4g when pulling out of the dive. What is the radius of curvature of the loop in which the plane is faeph-ev1f 0ncs(v3 .2f2 xex plying?

  A pilot makes an outside vertical loop (in which the cx9 fk2b4 x.-1ys o scd5puo+neenter of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down on hiesyu5-bcnds.9 xpkx 14 of2+o s 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 weig5u, 8dgjxpzi0t8k3v yl5 v ul9ht. What is the minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can tolerate at a ll5ud,jv0 88p 3ziyt 9x gu5kvspeed of 250 m/s?

  A car traveling 20 m/s rounds an 80-m radius horizontal curve with the ti/s jydlqcd1iwc 8yf3+-i07hxvj x9 2mres 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 each rcij3/fqxvhxd79y w+l82d c1sy i0j-moad surface.)

  A car is negotiating a flat curve of radius 50 m with a speed of 20 mw8 b;bu;g)i1 gpkvp w*/s. The centripetal force pru b;pg8w*kv ) p1gw;ibovided by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve of radius 50 m at a speed of 14 m/s. Wctrjuce,e **grbq (./hat must be the minimum coefficient of friction between the tires and the road for the car to make the tur*( jtq.ureeg, b*rc c/n?

  A car is moving with a co+iixzj400on hnstant speed v around a level curve. The coefficient of friction between the tires and the road i hion 4jx00i+zs 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 Olympic bobsled to negotiate a 100 u jk.95gm+jqzakie:;jq )o:q-m radie:+ogi;:qk) 9qj. ajjuzm qk5us turn at 35 m/s without skidding? (Ignore friction.)

  A horizontal curve on a bobsled run is ) :5 n+qu1e ft*r ;mefinwq;ejqb*k*sbanked 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 m, banked at an bcl5 -a:aj f9iangle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is b :uqmonn(y eq66 e i;7fso9q8tanked 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 xn3 4n w.(qfyrof a string is revolving uniformly in a horizontal circle of4.fw3n nr (xyq 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.vvdz6tm,x78 x9k l. obx:pbw the pit area, a race car accelerates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular track of radius 500 m. (only fill in numerical value in t vxmw9.vpxbl6:,kdbx8t .o 7zhe 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 con 4e7r i )-tfjkx.nt,rtsists 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 force on a 7dzo z; 1r(n 1biz2lv1zmpu;m4 0-kg person standing on the Earth, due to the Moon? Thvz4p ib2;(mz11lr; u nzodz m1e 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 tw ji8n bquw3yg-19b+mwo masses is F. If the masses are moved to half of their initial distance, what is the gravitational aj-bm1by +n8 q igu9w3wttractive force?

  For a spacecraft going from the Earth toward the Sun, at what distance fromrgoilto// ,gc7p mc27 the Earth wimrlg tgo c77oi 2//c,pll 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 is b)a4kxexc5k6$7.4 \times 10^{22} \; kg$ 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 distance above the Earth 9f 2)ue3zygl tequal to the radius of the Earth. What is her accelerati z3)lteyu g2f9on due to gravity?

  The radius of the Earth is R. At what distance abovi och 4; )/1gq3nhfuja.kpy 1ye the Earth's surface will the acceleration of gr1qopgfjy/41 n) hyikh c3u.a;avity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distancer ur.:x n ,ccbeqidf93c,tkm/ : +tl8f above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite,+ n9 cul3,:kc 8:tdqbr,e xf./fcitrm 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 ac.;aheb ). dt15mbm-kdu(f yofceleration of gravity is md;bmtyhobfk( a5)eud- f. 1. $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on the surface of the Em5j1, 9 /lbud tuf0lrearth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what isu0/e9bul, lm1dj f 5tr its weight?

  By how many newtons does the weight of a 100-kg per m*p+ksbw6y7pson change when he goes from sea level to an altit 6s7 pywm+p*bkude 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 100 kg is at a point 322 d7b5l 2lyd)d/whyap8 dlfor above the Earth's surfac wd8l2ad227b/f pll5dyd yh)oe. What is the satellite's weight?

  A spherically symmetric planet has four times the Earth'*dh2pv+7m s8x1r8/yv y 7kxg(mvz ihps mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface o/d m(7rms*i8z xvv8 1+pyhp2yx h7g kvf the Earth, how much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Eartho1 on *kz*j9uv, and Sun all lie on the same line, with the Earth between the Moon and the Sun. The Moon *nu vo*o9j1zk 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 transported to the s8u pi k2js.n4w06m nrMoon.
(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 abox30 se4e k2pkaut the Earth (i.e., it just skims the surface of tep2e3 ax0k k4she 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 abonp(jcxq++sa3*np f4j ut the Earth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution around the Earth? (Thna+pjp(s3*+qnfc 4x je 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. It i+8s/9 *ydwjn i j9k:n;yddt .yh7jafis observed to have a period of 89 min. What is the mass of the E7jws89 nh y;ykfji9ai . y /:jdnddt*+arth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an orbnl5 s-ojdeor2(5 dnc 7ital 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 j22vc tpzx5j wegj,8+ 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 circulaywexseg/m m9c45bq. x7l 6oe 9r 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 complete an ox/ .mgqcl e se674yxob9em9w5rbit?

  The planet Jupiter i de;6lfm +ara*s $7.78 \times 10^{11} \; m$ 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 12qe +7 s//wifdl years to orbit the Sun once. What is the average distance from Jupiter to the Sun? (The distance from the/swf el/+dqi 7 Earth to the Sun is $1.5 \times 10^{11} \; m$.)