Is it possible for an object moving with a constant speed to accetey(hvr.pspsw. ;nt1 e6:9 rdlerate? Explain. 91dpwv trh pet:(6 y.esrn;s.

  Consider a particle moving with constant speed such that its acceleratifnrh 8+ni,k766va6toeilth 2 on of constant magnitude is alwayvie h hkr766 tatn,olf2 +8i6ns perpendicular to its velocity.

  An object moves in a circular path at a constant speed. Comparb*mioua;1mk w6hgbm. + 6k5xztk2m4 z e the direction of the object's velocik 5ka61xmhmztwz6mi kb+ g;mbuo 24*.ty and acceleration vectors.

  When an object experiences uniform circular motion, the direct/ pr yrax-. nol0e.1t 9vg5 f7pqt.wxiion of the acceleratio .naw7/p yt9e-xlp1r..rg5o t0iqv fxn is

  Consider a particle moving with constant speed such that its ac 0 u25r 5n;ipj,0iwk-bvkl nhgceleration of constant magnitude in02jrb5n0ilp k 5hwu; -vkig,s always perpendicular to its velocity.

  What type of acceleration does an object moving with cv*akah2yz a72gt buqc62 pq7df2 8q5constant speed in a circular path experience2 avcah78b5 zdtq q c u2q6ygf*ka722p?

  What force is needed to make an objectq 7i;apyp)g)c move in a circle?

  When an object experiences uniform circular moti(p hw5z * a;hl.+dqeukon, the direction of the net force ise(qkh z .pa5d+w;l *uh

  A roller coaster car is on a track that forms a circular lznjyk0/ f ,p a)lvby65oop in the vertical plane. If the car is to just maintain contact with track at the top of the loop, wn,/ l5p6yf zja)kyb0vhat is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a track that form4pz4 6t kkbcg-s 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 minimuzk-pg ktb4c 46m value for its speed at that point?

  A pilot executes a vertical dive then follows a seminw4/)i hyasl5 -circular arc until it is goihli4/ a wny5s)ng straight 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 curng2,1lei: kf eve 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 constan1xxb)hvg ) p(fvb4y:ot 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 gobfpbogx:)v 4 x1v( )yhes around the curve for the second time, compared to the first time?

  A car goes around a curve of radius r at a constant spee -0gcmcnza :rz)ew -/e3xndp e4m(vig,g -2kyd 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, compared to the fi3/4z:cgnep2kgzcmed)ry vw-- n0mg (,a ixe -rst?

  A car of mass m goes around a banked curve of radius r with speed v. If thbguvj c+fh3w79u* x7f2nj j )me road is frictionf37ubx uv9)j7jmgfc+2 jn w*h less 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 magnitude to

  Two horizontal curveq;b61qrqq e5 os on 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. What is the safe speed on the larger radius6e5; q1bq rqoq curve?

  The banking angle in a turn on the Olympic bobj3tn,q ntv6( 3 egzqq1sled 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 turzq n6ttqv(j3q3 n1 g,en. Why do they do this?

  Is it possible for an object moudqf.ol2 v dc21 ;e7xg086te-pynhmoving around a circular path to have both centripetal and tangential a.7v0fh6noudd p- x; c822ote mle gyq1cceleration?

  The gravitational force between two objec8)eu tk1y1f ocjkar)5mob))x ts is proportional to

  The gravitational force beti89 tix vrm.b3ween two objects is inversely proportional to

  Two objects attract each other gravitationally. If the distance ;.n7lrv( k dssbetween their centers ilkdr(; v7.n sss cut in half, the gravitational force

  Two objects, with mas1xa h ,.cn hm*hgupk96bbch(khl+n 2 2ses $m_{1}$ 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 masses okthj )z id.;4$m_{1}$ 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 g55axz whro5p2 ravitation.

  Compared to its mass on the Earth, the mass o8wp9h7i aqb c-f an object on the Moon is

  The acceleration of gravity oe9rd vg -n63hjn the Moon is one-sixth what it is on Earth. An obn3jvgre-6d 9h ject of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earthv u b8ea-wc7.mw5(tv ww -fj9r's surface, the rocket's weight

  A spaceship is traveling to the Moon. At what point is it beyr ; c riuie87cer/5vo2ond the pull of Earth's gr 2cr7r ucer/5vie;8oi avity?

  Suppose a satellite were orbiting the Earth just above the surface. Wha jy)jx wn*uhp6 q8v32tt is its centripetal qw )t3nj 28hxpu6v*j yacceleration?

  A hypothetical planet has a mass of half that of the Earth and a radius olg, ;:fj 4u-tm,9bs8apyz lpm f twice that of the Earth. What is them,8;um ,y:zg9tbj alfps-4 lp acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the Earth?

  The acceleration of gravity c81 emd(o bf9 ho09j6d bgc;c pv)7icfon the Moon is one-sixth what it is on Earth. The radius of the Moon is one-fourth that of the Earcvfmofgipdcdcoj b)b;07 1ehc 869 (9th. What is the Moon's mass compared to the Earth's?

  Two planets have the same sur dy2v*-h77eh s qhjl2lface gravity, but planet B has twice the radius of plas qh2 h2e-*7yl7djhv lnet A. If planet A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, but planet B has twicez/mb(gzp6 9(wfnbyb2 the mass of planet A. If plane6np /zbz mwb9 yb2g(f(t A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a cira)m3 kpgpgc cv)ef60; f4se1rm. g8io cular orbit (radius r) about a spherical planet (mass M). Which expresm.fcgf8 goa )gp1s0m e 3v k;prc4)ie6sion gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and rotates in the same of,b46 z 4apswadn4y 8g9kj ma5rbit. Compare the two bd64, 9fs4 a5y84aaznjwk gmp satellite's speeds.

  A person is standing on a scale in an elevator accelerating downward. Cy* kobgs:g 3 exa-y*)oompare the reading o-g*ky*oseoyxbg : )a3 n the scale to the person's true weight.

  Who was the first pe(zyqy19.lmn fj. pha 0rson to realize that the planets move in elliptical paths around the S (hpyf9n0. .qlaz1 myjun?

  The speed of Halley's Comet, while traveling in its ellipticaliwwm, jy/nx0f)*cw; uw..u+y9f 3muz1ahzb d orbit around the S yhuww* x)9ubf1d,.0;yz3+/wz u.ci n afmwmj un,

  Let the average orbital radius of a planet be R. Let the or), hebdp dwro0f)r- zo31o t4lbital period be T. What quantity is constant for all planets orbitinddf reo thopo41)z)lw3br, -0g the Sun?

  A planet is discovered to orbit around a star in the galaxy Andromednxtlzis;z c xu(h4036-wwc0 ia, with the same orbital diamwl-zhu cznc64 ;i0t (30wsxixeter 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 il(wnq p :b p6nzud:7gqaz651h s defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-thir:gnnzp5a1bd zq6p:u7q w6(l h d of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.mrc chqa(9 5qlrdm:ce 5dl; 5+

  List the four fundamental forces b67x+e.7nyts- ttpd adxc +v6in nature.

  An object moves with a cons5 weg 3br5qfc-kp 2y*itant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the o fq*ew 55gpbyc2ri3-kbject?

  The maximum speed around a level curve is( 4n7 r)lckg y4x(tfho 30.0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all otlt 7 fxo )cy4rk(g4(nhher factors remain unchanged.)

  What is the centripetal acceleration of a point on the pejbe5vek vzh, c+7bd9j o5w vkw;(g;,lrimeter of a bicycle wheel of diameter 70 cm when (wc,b7dezv ; 5+ovjj9,bhge wkklv ;5the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m from the axis. h zy cqoz- -i(tzh+ijk+n 1.5qWhat is the centripet( z5tkic-- +1qq+yznhzh .o jial acceleration?

  How many revolutions per minute must a cir aeb(x,at,wcj(-l 0b1x 8tikacular, rotating space station of radius 1000 cb ai,1lx0a ta(bj-(,txe kw8 m rotate to produce 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 t+.)nsde .rq raurn at 96.5 km/h. What is the centripe. qd+nae)rs .rtal force on the motorcycle?

  A 0.50-kg mass is attached to * i (rrl1j* ,pygs74zrj1pkncn9 vn*ythe end of a 1.0-m string. The system is whirled in a horizontal circular path. If the maximum tension that the string can withsta(4y*zp, r7nn kc9r**i 11 svjplrn yjgnd 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 whirled in a u bn(/pew ps;k o2m 4 0m3qpu*0u4xjmyvertical circle of radius r. At the exac u;*0xky0e(m/sow4qmup2pum 4 j 3npbt 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 attc rl9u8l8c3: i m;1bk0gyjawybm f-3yached to a strong string and whirled in a vertical circle of radius r. At the exact bottom of the p mic;:-jyfy 3a8wyb1m cll3gk 0u8 br9ath 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 pullingzbg*j 6hs*g evs3+hs7 out of the dive. What is the radius ofbj*vsz6g*se+73sh gh curvature of the loop in which the plane is flying?

  A pilot makes an outsi084vx cy ,evulde vertical loop (in which 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 normal weight. How fast is he go0xlv,u4v ec 8ying?

  The maximum force a pilot can stand is about seven times h1 b- 5jn9; dzbx)wl12(si ugalibg;d zis weight. What is the minimum radius of curvature that a jet plane's pilot, pullingxi lb;9 s1ilb bzgauwn2j1;dz -()g d5 out of a vertical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/s ap7e64 kc4 he. ,vmvvx27 bhtcrounds an 80-m radius horizontal curve with the tires on the verge of slipppvcb24vmva ek, h7c. 6etxh47 ing. 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 radiusw 8g5aj9drtba ocs5 32 50 m with a speed of 20 m/s. The centripetal force providwdoa5s3 ra 5t9gjbc28ed 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. What ckyn55 nw v*0/hbxeg; must be thee ;vwxnk5 5ycnbh0*g/ minimum 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 na;.q4o+h7 6rgqta cpcurve. The coefficient of friction between the tires and the road ra.o+g q np47tchq;a6 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 5dy*:k i73bn s q0ckclan Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? (Ignore frictionq l: 5k3*kd cib7csy0n.)

  A horizontal curve on a bobsl2xf5)oa5tnz fb-jj t-ed 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 m, banked at an angle 4 30:h e jrqhu4lcymq wdd7n59of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80ti. brx/fo8 9p*7uz-aqubh b; 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 uniformly in a1,8 szu7j +bufc/dpwsyg ,vqy t/unt2q :3y)m horizontal circle of radius 0.: ,/qdy yn32fp)uj,1wc+ m8stygt7 /bzvquu s500
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 thz43 sd s3b e(1 qhbu+abp0wke)e 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 fik+bws4(u3ab dsqp1e)zh eb3 0 ll 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 mkc:.bkt v,oze vbr4axe;7;/ p ass $1.67 \times 10^{-27} \; kg$ 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 70szsa3e lav; j *(m,-xf-kg person standing on the Earth, due to vmszj (xe a- lfs3*,;athe 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 masses is F. If theo16f47cw4*ty ol plzz masses are moved to half of their initial distance, what is the gravitational all4 ycofw1 *674ozpz tttractive force?

  For a spacecraft going from the Earth6 1gxetab1p3 ncq:w 1w toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the Earth cancel?3:p 1 nag 6bxeqw1c1wt
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 Mooncu/3sp l*kwl( is $7.4 \times 10^{22} \; kg$ 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 "spacez*,k0y9aslcno fz r-/iu(i,ra )sh+e-walk" at a distance above the Earth equal to the radius of the Earth/zl +rk,unoa ,9fr)yi-s e*c h(s a0iz. What is her acceleration due to gravity?

  The radius of the Earthkie2s x 3 *di0al7xd7x+d1paj is R. At what distance above the Earth's surface will the acceleration of gravity be la70+ d3xxi ds2 ip7*jkax 1de$4.9 \; m/s^2$?

  A satellite encircles Mars at a distance aboune3z oqw 48rccv3e9 (ve 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 surfacq 34w3(z9 roncv8eeu ce of Mars, is

  At a distance of 14000 km from some planet's center, the acceleration of gravityrft *hs-+9f*uecr3n * vk liq j60:gbh 0ig:khje usfh lrn crb9 3q6-*f*vt+*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 N on the surface of the Earth. The Earth has radius zx 9 9i8xga9 fx8e3mkgr. If the object is raised to a heigg99axmk8ig98 fz xx 3eht 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 pw)w:,kh mf,d from sea level to an altitude k w,p),hmw:df of 5000 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite6t y 9h hntc4)gmj538aag5nzd of mass 100 kg is at a point 3r above the Earth's surfacc 8gh5m5jhdt 36) ta9n4znay ge. What is the satellite's weight?

  A spherically symmetric planet has four times the Earth's mass and twice *llh*i8ejv s6 dj8k3aits radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on th*8a vsk8 6hj3l jdli*ee surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lia p )z64swh3o*oep q6ue on the same line, with the Earth between the Moon and the Sun. The Moon has a mass ofs63e z6o)woq* ph up4a $7.36 \times 10^{22} \; kg$; 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 tzo1hk/b et4v a:m03ui wy 61mqhe 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 juqrw* r(tuel.lxz+u+2 st skims the surface .w(l+lue2rxr*tz q +u 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 low circular orbit about thex+ o9pl/h idiz9iw3 u je/o)e /ri0fd3 Earth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution arwir +pixh9ei9u/0 d /ojilf3)d /z3oeound the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circularvp,c ntl mihh on.0g n/6/3er6 orbit 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? (The mean radius of the E6p,c/en.ni/r6tlov3h h0m n garth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Juj) l:+zgj4o nc+fm pf-piter, 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 planet with av p,(q mj9p: :yjg+ifa 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 circularvmc5x8pj646ay ov 1er orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 day1j5mrevv cp64 o6ax8y s to complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter io c.zsrmv6d*/5md ovkc 8/ 9jes $7.78 \times 10^{11} \; m$ 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 togh84lqq 6u,f f orbit the Sun once. What is the average distance from Jupiter to h,fqlg8f6u4 q the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)