Is it possible for an object moving with a i1gq);jpz6pgv7 ju( /zo ufvln7z1l0constant speed to accelerate? Explaingigo z6f /vjp)zv 70l1 puuq;1jlz7(n.

  Consider a particle moving with constant speed such that its accelerationrkgsw 1(+p :*6t-rkq om gl8ru of constant magnitude is always perpendicular to its velocitrr1lowg:* gr p-mku+sqt8 6( ky.

  An object moves in a circular path at a constant spedo; ,yk0qb. jted. Compare the direction of the y kt 0qo.jb,d;object's velocity and acceleration vectors.

  When an object experiences uniform circular moti bzy-,hyuq87 n/jn 9sqon, the direction of the accelerays -qbn/n7,y juz 8hq9tion is

  Consider a particle moi 8m,0 : i1rgbpc7c.wup+ha h*q -wdtkving with constant speed such that its acceleration of constant magnitude is always perpendiculu kpa8h1t 0gqcpwi i b*h-cdmr+7: .,war to its velocity.

  What type of acceleratio: 3 j+tl:xljrsn does an object moving with constant speed in a circular path :j+tx: r3sj llexperience?

  What force is needed to make an object move in a civo7tvizzxuy) 1/g0ms .zj: v1 rcle?

  When an object experiences uniform circular mot) usmu ,+xzqd8ion, the direction of the net force isux,su8d qm)z +

  A roller coaster car is on a track that forms a circularf t orlmc*xmgb.g4t00 s/t*a: loop in the vertical plane. If the car is to just maintain contact with track at the top of the loop, what is the mxt4*tmfstclb/ r ga:0 o g0.*minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a/r , 03f1rf yvxbzod2a 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 valu,0fy1do2 arfbr3zxv /e for its speed at that point?

  A pilot executes a vertical dive then frp8 6oogoe1bm)xqu-2 rt 6l4rollows a semi-circular arc until it is going straight up. Just as the plane is a mut )goo 6o r86xrer4p-2bl1qt 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 curveth+ zf n)b+;qahdyq63 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 goes q;zb0+ mpr3hzv 5iw bds379az,w( bhdaround 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 tiwqhz d bv; (5ma7zs0 3,ihbb3z+rd wp9me, compared to the first time?

  A car goes around a curve of radius /m h bqbqa7:y g9p0iryq 8rv28r at a constant speed v. Then it goes around a curve of radius 2r at speed 2v9 8vqq0q:ym h8rgb api27b/ry . 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 around a banked curve of radiry(j-rm9,db uus r with speed v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizor(m jybu9- d,rntal component of the normal force on the car from the road is equal in magnitude to

  Two horizontal curves on a bo+ 8yuy lf p.-lug2*0glbks p(hbsled 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 th. +8-bg u hf0*2(lpuyl splygke larger radius curve?

  The banking angle in a turn on the Olympic bobsl k g:g wdx33hycoe65hmqd.51zed track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team w :eq6kx3w5 h5dc3gm1h zdoy g.ill intentionally "climb the wall," then go lower coming out of the turn. Why do they do this?

  Is it possible for an obj7w. 1dlfv6iv ject moving around a circular path to have both centripew7lvi 1 d.vjf6tal and tangential acceleration?

  The gravitational force between two obje0y 5chiw2,9coglgow; cts is proportional to

  The gravitational force between twta fz4onxjarrm610*u:)z mp i(n ; qx5o objects is inversely proportional to

  Two objects attract each othefi/yodr 80bs 0r gravitationally. If the distance between their centers is cub80/sr0 oyifdt in half, the gravitational force

  Two objects, with mas3unnxp *aqem 40c( w5sses $m_{1}$ 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 masse *janxjog0d 1xf8 j 3ezvx*:7vs $m_{1}$ 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 gravitationecijety dy/z +z83 .68uss6nh.

  Compared to its mass on the Earth, the mass of an object :gyaiuk.-nm0 on the Moon is

  The acceleration of gravity on the Moon is one-sixth what it is on Earth.,r,gcje89uek bqs w *- An object,e*c, 9rkw uj8b-sgqe of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, the9tt fel 4o 9p rexk66,pbn5xb, rocket's weight

  A spaceship is traveling to the Moon. At what point is it beyr7 (schj8ds9e ond the pull of Eartd8e(cshrsj 79h's gravity?

  Suppose a satellite were orbiting the Earth just above the surface. What zu (la/ xr.p(jg3 a lb3kup96ais its centripetal acceleu a/(l k63g a pl9r.j(pxz3buaration?

  A hypothetical planet has a mase9- wxzvno3*z s 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 -x nozw*ez9v3 g, the acceleration due to gravity at the Earth?

  The acceleration of gravity on the Moon is one-sixtd;j thuu ;db0iwdecw v330w;3uq u/a,h what it is on Earth. The radius of the Moon d 0,qauvuwhcue duwt3/w;i3d j0 b;3; 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 pladnahxs4v2ftkxw(/l r ;q,:c5 net B has twice the radius of planet A. If planetdhqk2wrslcfx;a4, (v5:tx n / A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, but planet B has lm6 w,t+b4mxzn o+g7 mtwice the mass of planet A. If planet A has radius r, what is the radius,mw n7l+4 +gom6 mxtzb of planet B?

  Consider a small satellite moving in a circular orbit (radius r) abouflm nf)7ct1,g j- yhy4l y)v/la.p 3nat a spherical planet (mass M). Which7)hnyylma)yj4v ,.n fcpfl /t- g3la 1 expression gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and rotates in tzo)-8nkh)qm6paqh rg/ r)d*hhe same orbit. Compare the 6)rdpz)r- q)hnq8hm* ho/gkatwo satellite's speeds.

  A person is standing on a scale in an elevator acceleh910d *i rapkerating downward. Compare the reading on the scale to the person's tru1pe9*rk 0hd aie weight.

  Who was the first person to realize that the planets move i :darwx3sx0+5 y(xf a/xp6ynin elliptical paths aroun+s0nr /3x xpdaiy :(fx5aw6 xyd the Sun?

  The speed of Halley's Comet, while traveling in its elliptical orbit yv:c/ie/mslm:;8f) l3vulg8z*fq qv 9 ,xbdiaround the Sun, ziy;)/mlf sqbqg*dvel :,mcvvf /x8u:l98 i3

  Let the average orbital radius of a planet be R.c2s -nmomaqrt(u h ovv) 0e2k0)nj 2n9 Let the orbital period be T. What quantity is constant for all planets orbitingvq j-h)ks(2oc v 2ommt2n 0ean9run) 0 the Sun?

  A planet is discovered to orbit aror+ x+yitkheg 3v 2vu i7tl40w5und 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 orbital pewt4uvyt 2 r0k+elix 7i3 gv+5hriod?

  The average distance from the Earth to the Sun is dh-; l xdso*;rhefined as one "astronomical unit" (AU). An a-h; so;lhd r*xsteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.0 *wnmha6:f q28rujke(ew .yc

  List the four fundamental 4ufx,hcyb f9yt/3oe9 forces in nature.

  An object moves with a constant speed of 30**odj b 5y*smy9 di6y/9t1 pd5xqlgbr 7sdsk 4 m/s on a circular track of radius 150 m.slimgd 6b dq 79kdx**9jr1 yyt5sybp/4*5s od What is the acceleration of the object?

  The maximum speed arous:3 ly;kl)ixc nd a level curve is 30.0 km/h. What is the maximum speed around a curve with twice the radxk;3lsi:ly) cius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on the perims.2mg*.j tm2sl g r* u(n co)k96meklpeter of a bicycle wheel of diametk lk.jsm. ()9uen*mgs*g m2p c2 6ortler 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.2t 3ce37x 5(t5(qk*lc zanbuzc00 m from the axis. Whacku(xneqz5a5*3ttz 3bcl(c 7t is the centripetal acceleration?

  How many revolutions per minute must a circular, rotating space station of xwj 0:zjml0jqt7g9f3radius 1000 m rotate to produce an artificial gravity gl3w 7qt0jzxf0m 9:jj of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius te n3ehd4/jo, lurn at 96.5 km/h. eh,nd3 eojl/4 What is the centripetal force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0--dvql:m6l 2rf4 iz*fkm string. The system is whirled in a horizontal circular path. If the maximum tension that the string can withzqk4md2-:f*l ri lf6 vstand 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 whirle5a3t-j i2vq;ln:pevgp5z775 nrp yiud in a vertical circle of radius r. At the exact top of the path the tension in the string is5up nni 2v3q je;y7rgp:va 7pt55-zl i 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 sk68-xky4svts6c1 ubssng( 6m z8p+ l xtring and whirled in a vertical circle of radius r. At the exact bottom of the path the tension in the string is 3 time1p zl 4ty(xcm6v6bsgs+kk-u8 8nx ss6s 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 gl9g:v,0 hlni pulling out of the dive. What is the radius of curvature of thlhv:gi ,n0l 9ge loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which thewr+7 md 0lal7-m vgi8 ymlqj07 center of the loop is beneath 8ll07jw7ygl q+7ivmmr dam0-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 going?

  The maximum force a pilot can stand is about seven /fv(veo+.zapvrqp eq 180ou-e7/ aal times his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can tolerate at a speed of 250 m/ a8r p1q-eee/ vv+ 0lova7op.zf/a(uq s?

  A car traveling 20 m/s roundsrp5y*cgj/kun3 :tr o/ an 80-m radius horizontal 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 each road sypnoc/ 5t grr k3/:uj*urface.)

  A car is negotiating a flat curve of radius 50 m with a speed of 20 m/s. ivs+0o 8xl00bkfhc; lThe centripetal force provided by friction i 8;0k+lifx0 lo0cvs bhs $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve of radius 50 m at a speed of 1tlp w)qmuom:57 4kz+i4 m/s. What must be the minimum coefficient of frict 7)4 z+m:uo wliqkmp5tion 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. The coefficibu6jz,c,, w x2e2fp cient of friction between the tires and the road is 0 if2 ,2cebz6 wpuxj,,c.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 ne6opcqxl s/)y qhd.s , m;s)nj2gotiate a 100-m radius turn at ), /;scq jy62 osmqdxhsln)p. 35 m/s without skidding? (Ignore friction.)

  A horizontal curve on a bobsled run is bankedw.+ h0 vkwij8zb.zy -n 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 o2avy7n 6+nl )ky+em9 pwzmv9kf radius 100 m, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is banked )qszs;py 77flqs i:tpm40n (r 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 horizi8wz-i9 mx8 nzb4nk x-ontal circle of radius8 n xz 4-z-wimx9i8kbn 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 thet *l/ql:u0 gtd pit area, a race car accelerates at a uniform rate to a speed of 45 m/s indtltq* /:lgu0 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 consists of a proton of ml fwv. so5;pkzlbf-zk: 2at; (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 gravitationaxms2kk3ny 6 ,bl force on a 70-kg person standing on the Earth, due to the Moon? The ,mk 2b x6y3sknmass 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 the masses i+zxuf1 c(.x bare moved to half of their initial distance, what is the gravitational attractive for(cixfx1 bz+.u ce?

  For a spacecraft going from the Earth toward the Sun, at what distance frrxchpv;k i; +vn4jb2,om the Earth will the gravitational forces due to the Sun and the Earth canx jknhvrpvb+;;, c42icel?
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 pgcpxdpp+(b7rmm+6(wp 5cd3$7.4 \times 10^{22} \; kg$ 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 ab.xttm1/5bx sybq1 o;move the Earth equal to the radius of the Earth. What is her accmbxmt 51by./ ;x1stoqeleration due to gravity?

  The radius of the Earth is R. At what0blf0i-c l5;;s :9qobya uqgo distance above the Earth's surface will the accelb0go0liso5l fq bqcay9u;;-:eration of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a din/a3fis1zv) o: v q),/g/snsdcss, ristance 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 surface of Mars, grs vzss,d sn:3co1)ifv/iqnsa )/, / is

  At a distance of 14000 km from some plan)d )m+km ,orrvszp2opbc-t3 7et's center, the acceleration of gravity is b)zcmstkvorp 7r32pd,)+-o m $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on thg)x)ak.e4a* ,bs awd+gyi 0 1hkq4huq e surface of the Earth. The Earth has radius r. If the4qk +awkax0 iu1h,*qs4))hy gedb .ga object is raised to a height of 3r above the Earth's surface, what is its weight?

  By how many newtons does the weight; it(*hwg 4bq d2gyim+ of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The meangy4h tqwi(m id*gb+;2 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 :pyldnlsjx,g +3* *pk l/wd -m3r above the Earth's surface. What is thl*xl, ndd:yjpw k-g/l+m3*p se satellite's weight?

  A spherically symmetric planigxzw 65d+rgla pyjdb :m*1: 8et has four 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 murg+ pz5w61mg:*ijb xal8d d :ych would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lie h8kvwh, /q , ip4pbuh4,vqsz (on the same line, with the Earth between the Moon and the Sun. The Moon has aip us,vbqz4hhw,kpqh(/ 48v , 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 Moo00i cc+h bmo n :qy(;efuxzy.)n.
(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 xn.ll,q*cv7nn6cb.:gd j7bxi* kfz*k( w pk* orbit about the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mel6. qdcbvnn7zxjkk( pf.n:* *klxci,* * 7wbgan radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit aboup-0rbykkjbb1 r:h*1 h c1*n est the Earth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution around the Earth? (The jh:b*1skr1ch0y1-k brpe* nbmean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 km above the surfajiup 3) s.e-ecce of the Earth. It is observed to have a period of 89 min. What is the mass of the E 3) pecji.-usearth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an orbit (trl/k 92*nxkm+.hk nn5xxpi8nj .sbal 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 plakhza6zbe(hb p eb97w6g f3z27net 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 orbi pfx1. 1gj0s+ym)tw wotal 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 complesp11jfmo0)+xw g y t.wte an orbit?

  The planet Jupiter i 4b hjrkb6v1p61 9lxgss $7.78 \times 10^{11} \; m$ 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 the -+gh4 nrow/j 6nk(ow aaverage distance from Jupiter to the Sun? (The distance from the Earthrj(n hg6o wna4-/+ow k to the Sun is $1.5 \times 10^{11} \; m$.)