Is it possible for an object moving with a constant speed to accelerattwlxy4r qy/mm, (z9b6;s ) heie? Explaih;w6m9tby q,4em xir( y )sz/ln.

  Consider a particle moving with constant speed such that its accelerationl4l3f/h vz8wh i,cb4u of constant magnitude is always perpendiculz/l8uw4l3fv4 hh bci,ar to its velocity.

  An object moves in a circular path at a constant speed. Compareof6upv,tz+a tjhdfw,+ppsy/9 a 8j,0 the direction of the objectv8jp/dus,+ t p z,w,a6ajo y f9fthp+0's velocity and acceleration vectors.

  When an object experiences uniform circular motion, the dfmfd4 9qt+drd3 /25ukel: h eiirection of the accelerati9i lfqd/mfu5:h2 e+tkded34 ron is

  Consider a particle moving with constant sp-;eoj.w/.is mam lf;reed such that its acceleration of constant magnitude is always perpendicular to its vel. aw;;jl mf-mi.s/roeocity.

  What type of acceleration does an object moving with constn0b 0n9bi5v46srsbnq mbgs 9 5ant speed in a circular pathq0 94bb mbr5is5nsn60 bgv9sn experience?

  What force is needed to make an object move in a ci cn +q:bw*wzy3xgf *f2rcle?

  When an object experiences uniform cic /kei)l w,4rwrcular motion, the direction of the net force k) cwe/w,lir 4is

  A roller coaster car is on a track,*m+thj8-e(8o io scggapfwj4(ub*k 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 centripe(ijfkga(8um o-o*e thwscjg b 4 ,*8p+tal acceleration at this point?

  A roller coaster car (mass = M) is onj6 7tp8-6oaorwdvuy2 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 mt v2ujy86pwoo6 a7r-dinimum value for its speed at that point?

  A pilot executes a vertical dive then follows a semijq6 *i:73sy b/lq;a vkfcuo5w-circular arc until it is going straight up. Just as the plane is at its / 5ov juy b3;qw7afi6sq *l:kclowest 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 radiwss);d7 kso09i:gfqp o3 38v8*xm jmbaclg6 eus $r$ at a constant speed $v$. What is the direction of the net force on the car?

  A car goes around a curve oftv r- csvx4s ew/g +4. gsf7u.s51mbtl radius r at a constant speed v. Then it goes around the same curve at half of the original speedu5m.vctf1r sss /e+wgl 4-gs t bx7v.4. What is the centripetal force on the car as it goes around the curve for the second time, compared to the first time?

  A car goes around a curve s)+ wpcpnmp 11of radius r at a constant speed 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 cu +)cp w1m1nppsrve, compared to the first?

  A car of mass m goes around a banked ct .l ,ubz(cqml h 2c ,gi)e.b1g/yzi2iurve of radius r with speed v. If the road is frictionless due to ice, the car can still negoqlg,hb2)i(g y.t b2/i izle1 ,ucmc.ztiate 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 run are i,ato341uf: x(weqva yn kk7;oof1-q banked at the same angle, but one has twice the radius of the other4o ik3tu a 1kno(a-qw1ef, f yv7;xq:o. 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 radius curve?

  The banking angle in a turn on the Olympic bobsled tracpy)k7jgp*p5i*3lxqs a3h wm3 thjc b,7 ku;/zk is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "climb thbzk/ailx q,w 3* sjkt5gyp7)u; pjmhp3 3h c*7e wall," then go lower coming out of the turn. Why do they do this?

  Is it possible for an object moving around a circular path to have boj(bpe1pp : 2m .ucpv76j zss*oth centripeta p2j p:mb7pcp js1*vz6 (oe.usl and tangential acceleration?

  The gravitational force between two objects n;-r* aww zft9is proportional to

  The gravitational force between two o1n8 gg+-c/jzmsf 2 ud*tx -ot9+ojqinbjects is inversely proportional to

  Two objects attract each other gravitati: 4l 9(:5elhcylvuna nonally. If the distance between their centers is cut in half, the g:4lh e:v95ul(cln any ravitational force

  Two objects, with massef+47 w go 4+eunoh)zmds $m_{1}$ 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 mas2f,kq/va6 zuxses $m_{1}$ 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 gravitatiow*l ;funb0 uvm)bvn4-n.

  Compared to its mass on :s 7oj4e1f voty, s3zrthe Earth, the mass of an object on the Moon is

  The acceleration of gravity on the Moon ru vh9h(w3cazos5/5tt u. w*x is one-sixth what it is on Earth. An object of massw .*z9a rt(h/ 3cwuxhou 5tsv5
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Ea5 px/ 7m.oimnoqd-+;gy8eq g xrth's surface, the rocket's weight

  A spaceship is traveling to the Moon. At what point is it beyond the puloxbj9rf9nd,z5ma2l *f uff,pw a-,*h l of Earth's *o9m,f*fw9ab ,z,d 2lxh5u jn pf-rfagravity?

  Suppose a satellite were orbitin**u)4 mvkgz cfg the Earth just above the surface. What is its centripet c)*gv zuk*f4mal acceleration?

  A hypothetical planet has a mass of half a8:e (xhlwrro/-g a v7that of the Earth and a radius of twice that of the Earth. What is the acceleration due to g:78xreg-l/(o a wvhr aravity on the planet in terms of g, the acceleration due to gravity at the Earth?

  The acceleration of gravity on the *:b0 mpfivlx+w k u)f6Moon is one-sixth what it is on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Moon's mak v0+6w )fmbfipu: l*xss compared to the Earth's?

  Two planets have the same surface gravity, z dtz01d5otc6 du xy)3but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet )d tzyot3 u5 0ddzcx61B?

  Two planets have the same surface gravity, but planet B has yflu+9g* r 3dfslipht/84d8dtwice the mass of planet A. If planet A has radius r, r8dd + y89lt3*h4fligfusp/d what is the radius of planet B?

  Consider a small satellite moving in a circular orbit xshk6+zl/e1 i (radius r) about a spherical planet (mass M). Which expression gives this satellite's orbi+lh1ixs kze6/tal velocity?

  Satellite A has twice the mass ob l, sb vxt+)dnhgg .h)o4g17yf satellite B, and rotates in the same orbit. Compare the two satellite's ssdx 4 bvl+7)nh.bg1),hg otgypeeds.

  A person is standing on a scale in an elevator acceleratr9 5enulz4rf 6t nvo.1vdw 3 mwp+h2a)ing downward. Compare the reading on the scale to the person's tr2zvmdw) 5wo9 renfahlpt.ru34+n v 61ue weight.

  Who was the first person to realize that the planets move in elliptical paths mn2 xmm45ug, xcs a/1f3xxk0baround b 4u,sxf32mk1 mgxcm0n5a/xx the Sun?

  The speed of Halley's Comet, while traveling in its ellipticetiywrl *vh .qt(04--dld1ep/ k cob*al orbit around the Sun,c l ybwp t. tql1ohid-v*ee0*r4k(d /-

  Let the average orbital radius of a planet be R. Lete p8rw er9/ vi7f7gau;is+ze , the orbital period be T. What quantity is constant for all pis 9+e zew;f ir7u /,v87gpearlanets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxy Andromeda, with th3bv811actob3i jc.x ne 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 o31a b n3xc vib18tjc.orbital period?

  The average distance from the Eartm8jp i4up*j4pit5u ( vh to the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroi4u8im v* (pi5j 4ujpptd's average distance from the Sun?

State Kepler's laws.9rmyvt tltw79n.t - u6

  List the four fundamentvx don71hoa26 p,7xw qal forces in nature.

  An object moves with a constant speed of 30 m/s+:mkbcce5vfv sld , k+6vkx nzd 13/:q on a circular track of radius 150 m. Whans5 vm+ 3dv lkv+xe, ccbkf:kdqz1:6/ t is the acceleration of the object?

  The maximum speed around a level curve is 30.0 km/h. What is theqz3b: *x q2j/zf p pzm6(fqgr(zl;z 2b maximum speed around a curve with twice the radius? (Assume all other factors remain unchangelzzr(bqzzpp q*(q m/ ;bf3fz 62x:j2gd.)

  What is the centripetal accqgbc jz1, m8y*eleration of a point on the perimeter of a bicycle whj,cm1* gy8 bzqeel of diameter 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.2007h,+kamx,zio79f vw1 a8h 7c rxtxiw.i* y1hp m from the axis. What is the centripetal accelerati fwi7 x+1o8ihr*a1 v .twpiyx9h,7hxm,z7ackon?

  How many revolutions per minute must a circular, rotatir o ,os*ws6a5g4o j/shng space station of radius 1000 m rotate to produce an artif*ho,4rw/ sosaj6o sg 5icial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn z1,2s/la.ku0kkm lxh at 96.5 km/h. What is the centripetal force onml/2 k k.sz xhla0ku,1 the motorcycle?

  A 0.50-kg mass is attached to the ea2ck ;y:s/licnd 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 maximuki :c sa2;cl/ym speed of the mass if the string is not to break?

  A stone, of mass m, is attached to a so7-i7/fx gmi o3rx:ugtrong 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 the stone's we-oo7m f/7r x:ugi3xigight. The stone's speed at this point is given by

  A stone, of mass m, is attached to a strong string and wmfd 52wo 4lbwe5apri+/l4)sn1t d x5shirled in a vertical circle of radius r. At the exact bottom of the path the tension in the string is 3 times thl s1 n5etl p)/fr552mo4d axws 4+biwde stone's weight. The stone's speed at this point is given by

  A jet plane flying 600 wp0k d1nyhin, 77lr7um/s experiences an acceleration of 4g when pulling out of the dive. What is the rhw0d i7nr71 n klpyu7,adius of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in whick4n.qvu jg11l 5nha )zh the center of the loop is beneath him) of radius 3200 m. At the top of h1g4n5 jl 1.unzqk)hva is 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 swhk.q *(pqkv0 w e:ja.even times his weight. What is the minimum radius of curvature tke.j(0*pww qq.va hk:hat a jet plane's pilot, pulling out of a vertical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/s rounds an 80-m radius qs wrx0yio(bj,; 2ns.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 surfacenix.,0qow ys 2j(rsb;.)

  A car is negotiating a flat curve of rad8b-ynz:cey( *7sd5 pwet7pmmius 50 m with a speed of 20 m/s. The centripetal force provided by friction is w*mm e8-:db7 s(ynp 7ct5zepy $1.2 \times 10^{4} \; N$. 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 must h2*8 iqmr3 qykbe the minimu82i*mqy3k r qhm 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 l+sqy2b/ti- -y2.zu bbh fnhg4evel curve. The coefficient of friction between the tires and the road is 0.40. What is the minimum radbsf2hin tu-ygyh z42/b+ -bq.ius of the curve if the car is to stay on the road?

  What minimum banking angle is requiryaakljz,x4v z7p1 )qyyg-( )wed for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? (Ignorl)(-zy) w, y zyg4ak ax1vj7qpe friction.)

  A horizontal curve on a bobsled run is ba4e ej hgvm+h: xic5t l(.a)c3 ifmb/l:nked 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,v9se702 mcwfss 3cuo/j b6c. l banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m il6ix3tevw5;quu 7( k(mi;ybbs 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 uni8gv+5jn/q wnw formly in a horizontal circle of radius + /q8nwwnj g5v0.500
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 pitaam/- y.esh j0 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 radiua/-.hejmya s 0s 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 p9 tuqz*m :uxn3roton 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 70-kg person standing on the Earth, due tfbg7,d s(byq i/82x zmo the Moon? is/x(,gq872bmb z fdy 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 attra p wpyxj)y04q;ctive force between two masses is F. If the masses are moved to half of their initial distance, what is the ;ppw04jyqx ) ygravitational attractive force?

  For a spacecraft going from the Earth to(sxd*r3d 9zo+h4 djipward the Sun, at what distance from the Earth will the gravitational forceid h 9zj3*xospdr+d(4s 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 5,qjzmbvmw- vbu74(w6 yj y3pis $7.4 \times 10^{22} \; kg$ 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 knf 59rlm:sfhn+4pb4 1r p4gqequal to the radius of the Earth. What is he+4nmngq k:1fl4h f 54 rpbps9rr acceleration due to gravity?

  The radius of the Earth is R. f050pr yaw esumje2)n.4 +ovo At what distance above the Earth's surface will the acceleration of a .voe5e0pr s4f2yw m+nuo0)jgravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its surface equa2 *uh f,7-xrbr9c4b/hodu uytl to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on /y-27u9*4ro rxufbu t hd bch,the surface of Mars, is

  At a distance of 14000 km from some plan1xc.luo6ez b 70 iu:ogl1jrc,7b 1ctoet's center, the acceleration of gravityg uo 1 cjib6lc:e 0uco7,71l.z ro1bxt 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,yk-. b,gemw s the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what is its b we,gm,-k.ys weight?

  By how many newtons does the weight of a 100-kgg, sm.dyed:qh*n4 bw4en 9vz,cm;lq: person change when he goes from sea d: *nm ,ych d;,mlqw qg4.v:4nz9eebslevel to an altitude of 5000 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of massrke k*3/p e3*,aau c7obva1xz 100 kg is at a point 3r above the Earth's surface. What is the satellite's erp3,**oaxk3 cebz k /auav17weight?

  A spherically symmetric planet has four times the Earth's mass and twi.qxw8ky39k; vde7zt9x(x qpc b f,z7 eph 2bm,ce its radius. If a jar of peanut butter weighs 12 N on the surf yf;3x , zxm2 d,kb79wq(9zqk hbp8vc.tp7xeeace of the Earth, how much would it weigh on the surface of this planet?

  During a lunar eclipe-/f bpm;:qk93j:)qq r.f ldn jx lpe5se, the Moon, Earth, and Sun all lie on the same line, with the Earth between : q q)r.llnk/-e;e dx5m3jb:pff pq9jthe 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 transportedb 6lykkhg 55kiu7+y2rsn q 8f) 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 just a3 qcpz()8;n :wvedu -p 9r*v.tmfhyrskims the surface of the Earth). Wh y9wt :c;vr83h* .fz-eu vpap)n(mdqrat 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 Easfc 6j fz*.wunmie 729rth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution 2ju7f6fz.* i s wec9mnaround the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular n+amq2 u/ dc1korbit 230 km above the surface of the Earth. It is observed to have a period of 89 min. What k1uandqm2c/+ is the mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an orbital diametzf3t:w1pz d *uer 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 0+n8 iietd(fgcyokp7b /ezh: 134 xiv 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 radju3ek sem kc(nzz -2c8p9;zt.ius r, and moon B has orbital radius 4r. Moon A takes 20 days c tn2ce(zz;9p-e.m8zkj sk3u to complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter i f tnp h0sl.9/ .ig.160wtgbeqj(rtu es $7.78 \times 10^{11} \; m$ 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. g7zpymhe optt10 ,;3m What is the average distance from Jupiter to the Sun? (70eo,3yh gm;1ttmz p pThe distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)