Is it possible for an oxv6m bdb. qtwon- 2b81bject moving with a constant speed to accelerate? Explaint 6nox1bb8-w 2md bv.q.

  Consider a particle moving with constant spee2y5;p5mpm wdgr6ec+4 b4yfepd such that its acceleration of constant magnitude is always perpendicular5 ypmrp2w5+f;6eymegb4d pc4 to its velocity.

  An object moves in a circular path at a constant speeklk7v d,;( v5sg1*2c ihewr cnd. Compare the direction of the object's velocity and accelerationdr,ven7iw* 1;clsvhck( 52g k vectors.

  When an object experiences uniform circular motion, the direc:l ju x8l8cz)rtion of the acceleration isll :jx8z8u) cr

  Consider a particle moving with constant speed such that its acck1ny-*-:z1jfxnw ga e eleration of constant magnitude is always perpendiculefy11ag-nwj z* : -knxar to its velocity.

  What type of acceleruo9w7yus isogt3j+), ation does an object moving with constant speed in a circular paw73uto+s,o9iygu ) j sth experience?

  What force is needed to m38zmzkc1 yrqwe/kr 49 ake an object move in a circle?

  When an object experiences uniform circular motion, the direction of thebz.pmp lk 0*l7 net force isl 7p mlzbkp.*0

  A roller coaster car is on a track that forms a circular y -:: gibgxcuwp5y-nz3uv v48h6 f/nk loop in the vertical plane. If thhpn 48cf 6b5 iy--k:ngv3:vygx/wzuu e car is to just maintain 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 (mass = M) is on nb1m ;d2u1 -hqw9glg6 j xk8ch5:zdgha 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 vl:cxkwgdhbh;- 95d gq umh68 nj12g1zalue for its speed at that point?

  A pilot executes a vertical dive then followjgqs1tb w- 6sfsrfi6 +26h7izs a semi-circular arc until it is going straight up. Just as the pw6sh rgfi 1 -jstqz +7f2s66bilane 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 rnxj--dw ye984o ta1qr y2v)etadius $r$ 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 aro*hc0hs(k/ eb ts *.v9vxy3jtzund the same curve at half of the zsbsy*hhv*039jv/e c t kt(x.original speed. 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 cu kqk3u s*f1het1 ,yv8pdcqz,.rve of radius r at a constant speed v. Then it goes around a curve of pcf3 1, yvkqes*q tku1 ,8d.zhradius 2r at speed 2v. 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 radius r with spe c1o o9 bg k+kgvk*lkj:7nv.:hed 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 magnk9*o.vv hk:k jg7co1gk b+l:nitude to

  Two horizontal curves on a bobsled run are banked at tvhfqs9rp ;b6sk+ 5wr 3he 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 sf+vbw5r 9 6s;q3 rpshkafe speed on the larger radius curve?

  The banking angle in a turn of-nbyaw .*lls ;; +o vabeoy)-;izzr8n the Olympic bobsled track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "clim l+b;8 vyaszlnar;).b z -ifeoo;*w-yb the 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 bot.g *ebyry mkrj*8+6x*+zvvqa h centripetal and tangentiab+6qj gy zr*m ke.8* vr*a+xvyl acceleration?

  The gravitational force between two objects is proportional toy 2*3ftr/efbx(y w*u0 obj(hw

  The gravitational force between two objecm, g21tt f:ennts is inversely proportional to

  Two objects attract each other gravitationally. If the distance betwueble ; /f19u3( k/zzbf4ln.ghwrp(peen their centers is cut in half, the gra./ b1pz ub9hl;( zepkfer uwl g3/4f(nvitational force

  Two objects, with masse ns;kuku zh(p52an n;7s $m_{1}$ 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 i.2;rhx *i*9s 3 wydbl/husbx$m_{1}$ 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+8 6d5 vef qym* )kgbixf8tnxt j4pj:( universal gravitation.

  Compared to its mass on the 7i zh4hr,ym . gw1foo-Earth, the mass of an object on the Moon is

  The acceleration of 2n-bgin 7r4g(iq o0yogravity on the Moon is one-sixth what it is on Earth. An objecibgg0n 7qi4o 2ro(-ny t of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away f. n- cz e)g5kwwepb1f,rom the Earth's surface, the rocket's weight

  A spaceship is traveling to then +mya3l5m474ygqqyw82hk av g:3mvu Moon. At what point is it beyond the pull of Earth's gravi3:3 lw hu485g q gvmmv+anqaymyy742kty?

  Suppose a satellite were orbiting the Earth just above the su7dc 7pl a mes7.sf.k97omb. x59eoghwrface. What is its cent f.oalewb m7xdsps.975cm kh79ge.o 7ripetal acceleration?

  A hypothetical planet has a mass of(1-dttwk6 8o agl nrmypg u39-94vnmj half that of the Earth and a radius of twice that of the Earth. What is the 8-3w4tdta vg(1pl9unj 6k9gny -romm acceleration due to gravity on 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. Thy y8zgm 2ptl a-292prhe radius of the Moon is one-fourth that of ryg m 29 -a2p2lth8yzpthe Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gravity, but planej7 q-jg8dl3422w.gr hmflhwp t B has twice the radius of planet A. If plalh. hj28m r7q-dj2gl 4fp3 wgwnet A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, but planet B has twice the mass of pl0.jbil,o3jyr nll -0lanet A. If planet A has radius r, what isn0,3l.l -ioj0y lbj lr the radius of planet B?

  Consider a small satell5rq0dlb6 gp6p ite moving in a circular orbit (radius r) about a spherical planet (mass M). Which expression gives this satellite's orq0 g 56rpbpl6dbital velocity?

  Satellite A has twice the mass of satellite B, and rotatesbw(8;akxqfjhw i2b1( p -bfcn3a*j /i in the same orbit. Compare the two satellite's spbfk2cb x-p q8fh 1 j(;/w(* aiwiaj3nbeeds.

  A person is standing on a scale in an elevator accelerating downward. Comsl.92ja(y dyazu/afvsu *qq:(c w.-l pare the reading on the scale to the pef(w cuyjl(s .v aa/ 9l:. q2u*zsda-yqrson's true weight.

  Who was the first person to realize that the plma1nz ; )(o,dwu,hi,+er juqg anets move in elliptical paths around the Sun;waz ,o n(iu qjr ude)1,+g,mh?

  The speed of Halley's Comet, while travo3 4f1ccpiy -;3lkedl eling in its elliptical orbit around the Sun,c-lp; fi dck3 lye31o4

  Let the average orbital radius of a planet be R. Let the orbital period iexlad vku+;l22c)6re4i n 8vbe T. What k8) i;adue6+x rlc2v i24elvnquantity is constant for all planets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxy jfjw96 4e-ip wAndromeda, 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-j6w iwf 4pj9e new planet be, compared to the Earth's orbital period?

  The average distance from the Earth to the Sun is defined as one "asp4m.sofe-qlma;zw3l 5 2r/ wttronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteropws5wmz/;2em 3tq4.ro lf l-aid's average distance from the Sun?

State Kepler's laws.;ec(u+n9tjoa8kc,bhu1 t2 sl

  List the four fundamental ;o r2i rb 8;9nzs0qxqdforces in nature.

  An object moves with a constant speed of 30 m/s on a)aa/ogtx*t k 9 circular track of radius 150 m. What is the acceleration of the o xt) aa9/*otkgbject?

  The maximum speed around a level curve is 30.0 km/h. What is the i r9) d,+b*ug+qz(l0mkv biw tmaximum speed around a curve wiiw,kb dlrmgvq 0 *)9ibt+(uz+th twice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on the perimeter okb2mju:v ou /;w:c) +y;mu(fdbdyx) zf a bicycle wheel of()bzjy u) dcufyu:v;:bxk mdm2ow + ;/ diameter 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.0qk8yt )v unau,/9)enz0 rev/s is located 0.200 m from the axis. What is the centripu,n tv z)k )anu8ye9/qetal acceleration?

  How many revolutions per min-qskfg b6lb 0p x.2v6wute must a circular, rotating space station of radius 1000 m rotate to produce an art pxwgqs 2bb-6l 0v6fk.ificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes abit75hj, k z 61rhtwd7round a 13.7 m radius turn at 96.5 km/h. What is the centripet71hik7r5bd wjtz ht,6 al force on the motorcycle?

  A 0.50-kg mass is attached to the end i o1twl yoip 75 ;9,dk oc1u0s8cw7qm ddw2js)of a 1.0-m string. The system is whirled in a horizontal circular path. If the maximum tension thc j1 c0o7yoq d598i7usm, k1wo;iw2dwp) sltdat 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 + e)a.z1chc rzstrong 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 theza+e.cr1 ch)z stone's weight. The stone's speed at this point is given by

  A stone, of mass m, is attached to a strong string and whirgqszh1jreju( 0 3 mf52c: vov3led in a vertical circle of ra 5v 3(z2r1ehusjm0cqg3vjo :fdius r. At the exact bottom 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 jet plane flying 600 m/s experi: l-cew6exv i68g1v wcences an acceleration of 4g when pulling out of the dive. What is the radiwciegve86vl6 xw-c1 :us of curvature of the loop in which the plane is flying?

  A pilot makes an outside vu mujoq(k* v4b,vg,b 4pz(:q wertical 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 weighb qu:mjop k4vwzgb*v,(uq, 4( t. How fast is he going?

  The maximum force a pilot can stand is about seven times his weight. 80/hf jsnvi) v What is the minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can toleratef)0 jnsv /hv8i at a speed of 250 m/s?

  A car traveling 20 m/s rounds an 80-m radius horizontal curvf (-zx1uy: szdef *vr2e 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- yf*2r x:1ef uzsz(dv's tires and each road surface.)

  A car is negotiating a flat curve of radius 50 m with a speed of 20 m/s. 7i,pqxiyss o )w5d:l:The centripetix:iodss q5p),w l:y 7al 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 radius 50 m at a speed of 14 m/s. Whb6i7vuho 6 8sqat must be the minimum coefficient of friction betw86hobs7uqi 6v een 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 coefficiey. yle * sl26eri3espg6k m2*hnt of friction between the tires and the road is 0.40. What is the kerl3gyse 62i*p.esy*h6 2ml 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 negotiatej,-*mr2m q:fhxq3 ucm a 100-m radius turn at 35 m/s without sm:-2fh*r,cqx mmqj 3u kidding? (Ignore friction.)

  A horizontal curve onp2+maxpogk l(p* ,+zw a bobsled 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 angwq) w9:-kbkh(; kqu eple of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bank;nv5i+ 7l emcued 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 unif9 uag bm4f*9uhormly in a horizontal circle of radius 0bmgf*uh9 9a4u.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 uniform rate tgqk ; uu jh1z(sade 9+z.7,ycno a speed of 45 m/s in 15 s, moving on a circular track of radius 500 m. (only fil ngh;y cjezquku,z7 .+(1a9ds l 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 consists9a;, fw2*g vqf0cdsyg 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 70-kg person standing onemd+270 nb3eja f+j0gh+e gpgf)gj0 r the Earth, due to the Moon? The mass of the Mopj nf)er+0f 02 jhj3gegbm 0age7 +g+don 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 theyp (d+; bew0io:o2 ssv masses are moved to half of their initial distance, what is thpisvos(:y+0db 2 w; oee gravitational attractive force?

  For a spacecraft going from the Earth toward the p3gniechkb5 5x.1. zf3t(uor Sun, at what distance from the Earth will the gravc z(.inoe x5 rk.p 1ugfbh5t33itational 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 10lxqau dtq+ 1is $7.4 \times 10^{22} \; kg$ 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 t3vs7ds v l ni*(ibj(a*he Earth equal to the radius of the Earth. What is her acceleratii73**v iaj l(sdsb( nvon due to gravity?

  The radius of the Earth is R. At what distance above the -hv 8x(cj.8yzy6ky9gjs; vww Earth's surface will the acceleration of gr(ww y v9h; 8zk .sjxvcj8ygy6-avity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its surface equal to 3 times the lur4bl h mc68-w3n+rv radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the -bucmr+3w6r v8l 4 hlnsurface of Mars, is

  At a distance of 14000 km from some planet's center, the acceleration)j r4)mw5gafj of gravity igwrj 5m) 4f)ajs $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on the surfaceqlvlj (+sc a)/6.b.l vx p/;qg zwxw6t of the Earth. The Earth has radius r. If the object is6+c)xbg ;xlw(v/ qjl .qwt6va./zpsl 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 b4uc)a2tk bq;q8n.zsperson change when he goes from sea level to an altitude of 5000 m? (The mean ra;tk z)bsq4acnq.u 28b dius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is i0+e skqw (0( nduiqs7at a point 3r above the Earth's surface. What is the satellkiewsnuq(+07s 0 dq i(ite's weight?

  A spherically symmetric planet has four times the Earth's mass and a.scv*h0xjf izg*8 9ltwice its radius. If a jar of peanut butter weighs 12 N on the surfac.gx **s9hzva jf08il ce of the Earth, how much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lie on the same line, witmpd+azl6k1 *c h the+6pl*zd kc1ma Earth between the 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 transported to the Moonl:2q hqbw 8k.2so /39jslptnf.
(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 ( (d.ttkvv64mvpsgf+ )i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radidt4vvpt(+6)mg svk f. us of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about the Earth7xs *ks 21qkb5 yl4xpnj5 c:bp*qht 6u (i.e., it just skims the surf psq6p5: 1xxuqy54knkj2*s 7b*tlhc bace of the Earth). How long does it take to make one revolution around the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 km above the surface of tr sv*f3wss 9f- 8nvdk9he Earth. It is observefv n*rv ks sw8fd3-99sd to have a period of 89 min. What 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 a:lwe7vr b(; r8 aj2kf 5kvl*bc+ ymrs3n 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 orbai;j7s m( fr/yw (s 1gqg(3muxits the planet 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 radius r: rdmesq *b-2zg6e8gabmo+c -, 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 orbit :6rb*-sed g2gq ocea mbm+-8z?

  The planet Jupiter is 4xd2u aj:kfm+8yt 7bli)uxba- nc + ,g$7.78 \times 10^{11} \; m$ 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 oncwp 3p-udrykpd0cxf+ r8flp 9zd5-n- 7e. What is the average distance from Jupiter to w plx d drd9p5p-pu 8c0-7fz y-frn+k3the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)