Is it possible for an object moving with 8j8i/ je30olyd0 mdkee8+ w. woqn0lya constant speed to accelerate? Explai88k/j0oilned ld3ewje+ 8y0 woqmy.0n.

  Consider a particle moving with constant speed such that its acceleration of conos obi)s cf:q:ai: ;n,stant magnitude is always perpendicular to its velocis :)sn oi::i;,acf oqbty.

  An object moves in a circular path at a constant speed. Compare the di-50mpvi, vupo5*r:ln yaj kb. rection of the obaklpjr bm v*ip0 :o5uv.,5 n-yject's velocity and acceleration vectors.

  When an object experiences uniform circular mo4a(lmfg7qc6jl51h23s 3vu epv f 0m bltion, the direction of the accelerati2u c0 (lglf63 v3bla1v4e5jq fs7hmmp on is

  Consider a particle moving with constant speed such t(es49yk og*qkhat its acceleration of constant magnitude is alway*k4 9sgkoyqe( s perpendicular to its velocity.

  What type of acceleration p thgl,mz-w hb; )6,xcdoes an object moving with constant speed in a circular path experie)w h; ,-,mgtz 6clhpxbnce?

  What force is needed to mlqya g/h: x1vg e/n56oake an object move in a circle?

  When an object experiences uniform circular motr(edk1 9v91 atfm bkf/ion, the direction of the net forcda(kr9ek /tv f19bm1fe is

  A roller coaster car is on a track that fontx,ucm:*(z x rms a circular loop in the vertical plane. If the car is to just maintain contact witnm*xcuz,(x :th 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 a track that forms a circular 3 -olk) bhoe:t1 exdohu f5+s7loop (radius = r) in the vertical plane. If the car is to just maintain contacto lx- 5feb)hu7h3 :s1o e+dtko with the track at the top of the loop, what is the minimum value for its speed at that point?

  A pilot executes a vertical dive then follows a sem zk,zfzp )0t jxq5-f3pi-circular arc until it is going stx03,)pf5zzk f j-p tzqraight 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 curvez zcy m)t 1r6u-;dgxr8 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 rw+i8khid h*:4icd,qy -jh 9 w2ugzdx( 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 to the first ddx( yiwkj ,8w4hd -hqu :*ih9 gzi+2ctime?

  A car goes around a curve of radius r at a constant speed v. Then it goes arounmz kw80 8hgd8e 8fxu;bd a curve dk 8;h 88g0fx 8wmubezof radius 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 arouno h*2w p q3vlw,-ibv8 ngf:5c 3b3cpehd a banked curve of radius r with speed v. If the road is frictionless due to ice, the car can still negotiate th*e3ww 3-qngp 2b h ,coh8icfvb:5v3p le 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 banked at the same a r+dmi 5gvsgbbde8fw ;2.bs;t90w8o l96 uh ozngle, but one has twice the radius of the other. The safe speed (no f g z.+reb9 2hfwog8bs9v6bd;u;it50wo smld8riction 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 Oll x,ua3fa7v*a ympic bobsled track is not constant, but increases upward from the horizof7 ,*uvaaxal 3ntal. Coming around a turn, the bobsled team will intentionally "climb the wall," then go lower coming out of the turn. Why do they do this?

  Is it possible for an object moving arohozv1oi4/c+ke u6hv;j:gyu +und a circular path to have both centripetal and tavy ie:4+hzuh/; uo o+kvc16j gngential acceleration?

  The gravitational force wne z81u/vf3w between two objects is proportional to

  The gravitational force between two knoc( lw wj()*h9q4o0w4n,mewa qu)vobjects is inversely proportional to

  Two objects attract each other gravitationally. If theff xkky4cif)/uqo )95 distance between their centers is cut in half, the gravitatioxf4kyk)/ifqo f9)5 u cnal force

  Two objects, with masse +qd qe5n09i ktw17frjs $m_{1}$ 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 zwzul58g 6r 9e1olo f05pc1jx$m_{1}$ 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 gravitati *hco kc:b,7pikj+k5v on.

  Compared to its mass on theri9;7qz qe9m- wfz ;oo Earth, the mass of an object on the Moon is

  The acceleration of gravity on the Moowl .a93ajhd;/ 9xctnzxe 3i+k n is one-sixth what it is on Earth. An object of mnja/xk 3acw hil xe+.;99 3tzdass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves awayak+f*1 tkgrsw j;kw* 4 from the Earth's surface, the rocket's weight

  A spaceship is traveling to the Moon. At whatmf;sg q,cvf.o / kal;9 point is it beyond the pull of Earkg;a l 9 cfqo.s;f/,vmth's gravity?

  Suppose a satellite were orbiting the Earth just above the surface.f5g9.0r u dfpb What is its centripetal accelerat.drub5 pgff 09ion?

  A hypothetical planet has a mass of half that of the Earth een s +w -x4f.ji2atohu (fgnj,u8a6 -and a radius of twice that of the Earth. What is the acceleratio+j j tn,a4--of enif2he.68uwsxg( ua n 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 w-sz cz8p a rj+j/ub.2qhat it is on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Moon'sjjzu.s+c bzar /p q8-2 mass compared to the Earth's?

  Two planets have the same surface gravity, but om uide2)ylyc/+f -n8 planet B has twice the radius of planet A. If planet A has mass m, what is the mass of pla on2/lm y+d-ci8 fyu)enet B?

  Two planets have the same surface gravity, but planet B has twice ao;6mh41lgel0 a8qc tthe mass of planet A. If planet A has radius r, what is the radius of a0h8ecgllq6m1;toa 4planet B?

  Consider a small satellite moving in a circular orq 4(o+kne 8pftzma;0pbit (radius r) about a spherical planet (mass M). Whicfp;oq 0t 4p8k e(nmz+ah expression gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and hb3kof * nq)(c1a bv;orotates in the same orbit. Com;hb ba1vf n(o )o3q*ckpare the two satellite's speeds.

  A person is standing on a scale* ifhp /6z.xs xwq5ulkx(4n. d in an elevator accelerating downward. Compare the re*u6f5xx d hwp 4l ns/zxiq.k.(ading on the scale to the person's true weight.

  Who was the first person to re+:4(fj, yn ;rqzfrs sialize that the planets move in elliptical paths around the 4+jfs(nr fiq ys;,: rzSun?

  The speed of Halley's Comet, wh sz2swby ,n, m6guabp)hw7) z6ile traveling in its elliptical orbit around the S,hsm)6 p z,wa )7yzb26snbuwgun,

  Let the average orbital radius of a planet be 8x l:fy+pmsi +c/g9f2h0ilo u R. Let the orbital period be T. Whatf0igc8+u i:shf+ml pxloy/29 quantity is constant for all planets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxib0 9hi+o( .sb8 l3h iptqqil:y 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 3 . bitl bq+:ip(ili89qo h0hsperiod?

  The average distance ff8 fb z1,bvpm9rom the Earth to the Sun is defined as one "astronomical unit" (AU). An asteroid orbits thebfm8fv, 1 9pzb Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.lzhiy 98iv- k+

  List the four fundamental forces in v i3v84ann veo:9r h9t,r uj3 re,b+shnature.

  An object moves with a constant speed of 30 m/s ovagxp7 i7mcbb(h paw:o 7;93xn a circular track of radius 150 mmai;77b ahb3:cxpvo w(px97g. What is the acceleration of the object?

  The maximum speed around a level curve is 30.0 km/h. What isev g up zdwew1(:clwh3/ tr0(7 the maximum speed around a curve with twice the radius? (Assume all other factors remain unc7wgw :(3d(uh 1ew0cr pt vlze/hanged.)

  What is the centripetal accozv 4;zkn6n): b-k/ jq9d mlfleleration of a point on the perimeter of a bicycle wheel of diameter 70 cm when the bike is-6n vlzqmd lk 4fbkzo/ ):jn9; moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s 8q)c w sxhs3btm(fd9 8x/bi 4tis located 0.200 m from the axis. What is the centripetal /s8f9ib xc3 (tsd8qbtw 4x)mhacceleration?

  How many revolutions per minutvak x/mh)i0z:xy36w mn ;my1xe must a circular, rotating space station of radius 1000 m rota6nmy1mk:;i/h m v zx x)ay3wx0te 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 turn at 96nm /1ltm5v v(yobd 4-e.5 km/h. What is the centripetal force on then5 /1b4ym-tm(dlov ve motorcycle?

  A 0.50-kg mass is attached to the end of aezpw-dq4u2:iu7 p (.j6uggb m 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 maximum speed of the mass if the string is n-d6qpg .2uu4bm( j zgp:wue7i ot to break?

  A stone, of mass m, is at-q*tyl2uw7 aptached to a strong string and whirled in a vertical circle of radius r. At the exact top of the path the tension in the string isu7la*yw2-tq p 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 string and whcxz f8,+v2ke sirled in a vertical circle of radius r. At the exact bottom of the path the tension in the string is 3 kc x+ 8e2sf,zvtimes the stone's weight. The stone's speed at this point is given by

  A jet plane flying 600 m/s experiences an acceler(* axl-l u4ct(lm/8g)mmot pyokq7f:ation of 4g when pulling out of the d7x)gkop 8 cu4:ofa-qmtl t/(yl(mm l*ive. What is the radius of curvature of the loop in which the plane is flying?

  A pilot makes an outs)w xp s7k.gck+ide 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 hk psg7+ckx w.)e going?

  The maximum force a pilot ca dq*j3wrk0ff-z5+qd.1eav s un stand is about seven times his weight. What is the minimum radius of curvature that a jet plan.v 03js*wqru ddqzk a+ 1fe-5fe's pilot, pulling out of a vertical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/s round*+k- danytexp cww.f7 0 3vku x(;)rets an 80-m radius horizontal curve with the tires on the verge of slipping. How fast can this car round a second cn7 - adpkwt*rxc(;eky+0f) wutxv3 e .urve 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 radius 5, u+be cer0kv40 m with a speed of 20 m/s. The centripetal force provided ,bcuee +04kvrby friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve(l,wy n4 yjmx/ of radius 50 m at a speed of 14 m/s. What must be the mi ,yj (nx4myw/lnimum coefficient of friction between the tires and the road for the car to make the turn?

  A car is moving with a cj+xq:y(f *s;gnl q 8qw3vay+o onstant speed v around a level curve. The coefficient of friction between the tires and the road is 0++(n :fjylq8 q wxavsq;yg*o 3.40. What is the minimum radius of the curve if the car is to stay on the road?

  What minimum banking angle isjxkvm6 /0nei1-i xov z; 6rb mu4f:vp. required for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? (Ignore fric.bz4vp /:j;i vn6e miouvmx1 f x6r0k-tion.)

  A horizontal curve on a bobslegh9f )5u1g4 kzmatowa0ho 7c*d 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 we j)gv+oa8u9jn 2d:rwdz ;lt vjo;00of radius 100 m, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 mm4ttt:-f- ju rwe0b+ k 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 a h(wrx5, fdd+le41vf(q3m undyorizontal circle of radirqd(ufd+415nfxmd,v( y ew 3l us 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 innhoo sa8 :cr li3g40r+tftk44 the pit area, a race car accelerates at a uniform rate to a speed of 45 m/s in 15 s, moving on h 4c+ntar ko30foi:8ts4 4 glra 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 ofe vh atrv-(5y2 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 f* jpurnx2) es5orce on a 70-kg person standing on the Earth, due to the Moon? The mass *psnr j)u5ex2of 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. Il 17a rg 2 keunyo,+v-sn)qfs4f the masses are moved to half of an-)l4 2gs17euf+r nykvs ,oqtheir initial distance, what is the gravitational attractive force?

  For a spacecraft going from thmr-9m0jk s;bbaxx)e*9lr2g d e Earth toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the 9gk2b;xdb ) mjl0*9rxasme-r 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 i s;8jp rr ;q1+ogtgkw/bvt:a 9s $7.4 \times 10^{22} \; kg$ 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 "s5au9lm4 fjy6zpace-walk" at a distance above the Earth equal to the radius of the Earth. ly 5mf9z6aj u4What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance above the xf t- 2+ d pvzvfjm)yj0sm4(4p;kkg4uEarth's surface will the acceleration of gravi (x0 z4-+4pg d4f)s mvyju;2tpmvk jfkty be $4.9 \; m/s^2$?

  A satellite encircles Mars at a-gx 5um79ac/wb.z mz yk u*y-a distance above its surface equal to 3 times the radius of Mars. The acceleration of grb/a za7c.9m-uuz- *xmkwygy5avity of the satellite, 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 pz/q17g.lps8cln6; 44p / zaztoyin eceleration of gravity iea;sz/yg pzo.1pn 6 qltz 87ncpi4l 4/s $32 \; m/s^2$. 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 1k apqk-9a smre)t x(4m.ip2 fthe Earth. The Earth has radius r. If the object is raised to a height of 3r abovesmfax.e ) 9ka q 4i(t2mpr-kp1 the Earth's surface, what is its weight?

  By how many newtons does t,v7ib ei)s3shxgwgb6 rcx(gc7t 89 8ihe weight of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radg8x 8s 67i hbiw gcv7ts)93(crb,i gxeius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite ome yg8hny (:jiwo-u* ,f mass 100 kg is at a point 3r above the Earth's surface. What is the satell egw-( 8h*y:ymo,jun iite's weight?

  A spherically symmetricdy;k3khjb2x g2vii g,z 1.q9 y planet has four times the Earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of thg bv zhki g 13,y;9.2kj2idyqxe 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, with yqj d,k/f-/z8 1imwutwfj2.gthe Earth between the Moon adfwkmu z/j2 8/,g y fiwj.-1tqnd 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*q;v+ad4fy;zr;pa for0 xd6.
(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 etxu;,fcc (89t-ty syu2t/p j about the Earth (i.e., it just skims the su,(8;xtf-yt9c t uupes 2/yjtcrface 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 abo8 ,6p..ejeq wmbs-se af33zkeut the Earth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution around ,jew3s. ae3e q8f6.pksmbz -ethe Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 km above th ngv32ak g5 *(f*ou/qhs*zulue surface of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (The me hlzsuo*g( **23fa vqgku/n5 uan radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an orbital f9p 0pg.opo9ediameter 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 plan:a imcwq-bbj:t-+ o h6j9u x(eet 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 nearl9xrr-xxh uki 6gze(wl.: +e4iy circular orbits. Moon A has orbital radius r, and moon B has orbital rgr-ex:hl.i (9e x4+wz6iku x radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter i idjzs8rmp.dj;h5, 5a8k cfb0s $7.78 \times 10^{11} \; m$ 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 Jupinz6/c, j3exf3xo.m ore w1e/l ter 12 years to orbit the Sun once. What is the average distance frjmze//o.n3f1 3r 6 woe, xlxecom Jupiter to the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)