Is it possible for an object moving with a constant speed 5f )gqqmsliov /(gz/+ to accelerate? Explaimgz fi/g/oqv s(q5) +ln.

  Consider a particle moving with xjw xx* 7rj w/gj.6k0jconstant speed such that its acceleration of constant magnitude is always perpendicular tow*jjr6xx.wx0 gj/ 7kj its velocity.

  An object moves in a circular path at a constant speed. Compare the direction ta5 4ym,j5ybmt g/j+um 1s*l yof the objectj5 a,14symu5tgt b+m ljmy/ *y's velocity and acceleration vectors.

  When an object experiences uniform circular cbj 9i,+n1ipnyn9xq2motion, the direction of the acceleration+jb piq9n,9yx2cnn i1 is

  Consider a particle moving with constant speed such that itsrxyax1rl7 -wq:l ph)ce5/e ;g acceleration of constant magnitude is always perpendicular to gpxh5qw :ar;71) y l/ele-rcx its velocity.

  What type of acceleration does an objecbjl+h(ef v3:u(6 mabi()uxvvt moving with constant speed in a circular path emu(vubf3j:a)vel hbv ( 6(x +ixperience?

  What force is needed to make an objey ygn9o8rsa.8ct move in a circle?

  When an object experiencz 9yqsnm5k gb8a-l 2w(es uniform circular motion, the direction of the net force zk2ys5l9naw(b - g8qm is

  A roller coaster car is on a track that forms a circular xa 7p;rbt2452,n-w: k vpfo g6 clfastloop 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 centripetal accelerats5 ,b- nglw:a kv;r7 ap2x4ff62otptcion at this point?

  A roller coaster car (mass = M) is 68yc ,jvv* womon 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 minimum value for , c wyvjm*6o8vits speed at that point?

  A pilot executes a vertical div:z utr va4,cvj--)cvke then follows a semi-circular arc until it is going straight up. Just as the plane is at avtvjcc- :,vu )z -r4kits 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 o7kv05udr(2n uoonl+ kf 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 radiu +hyjmb./j jh7l6dkhl4l3l b *m6szq)s r at a constant speed v. Then it goes around the same curve at half of the original speed. Whatjh lj3lj6km)h msll*6 .hb 7+b/zyqd4 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 of radius r at a constant spee2x:a4 :i1ekezodq0 uus2n b-kd v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the card2sux14-a 0bikne:qu eozk:2 as it goes around the second curve, compared to the first?

  A car of mass m goes around a banked curve of radius r + t fq jxr,,s1om3bhj-with speed 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 xom1tj3+sq,j-b f,rhmagnitude to

  Two horizontal curves on a bobsled run are banked at the same anglea 8i5nxra h/no9c8 8v y)0 qpkoppsk:3je:nn5 , but one has twice the radius of the other. a/i8ckop::qn095nnpr5 8 8)a3pe y okhjvxn sThe 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 track is not constant,sylto:2/,y wo5wbrlxd3 j.l1 but increases upward from the horizontalb. l53y woxw1y:rlsjo2 /t ,ld. 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 around a circular path to haveijvxqp5eb:-:x.v ffo z 1q+3a both centripetal and tangentiaievqq.o+xfbzfp 3: 1a- v5j:x l acceleration?

  The gravitational force between two obje,c24 1;skd 2 /ejsxeyav mwxt*cts is proportional to

  The gravitational force between two objec16f b t7m1b vr)rkzzz3ts is inversely proportional to

  Two objects attract each other9zup ;4tb-a qh gravitationally. If the distance between their centers is cut in half, the gr4zp;9haut- bq avitational force

  Two objects, with masy(u y i .nvj39olpxu3b (0/sbjses $m_{1}$ 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 massess yc):bg6xo,+yc1d0tsf xfs0 $m_{1}$ 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 universao/ 0po gxjwt80utz6e 4u p:;cgl gravitation.

  Compared to its mass onrv/m-n+tgzob i; m i0v8;)hyl u.tqk4 the Earth, the mass of an object on the Moon is

  The acceleration of gravity on the Moon is one-sixthd b2/rnm brvw)-jxn 1. what it is on Earth. An object of massbw vb r1-d)nnm.jr2x /
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's s p7kw5ct,xro* fwf+yj4ubfu1l1 8kj: urface, the rocket's weight

  A spaceship is traveling to the Moon. At what point is ie 9o,rnioc -q2f0+s cklb.v 1w:sxwf3 t beyond the pull of Eart i -0 c3+sc1orfe:s2w ,.qbvxklw 9fonh's gravity?

  Suppose a satellite were orbiting the Earth just above the surface. What isw. d)s( or klr7o( ykx7jxn-2k its centripetalx-(orw(7 kkroxl 7sydk .2j n) acceleration?

  A hypothetical planet has a mass of half that of the Earth and a j dajxo 6g6u r/8tlq1vq52f9 ixs0od 7radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravityjuofs2v51q tj 6x6rdx oi9a qg/8 l70d at the Earth?

  The acceleration of gravity on the rf80cp5uh 7dk Moon is one-sixth what it is on Earth. The radius ofdc r 0p5h7ku8f the Moon 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 planet w9bdbt5f:1ighaav ;w7w v 0h(B has twice the radius of plan ;aa7v9wthdgi0b whfw5b(1 :vet 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 twice the mass of pnv l*hsgkv7*1 lanet A. If planet A has radius v1 *gkl7vs *nhr, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) abuf j-fua( :j,fout a sphericfuj:f,a jfu(- al planet (mass M). Which expression gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and rotates ifnp7(,z.g l) hwl ag0qn the same orbit. Compare the two satellite'swlgl zq,. 0ng(f) p7ah speeds.

  A person is standing on a scale in an elevator accelerating downward. Compare z:yzozfv5u90,o q h.q tl-4bathe reading on the scale to the person's true weight.zhyq9,ta-v b fq0o4 5z:luoz.

  Who was the first person to realize that the planets m1szp75+vm5dyur vr y0x -)mibove in elliptical paths aroumyr0my sb7u 5 51vzp)-xv+i drnd the Sun?

  The speed of Halley's Comet, while trauw/uy:0qba)op;5h h q veling in its elliptical orbit around the Sh; a qbyh:u/opq5u0 )wun,

  Let the average orbital radius of a plr1rtwe:kuxl128adok f ; h8 2wzq.lctxc2/z/ anet be R. Let the orbital period be T. What qua .t 21cl/ x fzxuk;1wt2hdzckaqw8 rlr/e2o:8ntity is constant for all planets orbiting the Sun?

  A planet is discovered to orbirgrs5ovpf/6zs b6a9;t around 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 5pr9sbgfosr; / va6z6will the period of revolution of that new planet be, compared to the Earth's orbital period?

  The average distance from the E ip:n 3nyi:rc7iby.5iarth to the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What iriiny3ni.7cp 5b :iy :s the asteroid's average distance from the Sun?

State Kepler's laws.gg8w-ig(f pk( gkn0g2

  List the four fundamental fomq 6 neceit497nkg.r 0rces in nature.

  An object moves with a constant speed of 30 m/s on a cifl)kz lbb6) 7hrcular track of radius 150 m. W7l)kf)z6 bhlbhat is the acceleration of the object?

  The maximum speed around a level curve is 30.0 km/h. What is the maximum spe0w67cwuqk,zivs -+ f bed around a curve with twice the radius? (Assume all other facto6 w0u wzvb,fk+sqc 7i-rs remain unchanged.)

  What is the centripetaln (p8ns,s8j5(n n3vl3h3vjmq wm 5 d:v)lvydl acceleration of a point on the perimeter of a bicycle wheel of diameter 70 cm when the s(js5ynm3v8: l vl3 h5)l d nmnvwnqd8v3jp(, bike is moving 8.0 m/s?

  A point on a wheel rotating avbar31n.7brgkv 81 vat 5.00 rev/s is located 0.200 m from the axis. What is the centripetal accelerb vgbr 1va3 kar71v.n8ation?

  How many revolutions per minute must a circulancr+a+5tp .-o yx7 ntui3vj2 rr, rotating space station of radius 1000 m rota-n3+u+jra7prt.otx5 vi y2c nte 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 radiusyi1su-ji* nuo1 x-ym r(6g:zq turn at 96.5 km/h. What is the centrqm-: 6iguuynx(iso 1-rz 1 jy*ipetal force on the motorcycle?

  A 0.50-kg mass is attached to the end ohfw -meord 4+6f a 1.0-m string. The system is whirled in a horizontal fewm+hr- 64docircular 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 not to break?

  A stone, of mass m, is attached to a strm. / gpvft5x(jong 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 weight. The stone's speed at this point is g(pxvf.t m5 j/given by

  A stone, of mass m, is attached to a strong string and whirled iv 5r*gv4 ,a2 /qtunjzw9n y+wsn a vertical circle of radius 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 giyun,5+w n /a 4qsgwtvrv* jz92ven by

  A jet plane flying 600 m/s experiences an acceleratidu;*j*f1p+ l.htg r pxieux1); y9l *nmx2fwyon of 4g when pulling out of the dive. What is the radijp1xxyh*ryew)f u*;2ti.pn 9ud l1mg l+ fx* ;us of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which the cenei +ixm1 u myxqn::zn+m/h 6cuvy8 o97ter of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down on his seat w/o7cnm:9y emh+ m nix8x yuiqu6+:z1vith only one-half of his normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven times his weight. u p4ytb-88itz s y6p/yivrm 77What is the minimum radius of curvature that a jet plane's pi tp7 t7p84-uzy b6ivs/ yi8rmylot, 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 horizontal curve with the tires on u9a vr+nk clsnv1y)0 *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 ny r1v)uc0ank+9vl*s tires and each road surface.)

  A car is negotiating a flat curve of radius 50 m with a ys+ci ; i up2d*lolgwuuamkl /0,/8d- speed of 20 m/s. The centrcp/ dgkl - 2,dsylu0iaou+;umw/il*8 ipetal 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. f: a2m5kjlb9x What must be the minimum coefficient of friction between the tiref2:xk9b5 m ljas and the road for the car to make the turn?

  A car is moving with a constant speed v around a le+o(3vtvosu6hu ,:*qc3 owbssvel curve. The coefficient of friction between the tires and the road is 0.40. What is the minimum radius of the curve if the car is to s+vqt3 ohb svouou3 c:(s6*ws,tay on the road?

  What minimum banking angle is required for an Olympic bobsled to negotiate9rmmau cmy;6 ,hj2 j9l a 100-m radius turn at 35 m/s wmj6 cmarmju,h;y9 l29ithout skidding? (Ignore friction.)

  A horizontal curve on a b)e4yiufc) 1v b:i9ul cobsled 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, ban d;28(* p0qy fdkihfapked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bankedp:ddoc +g eu,gs.jy ;r8cu2 l- 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 o/:8rbekot q +jf a string is revolving uniformly in a horizontal circle of radius 0.500kotre 8b: /+qj
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 a1 rx la.m-d5h5hx-pc, .mmmymrea, 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 filyc1p,x.-x5 h5 rmd. - hlmammml 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 pr* e7o*sliykxud)60y roton 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 ,rs l0h+; bb vlrd8( zp./toskEarth, due to the Moon? The mass of t( b8 r+l0s;bh,zvd lo .p/krtshe 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 mapb;nt,( t4k0zfola5xsses are moved to half of their initial distance, what is th4n,t5 pk0aoltfx;(zbe gravitational attractive force?

  For a spacecraft going from the Earth toward thepzig7rk q4* zw u((8vb Sun, at what distance from the Earth will g(k7 qvpr4 *bwz(8iz uthe gravitational 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 ij1l0+ djup41fqy o:crs $7.4 \times 10^{22} \; kg$ 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-w):evdaxdy1p i6bto. 4 alk" at a distance above the Earth equal to the radius of the Earth. Wha o ad46txy1e:v bpid).t is her acceleration due to gravity?

  The radius of the Earth is R. At what distance abo6-ovk,rv/jmc9p2k t t6tz4ucg x5dm9ve the Earth's surface will the acceleration of gravity bk/k49o,6cgmt c r6-2ptzujmd v5 x9vte $4.9 \; m/s^2$?

  A satellite encircles Mars at a distancesuwb z-: uw40tse9pua*momz:3x7e+ s above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compau+9zu*t0 : a:m3- eos7 s4xezwbwumspred to the acceleration of gravity on the surface of Mars, is

  At a distance of 14000 km from somy*i pg 91hc4oj6im4 eye planet's center, the acceleration of gravitymg9io c yh61 *4jiepy4 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 ifl07r6 xoj0.jgo;zj surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surfa lr.gz6f xo7;jj0oi0 jce, what is its weight?

  By how many newtons does the weight of a 100-kg person change when hg* x v:1nnms :wblv-nyk: 7-hwe goes from sea level to an altitude of 5000 m? (The mean radius of the Earth isx-s g7 :ykwlv vn-h:n: m1*nwb $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg c6. +9a 0(xgfpx fqndnis at a point 3r above the Earth's surface. What is the satellite's weighng(q ac d6fx+0 9pxnf.t?

  A spherically symmetric planet has four times the Earth's mass and tju 5f;7zr9gehl6fh ; awice its radius. If a jar of pean;59f;6flh hgrj7au z eut butter weighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Ear7 xjftby:o9mrv s6 ;y:-fidt)th, and Sun all lie on the same line, with thef;)j6 fs9:tiy:yr 7-btv domx 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 Mm 0kc3zj -*;5vh3o 7jjjimglmc)pq8l oon.
(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.int,+k rao2glx j83pkex9;h,, it just skims the surface of the Earth). What is the speed of the satellite? (Tiagt ,ok;8,x+rjpx2 lehn 9k3he mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about thvv j.278f2 5aej*bwqbrw xuf 3e Earth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution around the Earth? (The mean radius of the Eabwr2 q.ufvja8w x*e7 bfvj253rth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 km abemy. rp k6srrnl*x3*1b:a5lnove the surface of the Earth. It is observed to have a period of 8:am **b l5 yr63nklns.rpr1xe9 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, hatyrq0n ss*(z:8mnhi5 s 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 Jutpca2byj.,* 9/kre;yucgh8 rpiter orbits 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 c.e g3u1ryj 2crircular orbits. Moon A has orbital 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 complete an o y.1rjc ueg32rrbit?

  The planet Jupiter is t7m 6yd whb/:iaj eb*4$7.78 \times 10^{11} \; m$ 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 onc7n bn5 ll cf-0i crwq13d2u,tye. What is the average distance from Jupiter to the Sun? (The distance from the Earth to the Sun i3 u1yrq lcf2i5c t7nb,l0nwd-s $1.5 \times 10^{11} \; m$.)