Is it possible for an object moving with a constant skm*gr3,zqrlq uihn3m: a7.7vql;d k 4peed to accelerate? Explain.i r q,v7q7a*ku:3z 4;dkhl 3lrnm.q gm

  Consider a particle moving with constant speed such that its accelerat8ev /jxkt zzkv:h *kqju*f *8o)y4lf2 ion of constant m )k:*zyqh2efjl4uox* f8zkk8vtj *v/ agnitude is always perpendicular to its velocity.

  An object moves in a circular path at a constant speed. Compare the direcnqaa j50g:m7yka4h 3f tion of the object's velocity and acceleration vectors03aa5 4f:ahgm nqyj 7k.

  When an object experiences uniform circular motion, the direction of the accxi1v.ax c :cyr e.ua++eleratio1 +ri.uevc:y xc +aax.n is

  Consider a particle moving with constant speed such tfx5 f n/rf5h5fhat its acceleration of constan rnx5/fhf55f ft magnitude is always perpendicular to its velocity.

  What type of acceleration does an object moving wit;hmpq- 3 x)e .z h)p*vmngh)ygh constant speed in a circula)m.yqv -);*zx hphm)peg3ghn r path experience?

  What force is needed to make an object ml6;cd+ue78ruf bd b8*e bn7e9k m-pnpove in a circle?

  When an object experiences uniform circular motion, the direction of the 9 c0ut h)fn*hxi)h ;sdnet force*hh u09tidsc;f)h n)x is

  A roller coaster cark )n:do;xfy3z j:no(suh3u7 g is on a track 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 t3 xn3k)( :fh s:ou;yju7gdznohe minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a track that forms a circula;cms1v5wpxgs3 k( (tasut6rb 7q0o4ar loop (radius = r) in the vert51qxbgss0acmorw svk6pt a37 tu(4; (ical plane. If the car is to just maintain contact 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 thenxe+z cf9gw6,t follows a semi-circular arc until it is going straight up. Just as the plane is at its lowest poe xw,6+ cgzft9int, 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 radiy;c 1ifpd ayqco +i2o(r *7h.zus $r$ 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.o,pm 2y4c d;jn) yfxh33tht8m1k8qtu 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 y,1py2;o q)n8tchthf 38mtkj 3ud4x mfirst time?

  A car goes around a curve of radius r at a constantfmx4hvlc,/7ni-tx z. q4 g91+n gkske speed v. Then it goes around a curve of radius 2r at citfgs xn4 q4/l9 x. z+1vnem7k- khg,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,lkx *g7w ywgn+/hh 3f (ou9v9nd+ezi banked curve of radius r with speed v. If the road is frictionless due to ice, the car can still negotiate the/+x3fnl*n9w 7wzey g +dhv kuh,gi (o9 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 angle, but oba5yhk1*0 0v bb04ryc pdt7ir t3.juhne 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 ci5kat7vb0h 13ujt 04 hy.brrd0p*b y the safe speed on the larger radius curve?

  The banking angle in a turn on the Olympic bobsle7ftpm ck l.l11nxft9yji) 2g-d track is not constant, but increases upward from the horizontal. Comitlkcny 2f 1t9 .) gmixf1p-j7lng 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 ozf* ihz* 5ub3lbject moving around a circular path to have both centripetal and tangential aciuz35 hf**zlbceleration?

  The gravitational force between two objects is proportional th( ls 0v7rpu4*50 veqn m3kckyo

  The gravitational force between two objects is inversely proportional to tc2cgvf+7l,-vom)zd

  Two objects attract each other gravita9pal i 6z-mjpkdsr. 04b xbx45tionally. If the distance between their centers is ad9 m0rkb4sjp iz 4lpx-b.5x6cut in half, the gravitational force

  Two objects, with ma2 wsf 9yhblj19fjwm063 4 waila5j tk)sses $m_{1}$ 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 massete+/z: yrg7o rs $m_{1}$ 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 univy :pvf(k3hy. versal gravitation.

  Compared to its mass on thewq8pr/5: jj,vfc dsm7k dl)/ f Earth, the mass of an object on the Moon is

  The acceleration of gravity on the Moon istv.d su- pr*pe+o/h/v one-sixth what it is on Earth. An object of mass+optru .v-v de*/p/h s
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Eart9f/gqm +1u3frhz7cv sh's surface, the rocket's weight

  A spaceship is traveling to the Moon. At what point is it beyond the pul0zj3nu s(baz j+g b2y3l of Earth's gra(u30s3zayjbjng + 2bzvity?

  Suppose a satellite were orbiting the Earth just above the surface.i+0aji cp ll39 What is its centri l cap0+lii9j3petal acceleration?

  A hypothetical planet has a mass of half that of the Earth and a radius of td9:-vp uznfijj j/+t1wice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, tu+-1 vnjpjj t9: /zdifhe acceleration due to gravity at the Earth?

  The acceleration of gravity on the Moon is onerrdfrj x gl3ed62;r ti 65(r8y-sixth what it is on Earth. The radius of the Moon is one-fourthg ef ri58(x6rrr6ytj d;3d2lr that of the Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gravity, but plydj:c0 hl q 95sy9l4ylanet B has twice the radius of planet A. If planet A has mass m, what is the mass94 :9yyhj q05 cdslyll of planet B?

  Two planets have the same sun) rb0we lp +6u2*bilprface gravity, but planet B has twice the mass of planet A. If *2lie +)b0w6run pbplplanet A has radius r, what is the radius of planet B?

  Consider a small satellite mov5 sfbsi6ldp :ue9tj 9(ing in a circular orbit (radius r) about a spherical planet (mass M). Which expression gives this satellite's o sd9li: b ujsf59(ept6rbital velocity?

  Satellite A has twice the mass of sgo su728u wh ymi2;-n1lt/v kzatellite B, and rotates in the same orbit. Com 8k1ys22 nuout;g/m7iwvl- zh pare the two satellite's speeds.

  A person is standing on a scale in an elevator accelerating down(n:orc0f fwm 5ward. Compare the reading onm(o:n5 rwff 0c the scale to the person's true weight.

  Who was the first person to realize that th xdmy/ilp 0 zf,3(s a1hg7t;hwe planets move in elliptical paths arouh, s(1g fwp;z3hym / x7datl0ind the Sun?

  The speed of Halley'a6dj a fd23xg/;hfx v5s Comet, while traveling in its elliptical orbit around the S dx ;x2 f36/afjvdgah5un,

  Let the average orbital radius o m1 d)6bd* zn:zqsss1qf a planet be R. Let the orbital period be T. What quantity is constant for all planets orbiting th sd1mssz6*b zq:1)dnqe Sun?

  A planet is discovered7 hz5c:p efz:g to orbit 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 will the perp: z g7hzf5c:eiod of revolution of that new planet be, compared to the Earth's orbital period?

  The average distance from hs- q,ge-q2x t2jz7smthe Earth to the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance t-mj2q,7zsq ge-x 2 shfrom the Sun?

State Kepler's laws.o87vh,: jtxg h

  List the four fundamental forces in nth +l4x gu)qie(y*3*z.hen ylature.

  An object moves with a constant speed of 30 m/s onrxfh7/ilw+*f z5:fi m a circular track of radius 150 m. Whatzi+:x if w5f7r*lhfm/ is the acceleration of the object?

  The maximum speed around a level curve is 30.0 km/h. What is the 4fua n5s2 cufer2/2 anmaximum speed around a curve with twice the radius? (Assume all other fa4ucs 2/fafur a2n2e n5ctors remain unchanged.)

  What is the centripetal acceleration of a point on the perimeter of (zzp.l aqb,k0.aj lm: a bicycle wheel of dlz ,l.pm :a0.zkqj ba(iameter 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m from the axikw j7x6k /7 2a,mcbbxqs. What is the centri j m cwb6kx2,/7ak7qbxpetal acceleration?

  How many revolutions per minulx/dv c ci*:pvh) z6m:te must a circular, rotating space station of radius 1000 m rotate to pr:cp /hl):*vdv 6x czmioduce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes aroundmsq,ad g/j9/e8hvv5+ azconb (9h k3q a 13.7 m radius turn at 96.5 km/h. What is tha/8hqc+eqh,ov 5mdzjvn sk 9b3/g9 a(e centripetal force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m stringuz,:: j))e pn+g pyuyl 9nc9b xy74ceq. The system is whirled in a horizontal circular path. If the maximum tensq+be u, zy7ucy: n cyp4g9n9x)lp:)e jion 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 strong string 4m+ii5rly,bwpd5q.cbp b+c:z 9e. w aand whirled in a vertical circle of radius r. At the exact tbi pc,cprm z4ww5l +biq. :a.ybe+9d5op 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 stone, of mass m, is attached to a strong string and whirled in a vertwzm7,6oof /n vical circle of radius r. At the exwmn/6oo 7z f,vact 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 experiences an acceleration of 4g when pull pf ml/r,4z*hding out of the dive. What is the radius of curvature of the loop in which the pd4zph l/fr,m*lane is flying?

  A pilot makes an outside vertical loop (in which the center of the looph/wp u x,xawo1qy4ge-4cb 9 *v is beneath him) of radius 3200 m. At the top of his loop he is pushing down op4* w9 owv1x-y,/ xaqu e4cgbhn his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pilot can stand is about sev3;(d:fdt-/3 p:lh 7le rxqrydgk, lexen times his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling oglk l -l;hyx ee( t3f/:xprrd,73 :qddut 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 cez a-cd .5gsb;2x(6vz3gp ift urve with the tires on the verge of slipping. How fast can this car round a second curve of radiug-2.pfi s3c(e6b a;td5x vzzgs 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 50 m with a spr;l2eq1ki x- rx-) kmw4/ d0zbsh3qn aeed of 20 m/s. The centripetal force provided by friction is )wq-xarh / dmkkiler3-n b x q42s01z;$1.2 \times 10^{4} \; N$. 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 b9, (lmd jqk:gkm9l(q ,:jk kdge the minimum 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 al-r*5kvffwi 36zry 1p round a level curve. The coefficient of frictil1y vf -rz*6rw3k5ipfon between the tires and the road is 0.40. 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 negoti5skzwq9 r)oc ;lwew; :ate a 100-m radius turn at 35 m/s without skik5c9:oq )z we;wwr;ls dding? (Ignore friction.)

  A horizontal curve on a bobsled run i e6x1bkww)i.y 2, skyes 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 p 8pydp5)dppxzr k*4f; m,gq4at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is b )rebi, si(5dl*g. jf xdt ei4dw-xdxf)-uu. 4anked 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 revocjp0 fdik * hqc ed1v(;+1m lotzg)e..lving uniformly in a horizontal circle of radius (+qtj;ef d1.o ip 1m) 0zch.kcl vg*ed0.500
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 uniforhr:0 agke q47om rate to a speed of 45 m/s in 15 s, moving on a circular track of radius 500 m. (only4 h 7qoakger0: 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 massazht)p d +66s(s*nvk u $1.67 \times 10^{-27} \; kg$ 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 forcgub4, p 4kgbvq1m.6.e. kxhete on a 70-kg person standing on the Earth, due to the u t4bxmgg4ehkek.v p.1 q,. b6Moon? 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 attractive force between two masses is F. If the masses z1q yc 2m0mo x/rtku4.are moved to half of their initial distzut 1qm 2r./0x m4kycoance, what is the gravitational attractive force?

  For a spacecraft going from the Earth toward the Sun, at what dipc p3aos b 2m - 3i,or,0jmkbwmajhh*a, e;01zstance from the Earth will the gravitational forces due m,03h -p,sk 1 ma*3ahmbiwe2zpj o0;oc,rbjato 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 ipm 9mximl,oq0 m) , -avmr78wg qd+v:os $7.4 \times 10^{22} \; kg$ 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" av6x l oa6,-rost a distance above the Earth equal to the radius of the Earth. What is her acceleration due to gravity-osao6r ,6 lxv?

  The radius of the Earth is R. At what distance ab)or c7y-3 yyp6 0dpeyuffx1mu2tat g+0 b*,obove the Earth's surface will the acceleratiotugamyux 20re+y*ody-tp7f c)1bb6 03p, ofyn of gravity be $4.9 \; m/s^2$?

  A satellite encircles Markoa;lsem 6la 4ksu30b; wmcw7-h mj35s at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as c3jum4;67sc kow lah5;m-0klb3wae msompared to the acceleration of gravity on the surface of Mars, is

  At a distance of 14000 km from someb7 o.4txaagm: planet's center, the acceleration of gravity isa7 gxab 4:tmo. $32 \; m/s^2$. 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 the Earth. 6gx .m:x+4c b wbmua*j The Earth has radius r. If the object ixb:+c*u b.ga4x wj mm6s raised to a height of 3r above the Earth's surface, what is its weight?

  By how many newtons does the wei:pi w /axoik(5ght of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radius of theiao:i wk(x/p5 Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satelliterfu*vfd mwk5b. )1wl nb (+i4y of mass 100 kg is at a point 3r above the Earth's )i f5w+v f4u lyrbn1kdwmb.(*surface. What is the satellite's weight?

  A spherically symmetric planet has four times the Earth's mass ani- lhbz2ogh2e9)rw ko+7 gk .cd twice its radius. If aokkgih .2c 9rl )+bzo-h2g7we jar of peanut 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, Earth, and Sun al8bx0-f0h xf yfsxd5(ll lie on the same line, with the Earth between the Moon and the Sun. The Mox0 0fxl5fxs(y b-h8d fon 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 Moon.1yc7ko+cyf kea/pysy-vhlzu()2+ p ;
(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 ci-inu) 5r2aijdr ye-4crcular orbit about the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean ecrdu rij i 4a5-)yn2-radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about the Earth (i.e., it just lt)6v rx ;f-w/rt/ ywsskims the surface of the Earth). How long does it take to make one revolution arou;r /-s wrflt6y/txvw) nd 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 the Earth. It is 7pje,a kbz*gp4tg/5 3a slu y7observed to have a period of 89 min. What is the mass of the Earth? (The mean radb3,5pekptuz sa4 7a/ 7jg lyg*ius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupkh 5 )knc6c(zziter, has 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 Jupiter orbits the planet with a radiu 7 1wcq xs.d0sai:m9flhdodd n;.* ;yxs 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 ne46t vcutwqzmtz d h8+j9d ;a5y)7p1aon*:j wjarly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Mo5 jddj1htp7:9+6yc u vtmw w;)jazaq8o* t z4non A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter is wnn x-pv,(-mywj-5nm $7.78 \times 10^{11} \; m$ 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 tox rzhl7e-g/47 mkrn ( j:z2wxhe average distance from Jupiter to the Sun? m7rz:x gnw/2hxl4zor-7 e j(k(The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)