Is it possible for an object moving with a constant speed to accelert .ystp 8x-:g/lmub+g ate? Explain.8t- utgmb:l+x/ ypgs .

  Consider a particle moving with constant speed)ef djops+bbl vu f39k3l,8i0 such that its acceleration of constant magnitude is always perpeflvu9b0jo sd 3, lp8+fik3) bendicular to its velocity.

  An object moves in a circular path at a constant zpe ( lhqy-a-okf0/o0 speed. Compare the direction of the object's velocity and acceleration -l0y /pe a(h0qkof o-zvectors.

  When an object experiences uniform circular motion, the direction of tky5w 5v-)x- e)yb pmadhe accele b-ke5d myav-w)xy)5p ration is

  Consider a particle moving with constant speed such that its accelec; r rzie-:k-enl4mw 2+md7 seration of constant magnitude is always- :m ;mi2k-4weerdezsn7+rlc perpendicular to its velocity.

  What type of acceleratiok3 d,lzrt.3ia n does an object moving with constant speed in a circular path experience?3.3kt aizr,ld

  What force is needed to make an objecb- aw:d(456k w sq 6mtpsguoq/t move in a circle?

  When an object experiences uniform circular motion, the direction of t p:si /7(gc))jcy8hmz1rjhuwhe net force j7)cz )chrj:i/ uwg1s(8yhp mis

  A roller coaster car is on a track that forms a circular loop intpc3 vmtv ge39pf4 .vzw3 y35rdl2( xm the vertical plane. If the car is to just maintain contact with track at the top of the loop, whatp3 x 3r2 tdfl 3gvpt9emyc(v.z 5m3wv4 is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a tr)2v:hkln hd3p9a 7esgc vg5 dn)k9;u 9rrbol.ack that forms a circular loop (radius = r) il9c9 k2 vr bo :n3v9)e5h7.lkdgsduna) ghpr;n 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 its speed at that point?

  A pilot executes a vertical dive then follows a semi-circular ab4h :pnx3 kk:src until it is going straight up. Just as the plane is at its lowest point,k3kb ns:4 ph:x 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 rawitk7fa. ;/w adius $r$ at a constant speed $v$. What is the direction of the net force on the car?

  A car goes around a cu4w4r rjp9s6ctd+r y 5xrve of radius r 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 t+cr jdx49r 65s 4rywpgoes around the curve for the second time, compared to the first time?

  A car goes around a curve of radius r at a constant speed v. The eiefg(*u5fv03bqze; qi 2/z qn it goes around a cei; zg izu3/ e(20eb5qfqq v*furve of 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 around a banked curve of radius r with spee-pec4 q3a8gaustoe- )d v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the normal force q4 ea)pcesoua38t--g on the car from the road is equal in magnitude to

  Two horizontal curves on a bobsled run are bankedt,2ba +use07jow 9j wz at the 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 safe sj s7uob atwj0wz,9e+2 peed on the larger radius curve?

  The banking angle in a turn on the Olympic bc ap82ba g)lw. m:h4ibobsled track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "climb the wall," then go lower bg:b2 4 awphc.m)lia8coming out of the turn. Why do they do this?

  Is it possible for an object movingaai*vgbhebmznyv nf;b0* ho+.4 b.; 5 around a circular path to have both centripetal and tangential accelerav fg4yv h.mhbea nnzi 5bb**;a;b o+0.tion?

  The gravitational force betw( )f)xjetwm4 i*vwza)-c9wqd1uskj+ een two objects is proportional to

  The gravitational force between : hr w zi9ey1b7y+gr2el6mjm:two objects is inversely proportional to

  Two objects attract each ot6cdc jxwy yl5c6f y683her gravitationally. If the distance between their centers is cut in half, the gravitatiyc6 cyxw6 386d5 yfljconal force

  Two objects, with mad x ox)vjn3v8161w*yx4vj dwhsses $m_{1}$ 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 6dhxy( ji3z :;tjfh( z$m_{1}$ 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 gravitjb*a: of* p0ffation.

  Compared to its mass on the Earth, the mn:i ;8k*5xwd:7n i9k( ghs vbwky/sesass of an object on the Moon is

  The acceleration of gravity on the Mou 0 nt :vnci 8.2beqv*k;+x dyyw5dn)ron is one-sixth what it is on Earth. An obn:5cvu tdbiwrd ).0y*;8 nkn +2 exyqvject of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's su,ik1k vg8b+5h nqrgu,rface, the rocket's weight

  A spaceship is traveling to the Moon. At what point is it beyond the puln8z/anbj0vi1nzu o q9-1:r o al of Earth's q a/inz-9nuz0rnv1jo1:oab 8 gravity?

  Suppose a satellite were orn(5oll hys2c t8h *9bebiting the Earth just above the surface. What is its centripetal acceleration?y(e8b2 9otnsh c lh*l5

  A hypothetical planet has a massdvcj7,am 23u o,sj3yuty+j ( uug:vd 6 of half that of the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the Earthdoc3jj gd7 u (,3u v+ty6:yjvma 2u,us?

  The acceleration of gravity on the Moon is one-sixth what it i( w; luocjlxfaff*3f. .6upq6s on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Moon's mass compared to the Earth'c 6f x f*fuqo; 3l6wjflp(u.a.s?

  Two planets have the same surface gravity, but planet B en-mea: 57ery has twice the radius of planet A. If planet A has mass m, what is the mass of e:ee7n 5m-ayr planet B?

  Two planets have the same surfampp;*mr:m vr, a3ao hde b6umo m6e+8(ce gravity, but planet B has twice the mass of planet A. If p po,bpa;8mhr +mvue*mmmo:(3 6da6r elanet A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) about a sphen8*qlj-y n cqw3,+bmprical planet (mass M). Which expression gives this satellite's orbital velocitn3-c ,+m lq8wqynj*pby?

  Satellite A has twice the mass of satellite B, and rotates in the same orbit. .ts:xh)d.ct j Compare the two satelthtc .s. ):jxdlite's speeds.

  A person is standing on a scale in an elevator accelerating dow uab6x+h1j/ c tcgp7;irfzw0fe; ;j q6nward. Compare the reading on the scalepre1 +c6f/zwgta0hu;x 7jjc;f ib;q6 to the person's true weight.

  Who was the first pep8+j fa v1igv; ,t,wgdrson to realize that the planets move in elliptical paths around tta;1p, g,vidf jg8v+whe Sun?

  The speed of Halley's Comet, while traveling in its elliptical orbit 1gh 7x2;j 5usxp7czz so,c0 ijaround the Su1 xo;su72sz7pz cj5g0j h cxi,n,

  Let the average orbital radius of a planet be R. Let the ozxqgs-; * gi8jrbital period be T. W zix-sg q8*jg;hat quantity is constant for all planets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxy Andromeda, with theuy- z6acdv4p,g( zdx 2 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 thd vpycg(z-ad4zx u,62 e Earth's orbital period?

  The average distance from the dcz.fgr70m 2 4pwgo8y o6 )obgq q4)l8:y qvdoEarth to the Sun is defined as one "astronomical unit" (AU). An asterocrg wd))doy2b8 gy04oq7ovlqo:.8 z gm 6fpq4id orbits the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.py 9hsm4p4je 9r wu88lpx(u* t

  List the four fundameed8h rqrc1cnt 16x-q: ntal forces in nature.

  An object moves with a constant speed of 30 m/s on a circular track ofz-( wtl( jauh: radius 15u:hz(-tjaw( l 0 m. What is the acceleration of the object?

  The maximum speed around a level curve is 30.0xfama7iv d(:0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all other factorfx (adv07ia m:s remain unchanged.)

  What is the centripetal aoep+bx( e79uwuu gl6-ogt ;x8 kcnv9s)o1 9uqcceleration of a point on the perimeter of a bicycle wheel of diameter 70 cmsv g)x7u1 okbeuuq+9lg;-ox99n optw(uc8e 6 when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is locat-gvniwbmz bl5gqi9k 4wv70. 7ed 0.200 m from the axis. What is the cent -g.wilbiwbv 9zqkg074mv n7 5ripetal acceleration?

  How many revolutions per minute must a circular, rotating space stati8;l va i2kt:ikon of radius 1000 m rotate to produce an artificial gravity of ivklt;2: iak8 $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn at 96.5 m*+2zxmcurbahq; (. t,eddj. ;royr 1 km/h.x*;muht , mdezac+1b q..yrrd(j2;r o What is the centripetal force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m string. The system is4 /6u5zc4voa 2mzss ub whirled in a horiaz 4s24 vu6uz5bm/ coszontal 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 not to break?

  A stone, of mass m, is attached to a l1isw0whndw(m3bpm5 bg3z+ 8strong string and whirled in a vertical circle of radius r. At the exact top of the path the tension in the st5ln3+ (mmw8s b0hzg3i 1bpdw wring 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 vertic6b dp01y byf80zvxgucm/ /w b9al circle of radius r. At the exact bottom of the pat 8b906vyfd1ybu0gm bp/ wc/zxh 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 acm n* qv6+imtt2celeration of 4g when pulling out of the dive. What is the radius of curvature of the loop in i mm*nt2+6tvq which the plane is flying?

  A pilot makes an outside vertical loop (in which (x 3mq g(:yvko g,q08m 8qhkggthe 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 hig 0 mgqx,yqok88hgq:(mvg3 k(s normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven tq3pcjz2 zt zie/80h/dimes his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling ouzzp/2hejq3 8z0d cti/t 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 tirehp3txx zvrx2ii*zd9k980clci0;g v0 s 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 a kd0xxiz09h;* 0zii2lcgc r3v89t px vnd each road surface.)

  A car is negotiating a flat curv4gxdzx 1 j1:wce of radius 50 m with a speed of 20 m/s. The centripetal force provided by frictix:1x1d4cgj z won 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. What mumls 4es o3/sza,*w ;fbst be the minimum coefficient of friction between the tires and the road for the cwz *;4msse ,/olbafs3ar to make the turn?

  A car is moving with a conca kge z++9so+stant speed v around a level curve. The coefficient of friction between the tires and the road is 0.40. What is the minime+c9ko z+as+ gum radius of the curve if the car is to stay on the road?

  What minimum banking angle is required for an Olympic btxf4sb8 5 mgb7d7 zloy5,g.svobsled to negotiate a 100-m radius turn at 35 m/s without sk zovg8ly5g ,d4 t.b7sxbs57fmidding? (Ignore friction.)

  A horizontal curve on a b22oe-o7 qz.l3homzsj*l*it m obsled 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, bgvd)8u rdsh**: tree7 anked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 aa* d.x( fsp cr*m02 ut00drs3am mzg6m 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 t e ts4.8umj2trevolving uniformly in a horizontal circle of radius 0.500 e8t u.tjtm42s
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 acceleratem3)65 m0uhm:7jzhw* gjnh dogs at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular track ) 7d6j5mjzh:gh0hu mgmw 3*onof 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 of mass je+ud9l 4tz.0s dksq) $1.67 \times 10^{-27} \; kg$ 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 gravitati d4o,ag3pfb) 9v+rb dzonal force on a 70-kg person standing on the Earth, due to the Moon? The mass v )o43fbz,g9rdd p+abof 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 mas;hona;n :r* zkffi fy0;*hovh 9a)pa *ses are moved to half of their inapnfza)ok;fivfnh roa 9y h;* ;h**0:itial distance, what is the gravitational attractive force?

  For a spacecraft going from the Ev;9ppnbs5tud1 and sc. ho*x8w )*3nyarth toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and thd 9pbn xhpw58;*3uoa dsvs1c* t).ynne 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 isvta h+)ba4df.j8,4 yvcu gw0s $7.4 \times 10^{22} \; kg$ 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 "sp6az +q mov)0qsace-walk" at a distance above the Earth equal to the radqs6zm+vo0qa ) ius of the Earth. What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance+9qz-ysbel s cjj1 mke6 l)n30 above the Earth's surface will t 69mkj0lbe y3qe jlz+ss1)- nche acceleration of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a dig+l zpirp6 6k qns2 5/tac9:cpstance above its surface equal to 3 times the radius of Mars. 6zc6kspppg59li q+r2 c/ ant:The acceleration of gravity 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 accelej;p*jx1 r peb4v:s92hgq l*taration of gravity i st*v1axb4ehgj p* ;2r:j lpq9s $32 \; m/s^2$. 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. The Earth has j fs:h; quvz03 hjk17uradius r. If the object is raised to a height of 3r above the Earth's surface, what is ih0 juqzh3:jukfv7;s1 ts weight?

  By how many newtons does the weight of a 11idb77 ram *c,jic :fo00-kg person change when he goes from sea level to an altitude of 5000 m? *db:7ic focjar ,i1m7 (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 10q q.o e13;h-vlfz xza w+7-omv0 kg is at a point 3r above the Earth's sur.wq 1e;homz- vvlz q3f7+o ax-face. What is the satellite's weight?

  A spherically symmetricq9 lrswn;vmjpj (a/3+qm 8ck/ planet has four times the Earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the s +j /rpcj(k8m/n lm3wsqa; vq9urface of the Earth, how much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun alin7a kii/kvh2*.wj(dr/p s7 f:p*fapl lie on the same line, with the Earth betkp.p7/* a2 ns (f/ rj*ii hpw7fvkai:dween 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 tkwwdx 0 ev1(,lhe 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 z 1,yzvn2h vj4b;vu;xf5sz ,b Earth (i.e., it just skims the surface of the Eartb jnvu2,z h5, sz1vvx fz;;4byh). 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 about the Ey1 0vhpu/g al,arth (i.e., it just skims the surface of the Earth). How long does h/1 0lvpa, guyit 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 sqf24j st5 7n2yn4nka of the Earth. It is observed to have a period of 89 min. Wh7 nn y4n2sks5q4ftaj2at is the mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter,yrv2/zrcuuoj5i;p 2 lmt /s ;q)l:/vp 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 radiuszyzjw(u yz46 5 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 n+j4 1hgiip/zqns -x6nearly circular 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 cxqsin+i jn-h4/1 z6g pomplete an orbit?

  The planet Jupiter i/qoe6bq0uwkd;c ,wz 2a-4 y wjs $7.78 \times 10^{11} \; m$ 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 w-*3 z1ig ok.f/aez g.6t xxoyJupiter 12 years to orbit the Sun once. What is the average distance from Jupiter to the Sun? (The distance from the Earth to the Sun 3g*i twy.gf1xok.-eaz 6 /zo xis $1.5 \times 10^{11} \; m$.)