Is it possible for an object moving with a constant speed to accelerate? Expld ,mt cg5 nsy3)t8en5nainst ,d8ng 35m yent5cn).

  Consider a particle moving wixsf nd+sa.2 3 z9.eteuth constant speed such that its acceleration of constant magnitude is dt+.uf e ss329.xnz eaalways perpendicular to its velocity.

  An object moves in a circular path at a constant speed. Compare the directionpj9- kl.*p/ t+-txxxxyggqf ; of the object's velocity and a/xkpxg.xjt*pgf;l q x- 9yt-+cceleration vectors.

  When an object experiences uniform circular mx4aq4.iljhfb w w .1m 8j0xju9otion, the direction of the acceleq8w4b. u mx w1f 9jl0h.4xajjiration is

  Consider a particle moving with constant speed such that its acceleratied.yt-4r fau /*a.g klon of constant magnitude is always perpendicular to ke fdga/.-*t r.layu4its velocity.

  What type of accelerapn u6g6 lpvf9. :)w ,mmr+nbwwtion does an object moving with constant speed in a circula.)pwm,6+ pg :nw ub6lvw9n mfrr path experience?

  What force is needed to make an os)8u q*fgex6uz; e4kk bject move in a circle?

  When an object experiences uniform ci4v d*;ec.g1eoh yym*mc-qk9x rcular motion, the direction of the net force iyvy;mh-c 9 edx*o e.c4m *k1gqs

  A roller coaster car is on a track dc:yk d e8*esuzsl0m :q9ai 21q7b dh)that forms a circular loop in the vertical plane. If the car is to just maintain c7s 92zl:q hqbekyd e0 d:da)i8ucms*1ontact 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 a track that forms a circular loop (radius)/g g+ q j4+siovkx/qs = r) in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what is thsq4 +ogsiq/k+/ gx )vje minimum value for its speed at that point?

  A pilot executes a vertical dive then follows a semi-circular arc until i q;wwx:6t .wyhc.4 re rl. u.on.gi6wwt is going straight up. Just as the plane is at its lowest point, the for. wctung .4w;yr.wi 6 rwqh .olex:6w.ce 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 cuuw ucbfak)gnw27 r c*z 7v62z1rve 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 r fjscth+q.v 8w j66,mxat a constant speed v. Then it goes around the same curve at half of the original speed. Whamqc8 s+ hj x66t,wjfv.t 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 az l ;::9em3gromvc 3qoy / r/s6vo1imconstant speed v. Then it goes around a curve of rad1vm vc9 ;oo3s:6/m lrazy :iorg /m3qeius 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 ba2ggsi oz6 s(pb .8dey7nked curve of radius r with speed v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal componeg7b(dps 2 86.zeosgyi nt 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 anglr4ky:x tr3j, mnnvo+;:vo8 m ge, but one has twice the radius of the other. The safe speed (no fric on4 xy gk rr:v,+j8m:onmtv;3tion 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, bwlzd beb; )aombqt*; a4j7b 9,ut increases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "ljw47 e),bo 9; qadb* amz;btbclimb 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 pat.qc:m aqrt: 6uh to have both centripetal and tangtqmqa:6r:c. u ential acceleration?

  The gravitational force between two objects 5*by )2pq ipunyk:t b1is proportional to

  The gravitational force betww5bt zx-1 j-uteen two objects is inversely proportional to

  Two objects attract each other grav5.d4 -r57hfdsh5 hxyeeuvua 3itationally. If the distance between their centers is cut in half, the gravitational vhf7d 5u4x r 3eh.es55ydau- hforce

  Two objects, with massesj) p -b-03bpc2:pehg d +hamay $m_{1}$ 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 massusl c: gq;tngaw88nl 2j3k)*ses $m_{1}$ 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 +h(ummq1l 4 gygravitation.

  Compared to its mass on the Earth,;p4*5oilgu5j 8;z o zuay b12fza2g mo the mass of an object on the Moon is

  The acceleration of gravity on the Moon is one-si2 c sg wmp9*wdncfu3a t9v8,c.xth what it is on Earth. An object ofa w gs.* uc9t93mp 8fcdnw2,vc mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earfequ0 t)m9( lcl5wwd:th's surface, the rocket's weight

  A spaceship is traveling to vp8*s1f pbawf ixn)66the Moon. At what point is it beyond the pull of Earth's visfw66x) 1 fpap*b n8gravity?

  Suppose a satellite were orbiting the Earth just above the surface. Whatfm q. ago,v8s9 is its a,9o8gq. m vfscentripetal acceleration?

  A hypothetical planet has a mass of ha:rir pbg3c o,ipt-+:ilf that of the Earth and a radius of twice that of the Earth.g-cpi :ripr:bot,i3 + What is the 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 nf* j ml;ls0-8.cfkml;0 jrjs Moon is one-sixth what it is on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Moon's l8j.-k m*f0 j slf0nmlcj;;rsmass compared to the Earth's?

  Two planets have the same sur nkx3pp9 z6,jqsp +t5rface gravity, but planet B has twice the radius of planet A. 6 jk9zt,5 pxrnqpsp+3 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,,eam7f q.qsh of planet A. If planet A hahs, fq7qem,. as radius r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) arsz2 t 3cy8bjg7vay*6y ypj2n*1; dvvbout a spherical planet (mass M). Which expression gives this satellit 6jrydvz7a3 1*t;2 bvcsv8*y ynj2pgy e's orbital velocity?

  Satellite A has twice (e z9nyh 15id +irb5oothe mass of satellite B, and rotates in the same orbit. Compare the two sat 5z1o d5yi9hrneb+(oi ellite's speeds.

  A person is standing on a scale in an elevy xpbnpm(2 ,.uator accelerating downward. Compare the reading .2(py ubn,xpmon the scale to the person's true weight.

  Who was the first person to realize that 9k) l4rxil 0k -q0kueew*eca/the planets move in elliptical paths around the Sunew 0/ku4x q0ekalc-lri 9) ek*?

  The speed of Halley's60bf2owl,,*edv zv od Comet, while traveling in its elliptical orbit around the fb0z ,dl*d6 v,o2veowSun,

  Let the average orbital radius of a planet be R. Let tsrhxi +(0gg 1dhe orbital period be T. Whgr 01h(+s dixgat quantity is constant for all planets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxy Andromeda, ie+ j8r5j4ews68( k p5ohs wxjwith 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 o8h jj+es s84j5(5x iew6kwrp of revolution of that new planet be, compared to the Earth's orbital period?

  The average distance from the Earth to the Sun is defined as one "astronomnf mi 6ie5-x 9i+z6,ybxdt vw3ical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distane6d5iz,b tf m+ix i9v-x yw63nce from the Sun?

State Kepler's laws.gwmabtt 9vi3t23 0:y)j4wck k

  List the four fundamental forc/mo 7nc ar(qx2y,p s.ues in nature.

  An object moves with a constant speed fxs+s3 *2liaj of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object?i23jx +fsa l*s

  The maximum speed around apk0/ x9jzk( rwj4 wfq, level curve is 30.0 km/h. What is the maximum speed around a curve j9w wkkr fz( xq0/jp4,with twice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a ;x u9d.ad *rwcwxjax:+u h9x 8point on the perimeter of a bicycle whe*axhcd xa9. duu j8: 9wrx;+xwel of diameter 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 ,,)ve ef+gack- z2yju axis. What is the centripetal accele,ea2k +c ,uyf-vge)zjration?

  How many revolutions per minute must a circular, rotating space sta6jlh+ njww-b*2e i+rl* q7o i0ug3nqu tion of radius+-2uo0nj*i jn bqlerl3g*iq76 +wh wu 1000 m rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13 4i+7s8s v6rb1iewvnj.7 m radius turn at 96.5 km/h. What is the centripetal force on this vj1iwbv 6nre7+s48 e motorcycle?

  A 0.50-kg mass is attache(-al/gic( n ( k2efyyrd to the end of a 1.0-m string. The system is whirled irg-2li/feky n ( c(ya(n 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 not to break?

  A stone, of mass m, is attached to avr1x /rg:gcu 2xx 1f)pestl5: strong 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 stonx)cru pvx 12:s x5f 1grltge/:e's speed at this point is given by

  A stone, of mass m, is attached to a strong str7i5j/7tivh hmsvp ;7 ring and whirled in a vertical circle of radius r. At the exact bottom of the path the tension in the string is 3 times the stone' ph;trivs7/h7 5m ij7vs weight. The stone's speed at this point is given by

  A jet plane flying 6 ktetat 1,tr7:wb z(.g00 m/s experiences an acceleration of 4g when pulling out of the di kwbt(e .tz ,g17tr:atve. What is the radius of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which the center of tdv99z 4v2(1z rn3wf(yprapp+ +dpwf ehe loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down on his seat wif2prfvd 3vypzd a+(wzpwen +p19 49(rth 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. What isr61 h py/1hvus the minimum radius of curvature that a jet plane's pilot, pulling out of a ve1y1hsv p/6h urrtical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/s rounds an 80-m radius hogkfy( 3:x)xmmd)hj: irizontal curve with the tires on the verge of slipping. How fast can this car round a secoh:)i(mxykg3df ) mj :xnd curve 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 50 m with a speed of 20 m/s. The8i:8 5+t ;par2l. qwfni7y8qm nsl vma centripetal force provided by frict 8ms ; 5i vq+.7wll8t:a8npqan2 rfmyiion is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curw7( *vqgufbg bm52inmh 6;q1gve of radius 50 m at a speed of 14 m/s. What must be the minimum coei(qug5*1 7hm;bn mv6f b 2gwgqfficient of friction between 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 coeffic g3 b3(uhtnqfovp tsyi+n0-p:7+p i/ oient of friction 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 ro0+p hg-+u7n:o/ t 3psvinqf3i op(bytad?

  What minimum banking angle is required for an Olympic bobsled to negotiate a 10gjcp:n.m7j2 h 0-m radius turn at 35 m/s without skidj.2n:c7pgjh mding? (Ignore friction.)

  A horizontal curve on a bobsj;w (ahe b6kzl43i *wj:sn3qn led 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, bagjon2zs;i/vcz ( 3w,fuq: h3p nked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bjze 577zcpx ;.x,awvs anked 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 oue2djaro)4y o . 7yyffv *df:;f a string is revolving uniformly in a horizontal circle of radoa;re7jy:o. d*vu dffy 4f )y2ius 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 in the pit area, a race car accq4( unb a c;czygfaizepy+2:z734*0vrad qx8elerates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular track of radius 500 m. (only fill in numerical value in the blanks) bizc4yqfaqa*xc0r a4;3vdp+y g8n7 2u z:e(z
(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 consiwl2p,5ga6lcgz- e64 w xav(t dsts 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 d whzgl+5 (pz m9qzbcy0.,yl3 person standing on the Earth, due to the Moon? The mass of them w( hzp9zg,03cybqlldy.z5+ Moon is $7.36 \times 10^{22} \; kg$ and the distance to the Moon is $3.82 \times 10^{8} \; m$.

  The gravitational attractive ffwox7kaz lv1ikh:17-jhws:fz*8 k/ j orce between two masses is F. If the masses are moved to half of their initial distance, w kx1zwk jhi7s8vfj:z:ofl/ah-*1 k7w hat is the gravitational attractive force?

  For a spacecraft going from the Earth toward the Sun, at whal))yo3tnhm l q9 0zkf4t distance from the Earth will the gravitational forces due to the Sun and the Earth canc)f9y30ml lhoq z4nk )tel?
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 isny 6a,9q+c qk7.ga t rl)av6jsa(cjl 3 $7.4 \times 10^{22} \; kg$ 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 "sp;lchggy,xs h:+b9pxtr1nl* 0ace-walk" at a distance above the Earth equal to the radius of the Earth. What is her acceleratps,9g0 ;r * +y1lhgxtnxcl:h bion due to gravity?

  The radius of the Earth is R. At/tirh0.c qf7q++ okt 1 k4nsqvbabu/ : what distance above the Earth's surface will the accelerahkqa1b o+ uti.n /s krt7q:/vqf4+cb0tion of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distan /iu2 (nz3gh3 j,b4mr2 vinjcvce above its surface equal to 3 times the radius of Mars. T izh/34,nvrbv3ug m2 jij2(nche 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 aik k+ss;2* tl6j;hl qkcceleration of gravity;kk+kishl;6 q*2ts jl 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 surface of tkms8 3. hbhh, xq7svxy.t:ph7he Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's sum737 ,.spt8xbh.:yvsqhxh kh rface, what is its weight?

  By how many newtons does the weight of a 100-kg p-cv)rr3c+ p1s1waz bwerson change when he goes from sea level to an altitude of 5000 m? (The mean radius of the Ear+zs)vcww1br3 p1c ra-th is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is at a 5c oh7sc e0v2ga7xc+ypoint 3r above the Earth's surface. What is the satellite's we7vos57a0gc ce2xy hc+ight?

  A spherically symmetric planet has four times the Earth's mass and tg6l+ltnmm*c v (gw *)r8yn 2kuwice its radius. If angu28v*c yt (m+glm)6nw* lkr 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 all lie on the same line, with vqd *+dtkuh d2ac9m :bf)d7w. the Earth between the Moon+7 fkd9vc w:tddq*hd 2.au)mb 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 Moo20gah09 fhn o2piga*7b+ e iarn.
(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 circularw7 iaa4 :u4xn6augnbqb++eh ; orbit about the Earth (i.e., it just skims the s4hg7uein ua;xaa+b6b+q n :4wurface 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 about the Earth (i.e., it just skimlb/jf,i(*uu r s the surface of thu,r*(lfbi u /je 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 surfxlybp . 1czp(-+y5ig6ug+o5u/gc grvace of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (The mean radiu /.+l(py1b zg6uropv-xg+55ggyicc us of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has o*7b;/rw dz n;vqe+wsms1: vr( tic1qfw()mpan 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 r/z.ot xi,l p vxt/l7 2+b5qxrmadius 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. ppj ed(o2o g/amd m:m818 w.ijMoon 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 moiw8o:jg2m a1 8jd./ omemd(ppon B to complete an orbit?

  The planet Jupiter i k7*p8j f x1io-dl+a+hqe*n,cl*p mdo s $7.78 \times 10^{11} \; m$ 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 year nyl2 mx74d*b iey9y1ns to orbit the Sun once. What is the average distance from Jupiter to the Sun? (The distance from the Earth to 4y e nxid1m279*ylbyn the Sun is $1.5 \times 10^{11} \; m$.)