Is it possible for an object moving with a constant speed to a7nbq h+1c.aftd a9rr.ccelerate? Explairqr 7.f9hba+nt1cd . an.

  Consider a particle moving with constant speed such that its accym:uziqe gr2lxd +z.r.lj..7n8 laq7of1h9 u eleration of constant magnitujq.o uy 1 l2x: zrznl..e7urd+fmlig a79q8.h de is always perpendicular to its velocity.

  An object moves in a circular path at a constant speed.9x4ato f z)nf +985dxas*cnqm Compare the direction of the object's velocity and accelera *o9saf d8 tc9xq4)zxan+f5n mtion vectors.

  When an object experiences uni9hsp adg d34e h.7.mw(kh g/msp*yy3mform circular motion, the direction of the acceleraa /7(439yyh. g s hk sphm*gmp.d3dwemtion is

  Consider a particle moving with constant speed such that its acl ,qxog feu-)6celeration of constant magnitx,ueo-)6fgl q ude is always perpendicular to its velocity.

  What type of acceleration does an object movi+rq,jxp7hv8kl9d p 8rng with constant speed in a circular path expevq8d78k+ ,prj9 xrhplrience?

  What force is needed to make an object move in a c arwr(/. litl9ircle?

  When an object experiences uniform circular mot;.9wn aq3+ mgdjf n45 wntpof(l7 uwd0ion, the direction of the net force a; nf+(dqww.05l 3 fmgt4nuojd9 7npwis

  A roller coaster car is on a track that forms a circular loop int zere1kfe a28zem+0( the vertical plane. If the car is to just maintain contact with track at the te2ee 1z +tk8r 0f(amezop 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 *gi+*zc0 3bm ep1f2 eh hxtb.vcircular loop (radius = r) in the vertical plane. If the car is to +1ec0 * h itbe .3fxvh2g*bmpzjust 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 dive2p jg3yd;omrzd ;n+s8 then follows a semi-circular arc until it is going straight up. Just as the plane is at its ;o3 pzg8d ;m+ysnrd2j 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 ,v4b8 bxau; plof 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 at a constant speed v. (zffq gzz d2e3/u6m e5 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, compare(5zf qzmu2ed6/zg 3e fd to the first time?

  A car goes around a curve of radius r at a constant speed v. T4ba:-ywqkc3p hen it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the seco4-: qwa kbcp3ynd curve, compared to the first?

  A car of mass m goes around a banked curve of radius r with speed vo w1rntb62w iwml;6 l:. If the road is frictionless due to ice, the car can still negotiate the curi6m6n2:wt1l;wb olwrve if the horizontal component of the normal force on the car from the road is equal in magnitude to

  Two horizontal curvesrcl.1lmxkex+h n k2s9r.p5h 2 on a bobsled run are banked 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 saf c rkkhxh5+n92l.prsle x 21m.e speed on the larger radius curve?

  The banking angle in a turn on t 7 awjn j-8eagvuo9/zbwc)d+1he Olympic bobsled track is not constant, but increases upward from the horizo/ +jv1j7 8 enzd9wa)uaco bw-gntal. 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 have both ceng z5 9fii/d(txtripetal axifgdz (i/ 95tnd tangential acceleration?

  The gravitational fo s(m .,9nwuzjzrce between two objects is proportional to

  The gravitational force between two ma mv4wrwb7a aa42;m 8objects is inversely proportional to

  Two objects attract each other gravitatiqh1z7b oktd 6(onally. If the distance between their centers is cut in h(zk 16hoqtbd 7alf, the gravitational force

  Two objects, with massp///jvudseap z)n r0 6l2 fl+oes $m_{1}$ 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 ma;/2 sow:guu s2j (uon9x* ;e( yy.nxrpg9mdk lsses $m_{1}$ 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 gravia3w+0t6ul2uyl muf:uq /0ie ztation.

  Compared to its mass on the Earth, the mass of an f/ .+get+ fc 7l)jla(j mrkm,mobject on the Moon is

  The acceleration of gravity on the Moon is onex8u +xd t:zpge1 :avvhf 8o66m-sixth what it is on Earth. An obxvvf o a6tz8:h1p6 g8eumx:+ dject of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, the rmduzj96 ppt-(ocket's weight

  A spaceship is traveling to the Moon. At what point is it bey fbo2 97-xpoi rny5ny5ond the pull of Earth's7 y5nf9o -nobxrp2 i5y gravity?

  Suppose a satellite were orbiting j/1-bdr df- xnthe Earth just above the surface. What is its djdx-r-1 nf/b centripetal acceleration?

  A hypothetical planet has a mass of y2(f5oiwkq5cvp *5b phalf 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 ofb(5y5p qoc*f2 kpw v5i g, the acceleration due to gravity at the Earth?

  The acceleration of 6fu4/l0b pi.ojk da-rgravity on the Moon is one-sixth what it is on Earth. The radius of the Moon is one-fourth that of the Earth diblk6u ar 0p.4jo/-f. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface g9)1h. ;d.q /zx kmx vcv*rnrirravity, but planet B has twice the radius of planet A. If planet A n;)*zk1r/ d9h xxqv iv.cmr.rhas mass m, what is the mass of planet B?

  Two planets have the same surface gravity, but planet B has twice th* yjqxctste.kw )q-iiqsi.qin0 / s71b, )u2le mass of planet A. If planet A has radius r, what ikwqe- .) y il,sttq1x0)nc s/*iub.i iqqj s27s the radius of planet B?

  Consider a small satellite moving in a circularoqtx mz)u32tp/q;q: d orbit (radius r) about a spherical planet (mass M). Which expressx/tmo3;2utpq )qd q z:ion gives this satellite's orbital velocity?

  Satellite A has twice the mass of savy f, 9j2c1yqftge m69tellite B, and rotates in the same orbit. Compare the two satell621 qjfg v9e9fy,yctmite's speeds.

  A person is standing on a scale in an e qnr ekhka2vy978rq mmx *x 8;ia;5(yglevator accelerating downward. Compare theixv*a (k5qmqr;8;2 ka 9rmgh7n yey8x reading on the scale to the person's true weight.

  Who was the first person to realize that rh0+ s 8 rvhq c:1(pu)lsgdmq-the planets move in elliptical paths around th:usc)pq -gsh d8lv+0qm r( h1re Sun?

  The speed of Halley's Comeuvxddrqn)66q sw kes+d (fp -w-0 t(l q4qz*+ht, while traveling in its elliptical orbit around the vwt0qlqxsdq(hdw6) +u6qfre k*dn sz4(+-p-Sun,

  Let the average orbital radius of a planet be R. Let the orbital period oeu,u iqwqf6 .r4(m,j be T. What quantity is constant for all , qqj.4oum ,f w(r6ieuplanets orbiting the Sun?

  A planet is discovered to orbit aroun/r nmv *(udjf.d 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 period of revolution ofu(nv* ./rdjfm that new planet be, compared to the Earth's orbital period?

  The average distance from the Earth * r+ +.xuwi8sob:5lxjjsg)g sto the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-txs .grui8+w:sjlx5) jso bg*+hird of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.7g4cix;+:g cqd:)r8mpukej t

  List the four fundamental fornyl(lqglq c7aos,cchz8 n . /-a8/rp4ces in nature.

  An object moves with a constant speed of 30 m gv; jr)dlsy6myo/ chcw6);5k/s on a circular track of radius 150 m. What 5dcwy);h6gm6csj yrk )/o;lv is the acceleration of the object?

  The maximum speed aroundgepdu:o t8 ;sopev 39: a level curve is 30.0 km/h. What is the maximum speed around a cuedp;ouv8t:9p e o gs:3rve with twice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on the perimeter of a xviprvc- 4/py yimlj5c/532ey*m/l w bicycle wheel of d55/cp c e j l*wlxryi3vvi-pm2//myy4iameter 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 thdtjnjr fwlh(0 5 p/+q6e axis. What is the centripetal acceleration5/l hfntp 0+(jrdw6q j?

  How many revolutions per minute must a circular, rotating space station lfm 2+l kq-;vzof radius 1000 m -llkmf ;z2q+ vrotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes arouv-algm* oa9 6lnd a 13.7 m radius turn at 96.5 km/h. What is t9l*-glaavm o6he centripetal force on the motorcycle?

  A 0.50-kg mass is attached to(rq;o-ir ne p9p-x ub7 the end of a 1.0-m string. The system is whirled in a horizontal circular pa9 e ox;rn-- rpibpq7u(th. 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 ,vvqd ps,*6uw*iur 5mpu8wf.feq02mstrong string and whirled in a vertical circqrvw*dumfqep2 ,w6.f p, s58vm0 iu*ule 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 given by

  A stone, of mass m, is attached to a strong string and 7 tt (lmesi; ofp-zb1skr)/3rwhirled in a vertical circle of radius r. At the exact e-t;/)rlp ki b mf1sotzr37(s 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 60 ;tgig ;zrss+ryg*b55 0 m/s experiences an acceleration of 4g when pulling out of the dive. What i;g r5;gszrg*+ s iy5bts the radius of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which tx,74aiszgfcj qvd (;jnq* 8 g/he center of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down ,q qfzcvasg*i78(xj;4dn /jg on his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven ti kc2hyv*lj 4f;mes his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling out of ykf4* l;vh2jc 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 tir * 8gqxc-q:wqxes on the verge of slipping. How fast can this car round a second curve of radius 320 m? (Assume the samxqc8:-xgq qw*e coefficient of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 50 m ws) xivdc4;*/3c vveuj ith a speed of 20 m/s. The centripetal for;ds43e)uvccx*/i v jv ce 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 ,cb4+wxahf3 -o sq9tz 1 :is5my0acwwm at a speed of 14 m/s. What must be the minimum coefficient of-qc49a1hw tcz5f 0:3my xs+wswo, bi a friction between the tires and the road for the car to make the turn?

  A car is moving with a constant speed *foehp5 u2hnz3 n): *t92,7qwvgdkbqu an-riv around a level 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 stay on the road?2 eiu,tob9zfh3a7n*n h dqw n v5)pqug -2r:*k

  What minimum banking angle is required for an Olympic bobsled to negotiatj .;.eye3zt cmzodn ,-e a 100-m radius turn at 35 m/s without skiddinc.o, ze;-y 3e.dtj znmg? (Ignore friction.)

  A horizontal curve on a bobsled run is banked at87-fsaj*yc(bx+ihz/ vcu e6w 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 at an ang09 y lii)7lo jnpd5ms:hn*4nrle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 ma80hrek p*sc 8 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 revol9 x)uk:3kq v /f/pezs pzvql, g6a89wbving uniformly in a horizontal circle of radius 0.50z39vqpf,/zag lqxskeu8/9 b w 6v:kp )0
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 accelerip0(mj8 8lgt xu2n*saates at a uniform rate to a speed of 45 m/s in 15 s, moving on a ciru8 gjasmitpl(*02 8nx cular 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 of massle x7m/(droy 2 $1.67 \times 10^{-27} \; kg$ 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 fd mgh9z (ol ei/:m3ntbt0:0g 70-kg person standing on the Earth, due to the Moon? The mass of tfd:zg/0gtb3l imn9: t(em ho0he 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 are m/m) pa*xu9hs1g i:mb moved to half of their initial distance, what im1 mh9/agi*sp: ux )bms the gravitational attractive force?

  For a spacecraft goi)nzd lksajf z/ 218iv0ng from the Earth toward the Sun, at what distance from the Eart0lafd z zn8v1k/)sij2h will the 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 isdtr; (+j 57n akh7vo,9asn gpjty-t. pvya v6* $7.4 \times 10^{22} \; kg$ 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 ,dm2-ney:lue67 m zuxc h1m7ealk" at a distance above the Earth equal to th le,:uc-zn7 2ed1m xme67myhue radius of the Earth. What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance above the Earth's suok/)sc 3 5 +jy6uowd; qg1qyherface will the acceleration oc1o d qysh+)wk3o y;jge6/5uqf gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its surface equal to 3 times o2l qda2x,h htuyltp)/850lrthe radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on tho/2u,tqx2l)lrd0ly 5h p8hta e surface of Mars, is

  At a distance of 14000 km from some plab+et ss; kpu;ih8 /9rjnet's center, the acceleration of gravity ;prisbuh+ 8k/s;j et9is $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on thzue(oq ay/9;yx0:xrl-u8 d zl e surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what is ityd:/xz;e- roy zx(u lau980lqs weight?

  By how many newtons does the weight of nzsx6i:ifp1 -7/dejt a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radius of the Earth ii ejditp7:s/16nx f -zs $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is at a point 3r a0i st+ u2uc o485rcehubove the Earth's surface. What is the satellite's we2uc+uc0 orei8st h45 uight?

  A spherically symmetric planet has four times the Eaku v inf t7 7lv-edkz9 ;4lz y2il(ku8;skb8t9rth's mass and twice its radius. If a jar of peanut buttizfi uvun l97tbyzv 7kl;8k;tke89d24s(lk -er 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 gv;/smiz 4*qqon the same line, with the Earth between the Moon and the S 4gm/qq; sv*ziun. 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 t-a(m5 y cof i tx.c6qal4;fi,jhe 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 abkss56r m( 5q zt9ypt 6flm7frg-0 rme(out the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The me (k0gf6p6ysz ( 5m5qrs 9e- lr7rttfmman 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 skims thek2q ; syvqi-8+z7utik surface of the Earth). How long does it take to make one revolution around the Earth? (The mea-kqyz8tqsi 7i; uk+v2 n radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit /fw cg5wz77mpb0 -)id uul(xc230 km above the surface of the Earth. It is observed to have a period of 89 min. What is ti(5 p m) lbzuw-d77ccg/0x ufwhe mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupitzkg mt1h7lzj2 x(ke)ps i7- :o;/rg jner, 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 ra57dgzn rk y*)c( bgo-rdius 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 circqzdyktx)d ha yb.+983ular orbits. Moon A has orbital radius r, and moon B has ob8xty9yd +k aqz h)3d.rbital 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 is+x6jvvf 1ui *0ya* fwx gvph8, $7.78 \times 10^{11} \; m$ 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 i ustvf6()4zkku2h c0eqyxuf::rx* z ( s the average distance from Jupiter to the fuc*z2h4uke (0sux y x tkz: (f6vqr):Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)