Is it possible for an object moving wi pq9i k csxop3b -ra3,1+zpr3qth a constant speed to accelerate? Explain pz9 qok+3p p-qb, 1icrsx3ra3.

  Consider a particle moving with constant speed such that its acceleratio fnm2m(04im kpn of constant magn 4kfmpm0m 2i(nitude is always perpendicular to its velocity.

  An object moves in a circular path at a constant speed. Compare the*epo4 q( 7q3febui3ka direction of the object's velof qq*473 (okbepia3eucity and acceleration vectors.

  When an object experiences uniforwz7pni+j7ouiy ), vwp)f /0ry6a)rnp 0t )hfum circular motion, the direction of the accelerwp0tpwuij) )zvp)n7r +)/yir f6a,nufy 7h0 oation is

  Consider a particle moving with constant s)9 e)ayv ym0nkpeed such that its acceleration of cons )v)eykam90nytant magnitude is always perpendicular to its velocity.

  What type of acceleration does an object moving with cjj,b sg m(2xo+y7h) yzonstant speed in a circular path experiesoygjz m ) 7yjhb(x+,2nce?

  What force is needed to make an object mhbi(gb8f90 uv ove in a circle?

  When an object experiences uncv62meohs,z ;iform circular motion, the direction of the net force ies2 o,c ;6mzvhs

  A roller coaster car is on a track that forms a cty d;6 ju9:i h+ra+afjircular loop in the vertical plane. If the car is to just maintain contact wit;ah djf9yr+jt +: 6aiuh 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 ta 3xz8u+i5,tdp wo 4ish s)c9(radius = r) in the vertical plane. If the car is to just maintain contact with the track at t+c shpu9wxiz)5o,3d8s 4tatihe top of the loop, what is the minimum value for its speed at that point?

  A pilot executes a vertical dive then follo3y,4uc1p 1pr, cq*ppz f2yqvcws a semi-circular arc until it is going straight up. Just as the plane is at its lowest point,,vcpp*z4 qyu31qy2f 1p p,ccr 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 cue7jvm7gj. o4nzj(1jd rve of radius $r$ at a constant speed $v$. What is the direction of the net force on the car?

  A car goes around a curta:g0d5(lu;s*vbwy zd;c/ b ive 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 goes around the curve for the second time, compared to the first tim 5:badiv(wlg0zs d; u;*bytc/e?

  A car goes around a curve of radius r at a constant speed v. Thmp0 tuljq(i+y )6t3 ciftfj 599mitx+yq y)k, en it goes around a curve of radius 2r at speed 2v. What is the centripetal force on th) p)jt i0ty6+9cm +luyf5yjfq 9k i(tqxm3i,te car as it goes around the second curve, compared to the first?

  A car of mass m goes around a banked curve of 7xr/qefa(jt:3 5lp qc radius r 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 fr 5aj tepcq3 fq(7/:xrlom the road is equal in magnitude to

  Two horizontal curves on a bobsled run are banked atm-vmplr:4zum 14;i rd -i.j5 a:azkzg 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 cur vamzzg.m z51-r-ia: u:4im pk4dj; lrve is v. What is the safe speed on the larger radius curve?

  The banking angle in a tu ,sk6en p tbh).9b3agorn on the Olympic bobsled 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 sa.et6),h3 b9gkpboncoming out of the turn. Why do they do this?

  Is it possible for an object moving around a circular path toz r-;6g8c5 py/ d yv8w8iqddkfb ,zz)0l6bphb have both centripetal and tangential acceleration?kbz,h856y zq8wbby /rvp 8l0 -i6;gcd pfdd) z

  The gravitational force between two objects is proportioqegmr .)1ymz- nal to

  The gravitational force between two objects is inversely proportionala4 dg8 7js+nnq to

  Two objects attract e n5s+fslk c6h+ach other gravitationally. If the distance between their centers is cut in 5sfhl 6kc+n+ shalf, the gravitational force

  Two objects, with ma; w,8rh 4q3nctv4c4o,y/iirb uo0yj gsses $m_{1}$ 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 massesmyowtts2ds70 f ap u,w pb0(oj8;l 5n8 $m_{1}$ 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 gravitattz of73ma /s-uion.

  Compared to its mass on the Earth, the mass of an obrf3lvs2osjnsgl t19sbd ,)2. ject on the Moon is

  The acceleration of gravity on the Moon is one-sixth what it is on Earth. jrawo ; dxz 3o8y1j2.4. v2*rxe0 xl9cfxetqf An objwo *0tr 4yo2 fxv.e13qxx d2.j;jlxf ca9 rz8eect of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, th*sm b1ui)ipx:h3c; 5 kaq9j cup 2oiu4e rocket's weight

  A spaceship is traveling to the Moon. At what point is it beyond the p4-.fj 9 vc wjaqcipz)/)o g1ofull of Earth's gravito i) 1fwfo jc-j/9zaqc.gv) p4y?

  Suppose a satellite were orbiting the Earth just above thi jlg9/-i zq*fe surface. What is its centripetal acceleration9/izl i j*-fqg?

  A hypothetical planet has a mass of half that of the Earth hggkm*8 : z: okvnf; z,zqyufif/ 5z8(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 Eartzukni, fmzh:gz*(f/:k5f8;yz vqo8 gh?

  The acceleration of gravity on the Moon is one-sii/rfbrl 8x84 2c+k*;)p kc lrcfm-kbuxth what it is on Earth. The radius of the Mof )2r k/4pl xl+c umrf8*rcbk i;8kc-bon 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 B hasym*jlfu: y2mii ymb ((p 3;(pbg55jvz twice the radius of planet A. v ;5b:y5ipz(ub (gylpmj *j2 m(i3fmyIf planet A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, bz8ygikvn fcfde)7 bn99(gn 3b.; x:v) z4 zcpcut planet B has twice the mass of planet A. If pla 8z39fz e)n()ig xzn.7v:cnv p4fc9bby;c gd knet A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) a4v zm7 d ata3( 2ll)t(ezcz)bhbout a spherical planet (mass M). Which expression gives this satellite's orbital velocit3t2 zl t (vh)7d(mleaaz c)4bzy?

  Satellite A has twice the mass of satellite B, andv0j2otf( o n7o rotates in the same orbit. Compare the two satellite's speed(j 0noovto 2f7s.

  A person is standing on a scale in an elevator a9276seds*wloxk rmz ;ccelerating downward. Compare the reading on the scale to the pe 9l6ekzs7 *omrwxd2 ;srson's true weight.

  Who was the first person to realize that the planets mk 9i + c1nm,iqnl 7(pcchsv86rb8zsw( ove in elliptical paths around the Sm7zvh,s lib+kcn( (r 8nwq8cs1i c9p6un?

  The speed of Halley's Comet, while traveling in its ez)au9p) 6 i; b+thgijhc27ljhlliptical orbit around the Suu cgtj27 hja 9i;zl+ph))bhi6n,

  Let the average orbital radius of a planet be R. L,4z+8zzzs 3b*p nend set the orbital period be T. What quantity is constant for all planenn z z*,4pb+3e 8dzzssts orbiting the Sun?

  A planet is discovered to or a7to1 s9obg 7m06eewbbit 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 period of revolution of that new planet be, compared to the Earth's orbital peribom9oe6 e1 7s7agbt0 wod?

  The average distance from the Earth to the Sun is defined as one "astron sh8m8* as/i )uggvx(aomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is tms i/h)gsu agv*8(a x8he asteroid's average distance from the Sun?

State Kepler's laws.*;tj aqewnve8 0.lo i3

  List the four fundamental for+ta yz,8s dnn7fh ;63djs) vwnces in nature.

  An object moves with a constant speed of 30 m/s on a circular track of radius 1me0e k/0zqq5t2jh kn(50 m. What 2k(zeq/ 05m0 nehtjqkis the acceleration of the object?

  The maximum speed around a level curve is 30.0 km/h. What is the maximum sp/l-1 vx w7(z dkw:edfteed around/td7dw:vwek(z lf1 x- a curve with twice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on the perimeter of a b 6h *kkw;x,acn; lt1asicycle wheec* a6;wlakx;1s n,hktl of diameter 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.0cxv2n a-wnlxjo*/ 5s; 0 rev/s is located 0.200 m from the axis. What isx*n a-2wl/jxc5ov;sn the centripetal acceleration?

  How many revolutions per minute must a circular, rotating space station of radi7:*puxqa*w ns * yzhh7us 1000 m r u h:*a*xpqzshn 77*ywotate 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 radius turn at 9lt-*bik/voj; o1 gq0fosswdn8 z1 2w 96.5 km/h. What oqg8 01kf dilwjbsn/ 9 w1;o*z- svot2is the centripetal force on the motorcycle?

  A 0.50-kg mass is atta kwbwihabpuf,2y5 , (;ched to the end of a 1.0-m string. The system is whirled in 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 tb5(w ,k2bph,uywifa ;o break?

  A stone, of mass m, ir81l5z pmxodb/wyxdqspq40 t 1(g1r) s attached to a strong string and whirled in a vertical circle of radius r. At the exact top of the path the tension in the zl8) 5d41tor/g p1pyxq 0b mwsqrx(1dstring 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 whirlgk- :t ij-tj q3.ob8sved in 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 st kbv -g:t-ij8oj3q.s peed at this point is given by

  A jet plane flying 600 m/s experiences an acceleration of 4g when pulliotys+-jp2 2e dng out of the dive. What is the radius of curvature of t2j2y s t-pde+ohe loop in which the plane is flying?

  A pilot makes an outside tqtl idbb8wnq: zf6:u :us i)g04m)2 jvertical loop (in which the center of the loop is beneath him) of dn)fj4 qq6ls) i :tgmbit b 2wuu:0z:8radius 3200 m. At the top of his loop he is pushing down on his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pir j ecio10b tt2q8 +)mmjdt54plot can stand is about seven times his weight. What is the minimum radius of t e58q40bm+p rt ojctmj2)1 dicurvature that a jet plane's pilot, 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 k7ihr:mj8b wpa-- b2o horizontal curve with the tires on the verge of slipping. How fast can this car roundiaw8- 2: jpbbm-7kohr a second 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. The cpo70 y3z-h vo yw1nb0vv.cem *entripetal force providm0 b-.c1 pvy *ovhvnew0o 3z7yed by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a q baq6 138 tgv apdf/rm89r.e/rjyqf/flat curve of radius 50 m at a speed of 14 m/s. What must be the minimum coefficient of friction between the tires and tymjvtrf6rd1 q 8e.b 8gr/3/9pfqaq/a he road for the car to make the turn?

  A car is moving with a c zb-fb 5 m(to2.hkj9yzonstant speed v around a level curve. The coefficient of friction between the tires and the road is 0.40. Wkymt. 9hfzo j5 2(-bzbhat 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 negotiate a d1y .o69zlm zx/ fwqiztx36rlp 8h5y-100-m radius turn at 35 m/s without skidding? (Ignore frihq6x3 diml p o6/rl8y. w 9z5tx1zfzy-ction.)

  A horizontal curve on a bobsled run is banken-* 0hqxekt - tnh6 fbqtw5a92d 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 radi upjpnfic:, tduu sj .:6+q)*gd z(f;tus 100 m, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 ehgvbw65 9z d.m 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 revolvinz,nyel*5. j)kl c h0dzg uniformly in a horizontal circdeyl hj0l*nz ,.)cz5kle of radius 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 accelerates at a uniform ratfayo(ifv1 x;m 4wp uf *vz;/zq:e:gnh:g54fv e to a speed of 45 m/s in 15 s, moving on a circular track of radius 50:zv4 ;gf:/mqa :ifzh f*4o;upy1f we nv5vx(g0 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 mnr )g/qzt2wjxk:z)5eu u 2v m5ass $1.67 \times 10^{-27} \; kg$ 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 70-7gxxk,gkmc aj6- o(p3kg person standing on the Earth, due to the 67jx, cako-3pg(xgm k Moon? 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 srxp;u26t y su9fv k3a 7nxki3l:cp66 masses is F. If the masses are moved to half of their initial distance, what is the gravitational attractive forts kv39xk6 urxui6ys:2pfpn7l6 3c;a ce?

  For a spacecraft going8a(j zlb x2b+o from the Earth toward the Sun, at what distance from the Earth wb8az(x2obl+ j ill 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 np,qcaaijsj: ix* m:/a 5-y6r np: -bzis $7.4 \times 10^{22} \; kg$ 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" at a dd7 1* ae1vhdlo1x c /iei5cvxy2ua ;+cistance above the Earth equal to the radius of the Earth. What is her acceleration due to gl +72 *a/vhie;d1x1xao5 ycccdu 1v eiravity?

  The radius of the Earth is R. At what6slv lpb2 x1/2-r eis5otw5xa distance above the Earth's surface will the asi ta5-e2sx5ovwl /lx1pr 26b cceleration of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above it vcbdk 2u/0(vqs surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared toq udvkb( 2vc0/ the acceleration of gravity on the surface of Mars, is

  At a distance of 14000 km ) nzlt*d5 xin+-:qf.vrs0lpf1 ta (jmw+wpo5 from some planet's center, the acceleration of gravity f(ji s.:mr+q*nl1- t n5o+5 pvztfxaww0dl)pis $32 \; m/s^2$. 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 radjr v acbkrb 6vzu3nmv9*b/6kjg-w79 )ius r. If the object is raised to a height of 3r above the Earth's s9kjcbwv jk3)6za6ng/rm9 v -r*bbv 7 uurface, what is its weight?

  By how many newtons does the weight of a 100-kg person change whyo 2y /a8-rioak m -.tfclf--o/ltt 0hen he goes from sea level to an altitude of 5000 m? (The mean radius of the E-ftfo/.hla8k a o/-t itly-- mory02carth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 f a.vj988zy7*n oxhc cefca3 p;.dm0d kg is at a point 3r above the Earth's surface. What is the f*8hd 98cjyc p .vc.;ax3d 0aoznefm7 satellite's weight?

  A spherically symmetric planet has (y 4h rb,sk67yhrvm(- wqxil9four times the Earth's mass and twice its radryy4s 9v7lq- khb(6 ri,h( xwmius. If a 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, Ea54its eyj9e7 xrth, and Sun all lie on the same line, with the Earth between the Moon and the Sun. The Moon has a mass xj iye974ste5 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 trvep8b9v jze1cx5 3tj3ansported to the 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 circul z-fwl/,tpk/7; fkc dk1oqg-qar orbit about the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The1c,7pokkg d /ftkf --wq; /zlq 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., e;g5q (ulvkhb7 tg/t4 it just skims the surface of the Earth). How long does it take to make one revolution around the Earth? (The mean radub ;get7g4vlqh /5t( kius 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 o h;(r0my ippb1.vn mh/bse(n 1m;0ph/yirbvhm . prved to have a period of 89 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, has an orbital diameter rdk97+n7wgb k 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 plan m03 e r :wba.7/txp,eyob6njoet 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 ney 6qq08z eit48c9obexvf6 -ymu 4l w6garly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A ta-zygteq8 lo 86 mvw4x6 9 q4iuec0f6ybkes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter iz j/q-f s-g-7viuqboa 2w .n9kixx,pqhb 0 k87s $7.78 \times 10^{11} \; m$ 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 the averag5,n fter k7zl0/8yh/mgs )q)vpz 1pac e distance from Jupiter to the Sun? (The distance from the Earth to the Su,z tzk g rq y)0v/se8ppml1f a5cnh7/)n is $1.5 \times 10^{11} \; m$.)