Is it possible for an object moving with a constantzurn(qz 69v*v(ot0noxvrl 03m0 whc+ speed to accelerate? Explain +mr o 0*n0tr9n0z( vlzvc6(hoq w3vxu.

  Consider a particle moving with constanj,i4a5uyxq kb3 tq;4 vzuki00t speed such that its acceleration of constant magnitude is always perpendicular to its v,i4 ;zuay jitq50vq 0x4kbuk3elocity.

  An object moves in a circular path at a constantqw x,wqy3(qxpb4.ary o d27m. speed. Compare the direction of the yw 47do3y .xmw2ap.qr ,bqq (xobject's velocity and acceleration vectors.

  When an object experiences uniform circular motion, the diu5 crnc ati+ muj7b6skb ma))olhdc(s0c-8 .(rection of the acceleration i7 sto -aan c0cm)lubum 8+jcrk hdb()is .56c(s

  Consider a particle moving with constant speed such 4m.qa yb;h4w+:+*t gy zcetyp that its acceleration of constant magnitude is always perpendicular to i 4g:tp ; b e.wy*tqhz++m4cayyts velocity.

  What type of acceleration does an object moving with constant speebhmsu ,01)u 1oxcj xd8d in a circular p0xc1o8suh 1b) j,xdum ath experience?

  What force is needed to make an object move in a circiar( de,2 qzl64 t4nyzle?

  When an object experiences unip038 n6as92jgfw i cizform circular motion, the direction of the net forcpniiagw j 896zf2sc03 e is

  A roller coaster car is on a track that fo ef6pgem2l: 0trms a circular loop in the vertical plane. If the car is to just maintain contact with track at the top e l2: m0etf6gpof the loop, what is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a track thah 5hfy/o4e 2rqt forms a circular loop (radius = r) in the vertical plane2ro qf4e h5h/y. 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 arc until it is gold+f hscv.41vp ; /.ga7 3f9ajom: gtdwl5pa fingop1t wa:g5h a dm;l c4j.dgvs/.vpf 7 fafl3+9 straight up. Just as the plane is at its 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 curvrjzy5v h3c/gqvaf 1h1p-ry 42e 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 at a constant speed v. Then it gqmo6m5u jn 4;koes around the same curve at half of the original speed. What is the centripetal force on the car as it goes around qo6m 5jk; m4unthe curve for the second time, compared to the first time?

  A car goes around a curve of radius r at a constant speed v. Then it goes axvf ft9z945e-q eiwb:p7 ac.ei5 pu4lround a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compared x94ul.v7 55fpebqcti9- ap4fze e: wito the first?

  A car of mass m goes arouqix6omz:ga ,)8zg,q k;ji; tdnd a banked curve of radius r with speed v. If the road is frictionless due to ice, tktoq:)xqd8,zm6ggij a ;zi, ; he car can still negotiate the 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 tjq (f1rn +imcs h/+j7angle, 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 vs+jrhq7 n it+(cjf1 /m. What is the safe speed on the larger radius curve?

  The banking angle in a turn on mz8w5kz)5z nqd3p;bw q1z i6 vthe Olympic bobsled track is not constant, but increases upward frwvzwn 855z )q6zb1p ;mki dz3qom the horizontal. 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 d lip 44x ,r/hgk))tpjmoving around a circular path to have both centripetax4tpg 4/i rkhdj l),)pl and tangential acceleration?

  The gravitational force be g oh9qey-hx4w4z47 6ufne:lbtween two objects is proportional to

  The gravitational foo3 *z ymwk-*jqo -p8brrce between two objects is inversely proportional to

  Two objects attract each xi l;1.w2m)oud9 zrm gother gravitationally. If the distance between their centers is cut in half, the gravi9 r2xigmul;1do. )mz wtational force

  Two objects, with maozp ;gtq*y fu18)xz9 hsses $m_{1}$ 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 7 1wjprz.re.osses $m_{1}$ 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 gravn njw+ -tqj9ate5a )n1itation.

  Compared to its mass on the Earth, the 2q:4p0t; z4ew ojwek yk jb5*emass of an object on the Moon is

  The acceleration of gravity o4q *:k bauame-n the Moon is one-sixth what it is on Earth. An objeck: au*-b4 emaqt of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away facivwyl k eb6*jw):apr 8)i7 ;lp.z6brom the Earth's surface, the rocket's weight

  A spaceship is traveling to the Moon. Atwkn+4oxd q v) 9 .kw1pk eg;)rgw7tjc9 what point is it beyond the pull of Earth's grav w99j)vcxkd)w onep.g4g;7qtkkw + 1rity?

  Suppose a satellite weretufsu (*+a a1z6gmo8u orbiting the Earth just above the surface. What is its centsf+ o8m 1aza gu(t*u6uripetal acceleration?

  A hypothetical planet has a mass of half that of the Ear-6q0h(bonthfrz i* r5th and a radius of twice that of the Earth. What is the acceleratioh6t r*qn5f-oih( bz0r n due to gravity on the planet in terms of g, the acceleration due to gravity at the Earth?

  The acceleration of gravity on the Moon is one-sizhdmgz1y d;3/ xth what it is on Earth. The radius of the Moon is one-fourth that of the Earth. What 3m;hgzy z1 dd/is the Moon's mass compared to the Earth's?

  Two planets have the same bv i;1yl(0yuf wixsii5n d4 :o4w4l6ssurface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mas0w ;1iw(yf sl4v b5:4lxi oisidy un46s of planet B?

  Two planets have the same surface gravdpp09;j9bf pk ity, but planet B has twice the mass of planet A. I9pj ;0p 9fbpkdf planet A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a ciruj-saxh av ch0s:bo z*h. 6u1:cular orbit (radius r) about a spherical planet (mass M). Which expressicuv s1bz: *hxaa0s :j hh6.u-oon gives this satellite's orbital velocity?

  Satellite A has twice the mass of satml*g11 diq aj): :(l 0tujhpofellite B, and rotates in the same orbit. Compare thaj0hltdlmio p q::g *j1)fu(1e two satellite's speeds.

  A person is standing on a scale in an elevator accelerating dv 6 fod8a *y,:p3fpyeiwa)9u4v lrr9 uownward. Compare the reading on the scale to the person's true weightdayr w ru upp3e)f* 49fyv6:a,8iv9ol.

  Who was the first person to realize that th ul/+8r 38apo hxmsj 6dvnht+ib.5 rd4e planets move in elliptical paths around the Su/3 6nadv ldobuiphj5t+.r8+r4s8xm hn?

  The speed of Halley's Comet, while traveling in its ellipticalem82 q )ygc 0vg2g ;mo4zplio, orbit around the Suom2z04pvig o2 8g;)g,qem lcyn,

  Let the average orbital radius oi 57qqy- 4g o2)gzcb-v- 3x pxfp,efoyf a planet be R. Let the orbital period be T. Wha4-2g)f qq5o7p-f3v cgixybopy-x ze ,t quantity is constant for all planets orbiting the Sun?

  A planet is discovered to orbit e4ah*1uafn)j6ee mc)qku6 3iaround 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 wila q6*akheu1f6)n3mej4ciu e ) l the period 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 onemu:dl*7z)j yq "astronomical unit" (AU). An asteroid orbits)q*:7 ljydum z the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws. )*mhyx;+9b je2virfk

  List the four fundamental forgwojz:p yv7.h c:q 6a0ces in nature.

  An object moves with a constant speed of 30 m/s on a circular track of radbi8 2n:a-gljiius 150 m. What is the acceleration of the obje gini2:8 -bljact?

  The maximum speed around a level curve is 30.q h5 )h,xfxwue7jc 64n0 km/h. What is the maximum speed around a curve with twice the rae6u,h f)wx74nqh c jx5dius? (Assume all other factors remain unchanged.)

  What is the centripetal accekz2 d-vix.ssgz u c-4po-, .eyleration of a point on the perimeter of a bicycle wh.vo sdc -z4pz- yxku-i2g.s, eeel 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 axis v8n /dwl+ym4w. What is n/d4l+y vww 8mthe centripetal acceleration?

  How many revolutions 9)rx:0uhv kvu 6 lg(waper minute must a circular, rotating space station of radius 1000 m rotate to produce an artificial gravitv6h guwkru(:x9lva 0)y of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m rad4msv6zv+urua 0 tz3)w.qed)eln8pu7ius turn at 96.5 km/h. What is the centripetal f) +muv n7qzltpd rs3.v0u84u)w zeae6orce on the motorcycle?

  A 0.50-kg mass is attached .gi3yd g2u wh2k8s3 arztghz1ioo2 31p4 2nknto 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 tsgk2zini3aw1h gp 23 8 rtn3zuy4oo12.hkdg 2o break?

  A stone, of mass m, is attacz 4:fxxbnnnm/ xz1,;/n1 8wehf. u xxghed to a strong string and whirled in a vertical circle of radius r. At the exact top of the path the.g x,8bx/zn/mze nx;x4fnu1 1fxhn:w 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 tf77x;iog gtx ,9pa/ e,omx)wgspcz); o a strong string and whirled in a vertical circle of radius r. At the exact bottom of the pacg)7 ;7/omxpp9x,w fa,ixotzeg ; )gsth 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 aeo8 s dd403maun acceleration of 4g when pulling out of the dive. What is the radius of curvature of the loop in whie 0m s8du43doach the plane is flying?

  A pilot makes an outwe l(5g7/ f kn)(8ta; x jcu.1prfbykqside vertical loop (in which the 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 7 cwnq1fag .fkku l;rje(xp5(/)yt b8of his normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven times his weight. What is tyb2l* ks0yv *whe minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can tolerate at a speed of 2w0*skv l2yb y*50 m/s?

  A car traveling 20 m/s repm lpt .66lh1ounds an 80-m radius horizontal curve with the tires on th h lmt66.p1elpe 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 and each road surface.)

  A car is negotiating a flat curve of radius 50 m with a speed of 20 m/s. The cend.d2-ythtn 4 jf/jo-rtripetal force provided by rtjy4ddn o-2 j.-f /htfriction 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 must btccj/+dq +v5)y,45i2.v po sffhp xgee the minimum coefficient of friction between the t)5h. jy 4+epgq/v+v2dio 5x sc,tcfpfires and the road for the car to make the turn?

  A car is moving with a constant speed v around a level curve. The coefficient)7j9 tg/sos vy 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 thosv79gyj /t)s e road?

  What minimum banking angle is required for an Olympic bobsled to negotiate aeu6::li4:y q c2gx 7wy0n loej 100-m radius turn at 35 m/s without skidding? (Ignore fricl4e:u cw:g eoj2x nq:l0i67y ytion.)

  A horizontal curve on a bobsled run is banked at aoxo8w2 6ljpc , $45^{\circ}$ 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 m8knw: q xuxqi 5g0ox9 i7lj6(o, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bant1jfe 1 .loqd h+igx07ked 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 revo j r)5fw .x vmt:qriyc2;lk(j5lving uniformly in a horizontal circle of radius5cxm5 yv) k.r q wil:jf2(tj;r 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 acceleratea +v)gqmxiwv30)n -lr s at a uniform rate to a speed of 45 m/s in 15 s, m v0x+g)vwain)rq -l3moving on a circular 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 ma/o5tt n :z/w+ xwewq3ass $1.67 \times 10^{-27} \; kg$ 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 o9j;lnb2 .7xd5nal s zmkz;mtll *k2r 9n a 70-kg person standing on the Earth, due to the Moon? The m* 9b9z; klln2 s;l7rm5zanmtdj.xk2 lass 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 tx*4i i bhht2euzul-4 ae;xg 66he masses are moved to half of their initial distance, what is the gravitational attractive forl g4t;6 u62z4hex*e-uihb aix ce?

  For a spacecraft going from the Earth toward the Sun, at ev7-z1mv(xvb what distance from the Earth will the gravitational forces due to the 7 1xb-vem vzv(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 ik a 3.qj ssc5x)gsc6l)s $7.4 \times 10^{22} \; kg$ 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 distance above; voi-s(dom/+yb,vde9g+rqf the Earth equal to the vo sf;m/,q+ er(yi -+gbo9ddv radius of the Earth. What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance above the Eqgt6gqs-b+ v8 arth's surface will the acceleration of grav v g8+t-bgsq6qity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its ue*x t .q2ub(ssurface equal to 3 times the radius of Mars. Thb uutx(. sq2*ee 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 so cb j7.pikqs+-me planet's center, the acceleration of gravity7p sbqjk-i.c+ 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 the Earth. The Earth caofrgn 8e3+i2 pu2*ic h.gfjkf(4c + has radius r. If the object is raised to a height of 3r above the Earcg onkc38+ep4+g c.22i u j(f*hfirf ath's surface, what is its weight?

  By how many newtons does the weight of a 100-kg pers/lxq6z uz(qj5vb 0rp/ on change when he goes from sea level to an altitude of 5000 m? (Tzzp/lx ( /0 bq5v6rqjuhe mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is at a point 3r )wnsxa(9 cluek8fw1 + 6c5zq uabove the Earth's surface. What is the sate8lwuw 6ez(x9qf+1nc5uk cs)a llite's weight?

  A spherically symmetric plantl n 67zej-.byet has four times the Earth's mass and twice its radius. If a jar of pebe.n -ltjzy7 6anut 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, yic4ywdlmd x4dk3*;4ve 3 lj:with the Earth betwee 4 y dld3ex:4;mydiv *j4c3lwkn 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 transpoqng fahksk,z*z)/ g6*vcx)xfq; y;5lrted 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 circular orbit about the Earth (i.bwlh /q 8;crt;e., it just skims the surface of the Earth). What is the speed ofblc8;rtq/hw ; 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 justetc 845k z(qg;sayhw 5jw8 ml8 skims the surface of the Earth). How long does it takcjy(84sz8 gmheq5a k5w8;t wl e 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 of the Earteg,ap -tntjj e*.a,p0 h. It is observed to have a period of 89 min. What is th ea a-,ge.p*p,t0jtnje mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, hmageyf wvv 8u5bzun 388 z5sw:r2 6ha)as 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 witn,n yy+( 3b;rzn+sf us /tphc9h 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 nearly circular orbitsvuwl-z,aq qh7hd96nic0ei* uw +5k; w. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days twuq-5lq7ac e; hhzu 0 d,iv* +9wikwn6o complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter i5wovtytgv,og.4(px+ qg v78 i n*e+yps $7.78 \times 10^{11} \; m$ 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 Ju1.k yh;fbo jzgz507tkybt3 /kpiter 12 years to orbit the Sun once. What is the average distance from Jupiter to the Sun? 7yk 3 /fg5.tztjko;z1b0h kyb(The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)