Is it possible for an object moving izzz6g-d :.ss with a constant speed to accelerate? Explai:zs.sg izzd- 6n.

  Consider a particle mosh 92(bfp nffl91r(jcm8csszg(* ) enving with constant speed such that its acceleration of constant magnitude is always perpendicucfmp*lsr jz f)1b9 (c(f8g2snse(hn9lar to its velocity.

  An object moves in a circular path at a constant speed. Compare the direction olwk2i 5w ,1os)3js/.mm(o lw,at gawk f the a.,2gok /mmjstw k o,lwww 3i l(sa15)object's velocity and acceleration vectors.

  When an object experiences unifw5+7 ,z/s8,qnoyt. engoymkk orm circular motion, the direction of the acceleration i5 qo7/km8tnk e ,z,.ywg+snoy s

  Consider a particle moving with constant speed suchgy8fq7 ,uu2e i that its acceleration of constant magnitude is always perpendicular to its veliyfu2 uq,ge 87ocity.

  What type of acceleration does an object moving with constant speed in a circul4lkx+o 4cmn.;rl0idh aebwt5 ;4(ne+ln ,vnpa ,n r4; xn+m ldbcpln;vwe htn0e.ia(4l5o+k4r path experience?

  What force is needed to make an object move insi): y7tiro7 zs9 g( (iyw--nkbqitq0 a circle?

  When an object experiences uniform circular wmu*tjxpjk,pq.bejc 56 .i 342a:okcmotion, the direction of the net forjbp i ,.w. 5 43*caox6kkpjqej:2cu mtce is

  A roller coaster car is on a trac qr; lhz+uhbn8yy46-vk that forms a circular loop in the vertical plane. If the car is to just maintain contact with track at the top of the lobly-zy8r v6q+hhn ;4u op, what is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a p* -k2gjk 2ca,hxndad*,y4 du track that forms a circular loop (radius = r) in the vertical plane. If the car is to just maintain contact with the trjk*dpuh-*yad 24x,2,k gna cdack 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 4lybu6 yi;h, tit is going straight up. Just as the plane is at 4b iyt ;,luh6yits 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 of lay29da5.oba 7mv.e6 stmm,lradius $r$ 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 ao6c6ik f+ +dant 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 a++dk6cafi no6round the curve for the second time, compared to the first time?

  A car goes around a curve .c,x 2 kxdhqw (xgdd7)of radius r at a constant speed v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compared(dk c2dd)whq7 x.,gxx to the first?

  A car of mass m goes around a banked curve of radius ugw2r uel w7j odn;9n2q-w:s7t;2xs fr with speed v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the7fs:wsou29nr gx 7l-22d wq wu e;tnj; 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 angle, butd . )hiuv7lu+o 2n6q(pw9 vsfwz5zma ; 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. fuaui.2wdz n5qwv+s; (m h pvol97)6zWhat is the safe speed on the larger radius curve?

  The banking angle in a turn on the Olym:dc56qeh.x/ *fxj lhtsq- l; 5g u+ysgpic 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 coming out of the turn. Whyj*; gx6l5sh5 qth+e-x f l yqcd/:sg.u do they do this?

  Is it possible for an object x5t/7ywslahps. rkf888p x9+ieak w:moving around a circular path to have both centripetal and tangentiaw s+sw85apx8x k l/ki.8t9 pafeh y:7rl acceleration?

  The gravitational force between two obj: 1j zn h-jfi9pb(na3rects is proportional to

  The gravitational force betwe x( nheak+o0u)nx-n 2mozq0 ,ren two objects is inversely proportional to

  Two objects attract each other gravitationally. If the dist79w- k5jw:j7a3n oyzo+ex yuhance between their centers is cut in half, the gravitation :7a x9w-5z7y+hyoj3kueownj al force

  Two objects, with ma)obk zv0::dz hxp *0gmsses $m_{1}$ 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 massemseri ,xo4 :nt0d4 j:xq+wr*ms $m_{1}$ 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 uniz7 k8vjb)om ;oversal gravitation.

  Compared to its mass on the Earth, the mass of an object on trm,e +8rrfq c0he Moon is

  The acceleration of gravity on their 09fbwa 3gty lbs:63 Moon is one-sixth what it is on Earth. An ob9w fsbry0a3 :gt6 bli3ject of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, th2.(pb uluz 7jmeba9j,e rocket's weight

  A spaceship is traveli5u:f p9,kwzaing to the Moon. At what point is it beyond the pull of Earth, kwz 5p:ua9fi's gravity?

  Suppose a satellite were orbiting the Earth just as*- :2;fw*bsm jbf yyo-d e1kabove the surface. What is its centripeta2fdsb;:j s a-*1wey-fk* obym l acceleration?

  A hypothetical planet has a mass of half that zp,, ksun 8ua6of the Earth and a radius of twice that of the Earth. What is the acceleration due to guas6k,z,pu n 8ravity on the planet in terms of g, the acceleration due to gravity at the Earth?

  The acceleration of gravity on the Moon is one-sixth what it is on tai y9t(ec6l)x73 iskEarth. The radiy69ckts)3x t7(a liie us of the Moon 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 q3 mn/ry7x5r svj1au4, but planet B has twice the radius of p4a1n yvxsr 5q3/r7jumlanet A. If planet A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, but planet B has twey .ft wymopl1c2k/-5ice the mass of planetp1 y.myc-ot el5/f k2w A. If planet A has radius r, what is the radius of planet B?

  Consider a small satelu-/uyj0e 5u:c a *oiaf e0k3wplite moving in a circular orbit (radius r) about a spherical planet (mass M). Which expression givesufp:5 0* w3juakoyiecu0ea -/ this satellite's orbital velocity?

  Satellite A has twice the mass of s9o/roh csn/aii 2,b0kij8/ 6rhx vt9r atellite B, and rotates in the same orbit. Compaj99ixin vi toh8rr rkh0/ acb2/,/s 6ore the two satellite's speeds.

  A person is standing on a scale in an elevator acceleratfb:6e) vxe+ u0xkt+lxtpzng ,5c, h0ting downward. Compare the reading on the sca0,x ex,+tv 5tczkfgex+ p0n:ubl)h6t le to the person's true weight.

  Who was the first person to realize that the planets move in ellippvse, (sn ee /mnp6a-3tical paths around the Sun/ s -nen(v ,pspame36e?

  The speed of Halley's Comet, while traveling g// kr/5r0f km b2r-a(ybrkslin its elliptical orbit around the Sk2gf l(//a mbyr -brr/ 5k0srkun,

  Let the average orbital radius of a planet be R. Lez-fip 7z h,m8bt the orbital period be T. What quantity is constant for-hzf7,zbi m8p all planets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxy Andb/0))f,s ieka g.rlspromeda, with the same orbital diameter as the Earth around our Sun. If that star f .ae 0pgsb,ilk)s/)r 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 period?

  The average distance from the Earth to the Sun is defined as one "ast+1ab qm/9rb-t shr7gug*( sz 5mcm 5ihronomical unit" (AU). An ast5/ab qmmr1bch+59 ih*( sz u7gmtgr-seroid orbits the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.h ea:xv(1ruy2

  List the four fundamentkk fcz l9,b*;v,:9z -9owx (mppdebgfal forces in nature.

  An object moves with a constant spee8y li 74)rezued of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object?7rlezye) 4 iu8

  The maximum speed around a level curve is 30.0 km/h. Wh7zhhk :dg0m8 bka *8mxat is the maximum speed around a curve with twice the radius? (Assume all other factors remain unchanged.7 *xmam :8h 0kg8hkbdz)

  What is the centripetal acceleration of a point on 8 9x kii9xitik9em itr,*s(i.the perimeter of a bicycle wheel of diameter 70 cm when the bike is moving 8.i isk. ii,xm98 iix99t(kt*r e0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m from the axis. Wvq( dlsq m( 2;3f-kjsvhat is the cent( kvq2fq sm3-;lsj (vdripetal acceleration?

  How many revolutions per minute musjw* )jiyktf4oa;o8 o)eb7 6 wnt a circular, rotating space station of radius 1000 m rotate to4jwikt;yooa)e j)6 f w8o7nb* produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes 7wzh9om w;5wjaround a 13.7 m radius turn at 96.5 kmz5m;wjow7hw 9/h. 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 is whirm z99h7 f8xwtj /akwd:led in a horizontal circular path. If the maximum tension that the string can withstand is 350 N. Whatm:xd7 f 899h a/ktwjwz is the maximum speed of the mass if the string is not to break?

  A stone, of mass m, is attached to a strong string a9 qh7e9w+g2eyvw,ribtltf .7(j p nh-i: 9ue and whirled in a vertical circle of radius r. At the exact top tyegn +9jiww-heu2rh f(.q, ia vt9e:9p7 l7bof 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, irdk5q6kqd 9c9s attached to a strong string and whirled in a vertical circle of radius r. At the exact bottom of the path the teqd6 dk9r9q kc5nsion 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 sw d wnsx*-d2+23oxsoacceleration of 4g when pulling out of the dive. What is the radiuo+oxd s-wxwd 2sns2 *3s of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which the center of the loop+i))k 22rpgii8 qjwom is beneath him) of radius 3200 m. At the top of his loop o wji+i)8igqkr)2 pm2he is pushing down 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 times his weight. Whgk sc+ xuq1*a1at is the minimum radius of curvature that a jet plane's pilot, pulling out of ax u1qs*c+1kag 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 th -bh.6 vci1 m,:qnz7p zfqc)vhe tires on the verge of slipping. How fast can this car round a second curve of radius 320 m? (Assume the same coefficien nz hvh1bv7,) :qp-cz6cfiqm.t of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 50 lr)q+m- m4ezbtkkjn m4s00n 5m with a speed of 20 m/s. The centripetal force providjbl0s5 m+04k-n 4kqze tmmrn) ed by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve of radu+-3i c59jmma bsjo u8ius 50 m at a speed of 14 m/s. What must be the minimum coefficient of friction betcjbao 9 iu+-3 s8um5mjween the tires and the road for the car to make the turn?

  A car is moving with a constant speed v apj9 (p,vym 9xfround a level curve. The coefficient of friction between the tires and the road is 0.40. What is xp (j,m9p vyf9the minimum radius of the curve if the car is to stay on the road?

  What minimum banking angle is required for an Olympic be2bu h.emcn./ obsled to negotiate a 100-m radius turn at 35 m/s withouth/ bue m2..cne skidding? (Ignore friction.)

  A horizontal curve on a bobsled runmlc/ furhesa *( y(3*p 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, banked at ur;;ps/ z s c7mfd,8tpan angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bankedy/dh . kzl;6ic 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 stringfd5ujmo pljtna: d2gp.9. s-0 is revolving uniformly in a horizontal circa-5j9futopd..:g m0 dlp2n j sle 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 areda-4x qcv0qe)ps h k0y t11wy)a, a race car accelerates at a uniform rate to a 1p1e yh0sc ykaxwv) -q0q4dt) 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)
(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 manhhxdko4 gwmmed762.a( y5t w os 7urdj 4e*/7ss $1.67 \times 10^{-27} \; kg$ 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 p ggnkol+ 07f3q0gy3juc hb.7person standing on the Earth, due to tho0 cjb h3yg.kf 3uglg+ 7qpn70e 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 betweek7; czr6rucd.i ex nsm /xn1(5n two masses is F. If the masses are moved to half of their initial distance, what is the gravitational ad.6zxs 7c1xemu(nr;kir5 cn / ttractive force?

  For a spacecraft going from the Earth toward the Sun, atbxw 31uui u 1ip ;pv+bvt9+yzkige)84 what distance from the Earth will the gravitational forces due to they1 utxb3i9 i)+u8gzvp4kp eu;+ w1b vi 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 lz7 15n-snyyh is $7.4 \times 10^{22} \; kg$ 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 el3wc)zbe8kun 3vw.) ;;jxmwalk" at a distance above the Earth equal to the radius of the Earth. What is her acceleration w8zljn; ) e3)wcm3 ;k. vxbweudue to gravity?

  The radius of the Earth is R. At what distance above the Earth's stfxo2k /ce+l*n)x) g curface will the acceleration oc )ktcxl o)g/e+x2n f*f gravity be $4.9 \; m/s^2$?

  A satellite encircles Maeks2l, v fsh)b+ :/epoz0/cvyrs at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of lhzvbse,+pk:/v) o y0s 2f/ecthe 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 acceleration of gravibx-w7k)+s3 hlq)cvv5 yvu8 sbty v+58suc)-svhb y x3) vbkq l7wis $32 \; m/s^2$. 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 Eajffx26 jok): lrth has radius r. If the object is raised to a height of 3r above the Earth's surface, what is its wj26f f:)ojk xleight?

  By how many newtons does the weight of a 100-kg pers9za/ milkj6jktsk7s4;2g p . son change when he goes from sea level to an altitude ofzps 4;/t.j7l 9a ki2sgk6jsmk 5000 m? (The 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 abo. 5gewcay+b;x ve the Earth's surface. What is the satellite's wei;bex.wc y ga5+ght?

  A spherically symmetric planet has four times the Earth's+ul/tezvp::sj ,gs 8 e mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it /s+jeusg v,le:: p8ztweigh on the surface of this planet?

  During a lunar eclipse, the Moon,d8kjc xe 2:qz4f+de4/c:i gfl Earth, and Sun all lie on the same line, with the Earth between the Moon and the Sun. Th:ie/f8 +4 eg24kjfdq xlc:zdc e 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 Moonf5-4zpuh 2 dea.
(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 aboutut;6p5elnodtk85ln5m4) w ut the Earth (i.e., it just skims the surface of the Earth). What is the );on6u5wttnk8ld m55 ept4 luspeed 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 skims the4 *sp/ri8 cubj surface of the Earth). How long does it take to make one revolution around the Earth? (The mean radius of the Earth i/ pj bsciu*48rs $6.38 \times 10^{6} \; m$.)

  A satellite is in circular7 -gqg egt)ktw8w:oc *yskkk// d mz16 orbit 230 km above the surface of the Earth. It is observed to have a period of 89 min. Whzkkk g)c6t71t*ym:-d /s8kgwog/ eqwat is the mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, 9hb-dse kak)+ 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 radl ., mcj92qfttius 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 oz3nyb+ a bj2-drbits. Moon A has orbital radius r, and ybnd+-bza 2j3moon B has orbital 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 f/)f)t m* a5nmnk)p f:h(nmch g,l5za$7.78 \times 10^{11} \; m$ 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 or/o:nsba0 fj d9.yxx7o bit the Sun once. What is the average distance from Jupiter tfo.s09xxnaob /j:7y do the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)