Is it possible for an objec);;qxiw8w-lg lq:( sg;mnquo t moving with a constant speed to accelerate? Explainql;l mu:n(;wg-;wsxgqi )q o8 .

  Consider a particle moving with constant speed such that its acceleration of / jwrxx3j(x/q constant magnitude is always perpendicwxr 3// (jjqxxular to its velocity.

  An object moves in a cimv ,4cbcy;6au rcular path at a constant speed. Compare the direction of the objectycm;6vuba , 4c's velocity and acceleration vectors.

  When an object experiences uniform circular motion, the direct- ttnz cpv/9o.4 oze: *ibkgzir tk+6;ion of the acceleratiorei t+9 ;z:-4*.kzoz/bk pt 6otnvcign is

  Consider a particle moving with constant speed such that its acc2nsh)zq h)xfli8 ena. jd4 8o3eleration of constant magnitude is alwa qi23fx s)n 4nhle8djoah)z 8.ys perpendicular to its velocity.

  What type of acceleration does an object moving with constant speed in a .9)9jexwnw l 5 +cxczucircularlcc9uw 59.z+xw)e xjn path experience?

  What force is needed e*-x4molsp* t to make an object move in a circle?

  When an object experienceh f.svs4xex4xgu1v3 ;u/ aqv9s uniform circular motion, the direction of the net force is3 4u.g9/u; x1vvefhaxx s vqs4

  A roller coaster car is on a track tvh 3ned9 csu,17 j:zg:fj a;gnmr5dg)hat forms a circular loop in the vertical plane. If the car is to just maintain contact with track at the top ofj ,m :zchvjsn ;9f gd:ng1g75 d3e)rua 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 (radipe f(f7o)u7 p w0.jbwmus = r) in the vertical plane. If the car is to just maintain contact with the track at the (p.7pboj)f 7um w0 fewtop of the loop, what is the minimum value for its speed at that point?

  A pilot executes a vertical dive then follows a semi-cirzhb 1cbv*5e;) sc aj,tnji+ 5zcular arc until it is going straight up. Just as the;5i*etb)jc,nzj b a+sv h1c5z 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 curz+k:8(uol ig5g gik 0wve 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 ; a8p20)amnykkf liv;7+rudthn76t i goes around the same curve at half of the original speed. What i tnf+y)i;82t0i dr anvl77;makkp 6 hus 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 rk9;ewe-fyl3 ggq r2yyj0;3s 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 a;; y2g3- l g0rqswkrj3ye9 fyeround the second curve, compared to the first?

  A car of mass m goes around a banked curve of radius r with spe2nont+zpiv,(x7 taw3 wf.. q qau)5noed v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal component oftno)atq7n3owfu5+q nix(wa ,z.. p 2v the normal force on the car from the road is equal in magnitude to

  Two horizontal curves on a bobsleu.lm/mnwh1x 5 .h wyv/yll1 p)2jum;ed run are banked at the same angle, but one has twice the radius of the other. The safe speed (no frm )hm2xyhe;v// 5w .nujlm. lwlpuy11 iction 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, but in)n0;f(nyk/ xqn9u8x caisa/ ncreases upward from the horizontal. Coming around a turn, the bobsled cn(q /n;sk8/ u ix)xan9fna0y 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 cenmn)+0i4kl b0x rdfl: ytripetal and tangential accelekdni: )yb0l4m 0+flr xration?

  The gravitational force between two objects is proportional t3.7zq gkl;psp o

  The gravitational force between two objects is i/ )tugcm3c /uknversely proportional to

  Two objects attract each other gravvtae d);6+ddbggt+jor814 d iitationally. If the distance between their centers is cuj8d t+aib6r gov1tg4 edd;+) dt in half, the gravitational force

  Two objects, with mashjnia)a55w x vii/vv;+ ms(,y ses $m_{1}$ 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 mabo;slkwgc.hl/yc /4h:ja (, ksses $m_{1}$ 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 z.+uyqa0ek)o;eeus v :m9+flzsx/1o universal gravitation.

  Compared to its mass on the Earth, the mass of anweq:i5 ;c)r ct object on the Moon is

  The acceleration of gravity on the Moon is one-siyvzh eddt2c12 q q2.m6xth what it is on Earth. An object of2hezmq.6 2 dv2tyd q1c mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's shidg n1vqp,w3 (/)/c j:lmfnfurface, the rocket's weight

  A spaceship is traveling to the Moon. At what poinbe 6bji- g bb2n0 8rxuhnm8t.;t is it beyond the pull of Eatr;6gb bb ne2.-8nb0mx8hjuirth's gravity?

  Suppose a satellite were orbiting the Earth just -mu6ez2jf-:fpuo pfaydcx/9 q.*r (eabove the surface. What is its centripetal acceleratio u-rdz2af:f qfe mj-pc/.6* (xe9y puon?

  A hypothetical planet has a mass of half that of the Earth and a radius ofg3(fehtc3atetcr/+p0x/9l,d( 9 4 xw o m tetp twice that ofxd3tt /(9epfwt4ch0 gtxtor3le+,/m ec p(9a the Earth. 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 Moon is one-sixth what it hf onr5nmv/di4:yq2 660 x5dgu-td uris on Earth. The ru-xdn dnu26vohfg/qm64r:tyd i r550 adius 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 ve xc q(n+g pa6a.pc;0surface gravity, but planet B has twice the radius of p+ 6pna xap .e0(vqg;cclanet A. If planet A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, butm9krhzb-mkkxpxhp 0 d 0:t.1* planet B has twice the mass of planet A. If ppkx:kzbpmh xd.m1rk *h00 9t -lanet A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit*-pq36g 8oqmed6q c im (radius r) about a spherical planet (mass M). Which expression gives this satellite's orbital velocityi6dmmqgec o8 q-p*q6 3?

  Satellite A has twice b 7a*wphhu:3rthe mass of satellite B, and rotates in the same orbit. Compare thewhh3:* p7arub two satellite's speeds.

  A person is standing on a scale in an elevator accelerating downward. Compapgy(-v h h:ed6(d 2znmre the reading on the scale to th h2 -6z(pvm:( yndhgdee person's true weight.

  Who was the first person to realize that the planets move in elli fhb9: nsjw; i1/)ic8l,itayhptical paths around twfbicihjh i1,:t/a8)yn9l; s he Sun?

  The speed of Halley's Comet, while traveling in its elliptical orbit around wbmru1f0h5 m* 44q-kjyho e+c7lsc7 k the Sun,5em*4fj c7kc71kyhlmh q0-u+br4s w o

  Let the average orbital radius of a planet be R. Let 1d6(r mjkwy(g the orbital period be T. What quantity is r( 61y kmdwgj(constant for all planets orbiting the Sun?

  A planet is discovered to orbit around a sta0+mm p*6 ;8erskiah4bo1j ajir 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, csr;10ai4ka+mbi*mjjp h8 o6 eompared to the Earth's orbital period?

  The average distance frd m5vm:ozq+ y 8dl(f,oom the Earth to the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun mz,58 ymodof v :l(+qdin one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.,dnf0iysa8p qap k10;:- im nu

  List the four fundame9+;qqvadza *sntal forces in nature.

  An object moves with a constant speed of 30 m/s on a circular track ps-ag.r sowi9)b6j :f of radius 150 m. What .gwf6saorbp ):j - i9sis the acceleration of the object?

  The maximum speed around a level curve-4b;kihzt .4q p, vdee is 30.0 km/h. What is the maximum speed around a curve with ;i kh,ebe dq4pz4.-tv twice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on the perim r-fz0*zkg9ly.st 3y+ yzayr2eter of a bicycle wheel of diameter 70 cm when the bike is moly2t s+ry -f yyzk*z3.g09 arzving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m yz x /wa1ah(p7aydl jer)l5h*. xgn,1from the axis. What is the centripetalw)* llze/r11ygha a,x5xy.hp n j( 7ad acceleration?

  How many revolutions per minute must a cpev+pmwe n;p-z yrj9,j7 0b m3m iwd*,ircular, rotating space station of radius 1000 m roe7db mnvpyr0pw p;3j i,z*e9,mj w+m-tate to produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 o2*jils0 .k d (0gqmagkg. It goes around a 13.7 m radius turn at 96.5 km/h. What is the centripetal force on the motg0olqi* ms0(k dg.ja2orcycle?

  A 0.50-kg mass is attach3e+pd a nb/ v;tx6vz7qed 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 madv67ezv3b n+t ;/paxq ximum speed of the mass if the string is not to break?

  A stone, of mass m, is attached to a strong string zd s4)l 1+/2ibxregftand whirled in a vertical circle of radius r. At the exact top of the path the tension in the string is 3 times the s2tr e+zbigl4fx s /1)dtone's weight. The stone's speed at this point is given by

  A stone, of mass m, is attached to a strong str9;8m.noh6llq1r voo t ing 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's weight. The stone's speed at this point is ot.nohrvqlm9o6l ;81given by

  A jet plane flying 600 m/s experiences an *0ujw s (/iev3z r;h)yyt0abbacceleration of 4g when pulling out of thuvtw/*y)i;(ej3az0 brsb0 h ye dive. What is the radius of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which throidgf qq7 -aw 39my73e center of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down on r9df733 gqi7-aqwoym his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pizigte/)2q4s o lot can stand is about seven times his weight. What is the minimum radius of t4/2ge sq) izocurvature 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 horizontal curv:npq,-3 vqo zm //uiyje with the tires on the 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 tir/pyn q,u3 im- :zqjo/ves and each road surface.)

  A car is negotiating a flat curve of radius 50 m with a speed of 20 m/s.q xa 1tvqptd8(0v) m+d The centripetal fort+p01v8qx v ma(dq)tdce 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 rayp,at.hz9f0 kt4 ul)odius 50 m at a speed of 14 m/s. What must be the minimum coefficient of friction between the tires and the road for the ca. h zo)k,aftl94pu0ytr to make the turn?

  A car is moving with a constant speed v around a level curve. Tx rquy0 ;:+-r bsqtbt1he coefficient ory1q-bqt t+u b0r:s; xf 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?

  What minimum banking angle is required for an Olympic b;ac+ij6g lb,zyv-b(2 hdzdl .obsled to negotiate a 100-m radius turn at 35 m/s wij-ih d 6g+zld ,bcbzl2( v;y.athout skidding? (Ignore friction.)

  A horizontal curve on a bobsled run is banked at a8ow(8e/ zsxxn $45^{\circ}$ 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, ba( ct- ,w :vhppib4 )p*ytu:vn*dzzyw7nked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is banked at *;u(i 8lb-rtyo)vpu k7c bv6a$45^{\circ}$. 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 revolving uniformlyc 7*,iqz-por vpm)lw2 in a horizontal circle of radius 0qc)w2*oppr ,ml7iz v-.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 rat rfc9jx v1y;s 4hwy9o7e to a speed of 45 m/s7yx9 rowc s9 ;41jvhfy 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 proxpwa:5 waq:97ms tzh:x (co 9vio// zston 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 person standing c3,xu+0 u,dp 5z7ce x 5o6vhki lyz7xlon the Earth, due to t5x7 5 vlhoe,3iy+,u0lzu c6cdk7zxxphe 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 masses is F. If the masse u(6h )3ohoui;++qotqpw sng6 s are moved to h;gn( uo)w+qs u6t+3oqo6iphhalf of their initial distance, what is the gravitational attractive force?

  For a spacecraft going frss/+( wm egm7rom the Earth toward the Sun, at what distance from the Earth will the gravitationals+srm /ewg( m7 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 4 fqqn:,z5bvp1mu1ug 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-wae4)ao5dn/mgsjo (aw7g l+u1d lk" at a distance above the Earth equal to the radius of the Earth. What is her acceleration md s 5ue 4n( w+1dla)j/oago7gdue to gravity?

  The radius of the Earth is R. At what dic (wc1jn 2wvj)zy* kz/stance above the Earth's surface will the acceleratiy(cvc2zj /j)n1 k*z wwon of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above i jm)x:lcw)i 6mrj-4j.j7j yj fts surface equal to 3 times the radius of Mars. The acceleration of gravity of the sa.jjflw-) j6:j xrmmjc jy74)itellite, 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 5 pdo);-up uckof gravity op -u5duc;)pk 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 has r5y5 5rwpumyt+fdq vzyp *2g8 +adius r. If the object is raised to a height of 3r above the Earth's surface, what is its wq55wu+ y+t5rvpg ymf p *ydz82eight?

  By how many newtons does the weight od fxhdbvn c);5t ti)fc oxe+ t;.r*g,4f a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radi v;b4dtndr.)fteih*g5 , +txc) xof;cus of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is amvc6 7eu 6*fc/i1/is z9rvik. ti2cxht a point 3r above the Earth's surfac17*2 /rc9.kxi/6cszii h fi6 e vuvtmce. What is the satellite's weight?

  A spherically symmetric planet has four times the Earth's mass and t7qak+)edni *c wice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, ki*)+7nc dqeahow much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, 7/s(ohwv4g7jy rm q8 6*zw mijand Sun all lie on the same line, with thwiv/ w7 4oy6zsj8g(jqmh *r7m e Earth between 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 transported to the Moon.4w8usww ;vz4w
(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 aboutx,3v(gwpjpck 6,nt3e the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radius of the E, kp3 j6e,cnwg3(vtxparth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular8gf/ba8 qt o+s orbit about the Earth (i.e., it just skims the surface of the Earth). How long does it take to make one rab/so8g q+ tf8evolution 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 Earth.y 2o x)r+of)sy It is observed to have a period of 89 min. What is the mass of the Earth? (The mean radius of to+y)rso)yf x 2he Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an orbital d khh 0sajr42he,6bgeh/6nn.u,-gr euiameter of $1.34 \times 10^{9} \; m$, and a period of 3.55 days. What is the mass of Jupiter?

  The innermost moon of Jupitery/x otckg5k bi/dp+1b 3;nw:cv r l1o/ orbits the planet 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 nearl-0m,-d tiz g7us6nvz ey circular orbits. Moon A has orbital radius r, and moon B has orv e--u 7s,m6zz0nigdtbital 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 isp42kgwydgee s,9w;f / $7.78 \times 10^{11} \; m$ 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. Wh bqjf u,d5x2h5at is the average distance from Jupiter to the Sun? (The distance from the Earth to the Sun is2 f5 hjqbu,5dx $1.5 \times 10^{11} \; m$.)