Is it possible for an object moving with a constant speed to au6ecjk ox inr4;l+9 1fccelerate? Explai6+l n9fu 4ic;ekjor1xn.

  Consider a particle moving with constant speed such *l .io(1:ew.vx fjubfz k* 8ixt4yke 3that its acceleration of constant magnitude is always perpendicular to its velocite : (v xf*b*..koz 8i1ufwex4tkjy3ily.

  An object moves in a circular path at a constant speed. Compare the direi99p0 a(efyal pk , y-stvw/m0ction of the object's velocity and accelemt90y,swka/y fapl-90p( e viration vectors.

  When an object experiences uniform circular motio0susyy01x-ml n j3 1 + 9zzen*shg2scvn, the direction of the acceleratiojm3gx*zuyeh09n-ss1y l + cznvs2s 0 1n is

  Consider a particle moving with constant speed such that its acceleratki pf163-;bm6lm kveiion of constant magnitude is always perpendicular to itblfmkvpim36 1;e-k6i s velocity.

  What type of acceleration 1 8-ume ey39(ikwz njor1 tf 6neyy:k(does an object moving with constant speed in a circular pai uer1jkyyk(19 6(3oe ym e:w 8-ntfznth experience?

  What force is needed to makeo8fmbpj +pl((pdx y 9- an object move in a circle?

  When an object experiences uniform circular motion, the direct bpp1 bk+ymuju3(ax4-ion of the net force ispa x-b+m 3 14bkjyp(uu

  A roller coaster car is on a track that forms a circular loop in the vertical pl8 lhbme-ms fkayj72/7c9 20p:zy1i ;cvj btvo ane. If the car is to just maintain contact with trb1v b- c9;vfm y27khp a7/lecs 0it8ojz2:jm yack 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 circul fmvlyg 3zp 333qnnk 8g)8nf,tar loop (radius = r) in the vertic3tnngz3f v k3,m)8qg fp8n3y lal plane. 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 u q6ih(pdd 4; ;tzu*fppntil it is going straight up. Just as the plane is (d;fpd*pp64 iqut;zh 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 c+j) d3gajbyr u21eji3urve 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 spee d4 8jnl.2f q)vq.aokdd v. Then it goes around the sam.d)jqdvloa .f42 n q8ke 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 time?

  A car goes around a curve of radius r at a constant speed v. Then it goes8v3qi9q c1i9vq 4tqca 8b0 pdd around a curve of radius 2r at speed 2v. What is the centrq cd49 bdqia3p q09ic88tqvv1ipetal force on the car as it goes around the second curve, compared to the first?

  A car of mass m goes arouq/ zv+my a aqvfk9+cv2gt3- 1 ;gv/itfnd a banked curve of radius r with speed v. If the road is frictionless due to ice, the tav+ vfy1/-3 v92m q/cf;gkt aqizg +vcar 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 banwxwp5w,ou, xghy y)p:v *0 p+cked 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 sm ,5wph:owv py gu *y+),0xxcpwaller 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 notgpl5n9fj.e 6 i;y-lkutp :m7;fmwux. 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. Why do they do thf;igkp6 uly7n: - j 9..pf5x emtmulw;is?

  Is it possible for an object moving around a circular path to have bo hhvetbg6nn,m4)9n n+ th centripetal and tangential an)th ehvmngbn 9n6+,4cceleration?

  The gravitational force between two objects is proportional tok:lazvn 27.+ egm5a xw

  The gravitational force between two :5y- m;pjndy.wxr oa7objects is inversely proportional to

  Two objects attract each other gravitationally. If the di+mxwj+:jvkqv hyd+: 6o 3 saar1 pl2:dstance between their centers is cut in half, the gravitationayskjva+32:d :wqj1+r 6x:lh vdo+pmal force

  Two objects, with masselc,jpn*g77)1 zrbb we s $m_{1}$ 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 masses*e,e ft1r 87gb3ixkrs $m_{1}$ 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 universalls83nf 4iebxh *65nbh i 3ay)w gravitation.

  Compared to its mass oj5zw 5l (8-n vtje39d-t.zlb y toda,zn the Earth, the mass of an object on the Moon is

  The acceleration of gravity on the Moon is one-sixth what it is on Earth.w+ct4 +q xmcx6cs7oo. b;(m fq An object o;scc .bm+4oqc w6mxox +t7(qff mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from thfhcwdr t uz+;9u-j h r*.fvql8/w9hi7e Earth's surface, the rocket's weight

  A spaceship is traveling to the Moon. At whp bvfa gs6t;5ib4mc9*at point is it beyond the pull of Earth's gravi*ftbc;5i6m4b a9v psgty?

  Suppose a satellite were orbiting the Eart b4:. aox0f8a.wxibka h just above the surface. What is its centripetal accelerationo:kf 4x8.wa x. a0ibba?

  A hypothetical planet has a mass of half tha7f uv.8fiaf cs.ye6, y;vyjei 0hy4 s*t of the Earth and a radius of twice that of the Earth. What is the accyfv;yh f *ysef.4y. i80cu ji,as7v6 eeleration 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 ;:s lhnrt f-18r 4xscxone-sixth what it is on Earth. The radius of the Moon if lr c-;1hx:ss4txr n8s 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 has tw+ mw;r(8jnn.pm m4vp c:afo9iice the radius of planet A. If planet A has mass m, what is the mass of planmnmj9r+4 ; mipo cwnv( af:p8.et B?

  Two planets have the same surface gravity, but planet B has twice9 vso2cwk/y7)e9 mqo qvs0lw- the mass of planet A.9e90c mlw /oq7 osv)k q-v2swy If planet A has radius r, what is the radius of planet B?

  Consider a small satelld yq9/xuww(gb-84 ujuite moving in a circular orbit (radius r) about a spherical planet (mass M). Which expre- wu8x9wgy4ubuqj(d /ssion gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and , n nk75unxh6irotates in the same orbit. Compare the two sankihnu,6n75x tellite's speeds.

  A person is standing on a scale in an elevator accelerating downward. Comparm l61hl u 7c.ouvou,y/e the reading on the scale to the person's true weight.71 ylu,mo6ohl.uv cu/

  Who was the first per-u 0ld l3ze(akson to realize that the planets move in elliptical paths aroud-lu al0k z(3end the Sun?

  The speed of Halley's C1/opm1 kxw dx+omet, while traveling in its elliptical orbit around the 1 +ow/k1xxdpmSun,

  Let the average orbital radius of a planet be R+io7387aglelhe l ;rxul 7d)h. Let the orbital period be T. What quantity is constant for all planets orbiting thag73xrh 7 hdel luo) ll+7;8iee Sun?

  A planet is discovered to orbit around a star in the galt3 68d w4wrbp-y-opwlaxy 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, coyt3o-wpr wbw- p d6l48mpared to the Earth's orbital period?

  The average distance from the Eart6/a* (kyme 31sa punrah to the Sun is defined as one "astronomical unr*aa3 s6uke(1am nyp /it" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.0(3lv;nts9pm4 l jbzp

  List the four fundamental forces in naturcpr*e t5ov/rfd8g 2,de.

  An object moves with a colq ,m79achkv5nstant speed of 30 m/s on a circular track of radius 150 m. What is ,q57hkva c9mlthe acceleration of the object?

  The maximum speed arou 92d9q *qeun8y70(a9athbj ykd-zwzynd a level curve is 30.0 km/h. What is the maximum speed around a curve wih7qy*d9kj89 a0qt-wyu ab2enzzd(y9 th twice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on the perimeter of ekco *6aev1l3m68tys66n ex w a bicycle wheel of diametery ex1movns6 w6e tae*83kc66l 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is l0 op n;e uq.)i,ji7jbnq/k4hq ocated 0.200 m from the axis. What is the centripetal acceler.0q n,b/j4jeipk;nohu )iqq 7ation?

  How many revolutions per minute must a circular, rotating space station of radl99v2dt kk wac5 0f3giius 1000 m rotate to produce an artificial dkfvc5gta 9 293i0kwlgravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes3 /gti odf9 *y1,ntpys around a 13.7 m radius turn at 96.5 km/h. What is the centripetal force on/ d9gif1ttp*3o yy,s n the motorcycle?

  A 0.50-kg mass is attached to t7q9-hi ev-0bhqf ll* ihe end of a 1.0-m string. The system is whirled in a horizontal circular path. If the maximum tension that -*0hqhvlfi97- b ielq 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 strong string and whizp+ ni7mj* qa3rled in a vertical circle of radius r. At the exact top of the path the tensio q*7mi3j+panzn 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 striag7y r.du f(k16 i4.j -kvgygvil1 b3fng 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 spfr.ifj vyb7 v4 1g1 (u6gyg -d3ik.klaeed at this point is given by

  A jet plane flying 600 m/s expelex6/r5ibex;mn*zkc: ,od v .riences an acceleration of 4g when pulling out of the dive. What is the radius of curvature of the loop in whxr6mivxez*;cn,5. /k :bleodich the plane is flying?

  A pilot makes an outside vertical loyw 8cy;e08/ rlnzeja5eoq6 +qop (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 of his normal weight. How f zy;r+jlow8 enae5q/e0 cqy68ast is he going?

  The maximum force a pilojxn ,0dv -fs1dt can stand is about seven times his weight. What is the minimum r x fs10ddnj-,vadius of curvature 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 curve with thjy8lq ;0g j ,6hbwz jwx-1(uwge tires on the verge of slipping. How fast can this car round a second curve of radius 320 m? (Assume the same coefficient of f6yjw( gx08 ujb hw-,1jgqz; wlriction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 50 m with a speed o gs2sjs:2 f2ief 20 m/s. The centripetal force2s 2gs iejs2:f provided by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curvfzk 81*:v6x/pl wy(h:0lxri m nrzs) oe of radius 50 m at a speed of 14 m/s. What must be the minimum zrl h:o1rxf/8nw(x: p*sizk )6l0myvcoefficient of friction between the tires and the road for the car to make the turn?

  A car is moving with a constant speed v around a level a+ lkwey, u*4xh/p ik.curve. The coefficient of friction between the tires and the road is 0.40. What is the minimum radius of thp xiauew l, *+4k/yhk.e curve if the car is to stay on the road?

  What minimum banking annv jawz0 12oxj ,08pa0wyooopz1,m(ugle is required for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s wiup1 ,o 2na1(wz,0jm 0ay z8wo0p ovoxjthout skidding? (Ignore friction.)

  A horizontal curve on7ias. :s m.qzn a bobsled run 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 radw9b )2f 2ojwl6haxag-2tqo- kius 100 m, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bb/xgw(1rvs; fw0ne-c anked 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 strinv-bzy,5 eof b0.6ihqf/f(g u pg is revolving uniformly in a horizontal circle of radius o hbf,vi. fgpe6bf /0y z-5q(u0.500
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 areavu9t91 8tflxj. *yhxg, a race car accelerates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular track of radius 500 m. (only fill1xlgj9 hfxt8ty v 9u.* 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 p7 kir5h0 7hbr9 ztkg xpz2v3o+roton 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 standir4be* wkn6nl 6ng on the Earth, due to the Moon? The mass of the M b*el6k6rnnw4 oon 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 theo69e1 bf3scu abe tzosi; l59/ masses are moved to half of their initial distance, what is thio5 tuf3b 1cbee9sl 69za ;s/oe gravitational attractive force?

  For a spacecraft going from the Earth toward the Sun, at what distanugl 0 je;cf- ;+d-m(xgnobd p-(odam8ce from the Earth will the gravo dp m80g -fe dan; (jm;-gu-o(clxbd+itational 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 isw73pwp e0w6,q)08qebz e bmbyvxj-yp,xh6 g( $7.4 \times 10^{22} \; kg$ 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 "spac3l; c,a ofn4p ,6 grc5yqpxpa9l 5xs0ke-walk" at a distance above the Earth equal to the radi6x5s alp, 5qak rfx4lyncp p;,30o9cgus of the Earth. What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance 1(. hr.2)fekydsb c hwabove the Earth's surface will the acceleration of gravr fds )ech..bh2 k1yw(ity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its surface equal to 3 times thtxm07 :n qfsl:e n t7mfsx:q:l 0radius of Mars. The 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 some planet's center, the au7- xh rgp4hbib30; oacceleration of gravity is3riga ;0p4xo-ubbh h7 $32 \; m/s^2$. 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 radni)enj(5ql :q, 9mlj+ebdkmk k( p2/aius r. If the object is raised to a height of 3r above the Earth's surface, what is itsm :ej9k5iqbqdnel(/) kl ,kpaj2( m+n weight?

  By how many newtons does rc5jze6q 8o1 lthe weight of a 100-kg person change when he goes from sea e5q1 8olrj6zc level to an altitude of 5000 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r.v, zvwbr *g*s6is+3dz A satellite of mass 100 kg is at a point 3r above the Earth's surface. What is the satb+ dviz6s v3*z, *gwsrellite's weight?

  A spherically symmetric planet has four times the Earth's mass and twi/medt*leo0 o3 (xp*dc; tgj s:ce its radius. If a jar of peanut butter weighs 12 N tj sdgdoep/ *l0;(3toxe:cm * 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 sa7 fa.76xg byyifzcx-: me line, with the Ea-: yg f.c6i7ayx bzx7frth 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 tom,m gytqa2 7z6+ f+9biz vjb6r 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 orbitw*y/ gn0q: har+nqac. a4)mpv about the Earth (i.e., it just skims the surface of the Earth). What a .: 0nqway4 n/hcvmgr q)+ap*is the speed of the satellite? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit abkgx1rt u g9gc)-x3rcepw3t8 8out the Earth (i.e., it just skims the surface ofxw 8r19cx p) eug gctr-8kg33t the Earth). How long does it take 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 *5jqs 6,1qt s y kge+vnywyegn4em0cp///y9athe surface of the Earth. It is observed to have a period of 89 minksqycyny9 eqat 4eeysn0+j gv5*,/ 6pg/wm/1. 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 orbitai::s qkw fy7wi;r j5*el 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 Jupiz-ykh jie;k0w*k3 nk vy*-kt 7ter 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 nearly circular orbits. Moonuj uzvj; h-c88/jq.3fhpkk j.ow(7apy;co n + A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orkhnca-owz/. ; (v chj7k+8u 8f;jjqpu.o jpy3bit. How long does it take moon B to complete an orbit?

  The planet Jupiter is + c.yt;cz wk1sap4ff)$7.78 \times 10^{11} \; m$ 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. Whatfs5 kuj: mp*p9 is the average distance from Jup 9*psfupj:5kmiter to the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)