Is it possible for an object moving with a constant speed to acceleratebg:p hiu( s +p;awhp0.? Explain.gahp;u pb0p(w i:+ sh.

  Consider a particle moving with constant speed such that its acceleratio.14wbm7bb r f/ neh(n) 2zmsag 74muyin of constant magnit 4b.(nm17ahbm 4 b2f i)syngz/e urw7mude is always perpendicular to its velocity.

  An object moves in a circular path at a constant speed. Compare the direction) /d)zlao gc1mxzt -9h of the object's velocity and at/x 9 z zcoh-dla))1gmcceleration vectors.

  When an object experiences uniform circular motion, the ckm0bt-esid:q)j kb3jj 35m; direction of the accelerat3j35cem;tk0)jm bqk- b:jdi sion is

  Consider a particle moving wizqtlt5j y6+1hgrb+ p1th constant speed such that its acceleration of constant magnitude is always perpendicu6 r5j+1ptqy + bg1tzlhlar to its velocity.

  What type of acceleration does an object moving with (ir.c y0-ysivconstant speed in a circular path ex.yi (is-vc r0yperience?

  What force is needed to make an obnv(hqfij*bi*mstqn0q: vp r:4*(o )iject move in a circle?

  When an object experiences uniform circular motioz4vzax wl/6wvm4d *c9gfi42sjik(; on, the direction of the net for4s v(wdw zo /4;kaj4xm6 vicizg2fl9* ce is

  A roller coaster car i)u3o2v k + uhc5c*ijiomm(pg0s on a track that forms a circular loop in the vertical plane. If the car is to just maintain contact with track at the top of the loop, what is the minimum vo c uc5(u30g2ip*jommhvi +)k alue for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a track that forms a circular loop (ra6f gspkexm lu,n,tbj;1: 0bp769h yasdius = r) in the vertical plane. yjtk 7;x6 ef n9s6lg,0,ab1h: pmpsub 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 digs)ys) 1til. d2ab:xeve then follows a semi-circular arc until it is going straight up .s)2g 1ti:adb)y exsl. 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 c lg/)qnct79 v a3ym)mgurve 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 kf+l.7qo)vufu c j5-h figm)/a constant speed v. Then it goes around the same curve at half of the original speed. -ufg) . o jhf+ 5flmqc7/)vkui 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 cufta i-/bi*0ykrve of radius r at a constant speed v. Then it goes around a curve of radius 2r at spk fbti0a y-*i/eed 2v. What is the centripetal force on the car as it goes around the second curve, compared to the first?

  A car of mass m goes around a banked curve of radius r with speedh3xs/ ic,;4f dv khtqjwf33 m:0+e enx v. If the road is frictionless due to ice, the car t,m 3q;ek3 3c:vsh0xwni+d fj/ f xe4hcan 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 angle, y:k2(v h yel ny:12;yf*+ odsfrko -tjbut one has twice the radius of the other. The safe speed (no friction needed to stay on the run) for the y tnfo(r o ;l:y2*kdvs1y+h-:fe2kjy 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 injicr w ..qs;5xcreases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "climb the wall,r.; c js.i5xwq" then go lower coming out of the turn. Why do they do this?

  Is it possible for an object moving around a circular path )lif ,3w yfvd9to have both centripeta3w,ffi)dl 9yvl and tangential acceleration?

  The gravitational force between two objects is proportionali8p sgl*aw;;:o/m t e7ne/p yv to

  The gravitational force between two 34uhooxft u 7p *zrh(0objects is inversely proportional to

  Two objects attract each other gravitationally. If t j3rah9s,n cblwak7)tk s00i)br2+ tvhe distance between their centers is cranv 2lha+swktrbstb07i j03k, 9 c)) ut in half, the gravitational force

  Two objects, with masses66r wsw(f k;qz z,xwp:xkr g70 $m_{1}$ 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 matmtz 9hla* q1:sses $m_{1}$ 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 gravitation.x wpc: ( 6rvzgrw36 ck,am,8kx

  Compared to its mass on the Earth, the mass of an obus i ;sq0ddorg6.:x g(ject on the Moon is

  The acceleration of gravity on the Moon is one-sixth what it is:chw m(hvlg,6vu u ;hysj4+;2el/ b/0q h omei on Earth. An objelv2b ;mlg4 oie cjmq /hh(e+;:y/0s6huw, vuhct of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, the ooo7 v,vt:r+t rocket's weight

  A spaceship is traveling to the Moon. Alrva f fl7wi,lr - wdsiuns9:b,((8,lqh4d u1t what point is it beyond the pull of Earth's gravity?4b 9u(il7,sl1fuw hr ,aln( lwi:q-rd 8 v,sdf

  Suppose a satellite were orbiting the Earth just above the f9,1visqxw:d bhc6 9r surface. What is its centripetal accelerati 9xsw9h1 v,rd6fb q:cion?

  A hypothetical planet has a mass of half that of the Eark+2hg d67 qvy,prd pj.th and a radius of twice that of the Earth. Wh pkddp+j2yq.g 6hr7v,at 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 is on Earth. q5rcr-/qj1pi 0r rld ,tbm :0z The radius of the Moon is one-fourth tb-lr:0pc51, jzmitr / 0rrd qqhat of the Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gravity, bbqi -0fkb:+i vr2i )msy0gy i3ut planet B has twice the radius of planetv iyq isy )bi0bmr-3+igf:k0 2 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 twice thedz.bnpr 6(sg; mass of planet A. If planet A has ;(ngs zp6brd. radius r, what is the radius of planet B?

  Consider a small satellehqz 8f4e3, ppite moving in a circular orbit (radius r) about a spherical planet (mass M). Which expression gives this satellite'3p4 zp8heefq, s orbital velocity?

  Satellite A has twice the mass of satellite B, and rotatq2 ;ce) 7lejt-qbmkg 6-ojj:oes in the same orbit. Compare the two sat7j b2l6 qo-;gkjm):et- jqceoellite's speeds.

  A person is standing on a scale in an elevator accelerating downward. Compare tr9iq -uzb wd;ldgk;9z1kt n;n39e:bt he re91 -twz;3drkbt ; 9bn ginzlkq;d ue:9ading on the scale to the person's true weight.

  Who was the first person to realize that the planets move in elliptaymn2e o ,xa/8y3)wyw4 yz+ vlical paths around the x on4mw)8w +yal,ze2a3yy /vySun?

  The speed of Halley's Comet, while traveling in its elliptical orbit/fnj u6dk dqw*mq;a:. around the Sun,;dqnj: u.a /*qk6d fmw

  Let the average orbital radius of a planet be R. Let the orbital period be T. k bsk+m3ge1vhj1b1e5cz4k- ; z y,em ib qek57What bzk7c, m gy4kezebqk31-bj5s1+ ;ev5 kehim1 quantity is constant for all planets orbiting the Sun?

  A planet is discovered to orbit around a star inj )aa(8*g1jrf wqu1g n the galaxy Andromeda, with the same orbital diameter as the Earth around our Sun. If that star has 4 times the mas)j8*afnw j g1u(1 gaqrs 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 tofb :la+ydv +omrhqg , :u3(vd1 the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the aste:v ,ubay :oq(hmd+flr3 1gv+droid's average distance from the Sun?

State Kepler's laws.zz(jvzph:(jdi uv(6 *

  List the four fundamental fqg vst 9n jama69k u+irm,k78pu4 *:ejorces in nature.

  An object moves with a constant spezurv. 1*yujqhb u8 7p,ed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the objb7uzq ,1 8*puhv .uyjrect?

  The maximum speed around a level curve jyba) l9r5zc:is 30.0 km/h. What is the maximum speed ab9yl5cj)a zr :round a curve with twice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal accelera0 eon v,fs:z+) xy,axmtion of a point on the perimeter of a bicycle wheel of diameter 70 cm when the bike is mo+0)yn:zxfx a,osvem,ving 8.0 m/s?

  A point on a wheel rotating at 5.00 revg t a+( w3r/(d8 wyv4vwjglu-w/s is located 0.200 m from the axis. What is the centripet-w+( utayv vj4 wrlwwg3d8 g(/al acceleration?

  How many revolutions per minute p3db,uvw*w*if 7 9mmol0o dj9must a circular, rotating space station of radius 1000 vd7u 3fwm9i0pd*m,j o*o wlb9m rotate 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 s b:8wx *y( s:b+krf- qmql2ivat 96.5 km/h. What is the centripetal force ovl8 k+*xsqwi-qr:: 2b(fm ybsn the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m string. The system is whdwce56+ o tumsv9i-b-g6y 7 ngirled in a horizontal circular path. If the maximum tension m 6 vg9 ted7c+-s6ugwnoyib5-that 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 whirled in a q(6r*tgb0zf 4lk dut+ vertical circle of radius r. At the exact top of the path the tension in the string is 3 times the stone's wrglb 4 tz0f(q+t*6dukeight. The stone's speed at this point is given by

  A stone, of mass m, is attached to a strong st 4v1 qt2v19 4 gw iozhhjny4u*aw5q.zrring and whirled in a vertical circle of radius r. At the exa4yh2q9 nvi4w t1a.1gw oz*u5hq jz4vr ct bottom of 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 jet plane flying 600 m/s experienw1vxzvg oi3)aos7lp -)tq,z8 ces an acceleration of 4g when pulling out of the dive. What is thzi o3-av)o,)qt1v8z7g lwpxs e radius of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop (in which the center of the loopx ;/oneg f0bijhyv(/pf m; 10d 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/d;nigmv(;hbjy / f 1x fp0eo0 normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven times his weighdxhib.2m. x5 4y0hztwt. What is the minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can bymz hh0.w52 idxtx.4 tolerate at a speed of 250 m/s?

  A car traveling 20 m/s rounds an 8 / mq:by7*2nojbp (gdn0-m radius horizontal curve with the tires on the verge of slipping. How fast can this car round a second curve of radius 320 m? (Assume the by:mg2p/onqbd j* n7(same coefficient of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 50 m wis u ,51 0krrfulwqhf-.th a speed of 20 m/s. The centripetal force provided by frictio , 1rwl qu5us-k0.rffhn 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 bac6u38;6yidjf: tja . nlgmm/ e t y.8jm;a lam36tfdgi :j c6u/nhe minimum coefficient 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 curve. Theyxs0a (nq- jyiz:*9zd coefficient of friction between the tires an nx0*yqz(da:9zsj yi- d 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 requiredi6v qe87qruf mq4+td* for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? (Ignore6v qdemq+fu78 q4rit * friction.)

  A horizontal curve on 8dlcqy csm6 o70e4 8xpa 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 radius 100 1cq0p,t kg(8hslfdob(w v:+ /ad g;v am, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is banked a5 5uvn0r)q+j4zns s tv38nx p1fbvh(mt $45^{\circ}$. 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 uno+f qy/ze f l:9y4dee3iformly in a horizontal circle eeqd f f3yzl e:9/+4yoof 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 uu3b+7gk5)nlhcl:e hx ( nt 2pzniform rate to a speed of 45 m/s in 15 s, m2lcz:ptk5g) 3h7n(xne+ bh l uoving 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 con i -,;key0iae6vjr6essists of a proton 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 stanzhy48. 5:jdir xfz5 fcding on the Earth, due to the Moon? The mass of the Moo.jd:zh4xrc zf58i5f y n 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 masses areb yu1/skodh*im 15 as7 moved to half of h/ ksoybm*u 57ia d11stheir initial distance, what is the gravitational attractive force?

  For a spacecraft going from the Earth toward the Sun, at what distanwv m;o3()x rjvqnzrs1wu*e5:ce from the Earthx3; er*nmsj)wv:r5wzuov 1 (q will 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 Moontzhqq3. qxp j72, l;gw 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 " wik 8w8-tjsz8space-walk" at a distance above the Earth equal to the88 8wktiwzjs - radius of the Earth. What is her acceleration due to gravity?

  The radius of the Earth is-mpu9 * fs)zsw: i a,m 4(rjwfgvsy(v8 R. At what distance above the Earth's surface will the accelerat pvysr*wm9-( 8g ,ifva ufs(): zjmw4sion of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars aqvpz(uv d jrlvn3 ,--.t a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on t 3q,u ldp.(-nrvz vv-jhe surface of Mars, is

  At a distance of 14000 km from some planet's center, the acceleraow,: 1xzhk 0uation of gravity is ox0,ua: h zk1w$32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on the surface 4) z.xab3mdp,1 ghmuuof the Earth. The Earth has radius r. If the obaxuhd m,.u1 b43zgp) mject is raised to a height of 3r above the Earth's surface, what is its weight?

  By how many newtons does the weight of a 1t93undl wqe0*3 onev;00-kg person change when he goes from sea level to an altitude of 5000 m? (The mean rad0v *qe93n3n ;udtewloius 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 aboveb67p6zh o;opw miw52 q the Earth's surface. What is 27pomz65 i6hoqbwpw; the satellite's weight?

  A spherically symmetric planet has four times the Earth's mass and tkc(kz4bnqg :4 we9wx 1wice its radius. If a jar of peanut bu( : z1wex94bqnkkgwc4tter 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 m2wicj7i 6w -dq3:wk7*pzx voline, with the Earth between the Moon and the Sun. The Moon has q276 pmwc*3vdi- wzw7jkx:ioa 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 .1fv; kbnc4nv transported 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.e., it jue u bhg04ocj(yg 6*zr0st skims the surface of the Earth). What is the speed of the satellbu*y0 o 0 zrcjgg(e4h6ite? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbip, jgrpa/ 5z:mz4cr 2vt about the Earth (i.e., it just skims the surface of the:z,vpma/4r jcz5 gr2p 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 the surface l/0* ghr27 lz4jwh 4xznssrk5of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (The mean radi*7nwk5gzhlsrhrx4s /j402l z us of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, ohdtwetz6 u 6(;x.iw0has 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-gs- t )yftdr+ 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 circu;ri1umk vb/bz0y ,6u3(dvgtc lar orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to cimtvb/,kzu1v3 urd;gy0 c6(b omplete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter i2g-w3 ;bhn a+we 6(zl7vkzcqv s $7.78 \times 10^{11} \; m$ 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 average 6s 58mekos2phzw0oc6 distance from Jupiter to the Sun? (The distance fromezwmos s02hpkc8o5 6 6 the Earth to the Sun is $1.5 \times 10^{11} \; m$.)