Is it possible for an object moving k)kyj r ca4vhcry z;+ )y7ba,+with a constant speed to accelerate? Explain.k byjac )yy7;zr+ a,crv4k )h+

  Consider a particle movi- mq tnjcm,48j50tuvdgoj 4 ;kng with constant speed such that its acceleration of constant magnitudetmkd8 j4ogmj- ;v4 c0tqu5jn, is always perpendicular to its velocity.

  An object moves in a circular path at a constantjro2e67pz+o-v9sz hybf c: s 4 speed. Compare the direction of the object's ysf2czh+-s:voo 9pjr 7eb4 6zvelocity and acceleration vectors.

  When an object experiem w,r9g8u)c0c 2oi *y(haobkcnces uniform circular motion, the direction of the acceleratia9() cgiy82whou 0o b,mc*kcr on is

  Consider a particle movj 9v;l(+rx6wpjju ,o g94dgbu ing with constant speed such that its acceleration of constant magnitu ,gjuov( 4;+p99bwdrx6jg jlude is always perpendicular to its velocity.

  What type of acceleration does an object moving with constant speed in a ;kdku7+; w1xu-g kwc+ 2edzhqcircular path experience k2; kd ++;xh7kucgq1w-ue dzw?

  What force is needed to make4xy 6jtjg3 ooji .ew3jky)t62 an object move in a circle?

  When an object experiences uniform circular motffn)zd3oti j cw8/n3i+)tdu: g h.l/nion, the direction of the net forc/ u)gdf.ni do+t /3fzncl wt):nhi3 8je is

  A roller coaster car is on a track7nq2nn/k33pa(anbqr xy hxm11n lt ,4 that forms a circular loop in the vertical plane. If the car is to just maintain contact with track at the top of tyn7t/m 3xr(nqa,4n anhlq2b3k x1n1p he 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 mhgytc o2 *-6dloop (radius = r) in the vertical plane. If the car is to yd2hot6cg-* m 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 j1*d.os 3nkb ufollows a semi-circular arc until it is going straight up. Just as the plaonu 3sb*1 jdk.ne 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 cur 9ej qp.p 4r4vfucqj:6ve 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 radiuafd .mojtj.u360 r-w( 5xk. j5ysniods r at a constant speed v. Then it goes around the same curve at half of the oridskuoa wdj.oyri x 5-0t (j5fjnm.36.ginal 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 edfz;,ntv)fn3,-n vz 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 secoe ffdt ,z3vnv-n;z ,)nnd curve, compared to the first?

  A car of mass m goes around a banked curve of radius r with speed v.2f. tw, :yd va;d7ut k gnj0v*hzpf/d. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the normal force on the car jafhy *0n,d;k 7v.gp.u/w z:fdt2d tvfrom the road is equal in magnitude to

  Two horizontal curves on a bobsled run are banked at the same angleu teu v9c2xwzy+m, - -fcs/j*v, 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 v. What is the s,u-t+ yw/xvc-2msvj9 uez*f cafe speed on the larger radius curve?

  The banking angle in a turn on thzjm; 9g f1 ot12xbcf+re Olympic bobsled track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will intenf+m91oc;1 xrbzft 2jgtionally "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 bomvt .cyzst/ )-th centripetal and tangentialm zvct.t)y- /s acceleration?

  The gravitational force betwisr 1(ig 3pxa/t(7m hteen two objects is proportional to

  The gravitational force between two objects is inversely p2ug*63jonki y-f v ho6roportional to

  Two objects attract each other gravitationally. If the dicm(jq ,w;:tdhs6n i0f stance between their centers qd6 i0h t,c;m(jns :wfis cut in half, the gravitational force

  Two objects, with massesowp/ bse;3jsk t(4a.b $m_{1}$ 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 maxwxu g:2* oau0sses $m_{1}$ 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 univewk ubq8igf(-)8g j d1ck3m;uwrsal gravitation.

  Compared to its mass on the Earth3s0qs;nmqz: p5i )7fq7vnyfx , the mass of an object on the Moon is

  The acceleration of gravity on the Moon is one-sipa iv,5ai *sym9+z gn1xth what it is on Earth. An object *+aizy gvp ism5a9n,1 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 rocket's wei:f mo78cju+ ofght

  A spaceship is traveling to the Moon. z tlmt 1cm/q)t18fn)em g22toAt what point is it beyond the pull of Earqg) 8ttoz1mntlm) t m22 e/f1cth's gravity?

  Suppose a satellite were orbiting the Ezp:nth9d idpo;8 g* 6jarth just above the surface. What is its cent*98 night pzdo6;j:dp ripetal acceleration?

  A hypothetical planet has a mass of half that of the Earth and a radiu7a /r ,gt) vt )/gwhplj8kg7txc(re. kd6q*hcs of twice that of the Earth.wgk,)e7r8c6g/tp rat xk(lj.*qc /g)hhv7 td 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-sixthwfm q+yn-7pb . what it is on Earth. The radius of the Moon is one-fourth that ofnp-7 bmqy.fw+ the Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gravu jnxux.pl)w9 vx(.s;ity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planxu(v9s pxxu ;)jw..nlet B?

  Two planets have the same surface gravity, but planetm0 lmu.gc5(4cx m*d ti B has twice the mass of planet Agtm(m. uxm5cl dc4 0*i. If planet A has radius r, what is the radius of planet B?

  Consider a small satell5w v6 *;i*hf:mpogqwa :bptw; ite moving in a circular orbit (radius r) about a spherical planet (mass M). Which expression givq w :bw;gma*w :th5fp6o i;*vpes this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and rotates in the same orbit.d-: +itbz l-f ysu7:kq Compare the two satellitds kz:blq +u-it -y7f:e's speeds.

  A person is standing on a scale in an elevator accelerating j8agq29ly(x 7ckrs+9-ay - uzllh8 qt downward. Compare the reading on the scale to the person's true rq2g-ljt 889+ syl79lzyq- (u aaxchk weight.

  Who was the first person vrsz- x5n-e)u:-9 azse.29jcej aof lto realize that the planets move in elliptical paths around the Su5-2 zefrcv.nee l:o)s 9asxz - u-jja9n?

  The speed of Halley's Comet, while traveling in its elliptf. ck/r4:lgohical orbit around the Sr.g /lohk cf4:un,

  Let the average orbital radius of a plane)vv n1 hmu)kx)t be R. Let the orbital period be T. What quantity is constant for all planets orbitin vn1u))hx)vk mg the Sun?

  A planet is discovered ry24;u isruv/k9ti+mz) 1 pmnto orbit around a star in the galaxy Andromeda, with the same orbital diameter asy9mt+;)vrmp i12 /kr u4uin zs 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, compared to the Earth's orbital period?

  The average distance from the Earth to the Sun4a lg wb 3han)y1x*f7b is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from theaw3 hyfgb n )*ab1lx47 Sun?

State Kepler's laws.m fqaj v z(1kva9n0wb5()fba /

  List the four fundamental forces in nt:slib9 g ; erhip226xature.

  An object moves with a constant speed of 30 m/s on a circular track of rz2mxwlo v.9)smz q9d 2pjt( z-adius 150 m. What is th dz( oxmw- 9 zlsqt)jv.9z22pme acceleration of the object?

  The maximum speed around a level curvu :ryjx y2(f q70y3u8koy5d ogkj5 xh.e is 30.0 km/h. What is the maximum speed around a curve with twice the jh35jgxf7o:y.k 0 8( 5yukuyyrq 2doxradius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration ofpp4j xr3e o22n a point on the perimeter of a bicycle wheel of diameter 70 cm when the bnpj 2ep3rx4 2oike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m ;z s4ae+a3lgpa7yx* lfrom the axis. What is *alpg+4; e7yas l3z xathe centripetal acceleration?

  How many revolutions per minute must a circular, rotating space stat+0t,uoe bidh y-:+z )n)jpzphion of radius 1000 m pbizehz+hj:o py tun ) 0-+)d,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 at 96k hah(. 0tx4tg.5 km/h.tt4ahk0h (g x. What is the centripetal force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1. s:eaa1rs q6,gq;z61 c ebmj-h0-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 to breaksgz;q 6acm- : hjse,b6ae1r1 q?

  A stone, of mass m, is attache7;xjo9x 3- fsjowq ks(d to a strong string and whirled in a vertical circle of radius r. At xs;kf- q9o(3jw7sox jthe exact top 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 stone, of mass m, is attached to v92 ..ostvk kea strong string 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 ve ov k.s9.2tkstone's speed at this point is given by

  A jet plane flying 600 m/q9laqfn ks/q1q7sw1 sk zl;ywu4* u c:6q+r.d s experiences an acceleration of 4g when pulling out of the dive. What is the radius of curvature of the l kfqk:9n/wq6sw r.y*4sl;cu+ l1uzqas 7 dqq1oop in which the plane is flying?

  A pilot makes an outside vert; 07ufpixv :kulli;/wical 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 of his normal weight. v;wpx;0i/fui lu k:7l How fast is he going?

  The maximum force a pilot can stand is abou-ce / hh.8l, xi,vgtudt seven times his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling out of ail, 8uvhx c,tg. -d/eh vertical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/s rounds an 80-m radius hgs:b( :b dvlep jtc61eo no) )o(*iw(morizontal curve 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's1jn :sitpb b((vwo(oe6e d gc:lm *)o) tires and each road surface.)

  A car is negotiating a2cm7nx0vfwgw 5xsu- 9 flat curve of radius 50 m with a speed of 20 m/s. The centripetal force psn wx5-2m u xw7cgf09vrovided by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a 8p0ta, + hnw /r +j(zg5tz-d vnbfl8ivflat curve of radius 50 m at a speed of 14 m/s. What must be the minimum coefficient of friction betwl( zgvv+h/z8if 8p -5jdt+t, brwnna0een the tires and the road for the car to make the turn?

  A car is moving with a constant speed v arobtae8-qgj0i87hr 8yzk8mo t 6und a level curve. The coefficient of friction between the ti7rhq8t6kzge8tmi j- yb0oa88 res 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 bobsled to negotiate a 100w1ea n )h/jhx;ve jg10-m radius turnavwhh0njje 11 xge/;) at 35 m/s without skidding? (Ignore friction.)

  A horizontal curve on a bobsled rjbb36 78ehewluv 00 ugun 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 an angle of lpazoet p 5wx6..co/ w85i2gt$45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is oauw rt-ubk 7 6j/ik;w51yy9kbanked 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 revolving uniformly in a horizontal circc2g hxc,y-wb 3le of radius 0- b hxcg3wcy,2.500
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 rate toz 2zju+ ka/l/n a speed of 45 m/s in 15 s, movingkz/az/ju l+n 2 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 pros q 6ywxr.4ct2lx4vv0ton 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 on the 7njvls 1t( h3sw)y3iz Earth, due to the Moon? The mass of71 nl()ssvwh3i yt 3zj 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 fory68saz73 )m8jizwdzn ce between two masses is F. If the masses are moved to half of their initial distance, wha87jadiz6 ysn)mzz8 w 3t is the gravitational attractive force?

  For a spacecraft going from the Earth toward the Su:oxsgj(p;) 7 sihypw2 n, at what distance from the Earth will the gravitational forces dxs:g hi;7y2p)s p(wj oue 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 Moontobr u+w;e+ad e )m 6qg,xt17e 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-walk" at a distance above the E43xyldk97:liza e oj(arth equal to the radz4 ae7j3: oik(y dlx9lius of the Earth. What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance above the Earth's sur.l h c2v hxlaqfv5jvh78+;c p+face will the accelerhpfx 5.lv+c+lcj2 v8;qa7hhvation of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance abkp rmjp83wit7:7+) agusq )yl+ joo ws 73bgr-ove its surface equal to 3 times the radius of Mars 8p m3 pgw)oa-+u 3lwg77+tr kybsjsi)q:j7or. 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 cad47ps b- j.qcenter, the acceleration of gravity iq.c4bd-j7 aps s $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on th8uo0p jk.n .rz 1c /vykp.6xose surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's s8k.u6 z sc1ovj on0y xp./pkr.urface, what is its weight?

  By how many newtons does the wj1 .rimg /bgmidl/ e,*eight of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radiu1./ m*dmig/ebr lig,j s of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satg wmk1fyk kw zyzzf 1qqbdl7 kh7u2*/.;ye)( ,ellite of mass 100 kg is at a point 3r above the Earth's surface. What is the .ugfwwqq2 k(/d1 f y kkl 7z,)by 1zymehk;z*7satellite's weight?

  A spherically symmetric planet has four times the Earth'qc0xa7vf 0am ff(im j y51-(kes mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weighfxk00iqff7j ay51em m(- ac(v on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lie ondo)* :iib )rxq the same line, with the Earth between the Moon and t *r))iqi b:doxhe 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+ )x3 cf 3kd)hpktkhp/.
(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 aboutcg1u8sk ,1 ipdfl5t s3 the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radius ougf 18k3spc ,1si dl5tf the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about the Earth (i.e., it just sf8 9tfpotbgr48 zx .w v)/o(vy+cha7gkims the surface .g 4v8y w(9az chpo7tb tvfxg/)rf8o +of 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 the surface of the Earth. It4idnq/wy : mw; jyj8:t is observed to have a period of 89 min. What :w ymyq:8nj w;j/4idtis the mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter* .myafs fa82w, 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 radius ofoaui0 5)m opus, +j9ns $422 \times 10^{3} \; km$ and a period of
1.77 days. What is the mass of Jupiter?

  Two moons orbit a planet in nearly circular orbits. Moon A has orbital radi uu 2: p6czzvr)xbp7*qus r, and moon B has orbital radius 4r. Moon A takes 20 days to complex)cuuv 7 6qz rb*2p:pzte one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter id o-6m8w 7u(n;oa -kyp-a1n05es /flyntet kms $7.78 \times 10^{11} \; m$ 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 h sfk1z(mks9/ to orbit the Sun once. What is the average distance from Jupiter to the Sun? (The distance from tf kks( /9mhsz1he Earth to the Sun is $1.5 \times 10^{11} \; m$.)