Is it possible for an objyn84, va/ 77uy0vqdz ;h)n ptnk f*dcgect moving with a constant speed to accelerate? Explain z8 akn0dcn,qdvhg;77pn/y ft4 yv*u).

  Consider a particle moving with constant speed such that its aq7al7e5n e2 sari9 zb+cceleration of constant magnitude is a7rnaea2iqbs9e5+l z7lways perpendicular to its velocity.

  An object moves in a c0o:1ou 6 :d4lwnqhtwcircular path at a constant speed. Compare the direction of t ldo6woq0t: :1nu4cw hhe object's velocity and acceleration vectors.

  When an object experiences uniform cwys8;8rsn c6g ircular motion, the direction of the accelera8yc; w8gn rs6stion is

  Consider a particle moving -n84n b6ikp qywith constant speed such that its acceleration of constant magnitude is always perpendiculapnk 8q y-4b6nir to its velocity.

  What type of acceleration does an object moving with constant speed in (vg*x h+ a61ztzr rd+6pjj t(ta circular path experi(rtdh*z1z p+a(gvxjt6 6j +r tence?

  What force is needed to make an object move in a ci 2ro*hlv4 qdnauc-b,v 3kv.8wu4ug 6rrcle?

  When an object experiences uniform circular motion, the directiouwc7sb2 7 s,q:go.futn of the net forcg s c.uw7:fsbqt u27o,e is

  A roller coaster car is on a track that forms a circular loop in the vertical plw4(3rlwu ,zmu f n54jiane. If the car is to just maintain contact with track at the top of the loop, what is the minimum value for its centripetau wn4r35(m4jufwilz ,l acceleration at this point?

  A roller coaster car (mass = M) is on a track that forms a circf03 u/xfyd 3a:qi )ryl jc(oo0ular loop (radius = r) in the vertical plane. If the car is to just maintain contact with the track at the top(x:ojf0 )dyfq r yo3a/ 30cilu of the loop, what is the minimum value for its speed at that point?

  A pilot executes a vertical div htlg-o +,:mb (2nhdik+br 2nwe then follows a semi-circular arc until it is going straight up. Just as the plane is at its lowest point, the obhgh rmtbn2w+kd:ni(+ ,l -2force 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 radwh(jg(muy9+ oius $r$ at a constant speed $v$. What is the direction of the net force on the car?

  A car goes around a curve olvi ;deq2v(s :f radius r at 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 around the curve for v;:vqi l (eds2the second time, compared to the first time?

  A car goes around a curve of radius r at bo7h9le+o *4i3habtra constant speed v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car h3+lorb e4h9a *bo7 tias it goes around the second curve, compared to the first?

  A car of mass m goes around a banked curve of radius r with speed v. If the roardhwj:a 77ui3 d is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the normal forcajur7: 7dihw 3e on the car from the road is equal in magnitude to

  Two horizontal curves o3xin9g kjlb*9 n a bobsled run are banked 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 smangj*3iblk9x 9 ller radius curve is v. What is the safe speed on the larger radius curve?

  The banking angle in a turn one6 vnz/jso kn f14/hp- the Olympic 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 th6v4 ksjn1f-/epo/nzurn. Why do they do this?

  Is it possible for an object moving around a circular path oq h3 wc15xs87kbikrszz,7+g to have both centripetal and tangential acceler3wos c,8q 1kxz 5g brshzi7k7+ation?

  The gravitational force betweerbi., 0ybu owb/ p;clcx66 9rfn two objects is proportional to

  The gravitational force between twok e,l)pys ls/,ewu54q objects is inversely proportional to

  Two objects attract each other 78w3 ,j )cork/z uavs*sytj:vgravitationally. If the distance between their cente 3sr,*vsv/w7kucy8za: ) jotjrs is cut in half, the gravitational force

  Two objects, with ma00db99-uyfi jth jx 12n.ylfrsses $m_{1}$ 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 maeb6kfwc za;s* 5)ve(mu86i ohsses $m_{1}$ 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 gravx.uk) i9i2hbi cbep+9itation.

  Compared to its mass on the Earth, the mass of an object (77 k*tgjn3thghe7dh/0,ut uh -vb ckon the Moon is

  The acceleration of gravity on the Moon is one-sixth what it is on Eah,pc ( uf)t+hgrth. An object of mas+gp(fch,th) u s
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, the rockfz3er38k c74qn,djbnet's weight

  A spaceship is traveling to the Moon. At what point is it beyond the pulxo4;f 3mqkn37doi9uwt w io51l of Ear4uk5wi 7d; i39wt1xmoo3 qf noth's gravity?

  Suppose a satellite were orbiting the Earth just above tq 3r 1zmn8bc2;wb5l arhe surface. What is its cen82z51n rabb wcmr3l;qtripetal acceleration?

  A hypothetical planet has a mass of half that of the Earth and a radius of twice,hzgj 1mjs4-8lv8p gn t gl1 4vsgj,njp -h8m8zhat of 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 soyl(2gb, / 2inu(aycjo -b/ uis on Earth. The radius of the Moon is one-fob2 u/ly (yba,oug s(/-ni2cjourth that of the Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gravity, but planebno617a pnf d kp,1v:zt B has twice the radius of ,7anoz kdp1: b1pfn6 vplanet 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 the mass .pu9ac/:*kj4yctn v jcii: /(9syd grof planet A. If planet k djijy*4pv/r :ga.cnc:/iy9uc 9 (tsA has radius r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) about 5idn ;un0u iyp3 ch/;)+k.u2 bijcmepa spherical planet (mass M) y)d3 p/ehcc25n;piuu.iunmi0 k;+jb . Which expression gives this satellite's orbital velocity?

  Satellite A has twice the mass h1r k;d(i a+lesxpw17+5ire(b5e khx of satellite B, and rotates in the same orbit. Compare the two satellite's speedsd+e(+ ar7h iip 5 bklxkr5h1xewe1s (;.

  A person is standing on a scale in an elevator accelerating downward. Compar ta8m sk7 :.ijc wzpze-fn8z7 n-;mnj7e the reading on the scanz 7mm7knniwjzc7t8 j; zasf-:- p.e 8le to the person's true weight.

  Who was the first person to realize that the planets move in elliptical paths fle vrpo18 8)i n b;uol20gz.lt +ou4naround;puoebno8gnollf.u41l+r v 8) zi20t the Sun?

  The speed of Halley's Comet, whqpca* / o4-jvix.qir4 ile traveling in its elliptical orbit around the Sv/p4.qx -i j qac4or*iun,

  Let the average orbital radius of a planet be R. Let the orbital period biya mc;b2w qkxp6.t// e T. What quantity is constant for all planets orbiting th6q;iac xky/tbm./p w2e Sun?

  A planet is discovered to orbit around a sta, ;gcxcr ji;af 1afp:7r 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 pla1,; afccpxj 7gr a;fi:net be, compared to the Earth's orbital period?

  The average distance from the Earth to the Sun is defined bdnjmwl)73 08bcz t8w as one "astronomical unit"n8zbj3 wd)0 t blmc78w (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.n/3nbu5by8jj

  List the four fundamental f qvy6nj t3uezp5stg 2r 83oq;7orces in nature.

  An object moves with a constant srte ( .ij53:t bs;snulpeed of 30 m/s on a circular track of radius 15j t;b3n5 st. elrsui(:0 m. What is the acceleration of the object?

  The maximum speed aro9z s : vjv7fj ,xtx03lk,hfwg/und a level curve is 30.0 km/h. What is the maximum speed around a curve with twice the0fgxkfv/9, tj s 3zwj,:h7xl v radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on:njji cw7c(.;pm s4qcg3n0c;( v b lun the perimeter of a bicycle wheel of diameter (i0wgm4n3(nbq:;nlpc j; 7ucjs .v cc70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m from 0 v e*:enodv6xb-az:8(kh z hathe axis. What is the centripetal acceleratik(0ozan 8:zde- 6: xvaehb *hvon?

  How many revolutions per minute must a circular, rotating s+ xt7sofu k .fwk9;yumz8z u;0hvl09 ypace station of radius 100tf v w;ouz yy08kf.u70 z9mk+9hl x;us0 m rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mas bf5mv4 ko*b5ss of 250 kg. It goes around a 13.7 m radius turn at 96.5 km/h. What is the centripetal force on the motorcycl5 mos 4kb*bfv5e?

  A 0.50-kg mass is attached to thhf j05fs3m9*q hs y:vhe end of a 1.0-m string. The system is whirled in a horizontal circular path. If the maximum tension that the stringvf3*s: hhmfs0y jqh95 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 alcx p; 1d9 (zh;da)hoyttached to a strong string and whirled in a vertical circle of radius r. At the exact top of the path the tension in the string is 3 tid;azhyp do)1x (c;9hlmes the stone's weight. The stone's speed at this point is given by

  A stone, of mass m, is attached/t iqqhqb6te ccw91. 0+fc8le to a strong string and whirled in a vertical circle of radius r. At the exact bottom of the path b wh80 iq6l1ec/etfcq c.t9 +qthe 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 experiences an acceleratioemeky99 mu v09n of 4g when pulling out of the dive.k m9mu0 vee99y What is the radius of curvature of the loop in which the plane is flying?

  A pilot makes an outside verticalzqaris1 t2g4r zttos+e c5 ro., 5p 9+2i)emqd loop (in which the center of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushiz1o i+t4 ,2e.met5z5+rird) ta 9 sqpcq2rogsng down on his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pilot can s9q(*0 :zdv 8 jvnn*+lwyx 1kt ap;ogjgtand is about seven times his weight. What is the minimum radius of curvanzy*ag8ok0v+p q (;gvd9l * 1jnxw:t jture 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/n:3s y*ts ny2tx+ favm3g de:6s rounds an 80-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 same coefficiemg6t v tss:*3yynn+f 3ed 2:xant of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 50x5oy 3-.q 4.da3zjiaj;m(ad)f ri dwt m with a speed of 20 m/s. The centripetal force provided ba(y tj5d-3.;z34qo)jdfmr ixwi.ad ay friction 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/. ;ay dts/a2 2zo7f9d:zk nvhgs. What must be the minimum coehn7.voz aagf;:t9sdd/ k2z2yfficient 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. The k ndu 6xrhtg1v;q-;4i coefficient of frg4k;rdt1x ; 6-vunhiqiction 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 atf64 wf/xmie, n Olympic bobsled to negotiate a 100-x/if6ft4mwe, m radius turn at 35 m/s without skidding? (Ignore friction.)

  A horizontal curve on a bg23)-au3v etw( ms6ds06w f pbxahk*yobsled 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 m, bank crh 4b;dnhjt30+o0 aged at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is ba,(;usk ,ww kk12 boeoanked 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 un) ll h ;h88s7lfkyox6ciformly in a horizontal circll87 8xh) f6l yksoclh;e 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 area, a race car accelerates at ql. vgdq-5 jveu,/0lqs 68eeza uniform rate to a speed of 45 m/s in 15 s, moving on a circular track of radqllu68vv5qe.zg,- e0dq/ s jeius 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 mass cz*ly vz46 83oac .l9h;cbh mw$1.67 \times 10^{-27} \; kg$ 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 Eakuvgwf/u/;u2b 41d 9we1pfqgrth, due to the Moon? The m1 g uvdegf1/uf;9kbw4pw2/u qass 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 theu (b9m w9jvpn) q1.atf masses are moved to half of their initial distance, what is the gravitational attractive force?1j9) nf b(mqu.ta 9pvw

  For a spacecraft going from the Earth toward the Sun, at what distancjt* z3 o8j,;.xu5ao-zk xcvab e from the Earth will the gravb ,t3zuavo8oaj cz* . x;kx5-jitational 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 iq3 p:k;cqbfmq ea*6/ us $7.4 \times 10^{22} \; kg$ 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" ay5bfs5 fh + my1-.0wlcs ej/fzt a distance above the Earth equal to the radius of the Earth. What is her accel ./bsy-+ lcj1f55eyhmsf0zw f eration due to gravity?

  The radius of the Earth is R. gmaf;- ux d lsvp81)pb4dm ,x+ At what distance above the Earth's surface will the acceleration of gravity bm lpmgf +ddu 1svbxp,8;4x-)ae $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its surface equal g r mty5y2+rl jgce+5*to 3 times the ra e+y+t*y rc5gmlr25gj dius 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 centet6x7 ppe, aok/hgy8x1r, the acceleration of gravity io1g /xt7e8h, kxpa yp6s $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on th+3gp f1jmtqx0e surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what ip1x3q0g ft jm+s its weight?

  By how many newtons does the weight of a 100-pk5pebco5 5.+9sbich kg person change when he goes from sea lec phbpe 5ki5c 9bo+.5svel to an altitude of 5000 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mas 9g* o82)owjd-.l qmnumjcov( s 100 kg is at a point 3r above the Earth's surface. What is the satell -ul.o jj(*co)wmqm98 ngd2ov ite's weight?

  A spherically symmetric planet has four times the Earth's mho8vx4e/ dw9f ass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weiwf8veo9x4d/ hgh on the surface of this planet?

  During a lunar eclipse, the 0 qs 7qe9v1o1rm2l)eu vhh8ku8hx8u+8k fh fzMoon, Earth, and Sun all lie on the same line, with the Earth between the Moon and the Sun. The Moon hh l71hxqmfvr8s9 8hfhu2kkeo)ev 18qz0 uu8+ as 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 tgc8h(pt (av ll9icr.2he 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., itkt q*/ wf 84:dtgjv-ln just skims the surface ofkjvd4 flq8t/n*- : gwt the Earth). What 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 abyok-j+57 sx)8ag yzv fout the Earth (i.e., it just skims the surface of the Earth). How long does it take to make8z ja5gy7s-x+kyf) ov 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. Itr p(hd1+z nbc) is observed to have a period of 89 min. What is the mass of the Earth? (The mean radius of the )1 drhp(bz+ ncEarth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupit) 1(xr voza-f*yf, xdeer, 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 orbiqq,q9i bzqd 1dbw od3 g,)+b*dts 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 j +fw . dew/0v),sm8usy e snj9f;5dmhorbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to s seywd+w vh80/m5fnd9)f ,u; se.jmjcomplete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter ijdx2/e(yeu3qf )q6b2k:j dv.hzk;hluc k4 6 ds $7.78 \times 10^{11} \; m$ 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 Skc6.ed g.ti o5un once. What is the average distance from Jupiter t te icg..okd56o the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)