Is it possible for an object moving with a constant speed to accelerate? :lxl( 4 +kksfm ro.y) 5lztvs6;2kwr y Explai+ls2yx5okzf(;r.sl4v r )k:tl6 mwyk n.

  Consider a particle moving with constant speed such that its accels)4+g 56ci .l;k teqkrjf :iwreration of constant magnitude is always perpendicular to its vkfics rq eig):t56 .jrk+ l;w4elocity.

  An object moves in a circular path at a constant speed. Compare the directj/x/ s4g r25bs gbd9ilion of the object's velocity and acceleration vectors b4sijr9g25 lxg d/sb/.

  When an object experiences uniform circu5 yy ug)gh5cpd0 3g1yxlar motion, the direction of the acceleratpc) hg1d 5ggy50uxy3yion is

  Consider a particle moving with constant speed such thatxzsl0mmotp dp)y+-z b6nf2q s16ve:- its acceleration of constant magnitude is always perpendicular to its velocittmyb6+o-mp sqe zsnz-f 62dx1)l0:pv y.

  What type of acceleration does an obxqv8)nqs , /8vltf 3dyject moving with constant speed in a circular,nft/ 8sy 8x)vd3vqlq path experience?

  What force is needed to makeh*v a 7d,n3okj az3uc; an object move in a circle?

  When an object experiences uniform circulofk; v izokf,(-m;+dt ar motion, the direction of the net force i,k(i v ;k;z om-fdfot+s

  A roller coaster car is on a track that forms a circular loop in the verv2x:z3lov+f: yarw1 .x -no mqtical plane. If the car is to just maintain contact with track at the top of yqmro23 vlfvow 1.:+xnx-:az 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 cirb tshn,+,m44p oc*i0ucz7x rpcular loop (radius = r) in the vertical plane. Io,rszpt,nb ix +cu0 74 phmc*4f 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 t ,v0 apfo3qigpe6lcp2* emr,4 hen follows a semi-circular arc until it is going straight up. Just as the plane is at its lowest i,c, rml*2e3 a6p4ppfgv oq0 epoint, 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 curvjl(ctyn4g9g5d9 ad2 bivr/ -je 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 :nf-jc3 .d0chnm 5 vlba constant speed v. Then it goes around the sh3.d-bc5 nc:jn mlv 0fame 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 g.okp :mer*t1o 3+uin ;zl2gb 8vo9gqwoes around a curve of radius 2r at speed 2v. What is the centripetal fo gkrz1g8qmle3 9vou tno+.:*pi2 wo; brce on the car as it goes around the second curve, compared to the first?

  A car of mass m goes around a banked curve ve3 :bc ,4/cdrgyuc ;. gnqn7gof radius r with speed v. 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 from theggdecrc: v.;g /4nubcq n,37y road is equal in magnitude to

  Two horizontal curves on a bobsled run are banked at the same angle, buohj/fy6 -6.b yyvz1u lt 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 t 6 6.j/1vlbfyu-ohy zyhe safe speed on the larger radius curve?

  The banking angle in a turn on the Olympic bobsle.4:cs)rho8 b p bjtx6jd track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will x)tp46r: jcob8jhb .s 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 k l :a6maez)97 2plgdjpath to have both centripetal and tapjl9l 6dz am2g)a:ek7ngential acceleration?

  The gravitational force between two objects is proportional ifkfw:x niid++g5 q,1 to

  The gravitational force between two objects is inversely proportio0x5emot1p3kpg1p( z7o( tx yxnal to

  Two objects attract e lruqb jr.qsm4i)8r0cb7 o3w* .wn p1gach other gravitationally. If the distance between their centers is cut in half, the gravit sm1rbub) wp* 78qwr .jl04oqic3rng.ational force

  Two objects, with massnyae8kw5 z4)os y 2ha1es $m_{1}$ 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 mau2 za3 2 umb+uiz2jlidzd*8 1gsses $m_{1}$ 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 gra4 33owktrwrlyg.+w1.,e7 m q,m gsn vhvitation.

  Compared to its mass on the Earth, the mass of an obou;uk:q8hy3g ject on the Moon is

  The acceleration of gravity on the Moovnd qn :/t6c(0mcfef 1c* .krcn is one-sixth what it is on Earth. An object1 fccrd.6e(:ctvn/0 nc m*qk f of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earf26j7 2 a(tj8l cfxqhxth's surface, the rocket's weight

  A spaceship is traveling to the Moon. Allwmx-;9fmv0;i-nmip-,w jx t what point is it beyond the pull of Earth's gravity?nv-mmfmw -i;pw xi l, 0;-9xlj

  Suppose a satellite were orbiting the E:36k)blq8-s omqt+ i jf2 xliiarth just above the surface. What is its centripetal accel xil8)3k sbqfm+-2 :io 6ltijqeration?

  A hypothetical planet has a mass of half that of the Exja5*/.zwcg lh y zl76rr4ep6arth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gzry6/*h6ze rj c7l45g. awplxravity at the Earth?

  The acceleration of gravity on the Moon is one-si r9hg :tvx a7pnmidq vu(z2s5(ljc,hh:2/(gzxth what it is on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Mo 7:qji ((vhln29/ 5hrxgta s:2gh, pmv u(zzcdon's mass compared to the Earth's?

  Two planets have the same surface gravity,1a r(g6v80wqog.a ojb but planet B has twice the radius of planet A. If p(ojwb1 avgqo8r0ag6. lanet A has mass m, what is the mass of planet B?

  Two planets have the same surface gravity, but planet B has twice 4e;o )08l1- :a3yeasbfr bbh hqfdnq,the mass of planet A. If planet A has radius rnr4 h 0sbhd;:boyaf,qe)q-b l81f3ae, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (ra3i5g)n nry1xz dius r) about a spherical planet (mass M). Which ex3n 5zn1 ryig)xpression gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellih ;*p(nmsi/fvte B, and rotates in the same orbit. Compare the two satellitev pf m*(/ins;h's speeds.

  A person is standing on a scale in ) 1m7ltu2 jqr8xt: y*r6q ymuph2kxj 3an elevator accelerating downward. Compare the reading on the scale to the pers22x3 j1r*)uqm kxlj:rt 6m y7hq8upyt on's true weight.

  Who was the first person to realize that thedq*j/ch k-4 (w c:tya w8-t f37zgummm planets move in elliptical paths around the Sun?zmahk(tfw7 g 4mq dm*-8c3ut- yj:w/c

  The speed of Halley's Comet, while traveling in it i2pgqgd0qh (* t)i3ees elliptical orbit around the Sun23 qtqhi )*e dg0(pegi,

  Let the average orbitqemrat,t * ku+x t. f06o/4wyial radius of a planet be R. Let the orbital period be T. What quantity is constant forrmew /qatxyttk,i fo4 6.0u*+ all planets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxy A1+ua9cbngsz/ z; w)eo p3jr +9p2ba /g;lnnrbndromeda, 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 t csg/wb 9nun3pb2az++ z;/r1o;rl) jag9bnep hat new planet be, compared to the Earth's orbital period?

  The average distance from the Earth to we4*jny( gy/bvvpp n0 0)-gd vthe Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is thegvw- d* 00)p4jyebvnygnv( /p asteroid's average distance from the Sun?

State Kepler's laws.qpllqa1a)i x,e /ukv-a+x, ;*xy xsc/

  List the four fundamental foa4g tt sq : *ejzs)lbam**dc7lxu ,4li:y5* wgrces in nature.

  An object moves with a constant speed of 30 m/s 6d-tvx z h6:zhug92:dc9jm/ ev (qscson a circular track of radius 150 m. Wcg 9/v62 (vxzq-j6dmzet9u s:ch h:sd hat is the acceleration of the object?

  The maximum speed around a level curve is 30.0 km/h. What is the maximum s74(:ld)jh7 .ikc1t;oek hiyoaf .sg xpeed around a curve with twic4 d;o7 fth y:k7axi )c(keglo.h 1.ijse the radius? (Assume all other factors remain unchanged.)

  What is the centripet)upw sg5c: -gmal acceleration of a point on the perimeter of a bicycle wheel o c)mu5wg g-sp:f diameter 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotatin;hp4dl0dga 9dvsl3c (t0z e*sg at 5.00 rev/s is located 0.200 m from the axis. What is t9l t(es*h0vg ddd04 saz;3 lcphe centripetal acceleration?

  How many revolutions per minute must a circular, rot (s5, oa+zjzujating space station of radius 1000 m roju osazz+,j5 (tate to produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 1un8lqh4,.p-u2 tu na h3.7 m radius turn at 96.5 km/h. Wp -a8tu nq lh4nh2.uu,hat is the centripetal force on the motorcycle?

  A 0.50-kg mass is attached to thecidazj rj )t213 :xxm u*-apt+ 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 ix:tmp )+r2*z3aaj-1cuj xdt. 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 ls41o0a,- nf 6r88g :z cpakuxelhg9win a vertical circle of radius r. At the exact top of the path the tension in the striku9cfswga :oh88 gean6l0,r pl-xz14ng is 3 times the stone's weight. The stone's speed at this point is given by

  A stone, of mass m, is 45(lbz* crzbz syn(b(attached to a strong string and whirled in a vertical circle of radius r. At the exact bott((b4bnb5cz zy l*z(s rom 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 expebe*rtwafg o1s00rcw5id3 z8 /riences an acceleration of 4g when pulling out of t*3t fwr1d az w5gb8 ieros00c/he 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 the center of the loop is b4cbcpkk-yk+ vq1k*9d+m5 d bkeneath him) of radius 3200 m. At the top of his loop he is pushing down on his seat with onlyvp*9b+k mc-dk +k1kbkd4y c5 q one-half of his normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven times his 6t a;sitrs/o;i:ns - uweight. What is the minimum radius of cur6uio-ns/t a:i;s;s trvature 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 horizon8rq-zkf4 7xsc.u q;zatal curve with the tires on the verge of r 4zxfcu.z-7s;8qakq slipping. How fast can this car round a second curve of radius 320 m? (Assume the same coefficient of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius .sklr q 4ho6f5,d6mif 50 m with a speed of 20 m/s. The centripkiq,fd r4f o 65.lhms6etal force 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 radiun (ixn0)i e2hgs 50 m at a speed of 14 m/s. What must be the minimum coefficien nxei0h 2(g)int 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 whi/rsl02n yjmv;rz1z r56gi0 o c,s,coefficient of friction between the tires and the road is 0.cs wn m2ir g;,zyo6/1h5i 0,rzvs 0jlr40. 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 100:r-iw8oc).ml9z fm wl-m radius turn at 35 m/s witho flc ilz 9-wo.8m)mr:wut skidding? (Ignore friction.)

  A horizontal curve on a bobsled r to7t*6ene) qi6 8zdawun 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 andjz-.fzz+ )kt0 c/-iurtip: ggle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is bankeyfjkd fs(*d62d hg8m( d 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 stw:ot+w sqip h;r -c.4kring is revolving uniformly in a horizontal circorq-.sc+iw : 4;thp kwle 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;he. n,l70jj7fd 5iih 5xt vhw accelerates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular track dtej 7h lhif.x,hj57i;50nwv 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 *fb ac* /+4xsw9z( qvljtg1n bproton 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 Eah(q o t1yb;w.bh 6cc5arth, due to the Moon? The mass of the coty b(a5;ch6w qb.h1 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 beo61dm 43 ds*vqt6b eactween two masses is F. If the masses are moved to half of their i6t*mq4o ce3dsda1b6 vnitial distance, what is the gravitational attractive force?

  For a spacecraft going from the Earth towaran(cfgl wpj (r7q57s 5d the Sun, at what distance from the Earth will theg j57q(sa5(rfln7cwp 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 Moon i/l* /ta sqnb-g ce:(ofs $7.4 \times 10^{22} \; kg$ 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 Ea(6 : wam.hrem niwjc59buc2o 4rth equal to the radius of the Earth. What is her acceleration duec6 b (w9 h5io4aejnm wrcmu:.2 to gravity?

  The radius of the Earth is R. At what distance above the Earth's 7 wf0,b6-ifdph kja9 sa 9r.mwsurface will the accel7j,kw 6 br haw afdm0s9.-ifp9eration of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a d;qxc1lb 2x0lswl4,f q istance above its surface equal to 3 times the radius of Mars. The acceleration of grfl0 , 21qxsl;qwxl4bcavity of the satellite, as compared to the acceleration of gravity on the surface of Mars, is

  At a distance of 14000 km from si5; 1hi+q mwspome planet's center, the acceleration of gravity is imiw ;+5 1hsqp$32 \; m/s^2$. 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 radius r.0 ,jrk+bic-y d /ctc, jhlbi)- If the object is raised to a height of 3r ct- +,jb-)c/0, yljichdrbk i above the Earth's surface, what is its weight?

  By how many newtons does the weight of a 100-kg person change when3cyoceb(z f miq3 /8i.r;- hdr he goes from sea level to an altitude of 5000 m? (The mean radius of the Earth isy rh/zcr 8o-( bq3cdei;m3fi. $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is at a vb v-fr* kt+dt1t*d-lpoint 3r above the Earth's surface. What is the satellite's weight?tv*dkt--v *+ fb t1ldr

  A spherically symmetri+b:.xbvg (qi u29h(. qov: 5dnttdosdc planet has four times the Earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on the qn(s. bd :g.udq2dxtboo v:5i(+hvt9 surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lie on the samenuq gg))qmn,/ee0 b*q line, with the Earth between the Moon and the Sun. The Moonq)qu)m*ngq0 b,ge / ne 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 mo3l9 pr3nw tbo(a8f,jw(se-+kup*n .
(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 orb1hx(-dv0n ws rvwael+13 w4yo qzs43yit about the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean4w1ny3 03arywz x+d(4e lv1- hso wsqv radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about 7fg8eqx(yu- myb/ qx2,pxot a**2xpt the Earth (i.e., it just skims the surface of the Earth). How long does it ta8uy*xx7qy(taqb pxtp gf,x 2 *m2o -/eke 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 the8l9wq0xjto 8 5ssczj7ik j, .ywk 91qi surface of the Earth. It is observed to have a period of 89 min. What is th0 o,9siq89ziq jkw8k7 .sjy c j51txwle mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an orbital diameter ofq p q2dq3pa33sl0x8un hzi75u $1.34 \times 10^{9} \; m$, and a period of 3.55 days. What is the mass of Jupiter?

  The innermost moon of Jupiter orbits the planet r9dsa+5btwg ya -.6/i dtj(xq 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 circul71cnh+ isesxv4ti84tpo;a m) ar orbits. Moon A has orbital radius r, and moon B has orbital radius 4 +th;pox4issm1 at4vn7c8 i)e r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter is5cbq 8dc23m rb $7.78 \times 10^{11} \; m$ 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 Sp fq(*:g/m u pj0xzz/nun once. What is the average distance from Jupiter to the Sun? (The distance frojfznug x (p/mzp/*: 0qm the Earth to the Sun is $1.5 \times 10^{11} \; m$.)