Is it possible for an object moving with a constant speed to acceleroxg7f y 4e;wn:g+anxlk j.u6 5ate? Explai5gxon+a4jk:nu7 ;6f.yxew l gn.

  Consider a particle moving with constant speed such that its acce)m09x8b.tsy8( x j+un qxhb mhleration of constant magnitude is always perpendicxs9xxmhh nq8(t 80bbmu)+j.yular to its velocity.

  An object moves in a circular path at a constant speed. Compare the fh0n4c q k:(xmdirection oxnc:f0m4k (q hf the object's velocity and acceleration vectors.

  When an object experiences uniform circular motion, the direction of the iti9jx3 (w 5cq l::*owswgxx/acceleration isxw: qx9/ gsi5txlow ji:w3*c (

  Consider a particle moving wi8jt;/ mpb :0kkotaf c7th constant speed such that its acceleration of constant magnitude is always peratfk;7 tmpjcko b8/:0 pendicular to its velocity.

  What type of acceleration t1ohq3uovo: *if6alaaxn p.hzs +, 6c bs39b( does an object moving with constant speed in a circular pathn hvabs p : i*3,at.6uhzc( o19o+s3abfl oq6x experience?

  What force is needed to make an objev bj5)4z(k o1bhq yst*ct move in a circle?

  When an object experiences uniform circular motion, the direction of the -yvf h,f;a0o unet force isv,u y-fof;a0 h

  A roller coaster car is on a track that forms a zj :cusf;* **,nl shz3be mp*.tuqw8mg*f/qu circular loop in the vertical plane. If the car is to just maintain contact with track at the top of the loop, what iszp8f uz w3 he n/*ulb**f:mjq .qmu *;c*,sgst the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a track th b+9o:d5 kefzu2egm* hat forms a circular loop (radius = r) in the vertical 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 pbe*5zdkhg:meu2+ 9 f ooint?

  A pilot executes a verlqr.w) 1 acung /lq6r-tical dive then follows a semi-circular arc until it is going straight up. Just as the plar1)g6 cqwqalu-rl.n /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 curve of raj-5kqxz,pbcs7 a9dn0b ;y7p(7syolxdius $r$ 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 af dgxh1 rli8 fiu(n)0a8wl:9p t a constant speed v. Then it goes around the same curve at half of the original speed. What is the centripetal forc prxflif0 a8(1:ld h8g)iwn 9ue 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 conge2avqb) 3h8(d7ge s sstant 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 second curve, compared to (qve) shg8 ag dse237bthe first?

  A car of mass m goes around a banked curve of raz*t x - w3e 2cgg2mpn*-hg5raddius r with speed v. If the road is frictionless due to ice, the car can still negotiate the curve if then2 ar- -dem52*3 hwgc gzgp*xt horizontal component of the normal force on the car from the road is equal in magnitude to

  Two horizontal curves on a bobsled run aruoh+ ueax h* q-98y+oje banked at the same angle, but one has twice the radius of the other. The safe spe-xae* ohuq 9h oy++8ujed (no friction needed to stay on the run) for the 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 is6 ;p pcjy-a2ac 3ca2aw28tgxez(d1g h not constant, but increases upward from the horizontal.;a8za3gcegta 2p pych(2 j c6-2da1wx Coming around a turn, the bobsled team will 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 path to h t vyha::ubiij.w.v7 o(iq186dod l7uave both centripetal anu:dd iqw7jlv o1u(ivb.a:76t8yo . i hd tangential acceleration?

  The gravitational force between two objects is pci:dlb.xn ; w6roportional to

  The gravitational force between two . xmk3 u 6m84ecexs9nnobjects is inversely proportional to

  Two objects attract each other gravitationally. If the distance between their ck* fd5xec 2gxm55pxf*enters is cut in half, the gravitational forc 5cxm** ef5kxg5pdx2fe

  Two objects, with massenpw x/zx h9lhh167/70kzyvcg ;r krl :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+ifuql wqqxt/),d(t8 $m_{1}$ 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 ofs +v s k*peiqzk,1i+zs909iu x universal gravitation.

  Compared to its mass on the Earth, the mass oy gf jxpv*;r2x05)wta u 7hp(/exxg .kf an object on the Moon is

  The acceleration of gravity on the Moon is one-sixn6031if2a lpd n ;zhlnth what it is on Earth. An object nnplz16n 2f0di3;h alof mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from te;se /kkvn m39/bsky3*1cpn 7ox9zcza 3vx 3phe Earth's surface, the rocket's weight

  A spaceship is traveling to the zhttsikh - d-52o4 k*eMoon. At what point is it beyond the pull of Earth'ko es 5-2iz4tthh* kd-s gravity?

  Suppose a satellite were orbiting the Earth just nr)f02my7pmtaxse. : q.3x (dmag +miabove the surface. What is its centripetal acceln(g: xmtp.s0m )+aa2 q if3rmxdmy7e.eration?

  A hypothetical planet has a mass of half that of the Earth andf 1eqks( ;a/62 huihqa 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 gravity at the 1hu2haks/(ae; qfq6i Earth?

  The acceleration of gravity on the Moon is one-sixk z:9)9vx/t1eiu , u;iz)bwi zrgvh,mth what it is on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Moon's mass compai t)krviz;:)u,v/w9umzhb,9z i1 eg xred to the Earth's?

  Two planets have the same surface gravit vlfc4 9-fw0 *youdx,ay, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of plan, wx0cf9-4*ly a oufdvet B?

  Two planets have the same surface gravity, but planet B has twice the mass offx1:g8ld i da( planet A. If planet A has radius r, what is the radius of plal xa g:1fd(8dinet B?

  Consider a small satellite moving in a circucm5ka ; 1d3kiair p*/blar orbit (radius r) about a spherical planet (mass M). Whichd/k5p ii 31c am*;rbak expression gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, ai+dhyjd(v:i + nd rotates in the same orbit. Comhd(v+ jiy +:dipare the two satellite's speeds.

  A person is standing on a scale in an eleva zsuw hqz,qno4d 6/5,o ,+khpz/hsat3tor accelerating downward. Compare the reading on the scale to t6zhsha/,qzu4q3o,t ,+hn/szwkpd 5 ohe person's true weight.

  Who was the first person to realize that the 2 o hzfikemq w ,ad8p3(z+3*vvyrv/* mplanets move in elliptical paths around th3 daz zkm,8q* (3re i/pmhyv+ v*fwov2e Sun?

  The speed of Halley's Comet, whiznn72qedhj f;/3 esa4le traveling in its elliptical orbit around the Sunh e zn2q;7efj4n3sd a/,

  Let the average orbital radius of a planet be R. Let the orbital period be T. uqw kbi( e1wp,cvg7/3 ayb5z5What quantity is constant for all planep,u5igcy/7 bv3 wzeq(1w5 ba kts orbiting the Sun?

  A planet is discovered to orbit ar: v93r gut8fizound a star 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 planet be, compared to the Earth'sgv: t r8z3i9uf orbital period?

  The average distance from the Earth to the Suxp,ds.btb +*hui n.l4 n 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 the Sb4btnsdu*+xhl.i . p,un?

State Kepler's laws.(euyh0icx: -9a9geusa (7 +7vwgr1gv qq lno1

  List the four fundamentac-ngt.4/ 0cztxo s4* jwf,jy gl forces in nature.

  An object moves with a constant speed of 30 m/s on a circular tr)f jzfgh hy3j+c9qh)2 ack of radius 150 m. What is the acceleration o qh+)3gh2 9hy)jfjczff the object?

  The maximum speed around a level curve is 30.g+d sp9 w,3qq 00q)cgnktb1ng0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all other )qng,0kc0twsd+q3 ggp 91bn qfactors remain unchanged.)

  What is the centripetal acceleration of a point on the perimeter of a bicyc(m9ui j e 0q,vdq6t .9mwkq9arle wheel of diameter 70 cmmqwr j0d9e q9tv,mk ai (9q6.u when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is locatel* zednc4u2me h05xcp cb7k-+zr;4m 1s*ojddd 0.200 m from the axis. Whacdme7e5-** 1d ckxus4dpzz; h2boc+nrjm40lt is the centripetal acceleration?

  How many revolutions per minute must a circular, whvr1:wr h3y. rotating space station of radius 1000 m rotate3:wh ry.hvwr 1 to produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around apw 7::c2jvon0mh -dlv 13.7 m radius turn at 96.5 km/h. What dh2v:-07:j vnm p lcowis the centripetal force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m string. The system is whidkd l/ p;g:e0d1y *zogrled 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 bre ;:y/o1dgg* lk d0pzdeak?

  A stone, of mass m, is attached to a strong string and whirled in 3ty vk)by(to58gv5eo ep -de 9a vertical circle of radius r. At the exact top of the path the tension in the string is 3 times the stone's 8be(d-egyt ekoy5 5 93otvp)v weight. The stone's speed at this point is given by

  A stone, of mass m, is attached to a strong string an tx7kq:a:wg 1gd whirled in a vertical circle of radius r. At the exact bottom of the path the tensi :gx:1agktq w7on 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 acceleratio1cgb1:0.afg kdgbnl.ia1-p y5a g5 zq n of 4g when pulling out of the dive. What is the radius of curvature of the loop in-pzc5gnfylk ad:qb 1gg0agb 5. 1ia.1 which the plane is flying?

  A pilot makes an outside vertical loop (in which the center of the loop+ e vd.1ufuq6y is beneath him) of radius 3200 deyfu u6.qv1+m. At the top of his loop he is pushing down on his seat with only one-half of his normal weight. How fast is he going?

  The maximum force a pilot can stand is alkydknj,m.4+js0 tgu6woqp vg9 + .l :bout seven times his weight. What is the minimum radius of curvature that a jet plane'snu4og. y m.ld: 0jq+ps l+kv6, jwtgk9 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 radiui9 i h/16 w3difvpb 3byu4tup8s horizontal curve with the tires on the verge ofiwb/u9udtf iy34h6pv bpi 381 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 50 m with a speed of 20 m/s. The 5h7xz( l08k jrqr)mcccentripetal fo5cqc7(r krm8) jxzhl0rce 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 radius 50 m g66 yag h9fbr.,0p ql;lkvp sq3v. j7aat a speed of 14 m/s. What must be the min60 lkla f.;q7hva g6v yg,s3bppq. 9jrimum 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 a gxy3mzm*sj3 jx7 4(fz9ln(r6wg t0otround a level curve. The coefficient of friction between the tires and o6(wr47lsfyt*zm n3zx m 0(ggjj9x3tthe 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 p6cgf,f9 cnuq/)gu9 e required for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without /q9 f c unfu)g9p,6cegskidding? (Ignore friction.)

  A horizontal curve on shq4kv aob ;*2a 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 m, banrt,g0)t(a 5mndw6d pvked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is*myzttdj:6d (.dqh58anoq r + banked 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 ubi.m dkb o;38a(q7b r;to2hjeuh/0a uniformly in a horizontal circle of radb2jou h/hibaromq0(;;7e3t ub8kd .a ius 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, az,;los. 7v hiz.nai) g race car accelerates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular t7)is.i,hl z v.zon; garack 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 ofe d1 oas/m0 /dz lz-or4oxd-3q 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 standing on the Eartj4qp;jhbkb7umz;1hd 78eg )8 jwnz f8h, due to the Mooz q7g8djjk ;)1p48fzjhn7 bebh8 ; wumn? The mass 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 folmi4zh.:8 y,ff)u ;oy 9h hejjrce between two masses is F. If the masses are moved to half of their initial i4yoy): ,.hhzhl ;uefjj9 8mfdistance, what is the gravitational attractive force?

  For a spacecraft going from the Eo0 ejytn 9u,j y5m6:)taijg*barth toward the Sun, at what distance from the Earth will the gravitational forcestt 6 y0ej,*n)oi:y gja5ub9j m 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 is uf7vh ss; o9nvntm0 )z5djv2 ;$7.4 \times 10^{22} \; kg$ 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 thzx 1ysg*fkso1sd 92he +h ea:qoz(yhk5(:0 for a "space-walk" at a distance above the Earth equal to the radius of the Earth. What is her acceleratione2(f yogyohqe:zxz1:k+d *5tas1 ks shh( 9h 0 due to gravity?

  The radius of the Earth is R. At what distance above the Earth's sur5k;f(vzzyc ger s45 w7face will the acceleration owcksey( gr5 fvz7z4;5f gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distance above its uokunj-+ d f -;: 8b))zhc-npp r;yysksurface equal to 3 times the radius )ysr:y fnhu ; czd-- kko8np-u )+;pbjof 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 i0r s5v)gxq xg.ntg.2acceleration of gravityr. gni2gx).v50x g stq is $32 \; m/s^2$. 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. If kqiv + qay-r5d4liw29the object is rai+yq9r4i l5ak2dwq vi-sed to a height of 3r above the Earth's surface, what is its weight?

  By how many newtons does the weight of a 100-kg person change jnjbr479nv 1mwhen he goes from sea level to an altitude of 5000 m? (The mean radius of the Eartr njj b91n4v7mh is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite of mass 100 kg is at a 0obzc nc-*d9p r d-73 qsx*boqpoint 3r above the Earth's supqqd9cd07x-o s r o z**b3-ncbrface. What is the satellite's weight?

  A spherically symmetricjdc*v( lj -j+eld 7dn. planet has four times the Earth's mass and twice its radius. If a jar of peanutv-l*l+ddd.( j7e cnjj butter 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 sc)9 wr,:+lc l )kf6veztq y8vsame line, with the Earth between the Moon and the Sun. The Moon has a + 8)lk:vr tccq69 sfy lv,)wezmass 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 *3in+. m crcxtMoon.
(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 ag:em.,j;db xpoy: tx:bout the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The :: jmt;ygxbde,p ox :.mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about the Earth (i.e., it jusznz *hoa*cj75fd0 cw wx1g/fx2s mq: gv6w y97t skims the surface of the Earth). How long does it take to make one revolution around the Earth? (The mean coc/zwnj vgfa *27x97y6 z*0dq hxw5w m1:gfsradius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 km aboxhp 07z0 m:loxve the surface of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (Tx p7x:0hlz 0omhe mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an orbital diameter ofq3-c(z pt.,v1atcwl3aqyar0 n 9)h nd $1.34 \times 10^{9} \; m$, and a period of 3.55 days. What is the mass of Jupiter?

  The innermost moon of Jupiter orbits the placoezrghwa66;/+1 im mnet 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. Moon A has orbitalu l4ydz5qy .+q; xk)la radius r, and moon B has orbital radius 4r. Moon A takes 20 days to yzyl.;l a)uqx +qd4 k5complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter is hw5 .9/rcu nyp$7.78 \times 10^{11} \; m$ 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 7vq 0 szgv)r.athe average distance from Jupiter to the Sun? (The distance froa zrg.)v7vs 0qm the Earth to the Sun is $1.5 \times 10^{11} \; m$.)