Sometimes people say that water is removed from clothes in a spin dr4bzpkla6o n16cg / assa1)pvy (a: fa)yer by centrifugal force throwing the water outward. What is wrong with this statecaa)( g s6/z4 lpaavybanko6sp) f1:1ment?

Will the acceleration of a car bs86)-o0skd/ a1iit q4 5 ux rdebq*yzme the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aroundeo t a/brk1) 04m*6u yi8xsq-s5zddqi a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car lx xfrp(hqu.53.0h w texert the greatest and least forces oqhwxt.fl5.0r ux (3 hpn the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a mev5 i4x-tiaq 9qa:1nkk rry-go-round. Which of these forces provides tha:4k9 q-5nqkt1 vaixie centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withoutwy /yja. ib,5j;7pucj the water spilling out, even at the top of the circle when the bucket /j .yp,cji7ubja;y w5is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three,u;1h8c yjiyi controls in the car which can be used to cause the car to accelerate. W cj1y8 i;,iuhyhat are they? What accelerations do they produce?

A child on a sled comes flying over the cruyrireia,*8q 375p;2 u ac cggest of a small hill, as shown in Fig. 5–31. His sled does not lege 5*yp2 8 ;iiqaac7ur 3cg,ruave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwa27;w0f tr6 0jnwwh ugbrd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bank1 4 my f*dzet1 kk)xhxf*hg1m7ing angle given its speed and radius of the tu11x*4t khm)hgfm fxyd1* ze7krn?

A girl is whirling a ball on a string around her head in a horizonta;nq/ju n-a :kil plane. She wants to let go at precisely the rik n/qua:;jni- ght time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forvrw n214s*6 cm +uke0 ux6edsbce *01s 2kc6msrwvude+nx6eu4b ? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s+uqk sy if22h: orbit be differe+su2q2iky:f h nt?

Which pulls harder gravitationally, the Earth on the Moon, ogna w*9 lv4wo/bg1s/w7b3 szzr the Moon on the Earth? Whi s wona31wg7v94g /wzbbs*/ zlch accelerates more?

The Sun's gravitatio yf4 21),.kbdp a5ml-is olpjknal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible forpm2)sbk oj 4ypi5 l. ,aklf1-d the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two ebrau+pooyi-0( k x5xw7n 7 l,h:jbrn:/no x 2iffects are at work? Do t5 2,0a:k bnr/n ix7 -b+lox wnj(h iou7yr:xpohey oppose each other?

The gravitational force on the Moon due to the Earth is only about half the7wn(vqz2bg8 tot5s7 r force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earv 8szq 7b75tn o2grw(tth?

Is the centripetal acceleration of Mars in its:fatpbd.4- j+4 bl.p +zkdymqr, j6f9j; mmuk orbit around the Sun larger or smaller thanb kmzp;julp .t6dq,mjj: k-+fm+ ay9d 4r.f4b the centripetal acceleration of the Earth?

Would it require less speed to launch a s eoj/oow6,tn 2atellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direction.,2 wt6 /enoooj

When will your apparent weigq2g4amz46 mpr z5z ;wmht be the greatest, as measured by a scale in a moving elevator: when the elevator mw;4z p2z 5qmmar6gz4 (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely aftof pms0(8v-t: 04;zork6c augyltc3xp8 p4d fected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (m3ppl8 k 4- ry:z ;0xov tusg6at d40oc(c8ptfc) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightw 67ql(+ 1zfe4rn8rd pdg;nth lessness” betweel17q;drgztnh8 rp ed (6nw +4fn steps.

The Earth moves faster in its orbit around the Sun in Janxj .j5. 5m w0tbzyv:lmuary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of itsw.:0mblm .jyxjv tz5 5 orbit.]

The mass of Pluto was not known unti*o 1uq h+*:njcx9v+uxl 6ocp ql it was discovered to have a moon. Explain how this discovery enabled an exq 6 c+ 1x+hoj*v: qc9uuolp*nstimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larg 4hc cbzqu prf7d4uab;b5(sj ,:0sbv6er than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]Aq644b 0husb7,ra5cjpv zdc:(u f ; bsb child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelin0 ilhg9uo+/os g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit aroum6n vigi lj8tul +nt0-olte0l- 4+ft2*glgi6 nd the Sun, and the net force exerted on the Earth8g6let l tlg vu i62+om l+fg0- t*jntnl4ii0-. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kgi oijs5 6h)m2p discus as it rotates uniformly i)o6hisji p m25n a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surlo *k43 g) lk7pfgv/qcface, and circles the Earth about onl7 opl/4g)qgk ckf*v3ce every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spezhz1py/1qr zr8a0o7cck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 3apr zz1yo81hqr70cz / 2 cm?   

  A ball on the end of a string is revolved at a unifor)weoh sxnyu;4,xv9(by/b 4og m rate in a vertical circle of radius 72.0 cm , as shown i;x9 (svy4/u o oyb4b eg)nhx,wn Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of ra w)3vy7n(qr rqcg :x gl*4y*omdius 77 m on a flat road if the coef)r *gm wyryl:4c qqx(3v*n7goficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coe72 9f-im 3mf(ceyso zb5t/dn sfficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of/mme(fc bsy9 5-fszi2t n do37 95km/h ?   

  A device for training astronauts and jet fighter co;7q*lbwe jzs;c:mjf+6q a u(u x-1m pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weibq;7* (zomc+jea;16u xq:juwc-lm f sght, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntln9d w; .w.wvf uvvl/qe,0l;f able of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is th fu vqw/ld vn.0v;lf9;we,l.we coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when8*m1;9rbncmh7f5 zmj vkkt5n upside down at the top ofzc8rm 5m7;fnkkv n 9tb*15mjh a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (includi8ih3c zvjev*fv 4) -omng the driver) crosses the rounded top of a hill (radius )zv4v*me3vo- fc8 hi j=95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Fer**ql)e t/ivy tris wheel need to make for the passengers to feel “weightless” at the t*itq*) tl v/eyopmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertianyhu;o ;7eo7dul(/t cal circle of radius 1.10 m. At the lowest point of its motion the tension in the rope support7al7 othunyd( ;eu ;o/ing the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from thut jb-l(x1ct lw *p;9ne axis of rotation is to experience an aj cx9-w1nb ltp*t;(lucceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cy1- lm*x2g/ev- i3ksz1uk89 i-u dmpbuyin t*flindrically walled "room." (See Fig. 5-ib 1 *2luxvsk*-mmt yfe3ik8u1-d z-n9i g/up 35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frzpnz,zk20 yc y ;i ,l.qoknxojxn4)7; ictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through, okx n7znzp0i;4.; j2)c y,q kloxzyn a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not igno-lb sih;(vy;q0v) xpjring the weight of the ball which revolves on a string 0.600 m lonhv(qs j; x-0yv)bpil;g. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is re37k g4.ikrh+m pp ;, cw,nabperfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massetm)gn/ :;p1spa3ktg8g pa m s:s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an elhnlys8;mj, ;k,9eq xvasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripefx.pxdkd;:-xp+ym ,0 b0rq* u+ xtb krtal components of the net force exerted on the car (by the ground) in xfbr +-*ybkup q d;+m xd0:.p0xkrx ,tExample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates -/tq;ghlxyz y/c. hh/uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tan.c lg;h- /qyhhz/yx /tgential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circh ;0rdnjyv7 lj1ik ,d lzuc2o/ o zr+x(xx;z/1le of radius 2.90 m . At a particular instant, its acceleration is;koz dunlz rj1hi/ +;o(xcr721dvyzj0xl/,x 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Ea ,9594zv1tw p.c fj1akgnpu 7u, vd,jhltd7jrrth radii) above the Earth’s surflthfgajnt9 uv , wd1c7u59j4dj ,vk7 .rp,1zpace if its mass is 1350 kg.   

  At the surface of a certain planet, the gecos/35,*xznh2+kjeo( ix vu ravitational acceleration g has a magnitune oh ucsi 2 *+5exk,3o(vxzj/de of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is ha t amk/)*vrs* -hg9m1.7s/kvht)*- h*mgra a9 m4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of uicl/cu 1;.vfsma.4 k:b4ysa Earth, but has the same mass. What is the accelerationm1 f4ya4ls / caucu..:vi;skb due to gravity near its surface?   

  A hypothetical planet hasv*:gz)ts* 5mq ztde:h a mass 1.66 times that of Earth, but the same radius. What is ht:e:zs5vd*tmzgq )* g near its surface?   

  Two objects attract f2x lscak cd*z)4svp kdne 8/4vo )f 6-.in2xaeach other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, aow)5dfb 3tu2it (a) 3200 m 5)f3iot2wdbu    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinzzivw)d p4k(5kl ntcvo.r1.+ t outside the Earth where thegravitational acceleration due to the Earth i(.v n+wd r ilok )z5.zt41vckps $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass olw9gn: liw lls/we,d- )f c1)sf our Sun packed into a sphere about 10 km in radius. Estimate the surface gravitycw9wnsl )/1gll,e)s id-l fw: on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like aa 8c- ryt,by6 uuv5fit:4rk 3our Sun but is now in the lakr56a4acuf vyt3ir- 8uty,b :st stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why ao0fuxqgplu-)+zp*bm hj -w4e. :n j n+stronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km ab*g b+pelj:j. w-unmf- q0pzh+n4o)xuove the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squzgimac5/fyqacp *210f bb02sare of side 0.60 m. Calculate b z/0 mqs1ga0fc2a2bf 5ip*ycthe magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of thehu;djxxx :0.q Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets auxh x0;:x.jq dre in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars - o86zw yu87 t us3sbojfivz7-is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine th z7 6f8s83vt-bzwuijyo7u o-s e mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth goz:j,8vv(xxe p( m*tand its distance from th t xx(z:*po8(,vjvg mee Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the ki5 kbc3vfxf4;w-3 gq Earth at a heigh3 k4cwi3bqg ;5fx- vkft of 3600 km.    $\times 10^3$

  The space shuttle releaseshrl zlvuf2 5z4tp(7m. a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rm4u2(p z.7zf lh5t rvlelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantv uw029:72aiz +j ee;v aegzyjs are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32i;2vjzg va ue29e:aew+ j70yz.)   

  Determine the time it take fmu y 0myxt;cc18wf2+b voz17s for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compa;tfmo2u v+zmfcc0w7yyb1 8x1 red to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the t-zk;+wxt rltbtxndi. -(ds * 0 d9q7ooop oid t *d;zwtx o.x 9r(ls-d-+q 70tnobkf Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar8:r g,51ld dofuag ;sc landing mission, the command module continued to orbit the Moon at an alt:adfgr1 cs,o85ud;gl itude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks ofhv6s 0 okl6vi( ice that orbit the planet. The inn06(hvosv lk i6er radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates oncj2x2 ca vaaa74e every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottav72xaa4c a2jom?
(a)    (b)   

  What is the apparent weight of a 75-kr.13 n4*nt bc4g ntrbacv9:dpg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) mon dcg4rnv.c3p 4 ab9 *b:ttnr1ving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary,pi51 v/baq rw(,do1hl vh)gy/8 vgyi-star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What i) 1gvv o/d1a8h/yrg,ip vyqb5,wl h(is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in r)m9 pvl8n g8x*r 7ippbw hxwz*z:j 51an elevator tham p :1npjh*w5x9r)wrib lz *8gpv7z x8t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. qh v r6bv,2jv8The cord can withstarh8,qb6j 2vvv nd a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surr+dzgef vk* +-face of a planet with period T , the dens*d+f+ ek-gzvr ity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to detenncau/oppdg1p 3yz, q)r/;/ hrmine the period of an artificial satellite orb n3g/ n/c1 ou pdph;,a)q/yzrpiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hul;g fb ijt7en312uxubb :(;m dndred meters across, orbits the Sun like the planets. Its pentx:f2;(i 3dl mbe jubg;b17u riod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.9 ggk0sohiu5f: fvm), em7 0df5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It c7x7pzq5 - sqryomes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from theyq7r x7zp 5-qs Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gaf ,azf+g ocpc02v)ic tnp66n .laxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest mo : /teplp*6lggons of Jupiter (those discovered by Galil6*ep/ pt :lglgeo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known phq1 r/:lp+yd lcjybcv)e) -:period and distance of the Moon. y+rl): )-pjc db:/qhpl 1veyc   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usinm o zt)ibii:z 1ap ,*4b5xmv(ng Kepler’s p n(z,a4bmto):m5 *bzviiix1third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (ckp,m p0(h ek,k0lp l(which some space scientist(l0ep (k,, p 0kcpmlkhs think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band nh.3xxlnkzi 7,8 k/-md5: towrnm (f7jx6g mrcompletely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun l- ikhnm 3gonfm5t6k,( z rwmdx7 x .78/rxnj:is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross im *7 evd8+g8jgf13 tg4wdzy pb*6fbaa gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a ftg*7g1z3db dw8iy*ve6 gjp 8 m+ffba4orce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of p7f 0ke (-ks;gw8g wq(nlf 2tcgravity be half what it is on the sut k2fp(fq kg- l;78ecg(w0snwrface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and sping .-vw iety df:i2.qf1 in a mutual circle once every 2.5 s. If we:2-ftev wdi i1.qg.yf assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelfpvax5 +59f. hfa chx/eration of gravity at tv/fafhxx95fhap 5 +c.he equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from th 6kvtx6i)f uqzf ,,,nylau1b 3e Earth will a spacecraft traveling directly from the Earth zy xv qntuk,aufbi1,l6 ,36)fto the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you j *z v z7* sclep/,(sahnp9umry9e.u: stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the upr*n:cu7 ,y(hm* ez.a/sv99l epsj zacceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station cons;0;bw6hq6,yq9u ybvlz d jbq 9ists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an eff,9u yq0;; q 6zlvwhb9dq ybjb6ect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft intr,1 mv1e:dnkoz- ( e.vsggswh;vl3 : a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accelerny2vr,4vj +zhf vh ,6jation due to gravity at its surface and the gravitational consh6r +,vz yf42 jhvj,vntant G.

A plumb bob (a mass m hangivq9ica- i *a-gng on a string) is deflected from the vertical by an cg-qa 9a *i-ivangle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67gs*gwpa 9 (nb+ m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement)b9 (w +sgnpa*g, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the e: nj za)r/ /pjf0vg6jyquator wera/g/:yvj j nr) zfjp06e apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a chs g-s-um tvm x/0b24bonstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radqo4je6h1+lcn i pf;5cius 235 m. A lamp suspended from the ceiling swings out to an angle of 17jc;i nqh64+ epo1l 5fc.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the6foh/i dpq 378msoid8 Earth. Thus, it has been claimed that a person would be crushed by the force psoh6f q 7d md88ii3/oof gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremewtgh:knt64ap* jw.9 dly massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of w4t.ap g hw:k* j9d6tngas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trav mgxq5.*c/cr zerses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car acc.x qgz5r */mt A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning olt.t(o92 :hz2xnedoSystem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these sa9:n tzo oxl2dt2h (o.etellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvozf8zjsd.70nmk h m 08fus (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 4hmz 0n fk0fd.8j78 mzs0 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a sate 9nufc(i3a3pgx -bz8xllite in need of repair. You are in a circular orbit of the gpx(u3n x8cbi z 9fa-3same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period k)0m1ch n-zph of 3000 years. (a) What is its mean distance fr m-nkcz1p0h)hom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of Gn*cy .acec4a8 would need to be if you could actually "feel" you ace8nccya*4 .rself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy ha2wk;g1(t au(Fig. 5-46) at a distance of about 30,000 lightuw2ta k1(g a;h-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses aqc 1u57ap8 fcaloh, a:re located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placedlc ,aoa:qah57f8 1up c at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbdnflbn fm(15i*6, vbhits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep secon;p)2r/rd0 ticts-b rad hand on your wrist watch? c)r;-r brtds 2/tiap0    $\times 10^{-4}$

  While fishing, you get bored and st*cs;t4mno ysu 9r)dx-art to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishin *;tom -4x)dscr syn9ug line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is6qjy e6yuj23 r designed so that a car traveling at r63j26y ueqjyspeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the A1twb fzt8)pc, cela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider a pz1,ttw8cf )bn Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$