Sometimes people say tha,ls /dng: p;u 61lgeh9e0eewot water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stathuds 6o ,e90:wee1lg;negp/ lement?

Will the acceleration of a car be the same when the car travels around a sharp jcc lz9* g9h+wcurve a ch9+z*j9l gwct a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along+qo .h3 cig1qw a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bhco.w13 ig+q qottom of a hill?

Describe all the forces acting+o:yya;p b2 tb on a child riding a horse on a merry-go-round. Which ayt:y ;p2obb+ of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wate2w1z-*n ,c 4v/syedkvxdo tt+ r spilling out, even at the top of the circle when the bucket is c *n ez4/,-+d vovxdtytk21wsupside down. Explain.

How many “accelerators” do you have in your car? There are at lei o4rp2)s,bjk 8zi:l *gxe qc +1w4qvfast three controls in the car which can be used to cause the car to accelerate.c2f:is4 ,kpoi4vgq x8*zej1lwb r +)q What are they? What accelerations do they produce?

A child on a sled comes flying over the9jq6/qz7c1 v+ gim2 grq3yz rs crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does n1 + 7q6cv3grrqij zy2qsz /g9mot 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 inward when rounding a curvyy6k l)1c 9cmc6te6dme at high speed?

Why do airplanes bank when they turn? How would you compute the banx/cnu; (a8p3n2ap7xt uot 6zsking angle given its speed and 7s6z a3/xn8 c2pun;xu ttoa(pradius of the turn?

A girl is whirling a ball 2 zdqnz/qat4);;m. wg+tv box on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will/ o;2z;4mx nwz.dtgvqta qb+) 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 lar8q+o)kk tcroj/amx;l t e-g1+ge a forcec+;m/)oex k-tq8l kajo1 +t rg? 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 tt(94 ;qz(w oitnu46tl fkm6c fhe Moon’s orbit be diffef6t( c( zq9uw 6inlmto;fkt44rent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E7 /jt j++bd xgl3sh qucd-v28barth? Which accelerates more? scu/ t l-x d+2jbgqvbd37h+8j

The Sun's gravitational pull z2 th/:m (dugqon the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from onet:hgq( 2/ dzum side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effecty ku1yo9lu3ev3h6x,n + cu9nhs are at work?69x,oyu3ye c31hlv n9+uh ukn Do they oppose each other?

The gravitational force on t 90egdbuk.*md6i oo;9f 4gecohe Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulle4di o 0gkd9 g*f6c.o9eueo ;bmd away from the Earth?

Is the centripetal accelejcsv( uzz/5kq** hhn ,ration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of z(n,cjqvh 5u*shk/ *zthe Earth?

Would it require less speed to launch a saxe(s *s-a8(s gpiz 6 m30rji5w3emb ntgu8b 3atellite (a) toward the east or (b) toward the west? Consider the Earen*3 w atag s85si0(p3siu-8z(bmbmexr63jgth’s rotation direction.

When will your apparent weight be the greatest, as measured by a uel8 ;fxog,7fscale in a moving elevator: when the elevator (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 youfel8u ofg;x,7 are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could k2 el0/k r1wccxrcm44be adversely affected by weightlessness. One way tok0le4r1 wc 4m/ccr kx2 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 (c) any other aspects of gravity you can think of.

Explain how a runner experiences “freemit9:e d k(.p*z zjbt8 fall” or “apparent weightlessness” between 9zm(ki tjd: 8 zbp*et.steps.

The Earth moves faster in its orbit around the Sun in January than in July. zmi;zfse+i 55Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasonsfeszi5z m; +i5 — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not k ,qy isgu hgl*acl+.- ,,8pvnhnown until it was discovered to have a moon. Explain how this discovery,hpq ,+u.-y,cggl* 8vniaslh enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on th 7g/jzztlz)nc v8l.5y e Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one sj7 z.vl)c/t zlz8 yn5gide of the Earth to the other.]A 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 traveling 198acylax z:.uxr )k+06ew) m+l h0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 around the t0;i6teq )rsfx n;hw3Sun, and the net force exerted on the Earth. What exerts this forcrhi 03e; x;tf qt6)nwse 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-kg discus bid b*6 k8ay7*waln4wv g: qb/as it rotates uniformly in aby4*v8 g:abb7liawq k6nw*/d 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 froaes l/ m/x5r.pftjcu vsla/c k.n :3;0m the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitatio k5/;0lta/fj xae .3srlcmuv. sp/n:cnal acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge g ()vgy-bt70jcni k4h of a potter’s wheel turning at 45 rj 4ycb(g)i7n0gkt h- vpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of almh5jv4(pf6* lob5lb u cxe hh) 89uj: string is revolved at a uniform rate in a vertical circle of radius 72.0lv mjefbp4 b(5olucl*6 uj:95x8h ) hh cm , as shown in 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 rav) 9rzjtj- ;tpdius 77 m on a flat road if the coefficient of static -jzvtj9r) ;tpfriction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the co511qcvgs 2ig*9 av kxkch/f 2refficient of static friction be between the tires and the road if a car is to round a level curve igrf1k2q*/c 92ksv agcv 1h x5of radius 85 m at a speed of 95km/h ?   

  A device for training astron -prxuwy4 r*d+auts and jet fighter pilots is designed to rotate a train-+y xrp*ur4 dwee 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 weight, 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 turnt*fls.*m w ft 9kfgd3lhm ):zc(able of variable speed. When the speed of the turntable is slowly increasedf.*mgmzf(:ck)l wfl3t* shd9 , the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when bld1)g icmmu +b1az7y a/ykw74 p. j+gupside down at the top of a1mj ay71wlc+. y7)zdmgip k4ug/a+ bb 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 g12,,qokgj za 950 kg (including the driver) crosses the rounded top of a hill (radius =95 o,j1,a2kq ggz$ \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-)x-frwh n 7)csm-diameter Ferris wheel need to make for the passengers to feel hf)c xwsr7-n)“weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is wa 7t lh8l/i zrhp97t8shirled in a vertical circle of radius 1.10 m. At the lowesth878 s lzl7r/htpai9t point of its motion the tension in the rope supporting 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 fro( wj6chm p(8lpm the axis of rotation is to experience an acceleration o(lpmc( pjh w86f 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wallew)m1a jb4475.d bmomm un -dvyk0 g+dvd "room." (See 5v )duk4+7v.nmbm4 ybg-d j1m oadwm0Fig. 5-35.)
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 t89,f6tmd 3ks1nzsfa in a circle on a frictionless air-hockey tabletop, and is,sfmftztsn k9da 8163 held in this orbit by a light cord connected to a dangling block (mass m ) through 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 , precisegfn zzfxkt1js;n9ay;mzv 1 ;h. 6ut(9 ly this time, by not ignoring the weight of the ball which revolves on. ghzzs9u;f16m( zf n;t; 9xantjy 1kv a string 0.600 m long. 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 perfectly banked for k7rib dc /xg45a 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 masse zctwqsu ilnm7/ s7w5*jw,d bx3 q30b*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 evasive maneuver by diving verti n2a6 6tdje(qqcally 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 centripetal components of qmo,b p :31w0hskj/j vthe net force exerted on the car (by the ground) in Example 5-8 whkoq /bj3m1vwj0h,s p :en 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 uniformly from the pit area, going fr a gglmu8 fn7mkk.0(d9om rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would th9 lmku (gg.fadk08m7ne 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 circle of radius 2.90 m . iwb7 lngi (1gx2 ypf(3At a particular instant, its accelerati 1pnbgy2i if l7(3(xwgon is 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 m.f4j;3ufh 7tiliu8jf45zsbhi+; m ikm (2 Earth radii) above the Earth’s surface if 4 ;tisf7m3 huu+ibfmfz h il4i.85jj;its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hasi8ua*hd wly0h 8sd m.) a magni)sy88lwihd 0am .d*uh tude 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 g+6mw;he9hmk/jza rg:ravity on the Moon. The Moon's radius is 1.7:m+a; h6hrgjk9 wz/e 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 Earth, but hai5 ,p ;1gmuzt(ve-bd ts the same mass. What is the acceleratzg( udep-t5,1v bi;t mion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but . 4wx/q*oyg tneeg1-w the same radius. Ww nxo y.gee/4gtqw*1-hat is g near its surface?   

  Two objects attract each other graviiy zw. u*r7e2 * d3ignfofjk:1tationally 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, at (a) 32: ,u p2pol-i*m8g dhzg00 m-g2z8:dglpoi,u h* mp    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point qiquw xld;36n uqe9/* outside the Earth where thegravitational q nld3u/ wq9exuq6*i; acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of 2z,t cowglm)8.lc( er our Sun packed into a sphere about 10 km in radiusg 2zl.,o 8cm(clwert ). Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a,uja amkp 3q20d *gct- p;gpi; z7it*qn average star like our Sun but is now in the a-qct*q7gp3 ;t 2ipzmd ujpig;0k* a ,last 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 astronauts feel we-xgt( +fxl)1ss jj w*rightless while orbiting in the space shuttle. Your friends respondsj(slwf+rt x *)1x- jg 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 above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres +sxevij1 46y 9,ejqkd)y vi9zare located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by theyi6ejvv,s+)izk ex d 1j9q 94y other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years bb 0zv hi ;7dk;zag0b8most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a hbbd0ab8;vz7;zg 0ki 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 accelerai 4b9ltgt8ov 8tion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ b t988 gt4vloiradius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the S yd:k/cq) )oexbc u.4n.hxa 4vun using the known value for the period of the Earth and its distance from tuh4)y:vkaq .cxecn xod/4 b. )he Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a 7 j:j k6(gxanjsatellite moving in a stable circular orbit about the Earthn:xk(7a 6jjj g at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circula9:uc fvyp j:1qr orbit 650 km above the Earth. How fast musvu:9 cpj:f 1yqt the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotau: 4*og/fz3 jc9jkvs ate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time neej9f/ zu3:gj*4vskco aded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to /qgemlw2j*b f:gza+w 1o* fq4orbit the Earth in a circular “near-Earth” orbit. w wge*+/:2qflqaj1go zf4b*m A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity row4djqi9g 0(would a satellite have to be launched from the top of Mt. Everest to be placedj qwdr9g40io( in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command mo:8h0 um9c rd* upgmh.ldule continued to orbit the Moon at an altitude of about 100 km. r plu:m c0um.h*98dg hHow long did it take to go around the Moon once?    s

  The rings of Saturn are mc5jg xc/*fe, composed of chunks of ice that orbit the planet. The inner radius of the rings is 73mcgc* fjx5e/ ,,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 rotnfz a:b;a5gr;ates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s ap :a fbnza;g5;rparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg asx/ ztkzes5 x,w4a6r)vtronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at const4 / wktz,e65xvxr)zas ant 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-star system cons 9; zqgr9qdmz/ists of two stars of equal mass. They are obsem9g z;qdq9 r/zrved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman euh15 6zhdbsc7f1l5 uin an elevator that moves u sef516b h1u7ldzh 5c
(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 ceilim xf7h(ov fk4fo.*x3bng of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and di .3 f74o(b*h omfkxfvxrection)? a =   

Show that if a satellite orbits very near th j7jmgsv a;af4loll.e5q k)o8d .g4;se surface of a planet with period T , the density (mass/volume) of the planet io.8aqd7s)mkjlgg 4o ;le5a. 4j;s vlfs $\rho=m / V=3 \pi / G T^{2}$ .
(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 xxdx48ps)+ap 7 k,rzb) to determine the period of an artificial satellite orbiting very near the Earth’s surface.dxk,p z+4r7p 8ax b)xs    s

  The asteroid Icarus, though only a few hundred meters across, mwtyo we /s8i g fe*f-kb,/5ti(oq);p orbits the Sun like the planets. Its period ise/wqf- efoo*y;i sk)b,pgt 8wi/ t5m( 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4oex.+ ( m2j ez1jrrt7b.5 $\times 10^{9} \mathrm{~km}$ 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. 37 yf+emo7sayx4ld 9sIt comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the 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 ansys+3 ym7lfa79o4e d xd farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center hfzj3*qjmpg qmqg t07, +3 *nb5bto(lof the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 foucv. yv+ odl tm7hja)2)r largest moons of Jupiter (those discovered by Galileo in )h dvj+2a )omtl.7c yv1609).
(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 Ear(j (y+ ezg0pvxth from the known period and distance of the Moon. xep(j+ y0zv( g   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moo opi5mkf: 0q7b ys7hu,ns, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the :pk fuo70im5,yq 7b shvalues 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)hpzhj4us5ygt4 u)y -g 2+fq f many fragments (which some space scientists think came ffs 4pg-g)5yh2)tuy 4j+ hfzqurom 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 describaf6,eey 7h, ;js0rtjyes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun 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 safej0,h7yt y;r e6j ,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 a gorge by swinging in af/a n)qnf) tlf u4i26k8as-ymn arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his sfann2ftaqks6i/-fly 4um ) 8)wing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration *bpgj2c*pg i0d 0 rd( nqk3dw1of gravity be half what gj3c1n d(*gwdb20k q rd *pi0pit is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grtq7gyyyd,nz ;+i 32 qax.y3gvab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their indivi gti 33 gyyn.qy +z;,xavy2dq7dual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the ap,s wl)fetf:mndb)3q09qm, dq parent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractiodf9 m :bd))w tqqm0s,e3flq,nn of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly frouhz;6)xf ko: im the Earth to the Moon experience zero net force because the Earth and Moo:ui 6k)h ;zoxfn pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in oxbz 8tqsrls 1(i49x(t+usa( an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whichq(+rb o 8tiausxzlts14x s 9(( direction?     ----待选择----upwartddown 

  A projected space stationmcx5 zv-zkq l,am(49b consists of a circular tube that will rotate about its center (like zmxkzmv(9 ,alc54qb- 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 effect 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 air1 r*ru 9s7bofn /bnj wpt(9)+tejdt+zcraft in 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 (e14wibd(u4- xrgpawnm-m ukah +8c, radius r, the accelerati icbp4, uauwnxg((m84awe h1k+dr-m -on due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) . )1-i1pdr ekp7ntosil;m.td is deflected from the vertical by a) m. ep1r.nd7lidstit po-; k1n angle $\theta$ 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 67 m is banked for a design speed of If the coefficient of 3nr;v be3n9cw static friction is 0.30 (wet pavement), at what er 3; bw9cnn3vrange of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating ,pd 3si m f71eikkko/8so fast that objects at the equator were apparently weightl1imeik 3s7d/, okf8kpess?    $\times 10^3$s

  Two equal-mass stars maintain ae8 r4vs76z8(3p5yv; ok prv 2mjczion constant 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 ain8g /k 3;qtqt curve of radius 235 m. A lamp suspended from the ceiling swings out to an8; 3kqnt/qt ig angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been clzr8 - qz ) h:v*g,rssg2xmmx+daimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive mo )-rmg:sms+v2xxd8q rzh zg*,re 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 Hk6.uuvf4 (xnpjcr(:qj) ctq/(9g ceuubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be agkv: ntrjfc./u( cq u)pe( 4x9 uj(q6c black hole (from which no light escapes). They did this by measuring the speed of gas 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 tp9 aj/peorl n2j: bzh ua97f2i d/t1)rraverses 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 at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Wh7 p j rjo2lrn/u/91 2)bafat9i d:zhepere 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 System (GPS) utilizes a group of -,:issqr3 pzlsj: /ol24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the E 3r z:ss,llo-q/sp:ijarth 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 Rendezvous (NEAR) rswf*)ru +69cpbm,);mhu bwa , after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km .rubp,)wmchsb +*a) uw; m6f r9 Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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:kh,lk n tw kt:l9p(j1lt ;9aa pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above tl :kal,w(h1:tpna ktt9;ljk9 he 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 of ooybaba3,;7x3a lq 8g3000 years. (a) What is its mean distance from the 3qaoaa ;,bxb3 87lgyo 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 G would 6ljy s-i 4lys2need to be if you could actually "feel" yourself graviys-jy24ll i s6tationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arou2)z ieyqvj:r fbg w-5:nd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about eqfz2gi wb:vj- y):r5 30,000 light-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 are located at the corners ofugall hb i7 1rim2-bs,69ebz35j vvl; a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fift rb,b9 3ii;g l z7llb51u2evjmav- sh6h 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg o0gh+u 9br7ru * h3sx7cbo( eherbits 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 ecaw df,v (s5.qsd. g,1.5-cm-long sweep second hand on your wrist watch? w sq5g,s f(dv,e.acd.   $\times 10^{-4}$

  While fishing, you get bored and start to swingzwg)y r :l sf ,l,-hrue*n9m9w a sinker weight around in a circle below you on a 0.25-m piec9ln zse,rg*yr:h w-w),lf um9e of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designe6zg,4pl- v 7g wc /nt)hf1hzrsd so that a car traveling zglh7 nt /6w4rzgs)1-,hvpcf at speed $ 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 Acela, utilizes tilt ro:e6o irtc70of 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 an 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 oc:i760rt ero 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.$\approx$    $\times 10^2$