Sometimes people say that water is removed from clothes in a/zilo2vi8fkr 5p d-*8zptax0q *wxn: spin dryer by centrifugal force throwing the water outppi5 *:qwk x zifd* 82nz0x /tl-voa8rward. What is wrong with this statement?

Will the acceleration of a carjgof;u )w l.2f be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explainof )g2wlu. ;jf.

Suppose a car moves at constant speed along a hilly road. Where does the car e h )w2 +q/ s7xqb6ph5w.oetuloxert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two op5x6ths/l2ww boqq e7 )h+.uhills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wh v+agx 4ne:e*hicex h:n*ev+a g4h of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in2h5) 8ngkx2qz:r-smc:(zmj o4xix rx a vertical circle without the water spilling out, even )zrxs(q-mj2 cx5 :8xgki4zornm :x h2at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do*)9:pvd wom894/h jgpmcuuxd c0x 1ib you have in your car? There are at least three controls in the car which can be usm40:d/ )ump8 bhwgv upxdi19c*x9 cjoed to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shownq0gr6 zl2w ml) in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels )qr llw g620zmthe 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 curve at high s7w5iyi/ihv3j 4 aotc v v+m/k6f)yk4 ppeed?

Why do airplanes bank when they turn? How woulevq:9+ a avxg8q n6fx4d you compute the banking angle given its speed and radius of the tur9q:fa4 x6 +xnaeq 8gvvn?

A girl is whirling a ball on a string around her s.9cyodr-fp u5xv w *xl283ak head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other sup3d .v8w 5xcsy *f 2laor-xk9ide of the yard. When should she let go of the string?

Does an apple exert a grt+hu m mz,aa.t)0 ,ikzi* h,zvavitational force on the Earth? If so, how large a force? Consa * uhhz.kit+vzit)zma ,0,m ,ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wh9t. hokj fy:,d/e5noca 1lyy)ki m8g;at ways would the Moon’s orbit be c:j eoo.n8h,k9 mldt) ;iyfy/y1 5kga different?

Which pulls harder gravitationally, the Earth on the Mkal6(6hirk5-i*8urhuw a2 pe oon, or the Moon on the Earth? Which accelerates mo a6u*8 r( u5ri2lw6-p eahkhikre?

The Sun's gravitational pull on the Earth is much larger than the Moon's.y8xe2 g1ygex 5 Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pul1yegyx ge85x2l from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effectw0oz6 oup6(fk s are at work? Do they oppose each op(fo zk0w6u 6other?

The gravitational force on the Moon due to the Earth is only about half the fob 0f 0dqf(;atnrce on the Moon due to the q f;0( nfd0tabSun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of x ou0,n7yi 13jhd/h bmMars in its orbit around the Sun larger or smaller than the centripetal accelera/m71jxi,uy0 hond3hb tion of the Earth?

Would it require less speed to launch a satellitw8c62rox bcclym9e/,e (a) toward the east or (b) toward the west? Consider the Earth’s rotatcmxew9ycr2 bo 6,8/c lion direction.

When will your apparent w 0.d*blb3jd 4ztlm41+my nzo ueight be the greatest, as measured by a scale in a moving elevator: when the elevator (a)*0ml4 4 o3lbub1dt zn +z.jdym 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 ou 80g2lcvne 4vuter space could be adversely affected 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 objectnc0ug ev28lv4s 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 “free fall” or “ar45 4 gfgw*o 7pzlg.j.lqrf +ypparent weightlessness” betweepqlzw+r .f7oyfj*.rg45 l 4ggn steps.

The Earth moves faster przvv o/-x s:k+om1z. in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explav.sorx- zm/ zk: +p1ovin. [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 its orbit.]

The mass of Pluto was not known until it was discovered to,rrz/fzdutw)op de-w 3 ek/9v n ;e83p have a moon. Explain how this dk f/3w-z;3pwedeo/uv 9en d zt rrp,)8iscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Ye 37 h-cdfulun m/u12uxt 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.]A child sitting 1.10 m from the center of a merry-go-round movesh 3/unclf71 x-2udu mu 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 travelingbzn2b msgzsre5 aq,2ufv8 0q9(-ckv. 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 around the S.zq) v i ma+t-v6mf1oqzsk1ou076sp r un, and the net force exerted on the Earth. W q6. s0i-mfratos61m)+ozvv7zkupq 1hat 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-kg discus as it r i3sba17e6quzotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. ue3qs z6i ba71Calculate the speed of the discus.   

  Suppose the space shuttle( vuyej9o t+8g is in orbit 400 km from 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 gravitational acceleration at the Earth's surfa tjy+8eu9o (gvce. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a/x5, mg6q3ta 9p )edmudp aqe. pot)6 xa5gedm./ a9,e3 dtppmq uqter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratvrc: m (a9epydg; 7f6be in a vertical circle of radius gbmp9 ;re(7 cd:ayf v672.0 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 carn9l y 1tfoyf2aq3s,y * can round a turn of radius 77 m on a flat road if the coeffi tyy*,ya of1f9snl 23qcient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficvi/l :ujvk o5 (eox8/oient of static friction be between the tires and the road if a car is to round a level :vjx 5i(oku8 vol// eocurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is nf6ndt, ;4fhq4ohg3v 8xd0 mpdesigned to rotate a trainexpt6f,md v ;nqh3f h4go8d0 n4e 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 rotatin-tc 9fe*s0gvk4e f2syg turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpf-ef4csgs k0 *vyet92m 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 upsidwp 4jln3q+/hrsy 267cughnq2 qrr +k2 e down at the top of a prsqhc hn2+ r+6k3jqr g2/qwly7n2u4 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 (includinj. qg2fouk f6wi:qv4c;e xps;3 l045 lkulh8wg the driver) crosses the rounded top of a hill (radl80lqx35j wg;ok;4 pi :hffs4evulu.wk6 c 2q ius =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 (szdnpo4r4geq ,ma f7e 0tx1:fp x91rminute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless p 1o fazpgtxredq:m4, 9fx7(4rsn10e” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical c h 2q v6dazr0v1-pet 8)qa6bosircle of radius 1.10 m. At the lowest point of its motion tv b 8p)d1ta6sqvh0e aroq62 z-he 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 cc sier veirb d280qwq91t6+z 2m from the axis of rotation is8it1v 0reseci2+9z rq 2wd6qb to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people s wuu2; ti76glare rotated in a cylindrically walled "room." (See Fig7u i2gw;ut6 ls. 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 in a circle on a friczww l10a(u(hdt h2u:9cu+j dutionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass 2 (w ha 0uu+lu1ctuwddjz 9h:( 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 , precisely this time, by o 0b8x)d c)2uq6mikzx;z,o otnot ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitu 6cx ) ,txobq;o)0udozi8km z2de 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 mb(rtq988ilne to0 g dto:7 rf; is perfectly 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 masseq:ubk*vte5 ,ajenc 9q9,4 0 tmb fw2fks $ 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 divinguvw)n(v;b tplv 5i*t) 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 centripetal components of the net force exe ;i (r + uu*2iydysd*auqmg1qu8m9em+ rted on the; 2m+1mmuq+*dirqyga*idyuusue(8 9 car (by the ground) in Example 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 uniformly fr2 skn 3fdko0hl ge0p63om the pit area, going from 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 the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skiddins glo03n3hkd 6f0ke2 pg? $\approx$   

  A particle revolves in a horisl6q o ,wzx*xo,2fq a:zontal circle of radius 2.90 m . At a particular instant, its accelerlw26a x,s *qzqo:f o,xation 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’sxmy e-72 gq4-/wc yv1huove1 c gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 13501gequv 7hwm yv/--42 cco1x ye kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mag3c5w9l9z nhkc4cp h2kr8xy*7zjv 5 j jnitude kzhl j*j5x2whrcp395ck 8yj vz9c74n 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 Mo.a q 3+9/ unvtxf;ve+3t cpoj5me xil2on's radius is 1.74t3 x q;n2vxee/pt . +cvma59io+l3 fuj $\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 has the5)d 9puv ,(km6z2no ;e* qga. eykvnnh same mass. What is thev(5eua 29nkygm,p6e.kh)*no q zvdn ; acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 dt.j,p *bjvnlgp 9w5d-u(nry 4fhr 98times that of Earth, but the same radius. Wha lv (r*b,f9d.t- pu5 jrn gpy8jwn4dh9t is g near its surface?   

  Two objects attract each o8l 9svw0po+r-y dm*6afv 6glather 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 v1trhy9t4 f1 e*y4dtme:+odle alue of g , the acceleration of gravity, at (a) 3200 mtefo 1y4 *+ 1mtte4ehddr9yl:    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from thog7yo* 9(xme)hyfeu /e Earth’s center to a point outside the Earth where thegr )yo ( fme7oxh9/gue*yavitational 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 our Sunbeum 4:ssg 66j packed into a sphere about 10 km in radius. Estimate the surface gravity on this momsb6g u s:ej64nster.    $\times10^12$

  A typical white-dwarf star, which dniknm/h kf*0a mzpvo;(28;m once was an average star like our Sun but is now in tho;*n/ 8n2m 0(hmk;fz impk dave 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 weightless while orbiting in xtat u/w-k,6b i2oz)mthe 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 calculati-bzt6k,)at2 mow/ xu ing the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the c:p.ayo+c bi t6 .c(vgaorners of a square of side 0.60 m. Calculate the magnitude and direction of the toy.c vioab(cp6. t:+ga tal 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( -drga(wyzfh;y 7 x-c the same side of the Sun. Calculate the txhcf- yd7a-z( (yg;wr otal force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are 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 Majky zn9(s-t m:l .fpu26urr7: zolhf+rs is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determif 9zh2 ofzspmn( 6y ur l-ltruj:.k7+:ne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the pe02bjfc 65ty2dp qnp7h riod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawsfn0 tpjdyb5h q2p72 c6, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of oxxak799 1quu a satellite moving in a stable circular orbit about the Earth at a height of x 1o97u9 quxak3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 qm9 zt1 o *mwf96vrain t5is/0km above the Earth. How fast must the shuttle be movin/a9mrf*10ztvi9 iq5t wos6mng (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantz.b*r)r8r:vat hz/gzs are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needavg*rz:r zhb r) /8tz.ed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “ne )(r*iiik6xkyar-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whichxy(6)rki* iik 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 would a satellite have to be laun(aztp2+alx *sg t;-unched from the top of Mt. Everest to be placed in a circular orbit around the Earth( tu xansz2gt+;a-l *p?   

  During an Apollo lunar landing mission, the commjj:z 3 .jj,lj-r ixo,oand module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moonzj.r,-oo3x: ij ,jjjl once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. T b)qlg -eck2b (p(;kznhe innc beqkn2((-b)z;l pg ker 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 once ,sf/9 do8dmuw 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 bottom? ,u/f swod d89m
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from thedas:j3;kc2:qtb6ix q center of the Earth's Moon in a space vehicle (a) moving at constant vajq: sq:tkc;326 bi dxelocity,     ----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 consists of two stars of equalh-ty*8 3)klfyru9 t7qf7 u+0 dyhmd3h kz( exp 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 is the mph udx*hy3t+0(k-kdztf9hf38r)7 q ulyy7meass of each?    $\times 10^{29}$

  What will a spring scale read for the wpy 00 ;yzxgn9height of a 55-kg woman in an elevator that move ghzy9 x0ypn0;s
(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 5yttsp+ 95zbz(qttm . of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates.pqt5t . tyz(m 5zs+bt9 What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface7 uxa7y 9n;yjf of a planet with period T , the density (mass/volume) of 7ja 9yfx;7 nyuthe 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 determine the perior3 c v18-2z 3tdtus 4ahv y2ok7t;nomkd of av -ctost 337vor48mhynt u22z;kk1 dan artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbiterkb,-dvb 42 cv16uu rs the Sun like the planetbdcvb r,uu 61e-k4v 2rs. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagekapoyxyd-t8 v8r .6ttu6: b7x distance of 4.5 $\times 10^{9} \mathrm{~km}$ 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 e obdka)xwl-7ad24l ( wqtr .4nvery 76 years. It 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 distancelw.xt ) a r4kadwonlq7d-42(b 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 ofipp;f(ec 0-y6 2v oflo 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, perip7s:vxo0n n j(od, and mean distance for the four largest moons of Jupiter (those discovered by Galileo vps oj0:7xn(nin 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 period and distans ( iua(4-vc7s8tmomlce of the Moon. s4o(atcvm7si-8lm( u    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jup9vpb 9;g b(mdpiter’s moons, using Kepler’s third law. Use the distance of Io and the b;b9dvpgm9p (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 conrwb1b d5 5u9rg kyv12vsists of many fragments (which some 29rgb5yk vuwbr 5dv11space scientists 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 -o15phf )mto+dty l g-+fh7xuof 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+t5fd7- tyoxpofh1u-+lg )hm 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 a gorge by swinging in an arc from a hanging vine (Fig vq94v4/w)xu* u zdbdfo).nsv. 5–41). If his arms are capable of exertin bv 4 /9)z *fwv4uddouvs.nx)qg a force 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 acceleratio njww/ dd9duv-w41adbg. 7)kp n of gravity be half what it is .dugkp 7) 1vb9 dwj wnadd/4w-on the surface?    $\times 10^6$

  On an ice rink, two skates5(g 3cn3a9u4 zflnhw rs of equal mass grab 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 individual masses are 60.0 kg, how hard are they pulling on one a snl4h3gn zw5c(9uaf 3nother?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity gxwz4v*b7 js)l. g5 qxag) (ldat zx)7 *( ).djllgqxagbv5 wsg4the 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 tcp1hsqdg l ae3dxie3m1w)+ v8uaqp5yi 91/0 t he Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equa aev 3up3 cexl8q1w9i5pig q 1dsd h+my1/)a0tl and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in awqot)yi1 du/qny5: 9sn elevator, it says your mass is 82 kg. What istw5d y)o9n s:q yq/1ui the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station c),),h6 aq y 3gm a453bulk srabvjt) gdzmo0a-onsists 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. Wmh -q3)bdz y a65,gj0oam vb3r4 a)k)a u,lgtshat 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 airp dunmh x+qalm7//m)1craft 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 plan/)wq4- l jvpb5r mi; gq 8mxsgs98y7cvhjg88s et in terms of its radius r, the acceleration due to gravity at its suji)hys-ws8;l/sg8xgv8 m5 qmbqgj9 cv rp847 rface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected frozy+01+x 0yep1vwk 8o;g esq fmm the vertical by an aq0 gy1+80wypvf1ze;xk m oe +sngle $\theta$ 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 dn/m*6m5e ip cdesign speed of If the coefficient of staid*c5/m mn6e ptic friction is 0.30 (wet pavement), 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 bdp eh/f0b 2b1b34 kefthat objects at the equator were apparently weeff3/ bd1ebbk4 bph02ightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanm5okr . q/*m4wm8xicbce 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 0aho-kn* gjp8vk4zs 1a curve of radius 235 m. A lamp suspended from the ceiling szs o0g jvp48a*-kh k1nwings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the 0*izw1j4 3tfm6ndsa e Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since peopfa 6new*s0j3m4d 1i ztle 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 Telesz+t iud, r/kif6 fq1 a7v12ikycope deduced the presence of an extremelyt 2u vydi+fqi1fiaz 61,kk7 r/ 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 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 traverses the hill and valley shozp 3o g4:7fyjqwn 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 a7g pyf:zo4q 3jt 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 System (GPS) utilizeg cy4tj. .vj3xs a group of 24 satellites orbiting the Earth. Using “triangulation” and signals trans4.jjc x3.yv gtmitted by these satellites, 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 Rendezvous (NEAR), after traveling5ozda)a axxmjm ,+ -7e 2.1 billion km, is meant to orbitx mo za,dax57 m)-+jea the asteroid Eros at a height of about 15 km . 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 beglp-:-6 6ownl m26ar+wjnm space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400w-p-6wloge62ban +:mmrlj n6 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 o8dl -:nb r,hea rr7gwi c,:,dbf 3000 years. (a) What is its mean distance fror ,bhrdiba,:dc :r -e,78gnwl m 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 p*bpxeesq+q-dy6- . would need to be if you could actually "feel" yourself gravitatioy6n*+eqd bp seq. p--xnally 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 (Fig. 1ka 3tvi) xcd9, i3eis5-46) at a distance of 39is,k iveiax3 t1c)d about 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 locatedvm,+ 1kalafbd(cobnp,. 3: wh 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 placed at the midpoin1fnbd o:l(,c3mwb,p.a ha + vkt of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5r trq0(v/lg1o500 kg orbits 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-ls02+rixeletpl x6 -+ yong sweep second hand on your wrist +x0 tilxysrl+e-62ep watch?    $\times 10^{-4}$

  While fishing, you get bor)j.pjeyw b d(y ma-y5:ed and start 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 m y: jjw)pb dea.(5-yycircle 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,, fuba)chlr) 8(ijk 3ftdf5a new highway is designed so that a car traveling at speed)hf(,d jkic )a5b3 ft8lfr,ua $ 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, utilis 33:d gk 2xpgfm ni:fnvj( 4:q;fhoq9zes 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 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 os(2: nqq9xikj3d 34g: n:gf phvff;mo f 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.$\approx$    $\times 10^2$