Sometimes people say that water is removeodo q6px 0729dqbo 2mid from clothes in a spin dryer by centrifugal force throwing the water outward. What i iox09mp62ddb7oo2q q s wrong with this statement?

Will the acceleration of a car b c-qgz r+ q:zcqc+zq.5e 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 th+q gc :q.qcqz 5rz+zc-e same speed? Explain.

Suppose a car moves at constant speed along a hilly road.pf+s hs+t fm49-)vfha 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 bottom9)4fhp av- +f +stmfhs of a hill?

Describe all the forces acting on a child ridqqp;d9w.z;e hing a horse on a merry-go-round. Which of these forces provides the centripetal acceleration ofhw .qe;pz;9 qd the child?

A bucket of water can be whirled in a vertical circle without the water s.;+*tu(nu h vatw4i tapillinguntvat t( h .4;iw+ua* out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” dmc: v5;tecd dm: 57cr(mbv6zk o you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What :mc( v6e; 7cmrdtmzb dkc5v5 :are they? What accelerations do they produce?

A child on a sled comes favi zr.xy7/tm.xs aic *0svk 252-zj rlying over the crest of a small hill, as shown in Fig. 5–31. His sled does nox.y7 .zr*5 v/a-22vkriaxzc is0msj tt leave 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 inward when rounding a curve at high -w4p0wh pwjz, +qcz6 sspeed?

Why do airplanes bank when they turn? How would you compum4 e (n. jig-wfpd4cy:nnz1*ste the banking angle given its speed and radius of c4- n im4psnnw.g:(fy* z1jde the turn?

A girl is whirling a ball on a string around her head in a horizontal plal/gp*e 6zqxgjut 48s5 vb8p(me gizfvo- t.*8ne. She sgbvvzi e 6* xuf8* ( gj4pe-qp .8/gt5lot8mzwants to let go at precisely the right 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 o9npmsoc1y8/ t ;x10jy;mcrtm n the Earth? If so, how large a force? Consider an apple c1s0t /t mm9pcy;81xyjn m;o r
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubl5f04jzlgs3cg y/66jzza s cj.e what it is, in what ways would the Moon’s orbit be differe0zsc. j5ca jgszy/ 6g4z63jlfnt?

Which pulls harder gravitationally, the Earth on the Moon, or the Mb+ on.kbtabrl9)u,:n oon on the Earth? Which accel arbtubnl:+b ok9.n),erates more?

The Sun's gravitational pull on the Eari7 1e 7ax+j0*qgzds8qf4 ghimth 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 side of the Earth to the othe+7jsfedq1g7qzam* ix h8i 04gr.]

Will an object weigh more at the equator or at thew19dxb, eyd0d m7-cqc poles? What two effects are at work? Do they opposebyx ,d1cqde-7wdm9 0c each other?

The gravitational force on the Moon due to the Earth a wn0bu ibi ioov82g:b1)dd 2)is only about half the force on the Moon due to the Sun.dibd v02a))1n8:ogw i2 i obbu Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger) izi6t z9r3he or smaller than the centripetal acceleration of 9tirz6i3 zh) ethe Earth?

Would it require less speed to launch a satelliteh*td( m,(f.ooy/ 2owvke k+ o;r3dote (a) toward the east or (b) toward the ( wkd,mtro/ h eyo(.kotev*+o ;3fod2west? Consider the Earth’s rotation direction.

When will your apparent weight 1 osk ht1/t 70ynsu+jv l.hh2pbe the greatest, as measured by a scale in a movings 7h2k.nljtusvp0 /+ htyoh11 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 you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods 97j3u+ xtukoc in outer 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 objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can t o juuck3x+97think of.

Explain how a runner experie9eh5zr32e 1 jk,jeov onces “free fall” or “apparent weightlessness” between stko9oeh3,rv2 1ze e5jj eps.

The Earth moves faster in its orbit around the Sun in January ol2n d-asqk,lv. 3+ tzthan in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much o k,a2lo .3t ns-dv+lqzf 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 untet0xjatplz90-u eh 5fi*(r0jil it was discovered to have a moon. Explain how this discovery enabled-(lp0 0 90 hiazxjj5rf*u ttee an estimate of Pluto’s mass.

  The Sun's gravitational pull on the E8g .0an/)w pj wuh*itfwgg+z9arth is much larger than the Moon's. Yet the Moon's is mainly responw *a whzgg.nt 9iuj+p8)0g/fwsible 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 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 k+jvymt, oa9 +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 *yl3 cq kkh)xlhqyw) 0:h3;z :oqq.glin its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth' qk y): h:l gqk)lhx3q*h0w3ocqyz.;ls 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 rokn(x nshyakc r:ss 87t;mp4 )+tates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. C as+npkx4;rky:tnsh )7 m8s( calculate the speed of the discus.   

  Suppose the space shuttle is ti /bfwkmrwn07 6u.9 pao cf;6in 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'frtw 6wkpnf.b;9 u 0am/ 6io7cs surface. $\approx$    g

  What is the magnitude of the accel1e(38aq 5t sqgo v6znqeration of a speck of clay on the edge of a potterqqn36e go( taz5 1vs8q’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 rate in a verticanwdob- n3 xs:x2m ea l:1ib1m,l circle of radius 72.0 cm , as shown in Fig. 5-33. If i-o s wmxnxbn1 ,eb d3:ami2l1:ts 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 whrxx/3 d mx8,djich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficixd3j8 /x,r dmxent of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of 1gj ;6pjncfh):e d ee2static friction be between the tires and the road if a car is to round a level curve of rag:p 6c j)d1hne jf;ee2dius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet ks. /tp,rzr21ic n;ya fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by thr2 rnpz ;1csit./,aky e 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 c0p9r;fpx f9 yrotating 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 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntablep rfy 90cf9;xp?   

  At what minimum speed must a roller coaster be traveling when upside down at tenzdm47g 7 glu9r9h: fc0ql1 mhe top of al7 f99gu0zmen7q dh:4lg1c rm 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 (including the driver) crosses the rou(hpf8qouwr9j3x u0c: gn b(v3nded top of a hill (3gqw( p( :ob vu9xruj n0h83cfradius =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 Ferriy1o1uzzr es8: s wheel need to make for the passenr uy1zze:18sogers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m0n2 w kub2bc1pkr5fj snl g7;/. At the lowest point of its motion the tension in the rope supportinns20gkrj7k2w nb5 f;lcp u/ 1bg 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 rotac.q9 df2vf.ii 5itu q*5qx, xrte if a particle 9.00 cm from the axis of rotation is to experience an acceleration ov ricfqi.fxq. 95, utq*5 xid2f 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "a n6ao 2f+tti,room." (See Fi2tf,a 6anto +ig. 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 frictionless+gl-7w.m -pi .tr,go 0 (rwbv pkt)cof air-hockey tabletop, and is held in this orbit by a light cord connected twf0k-.pp . ov rwgi )ol+b, r(t-mtc7go 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 , precisel+rne vv,*num( lf1(gsy this time, by not ignoring the weight of the ball which revolves on a string 0,(f gum1nvnv*se + (rl.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 (s0tm . v9ned9 m nkyffkam;0288 m 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 massesuzb8k0;4fur r $ 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 -4y 7u5(fmfyd u tpl*ldiving 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 anb0 * saj4jxbe0d centripetal components of the net force exerted on the car (by the ground) in Example 004xsbb aej*j5-8 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 from the pit are voo a7* l82iy+t /oy.bdcf0jpa, 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 havetcbi7pojv+ 2ao dfy /*0ol.y8 to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circ2onh3cyvrx 5t68-yyiuu)lk.l( 9 htq le of radius 2.90 m . At a particular instant, utu i.y 2(y8vl)-hxo9hqtc63k5yln r its acceleration 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 km (2 Ear,domx-eunmm5d6 .c;wvv q)+ lth radii) above the Earth’s surface if its mass isqv;-ld 5 cv m)6o. we+mxmudn, 1350 kg.   

  At the surface of a certaiohx,l8jbcny7d2crf8 o;0y o 8n planet, the gravitational acceleration g has a magnitude of 12 m/scb0j,l f88d y7cooxry8o2 ;hn$^2$ 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 grahwzc8cz. j9+bia.am : vity on the Moon. The Moon's radius is 1.7z.amc9wbjcz h8:a.i+ 4 $\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 Ear6 +merui0 is8c 8yf:ymth, but has the same mass. What is the accem 8:ismf6u0yc 8rei +yleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earthe a4eb6xg )hz3w w3fe(, but the same radius. What is g nea3eb fz4xe)6g awewh 3(r its surface?   

  Two objects attract each other gravitationally with au -izpv-(yfhk9 h0oy2 n)w3cb 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 (9sdwg 1k7(y 8vn1yfaea) 3200 m 8v ek(sgy ya91w71 dnf   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from th 2ytf au2g min zu0.y.cs*0,tze Earth’s center to a point outside the Earth where thegravitational acceleration duu.*m, i0.2 yft2ygazc u0snt ze 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 x()/zj kg,t81 mbli ymky/gh5 of our Sun packed into a sphere about 10 km in radius.zy b k tyg8x/h,ik)15 jm/gml( Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whicd6( /6roqy bfwh once was an average star like our Sun but is now in the last stage of its evolution, is the size of of( y/6o rbd6wqur 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 orbitind79cddsjwtf:23 :z5v4dlh fgg 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 accelffdhlj7 :w s3dd9d2:g vt4 z5ceration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at th :. qzw j4rceou+jzy ekb+.f:;e corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other threoe;+zk:yze j+r: f.u bc4.wqje.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of cy/:w0p map;; ev,jp jthe planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sat/ ceyv,a;; p:jj0mpwpurn, 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 thak 07j8y:fkfje surface of Mars is 0.38 of what it is on Earth, and 0 :kfjfyja7 k8that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for thuk7 kgi6rtwk7d/r18 1- zwj 3yharnq0 e period of the Earth and its distance from the Sun. [Note: Compare your ans1y16dhrk73twa78kn gj0 qiw/krz u- r wer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbixh t w2x9om8n:t about the Earth at a wxh89mtx:on 2 height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular or5i4 qtgvo x0n, mga;d6h7nd-gq6n h2ebit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth)a0v2dn gg4xd6-nhmq6no7;5 qghe it, when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants areb/ j)slyq h elz go989yoq94yn87fx-m to experience simulated g-9zfb n/8jh )esloy7qo9l 9gym 4q8x yravity 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 5–32.)   

  Determine the time it takes for a satellite to oqq, xfeo/f:3 guti6i2z3 mr 0rrbit 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 compared to the radius of the Earth. Does your result depen, f02uimg/3etoq i :6xfr3 zrqd on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satell9g*0s/)ja6xc k/:r iqz uq i*gchv:o uite have to be launched from the top of Mt. Everest to be placed in a circulckghqj)/ao/9i q**ug0 c6:szvr:uix ar orbit around the Earth?   

  During an Apollo lunar landing mission, the comex8cbm(ku ):p 7hdj .tmand module continued to orbit the Moon at adj.: bck h7(tpxm8)u en altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice tw6l xm4n* 6u;py eha8grev d)4hat orbit the planet. The inner radius of the rings rmv8n)a6 lhygu*we;p6 x4 e4d 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 diameteiee3fy ** s:ogg x,3ccr rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real we g*3csiy:fxgc *,3 eeoight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of th y 5*df1iix8uje Earth's Moon in a spa1y idxj8iu*f 5ce vehicle (a) moving 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-star system consists of two stars of equal mass. Th( fb iju.w4m63l cx7g *a5pyhdey are observed to be separated by 360 million km and take 5.7 Earth yearg.( p3m diyc*4w5jufh6xb7l as to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scq6g f)mts5 vd4n )(evtale read for the weight of a 55-kg woman in an elevator that mo 6qm4fgdvt)( v)tsen 5ves
(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 6uvla(q; kfz7cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N ;lq7(6vauk fzand 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 surface of a pj;/c.ll)nk: rrvmg 3bnj0lk8lanet with period T , the density (mass/volume) of nv/0lkljn8)lg. km:;b j3crrthe 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 per.y0 cbl-gjp. ;4hssyliod of an artificial satellite orbiting very near the Earth’s surfac0ysglj.;ys.4lp -bche.    s

  The asteroid Icarus, though only a few hundred meters bxvzx84jf pij. xv+x+ee9i,lt v- f6, across, orbits the Sun like the planets. Its period is 41 i vefx9zt-,ji,+vv 6lx.px+f4jx8e b 0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average ou h ks9/p:-d;wtijv(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 every 76 qx07inpuv9 jx5z 6hi7hv no1/years. It comes very close to the surface of the Sun q x61 i 7/pznx7h5ui0ovvj hn9on 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 and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gal +lpnw 6l5-iu9kock 7gaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 mej7+vbc1qr-;js + z smpan distance for the four largest moons of Jupiter (those q-+c 1; sz7vsm b+prjjdiscovered by Galileo 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 91 ew/lwxe m8vthe Earth from the known period and distance of the Moon. w /1evex 8mwl9   $\times 10^{24}$

  Determine the mean dists+iq, vs zjsad vlg+80kv/ 8e4ance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to tej s/8+g iv+0as8v l 4dqksv,zhe 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 *4t hr7 s0bx5zc2gy5m 8nz+piw dh6khfragments (which some space scientists think came from a plgzzc+sxim65*b25 dtnh04 ryhhk 8p7wanet 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 ofip iu3q *t)6eq a band completel*i6)3qiep qu ty 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 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 inxos8. .io(d a hanging vine (Fig. 5–41). If his arms.(s8ido. i xno 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 swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surf 7dsqo3kilki3f,.upfw1 jqhyz6 97: e u-zp,oace will the acceleration of gravity be half what it is on the surface7,79ik1wl jz:qd,p3qip yfuse.3 fuzho6 ok-?    $\times 10^6$

  On an ice rink, two skaters of equal mas6t 7qfvk;j .5a z/3izr ;bjdabs grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 3 rv;zz fb.a5 djkb ji;6tq7/am 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 ped92e1 mvm v2h uf677rcspd u+dnza0: nr day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this2hvdmre2 mzp7s u9v0 6+ :nf1ddunca7 effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trad)w ;* opppz1gveling directly from the Earth1 ; *pd)zpwpog to 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 stand ob8635)v s1l g a-wagwfalqi ,dn a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in )g6f a8 l3 a-,dqaw ivl1wbs5gwhich direction?     ----待选择----upwartddown 

  A projected space station consists of a ,u z*)z 5mldvh5o oq/.2r* alogcwp.y 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 effect equal to gravity at the surface of the Earth (1.0 g) is to be feyzz5 qgh d)rp lam o* ul*.c2ov.o/w,5lt?$\approx$    $\times 10^3$

  A jet pilot takes his qrhm am7z9 wa;s *g+9gaircraft 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 planey q89i72h nkflzs1 s(dt in terms of its radius r, the acceleration due to gravithlf( 2i 8n qz97s1ydksy at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the lkqc b6tdhkjy)*2 l5*+msplh gzp 7;(vertical by an a ldllh+)kc2(s *pm hgz ;jpk657qy* tbngle $\theta$ 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 coefficijwnj4fj1oif2wu547lg53wt dh d 0+uz ent of static friction is 0.30 (wet pavement), at what range of speeds can a cadnuw1 u4diz f5lfjo h4g5+03wj7 wj2tr safely handle the curve?

  How long would a day be if the Earth were rotating so fnr7w ukd 2ni6s 0f 9hwcuq;(kz35h7iqast that objects at the equator were apparently weightlnu7khqfi56 nc7wsh ;i q9( k3z2udw0ress?    $\times 10^3$s

  Two equal-mass stars main33 -e,.ufmpmw rvml04elc ox7 tain a 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 a curve of radius 235 m. A lamp + o y1lm )4rqa56ivdawsuspended from the ceiling swings out to an angle of olvydariwa qm415+ 6) 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as 8fd uo*iyif8+ the Earth. Thus, it has been claimed that a person wo u8*i8dofyif+uld be crushed by the force of 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 thehn0w /z 5e:nie1umf8 a presence of an extremely massivw 0fe5him1aznu /n e8:e 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 speed0 p:wcr e; npc,qjbt.. as it traverses 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:ppcjeq t,crb;w n0.. on the car at 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) utilizes a gr xc3rgzhwm jn a2cdi5 ::5x; 7hbpji2-oup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimetersj55b xx2-c7hp3m;h: ia:ni g z rdj2wc. 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 uk0u5(,z i+hjl noxux;:m8vnRendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roui k(zj0n+xnuu x,l: 8; mhov5ughly 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 sp uy;s 3cy tpac2j+0ql+ hd6h)pace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite hpa32 0uc+6 ypqjst dchy;+l)(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 of 300zzi, l bb/syb8;a 005( eltkee0 years. (a) What is its mean distance from the k,0(58a;iszt0/b elez leyb b 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 wy1jjd5;r,e, z hnecp)ould need to be if you could actually "feel" yoursend,p)1 ;,zr5jeh e yjclf 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 (Fig. 5-46)hshx 7 e,cxn-: at a distance of about:csx,7nh -xh e 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 of a square93l;o 4sv1me ldh(t oh 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 midpoint of the bottom side odot;el3shl 9 vh 1m4o(f the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbiup82ub fm24,hfu rqh- km:8e m-he9bwts 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-lony q tboz. u 1hexy+9xm(r( 9g(60pqrdkg sweep second hand on your wrist watch?z(gpyeq yxm6rdtk0. oq9 ((ruh9xb+ 1    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cie6d21 vdnjgw, rcl j21n ,6edgvwde 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 fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hdq xwr)4w d1cyxi:k 1,5iirv5ighway is designed so that a car traveling at speedirdw1)i wry1v dcixq,k54 x: 5 $ 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 trai sfnupwh*e3bl 2.3co.*o:cton, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjustede ls2t *:o.ob n.3 fwhpc3c*ou 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 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.$\approx$    $\times 10^2$