Sometimes people say that water is removed from clothes in a sp ;zc fmqe ulo*2 oj8s(,*kpj7kin dryer by centrifugal force throwing the water outwau;kl2* jec f 7(*k8mzos ,jpoqrd. What is wrong with this statement?

Will the acceleratiobgv qm9,t7wv -n of a car be the same when the car travels around a sharp curve at a constant 60 km/h as whg-m7,vqtw 9bven it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where (k+5utd:y 8w5u2sp wohv xvh9 does the car exert the greatest and leas5 t5 9:vhwd2w(kux+8py vuhsot 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 bottom of a hill?

Describe all the forces ac2zh5av+- bqe n - (eoay(yucp:ting on a child riding a horse on a merry-go-round. Which of these forceoeque-hyp a+2 :zv(-a( nyc5b s provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci-a +vpe ,cdn/ e.)hpui.i/+f9bwg ccmrcle without the water spillingcmwi)e+ci/ nu-vdaf.e.c, p9p+ g/bh out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least m 1+b4d srt+aamj gr f+ q4b4v;t23qeythree controls in the car which can be used to cause thej b2ar +ymmte g3+ft41vas4dqb q ;4r+ 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 shoq,x ;y+0i wqwi/nrx8x wn in Fig. 5–31. His sled d8x /in0 ywq,;i+ xqwxroes not 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 curvhlxh;ndn. s.( gl;5 nve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle ph ;bods 915wthn+lj(y1t b k-cj nt53given its speed and radius of the turn?h c9tn(+l5tpnjb h;3-s15b td oywk j1

A girl is whirling a ball on a string around her head it+ rd nd+bs0u;n a horizontal plane. She wants 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 letn+sdr+b t0d ;u go of the string?

Does an apple exert a gravitational force on the Earth? If so, ) nbhat)b9mv5 how large a force? Consider an ah na59bbtv)m) pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Mool4-buc;ek- pj k(/omen’s orbit be diff-bu ok-4e k(lcmpj/e ;erent?

Which pulls harder gravitationally, the Earth on the Moon, or + y* , r7n8*psfzng ersn3pw(wpg7s) vthe Moon on the Earth? Which accelerates more? * )p3sfvp7ny+g,7sg*zpn 8wr( wsner

The Sun's gravitation s+pl,7;)1ftufkw l pgal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsiblsl+gpp lk,f1w;t) 7fu e for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at thbg eb +kwlq8).j9vpm6s l by+(e poles? What two effects are at work? Do they opposm l.y+bbepw(l vk8+6)9 jbgqse each other?

The gravitational force on the Moon due to the Earth isz:* g4td ctzv.:hnlkw-g06+ryi/ iq x only about half the force on the Moon du4hdlzvt cy-x:q/ +w 0.gziit:* rkng6e to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largern ka5wcqk9 41jwb (-my or smaller than the centripetal acceleration of the Earqw (m k 15a-y4wcjn9kbth?

Would it require less speed to launch a satellite (a) toward th t9h8dddxjde8d uy7*9wa p2s 9e east or (b) toward theydd9 w9j9eda tx8 du h*827sdp west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as mea2t7q34b:oo0ahoo/o x vxyac. sured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) /h o4avcayxqo.3ot 7bo:2o0xaccelerates 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 peri0sq 7ow r0p+jyods in outer space could be adversely affected by weightlessness. One way to simulate gravity is toy+rop 7j 00sqw 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 “free fall” or “apparent weightlessness”-zguim6rtz4*5t pb w+z, dvzh- : iar3 between stepv -uat-dhiz:zm +tzz6wipr 3rb54*, g s.

The Earth moves faster in its orbit around the Sun in )szia9 15szf xJanuary than in July. Is the Earth closer to the Sun in Janx 9z)i5 afs1zsuary, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known untilytnv: 8-i6 fgyxkov*9 it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass. g*k-nx8tfyo:vv y69i

  The Sun's gravitational pull on the lw b 0;7b0dg:nyi1booEarth 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 other.]A child sitting 1.10 m f1o:gy0oi db 7nbb0 wl;rom 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 19 / ,bji4m5.wnoxqc8f ortkz:( 80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thabe 0tvw.24ge e Earth in its orbit around the Sun,v0eebt24wa. g and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-k w46+xgv-t( (wfqaj hsg discus as it rotates uniformly in a+ xthsww-4 aj(qv 6g(f horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfaimd +3n(hfo0 sce, 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 acceler+ onf3m hsdi0(ation at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a lqq2(t n h-g;plln00m4y8c * odxecn- speck of clay on the edge of a potter’s wheel turning at yl0dh *8opeq (mxglqtcc4l2nn-;n0 -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 x,+)b +mgf9+ pht +m4cb0onyfzb hv e)vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is+fb t+bg0 xo pe vm9+4h)z,fhy n+bmc) 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 x tm2rc2m 0ocbuttxc +1dj04 0which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static fcc0u 0jtxm ordm0x+24 ctt2b1riction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of st+g1zkh g e+m n(g*bsv;atic friction be between the tires and the road ifk *gs1;eb mvh +(nzgg+ a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and onf f cvg7p, (qpr khi3m(k* (6an2/ebjet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating? 6ig7aq2o e((/f(k rb* f3cpk p,mn nvh   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 turntab h* li7-prhkl(le 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 turntaip7r *hll-k h(ble?   

  At what minimum speed must a roller coaster be traveling when upside dow 8mt)(if.nl4diyg)latn8g7z )s +lz un at the top of a cim)ni)tl 4 f+7iynl(t)8z 8z.dgsgl aurcle
(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 (includi,cb;abb3yomj y, ;l 9hng the driver) crosses the rounded top of a hill (ra3cby;,bha;oym 9b,jl dius =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 woul.dd 3)m ku bwu6yh*f* tmru: loal8),rd a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmr8ur6,*:u yfl3w*l dkb ).mda)mtu ohost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad+yrduv dubs-4t.iz2 0j)) az bius 1.10 m. At the lowest point of itssibuzt) -db0u4 )2dr.z +jvya 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 pav*rvnn+,q b hn1qr 21srticle 9.00 cm from the axis of rotatioq nvv2*+s r q1nh1nbr,n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated injz*2g/ jyxx;bp* jccaegk7b q8e(,9 e ,rx1y q a cylindrically walled "room." (See F1 ec9jy(brc;* g j,q*yz7p,ex x/28jxbaegk qig. 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 b 5*;nqn 9mtvr4qdtaf )i1yk2) is rotated in a circle on a frictionless air-hockey tableto 5qdn 9tvtynak1)qrm*2i;4 bf p, and is 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 , precisely this time, by not ignoring the weight oman5qgw g7*:z sve2b0 f the ball which revolves on a string 0.600 m lon5ge0 ga2bns qvz7w:*mg. 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 vce eek21v n23-zcl+b 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 massesc0 vm4uk 2h1uy $ 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 vertically at4wacpxgk+cdpp:q7xd.w*; 1 / j mz.v b 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 exerted r 3)z/81d ho22jzoju1cu oewr59ofs g on the car (by the ground) in Example 5-8 when ieo2 j 1u1g/ h 9)z538zu2rwodoj rcsfots speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis50wrv5a frj4c9oao5 o 500 accelerates uniformly from 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 tuvj5oc ow5 fr54ro aa90rn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in.txhl;z0fucc. r4y1k a horizontal circle of radius 2.90 m . At a particular instant, its acceleration is l;hc fz.x tr.c1y4u 0k1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 ogxs35j9 r01s 7qcbku6 c g6quqn a spacecraft 12,800 km (2 Earth radii)ckc g q u 1uj75r69gqx3sbqs60 above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magymm 1c/uzmw/rzl,h ysy g.1 48nitude s.z,yhr4m ucyyz/1 wgm1l /m8of 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 M9f3aijp bnh3 )uf2ip-oon. The Moon's radius is 1.742 f9pp3fa hu)bn ji-3i $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiui(bjp e-w/7/-h f iqtns 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity ne j q/ipb( -n/weith7-far its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, butlc (x6ihikt09 the same radius. What is g ntxhi96k0lc ( iear its surface?   

  Two objects attract each other gravitationally with gwfhfr;u/g9f r *) ffo0av4yz6f) mn, 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 valueo ;ylx/amlzv;pk 3:(t of g , the acceleration of gravity, at (a) 3200 m/ lmo :za;xv(pt3ykl;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earipusee; rpb3mt;297smy1i , rth’s center to a point outside the Earth where t;sme3 r,up;r7 is19pite2bmy hegravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron starlxmy .i ,7ldg* has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate t*g,lml i.d7x yhe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our igl)8s*7kj 0ptddb;km:l k b .Sun but is now in the last stage of its evolution, is thej8dmkt*kl; b l)dk.0b:7 pgis 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 astronaud7x lc096:kooa d8j duts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up thcoxd9a8 :d7uj0 odl6 kere. 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 are located at the corners of a square of side 0.60 m.ievm r6: t 0h4ptg9hx, Calculate the magnitude and direction of the total gravitational force exerted on one sphev 40:mp6tei t9xhr, hgre by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years8 qmgd11;; ga /jccmns most 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 line (F/nmcm 1gcsajgq81d;;ig. 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 ) qje8k28g4;i rg yuehat the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Me 4juk8gqg)8ery hi2;ars.    $\times 10^{23}$

  Determine the mass of the Sun vg exr;/f kvgo i13+(k19osjv using the known value for the period of the Earth and its distance from the Sun. [N(jo voev k f;9x+sg3vk1gr1/iote: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mr)g1 d (cgei+yoving in a stable circular orbit about the Earth iec()+r1gygd at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circul:vizwfg:mfn 7c 5 v71ie5e y-var orbit 650 km above the Earth. How fast7g: y71-cmviwzv 5 efv:en5fi must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupaz llqgjb7r5kp.tyvth 8:e 6:1 nts are to experience simulated gravity of 0.60 g? Assumet::85gvkyqlb6l jt.h7r 1e zp 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 orbit the Earth in a circular “ne b/fprpf1hs09 ar-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 Earrfp /1bfh9 p0sth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a sate l)6nu412bi.9zxl-y4p v hqya +qwkgvllite have to be launched from the top of qy64.puw4xlqyv)v2l+baz n- hk g9 i1 Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar t9qytuz.9gd / landing mission, the command module continued to orbit the Moon aq.gyu9 /dz t9tt an 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 icec+p6 yi51dfk6*xpy: qmkc c+ e that orbit the planet. The inner radius of the ring 616f :5pcyykd +qcck+xei *pms 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 eve q,nkqv4yn )7 iun50kp a-m7siry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weigk7sp, nm0q-qain5ku4iy 7n )vht to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of wvu h *j)e z;8gf0 jgso/0-rzpww p;p;a 75-kg astronaut 4200 km from the center of the Earth's Mo; gu;;psj*pr)08z0 zwfwwvgh ep/-joon in a space 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 syst* j.rg zipv28gem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midwgj.i zv *2rg8pay 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 in an *;k0pyw4j 0f wlu+ltielevator that mov4i+ yw plj*0wltf0 ;kues
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatm 1cbl3g ,a2dv 3ve1bfor. The cord can withstand a tension of 220 N and breaks as the elevator acce3l1 ce gvf1,3d2bbamvlerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the su*ad/avarjywtq.,-1 e rm d8v,rface of a planet with period T , the density (mass/vorya1a*/d8j.v , d mq-ra e,vtwlume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) tyg(yq3 8:mjj to determine the period of an artificial satellite orbiting very near the Ea(:jymy j8q gt3rth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across2zun:5 m s1 .kiq*nrhe, orbits the Sun like the planets. Its pe *zk eh.sr1q5nu:mni2 riod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance -0y/+l wmyys: uujz o ..bov;oof 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 years. It comeyw trj..gza(eei w1n .ef(/i 1s 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 Key/e1zajr .te gwfiei .1.n(w(pler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the *rjv 0 jri7a8v)embf-tj(l:z center of 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 ma3 fwum07 jydb8ss, period, and mean distance for the four largest moons of Jupiter (those discoveredfd w m0yb83u7j 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 the Earth frox(9 m7sj goeed 3(x+ f.bh9odom the known period and distance of the Moon. h9(ds7f. o3 9gx(edxo+bmj o e   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using ;)+,v0c-qifwf9jo adrw*epwKepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valadf 9 -o)rw; 0fw+,e*ijcq vpwues 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 bei iz,yy+w ff d vr 3m4ni+,lda/9a:a:etween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed). ,y:afv+w/mzf, : n a aid3ii9e+rdl4y
(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 artifici awft3/*iah: dal "planet" in the form of a band completely encircling a sun (Fig. 5-4 awa:/ itfh*d30). 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 swings5o +m wy4m:hqing in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 4:w h+qoysm 5mN 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 accelerati n okg,ccz5 ze:gb4/3qms qe-6on of gravity be half what it ic 6qmg,3qe4bck zgsezo-/n:5s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab zcjn/5y,qx/,q m2l) wj(; d2agpnizohands and spin in a mutual circle once every 2.5 s. If we assume theij(z aq2dc5,;mj l/io qn, z2pgw/ )xnyr arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of (3 ma1 gtij:mp 7jl5j zh2o2bmgravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractionh ijpa(5 mlgjm tj3 2:7zm2b1o of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecr ymgkk-)2ztech.3do2/: r ko v(j 1tcfaft traveling directly from the Earth to the Moon experiencetj-c. y3rz: of tvckg hm/2ke(1dk2) o 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 whe::4t)vxqi bf shyl a/e :m1x/ jp1-vecn you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?tf x)c1:ple: y/m4qsah v j-1xebi:/v     ----待选择----upwartddown 

  A projected space station consists of a circular tube x3a3d;o0 rgzy: i:rn ethat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle forryn0:3 egrzd:;oxai3 med 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 aircraft in a vertical loop g)bsxs9 7 +wg)2bj eik4qb*tiuf6,je(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 radj gcxn h(;4p 1)fllz;zius r, the acceleration due to gravity at its surface and the gravitational cons)pj4n;fg xzcz1h;l (ltant G.

A plumb bob (a mass m hanging ofr(o3akjg u; 7n a string) is deflected from the vertical by an 3fj ( a;ourkg7angle $\theta$ 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 cop z0a3 5c)aev v(ttj+wefficient of static friction is 0.30 (wet pavement), at wz(a pt+w03va e5jcv)that range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotationuifj e)33 8ong so fast that objects at the equator were apparently weightless?3oi3nfju 8)oe    $\times 10^3$s

  Two equal-mass stars maintain a conwpv(w 8;x8 hm68ua ionstant 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 roundw 4lm kok)-xin7ebh*o8p,wy0 s a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle ofhokw w7oiyebl,p48- nmk* 0x) 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times kph4 xgkk5ect/)o 6e2as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet k h6te x4pg52ck/)okethe 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 d,twx.ze 0z,s h53hdz leduced the presence of an extremely 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 coreezzd3zh sxl.0, ,5 twh 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 asi ;)n7f2hm+10ayoj if z*rfxy 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 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 r* n02;z7+oi fm )hyfyfx a1jiwith the road at A?

  The Navstar Global Positioningqd 7ri5lztgq9 g,3ha*pl /4xv System (GPS) utilizes a group 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 fewir vz hqlg9ptagx lq/,5 4*73d 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 traveling 2.1 billion km, ic8l)zxl:e e :ns meant to orbit the asteroid Eros at a height of :8lee)n clx:zabout 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 sg6onb ky3c1b6aqw z.y ;y x(w,pace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius a1bwq .; n6 z6 bo3g(yxk,wacyys the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp hasr1bu.i0b z0g teac 6xcbos+ 7: a period of 3000 years. (a) What is its mean distance from th0xe7 : r0.tg+cob16uzcb sbai e 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 need to bekti3fj f z.qj a4a()fi8.7tcv if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptit i8 a.jv)za3tif ( cf7j4f.kqons, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-aponl2oa3f2 yx +t i()6mcl)f46) at a distance of abofanxyipo c)otm(6a+3)f22 l lut 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 square 0.50 m on each .8+ajjgcsw8 pside. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square. j.a cw8sjpg8+    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thgr ;mxw.i pq5.e Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long swee5tngg x ;7se0tp second hand on you negtx;t7sg05 r wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swi-zh0 8crom-yzng a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. Whac-zzh0 8or-ym t 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 designed sop9f htinqe0 50 that a car traveling at speed ihn 00 p5fqt9e$ 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, utili j 8s8w/o2gsu6r9+bs ei8wxhzzes 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. sw 8i882 s/e ug9w6+hs bzjxroConsider 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.$\approx$    $\times 10^2$