Sometimes people say that water is removed from clothes in a spin rie c+f:ad;c79w.rkgdryer by centrifugal force throwing the water oucrirc+;:g a7wd9kf .e tward. What is wrong with this statement?

Will the acceleration of a car be the same when the cat9n1gg /z e.mvr travels around a sharp curve at a consz/gt .91gnev mtant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hoc;uut6;e72qr-xl z vywwv7 5illy road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip xww6vz;cy- oruev q5 77u2 ;tlbetween two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces / .w(k ypjl9,kor+p gfacting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chil+(r./ kgfkp,o9jy plwd?

A bucket of water can be whirled in a vertb;5so2j aax47al*(inv2h.cd d 1opul ical circle without the water spilling out, even at the top of t4o2jvsical don(5d1hpblu ;x72* a. ahe circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There ak yhy ip3cknp .6 0r1vqy3vq),re at least three controls in the car which cyypk6rhv1 q3y) c3.ik qp,v 0nan be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying oveojtx/ o vm+9j(r the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “ajo9x ot(vm/+j ir”), 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 hib.2vj* ht ;cm *iy6kwik:g(l,u 2ov iigh speed?

Why do airplanes bank when they turn? How would you com9nm p-ac rj)w,pute the banking angle given its speed ,mn9wrac jp )-and radius of the turn?

A girl is whirling a ball on a sd:k9l*iruxt ;3eh3a6fw+w a:k.c qbk tring around her head in a horizontal plane. She wants to let gc:.tlaax hk3r3+q i 9:wkwfud;6 *ebko 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 focy1oc8jvk 0)q jv;):e eq-fvi rce on the Earth? If so, how large a force? Consifckvq-10e vj 8voyq)j;e ):icder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways y-h a9o u-c/ifcr y4gg)w .i;l7mk5 mjwould the Moon’s orbit be different4gli-kg;j yymh7)/ur i - c.moa59fw c?

Which pulls harder gravitationally, the Earth on the Moon, or the Moond6diti )zx+0j on the Eardzi tdixj6)+0th? Which accelerates more?

The Sun's gravitational pull on tcimj06(zfg cbjqgx; +8+m vp 8he Earth is much larger than the Moon's. Yet the Moon's is mainly rc6m; b+(8vip8g mgq +0cjzxfjesponsible 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 the poles? What two lv92gj 5bgxn2p vzx/-j)tj jf/()wps effects are at work? Do they opposev 5wt/2b x2xs) /v(jgj n-jzflp9)jp g each other?

The gravitational force on the Moon due to the Earth5 uf/:m0mv4hh7jcha ; 9 b b:arfywhk* is only about half the force on th04 hkacywr5fv:hm7:hf * /b;ubmj9ah e Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal ac c+n hy35mcph9g) ewmy:xl(d* 0 shhu4celeration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration o*w 4hhd0c x:lu +y9 m)scg(h35enmyhpf the Earth?

Would it require less speed to launch a satellite3sy mu*4 -bjz cbw-v5p (a) toward the east or (b) toward the upwybj *534-svcmzb- west? Consider the Earth’s rotation direction.

When will your apparent -nr a m53rauqg4m53x:a+hwk u weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d)m+u:hr xq 5arn 34kug-aaw3m5 moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space mvw6 p*o)kd5/+qhz5jskbvqz o- d*x k6rn+8 tcould be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, withqkwkno 56jr6*q*zvovd/5 +8p kx)szbdmh- t + 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” betl)z-0dd .8rtb jbk cmb9 -ivk4ween stv9.8 bdml0bkbjc4r itz-)-dkeps.

The Earth moves faster in its orbit around the Sun in Janu/cbe*h m qx1x7xhj +ohb1 ezr)g)x0h:ary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane o /gex)1: zomh1 hbch 0jxxrxqh *)b7e+f its orbit.]

The mass of Pluto was not known until it was discoverfp83 o31*u6fxnqtvn/qt* o vaed to have a moon. Explain how this difuvt vn*13a qqn3o /ft po68x*scovery enabled an estimate of Pluto’s mass.

  The Sun's gravitationa n9umcg6) gyga1 5z.lml pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Coln6zc 5gm)yag.g 9m1u nsider 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 travelinvgz .1la ao9 g/u efhj76v;*dkg 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 t wwl-bl8nfe:hv0(/ 8fx1zt k ehe Sun, and the net force exerted on the Earth. What exert(v hwf 8-fbl0n 1ee:tl /kzxw8s 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 k+l8ld0;hqru1a1 oi .e,stm lis exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of th,m1l0eqr8ihku ao;l1td s+. l e discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surlv716pr tv eruc,:wn (wj 08drface, and circles the Earth about once every 90 minutes. Find the centripetal tnw0cwrvd: 86rv( r lej,1u7pacceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on tpgcn xuy 5,5bfe7 :)cche edge of a potter’s wheel turning at 45 rpm (revolutions pnfypc7c5) :e 5c,g xuber minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strik/zz rshz m-, l2um+o)ng is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in -lz2hszz/ +kmmo,)ur Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round ajg 2,sds3k6zn turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of zs2,dj36 ngskthe car?   

  How large must the coefficient of static friction be between t3x0hhhp rq ()uhe tires and the road if a car is to round a level curve of radius 85 m at a speed o3xq ()urhhh0p f 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to yxtpf/vm)7z( ,(pf q trotate a trainee in a horizontal circle of radius 12.0 m . If the fzp ((),xf m7ft/tqpyvorce 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 n x4 3 ddf2dmu9yt5b5ca rotating 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 coi x4ft9y5m35dubc nd d2n and the turntable?   

  At what minimum speed must a roller coaster be travvo2:yc ed j-.celing when upside down at the top vy-e c ocj.:2dof a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including-h0 .m* jkf*maa9niftnt p2qb r)/ as: the driver) crosses the rounded top oftkj*/amr*bap:hi tqsa f.m-0 9f n2n ) a hill (radius =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 Ferris wheel (ep5 7u/po:1c bfnb3pdnsq7eneed to make for the passengers to feel “weightless” a 77n(o/dcq1e3b pfns5 pue:bpt the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius ;9 4(+d rwo m)t,4 yr4zhewogl6tk any1.10 m. At the lowest point of its motion the tension in the rope supporting the buckywrdlg4) okh4,wtr 4y9+an e;z (tom6 et 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 centl ,orr i0bg08xgdvnxpy,p-84udas .0p5a er (rifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 11rp 0yrgx48 gpo,ur0a0 8pv-snd5 .ex la,d ib(5,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rottn:8f z85g 7d oxj 9wkbebjy11ated in a cylindrically walled "room." (See Fig. 5-35.)8 j751x1ybfgno:k bzj89wd e t
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 air-hockey tablqasezd1n )i5 4445 qccp*jqacetop, and is held in this orbit bydcceqni4j 54 1qq5z cas)4pa* 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 ignoj.. 1cph; uk*nnkrub:ring the weight of the ball which revolves on a string 0.600 m long. In parti.hn bkup 1nc;: *krj.ucular, 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 ai9wa k *4o5v0+k)8nfjcssjyo 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 masses.: mcn)8hetwnox yfodh qi;-9yu-q33 $ 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 velg6xp0cr +,d j,r5 (uajl*di ertically 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 co5 opbn*hsor2k4b 1j*y mponents of the net force exerted on the car (by the ground) in Example 5-8 when itob5* b j*4yrknh sp2o1s 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 unifor mh4uwwg;t 5.hmly from the pit area, going from rest to 320km/h in a semicircular arc with ag.wwhmu ;h4 5t 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 skidding? $\approx$   

  A particle revolves in a horizontal circle of r8vrz8h3jqujszb-7 t2adius 2.90 m . At a particular instant, its acceleration is 1.058zusjbqt3hj-8 z r7v2 $\mathrm{~m} / \mathrm{s}^{2}$ , 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.qa v jtf8rf-- 12,800 km (2 Earth radii) above the Eartff.-8 q tva-rjh’s surface if its mass is 1350 kg.   

  At the surface of a cert3 n983j vehd q3hsb(bwu(a3x tain planet, the gravitational acceleration g has a magni3a9eq(tsh8(n bb3 w vjx3d3hu tude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's roarn2 2-q/mdladius is 1.74 r 2anoq -2md/l$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius h) z)4w 2pe3ef/ zrp)p5.gkulswb (wn1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfa4 hu)r(.wfwn lz 3 e)sg2ew pp/zb5)kpce?   

  A hypothetical planet has a ma7btk p gvgwgs14j2i3 4ss 1.66 times that of Earth, but the same radius. What is g near its surfswbp tjgvk32g g4417 iace?   

  Two objects attract each other gravitationally with ;ase;nvb ak99co ft0. a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration cn.k8r- w)i igl:v *pd9ugzbzk-ob, : of gravity, at (a) 3200 m irivg9 o)bk,g8lkc:z pb:u-- wd *.zn   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where gm 38j,w 2giiginn( 4lthegravitational acceleratio g,jiggwli8nnm (3i 24n 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) h0-aartobbtpl.(.s of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thibaoth0r(.. )p s-bt las monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star l)unkrhsb0,wl ts(z)f /0kl6kike our Sun but is now in the lb s)nks l0kl0/uh )kz6fw, (rtast 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 whih8i /x4peoz2q +umag7 le orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convincam87h2u q+zix/og4epe 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 mt7 527 e(v yyvs1jpyko. Calculate the magnitude and direction of the total gravitation y 5s1vopytj7ke (yv27al force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetufptwh)67o rsbn 29 ;es 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 (Fig. 5-38). The masses ab n7ptrs;uh62wfo 9e) re $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 /bfd ds7wok0bd)7m, ks9b sm -surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the ma9k0m)d bs ,7 dmkodbs/-bws7fss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using yk4 n yswtb9-,the known value for the period of the Earth and its distance from the Sun. [Note: Comp snkyt- 4wy,b9are your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of 4 fo.flr w7ifpq2y/no *;s4p ha satellite moving in a stable circular orbit about the Earth at a height of 3600 km. 24wfhos47*l; fpqp orn. f/iy    $\times 10^3$

  The space shuttle releases a satellitee*v:x xx*.vz q into a circular orbit 650 km above the Earth. How fast must the xz*x *vq.xv:eshuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindric4b/pm fb1vnh7 al spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time np 4fbv7n/bh1 meeded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a -;wah)q2pg xj satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result dependajg)ph 2 ;xw-q on the mass of the satellite?    s ~    min

  At what horizontal velocity would a.trpf e qrs;.5 satellite have to be launched from the top of Mt. Everest to be placed in a rr.;t 5e.pqsfcircular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued hw c8mjasn,2,aj g9 w5to orbit the Moon at aa5h,ajjs ,g mn8c 29wwn altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn ar9; n-auyl g ryy;ey;73c+3oqer,qetvdmo 11le composed of chunks of ice that orbit the planet. The inner radi+qvmyoeuay1 33 rye9y-;e dlqg l,t7;o;c rn1us 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 every 15.5 r wzr6jss b+1, ehbe3.l/ tj2gs (see Fig. 5–9). What is the ratio of a per2jr3eb1 .t,ebswhr zj/ 6gls+son’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrod.y )km(omv.* ys5kpgu :x0 genaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constan mvyesg:(m*gk .xpu 5od. )ky0t 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 nl+p rgb;3 (ijof two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit al r3;gnibp j+(bout a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale reawl2oz- :yb frg:u x(f3mgk8k7 d for the weight of a 55-kg woman in an elevator thato(yukwbfl23fk8-rzg : 7 x:gm moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an e 08ko) qbha(::er xzbklevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnith ()qb zox80kkea:: brude and direction)? a =   

Show that if a satellite orbits very near the surface c iwl 6lskw+so5: oc( 1w-h6laof a planet with period T , the density (mass/volul:w s+a 6(iwl6kooc h1lcs5w -me) 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 M4hj,bwxp/ /a- hbwrqf ibs, 70oon (27.4 d) to determine the period of an artificial satelw7 0 //h4ahsijb wxr,b ,-qfpblite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a 74-sq pp jlllr nl5my hf,8:t-few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean dthm-,rnly l8fq 4pl:p 7j-5slistance from the Sun?    $\times 10^{11}$

  Neptune is an average dex+,ws :pqvd44z hge: istance 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 years. It k3leo:pbwb l +m5-:7fq /jmfd comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law islme f+j3 bw- /:obmdkfl7:p5q half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centt; dd/ 1-gtdojg krq):er 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 mass, period, ad3r 2s vhuo2 r/t5pnc5nd mean distance for the four largest moons of Jupiter (those discovered by Galil u5 322 dhsr/5orvntcpeo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distanc)dc *h(oaw6mypk 2lf d; snntl;h84 -ve of the Moon. )8yva -ndh hpc6;lfo4*m;s2d( lnwk t   $\times 10^{24}$

  Determine the mean distance fro6wt- mg2x f2rpm 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 the values in the Tgw262m trpx -fable.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt bet:l+8 m83a2 que5j poe0nfryoy ween Mars and Jupiter consists of many fragments (which some space scientists tlyfueq o e3mo:a+ r28y0jn58 phink came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a bandge7 zl*mn6k*zqr )s y8.(rlh d completely encircling a sun (Fig. 5-40). T)rrd nk(* qh .lz86smlyg7ze*he 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 a hanging vine (Fig.qx*ld q k7c5utpni.o 6+*(p ei 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the qp+*i7 eunxcodq i.t5k6p (*l 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 m8it,le bqd2*will the acceleration of gravity be half what it is on the surflbim t* 8d,qe2ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and*rqh* o is5 gcmi8cw zur:d6zdj 9f:,) 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 ah uddc6f9,wj:zq:*i*zgrm5 o rs c8 )ire 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per8tc nnfa k f7xhp9kf()/2r7eusfo31 c day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitudex9 k 271)uffn3 t/chp e7sack8( fnorf of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wig )3vt j0vee4yezzbvr u54g7 5ll a spacecraft traveling directly from the Earth to the Moon0 er)v 4tzje575ug yge4 vzv3b experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 .ph5od,d l2 hjpfu39j kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevat 5 hjohd,2plud.jf9p3 or, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube f j r8gvaqv+ov ;w1vit ./*9ivthat will rotate about its center*q i1vo r av.ivfv+98/vg tj;w (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 felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in hy:. v2a b(csayh0)dwa 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 poo /futg+m5d.te*q 2u+0 hwqolanet in terms of its radius r, the acceleration due to gravity at its surface wh/*too+ gf 0t2dq+uu 5mqe.o and the gravitational constant G.

A plumb bob (a mass m hanging on a string)-hl3tohvp4oe3, ii)mksh8-m rtuz; - is deflected from the vertical by an angle -l h8v tmko) t-4ph-iirm,3oseh 3;zu $\theta$ 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 desifgk 0q6ji7i c31 x 9xtmn2*n9)tquwolgn speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a 1uw2 mxotf39kqx)609i g*n c7ilnt qjcar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects a+2o5 af hlpxn(*8exz (n6tzs jt the equatora6s2 hxlznx(z( nf+*ojet 5p8 were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aeexozr: z m8 f1to;50rpart 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 s:vc)9 om orm7upeed rounds a curve of radius 235 m. A lamp suspended from the ceiling swrmv9: muo o7)cings 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 Earth. Thus, it hahc8;9 xdymz6us been claimed that a person would 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 number8yc z9mu;hdx6 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 th4a of.)0xkt)l9ub vme e presence of an extremely massive core in the distant galaxy M87, so dense that it)4av.euxo9fmlt )k 0b 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 shown in 8luybig ..y;mFig. 5–45. Both the hill and valley have a radius of curvature R. (ymy.li.g8b u ;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 with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a b3o yhw1jv p1y6x4fw, 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 few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, ahwobj3yy x,v fw p4116llowing 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)omf0kfm uwi21j/+-t l , after traveling 2.1 billion km, is meant to ojf2ku -l1/o0mim+w t frbit 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 tht2awa2q 2f zlyz 5nz40e space shuttle pursuing a satellite in need of repair. You are in a circ za5q2lzwan 04y2fzt2ular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Whw(;mpd/fl- +)ytc 8 at+7sh k 1uylzrkat is its mean distance from the Sund tza ;y8+-7 tph1kkmuf(ll/+cywr)s?   
(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 be if you could p+ mzv2nsq;.z+uk mt, actually "feel" yourself gravitationally attracted to someone near you.su;zt+ q+mnkp2,z.mv 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) at .33.1meg:vimqq3v wwo hujwo y87j:ka distance of about 30,000 light-years from the cent3 . wi:mo3wo :hugkvjqy1 .ej7q3mv8wer $ \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 squa7 ej2 g0xen0dr qf-zb6re 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at bjr0e0n7 - 2gfzxdq 6ethe midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth vcb83i1t:nx v$ \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 acceleratio.cv p5:ixg;pdn experienced by the tip of the 1.5-cm-long sweep second hand on your wri p.dxc 5gpv:;ist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around ilpx l4rtk55 pv0fq,f,n a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle evlv0p lk5r,4 x5q ,ptffery 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a c; ysec ;5 9j8e mar;yw5ndzp)nar travelingsdycmn5pjr5 ezw;; a )n98y; e at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizesh -c;ya/ dtxn ef0(b.s 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 of mass 75 kg if the track is not banked and the train does not tidh.0be-x/af cn s;t (ylt. $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$