Sometimes people say that water is removed from clothes in a . - e7sprr-xp5*m ewe1zqxs p:spin dryer by centrifugal force throwing the water outwar7rese:.-pxqwrxp ez p15s m*- d. What is wrong with this statement?

Will the acceleration of a car be the same whcp.yhdcd4k-u (w-b b; en the car travels around a sharp curve at a constant 4(kbyp- c;-.dc wb uhd60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed 5:edvxacd65w /)4xabsj 10g l*d qvqpalong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at1jqxv b40* 5w 5/ac6dddp svxqel a:g) 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 acting on a child riding b :gw0, ffd,a 6glgc6vqh mad--3u 3mba horse on a merry-go-round. Wh,mcf : -6qg db6gbm fuhvg0dlaw3 -a3,ich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical,bv9zsd pb ex1j ,s88u circle without the water spilling out, pzxbb,1v8s u9s j8de,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 three contr+b*u ssqgxsyt,)) nc9 ols in the car which can be used to cause the car to accelerate. What are they? s,u)*) bs sn+tyq9xcg What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in feh t ccmm9 vry63:ko 1bn5-g-anv6;rFig. 5–31. His sled does not leave the gro9 6g1 ak-5t:myb mrhc;-vnc rv3f oe6nund (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 curvejctn+vm (b6ix ao eep+7vb:59 at high speed?

Why do airplanes bank when they turn? How would you compute the banking angldd 11 c:zqakoa0r g*y)e given its 1 r :acqdak 1ozy*)0gdspeed and radius of the turn?

A girl is whirling a ball on a string around heeu3l2l , *kco- lu8lpkr head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of oc l38k*k l2-llpu,ue the yard. When should she let go of the string?

Does an apple exert a gravitational force on thentzhv3 2,f ca typmf t*tw.);: Earth? If so, how large a force? Considef, a;ctw f*:tzmthn3ytv2 .)pr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it i)ood0 9da3bc mb u4+mus, in what ways would the Moon’s orbit bm3)o+u4uad dmbo90bce different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon 9pw et0viru:,on the Earth? Which accelerates more vtuwirp:e90,?

The Sun's gravitational pull onun:m6ldkd ; a/ the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fromm l/6da:un;kd one side of the Earth to the other.]

Will an object weigh moret9ght0+k xe e; at the equator or at the poles? What two effects are at work? e etk+ h90t;xgDo they oppose each other?

The gravitational force on the Moon mwdsj1z 9,w.0 rmora9due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away f.r dz,ww9a9 s1moj0mrrom the Earth?

Is the centripetal acceleration of Mars in itsyayjt+ ;dcwun 9i1; f*3lsup5 orbit around the Sun larger or smaller than the centrd9 *a5 su1fnti pulcw+jy3; ;yipetal acceleration of the Earth?

Would it require less speed to launch a sab;mzka;9.v7t oh zq+ ztellite (a) toward the east or (b) toward the west? Conszt9.b+m 7zv qkoaz; ;hider the Earth’s rotation direction.

When will your apparent weight be 64yp -5tbj *umd3igj9r je t(othe greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free frije6( ygub t94t m5 d3*-pjjoall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer s(u/9wm yfj )mdv(;yx jpace 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 gravi9;uxj/yy)wmmdv( ( j fty you can think of.

Explain how a runner experiencxv.:j0u wkxej b ,i;w7es “free fall” or “apparent weightlessness” betweeeij,;.kw xuxbw7:v j0n steps.

The Earth moves faster u,,ne3x8to hxmrw +a5in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or inenm+ru5xwt,x38 h,ao 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 until it was discoverhqm) bt8ziw +8ed to have a moon. Explain how this discovery enabled)mh+8bw8 t qzi an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Y4/c0b rr yos(set the Moon'4 crr(ssbo0/ys is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round 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 n) e i+-r y.kqmmy9a*v* c3a9lp7dlye1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratiohi, 9 mwz 1i s8 as)-y1nx9f6z8yq :vqzn.bljpn of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts thy v9qmb.1z l81 i,)zzs :iy-npw s8fq9xj6 nahis force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rg7rh7idav2n jk0 no (ywhg)4/ otates uniformly in a horizontal circle (at arm’s le an7vy /72jk 0g)(wdrohhign4ngth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from thebhy/0s*z;kz3vu:vb9 m+ij f u Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the spvub* /:;zbk3+ fi vu9y0 szmhjace 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 acceleratioaw2:w4 kxf;fg n of a speck of clay on the edge of a potter’s whefkg xa:fw2w ;4el 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 y-gai6/, m r p2j-awdrin a vertical circle of radius 72.0 cm , as shorm2, paa-/6 ig-dwjyrwn in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg 2bpu l(. e,d1 )z9op9dmzlvpvcar can round a 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 inv(mv2 pzbzu9o9ddl l. )1, eppdependent of the mass of the car?   

  How large must the coefficient of static friction be between thpacne o :o wz,.8p*kj*lhgy(8e tires and the road if a car is co. (hz plgj,8w*: n k*8paeoyto round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astro etm8* 7qpoiu. 7x -gx9hwgwkr/+iik6 nauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee onrgo/k-g7+p.i9w i*tw6 umiq eh7xx k8 her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of varouk mahk 4hju++du 43a*.5mytiable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm isum4.dkh+hmkj u4 t5u+y3oa *a reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at thlsiz8. bed5iyxxzm-2 o an979e top o- mb7z2 ao9xix9sz n d5l8yi.ef 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 the driver) crosses the /g :yw z10qdvkrounded top ofzv /1g0w:y dqk 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 z q)ydr eixy*sc2o9*( wheel need to make for the passengers to feel “weightless”*c qxd(e iy s2)ry*o9z at the topmost point?    rpm

  A bucket of mass 2.00 kg ,jk ku646 fyj9pg3m6 vgwl7s eag2z k+is whirled in a vertical circle of radius 1.10 m. At the lowest poinuvm69kj6kae7psggj3 fzg 42w ly 6k,+t of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotakvv6dby19 e l2te if a particle 9.00 cm from the axis of rotation is byl vd1kv962eto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivalrv uq-ky 1*0ue 9aciq7zdxi*), people are rotated in a cylindrically walled "room." (See 9 qav1i*x*keud-) riu z07yqcFig. 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 rotatedf(+b,bd )d4 jzmbozg4 in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a (f, )bz4b+bozmjd 4gd 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 o8tz92wn utfxbn p f/5;wp:fd 5f the ball which revolves on a string 0.600 m long. In particular, find t8wud2/ twfp 5:xbnnpt;fzf59he 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 a cdq:zap+ n 2nfz2hf4sy/wk2u is. u t0,ar 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 massej l.1gdb* j+dnla5 (vmg:o u:ts $ 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 at:+b mn ydb8dqd*)7txk2 mr1y c 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 an8-+sxog-vaqi cirqvi 7(ws *1d centripetal components of the net force exerted on the car (by the gii8a vso7+g iwqsq*(--1xrv cround) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapoltjsf m74+r h8gc(pnj (8 +zdjfis 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 trfzgcd tmn jfp(8+(+7hs 4j8 jhe 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 a7gdeseb) yp*di;k e)dji+7-n horizontal circle of radius 2.90 m . At a particular instant, its acceleration s edbg+-eidie))7 y j;*pdn7k 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 ./ez uy0l xah3gi8dii-8:d yz) 9fbccspacecraft 12,800 km (2 Earth radii) above the Earthig/fieyzyi8c d. uh3c:0x8lazb 9)d- ’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a34 13 v-jfj/itgngt vi7:rcbm magnitude of 12g /mfntt 7 -334b cji1gjvi:rv 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 ;dlfyz/-+.k5 mybqfr-mf1 h ygravity on the Moon. The Moon's radius is 1.74z+ . 1rl-;-fymmf5kfy dqyh/b $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical plane hb2kyst 4rv5u0kt,9i t has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration du9vkt0r s45th2bu, yike to gravity near its surface?   

  A hypothetical planet has a mass tkc:7ijl+ va :1.66 times that of Earth, but the same radius. What is g near its sur +ika: tjlc:7vface?   

  Two objects attract each other gravitationa zyh/ 7faz2x)zbn(p6 plly with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration ouhd - 9j ljo2l x.1ft9g+lpw,ea28uetf gravity, at (a) 3200 m t hj,ju 2e2 lwux dt8fa.9+ole-9p1 gl   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pointuny::y53rgt z outside the Earth where thegr:3tnuy:r gy5z avitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of o3y m+/ zs1 3snmprffy4ur Sun packed into a sphere about 10 km i3rsmz +yf3sm/y f1 4npn radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf sta4q;2z,gja0 fzr - tnpsr, which once was an average star like our Sun but is now in the last stage of its evolution, is t0g rnf4q japt2 z-;,szhe size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spaceru c t94z9lb*onh1/z7gw 2dge 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 accelerati9 g14hd ug7*et /br2lowzcz n9on 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 sqb +tj/qn5 oaa5uare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the otheqn+a/ta55 bojr three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thehtysf8s/:u2cyzo 5*;qtk0 jr planets line up on the same side of the Sun. Calculate the total force on thc: sr jtyt8qh25ouzk;f0 */yse Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfavm8: iw28pu/knn o x4fce of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, detefx u24wm8pi o:8 k/nnvrmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known ,fd(q4 sro8- ynyc m6vvalue for the period of the Earth and its distance from the Sun. [Note: Cys q cord(,yn-vf8m6 4ompare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed l.*7*yjyuos w y-ouyjqt7 (2fof a satellite moving in a stable circular orbit about the Earth at a h.*jo 7 (-souytf*2ljqy7wy uyeight of 3600 km.    $\times 10^3$

  The space shuttle rele7v8b 3k5tk mloases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the releas7 m5vbk3l 8okte occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arlummb8 p7.v uc6 ;(hjee to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revol(l;6euh j8m c.u7pbvm ution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit t yun.ralwd 4g,m,+bc i:,.cuvhe 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 depend on the mass of the satellite? ya.4:,b rmg+lcui,nwv d.cu,    s ~    min

  At what horizontal velocity would a satellite have to be launched from the tf+-o6yb te.gm op of Mt. Everest to be placed in a circular orbit around the Eartheyfb t.go -+m6?   

  During an Apollo lunar landing mission, the command modut4dcnys1t8f1a iy zc1x)m1 ygcg7;o1le continued to orbit the Moon at an altitude of about 4y y nc )i otfyc 1a11ggt7181z;sxmdc100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of c8pfnm/r*f74 tl 8 hu rmpjnm3:geo ,l*hunks of ice that orbit the planet. The inner radius of the rings igmmh*4/fepn:u7 fnr mlo3 ltj88*rp,s 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 diamc x,nahsf vs ,, j-l+mp;6m/hqeter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom? jlvs;fh,+sq ma/c hm ,6p-nx,
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fror1wzj0*m6(bt a4j fce m the center of the Earth's Moon in a s z4f0b61c*jt( wrmeajpace 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.uge j;/; jk)xyz00e fj They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What isg;0 jek /jxfyzje; 0)u the mass of each?    $\times 10^{29}$

  What will a spring scale read0jth5b,gxup cev ,m;/ 3nq*iwm*rz4h for the weight of a 55-kg woman in an elevator that mov w5bu*4q3 zpcn ,r*iejt0 hv/xmg,h;mes
(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 f .hellb+ ;ht *2r44stabqkdt 5rom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acd*2et l5alsr44t + btkhq. ;hbcelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface-z+npo1vs 1d1qqbmi 3x,jq) p of a planet with period T , the density (mqp+1 n,dxjqzms -1 q3bipo)v 1ass/volume) 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 3/.y4 3b ywx /rogvi/b2enqo.atggt1the period of the Moon (27.4 d) to determine the period of an artificial satello ot/etbg/iw23qyr3a.14ny vg x gb./ite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only al f 8jyice dx6.1p0em* few hundred meters across, orbits the Sun like the planets. Its periodiecej .*mlfy6p8x 10d is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancecjzn: fcov)0- 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 k6zbl * ss,4cg76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest dz k 64lc*s,gbsistance from the Sun.]    $\times 10^6$

  Our Sun rotates about the 0fd75u bijxj /3k j4i6w+px nkcenter 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, and mean distan nkvu iry+bial//2z6 (ce for the four largest moons of Jupiter (those discovered by nyzb+6 ak/l ir/(v2 iuGalileo 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 kkt*1nm nmv4jn lz, :f08pxes;8n1 r urnown period and distance of the Moon. vnl8rz;1 r8sf j*:pktu ne0,n 1mnxm4   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, xjlq77 j/ mh6susing Kepler’s third law. Use the distance of Io 7mjlh/j7qs x6 and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which sq lhyd:e)z i;7ome space scientists think came from a planet that once orbited the Sun but was destroyed)zh7;l)qd: iy e.
(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 o jz( c. -oxr d48zcnl(fits2y+f a band completely encircling a sun (Fig. 5-40). The inhabitants live on the insid4-zjtl( 2x (z.fisc cro8n+yd e 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 vilm ujol+d15 lfu0x/)xp- tef izh zs,i( s8o99ne (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.u x)-i p m 0+u/5ixzzo1oh9flfl9tlse8s (,jd   

  How far above the Earth’s s *6h1yn-uzmediu(h9 a,rh vz 2urface will the acceleration of gravity be half what it is on the surface? ye,z izv-d( hnur9h6h2*mua1   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual c:4cu+a5rpu ge ;awu+ *.jwk rfircle once every 2.5 s. If we assume their arms are each 0.80 m long and their indfrwkg*+uu54j.w;:+eu a rca pividual 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 grav)j2tdu5f)u hphar +h-- g.kr kity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the mak5 prgh+ u-rhdtf)u2kh.j) a-gnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a space1-hg+pvu tlh1zgq+ ljpx c-73craft traveling directly from the Earth to the Moon experience zero net force becu7+pz g3q1l jc gtx1+-pvlh h-ause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in at)jsvg. bqd) 1n elevator, it says )j )d.bg1vqstyour mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wia*ih i-/s1bm 0/vrsboll rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle fs-/1 b /ois*0marh vibormed 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 vert0uam7ai4kui3 erl*8x9n rb4 g vzg7 o-kv7v*uical 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 thev8h/waci40k f mass of a planet in terms of its radius r, the acceleration d/ciak8 0hwv 4fue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticaq ax*ik0m)a2 r67avc fl by an ang k va)mc6faaqr7i0x 2*le $\theta$ 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 ba wa p xi0d3ggr(dolg:g6* m39enked for a design speed of If the coefficient of static friction isx: d a3iropewmlg39g0dg*6g( 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fz a(qfdlfz ) 5d:t ,fn2w+ai4past that objects at the equator were apparentlf(pfta 4q2dda+nz) fziw, : 5ly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance m5 n frjoo6-o3apart 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 ra0, p5ldy:v bwidius 235 m. A lamp suspended fromyp 0d5i:bvw ,l the ceiling swings 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 ask+g ipwz5n2gu / i+v.l the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more t5.wz2+ n/vli k iggp+uhan 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 the prese7 eg (8li1(ae;g iuezance 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;a lgiee17gu ea(8(iz 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 iv:w1;gu-2cyg z+ vo-g g jc-nrt 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?ugg 1 coc2:+-n; vwgzr-jvyg- Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizvp5pm5g -qgtl 1b tp+:es a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on t+-g 5tg:b15pqltp vpmhe Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km,gq b 9aebpw xh7;ca+zv9-e7/p c94dwj is meant to orbit the asteroid Eros at a hea9 qpw ; hd7jc+vzwg/ac9e9px7 b4 e-bight of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing aq,o; tw:+t ia6b7fzfw phzn+/njh7 4h satellite in need of repair. You ar ;t7nqt4hb+/hzap+:ji ,76wno fzhfw e in a circular 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 ptchl.: 4s v b7uowwo(a2-wqx*eriod of 3000 years. (a) What is its mean distance fro*owwt.ws7a ulo-xh b v2q:4(c m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actual7la0dyn6oy ;0u2 i vk*fb3ah)/-orx ox)begsly "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, la)aox37 x00rd2hev* ofykl6u-yb ;n/os b)giike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gabmd/bt.q.g x 4 +i.lkylaxy (Fig. 5-46) at a distance of about bg.m.t qkxd4i/ l.y+ b30,000 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 m 0ken*xbz98f7 b5p fqof a square 0.50 m on each side. Find the magnitude a7kp95*mez bfxf0q8nb nd direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbiw sc392t.loen/ lsrg6ts 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-lo-;f7hdc o,qxhy1 em2bng sweep second hand on your wrist watohq-1x f h ye;md27,bcch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sink37 ,8*wqbjukn k1kfxd er weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complebw 8fn,udkj x31k7k*qte 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 lctr, iwyvxlg;2 *q8 6R in a new highway is designed so that a car traveling at speed q,wrvt 68 *;llg2ci yx$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars wh tt:+aom-sm r5r)ulksxw k(7 .en 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 (a-kr( lmu 7x:srkw.mo tst+)5a pproximately ). (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.$\approx$    $\times 10^2$