Sometimes people say that water is removed from clothes in a ydo,eah/d6e) t u/ bfj- +h,cfspin dryer by centrifugal force throwing the water outward. What i/a of/tyddehf uc)b+je6, ,-hs wrong with this statement?

Will the acceleration of a car be the same when the car travels around a f)jxt7 4-:hnwf)y p wjsharp curve at a constant 60 kmtxfnwh )yfjjp:-w 7)4 /h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car/hcots a ,u8pkx( ql4+ exert the greatest and least forces on the road: (a) at the top o/khl(+psu4c,t qa8x o f 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 a horse ojgji.(iwb x )dw6 0soksj8,0mn a merry-go-round. Which of these fo(m8 wwx )j0id6s,g oi j0j.sbkrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without sd n)4:r nwa( e.4aaowthe water spilling out, even at the to.(n:ae)rdww 4 asaon4 p of the circle when the bucket is upside down. Explain.

How many “accelerators” do you h(wgp uk.* kcp39iq8wnyrs;;rave in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations k;9r (p*wpusi;w8g. nrkqy3c do they produce?

A child on a sled comes flying over the crest of a small hill, as shown inf +3m -pwbhij1 Fig. 5–31. His sled does 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 seconmpwbi31j f- +hd law.

Why do bicycle riders lean inward when rounding a curve at high s3ih1(l6bq sk ;7 etpcqpeed?

Why do airplanes bank when they turn? How would you compute the banking angl;o yh40(6d ah) rblwjdn-t n 6xnb7+qee given7 n;ehhnl+4 aq j66y)(0w-x obrn dtdb its speed and radius of the turn?

A girl is whirling a ball on a string around her he-spc:y*r2 ij 5wi4o iead in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on th 2yio:i4p*5wesj-rcie other side of the yard. When should she let go of the string?

Does an apple exert aa y 87d h,vuy.:9ibv o;+n c7m/qvqlzh gravitational force on the Earth? If so, how large a force? Consider q/hlvdb9.uocm q 7ivv+: h yz 78ayn;,an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbitl-tvbpzt.j , / be d,/vpjtb-l zt.ifferent?

Which pulls harder gf6pitb h+xu1pamq( 6, y,jtwdew;7v 7ravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerateyt,7 bi a6;mdv7ju x(htq6+ e,1wpfp ws more?

The Sun's gravitational pull on t1qz) s 5q)znyuhe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: C 5zs1 quqz))nyonsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh moreuxqw k++e gd0j sw3zr+c3y7kq0l 37px at the equator or at the poles? What two effects are at work? Do they0w33q+kw exldgxuq7p7zycr +kjs+30 oppose each other?

The gravitational force on the Moon due to the Efu ( v5ylp(zn 9dx;-xharth is only about half the force on the Mooz-xpyd(u 5nf(h 9 x;vln due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orpxnmeth7axg/ 46 ih/)bit around the Sun larger or smaller than the centripetal acceleration of the Earth?74 ea6ghx hx/ t/)pnim

Would it require less speed to launch a sate bxq:(qifcx rg,h(9k0llite (a) toward the east or (b) toward the west? Consider the Earth’s rota9(:qxkxq0(bgh fri , ction direction.

When will your apparent weight be the gr 2zm4 j*sqdlh3r*ea +ieatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which cae 2da lh*m3*iz srq+j4se 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 bit:3o)6de m, uku(7 g-mgyl jlong periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Exp7g(metu3 o:y6u- jldg, )kbim lain 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 eg1(w fk8*w bjkxperiences “free fall” or “apparent weightlessness” between stepsk8w( *fkwgj1b .

The Earth moves faster in its orbit around the Sun 8x ezix1 j.x4jin January 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 of its orxzi ej4.x 81xjbit.]

The mass of Pluto was not known until it was discovered to ha mi:3sa13xbj ave a moon. Explain how this discovery enabled an estimatej3m3i:s1baa x of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larkuh;1zw0z7 h/a 6e 6wiaaenl8/ude -gger than the Moon's. Yet the Moon's is mainly responsible for thkg 8u6hwu7/eh0a w 1zze/ali n;- d6aee 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 1980k15 wnkz f)bknm94co 7 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ct83b wv.:x tvl9ocx3yyy q 2,its orbit around the Sun, 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 v l x ,w9cvbt32:o3qyytx .8ycradius 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-kgugs;7;6 /gq2w awsspqql r5s3 discus as it rotates uniformly in a horizontal circle (at arm’s length) of 7 alss; q/q ss;gp3qug2w56wrradius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sur qp)4r ;g3ymhpk 7 d/x;kn,xikface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the E; qxiphx)rk4knk /3d7g,y;p m arth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on nlzk -rvs) ;s*4qmdx(the edge of a potter’s wheel turning at 45 rpm (revolutions per min ;s)dk(svm lnzq-rx4*ute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratt1l7if:n3fwn wr );tz e in a vertical circle of radius 72.0 cm , as shown in371 ftztfw): n wn;ilr 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 a turn of:pb4 dbv83plc7hyei- radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is th i-dceyv8:bb 7lphp4 3is result independent of the mass of the car?   

  How large must the coefficient of static friction be between the t0m/ns4v4*xpxhaa- hv q-x8 8tgp b i.aires and the road if a car is to round a level curve of radius 85 m at a speed of 95hx8g-*vn40aq mxap /vpt8.h i-asbx 4km/h ?   

  A device for training astronauts and jet fig b- wh42xoh.w wj59np4hxp2b jhter 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 weigjhwbxh4px-wb o.4n92 wh2 jp5ht, 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 variable oiy2/o;av (gx( nfx)rspeed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rat2nvgr/(f ox)a ;o(xiye of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsideb re.sy* 2wdi) down at the top ow2byd*)s ire .f 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) u4nz:y ijkuu65bsm5) crosses the rounded top of a hill szu6i my:k4nb 5j)uu5(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-t)+u(plr ,lltzx;+rf diameter Ferris wheel need to make for u(r llp,rtt++ zf)l;xthe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle r q4kr. c):jwgof radius 1.10 m. At the lowest point of its motion the tenskq .) 4wr:jcgrion 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 pard; 7kccj-wwgi .k1b 2hticle 9.00 cm from the axis of rotad.;k i2 cbw7cj-kw gh1tion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at /uoktn6st 1l ua8:sl4s d q q4sb,h00na carnival, people are rotated in a cylindrically walled "room." 4n: 6qaontsh/ l s1qts8dul0kb,u40s (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionles)q4 0qs k/yta4 okuq+ls air-hockey tableto 4 l+/qo 40)tkkyqusaqp, 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 vx)t /a/mvh 0dof the ball which revolm t) hvd0/vax/ves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car 6+ jti+cei)fw 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*;/uu uis, yut $ 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 1w+xq ( idwm,d 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 centrx7fwx:8 9.jwy*/iw6jk ;zxtl uw zce1 ipetal components of the net force exerted on the car (by the ground) in Example 5-8 whex ylei9;juj6x1*/fzx wwz8wt .k:w7c n its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates un19vn08jtz 2;s xzgjtyido ;urqh(p 3s)z9 * cfiformly 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 ha *9znu)hp z x;1zvqf2j0r;gcoyt (jsi38 sdt9lfway 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 radiupq,0u6 3ai ljws 2.90 m . At a particular instantj,pl0 w a3iqu6, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii)18i17pxr pk.cq9 go ih above the Earth’s surface if i.hixc 1o1r 7p8gp9qk its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational u5 cq5in,yegp i -;2vaacceleration g has a magnitude of5qpiueag- yc5,2ni ;v 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 Moo))ulse:n;ubeo,8 h7i 6jqwn l n. The Moon's radius is 1.74 8 qnsuewu6;ln: 7i)b,h)eojl $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timesz7 pi;+ec4-m 28z.gkbo2 mda s) llzcm that of Earth, but has the same mass. What is the acceleration due to gr m2 c;-kcdim8l+)a2oslbz4pzm 7.ezg avity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sam:fc b:+l8 6i,r+q uux oprdog+e radius. What is g near +po:dq6gxu r:+io+ rfub, l c8its surface?   

  Two objects attract each other gravitationally with54o(j hck+ +joo iva6o 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 accele;3a evqfdl bl*482 mkesu8 c gn:(t3zxration of gravity, at (a) 3200 mu cmb:ds*v 3fx; lkzagt(8q234e nel 8    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth*g9k 7pe6gek t9znk q2 where thegravitational accelerpk9ez gk2t9neq7k6 *gation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sra;ek8. axuy/3nztg:bd/bj lmcb5*1un packed into a sphere about 10 km in radius. Estimated; nytbc ura*ab.j5 81:bmg/ xlz/3 ke the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf st 0+:tkpmidi e5ar, which once was an average star like our Sun but is now in the last stadi im5: e0t+kpge 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 whil/igo r7+ll. hpa6lqd* w,pi5og a.sf-e orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleratiip+g sl-f 5dih/*,7oqo.lwg 6arlap. on 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 osofp i+1fo/n0 f side 0.60 m. Calculate the magnitude and direction po+nofis 0/1f of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plxpy cs 58h0:).phvmnnlmp n/2anets line up on the same side of the Sun. Calculate the total force on the Eart )h2mxln0nvpy /ps8.nh:5 mpch 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 accelerati 5zr3n4yqsz /zon of gravity at the surface of Mars is 0.38 of what it is on Earth, and thyzz/4rs q5zn3 at Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usingwbs- r/h+em, p the known value for the period of the Earth and its ,-s/mphe r wb+distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circularq o4ilodgy9179nlvi) orbit about the Earth at ql94n19)o io7livgyda height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitel 7oujwd3zffn 2ik4 (9 into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? 7f 2w3n (ofk dj9iuzl4   $\times 10^3$

  At what rate must a cl l7 d0ezf*l1oylindrical 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 needed for one revolution. (See Question 21, Fig 5–32.) fol* dz1el l70  

  Determine the time it takes for a satellite to orbit o4, y:i ed;z)bdwn-x21uj gn gthe 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 re wg4,d g-i;xnu )oyd2 :jbn1zadius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wou 2l1wi9ul k5teld a satellite have to be launched from the top of Mt. Everest to be placed in a cilkilw 1ute925rcular orbit around the Earth?   

  During an Apollo lunar 6,+ r mid/7mvngy*yj jlanding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to g jmm*yij/vd67n,y gr +o around the Moon once?    s

  The rings of Saturn are composedii0l70ary 8ha y2u4rwelk,5vax((3sp8fyyv of chunks of ice that orbit the planet. The inner radius of the rilx(fu 7 eip 04 vahryyavisyyr520,8k(3 al8wngs 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 s (see F4ix4p +m(cmk sjgik 3.ig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) 44cs gi imj3kx(+pk.m at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the i e54q rccx-fw3pab),center of the Earth's Moon in a space vep-qe xfiwrc4a5 c)b3, hicle (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 mauli6 w0(tc4sauq:s -lk,w9 xfzks- f;ss. They are observed to be sep0sq,ck uf is -l69u; wwk-l xf4a(tzs:arated by 360 million km and take 5.7 Earth years to orbit about a point midway 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 elevator ths;ch4 sd v ztvk(.:a;pd3y mx2at movd 3dczpsv a;thy ;2x.sv4k(m: es
(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 elevatvz kqmlk,hpq98 g8;yy:)-tn j5 zxab,or. The cord can withstand a tension of 2z l nphja)5yqb-mz;k v9yg,x: qk88, t20 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfhqxy 6e bjr md79 wy)f,5zv5*dace of a planet with period T , the density (mass/* d) yzyf5 mhwbxd7ej, r9qv56volume) 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+30 hyjdnm)q6d yrqdej.l 8)potyq 6 3.4 d) to determine the period of an artificial satellite orbiting vetqml63jy hdeoq0q n) d.j 8yy3d6p)r +ry near the Earth’s surface.    s

  The asteroid Icarus, though only a fe9yzfpt y k,0ejbulwk( -h9x ) nfb061ew hundred meters across, orbits the Sun likb)enykjyh0k0 t( wb9fz9,1 e-u lx 6fpe the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance a;zp:w2oy m :tof 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 comes very close6qsb n jla7.x: to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun67anx sbql: j.. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga8nb0ey 4k qi0elaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distance for the fourl)ds/82vsx 2dxrzv q6 largest moons of Jupiter (those discovered by Galileodqrx ss)/ v2 v6d28zlx 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 k+ h rso/o,k1+p)z l di)bee)kxnown period and distance of the Moon. relhzkos/+e1pob))i)x, dk+    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kepo8 *a 61 ozu2 iwdd gub34*gy.ytmzj)bler’s third law. Use the dis b )tgi3g6oa.b81*ou udzz24yyjmw d*tance of Io 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 andy4mr iv8tl3c 0 Jupiter consists of many fragments (which some mlcv 38iy4tr0 space scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the9 g9pcl xz.t53t y)skd form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our owntp9c g lt3y.9dxk)5z s, 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 (Fig4 l*dulyo6 3js. 5–41). If his arms are capable of exertinljy64ld *3uso g a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravityz 2-; nsqo sjhb;.ga/k be half what it ;./osabh -2 ;k sqgnzjis on the surface?    $\times 10^6$

  On an ice rink, two skater4a p kqqhj9t31s of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pullha pk1 tjqq493ing on one another?    $\times 10^2$

  Because the Earth rotates once per danm*iggrv f3 sh1 :cq6.y, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’r.hsf3mg 1q gc6*i n:vt rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth:u)0 pzlgjp0pfq g/ 2:9gm fyu will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth an ml fgzfu0pgg::y0 pjup2/)9q d Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when y3 m),jzviwt 5eou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the ele3zm5i), ewtjv vator, and in which direction?     ----待选择----upwartddown 

  A projected space station conxe ,q.q*1lntt sists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity a.qqxln,e*1 t tt the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his2o+hwg 2 ,5n.4 ;usuercwj(hvakm7 e z aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius 7e2db t)gspa,qlht*4 r, the acceleration due to gravity at i,p4ah*se7 qgtd ) l2tbts surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticato,7n z r/.qf:jxn5uul by an ,rux.j: q 5nu7/tzfnoangle $\theta$ 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 7;ib5h9,;xl a9dmqu ( fkxcbe coefficient of static frma ;;9cilq,f5ed( u7hbxxk b9iction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating n: u..ffng q)ato.u n0so fast that objects at the equator wereqtn :0fo u.. f)ugann. apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 +,9qh,gtrtu3rp eeipr: ya0 ,v1p: soqc 12ge $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m :5ae pgr3v7 thn6jd(t. A lamp suspended from the cp nha rgjet3(t6v d57:eiling 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 massiv. t /wqd-0u 5h8hkaifre as 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 r.0 5qiaht k8huwdf-/ 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 thef+g22b/n;veu o:nmmta -6laa Hubble Space Telescope deduced the presence of an extremely massive cov la/22ab:una6fgeo+n ; - mmtre in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it tr*pr mpkaz7a*zd22 p+*h7iqs caverses 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, d*haa*7cp+ks2r2i7mzp* zqp 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 n mza tp6czm8;oi(4 h0(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 accura0z4;mhoa p t(mi6z8 cncy 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 bi2/gdillz i 5v70j/ h thf-u4lpllion km, is meant to orbit the asteroid Eros at a j2iv pl5/thil-/ 7l h4f0zgudheight 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 a satellite in need of hno5 ve*qb1;g repair. You are in a circular veq ;bn5 1*hgoorbit 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 ha vkc9 uk,5, uw-k7xxvys a period of 3000 years. (a) What is its mean distance from the Sun9-yv, 5, x7xcvkw ukku?   
(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)g jsg 2y,e 5ee4q xauid4-bu+ of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you.54e gx ua u-g2bdes +q,)jie4y 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:7cjeeye1ajrhcab12t7 ;3io ;x(yoy*rv ;xi a distance of about7xy arecc; hxoa1bo 23 t(j *1erj:yvy;ei7;i 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 je:)f n*bfg *lat the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational f):nblefj** f gorce 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 orbits the Earthk) 1g 67 nej)bniz+lyp $ \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 theupfls*j /oncr*g3 3i:t w6m .ilrl .h(m5)pqj 1.5-cm-long sweep second hand on your wristj iplnh*56.p.lsmw*o r(c :jit33 /qf) l murg watch?    $\times 10^{-4}$

  While fishing, you get bored and start i6uzo m;njl d84yp* 4r crcui,:e*i )fto swing 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. What is the angle that the fishing line makes with the vfuz 4)ijic: * ;oiy6lmdc, 48ue*rrnpertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiuszib r(l)6 njckh2a y0v 26d0ne R in a new highway is designed so that a car traveling at speed 2 anlhb(0jcni6re60z2 )dkyv $ 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 when negot (e;tr ,n*gfzbnsfbj6f 0c- a3iating curves. The angle of tilt is adjusted so that the main forcesg3fjz,nbcrf(*; tf nb06 a-e exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$