Sometimes people say that water is removed from clothes in a spin dryf r atn 2l/0ikbr.(u vqnt,91yer by centrifugal force throwing the water outward. What is wrong with this statement,r0n (1qt/tkuynv 9flb.a i r2?

Will the acceleration oflp 1wnt h45dq *k67ffy a car be the same when the car travels around a sharp curve at a constant6 5qdpyhw f*f7tl1k4 n 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 6acdylc.rd 72( abfew8,bc 7bhilly road. Where does the car exefe cc,7 r6wl(y bba2db8d7 c.art the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a chil6. k6fphz7npwd riding a horse on a merry-go-round. Which of these forces provip. k67n6hfwz pdes the centripetal acceleration of the child?

A bucket of water cap9ne;1bo ,fjk n be whirled in a vertical circle without the water spilling out, even at the topnkob1 j9pf e,; of the circle when the bucket is upside down. Explain.

How many “accelerators” doivbg5l3m1 zg, you have in your car? There are at least three controls in the car which can be used to ,3blvi z 1gg5mcause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flv-nn e4+2 x2qdd hm jzl4ip)x6ying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his 446m)l2zv hdiq +n2xj nd xp-echest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speedj+ti)s z/4k sod/8+fkhslrc:4* ylsb?

Why do airplanes bank when they turn? How would yougsj+let89,9 ifbjxl;pdze. 1p(,i wo compute the banking angle given its speed and radius o ;jg. f8wiz ,sxo9b+pe1 9illed(p tj,f the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.mhb0 jjtynw48l g y9/* She wants to let go at precisely the right time so that the ball will hit a target on the other si9g mw b8ytj/*l4 hjy0nde of the yard. When should she let go of the string?

Does an apple exert a gravitational force on (k a yy-x,b1btthe Earth? If so, how large a force?,-ytka( b1x by Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it iss;ny jr* g 9 ltoj:) jw*6t+e89zxpdnd, in what ways would the Moon’s orbit s6nn + :z;)jd 8ydgj9t xo*rljt9w *pebe different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on us 5r20ys07gmutetxuq yr(( 2 the Earth? Which acc urx75et(u s2u0ytrmsq y20( gelerates more?

The Sun's gravitational pull :ju 8r2w8v:zz bcb,c)gz )uw)hzmq2bon 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 from one side of the cz)q2bzv2gr:,wzc8jbw )hz:m uu 8b)Earth to the other.]

Will an object weigh more at thcqc1v) .ce q(ye equator or at the poles? What two effects are at wore(1yqc cqc.)v k? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only z4 -q5t5ew rw afi:jwu l3j47iabout half the force on the Moon due to the Sun. Why isn’t the Moon pulled away 3wi itq744j-rl u:5zj5w wfaefrom the Earth?

Is the centripetal acceleration of Mars if7tv3l)-okji q 1tky+nrz 69jn its orbit around the Sun larger or smaller than the)61tni+ ojktvj rz3f7- k9 qly centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) to 94wqbcy :5lt qa.sdc2ward the east or (b) toward the west? Consider the Earth’s rotation dc2q .d waq95cb:ls4ytirection.

When will your apparent weight be the greatest, as measuran4/mcl8qj.d ed by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) mov4n8d mq/.c jlaes 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 pepa5/v* ob ie1friods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on f5eo b*/ia1pv our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betw6iec6 u/0e/fefgm s -7vlm or+een step m ogvfee6imus7f//lcr+ 6- 0es.

The Earth moves faster in its orbit around the Sun in January than in July. Is t9 jb xhz(8qvt4kio: 0-,skngd he Earth closer to the Sun in January, or in July? Explain. [Note: Thisdoxz08gi4,9 h q jtvk b-(ksn: 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 quz)up2 h-v- g:s*fmq until it was discovered to have a moon. Explain how this discovery)fq :h mzug*-vu 2pqs- enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lar6 v0gup/6ljo(e)z a0dts( a hm :sq1ijger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from h l60te v06ss( /1zo)(:dupimgjqaa jthe 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 1-sq*8 oc.zafz4i29 s uf)jjt st6lis9 980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 it;0j* 40d8rmuony ecgy s orbit around the Sun, and the net force exertedge nr*jy 0dy cuo048;m on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2vbws -ey::-ns .0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate -:sye sbn w:-vthe speed of the discus.   

  Suppose the space shuttle is in orbit 400 km f i:k0gu6dfs, drom the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitationa6s:gu dfki,d 0l acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge ofm*cu(*p 3s a)jezo0t l a potter’s wheel turning at 45 rpm (revolutionu tp0 3joz*emc*l s)a(s per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rli,*n-:j2 k4frxo*1 8yrl9j jcysahkate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If itsysj* fca*1kni4j xkh ,lo:9jry 82lr - 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 gw*cj4rv/a8q5yowv - which a 1050-kg car 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 independent of thev*wya4 5/ -vj8rowgcq mass of the car?   

  How large must the coefficient of static friction be between the tires and the fv9 p9 k9oyfal-04j2 zho 8tnuroad if a car is to round a level curve of radius 85 m at a speed of 95km/h28 a4ofvo9fn yl90u-z h9pt jk ?   

  A device for training astronauts and jet fighter pilots is designed to 59 ;e y50ssvxz0dhmazrotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she ro vh0s sez0dam9xy5 5z;tating?    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 turn p**ijmzyr;wi 86ch) maw3g;itable of variable speed. When the speed of the turntable is slowly increased, m haj*w3 86)mypi w;zi*rig;c the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mn8rarvf-+sn vnn1r9 434rx ufbnc 9r,ust a roller coaster be traveling when upside down at the top of a 3nfsnn rnvrfr, r1+-a9nucvx r984b4circle
(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 rounded topjnbqu s-w)a410r v6ju orj )-6s41 uvj0qawu bnf 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 wzy4k , ,0ilzg vc7qr8dould a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point 0,rgzzc 7v,4qik8 ldy?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radi66h7d3s8thefex )dp 7;mtt idm/ra 9wus 1.10 m. At the d7t3r/h6mhtf pis;t6dea xed8 m97)wlowest point 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 rotate if a particley/rubv 3j0w9 6jod0xr 9.00 cm from the axis of rotation is to experience an acceleration of 3 uxowbjr0 6r/j9d0vy115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people a e7ol,oi;o he-tgbt5: re rotated in a cylindrically walled "room." (See Fi 5eb-t:,oeho il7;togg. 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 cb7re n*xh lv i6f6m.1in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected t*f6c.vrm x7lhni b16eo 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 of the ball -.8u ll/ syi shzz(4eewhich revolvyl4 z-h us.l8/ez(i eses 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 radius34 xe 5 mnkexk*nq/j:z of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesno (wygw+,t 4ggdnl: 2 v/xgo3i n4.zg $ 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 m(yxt sjwpv+xt+qlb0)g)h (o28m9 yyvaneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripesg :6mo)fcs.awhk4f* tal components of the net force exerted on the car4*hwk ).somcafg sf6 : (by the ground) 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 Indianapolis 500 accelerates uniformly frohrgur 6xiu7p,7 g4ov)m the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tan6goui7xg,4 7r) h uvprgential 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 cir icrv2 ,mhgv98cle of radius 2.90 m . At a particular instant, its acceleration is 1.052 vc ri8,gh9mv $\mathrm{~m} / \mathrm{s}^{2}$ , 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 gra5 hqaa;9:sjekarq ro,35: xpzvity on a spacecraft 12,800 km (2 Earth radii) above the Eart;qqzrhpa:r s559kjoa:3 ex, ah’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleros k/ ve 2adjx80h:.rzation g has a magnitude of 12 m/ha/ 8:r esvx2z.d0kjos$^2$ 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.y)1rjgu +o g0l2etf o) The Moon's radius is 1.74l gft)uy2 o1)ore0gj+ $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but haq)i6: 5x g fnqcz(s8oxs the same mas8icqgz:xfsx6qn 5 ( )os. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same r4q h-dq2sha ew h lfk5*)qgy85adius. What is g nea ew-s8k h d2hh*g)alq 5q54yqfr its surface?   

  Two objects attract each oyfi frl30m.de 2arbs3 d75p* uther gravitationally 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 of gravity, at (a) 3mz8eimlzs*rj1 zc(7 6rr --tu200 mj z rc(ru 8e-16mr-ms*7zl tiz    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from thea4. :ion-jbcf Earth’s center to a point outside the Earth where thegravitational accelera:b.ani fjco-4 tion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times zbj u 8u;2 bv3mh1km-/nnax;ec2t a2ethe mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster2j-tuaueb / ;2 ke nv8cxn3mh12zbam;.    $\times10^12$

  A typical white-dwarf star, wfi4( s+.k1xrzfz:zf9 ak 8 n-p3uiyp7 x -dptghich once was an average star like our Sun but is now in the last stage of its evolution, f 7t.3apngkxud :-+p14y9 -pzkxr ff (8zziisis 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 while orb3 t ckv+7ot1wmiting in the space shuttle. Your friends respon1to +7mc3vtkwd that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squakjfc+a8q mz28m ea gsb5t583p re of side 0.60 m. Calculate the magnitude and direction of the total gravitational for+q38 batmc 2pj8sge k8amz5f5ce exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years g2uug 4te*pz3x,e6q lmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupigpt6e3 uu*ezgl4 x,q2ter, 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 )ksy7v;)xwxk.g eao5 surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, det;7)vo.k5kg )y saxx weermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periodok4vk,vgd 6-o of the Earth and its distance froo- 4d,vk6g kvom the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a 0lgae:li;ap lo 3k3x- satellite moving in a stable circular orbit about the Earth at a height of 3600 io-al 0a:epx ;gl3kl3 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above th2 /c2rz *ukkdwe Earth. How fast muk/u22*d rc wkzst the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expe+6 l / 20u8rm5g-l+qatxni bug ,uintgrience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one rev5g-2tn uuxgm,+8tb6 0ri+u/la gqn liolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a sa 9uz*4pic6v1e; 2 thm5dunp tntellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a heig; htpuz4t9iu*n1 c6ep2md n5vht 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?    s ~    min

  At what horizontal velocity wj:a; wdydfb**q,7eah dy8t :dould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit aroua w *ah8dt,b7*d; yef::yddqjnd the Earth?   

  During an Apollo lunar landing mission, the commp5rnjpe)xn34 / o xkzmdl9ug,,, uu,hand module continued to orbit the Moon at an a4kugo,rnxnz9ej d l/, hm,)u 3,ppxu5ltitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn arrwaj1 8nw9iywdg(he.8+5 hy me composed of chunks of ice that orbit the planet. The innea(ww8n irdy hegmwh j 95.18y+r radius 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 s (d/a ,ny9om cl6see Fig. 5–9). What is the ratio of6n9a d, oyc/ml a person’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 astrk92 bbfnl6+ mmjy(c; konaut 4200 km from the center of the Earth's Moon in a space vehicle (a) mov6kf9bc2ykj nb l(m;+m ing at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. Th p(t; ,ecl.ousey are observed to be separated by 360 million km andp (t cs,.o;leu 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 wsgg m7m3 :+6irce s2ddeight of a 55-kg woman in an elevator tha6e:2dgss3m dgir 7mc+t 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+gloteu,, v7iy0fw4bt 5g- dblevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a = teggl, u0 wf, bb5y 47-+tdvio  

Show that if a satellite orbits very near the;fsy 5trs. (pq surface of a planet with period T , the density (q5ypr st. ;f(smass/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 the period of the Moon (27.4 d) to dek6g 1yh(5 -zszka-yri 2l7g cpweb.7xtermine the period ofik-pzyrg(2 - hza6w7xkblc g517sy e. an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, t a351g-l4ejms2 nukz yhough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is ng4aslu 3-2yzk ej51m its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance uuf.t/hr- d1j 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 uc qj:ae,p*bd2sat7 xeq2 /,ySun roughly once every 76 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 s2j/a *2 7 ,b seeyutaqx,pq:cd 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 t2o ; +fz7s5ij ;it-m 7rscwtruhe center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest mo ed g3(8cutw*ions of Jupiter (those discovered by Galileo in 1609). *t(3i dg8ecw u
(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 distance of tvgw2, t(0rsn: tz zgs)w3u90 vdv6phqhe Moon. ,vvd h w0(gw 9ntsz:zq)0gr2t v u6sp3   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’:ebckh4 tfd/z:+ki 4o s moons, using Kepler c4 khozkb :f+t:ie4/d’s third law. Use the distance 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 and Jupiter consists of man)/(yzefumc4.js6 j xp y fragments (which some space scientists think came fcu ze/j)j ms.y(x4f6prom 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 talj *ls- *r0xjswe describes an artificial "planet" in the 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 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 pla j s-rljx*w0*snet's year, in Earth days?   

  Tarzan plans to cross a gorge bw,k:y 3:yo 5r2ue 9p8clpk.3drbh zxfvk06 w hy swinging in an arc from a hanging vine (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 lrx:eylu:0b3 w69o f5 zhk,phcyv3 k8k2 dpw.rong.   

  How far above the Earth’s surface will the aj 9i ,i,l:e kpetyk4y :*peqo3cceleration of gravity be half what it is on thkek , 4pq:3:i pj* yeyteiol9,e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hm p 4h+g dn5* n)q;7s2ov c,.fiswhdbkands 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 pulling on ong sb k d2 ;si.o5ph+mdc)w4nq fn,v*h7e another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravitcr9aanzsyr8m 2xwbek j;u4( c5-;bd *y at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is thb4dmnzr 9brs8 5a ;cjxuy*- (k2;acw eis?    $\times 10^{-1}$

  At what distance from the E:( m 7m+wirgdrh iw ,24w(zxajarth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth,z2rwmwd hrjgia7(+ix 4 m (w: and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you sbzr p/f 5xy q lp- pt:sk6/2k6nsh2k02c,c xittand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevato cy0x2bi5t r6p2hns p2 -ps6 kc k:/lxtf,kq/zr, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate v o8 t/s9uhdmk h12i(n9sj7cwabout its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) ijshs ktcm 19 8/w 9i27d(uohnvs to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4f-9 qck/avyrgxay 88 pdhk+4-3).
(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 planemzjor7br9-00m i8yc20oab io .l/rubt in terms of its radius r, the acceleration due to gravitybol9am0b z/-0rbr 8oc r yjo0miu7 i.2 at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on 6k3x klnzp5v6*f jvl. a string) is deflected from the vertical by an a6k 6j lvv 3n5xkz*l.fpngle $\theta$ 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 coeffici35r qnz4 a+thv7i ).zsr h/ghbent of static friction is 0.30 (wet pavement), at what range of speeds can a car safelyztir.4+nr hsah/ 7zqg5 bh3v) handle the curve?

  How long would a day be if the Earth were rotating so fast that ob;2 fv u5yvc9szjects at the equator were apparently weightsvvz 52y9u;fcless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance anp 7 oini.m ,+:uqv vbz;p50jgpart 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 89 r ezgf0tbco z*db*7a curve of radius 235 m. A lamp suspended from the ceiling c df8*7bbrz*90zoegtswings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 z5v-mm 0y+ g:r(shb7 a qn oa;tj0ljt+times as massive 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 since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the:+m-mq tlv0z5jt y naog0bas; jr7( h+ 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 dedn iuk, p:iwjag2q.zw4 ez9+, vuced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did gqn,ke+,iv zau49w2 :ziw.pj 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 sf270gm 5i*sv9h zr7 vu4qjkkxbe s+6epeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting 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 v6h4vsjs x0e7bri*q97 kfz ukgem52+ the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orb/g.k;/yqwv2mht;)mny ( p pwbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an acc gwq.hnp)vbm 2;yy(pt; /wkm/uracy 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), aft0a88op )eqfnsb o8ve6er traveling 2.1 billion km, is meant to o8vf06)e8p naqbe8o osrbit 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 the space shuttle pursumrric79i+m:k i; kwd (ing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above theicrmkdm: +i r9 wk;(i7 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) What is its mek .e ia:rng(0kan distance from the aig(0e:rkkn. 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 valh sko iee,e+xx5g 0*x*cc0j; h ga18ziue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptionsg+iac e0 e*xx*80ch;egiz1kx j5hs ,o , like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galo54 +nkb uaf;b 0a9psyaxy (Fig. 5-46) at a distance of about 30,000 light-ys9o a+bfa p05n;4kby uears 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 locate ajl.:0rffp pdtoq r3*u0 b3k7d at the corners of a square 0.50 m on each side. Fd0l7 r t 0paoq:f.kbfpu jr3*3ind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi 80p jb4l exx6uf3ko(tts 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 acceleratiopd(p5qr w0 u8fm6l(e un experienced by the tip of the 1.5-cm-long sweep second hand on your wris5pmr60p wuu8deq((lft watch?    $\times 10^{-4}$

  While fishing, you get bored and star / 7viqy0mrr7mt to 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 w vr mi0yrm7q7/ith the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designgd6 bxeb pvgj:/k(88f ed so that a car traveling ab gejf/pv8 k d:8bx6(gt 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, utilizes tilt of the cars when negoq6iv.h5a b(5a)ayyk as 0 sn )l+ktwl-tiating 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 ros)a .0v+yyia5ka- n(wqballht 5)k6 s unds 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.$\approx$    $\times 10^2$