Sometimes people say that water is uk2dl n1*h 2dkod/pk: removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemuld no:1k 2kdh/ 2kpd*ent?

Will the acceleration of a car 71 ss;nk .zzzbbe the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at t.;sb1zz s nk7zhe same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the cpaa 18z/9st rsp).yrxar exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dipp1. yatzsar xs8 /9rp) 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 on a merry-go- cx9accrt(1+aoge (n 0round. Which of these forces provides the centripextgc cc1+e r9o(0an(atal acceleration of the child?

A bucket of water can be whirled inhhsobf4sl8/7-lt hg 2 a vertical circle without the water spilling out, even at the top oft/h7g2o8shb-l f hl4 s the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are a edx yua.(/l623hblwh t least three controls in the car which can be used to cause the car tobwhxl e(d/6 2 .uhyla3 accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig.sm(w*z+hawx93cl ,ni 5–31. His sled does not leave the ground (he does not achieve “air”), bu a(xil9zsc,nwm+w*3 ht 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 ridero3f7*b 4-w m+ddv:kojv qpud.s lean inward when rounding a curve at high speed?

Why do airplanes bank e*c2r3 dj ai(hwhen they turn? How would you compute the banking angle given its spj (aed*h 23cireed and radius of the turn?

A girl is whirling a ball on a string around hepi cdwpl* :u apltt6 4;,0f4vlr head in a horizontal plane. She wants to let6c lp0up tfi4apl4 wtv:d *l;, go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a for-3 b.ith.k 3gt 1r4t9 oonzzzuk()vhtce? Cons33ho t tzk-1n vgzt(tuo9zkhi4b..r)ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wha,f/3ew8jf wztt ways would the Moon’s orbit be differ8te z /fww,jf3ent?

Which pulls harder gravitationaltyqe-h l4bjf3* oh ((x)vkk w.ly, the Earth on the Moon, or the Moon on the Earth? Which accelerates4bfy joxlq-hvk w3(e.)(* hkt more?

The Sun's gravitational pull on the Earth is much larger than the Moon's coj la pcl*mduf858 y7h;8p 7a.bjz+/dxfs/z . Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the d z .ph857cdm zx/p fa*jb dc;l7o8 +/ja8ylufsifference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two e hbs l16d1sue/ffects are at work? Do they oppose each other?u sb6 ds1le1h/

The gravitational force on the Moon due to the Eab 1(pj) (,;mo.pf k-e rzkcxwoo,k5ek rth is only about half the force oz5)omo(- ocpr ebe j 1fkw. kx(k,;kp,n the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the p o2v+ixb2.o6o 9bn reSun larger or smaller than the cen6 o9o2+rbniepbxov2.tripetal acceleration of the Earth?

Would it require less speed to launch a gtho74 scfx/09 +hdl hsatellite (a) toward the east or (b) toward the west? Consh c4 9og/tlh0x7+hsdfider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by aipvc0e p-0id4yw0c t , 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 case would your weight be the least? When would it be the same as 0wccp, -ei 0y i40dtpvwhen you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversel cnrdop 7 6c*l:4x8zsjy 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 gravity you can think of.cnj:r z6ospc*d8 74xl

Explain how a runner experiences “free fall” or “apparew-p8t o0a jmq upsv3,.nt weightlessness” between ste8,q.tm0-vpp uswoaj 3ps.

The Earth moves faste ab+or9dy jy5nt-ga2 (r in its orbit around the Sun in 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 5aj2b-d 9g oanry( +ytaxis relative to the plane of its orbit.]

The mass of Pluto was not known untilxvzi9*7, jgv-9p wl mz it was discovered to have a moon. Explain how this discovery ena*g zlpjxiv 9mz7 -9wv,bled an estimate of Pluto’s mass.

  The Sun's gravitatio8qs5yha w.4q/l 6lwkc nal pull on 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 Earth to the other.]A child sitting 1.10 m qykw/.54hs8 q6llac wfrom 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 gk(e ;gf*2shu1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centri h)cmh*;i; od)voo 4rppetal acceleration of the Earth in its orbit around the Sun, and o*o;hvo;ci m4p )hdr) the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted o/wyrhf z9u 8e7uap* d;n a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Ca*za/u f7eyp 8ru 9d;whlculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circlw3.ivbbdf0 h1 es the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of b.0 bfhd vi1w3 g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck ofavy fpox pf8wf5jyfq xp,+bk;(b*3-- clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the whf-pfj3k yaqobf*x+ f (5-bp8yp,xvw ;eel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ve6 iswd f+44hktrtical circle of radius 72.0 cm , as shown in Fig. 5-33. If its 6+wfki d s44htspeed 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 aqko-7p r9b : 47vy:htphz0ov b turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is thihz t0o97 :ph4 qybvopvk-:b7r s result independent of the mass of the car?   

  How large must the coefficient of static friction be b wp fjve.3cbm fhk1 (j+7c4qm.f,uv -metween the tires and the road if a car is to roundc hpwbvfjqk, 7vj+4m.m(1c ffm.e3-u a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauglr2 y4s.r fv)ts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If tsl2rf .4)ryg vhe force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis ofs z5gb rmabvwpc8mh16a 9g8 5- a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntav rgwa c 65hmg8bz8s5 1m9bap-ble?   

  At what minimum speed must a roller coaster be traveling ws7+pcw *.ljr:b)dst cn emu/3 hen upside down at the top of a n3r:jlct/7s bdp u+s. ce*m) wcircle
(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 vv(g gb z+mp,qj 9na /(6ceb2m(tc8by+ zb5w p950 kg (including the driver) crosses the rounded top of a hill (radius =9b /5j+z ((( g8vp n2cygvebapb6twq9c+bz,m m 5$ \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 1 antt+v,ns r+e4eag:.5-m-diameter Ferris wheel need to make for the passengers to feel “weiaee4.nvr+:gt ,n tas +ghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circc.ijuwx t3*k g4p ,if*le of radius 1.10 m. At the lowest point of its motion the tek 4c.,i jfpt3*wu* gixnsion 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 cenckpe 87zj, zc+trifuge rotate if a particle 9.00 cm from the axis of rotati8, zpjc7+zkec on is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people :xelfd(1 ggs .:+wzveare rotated in a cylindrically walled "room." (See Fig. 5-35.) .(sz 1gx+ede:gv:wf l
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 rotpc8r.jg:f*q,s5sm4d jy7 s leated 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 csj ,r7ec*5 8fdsy. jlp gsqm:4entral 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 ign) w;h 07 tz-pqrwf.kcloring the weight of the ball which revolves on a string 0.f q;.r7w)-ctlp0 kwzh 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 ade7 ogplpkv,9*)a .pb car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses dgij;j z3r m(5$ 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 vfq55bl9 1cf jd n3zsg*ertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net b 19gv/ .ez m2l +wkedxwd1x/mforce exerted on the car (by the ground) in Example 5-8 when its spex1kb zvm/wxedl./9 e 2+mdgw1ed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerao, 4pj:e g1kamtes uniformly from the pit area, going from rest to 320km/h in a semicircular:o 41k ejm,pag arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular i 9)whaf*2jwhx /7k)nzc nwkerwr4n 5 fn**p4instant, its acceleration is 1.j znnp/k4nk)*i9)5*fwx 4f2 wac r*whhw7ren05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 Eamg l7d*a1bs pp-n9* qwrth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surp*1*pg97 w lbs-dnq maface if its mass is 1350 kg.   

  At the surface of a certain ply(ccn,,: n huu4gk(bfanet, the gravitational acceleration g has a magnitude of 12 m,u(c y,hu 4 :kbngf(cn/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius(:8o8 zse otr87l ooqogq5whdz 23dd0 is 1.74 o(0wq 87d8zzoqh :8oos5ddreglot 32 $\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 t4x-w1a f8wt:fq47gb63holbx pz pvln-x- . xxhat of Earth, but has the same mass. What is the76wx:ln-. - 4aqxpxb1g xvt fx-8l bwp f3zo4h acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 tj mskkq**u-d 1imes that of Earth, but the same radius. Whujkqk ds* m-1*at is g near its surface?   

  Two objects attract each other gravitationally with a force of 2.5y/mpe lk aszl;zty;m0s8la:/qxq .*q* .rx 3d$ \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 acce1 7nm5uwof45duxa)zh leration of gravity, at (a) 3200 m5oh71unamu wd5f 4x z)    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s ce75h: wogu ek f9mao-i6nter to a point outside the Earth where thegravitati:9khw mo- 5igau o76feonal 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 our Sun packed intos0*yia *5 vt w:49iwcyje 9ual a sphere about 15a ii4etu0* sw*yw:lv9y9j ac0 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which onc r7tfptz3)eu+e was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on tezf+u r73p) tthis star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the s1;lya* d mtqzr9opb/nzwy mu8/ 2s 8.ppace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’z8srq/8z9n lpmw2 *;y . d1/maupotbyt so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square 6 bhhgbkbl d3,yb32b9 of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sph,d23kbby hbghb63bl9 ere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years myjcir ,u0.4q gost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masu cr0 g4.,jyqises 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 thak1nnj :gj(p;brs (, ye surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determj:a(np kg ,1s;bnr jy(ine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the k)7vwmxtw5a3 .asy 4xn7lt( xe nown value for the period of the Earth and its distance from the Sun. [Note: Compare your ant sm(vxx47a.)t75ey3x lww answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a4ctj w)pr712 h k,uamh satellite moving in a stable circular orbit about the Earth at a height of 3600 ktk4hu,2c r7hj) 1mawpm.    $\times 10^3$

  The space shuttle releases a savq;s( a*zv9 ea3ja: notellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when3joqn: zs9 (;aveaav* the release occurs?    $\times 10^3$

  At what rate must a cylindrical spacmryuhm57s,1z- g81p3jceak o eship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, ahyo 5zjsr1pc mg3amu7-ke81 ,nd give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satelltftq0 jc0h2w lss,.07b 5qtveite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does. vht jl5bfwecs 20,t 0sq7tq0 your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launo wzcu7g(wh--vvi4w 5ched from the top of Mt. Everest to be plac 4(7wh ov5u--wci gvzwed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, thsp6s.0p c p;uhe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the0;hss6cp. p up Moon once?    s

  The rings of Saturn are composed of chunks of icec3r,hs .zfe:x (wcg,u that orbit the planet. The inner ra,uecc3gr.s:,(z xwfh dius 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 diametd9*)z4 wvu p j9;gprsier 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) up * )9rv 49;wpzijdgsat the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cent 5u4 ;4h;bs1px8ch dm9kuxxt uer of the Earth's Moon in km ux 1sctuhp4x4uhxd85 ;b 9;a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mas psd; f6 /0daw,tvj,sqs. They are observed to be separated by 360 million km andsf6w;sdj,/p0v tq d,a 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 weight8scwxf t6at n8y7q( lht8tl.0 of a 55-kg woman in an elevator that movxft78t( 8y 8a60n qlwchst.l tes
(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 suspxt+bb-sr21/b( 0w ysn iog )8 /spjqdtended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevatops(1b/dy+jt -2t wb q/gbirs)x sn08or’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planesp pd;gi .)n g+9 q+ytnz p:34*qmqhxvt with period T , the density (mass/volume) of 9nhq:*g4pmp+3+vs)g; p.i n qy td xqzthe 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) t/sh:dx op9m(r/aqe*r 48ggczo determine the period of an artificial satellite orbit rh/q4o8r:m/zgd 9px(cea g*s ing very near the Earth’s surface.    s

  The asteroid Icarus, though only a)iq 7izl/d s7tpgto8u)x; o) o few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the i)iz ot)ox8 /to7dg;lq p7)s uSun?    $\times 10^{11}$

  Neptune is an average distance of 49i2p 5cb1+nfa 2jq(qh8luprj.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 9u jk*,bh/zeg. 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 S/e *ku,9hzgj bystem? 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)8ue/u l *uavcw n0t)s 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, cjg2a ,ca4fn0 period, and mean distance for the four largest moons of Jupiter (those discaag 04f jcn,2covered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known perios wn ;8cr::pc2,x ovetd and distance of the Moon. c:2; sv8:epc ,t wroxn   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupi-ok4ob8 v bb;kter’s moons, using Kepler’s third law. Use the distance of Io and the periods given i4bvbb ;8k-ook n 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 oa (0qio2q5(b7d/y3j cafwn cfragments (which some space sciioafy(2 o/qq(cj dacb0 3 n5w7entists 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 artb ) u) +zomuxxcc x).ol7rv*7tificial "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, tbu.)x ctv+m7c l7urox*o ))zxhat the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig *u bxf; m15tejz-fx-y. 5–41-bf*y 1xe5 jf;x-u tmz). 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.   

  How far above the Earth’s surface will the acceleration of gravity be half w r 5144+lidc znsrzzp;hat it is on the surfa;+id s4 l4r5cz1n zzprce?    $\times 10^6$

  On an ice rink, two skaters of equal mass g5:q.oqxxt v*: s,cwqn rab 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 theys,*wx tqx.: no:qv5qc pulling on one another?    $\times 10^2$

  Because the Earth rotates 0)f,xbax7zl /wd: ia2g *rwwmonce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimatfz:g2mrxb,l0 7aw xdwi/ *a )we the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from thr /,rezquowu0chjf5t,wi.ss 70 4f(q e Earth to the Moon experience zero net force because the Eart7,w4hsuu r0w qf,si tjf/5z 0 .roqce(h and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand o0oo gj b+e6iz:y8v8xy7ca6tqn a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the eleec8xv:tzqi60y +86ja7gboyo vator, and in which direction?     ----待选择----upwartddown 

  A projected space station cons5-+.ym tw qa)3c( ugtu-5yee zrgjdv- ists 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 y -v-3g)cry5a+mt.gjeu5uz teq-dw ( 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop5wu 2 spwd:w(k ox0pgi7 mgi63alv+i4 (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 r, the acckrvccdnk 72pqk8eyr* */ q1haghm5) )eleration due to gravity at its surface and the g*h7cyqkm*8k21)) q hr dv c5neprkga/ravitational constant G.

A plumb bob (a mass m hanging omkljr0xgyz l 2xb git2t.scp))(*65t n a string) is deflected from the vertical by a 6t)2 cb5yxmxgj l0 (ipl)gz*.rsk tt2n angle $\theta$ 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 coefficienn3w 2b(btjdg pjj33m2t of static friction is 0.30 (wet pavepm2(jj3ndbj3 2g 3tbwment), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that pm;:93ba8e gk)ydk,h 6dldk b objects at the equator were appa )pd8g6 l,d9 ekmakhbd:ybk;3rently weightless?    $\times 10^3$s

  Two equal-mass stars mailkag:rvgpl nt0(81f, ntain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at aa c y3fmh0/vqr+(uw;gkj *vw4 constant speed rounds a curve of radius 235 m. A lamp suspended from th w;ygv*wvuk04ac3j+/(qr f hme 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 as the Earth. Thusvia1c;18gqx:u6 h dhm2j8 b hi, it has been claimed that a person wou1v:dh hu;6 mhi8b82icjag 1q xld 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 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 62fs 10 wccrooSpace Telescope deduced 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 esc 16 rf2occosw0apes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley showdubsw5za)w 7 +n 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 gs du5bw7a +zw)o without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellit)z i0v amiovq3t8fx*+es orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four sa vi3xm0)fivtoqz*8a +tellites 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 travelizdl kzdwk:s sgt( k/x hf)x:.h6+9a5jng 2.1 billion km, is meant to orbit the asters:ak:ldx96xj z kw)t5s + hg(dzk/fh.oid 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 4 25 8w mr(kzobrgly*cthe space shuttle pursuing a satellite in need of repair. You are i(8rkwmyc2o54rblzg * n 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 period of 3000 years. (a) What is its mean dist*xr b ueb iq/a n7f)7s+io16woance from the o6fe b7sr*1o xqai)bi/nw7+ uSun?   
(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 u8+j6aus+i yawould need to be if you could actually "feel" yourself gravitationally attracted to someone n+us6aaj 8 +uiyear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky+u:ncsjt7 9 xu Way Galaxy (Fig. 5-46) at a distance of about 30,00: x u9jutn7+cs0 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a sqlp(4ori 2n jy)uare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kl)r4(yjpion 2g 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 orb;.l)u3 3eagidc uae pg2x*la9its 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(j;a8x *m vipviwh5a ..5-cm-long sweep second hand on your wrwx (amj85.* ipv;ivha ist watch?    $\times 10^{-4}$

  While fishing, you get bo+//.y: dxy* va pmqsuxred and start 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 with the vertical? [Hint: See Fig.m *vpyax ./yx:d+us /q 5–10.]    $^{\circ}$

A circular curve of radius R -l*/thox 9ja 0s6drxvuxh0hrj*v/t 9 in a new highway is designed so that a car traveling at sp hr9/h thx0uvsdv/0 jxlx9t*- *jo 6raeed $ 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, utilizeh+bg ;wog2qk3 f)emw3s tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ).;2h+w fwg3qk3m obeg) (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.$\approx$    $\times 10^2$