Sometimes people say that water is removed f*yb .tikt, )mfrom clothes in a spin dryer by centrifugal force throwing the water outward. What is wr )k,it.y f*tmbong with this statement?

Will the acceleration of a car be the same when the car travels ars+advokj/ao b 8s4m +;2 s3tkvound a sharp curve8;tvak ks4 a+ os32ov+ /jmbds at a constant 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 hilly road. Where does the carn,k0 su2kr* qahk,1k(6sut7 vtqd: bf exert 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 levebun,sq71,sh:k02t*ufd6k ( v raktkql stretch near the bottom of a hill?

Describe all the for4w .uy+n8kbx1jjo+ty0 ao g8gces acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acb4y oawy8o+ jkgt8g x1 j+u0.nceleration of the child?

A bucket of water can be whirled in a vertical circle wl (7sa/ykob8r jzds1b: 3lj(ouwqz6 + ithout the water spilling out, even at the top of the circle when the bucket is upside dor3(yzjdbo w(1 q s/8 :6ou7+zlj kalsbwn. Explain.

How many “accelerators” do you have in your car? Thetvtgp:f 3( :xtre are at least three controls in the car which can be used to cause the car to acceler:( pgttxf t3:vate. What are they? What accelerations do they produce?

A child on a sled comes flyip5azw(zi x ,ew5 6i1jmng 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 chest and the sled decrease as he goes,w ip5iz(1wax6ejmz5 over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high)z imxj*3y1 7b bgol*ei dh1unu4p7m9 speed?

Why do airplanes bank when they turn? How would you compute the banking ant+w)(-wfx u*dv x j6zogle given its speed and x6)zw*tx-j dw(ofu +vradius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. She gk ax72kp jf1u:y nqxq/z3,tr dux96; wants to let go at precisely the right time dn/1pxxtz ;u96jg a q,fx2ku 3r7 ykq: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 forcy*d pbcnr i*zvj7f : xn byv5n h2lc9j,l8080xe? Consider an applejjc c8vzpl5y *n8 ydb27x0nh iflvn*:90x,br
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wne/* gh mjiovz7g 6i9i5q2y p5xyb(+j ays would the Moon’s orbit be diffn5yghm7j jibpq(6ivi 9 2geo/yx z*5+ erent?

Which pulls harder gravitationally, thq1y +-t7ktzi le Earth on the Moon, or the Moon on the Earth? Which accelerates mort 1qizyk7t+l -e?

The Sun's gravitational pull on the Earth is much v)7m (a(mjdwtlarger than the Moon's. Yet the Moon's is maijdw(m7 t(va)mnly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What3,w kgwjs3 5k) mygq,l two effects are at work? Do thjq w)5g,l3 3mksykg,w ey oppose each other?

The gravitational force on the Moon due to the Earth is only ah avku.svh;29bout half the force on thak ;9vhs2.uhv e Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mar2doj8q rw an6av5(8r vs in its orbit around the Sun larger or smarv nr ajw6vod2(q85 8aller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or wxeji, mc5q5:(b) toward the west? Consider the Earth,jxwe m 55c:iq’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in 12a 3bd. tzolphse r/lo6in62a moving ed.h2 iz /26sl oopalrne6 3tb1levator: 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 when 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 adverses31 rnx5hk0qn8b2u-jliw ,u gly 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 sx l1,uu gsnjn 23h058ibr- wqkurface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free pasly h*qnji (v ;,h,;fall” or “apparent weightlessness” betwee;i vh,y;a,s nphl( j*qn steps.

The Earth moves faster in3 kzmf8luw)7nih7 z y)6oj2n4utf2 q n 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 axis relative to fkz uoj7tn87)u nzwl4q)ih2 m n6y3f2 the plane of its orbit.]

The mass of Pluto was not known until it was disc mufukf.w1 ;g.overed to have a moon. Explain how this discovery;fm1gkw. u.uf enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than th:txogsgmjwv )g)f-2 2e 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 the center of a merry-go-round moves with a speed of 1. jgg-2 )fg s2ow:mtxv)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 1980;;y cgll5,nva $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 d az 5t41 -m.nfq8ayjrnqol+3of the Earth in its orbit around the Sun, and the net fofml 51+ynoj rq tzan 8d4a-3q.rce 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 on a 2.0-kg discus as it rotates unify1;w ;8 -toxy+ )wtyrew 6o- jwnti6cbormly in a horizont-tob w+ 618;yj yot6) wcrne-twy;xiwal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km/0qav9 xrg-, ef6zyxs4vkvh:a)x n3 u: b)o ei from the Earth's surface, and circles the Earth about once e0axb-q/ e4x)nvhfg 6 u:r:ke9oiav)x svz3y ,very 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 Earth's surface. $\approx$    g

  What is the magnitude of the ac* )wotmg soz/3qy vrp1. 0pfi lha194gceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameteo4pv9pm glfy03sg t)/or1wzaqhi. 1*r is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical ci5a c-zo 9h*w u0k,z ejumbp5t9rcle of radius 72.0 cm , amu9pta5kc90-z*ho z5be, uj ws shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with wh:.rpt om -;iepw ql48kich 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 roakio-4 l :mtr ;p8wep.qd is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffic,eqxccp/ qjrr2 mk+nhx 2 x.p+-; ww;dient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m p x jx.hcc22qm;de/xkq pwr -+,;rwn+at a speed of 95km/h ?   

  A device for training astrywlwnmz/)q:941 o ms *ilx9bgonauts and jet fighter pilots is designed to rotate a trainee in a horizontals / mwz4 9:l im)91lbw*xgqnoy 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 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 vmd6+htd (8i sog3bkvy.mqs:r 3 y,-z/vx0cl uariable speed. When the vi(zv3 ctmr63ddxy0s:/8o,bm. s l khygqu+-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 turntable?   

  At what minimum speed mus7ju6b7lf h h:,e ydox*t a roller coaster be traveling when upside down at the top o7hj,hfbu xl :6*o7deyf 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 (inxxp0h f (fpo7k ;o2/okcluding the driver) crosses the rounded top of a hill (radius h(pofox 7;x 2 k/kpf0o=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 perfd: vbp+m8n 7g minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weivf n7bd pgm+8:ghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle2w7 lrl5cf;e /aqtou m: -emb8 of radius 1.10 m. At the lowes5b8f r/ mmlct2: o;eu-qawl 7et 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 particle 9.00 3gs+0 bvtsv;0hbwus, cm from the axis of rotation is to experienc,svtsb vb3g+0 0h;swue an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c:,) /hhj (cumjril(q7mgjr9 +hm 1ccwylindrically walled "room." (See Fig.julcgc79rh m +m h(, mjw/ijr:( )q1hc 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 circle2-.op*86+iajq. s :rimhw qzwty lpf8 on a frictionless air-hockey tabletop, and is held in thiq88.ih:r* fypwt.o+swij zlma2- 6q ps 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 of the ballwy3o8 n9xc*eikw dr) + which revolves on a string 0.600 m long. In particular, find the ma83+nrykw9i* o cw)x edgnitude 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 radizi(:*pzdx59go usx,yr y 0ma9*a8vf ius 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 masses bd ezu7.t5 gsqo*j9,un ur.u9$ 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 evasi4 2-iqi(t3 mruzmd(v lve maneuver 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 0yj z(nvo 8s;q2w z-yj4,pyagand centripetal components of the net force exerted on the car (by the gr-(y 8qpov;z 2 4ayjwnsgz0y ,jound) 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*i gg jnm-lcw29g. w g0vc79tg accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway thmcn tlg7gvj 20iw9*c9gw gg.- rough 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 (01: y/ hrm jjesyd8grto:3kl. At a particular instant, its acceleration isholjkj1:(yys g rm80/td3re: 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 nm7cw -8*6acyssj j(y12,800 km (2 Earth radii) above the Earns a*yc8m6jy( sj7-cw th’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerati; -pev2 jglu+9g7ghz ion g has a magnitude of zl v7hgj ;e9gig+u2-p12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Mr3;p pt, ;;rpab,ukgpoon's radius is 1.74pup3r,k; , pbr;;a tgp $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 dz pm7uw vyo vm6+s3dx*anmk2m) 6g) (times that of Earth, but has the same mass. What is the n )m2ugys)7xdma ( vp*dz vwm6 o63+kmacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that 3qsx yt/)r6r,r7vnsl of Earth, but the same radius. What is g near l 3 sr/,rn6q7rtxvys) its surface?   

  Two objects attract each other gravitationally with -rc 0h9s39eq .smzcxou/ o2 bsa 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 val+h+t8hfa /l0gr uq9gm ue of g , the acceleration of gravity, at (a) 3200 m gh+ur+a0 h8lgtfm /q9   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eart7dx t )m+3xrigh where thegravitational ac+ x3i7xrg dtm)celeration 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 pa oi/pi4nc :jc0cked into a sphere about 10 km in ccj:p 4/o0iniradius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our u m0kln,ev) .ySun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Whaeu lvm,yk)0 n.t is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feea9z5 6qnn sr(ul weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that s 5nunq9(zr 6ait 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 ao wgur,8-:gc u square of side 0.60 m. Calculate the magnitude rwg c,ouu g-:8and direction 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 planets line 7t e-mav0nrg;h(m vpew8ojx0 8b0sd8up 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 li0va8 m;00pet-x( ws7enodm 8 brv jhg8ne (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 surface of Mars is 03pa/c f lsk(evw0ne) 0.38 of what it is on Esl )/(nvcw 0fp k3e0aearth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuepc*5t:q. nzh s for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained us z*phsn5 :tcq.ing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving6y k ,--nzgqpm in a stable circular orbit about the Emg- kz p6n,q-yarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km aboveax 3v8bxl;hi 8 the Earth. How ;ixv8 83bxalh fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship ro-q,3zipdj*;ju2-buewzap - ztate 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 Questd-z j*u ai- pej,qwb3zz2up;-ion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit kto z3f- rucp6cb1 gs9gv1,e4 the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the masb411kepcfu9, zgc 36 r tvog-ss of the satellite?    s ~    min

  At what horizontal velocity would a m:;p tuw y yobi;+ewc*w-+rtb0(oy9h 0avs 0 usatellite have to be launched from the top of Mt. Everest to be placed iu;wyb0sy-t t(0r: vw aobuch*iy; pmw+e 0o9+ n a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t)i ;.y2:cpfp kuawby*he Moon at an altitude of about 100 km. How long did it ki 2acpyf) by.*wpu:;take to go around the Moon once?    s

  The rings of Saturn are comp 2m s2;i7ph2ndlc y+yvosed of chunks of ice that orbit the planet. The inner radius of the hs+2d2plyvnc7i2;m yrings 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 r6qitk9i+p 00z sm. qsaotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real ws pkq+9m6itiq0a0z s.eight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-oz9nk0 z q jn3+sfr6yn1 5,bhgwb/ pc(kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (an c53gr0pn9+wq /h, z 6s1oz bybjk(fn) 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 tmc*z)vdj1m4 of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit aboud14*v jmt)mzc t a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the qeisxdl *knvv3nv* 9i5c *97wweight of a 55-kg woman in an elevator that movecn*v*7widi9s935v qkelv nx* s
(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 suspadb1k,q ,rxq8q x4tmlse v5.;ended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s min.ktq 8q4,l va,x qe5d1b ;rxmsimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pln57j7k4/ilo)ti/9 gkynoa v xanet with period T , t/o)oy9kvx4 gal /i7kj t inn57he density (mass/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 an (mo,bv ghuk6)d the period of the Moon (27.4 d) to determine the period of an artificial satellite orbi gmhbu6v(k),o ting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundredgm e1 s d; u5qs0z7aae*(i+dbj meters across, orbits the Sun like the planets. It5ea1( s+m;* 0ads zbe gduqij7s period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of k;72x/ +o vf1e*waat4x/gvku 7nye lz 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 eve n;wb 1tp870vvh 2ouhory 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 pvt pb 021u8 vh;7hwonolanet’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 ce3bwouujl*246h j qz9v nter 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 mf a bd yuwzv9y95y655roons of Jupiter (thb y69yz d559arwvyfu5ose discovered 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 thelfyk/gq2am*g5v:to 8g zl s :; known period and distance of the Moon. l:g*q yv 5skz:o;2lmagt8/ g f   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s h0f3y9 pgxcj0moons, using Kepler’s third law. Use the distance of Io and the periods given 0p gfy9hcj0 3xin 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 fragmentso(6cq+. 9m:hr vjkdm()xctod c+cr- v (which some space scientists think came from a pladro c:vm)(.vcc(txj+-6 chdq9r+ komnet 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 descr8u owh.j zwwwq+80p,qgyx: a0ibes 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 ( jqp.wwwyx o0qazwh8+:u8 g0,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 swingin xbr g8efh3s ywr3/a8c 2u9s)wz/ebe+g 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 txy)s9 /br ere 83 zfu w/ebgc+3sha8w2he vine is 5.5 m long.   

  How far above the Earth’s sur-r,bfixnk( -oface will the acceleration of gravity be half what it is on t-o,fx(kr- bi nhe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and s/e2 igivj(kg0b(t;n(/ib jx2e t xc g3pin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their inxe(cbjjvg tb;gi 0 2ki/e3i gt2 x(n/(dividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparejp 0/a6imdv q;nt acceleration of gravity at the equator is slightly less than it would be if the Earth didq ajd 0m6;v/pin’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a sydyzncx4byt ,(j3coz8/gh 5 z-dq)4 zpacecraft traveling directly from the Earth to the Moon experience zero net zz)h-n/4yx(b5dc ,yqdyt j 8zgo3c z4 force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on si41 s (c(mqq)1mwa2o .iz dm zlte9b2a bathroom scale in an elevatoaql(d212 mqmzsitem4 (w) bc .izs91or, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that w73ermsh9 ,hl 3.vqxvj ill rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a sx7ml v3.hv9eqr j3,hdiameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertic- ( ch)xqvyiv.al 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 r, the2wuhf65 bha r6 acceleration due to gravity at its surface and the gravitationhu r26hfwb 5a6al constant G.

A plumb bob (a mass m hanging on a string) is deflected mv*)lup77t 9y2 thy1g 4rcxud (g4ihe from the vertical by an angle 4y 71p tlm*ighy gu(2vru49h xctd7e) $\theta$ 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 s 8, +zlrrvhym 6h:pqj2peed of If the coefficient of static frictio j,rzr +vy:lp2q6mh h8n 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 sox ra0:f7 f)nmv fast that objects at the equator were apparentlyfv0rx):a7f nm weightless?    $\times 10^3$s

  Two equal-mass stars maintain a c/n55w*l :nnw gwn +)vxpz 0bqtonstant 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 a constant speed rounds a curve of radius 235 m. A lamp soc is;j (gpox0:f(i7i uspended from the ceiling swings out to an an: i(f igxoi0c j;ps(o7gle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as)d, , vznnl1l9b gtap2 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 p a l9b gvz,dnt2)p1ln,erson would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope+nv *m8q /wnwrgknq6+ deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black ho*+mn/kg86 vw+nqrnqw le (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley showtm9y ):v.vvkpzbi b/xa72lbo i551iun in Fig. 5–45. Both the hill av2 x. pii)kb abmol 95t:vzb5yu/1v7ind 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 the road at A?

  The Navstar Global Positioning Sys1ytda+ x rlxo1:j3o;p tem (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 accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, witr jpx +3d o1:1xyltao;h 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 aq)mv57g9 oamu 8o1uobillion km, is meant to orbit the asteroid Erosumo1) 7 8u59aqoovmga 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 pursuing a sat*lc zsws+ ds.of)9a ny44ae.gellite in need of repair. You are in a circular orbit of the same radiusaa yd9e.sn*w) lcf+ g s4zso4. 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. (efw/+. peomg4 a) What is its mean distance froe pemg+wfo/4. m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the val8r) gv h o5bam7.vke 11u/fdmdue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable ase1a75kvod rvm)/ dm.hb8 1fugsumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way p y5ijv vzkb8: kw(05xGalaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centb5 p08(yjvk wzv5kxi: er $ \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 the2(pek-s+apgh 3nr(u a corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1pnp hu a(+- rk2a(e3gs.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 Earygnld.w43 lo1 th $ \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 theryta 1hlc 0y3: 1.5-cm-long sweep second hand on your wrist watchy ry ah1lc0t:3?    $\times 10^{-4}$

  While fishing, you get bored and start to k.r c9ho*1mgn c+ vso6swing a sinker weight around in a circle below you on a 0.25-m piece 16so +ch9* rgv m.kocnof 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. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tra08di08ykpx;7 grdg 5nm/i*hm h*s y b()dcuppveling yc0h/rhx* 8mi 5)idyunsp dkg g78dbpp*0(m; at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the ce,00zq:0wr k b- urhon q9nm+9. thhucars 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 .0-ob nn 9h,00q:9m rhqwkc+huurtzeof 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.$\approx$    $\times 10^2$