Sometimes people say that water is removed from clothes in a spin dryer (mv;qtcjr0fa p2+cay /pc.sg ew y -)nis,9v)by centrifugal force throwing the water outward. What is p,)c+g/. i-vw 9ny (a;rs 0q2fcsyt)cjve map wrong with this statement?

Will the acceleration of a car be the same when the car travelspxm4dx)q.-qwihg2l 42k z ci( around a sharp curve at a constant 60 km/h a ghq wiilz4xkx2-)( .cdq4 2mps when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at con90r-.sl1 bvabv2f jaddu :2r lstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of:2 ddjs. aubl9- va2fr1b0vrl a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hors2*imeba 2rat:r11 r ose on a merry-go-round. Which of these forces provsrb 1m a ir221t*eora:ides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertica-qq :d ) ocdh3q nstc6z2rg31ql circle without the water spilling out, even an61c)32-z oq qrdq hcd3gs:qt t the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There ar4gh:my- uugaj1na5c p;jo 8* b99tqtre at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerat 85-9aaj1:g b op9hug yqm*r njcttu4;ions do they produce?

A child on a sled comes flying over the crehoh2. t f- :n0,zhgpbrspgh, )st 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 over the hill. Explaitbf hgg)opn0:zp, ,.hh2r- s hn this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounnlxv/h(eki dn+tv*w 5r h0;2lding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the ay 9yz-uc/f4o banking angle givea-ou f94y/ czyn its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal p otzq6 sa8kk25lane. She wants to let go at precisely the right time so that the ball wil qtak6sok58 z2l 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 s-xmx.)gvl 8 p0ovk.tr o, how large a force? Consider an apple tvmrpx).8 .ov l -k0gx
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whatjs2*ntdwwb /(wgih fh9p. t ot87az7( it is, in what ways would the Moon’s orbit be dfihab t8*(z7 wts2 t 9d/p7.wjn hw(ogifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon (hhzrto z8;t9 on the Earth? Which accelerates mor( ;zhr8ot9t hze?

The Sun's gravitatio iwcez86/;4oej o qipw6,-m hjnal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for to-8 6;i/iecmp6 4ej zj oqww,hhe tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mq0x 9)tlo3 c--ayz xy)r ;dlj2cv+bprore at the equator or at the poles? What two effects are at work? Do td+y -c-x0cql;3 abtxo 2 lrprjz)v9 )yhey oppose each other?

The gravitational forcey4n( jlllpucv81:cu:3q odt 8 on the Moon due to the Earth is only about half the force on the Moon due to the4 t3:c(ln cdly:p 8l1ju vqou8 Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sunq oc26x m yg4r9vdox:) iq:9nm larger or smaller than the centripetal accelxn v:2ogq9r:4x )dc6 mi y9omqeration of the Earth?

Would it require less speed to launch a satell l.w6essj9: iyite (a) toward the east or (b) toward the w s6. e:l9jwyisest? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a cx5/vz.esnk; b -z9wa scale in a moving elevator: whee -.xz/bwk 5z;nas vc9n 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 adversely aff/p2 op r:p*dyuected 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 ( op/* d2:pyrupc) any other aspects of gravity you can think of.

Explain how a runner experiencjyb1y6i u-(5x z/ hefzes “free fall” or “apparent weightlessness” between 5ey z- by(z6jf/uihx1steps.

The Earth moves faster in its orbit er71 xsid8- yfaround 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 sxfdeyr -87i1Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. E 4nkry38c p(ffj(cmdrpc6+h+ xplain how this r+c c3+pmp(fdy( rh8jfnkc 64discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger5pbv j,8k7r yhkvm5 1a 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 fro8b,5kv pk v5y1 am7hjrm 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 m+r;yi h; f1s u dljs)cm3)0iz 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratmc4* fmsr 36veguc(e2 ion of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What mecc2(6rg s*4uv3me fexerts 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 exertezoo6i3h ,vu+4gy89q slzwu/wp6 p 3kgd on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. 6uyzv p39uwo4,z+l3/gg8 h6i k wpqso  

  Suppose the space shuttle is in orbit 400 km zusd,pal,87qk: ad r0 from 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 dp7rq,saua lk0 , 8dz:, the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitudeil6l4.cbgz :(b).9mv jasj gy of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions(j .iyj.la:vzc slg4b bg69) m per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circwe(wn m g3ze(w(4 uy4mle of radius 72.0 cm , as shown in g uw34z((wn w4 emmey(Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-knhkiow: tfbs6 7r9 6,wk4vf sn wo:5s,g 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 b s,hosv ntsfrkki,5w796w4:wf6 o:nthe mass of the car?   

  How large must the coeffici)z/v q.7 t-ger*t72drky pmntent of static friction be between the tires and the road if a car iqm/) eyv .tnz *kp27r7ttgrd-s to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotatrdau */, j(skfe a trainfa( u /kj*d,sree 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 rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable spee+91i 1c8 :bp spuo b3x/c ue4qdn3 vlrexq;+mcd. When the speed of the turntable is sx3eumo n; s+4cl :qxp vd1iu bq/38ce9pbc1+ rlowly 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 must a rolle( etlwn)f7u qns*zs zc;b6d 27r coaster be traveling when upside down at the 2) w7s7d;ulec*snz(6nf zt qb top of 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 k*lzxoz4qho1p/ dv6 7n g (including the driver) crosses the rounded top of a hil hdv1xn6 *zoo 4/7lqpzl (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 pe;hada:b8 rm,:ke; d.lgh1*qa 5s lkl pr minute would a 15-m-diameter Ferris wheel need to make for the passengers k;pl ;gr,kd ha sdh:5*1.lel m8b:qaa to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg i;(4z re 2-s6bbuwucz 2+ex 1 cvk/puvxs whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the cxeuv6ub zxr + ;b242e vu-(ws/zk1c prope 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 part6 10qzl2gn 8g6sdwnv nicle 9.00 cm from the axis of rotation is to experience an acceleratdl6wzng62 ns0g q8 1nvion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindriw ka2edc9pg0+mt,j (ih5r p 8ecally walled "room." (Se,+ct pk g8d5e2 w(ir pe0jmh9ae Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionl wjr0w*x.6kj sess air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Figk 0.sw* xjrjw6. 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, byeb0fdz20z/ .is-e0 w xvq*kv f not ignoring the weight of the ball which revolves on a string 0.600 m long. In pe .kw0z0 df xvvz/-q20sbie* farticular, 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 perfectl3jhm lx6s2 pzm/-;vp x9+njq zj2qb,d y 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 massesu(itqxbl ) 8f g4vap ukg:j:);3r* alt $ 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 maneuixbv8ig) veet jce48/ x :yr zdd**lun+h/;q9ver 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 centripetal components of the net force exe p3;t5lz8b7 d q3rh6ekn l.dhvrted on the car (by the ground) in Example 5-8 tvel 5z;pn3hb68 3dhq.7lkrd 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 from the pit oexyl,5jac )+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 through the turn, assuming constant tangential acceleration.l ao)xy,5c+je 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 particulu +dfjcf w:eic*3e 2d(ar instant, + iecuw d:3f(fe cj2d*its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of kfp;nq lgh*23 Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass fq 2 hnp*k3gl;is 1350 kg.   

  At the surface of a certain planet, the gravitatlsn/el13rtu 7ional acceleration g has a magnitude of3lr/s u1et7 ln 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1 iwajw*x;h 5hw 2 /wlj9gs;ov0.74jw;sj0gwl2i9 hahw v*;o5/wx $\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 has the same p f esj+b)2vuw(t+(vqmass. What is the acceleration d(qeuf+stv(b +2 jp vw)ue to gravity near its surface?   

  A hypothetical planet pw9r. lgxrpbskkx+8m:r(44bmq6 ga 6 has a mass 1.66 times that of Earth, but the same radius. What is g bx6(pk:lrm pagwxm6kr 4sr8.4b+q 9g near its surface?   

  Two objects attract each other gravitationally wiay1 r1rku(lnhs h+/i+th 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 grsn(jkg7bug/sn. e2 +bt 3kkq4 avity, at (a) 3200 mnub +gt4 k2(.sk/knebg3 7qjs    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poi )8eaplne:zcu.goy55 q c7)cqhj5 ye,nt outside the Earth where thegravitational acceleration due )jccuq,5a 7c hen.yee pz8 :)yqog5l5to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five tim ;x6r v7ej9 uxy0ux0vdes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface grav;rx0ex0uxdyvv679u j ity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is r7giwmxek;1g6 5t2w m now in the last stage of its evolution, is the size m7t1g2e krwgx i56mw; of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spapyc 3 0b:1ur 3duxn;ghce shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince themyx1r 33;nb gup0 uhdc: 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 corner9 7 b5mjyvh-lys of a square of side 0.60 m. Calculate the m m7yjyb9-lvh5agnitude and 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 up o88gxrli ga;ih ; 1di7in 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. 1xa 7l ; 8rh;igii8idg5-38). 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 gravityhqqp773qwygp te(n bvn, gc3e3 45; kz at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determih( qn3t qbg 3pcygv3 n;47q 75kepw,zene the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the c4lh7 tu3ma:vv5ylbi, dul c0.5i +flEarth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exampiay,tvllfd 3cl+ v40mc 5bi.:lhu5u 7le 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving i8egt.m qy12(g:v4lj1o4x+c ngnyl w en a stable circular orbit about the Earth a +lg1jgl(ngvx 144w 82yet eq:c. yomnt a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km a . wzxc// :fk6ejcko4ybove the Earth. How fast must the shuttle be moving (relative to Earth) when the relea k6oj:cx4yzf c /we/.kse occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate ifmpa2x 6++h+ rlde4yyr occupants are to experience simulated gravity of 0.60x6lhyya+re prd+ 2 4m+ g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes fby3 ; .hy-,znmtae*tx or a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is -xen 3y ,thbma. *ty;zone at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched *zh2x (2xmxw ffrom the top of M (h*f22xxzxwmt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, yt-iwp f8a6tj/hb q,-the command module continued to orbit the Moon-6 q8 p/-,tfwbathyij at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ih,+6po .19llok7yx vhk+a vjf q(v(nzce that orbit the planet. The inner radius of the rin loa1 6+9 qxjv+hfnp.vkz ,ly((7okv hgs 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,wz:qjog3a3gpf uqz 6 ioq1 ;9.5 s (see Fig. 5–9). What is the ratio of a person’s pq ; quzjo:1qz3i3a,9ow f6ggapparent 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 astronaut 4200 jia7v3c .ag)hji; ny fr7f,e; km from the center of the Earth's Moon ;a ygci;heri jn,f7) v73jf .ain 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 sl y vh6-jz/kbg:bu-+ itars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to o ih k6vzj-+lb:u-gby/rbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale readc5 m6n3vcc 2xn for the weight of a 55-kg woman in an elevator that m5cx32 6c cvnnmoves
(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 o.sles8l2kt4o h2,q zlf an elevator. The corlqh,ot l42zlse s.8k 2d can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a p+vbxuabk z8lziw/, f77wf .- alanet with period T , the density (mass/volume) , v/b.+w-laz f 7bza8kwxu7if 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 determine the perif(qd5 /k0zrrb od of an artificial satellite orbitik0rd r5fz/bq (ng very near the Earth’s surface.    s

  The asteroid Icarus, t uvy 7;yb s03+hng bas24gw;(8aginzchough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What issbn72z hi8g ava;(g4;cswy +by0u3gn its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 un nji6nr( (rnf s*-y +ityt)2$\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very cloian ol79v34xase to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from t3laao9v i x47nhe Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxj (4qqqs us55*7lj:ea9 l yqemy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 koj 4taz5v5x8distance for the four largest moons of Ju5vx ako4zj5 8tpiter (those 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 the known period and distance of the Mc3r(fij1jope -cr*+ o4gi yu 5oon. +3grc p1jo5*fo -iuy r4j ci(e   $\times 10^{24}$

  Determine the mean distance from Jupiterw dx75+t:wltkkcsm7 xaz-k1f- 7 ma y1 for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Cotm1 kk7 5swyxa:w kt+-fdac7x1zl-7 m mpare 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 consis1f/r vhl2(l ty6lnzeg3ru w*9ts of many fragments (which some space scientists think cw(gl1 / 6hve tnyrf*9zl 2l3urame from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "pla,la;f8herdx l,4d1q q net" 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 distaa q1;q4x8f r hd,ed,llnce 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 crosrbwq4tety1) pmg.t2 f l-oh355o *giys a gorge by 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 theo3wm 5 1-pth4 *oqlf yyigt2)te5.rbg 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 sur/e/,bc* rjuc a1(kp rfface will the acceleration of gravity be half what it is on t1 c*r(/abjef rck/ pu,he surface?    $\times 10^6$

  On an ice rink, two skaters of eqy4hu2d kri9m ;ombfq3mxs5u n4gz *)(ual mass grab hands and spin in a mutual circle once every 2.5 s. If w49f 2m h;5smnrz*g mk 3iou ux(q)4dybe assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent rm/3s v ygpz41,bpv6ejcz4zid5)s0 nacceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of th negm) p0ysi44 jvb/6z 1,vd5szr 3pczis effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly tyevjb.2cow 55;duf0 from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? 0;fey5j. 5woc v2b udt   $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an eldfb4lem6i0f ,evator, it says y4b,fl6i f0ed mour 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 bmg+d*.-tls ps/p rk( will rotate about its center (like a tubular bicycle tire) (Fig kpg-m* s/(+rd.lp tsb. 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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43).jkniy z*bn (:2*lvgq6
(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 owzo 8n(1*5 gp1 k)b( luoqnhd9+g wvndf its radius r, the acceleration due to gravity at its sur 9l noun(d v 8ng1gdo+w)hb1wq*kzp(5 face and the gravitational constant G.

A plumb bob (a mass m hanging on a st okajd ciu)6k+39r;ncring) is deflected from the vertical by an anglci 6k ;k9aurj)o+ cd3ne $\theta$ 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 cim,mai 0 kh/d-oefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the cda,- i/ mh0mkiurve?

  How long would a day be if the Earth were rotating so fast that objepcw gu6nw) zx07t,z* ucts at the equator were nuxzcgz) t,6 u*w0p7wapparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constan,s. pq hp*xq1e63pweat 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 (gjmn ojogfx1li :pf+sm034.radius 235 m. A lamp suspended from the ceiling swingsfljx3m+ gj04isf .no1mo : g(p out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times3av, 2b n9q9 ax 0n7wqdlwgqf8 as massive as the Earth. Thus, it has been claimed that a person would be crushed by the fx8q wq vbf an9dw73 9a,20qlgnorce 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 Space Telescope deduaq p7 4,vua:gtced 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 this by mea4v ,apg7au :qtsuring 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 trcqv1lpd4 tw6j-n3. nqaverses 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 w - w1cqdl n4.qt3vpjn6ith the road at A?

  The Navstar Global Positioning Syst 1+ky8nlo xdq8nwk7d*ym .ua9em (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, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately noa9y7+8d n1dk*.yx8w k qlmu 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), aft jkw;r l988v:bv6eu :nsrg v2ber traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height oskbjg:v298 u: v l;ew vn6rb8rf about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in n wbyb )cq,kq6xz7e - d.ay6f1pk)cc:ceed of repair. You are in a circular orbit of the same radius a )-cy wk7y)kxbfc 1q6 :e,cqazp.6cbds 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 3000fz.6fng,:+ tx0s yr xl years. (a) What is its mean distance from the Sunf,l6rxf0zs.:y xg+tn?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you coul-e rd;fp8*1 .axenv,d ;yvqpdd actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions;dp*.8vnv qexyp; f,a 1redd -, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arouatn6ha2 f m6 :g j e/-r0/dq/rzbiuqh+nd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fro/ueq /m a/f+ a6hzq2 b06d- :higrnjtrm 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 locsri elwn-9.rx9g 5a(kated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravit .ig5wrl-9rn9sea(x kational 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 1jcp2kq 8av,p kg orbits 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 on2)g z/ jtd1xwixm 0s7f the 1.5-cm-long sweep second hand on 7 /nmjwixx0ztd2s1 g)your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored ands 9yya/4eyrm; 07 m7m5/5n zg a8zwktavsi p5w 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 thea9kz/mm trwsayyw5v75gsy 74me0 ;p n5i 8a/ z vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a caltty, (qsk6ifv6 0( 7wer t14p-f vdvzr traveling at speed e(fvq 6td7i1y0ttlzk , s(pw4vf6v r-$ 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 Ac1 k6nl z+wp7viela, utilizes 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 17+pz iw6lnkvpassengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$