Sometimes people say that water ishcqlkf5r uf1b):u0u rn251x h removed from clothes in a spin dryer by centrifugal force throwing the water outward. f1n1)lhu5 uf:b hc r urqk250xWhat is wrong with this statement?

Will the acceleration of a car- v8athy ju)f/jmo(3 l )hl*oq be the same when the car travels around a sharp curve at a constant 60 km/h as wu(mo 3h*)tflhjoaj8 y/)-qvl hen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alongslcw(*o q 7/u8dzy j(e a hilly road. Where does the car exert the greatest and least forces on the road: (a) at td*s /uz7 q((ew8ycl johe top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forceqice x q pv02(qyd+3jqe i2 t,k6r/5krs acting on a child riding a horse on a merry-go-round. Which of q22 y+iejxkdqi tq,/vep5crk6 (3 q0r these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spigq,1 te:mku 7vlling out, even at the top of the circle when the bucket is upside downu q7tmg:k v,1e. Explain.

How many “accelerators” do you/co)yo vv(q8j have in your car? There are at least three controls in the car/)voov yc8qj( which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cresjo9x g,t, gc1ss(wg2mt 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 deg(jx2,s w g9 oc1sm,tgcrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundrjyq y2rpy 1-7cy9- vming a curve at high speed?

Why do airplanes bank when they turn? How would qs*7r zo+vnu-you compute the banking angle given its speed and radius of 7zsu+- on* vqrthe turn?

A girl is whirling a ball on a string around her head in a horizontal plv aqw)9rq.f:3dg5kyr 9 yjtp5ane. She wants to let go at precisely the right time so that the ball widg5 )kwr 5yr:q.taf93q pv9 yjll 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 5b ; .s-ronyhca force? Considry5on- hb .;cser an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it tohxnz489qlzvly -w b1hu:*k9 3 mf8*hg 3inx is, in what ways would the Moon’s orbit beuh9 wx vkf8t:lqx*-l hm3h8zn31 b* y9ngzo4i different?

Which pulls harder gravitationally, thd jrbp8 lc(h r7c/g+0hpwbeo0rc j+31e Earth on the Moon, or the Moon on the Earth? Which accelerat r hrjgp8+ewl00jcrbdc+p ch1o b(37/es more?

The Sun's gravitational pull r m012t,w 7r*/,lgk wf5ds iub+jlb olon the Earth is much larger than the Moon's. Yet the Moon's is mainly responsjkw,l 1lrrw2+/7, btfgmouil*b 0d5s ible 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? Whatw7dz0tpe. zn * two effects are at work? Do they oppd.zwz7 *e0p ntose each other?

The gravitational force on the Moon due to the Earth icu756k lo pdsm-+,j)cyv rvisz 8,t g8s only about half the force on the Moon 8 l iv,jg8)-rvcu kd+ syz75,tco sp6mdue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of ziea8ee . 6wikoh+k ;3(vh; wtMars in its orbit around the Sun larger or smaller than the centripetal acceleration of the; wzk 6 oikte;v e.38(hiawh+e Earth?

Would it require less speed to launch a sat s*w:dz -bem+hellite (a) toward the east or (b) toward the west? Consider the Earth’s rota m-*sb:+dhwz etion direction.

When will your apparent weight be the greatest, as measujlvz/, v c wxo. d8e*3t7ko,qjred by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you vz8e od*7x.vl/o3 j,j qwk ct,are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long pe;fj ihsf wte5+ (5)zi(b3nqqngzm +w, 9be6vvriods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of. b f+zwigqm,5 3 v 5(j9efsn hw; e(z)6+ivbtnq

Explain how a runner experiences “free fall” or “apparem i ,3vwftmvhd5( b:0pnt weightlessness” between ste5bmmvf30t : iwpd,v(hps.

The Earth moves faster in its orbit atram 9,s(4 /hd1gdtvmbclh7,round 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 m h(trb,d7h1 vc, mag t/d94slto the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a mooxl57fsnyumr99:e by7zm *v y ,n. Explain how this di mn 7*y ul,y7vmyxf59s:eb9zrscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pur nltq5)19y*ck6 /j1it6xa.c1ihpojyzq v-jll 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 from the center of a merry-go-round movi11cvhq/56 z r tpx jacklj. t*oqiy1yn )-j69es 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 )anp r.gkiy9fp,2j 4 c1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its o,dkj;oh/.du g6 np ox3rbit around the Sun, and the net force exerted on the Earth. What exerts txo 6;k 3oh jg/.,undpdhis 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 bv8-spph8/ hh 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.9hhp-8pb8 h s/v0 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km s42 fuig6mqti 7 iz/v ;e432um s2ckyufrom the Earth's surface, and circles the Earth about once every 90 miuf 2t muiz37/2gs2mi uqvsk y;4c 46einutes. 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 acceleration oyi-f**as8b qnt9h .nw f a speck of clay on the edge of a potter’s wheel turni.-98asfynh wqti* b*nng at 45 rpm (revolutions 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 verticx )2w(4vut v4 ggmip(cal circle of radius 72.0 cm , as shown igi2v mgw) (4u(vptcx4 n Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius 7r:6axu3m9v *;et:yesml eu c1y,/yf r 7 :cl3m1ftres, ay 6*ey;ur9/ em:uvy xm on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fripss oy, ckvg:2th79 a3 1h.zopction be between the tires and the road if a car is to round a level curve o9po:z yo c2t ,ka3v shps.7g1hf radius 85 m at a speed of 95km/h ?   

  A device for training astronauts m1xggq8zx+ p01/y tlkj k9up+and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her ow8ty+lukg +0qpp1g1xkx9m/z jn 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 rotatingvt.0tgx 1ra k: 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 tgtk a:r1.xv0 the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller ckwy)y9c9ro* ,aw:jq e oaster be traveling when upside down at the w*9w9,y :)yojckqer a 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 kg (includizrg 2 tn8gj5-mng the driver) crosses the rounded top of a hill (radius =958jg ngz 5-trm2$ \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 wouuc+i u*s*xygt37q cgyu84 gx8ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost83+s4xiguyu*g7u x8cgqt y* c point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. w,je54,fsytvq */fkx At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 Nw,jfkx yv/q,fs4te *5 .
(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 cm from they7se p: qu/sj: axis of rotation is to experience an acc:s /yeq7suj:p eleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotat8sp /ugg:+bg.fcim/ p bl(i1eed in a cylindrically walled "room." (See Fig. 5-35.p. g pii( +fcse//:mbu l8bgg1)
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 af 9:gst;dzo, k circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ,tz:fos 9 ;gkd) 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 ts ;sbid/(t 0iaehe9,jhis time, by not ignoring the weight of the ball which revolves on a string 0.60dei9(/0 he;s s,a tbji0 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 fors juzd.zg+qm6/ (j xii5z(-gcs7hp c/ 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 massecn dz qu:6.)mws $ 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 evasiv1va 8 nex0*lr 49l2fhshmblu *e 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 and centripetal componenm ipdfy /o:4evi3c/ d/d;gr; nts of the net force exerted on the car (by the groudcre pod imdy;/3fn g:v//i;4nd) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from thek5zw 85/+c9d/d(stu hgus0anq aqmk 0vdm)5 x 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 through the turn, assuming constant tangent/9)wdh vu/cakmz(sa g 0t5 n5qxdd0 8sqk+5u mial 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 horih+ 71u7iv mqkw k;)rrpzontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.p kk+) ;1i7hm7qrvr wu05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth wch*(x*j , b nj7a0treradii) above the 70(w j* atcrne j,*xbhEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gr ,x)teytw p-t9avitational acceleration g has a magnitude-xp y,ttw 9)te of 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 M thh*:+l ma5h:,vo30 qdkccskoon's radius is 1.74 vt kskqc5,l am+3*: 0ocdh hh:$\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 oh;4zu,i 7s cb044 nivqxcxgp6f Earth, but has the same mass. What is the acceleration due to gravity near iuxs cixg,pv67b44;q cnh4 i0zts surface?   

  A hypothetical planet has a mass 1.66 t:h1p. x9 lvial* y*qgnimes that of Earth, but the same radius. What is g near its surface9 * x*vihnay.g:pl lq1?   

  Two objects attract each other gravif);n7g f(wljc tationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3zyntx5 vtna ln/1;:ep e mzgv )j+s8r.0zk(5b200 m( g;tzvkyb5senm)5pz+x j: tl ann/vr. 1ez80    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eabfifhf6a0 4u-zz* r 3arth’s center to a point outside the Earth where thegravitational acz fa03i-4hffubra6*z 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 packed into 4eznojlpa ;rd5)0x e*w *z5un 4 wc/kqa sphere about 10 km inw*o) 0 4 knpjalre;d5znxzw5/uq* e4c radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avera.r l y.k:9php )jwtrcby2;3u uu9f sx/ge star like our Sun but is now in the last stage of its evolution, is the size of our Moon yp .bru9kr.9ul xj/u wcsf:h)t3y;2pbut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightl kit:0 sevk:3oess while orbiting in the space shuttle0o e:st3vk:ki . Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at t5qrr a)os4 z(qhe corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by thrzqras54q o )(e other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planebfle0 t4 m:)er8v 2kyots 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 lifyb 4mvktr0 ):eol8e2ne (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 t)/(etm g7frm of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine tfr) 7m(et/g tmhe mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fjn)jr/ s6 1 a4snoa;a 57:csekixw 6czor the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Eas1r /6i5a:e6nx)jza;s c7njks 4ow cxample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circulafo dce(3(s+k g qb2tv)r orbit about the Earth at a heio+)sq(gecfkd(t2 v 3b ght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km (x 7r v5hp+f h13izjknabove the Earth. How fast must the shuttle be moving (relative to Earth) when thr7 (nzvxih3kj51 f+phe release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occdco))u 5/t min gb6:ljupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, an u 6tdimgjn)l/:oc) 5bd give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satelli7ndwxv jr)pl v*6l-d 3te 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 your result depend on the mass of the satelliv*) ljxv-3wn7ld d6 rpte?    s ~    min

  At what horizontal velocity would a satellite have to be launchepfxb:4n h7)mp d from the top of 4f)7 :mxphpnb Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar lsvlqhb+ p-)v plj )(jark)j0- anding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long dvl a(+-pj) sk) -jlr0v)jhbqpid it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbixjvh ka-*mx2n i6 /8exfmp 9d4t the planet. The inner radius of the rings is *nmi/pvk xhm 6dfe4-ja892xx 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (sa;ev*jzu 1yq, ee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the tjqeu,zy ; v*1aop, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 42000snwt lw2c -wu 6m1ga8 km from the center of the Earth's Moon in a mncgwtuw 0a1 6-8 l2swspace 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 (cfd8qyx cds 1rq+ ;n-of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betwer y qc -(qsx8n;cddf+1en them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight ii1 e9t:/9zh gbqz:ne of a 55-kg woman in an elevator that moves nbez9 iti/1:eg:9zh q
(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 f.d4 nvb djxf;+8kvn6wm 0z(sbrom a cord suspended from the ceiling of an elevator. The cord can withstand azk;f4j v0.8nd bdv+x(nb6 mws 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 planet with period cok9tgl0 r.ceq 0z)r4 T , the density (masl4e 0o9ckz .)c rg0tqrs/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determi : t*6hcbhzhd(ne the period of an artificial satellite orbiting very near the Earth’s surhdzh ch*tb6 :(face.    s

  The asteroid Icarus, though only)+n:uqkx f vai x/kd9: a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from )ui:9 a/:vfkdqxxk+n the Sun?    $\times 10^{11}$

  Neptune is an average distancbrvd+k(f*,oa e of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every wbi 3acj*3to4w-v+ x z76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.b t3 xw+4a*j-vo wizc3]    $\times 10^6$

  Our Sun rotates about the ce (byqtp 6sesc w* 0g:+ly/1scanter 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 meaetik 7 i7j1t ss e6qb62b.8xwln distance for the four largest moons of Jupiter (those discovered by .l6t 7qksb6 8jitsbew71x2eiGalileo 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 kno834ql euj-s ota.ir o :j,eqc7wn period and distance of the Moon. j lo.:sret, qq4-ijaco8 3ue 7   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usingo93 z9bj*m. yfd /zxqt cv2i9u Kepler’s third law. Use the distance of3.jv9/ qfmb2d9 y*ozxut i 9cz Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragment z3rfzqzm v*;it.+x:(ssuga -s (which some space scientists thinkrzsqs-(g3 u zmt+ v.a;z:x*if came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a bandxwy6yho lh 5cu( :-o5m completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun yl uw5 hhooxc-(6 y:5mis exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging zt ui2zp,zhz05 jc7c7t3x8chr:w/xcin 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 ca tct x r 3z:c/58zx i0,zhcjwh7p2ucz7n 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 accelerapo88u. bvp)h+ alb :cttion of gravity be half what it is on theopp8ab t .b+clv)uh :8 surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutur ddrl7l0 rk1:al 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, howldrkrr0 dl71: hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates oncbf/ vds l.fwlk 1xn,w+c4;:wztwgq- ld. 3m1fe per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effectwdd1 vwnk,:s-;w14 /xfwlf+ m 3bct.f.gl lqz. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spe cms7f3+km,.: llz73iz sv9 3paxk xwacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite fov 3pkx.as9 smmel7czkilx 3 7,w+: fz3rces?    $\times 10^8$

  You know your mass is 65 kg, but when you st0 kkq8gttxfs7+gv (q)bngt4 qv(/sk)and on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in w 0ks)gtkqg/x(+tvb kv )7qtq sn 8(g4fhich direction?     ----待选择----upwartddown 

  A projected space station consists of a cirp+ uu.tyc2(+f d3 8sf*ex+ia d2yxjvucular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (rsxyxeuy8d+f+.atp 232 cju+vu( di f*evolutions 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 loopz 6aqnq+yio:4gjp l,4 (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 ocd7tr9 o7(blfyt.vf6f its radius r, the acceleration due to gravity at its surface and the gravld 7vb(fro96t7yfc . titational constant G.

A plumb bob (a mass m hanging on a string) is deflected frof-pl t4u5hv75sprz+zm the vertical by an angle4pflzphz u+s5 r5t-v7 $\theta$ 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 coeffim-ut cv)tfxl1prid4ul*0t o7j 0z.g6cient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle theuz4u lv67tjl*cg xd0)m rtip1t f-.0o curve?

  How long would a day be if the Earth were rota)5z:v2+ tbr+vxk p vk z*ijyj6ting so fast that objects at the equator were apparently weigk*2j)65bjvxpt y :vr+ kzzi+vhtless?    $\times 10^3$s

  Two equal-mass starsksg66lr3vb2mm1 xbs6 .lm g6w. n)zj c maintain 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 a constant speed rounds a curvgkeryry )o3*3,*l+mmuwls l 1 e of radius 235 m. A lamp suspended from the ce)l yr1ms,rl+u* y wmo*k33leg iling 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 n::3fswy1(q ,h zf ajhas the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mfzn(hw:1 a,j hs: yf3qass =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 deduced the presence of an extremelm*rs l7r- h0lmuai ,/iy 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 measuring the sp7sla* l/ mhrmi0-iur, eed 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 hillxgbjsv3 d (b ,xp*4u( cqyjrjgcb3+3* and valley shown in Fig. 5–45.j xb,jdjc3(uygs( xbvr3 *g q*4pbc3+ Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group jpnz7s uxp7l0. s9bk+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 accura 0snjz9l7px +bsk.7 pucy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billiosq q*+m6rxp6c/ q*h xtys: k/xn km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is ro ph6*/c:rqqk +xs/*yt 6xxsq mughly 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 satellite0fq- v*1337b7pkptsa hojrc s in need of repair. You are in a circular orbit of the same t*p70rph1k3f cj 3o7vsqasb- 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 its38 ax1lzmz/(c adjq-vt3bi5i mean distance from the 3 ( xz-zmv5a3 j/qc8b1l itiadSun?   
(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 beql 6duz - )s85nevm1 0etns(xw if you could actually "feel" yourself gravit wvqx(1)ns 6l- szeu 0d85enmtationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wajlnv74:vbxk wp6 g+mk5p7* mx y Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centernxpk x74v*mjg76+lm k5p vb:w $ \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 ukcw:h0v.r 2ibz8 7uvm;3 ceilocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed v8:i0b7 ucwuvc.rze32k im; hat the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kn9:hvfyae ytj4 1; r3/ jnz-n9nmkn/ig 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 of the 1.5-cm-long6h3/d8+ e rtsqf nc/*qy ku)9+atyk ct sweep second hand on yo/ +/etcyshn dy3kaqct)kqt6 *98 +furur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a ciwsu3 pw v9i4djgg2 x56rcle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 5d2wvggu jp94s3w6ix 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 trave:ye wz/o9 ig7ylini/7 yz 9yewgo:g 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 c. oq;sg tvp,ln8vs+9mars 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 radi8,ovsv;.q+ ts lm9pn gus 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.$\approx$    $\times 10^2$