Sometimes people say that water is removed from clothes in a s)2zkww g-u6- jvr;yvfpc yy;(pin dryer by centrifugal force th p-;w ;ru6-2fvwvgczy (y )kyjrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same whdo q36 j4atmt7zc.o-t en the car travels around a sharp curve at a constant 60 km/h as when it t.j47 - 6mctttoqd3azo ravels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speedf97aeny(qqtrg : /;mp along a hilly road. Where does the car exert the greatest and l(pmga:;n 9qq tery/ f7east forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-, a0 rfppxv;;*(ndmp xround. Which of these forces provides the centripetal acceleration; (r * vpm0dp;nxpxa,f of the child?

A bucket of water can be whirled in a vertical circle with8o-c)de 4; g cbugu lpo u;van1bn;19jout the water spilling out, even at the top of the circle when the bucket is ;u) abcn1u 1 lgcog4uv8oebp;9 n-d;jupside down. Explain.

How many “accelerators” do you have in your car? There are at8vh ve(ceirj ,8*ubqy88jdi:: m t/ij least three controls in the car which can be used to cause the car tt/*vje888 cdj:8ib h v(y:jim, reuiqo accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest gq( 68ay:dpbl 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. Explain thiag:q6p l(d8 bys decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speede dq+(tocuv*y3 g7(op ?

Why do airplanes bank when they turn? How would you compute the bang7sr ipvzv)p2y7+6m7cg ; sgsking angle given its speed and radius of the tuv2 7 cg6 +p7mss)gr v7z;sgypirn?

A girl is whirling a ball on a strin, /53cbym3clp jl/ fiuy(pu+ng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the p n uyj 5li plc3/b/yc+3fmu,(string?

Does an apple exert a gravitationalxotv w4v. 7g/g force on the Earth? If so, how large a force? Consider an ap/g7 4owt.gvvx ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orb3vzssk yq6 a 6g9:gxu,a*j i8x1ro5m sit be differegxo 6g*13 uar,xk5s9z ssia:8ym q6jvnt?

Which pulls harder gravitationally, the Earth on th:6plp-k omyi1 go8,qle Moon, or the Moon on the Earth? Which acceleratesoyg8pl ol1-q6 i,m:k p more?

The Sun's gravitational pull on the Earth is much larger than the Moon's.avppr7h l6b)23 ..oj ;jleve2 bigz1t Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the 2r. 6blj v 1) epz23bahpje7vg;lio.tdifference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equato0oj5hkixu5j74psne)pl qf,o 4rp 6+yr or at the poles? What two effects are at work? Do they oppose each l qo 4py)5x5p7 sefurnojh46p0k+ ij,other?

The gravitational force on the Moon due to the Earth is only about half 7 yn; kd(3t-fzptgc ,nthe force ony(c7g kt3,-d z pnnft; the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroun4o.zk 3yatrq,48i lk hd the Sun larger or smaller than the centripi8 34t .z,q4h olakkyretal acceleration of the Earth?

Would it require less speed to launch a satell*(xq yt;h wc9esjje.2 ite (a) toward the east or (b) toward the wes9wxj;ycj ee ts.q2*h (t? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a mujsg4 0-apwra:8v0ru)ns,ode c3e elycg )8 9 oving 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 wev0 n)0l:g3 4wj8d8, s a re9eeuc) rsac-yugopight 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 sgzxjtohid+rd7 n x1 6d)t+b0,r) - ttzpace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell thatz1 g6d7n+zih), -+xjdo0bxd rtrttt ) 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.

Explain how a runner experiences “free fall”4xeh7j .j-lp w or “apparent weightlessness” between selwj47 j.-h xpteps.

The Earth moves faster in*fg w1xye.*i*fp* mrm its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July* r1y fxpm*.gfim*e *w? 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 the plane of its orbit.]

The mass of Pluto was not known until it was dist r mm:i+ bv*w7t7wpyzo 83j.ccovered to have a moon. Explain how th .wt:ro8z*cimv7+bpj y37 wm tis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the 0(sn ;zmak*yq 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 move amk *;qsn0(zys 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 198k/n z /grwxca f/n1 ukundysy* 3j(56e2v5vl/ 0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earthrve2vx z. b+(w in its orbit around the Sun, and the net force ervv(2.bewx +z xerted 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 ajg.d.r s.qv k6+*d*w rdmdf,hs it rotates uniformly in a horizontal circle (at arm’s length) d*d+fs.wh dr6.kjv q *r.m, gdof radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle 1hs dqaokv+9v36zh 0wis in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Finwo +qvz136hs 0av 9kdhd 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 acceleratioa ziss6 5u.lvuzj3qk. n2d;;tn of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revo5kis; tnqul s3d; zua .6z2v.jlutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved .n;gq t:2npl pat a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fpltqpn .g n:;2ig. 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 w;au ,lyu:zht 1hich a 1050-kg car can round a turn of radius 77 m ou;:,1y haz lutn 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 coefficieno7knhss.5s rf -7:q ma*zepi ,m:mo,lt of static friction be between the tires and the road if a car sfq,*hnopio m5lre:zm7s- m a:k7s,.is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fi cf-ia.h))3fbn epg4bghter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the forf)hiab 4 3nepbgc-.)f ce 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 oa3y a5 cudn5-mf 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 co n5ady5acmu- 3in slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mufd0pikvqk/ -k (r a9n (59yfpnst a roller coaster be traveling when upside down at the top q/( p f9vyr-nfnda50k(k pki9 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 (including the dri nj8ch+ pcsw(5ver) crosses the rounded top ojw+cph5cn (s 8f a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to m cpd3.omg160qg poc l1ake for the passengers tolp1dpc g q1co60g.3om feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At t5nh;nq 1aygugzbu03+3dqx sj; uf j 9;he lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.q du1qgz 3nbsu ;03guj9nj5;xaf;+h y
(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 fro *m:cb, kxm7wum the axis of rotation is to experience an acceleration of 11 :mbkumc7*wx ,5,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricallfocw4hc .jd +;y walled "room." (See Fig. 5c c4jh;.fo+wd-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 fs (9oe lmb-)zwrictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) thrw z b9-)mo(lseough 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 th5ll-4e: pykd pe weight of the ball which revolves on a string 0.600 m long. In particular, find tlp d4: 5-epylkhe 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 foagd2 tmy1cw1 k.n3 vx6r 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 massesd*k2 ivj6c0 id $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at ezrenv.6gr.5310 $\mathrm{~m} / \mathrm{s}$ . 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 fowc+wb zx*;u* srce exerted on the car (by the ground) in Example 5-u *ws;wz *+cxb8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolisu80ne1r irbeij x3f8 - 500 accelerates uniformly from the pit area, going from rest feij18xe r8r binu30-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. 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 k+ 82bk8kwkpha horizontal circle of radius 2.90 m . At a particular instant, bkk kw 8p8+h2kits 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 Earth’s g.a:9(kipccd iosw 2w/rw96r t ravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. r9d9 w6w(wis c ctor2i :./akp  

  At the surface of a certain planet,z1sv(sm e)w sxg4k 9r )..tcdb the gravitational acceleration g has a magnitude of 12 m/stx)ksv smgwez1)rs .b(9 d4.c$^2$ 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 Moop*rqb* o0oz4l g .huu*n. The Moon's radius is 1.74g u hp*.b0qlo* u*4roz $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timehp /*8 0ctism lvgl:c l:0(ayss that of Earth, but has the same mass. What is the acceleration due to gravitc: 8c g lstypml0i/vhl:(a 0*sy near its surface?   

  A hypothetical planet has a mass 1.66 xvu2j9+m v+zqj.2ll-xun6jrtimes that of Earth, but the same radius. What is g near its surfacuvlljrx-9jz++2jnu xv.26 mqe?   

  Two objects attract each other gravitationally witclgk,i2 mg,t.h 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 accelerationucsj5yl .try359j -w w of gravity, at (a) 3200 mc wy359twl.5 r ys-juj    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the oockmrxb +:7-Earth where thegravitational acceleration due to 7o:r+xcom-b kthe Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron strvw5(t fmq/ 3var has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfw5rqtmvv3( f /ace gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is;(zrow y-of+ t fvn;a2 now in the last stage of its evolution, is ty f;zv a;w+fonr(-2tohe size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spacpj7th)1 ah5mb e shuttle. 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 abm)a b5j 7ph1thove the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are loca2 z(y hhb 1hx1fq8utj4bf7sc7ted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one s7 u j yhf1fbszhchtq82 1(4x7bphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line u)i.j , y jn y8bqrtrkew*6a;a;p on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig jqyk.,wj*e6ya8bn)at;r;r i. 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 0.38 rx8.gck xihw 1//)h5eub ph+oof what it is on Earth, and that Mars’ radiushgbh cr px)8hxk//1+e5w. iou is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value forg/yhi m bjdmqe67 yygoh;wk+1(v/ +5f the period of the Earth and its distance from the Sun. [Note: Compare your a;1k//e5j (b+6imymg yf7wvqgd o+yh h nswer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cixhdijrf -bk j/ d/2nw8;w *d:vrcular orbit about the Earth at a height of 3600 km. /nr2;8j ddb: x- kjidw wh/*vf   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ea p0+yqw)txnmnlo/ 7v;u l79km rth.)ux vko qypnt m +/ln9w707m;l How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupa,fcvi wgh3qc(z3z7 ;lnts 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 Que g,vz(lzc33h7 ;wciq fstion 21, Fig 5–32.)   

  Determine the time it takt uv* 24ej8irmes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one 28r evu4*jt imat 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 sasq kn a8xi)4k-tellite have to be launched from the top of Mt. Everest x4s8kq- )ani kto be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbp w 4wpr74vjfpnwu: .bln.+0d ghy3h/it the Moon at an altitude of about 100 km. How long did it take to go afp4. : b/uhp3jh.g4rwp l 7vnnd0+wwyround the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit8m twft,96crc the planet. The inner radius of t8 wt9 trcm6,fche rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s p fuk,*gv 9wmhoah7k3bu3;1 n (see Fig. 5–9). What is gb3hum*k; p vw3,kn79ufoha1 the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weix bc66srxl4ga -qqzmqpx+t:1 l1c28 j ght of a 75-kg astronaut 4200 km from the center of the Earth's Mo6g-q q84x l cqpr6jb+tzamx1 l2x1:scon in 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 starshcut6 vqg lve)t,j0:9 7jyg+ b of equal mass. They are observed to be separated gl ,0 v)9vg je6jbc+7:tyq uthby 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg womao*y1e;d 8ls1is ge qu8n in an elevator that mogduq o8y81;es *e1 lisves
(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 frobqbmp3 bdr06 9m a cord suspended 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 minimum acceleration (magnitude and direction)? a = 6dbbbmr903 qp   

Show that if a satellite orbits very near thc.(5q c( ze*wrkriz;f(mg6ku e surface of a planet with period T , ( c5ck6fewzrrm( .k z qu;i(*gthe 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 and the period of the Moon (27.4 d) t6qtjj *-fb 4ar e26a) eum.kwbo determine the period of an artificial satem q 6a2ejk.r fw6j4e)aut b*b-llite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, d0mfd -5:ienx g3lrcgk8w .w.orbits the Sun like .3d5 m fe- gkdw80lg:rcxw .inthe planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o,ownvxlaflqyhb+,v zp yl3 06d 9v0),f 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 76 years. It comes vl6u*d aex8.*oejpur 4ery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet fro xldp.r*ej68*ue4 uaom 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.]    $\times 10^6$

  Our Sun rotates about the center of the Galax * 3qi6(tpyjqrjb qk.et)bw :47:shlky $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 largy0fb qz3s:+-gp 1bi)jl k9qqiest moons of Jupiter (those discovered by Galileo in 1609).s )bgq-y0:b9+1p q3 iikljzfq
(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 pih4bvtwej-t ,q*me*/03f7-djh j sd and distance of the Moon. shi4tmt7ep q,b* * /3dhwjfj ev-0j -d   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiwhq 2p3t/w6vpbmmo 3 xo+ 1f7fter’s moons, using Kepler’s third law. Use the distance of Io 7h 33f+/mqfwb movpox 6p1 tw2and 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 many7xn- x9gaqv /ql2ao d +v5fp)a fragments (which some spacel vd/79q2x5)af naxa-v+ poqg scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describe, c q7s/ (d.xmt5ssgo.j ktdl8s an artificial "planet" in the form of a band completelyog. ,5s tt.dlcx d8k7j s(m/sq encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge bywa0+s w ,;erpb swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass isbe0w +sapr, ;w 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerati p bph:ht1:8pion of gravity be half what it is on thephph t1:i8b:p surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cir).a x (ytt+b *.pteinocle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, h+oyp* t.n( bt)e i.xtaow hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration ol r31.zmt7im8wgv8 lgf gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Esrw m7izg1g3 8 llv.m8ttimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dirdzd-(h53 zte/gu;0mp pqx8u l ectly from the Earth to the Moon experience zero net force because the Earth and Moon pull wi/ (xp38-m5zdz petl ;qghuud0 th equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, 5y)ksldl9sz.6a lau.xw.ob1v/ z 2jb but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. Wha z5dkav/b2b.6sl)9z1al.xo juy ws. lt is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate a :;h.5xc7l air(o jjaqbout 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 b: q r7aalj.i oj;5hcx(e 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 vertic7 vktab2fq-9z 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 8fs*95qa en usr, the acceleration due to gravity at its surface and thu58ssqfe 9na* e gravitational constant G.

A plumb bob (a mass m hanging on a string) /vozce2pdqf aa.+ookg38 9u; is deflected from the vertical by agq;fpu2a.oavo c ko98e z +/3dn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the f a1k h3zv 3fif1zo.vrg(fpn+;avk0 ;coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car saf k+ 0 1v va3igf;.3;o af1hnkpf(vrzfzely handle the curve?

  How long would a day 7p op,m uez0tali q8j 6yeq2-+be if the Earth were rotating so fast that objects at the equator were ap-u6qqle o8jpiye ,a pzt0m 27+parently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a c ;zmxv l;epc;/:vgo2xh-ub g 6onstant 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 l7 tr1ug5w)dy constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings7 trlwy g1u5d) out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the w)dtp;0a(r fhx4oc x2Earth. Thus, it has been claimed that a person would be crushed 20)rxcfwtx;(d4poa h by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope ldp7(;o otcfe5;n 8x;,8ev+dyvksto deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a blackt ,d 8yvlo(;kc8;pn5t;svoxe7fo+ d e hole (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 trav.1 nrqs qznpu323zvrqo;lp60 erses 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 sq63z vpo0u1qrz; 3n r2n. qplA, 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 (7 g9sjw:8ddp 8lqtu-fv3 x y6wGPS) 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 t8-:p6squ3jd9 wlyd xf8gvw7 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 bily w n6wijq6p9 :,l9ovllion km, is meant to orbit the asteroid Eros at a height of about 15 kmv,:9oqwwlj9 lpyni66 . 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 c-mc4cy 1uhpucd9;4a pursuing a satellite in need of repair. You are in a circular orbit cuy u1cca -4;mpc 4h9dof the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) bb 3 /lg2ylia ,do;2fxWhat is its mean distance from the Sun?/dx f la2oi23b,ylgb;   
(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 valj11ydfu; cie *nvz+j:ue of G would need to be if you could actually "feel" youj 1u;e1nf yd*:vzcj+irself gravitationally 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: eh )zcw2st9w Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cen9whs:w)c te z2ter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on i)n--yk 9 kcgk feq5pt:/2s8 bffryz(each side. Find the magnitude and direction of the grk/esfrbpg n c8) fy-yz 5(q:k 2ti9-kfavitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thfi c9s wgml/2 gdt(9:osi6 gn+e 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-long swee1ws(rtci2 5h gp second hand on your wrist watchw(itrhc sg21 5?    $\times 10^{-4}$

  While fishing, you get bored and start v(4tsk s zlo 5ni)z(y; 3q lmk,1webquy/3d/m 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 t/,ws)1 moy(5s43dki(u/ml z z eb3yv n;ltqkq he vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway n43 ymg ;.e ;x+uq,wmluqe8kuis designed so that a car traveling a,l.xg k8 uwe;yqq uu4em+m 3;nt 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, utilizhx fywg*ge 0hb. x a5bm;.80oles 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 no5bhwxl ;a .fb.0e x*g80 oygmhrmal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (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.$\approx$    $\times 10^2$