Sometimes people say that water is removed from clothes in a spin dryer by xqkp.vxpon vcv919) 2centrifugal force throwing the water outward. What is wrong 1p9c2 nxk9vvxvp qo.) with this statement?

Will the acceleration of a car be the s-ayeowpi*am(d , /zi6 ame when the car travels around a sharp curve at a constant 60 km/h as when it */o6ap,izdawym-e (i travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the carj8fv;d;+k3gpp f kfb6 exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between gjvk b 6kpp3+8f;fd;ftwo hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding :q tat2e9nb c); +rzvfa horse on a merry-go-round. Which of t+;q c)e atrnfvz9:b 2these forces provides the centripetal acceleration of the child?

A bucket of water can be wknvl(aba/2q qvx i4 o i40v-(qhirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside dow2vv 0/ -q qkoqaa n(i4bvi(xl4n. Explain.

How many “accelerators” do you have in your car? There are at least three contrfepqq o*uhw90.w 4+ myols in the car which can be used to cause the cau.my fwqqh94 o+wp*e0 r to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shoz7 agd,:h1 gyiwn in Fig. 5–31. His sled does not leave the ground (he does not achieve agi hg 7z1d,:y“air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders +hv/e op r 7tr1p+n5as2i m:fslean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute tk:m..i85i mjkpl:ii khe banking angle given its speed and radius of 8:kjk ii.5i.mkm:li pthe turn?

A girl is whirling a ball on a stru 28wj+s71zuxo17pcwf wh.ql )(jbg ning around her head in a horizontal plane. She wants to let go.pnjfwj u ww128 b c)u+7hg1slx7zo q( at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a nrmr o*7r(gd wf /j (nshf412pkqt9x1gravitational force on the Earth? If so, how large a force? Consider rtdqr/wks(1nr f21of*p4jxg7 (nmh9 an apple
(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 orbit ;zkhz vc/)g0m/ mcvzhg)0z;kbe different?

Which pulls harder gravitationally tz,k7le+kwi.m e9g 8j, the Earth on the Moon, or the Moon on the Earth? Which accelere9mt. 8,wz kl7jgkie+ates more?

The Sun's gravitational pull on the Earth is much la bykvv1 w6.. 0dhll-jerger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fr.v.l 6 kv0dw hl1-yejbom one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles?xjs3hjj0;o ggo o/6n) What two effects are at work? Do they oppose each other? ;6oj)j /oxg3gjsnho 0

The gravitational force on the Moon due to the Earth is only about half the fo8qoytmlt6o91wc ;h i, rce on the Moon due to the Sun. Why isn’t the Moon 9it1;,o6ot cl8mqhyw pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or jvm df 881zemz) ;iky-smaller than the centripetal acceleration of yj 1edk- z8imf )8vmz;the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bd0.f,mm4 j(4zr xenpu ) toward the xrnd4f 0e(jm z4,m.upwest? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a sdb0a84k c5 o)llo 2mtrcale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant s2m5cl l0 odt kro8a4b)peed? 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 adverselypq,8 a, wp.;+gclpzi2zx8 pts affected by weightlessness. One way to simulate gravity is to sh i g lz;.scp8ppp,a2q+tx8z,wape 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.

Explain how a runner eh bs nvx :+mufox;1/gse/bl 2w.,xm l7xperiences “free fall” or “apparent weightlessness” betweensf m7,vou+:/ .n;2 /wg bxhslmxe 1xbl steps.

The Earth moves faster in its orbit around the Su4x,dn0b xhykcb d lr s6z;(4d6n 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 pro,z0xdbcdr;ny 46bd 4(xs kl6hducing 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 k 3f5m4q9 ru,maim, oy2 ;a zzh-shv5iknown until it was discovered to have a moon. Explain how this discovery enabled an estimateziz q3a9, ;ari,vmh 52- 4m5fykhuosm of Pluto’s mass.

  The Sun's gravitational pull on ta2e*dr: cj kk u(d/qp:he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hin:d *dukka qc:(/ep2rj t: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 1980jp5(: mkyo5sy $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 itshnxh7z3ktg-szl1 *2 6r/ej5q l b uds9 orbit around the Sun, and the net force exerted on the Earth. What exerh 5 dzrhgkq1sx72st/-z*njb3 l uel69ts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates u7bzr, 1t zk,j . xmkdq8qg7i-bniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Czb7 qjg dk, rq,m iztb8.1x7k-alculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km j/ wri7n p eo .8c92azllz9.mrppe-4z 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 ,ep9amrprz2 jw 97e-.4 i/pcozlznl.8 the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of asr 9i/f(bl y.z potter’s wheel turning at 45 rpm (revolution.ziy9rb (l fs/s 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 93 r i--ng1fldxrkw o5circle of radius 72.0 cmdg-rr 315n-fi9wko l x , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-ke 4o g5cbw+ge4i f:t)tg 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 cg e4et+:otbi4w )f5g of the mass of the car?   

  How large must the coefficient of static friction be between the2a; .( dl;ghmkq (xgin tires and the road if a car is to round a level curve of radius 85 m at a s(g ;gialdn;qkh(xm .2peed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotatwcu l+mumi:/ /e 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 own weight, how fast is she rouu+imw/l :cm/ tating?    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 turnt,f)qh f5yi+e pw/ +nfyable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between tw5 n iyf+p eyf+)h/q,fhe coin and the turntable?   

  At what minimum speed must a roller coaster be travelinty.yy k/.xdc 1g when upside down at the dxyk y/t1y..c 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 (including the driver) crosses the ro,zrmj+x: offp . uy1w1unded top of,1m .jru z1+p:w fxfyo 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 157yj*/y2kmv r:pl nuhhl--:4 doxuit; -m-diameter Ferris wheel need to make for the passengers to feel “weoump/h- vykyl-lr x4n: id: uj;ht2*7ightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ohf) 7liqx7lje,o t vv. ;f.u7vf radius 1.10 m. At the lowest point of its motion the tens.f l) ;qe.lt7oi7 vfh7,ujxvvion in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a w(xz n(h2s1- z3 2kunk:ibdsx+wv+lyparticle 9.00 cm from the axis of rotation is to experience an acceleration of hb:z nn+sz(1 ikd2xuv2- xk3 ys+w( wl 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnc5gj)i 5e vx ww+ 7xkab c1v**apv50ovival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.) w x**i jvxv+ w7o1aacb)v e5pc 5gv50k
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 fricb: 78ofl6h funtionless air-hockey tabletop, and is held in this orbit by h:f6 n7fo 8ulba light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this timjdd4ts-sr7x.w q j;9ae, by not ignoring the weight of the ball which revolves on 4-9s a.jd7sdt rx;wjq a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a catqr2uj)e (3 6,a6kw79jcgd( srtan kmr 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 massen47wbxg f)6kis $ 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 vertiq*cq;wx)ti go d1yu-;cally 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 componenl;ap a 1)fyv7v*d(i gtts of the net force exerted on the car (by the ground) in Ex *v;ydp)i1 v afl7(tgaample 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 cd ;bo3l+h1 ;nw)yzg maccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway 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 witmd)n3h gwz+ c;oy1 b;lh no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particulaufgwy2u;9p 2t 5gptl 3r instant, i ft2 lp; t935ypugw2guts 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 gravity o:eui zrfj,,c gho ++/fn a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if itzejfo/i , fg ,h+cr+:us mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnqo ycuwi f+3g2h y9-nch,o*. ritude 39chqro+yfn.,owg-i*hu y2c 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 Moon's radius w l5:fbt ;)jyj jw*2 hf4bdh0fis 1.74lb j:h2t;w) f4d fhw jfj5b*0y $\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 Ear4chw7w: ;;4zt9e(m -rj qwhs/ gkyil;0duqfsth, but has the same mass. Wha;mczkyq47j0r fu;w-iw h;/:e ssg 4 (tw9qdlht is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samu 6 g,t/b8pemwe radius. What is g near its surfa6,wugtm 8/ebp ce?   

  Two objects attract each j57woh8iqp ed1 wnxtf8ea8xt/ w 1u6*other gravitationally 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 acwl1/8vt;f yt kjv8)1k )mauaan7hj c:celeration of gravity, at (a) 3200 m j)t:a88v m;cfy n11u vk aklj/w)hat7   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsi1z;6r+ ho)sgej5qc9jy hh k;ide the Earth where thegravitational acceleration due 1ri h6 ;cy+s 5hkj9z)gqoh;jeto 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 int5766t p8 bizsh vcvv2mo a sphere about 10 km in radius. Estimate the surfavv b6 6zshpcm5vit 872ce gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wz(9; d yhreub/as an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star? (b dure9zh ;/y   $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in tx yp+,+,d8ql o6qitduhe space shuttle. Your friends respond that they thought gravity was just a lot weaker up ther+ ,y +oxpqu6dq8,ldite. 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 the corners of a square of x1men cw+;*mxekun4: side 0.60 m. Calculate the magnitude and direction of the total gravitatioxw n1e xmcu*;mn 4+ek:nal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most gm lrxga)2ufl9 ml5oz1 qfj8mb755h2of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. lh2mlm)gl2zr91q5bm5o f57 x a8ug jf5-38). 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 ztm:k q(q4c c5a2aqg:of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, tq54q2(cm: aqagz c:k determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for tulkqo2fysn/4r;+ 5aif 1v4 zshe period of the Earth and its distance from the Sun. [Note: Compare your answer to than144yf 2z qs/s kio+5l;ua vrft obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving inc g1iqt, z/gwwv c-w;4 a stable circular orbit about the Ear zgwtciv/w- g 4;1c,wqth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases 89 ietisto/ ocqk8st+o h-n3.a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when th titcoh-+s itk8qn o 3./o98see release occurs?    $\times 10^3$

  At what rate must a cylindrical lw;trqjr m 69b v/c:4kspaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameterrj lbwmrtc:;v46 9qk/ 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 for a satell7h+mslzh s3 :tite to orbit the Earth in a circular “near-Earth” or:l m+tss 73zhhbit. 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 satellite?    s ~    min

  At what horizontal velocity would a satellite have to bl74g w-sa)kqp e launched from the top of Mt. Everest to be placed in a circular orbit around the a7l4 qsgk-)wp Earth?   

  During an Apollo lunar landing mission, the command modulefhuu ozlf/t q g;;.7/xcf- x)e continued to orbit the Moon at an altitude)g/ou x lf-/.ufeth ;; fz7qxc of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are co08y* h+qj 0jev f,eiuqmposed of chunks of ice that orbit the planet. The inner radius of t q0+e0fyuhj , jqv8*eihe 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 e li5 8zj:7 bxoxw8m:ruep3 g3kvery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to he7zugp 85k 83ix wrm3l ::ojxber real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from t0)jnh5u r:vie he center of the Earth's Moon in a space vehicle (a) moving at constant velocity, h n:)0eu5rji v     ----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 ofiln ,cu)0yhu/j-*uao two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about 0u/ a ,y*ulcj)hiu-ona point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read 61t am(zzh12sux5xu y for the weight of a 55-kg woman in an elevator that m2a5xh1x u(stu z6 m1zyoves
(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 of an elev4 c,k 6x,l.lt sdaswqyohu86hq 0-,o nator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitud,,8y6u lch qsnkx6 s0ahtoo.dlq, 4-w e and direction)? a =   

Show that if a satellite orbits very near the surface of a plan p 4m fuarm(jfsf9s340et with period T , the density (mass/volume) of the plf(3r jm f0psu49sf m4aanet 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 jw6*s+sy;t3 1yowppqr k6)2g lu nv *ndetermine the period of an artificial satellite orbiting very near the Eart pvt ks136gqp; ow2+*yn ryw)snl6* ujh’s surface.    s

  The asteroid Icarus, though only a few6 pkg/dnh5 6f-q+ uosn hundred meters across, orbits the Sun like the planets. Its period is 410 d. What u-s/nfqkn6+o6pd5h g is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distva5; g6h 1z.vtexthjbsyg73(ance 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 orbittbootj+ )6 ne.r wt0)rs the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What 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 dist)to.nb ojw)e+tr6 0tr ance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center t58l4 2c4mslx7n:euh hxfpk 3 of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean dih jl1 mbeye(qp3 8hzb 1l(f3e(stance for the four largest moons of Jupiter (those discovered by Galileo in 1609jh(e llbm f(q1y(z8eeb 3p3h1).
(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 Earthli.eaf5usf 6b7.ahpwws: s 59niir* * from the known period and distance of the Moon. s9*wie* li :bswf ra65.ha7.ipn5 usf   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, bhpg -vem- 1ml/w g* 5etlq,mt ja5;,nusing Kepler’s third law. Use the distance of Io and the periods given in Te,-1;jg t-b/m*ll5 n h,m v5gqwmpae 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 fragmn62r.0zc .gw/d5rwy4 q mgqae ,biit 9ents (which some space scientists think came from a planet that once orbited the Sun but was destror.eaq, w.y 29gdn6zc5ib0/ mqgrwit 4yed).
(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 artificias x5eaotc(y/b 87v7f0h)jfb dl "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that thisb7(8)va7 bjeyf 0sd5h/ tocfx 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 by swinging in an arc from n1n+2it 9zwne a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is wiez2n9 nt+1n the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration 13/tm+ whgjgw2bj(mis2f0 h zk br5 ,qodu;p8of gravity be half what it is on the s3 fz,b;k(dw8p01ji wsu jb2hrgmhmq2 t 5o/g+urface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mr(ban; t/kba dh( (di6utual circle once every 2.5 s. If we assume their arms are each 0.80 m long and h6 rb adak(td(/n(;b itheir individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per d39ed f0hk )ke+5zwh jl .bdm0kay, the apparent acceleration of gravity at the equator is slightly less t.5mwze9jdf l k3ebkhkd+0 0 )hhan it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth8 zkck*eel:r) 5j:ylb tm;mw- will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces: ; rem-k z*bwj8mlyt:)cl5ek ?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a 1h g+kgm6er7(hm h d 232ksv ,wn2banfbathroom scale in an elevator, it says your mass is 82 kg. Wha h m(n6fwehgm2b37n d,kh+s g2rkv2a1 t is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consisw, m z*rh,:uoimw: s4g o4s6wots of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 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)6 hiouw r4:ws*moo w4:zms,,g is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aiwpgb(c k h9r-q1bb57 grcraft in a vertical 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 9oe,2:k ohfy4zx /cakplanet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational co/oxzkc4a k2, oye9 hf:nstant G.

A plumb bob (a mass m hanging ojo nm;3ke3: dik0 6-ytskbwz 6n a string) is deflected from the vertical by an a0:3;ktzbsw o-3e jkn ydk m66ingle $\theta$ 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 spr ehhtw 1-(jj0o),zwzeed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds z-1owwj0hreht z (,j)can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects j)hnfs99 basbwwdcc6*gx5/v/sh 67 vat the equator were apparenb/cx*cs g7d5 6 6wswj)fvb 9han9s h/vtly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distbhm7+a ze.ic*z7)p xa2s no0ly1 xpi:ance 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 x4hg8 men (ok c4m6nz;constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angl(nmh;no 4g zcke8m46xe of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, iq :a3ja-d. qgnt 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 qa3d:-jgnaq .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 Spajwar 73a n+,drce Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense twdar+rn j,7a 3hat it could be a black 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 traverses the hill and valleyapnqo)3/ qyuwol;-+ u 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 with);yo3+qa-w ouuqp/ln the road at A?

  The Navstar Global Positioning System (GPS) u:.0jpa )0cce5sj jpsfsp3m d0 tilizes 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 a .csfjcpj03:)sas5jd e0pm p 0ltitude 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 tra j4kdq z/ p4p.yb/nxk(veling 2.1 billion km, is meant to orbit the asteroid Ey xpkdb/nz.p(4k/j4q ros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satell js32f wooca9 /*cqvh0ite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 s2 v9fj3co0cah* oqw/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) Wha 44ec;iz.ht+c rmk*c ft is its mean distance from the Sun? m4*;c ce+hz4kr c tfi.  
(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 Go49c .0 ryxb4gb*ezh t would need to be if you could actually "feel" yourself gravitationally attracted to someone near yz9 y0*4 brtg4x. ohbceou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky) uyzy./4 ogvo Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from 4/)oy yvzuo.gthe center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the cof/eli(9s5 qmxhcuhdu*,71ct rners of a square 0.50 m on each side. Find t */ed9f( shql7tixmuc,c1u5hhe magnitude and direction of the gravitational 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 orbi.b1oie u7 **/m ihgzqzts 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 t d ;)mkdjai,ei 1fv(l:he 1.5-cm-long sweep second hand on your dkail(:je fmiv d,) ;1wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker6b:z- pts 3eny 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. Wpn6tbz s3:ye-hat 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 uz2 ae mcgb)e,2jn7 a+traveling at sn,uezeb m 2j ca7)g2+apeed $ 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 cars when negotiaho9 6hfeg4oa(e - :1v 7sz.vhnygy.d6zw js(zting curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 mzyhhezzv s.a(sf7.:jv4oo ygw1n9h d -ge(6 6 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.$\approx$    $\times 10^2$