Sometimes people say thv:mbr;nqq)y4 t 2u*gofn7)q(*zh ilvat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with thirv()nbqh q2z)qv74i ;ol*: uf *mtngy s statement?

Will the acceleration of a car be the same when the car travels around a hw5oxmvt* i*ojdt xm b4)h6x;.bn:i; sharp curve at a constant 60 km/h 5n;h;): 4o *xtvmi mdxjx i6hb.tbwo* as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant sa(.j4zpar l5fpeed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dia .(f p4ajzrl5p 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 ail5x r3gz hro1 qbo+klb ).u.7 merry-go-round. Which of these forces proviz r3lxibugl obhq15 7.) k+ro.des the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wa6 h 8(f dgokf8x.;dd9l mecdb+ter spilling out, even at the top of the circle when the bucket is upside down. Expl e+fkh x89 l m8.ddddc6o;fg(bain.

How many “accelerators” do you have in your car? There are at least three ca,7/vkut( /n,jc omzui 2ix*yontrols in the car which can be used to cause the car to accelj,/(ii t 7aumcnu,v*2 yzox/kerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown inm4/ eho3 wow)no5a :fx8y-jh h 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 sledyjw83fah-4 5oexhoh on/wm :) decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curvw6ku-zdb55no+r coh7e at high speed?

Why do airplanes bank hzgv/09mu- ueu 6wn1cwhen they turn? How would you compute the banking angle given its speed and radius of the tuv-1 mn uzge0/h9wuuc6rn?

A girl is whirling a ball on a string around hemgeagpa o jk a7c5n /;6niu(+6r head in a horizontal plane. She wants to let egu ajo7a ; 56p+cnim6ak/gn(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 string?

Does an apple exert a graviu 0 +-k lrf 0a+hbmhsnu;d xgv/c94+qjtational force on the Earth? If so, how large a force? Conside; lvd+uax 4shmfrubkgj-0/+0 n cq9+h r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double waj),c, dxbx1o hat it is, in what ways would the Moon’s orbit be differe , c,j1xdbox)ant?

Which pulls harder gravitationally, the Earth on the Moon, or thyx5 8oj58z .y9hvsqtni-e pj8 e Moon on the Eartpov9q ei 8n.58s yyhz 5xj-8tjh? Which accelerates more?

The Sun's gravitational pull o6(/ q5 b 4onk.ftev//snye mrsn 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 othnq6vbkns eo(e .t/ r4f/s /y5mer.]

Will an object weigh more at the equator or at the polesi1md crd2 g)d )bnf63s? What two effects are at work? Do tbi) g3s )d2f1cr6nd dmhey oppose each other?

The gravitational force on tx s4b3m6.au4pilhax oxe65 e6eh( 3fhhe Moon due to the Earth is only about half the force on the Moon du6 o fuexph6s. ai3(xmhea5elhx3b 46 4e to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratiowji 2- qe-gu.en of Mars in its orbit around the Sun larger or smaller than the centrip-wjeq2. gi ue-etal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (.pvm 6gxt g(-p jws9rs-.mnb(b) toward the west?g(6n.xtsvpp-rbm.(mwg -s 9j Consider the Earth’s rotation direction.

When will your apparent weight be4glz g f-5nt:s the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves up g z:-n4t5slfgward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adverselycle.c u *ht,5bo1.j rr-naim- 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). Expoj.rer1 b.tminu5lch--*a c,lain 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” or “apparu5vglkw;+dh8 4mgj k.ent weightlessness” betweeu+m.d gkk w4l5 vg;jh8n steps.

The Earth moves fastetjtao7uhni(,h/ m 1g (r in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factnu,a(/hti(h mgo7 t1jor 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 discoveriund,7i 5vus.ed to have a moon. Explain how this discovd5u in7.iu ,svery enabled an estimate of Pluto’s mass.

  The Sun's gravitatio*y *4lr(k2lwep/,s miys- iso nal pull 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 ,4ri/symi2ssew(*- op ykl*l 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 1fha t.j xw2/w,3i0 nzu980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 .k-f9nt cpsa+9g ba7m5t 1 bjiits orbit around the Sun, and the net force exer9m -.pa7bb1kitjfs5+n9ca t gted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rvjnriyf u+no (.w7:m ;otates uniformly in a horizontal circle (njw m .(v u7:onfiry+;at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's su a;e+c( odwmi(rface, and circles the Earth about once every 90 minutes. Find theamd( wc+(eo i; 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 of a speck of(3uguu:ybmud :4 yda/t: c:qo clay on the edge of a potter’s wheel turning at 45 rpm (o/dayd3mu::( ug :bqu : y4tucrevolutions 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 v*0wv 5+)jvw lj44axo mprlk-vertical circle of r *0vo5-w 4avk+jwlxvj pm)r 4ladius 72.0 cm , 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-kg car can round a turntv8* ux 0vq9kdin;, ff of radius 77 m on a flat road if the coefficient of static friction between tires and roa9 8vf,kq uidx;nvt0*fd is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires ans l v8+f o*+te9tx9rxdd the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ?s+ +9*exldtfox 9v rt8   

  A device for training astronauts and jet, ;:e,0k0emcir0 w(coku2omi r *-qhy;wxauc fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force fwk:oe umqk;2,o, mic0 cc;wu h r0i(*yr0x-aeelt 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 turn -r44oyc(d phdtable of variable speed. When the speed of the turntable is slowly increased, the coin remains ryopdh -d4c(4 fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller cev5/ vzp( 5; guibiqi9oaster be traveling when upside down at the top (; v/izbgui q9e p5v5iof 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 (includier9)3 s7f : reswr:ovwng the driver) crosses the rounded top of a hill (radiewrr3rs fs)9v ow ::7eus =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 gjw:nsk0*-;k2m rwz n Ferris wheel need to make for the passengers to feel “weightless” at the topmost point? - kn;j *:sg0zwn2mwrk   rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 wqi,2-den/nqa0pvtoi) / n ;0x 0engo m. At the lowest point of its motion the penoi/0;o)xaqigq 2,n00d evtw -/nntension 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 pn.q t r6gyx4/vov b8j:l ,p9zearticle 9.00 cm from the axis of rotation 4/ozq6g.v bl:,xyjn8re ptv 9 is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa:mdjy7::(7 wyt nynjelled "room." (Syjym:d:e7 : ny7 wnjt(ee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless jew )spg -j1;)tsk, ymair-hockey tabletop, and is held iswt j js;- )k1gyp,e)mn this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this tii:wvfsw+ zjm8pj381h me, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitu1v:w+8 zsijhmjwp83fde 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+0srdu00i w8hka1j ds 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masse:r11 p*wi5*y gbokytms $ 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 divion5g hd+ix myu12mm0 (fmgi07ng vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of0 y59 dbc (a-t.r(sxpkn vu6jj the net force exerted on the car (by the groun(x jpv 0yd-.nujba5tr9k ( cs6d) 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 50a oar5aqsg8e4 60sub90 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming con9 5ra4a 8ebs0usogq 6astant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontaljyvb l +l*sk65 circle of radius 2.90 m . At a particular instant, its acceleratio6bvl 5+k*ljy sn 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 on a spacecraft 12,800 km (2 Earth ra1;/m-d/h9j uuf(qrxh 0,t fazxv xmh)dii) above the Earth’s surface if its mass is 13um uf-mh , 0(/)/9hvxratj xh;zfxdq150 kg.   

  At the surface of a certain planet, the gravzfbqlf13k)vd1 e o1l,itational acceleration g has a magnituk)1b3zf ld1vof le,1qde 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 kqv e-;jzo, y-Moon's radius is 1.7-k,-eyqo; z jv4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has tc9 (qr 9d0ws)v kctw:ohe same mass. What is the acceleration due to gra9(octkv )rqs0dww :9cvity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sawjhr lr8qd ufxv2+353 u(t-iu me radius. What is g near itsru8jhi+df uxq 3(53w- turlv2 surface?   

  Two objects attract each oth a 3j72b4tmiq1,o0s*vuzdbf y-k urr) er 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 effect7+t.wa puzol.bp7i7z ive value of g , the acceleration of gravity, at (a) 3200 m o ib a77u lpwzz+.7.pt   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pon )zna2n g8*cvint outside the Earth where thegravitational ac8acnz*n 2) vngceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five tim,/ipx7c8 b+7y q uquyxes the mass of our Sun packed into a sphere about 10 km in radius. Estimate th qy8b xq+7xpui, cu/y7e surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was fgbmq;(ychz5yb d(*p2f 6 f/w*o0dwq 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 thim2 6h/wgqfb d(wofy; 0y 5*zf*(qpdbc s star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbt56 )xk wot td6. nfq2usgl+,ct;wv*hiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them a)l h6wufd5ot6+2c. n *xqtvwtk, g;s tnd 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 s b2 -ubpdosil4:6-*nv: zofsthe corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted onud -sbb2zlpn *fiso:osv :4-6 one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on ;.m wvpal(h a 1j0dw :zm/blp+the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter./m+ lzmw0l:pbpjv ha1 ;(daw, and Saturn, assuming all four planets are in a line (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 ofh;cpn 8l7j*z pc2.4nrqxm mo(h*j1be gravity at the surface of Mars is 0.38 of what it is on Ear;c pr (n.z42clmh1mx je7p*n 8qj*ob hth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of q 8wy7xxr ukbkv(5(zzk8u+w9 the Earth and its distance f+kw9w8 yxbxz5v 8zq(u r(ukk7rom the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite.7o, *v2cs1hmowh jeu moving in a stable circular orbit about the Earth at . , h2e7mwojsu1hov c*a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a cirylz(yz ) h:*zggeix.j4ca0z, cular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to h4z: z)i0z(galzxg y jce,y.*Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rota*1 ych ziz.ds:te if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revshi.dy 1:*czz olution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbmkpsyhf r h3( zm4(i6y1xjmo/d 3 +z)eit the Earth in a circular “near-Earth” orbit. A “near-Earthd+xhz(4zeyy3 p3 h rmm6)j(/o1imf k s” 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 oa5zfo kxk.n34e w/1mto be launched from the top of Mt. Everest to be placed inna1z .5 4 ok3omfek/xw a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit 2fm n9:cm)uyu the Moon at an altituu:2 ym n9um)fcde of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chun hp4w,h; fu: fewng2e6ks of ice that orbit the planet. The inner radius of the rings is 73,0h;:p, fw26gewheu 4n f00 $\mathrm{~km}$ , 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 ;yps0 ncow0d9+lwl+iin diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s appac dy0li0+l;ws 9 +pwnorent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center oo2+ /zus) bil8f am w(6+wbme,/oh bsof the Earth's Moon+sh,us6 w8+omo/bz( ma /b oi2 f)lbew 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 stars of eq7x/ t.*e9 ps ecrhxb ob)ym+p(ual mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a p/ m+.bch7*yo) pstxeer (b9xpoint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a /fb8oe1hl5y 5ht fz vrj 9+xb955-kg woman in an elevator that zfxrht+hoby8ejlvf591 b /95moves
(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 ceilixsr-g :s5cwc 9ng of an elevator. The cord can withsta c wsx9c:r-s5gnd a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits ve zbbv xv r.1j4+2vkz1+l,lcbe8 n:eyhw)o4msry near the surface of a planet with period T , the density (mass/volu+czln8brse x vvz),b:y4 h1k ebv.wjl1om 42+me) 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 tcz*mosra/5l h b:wtv2d*,b; khe Moon (27.4 d) to determine the period of an artificial satellite orbiting ve tcm, * 2bh5saokdvw:;zl* r/bry near the Earth’s surface.    s

  The asteroid Icarus, though only a f36uetrkr ync9p 2 8.msew hundred meters across, orbits the Sun like ru c.sntk 8p62y 3emr9the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance oflrorsmb*0tj( (vp 6,x;j:d/r 6hfu jo 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 yeabjwtvas, +6r 3rs. 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? [His,+jarbw 6 t3vnt: 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 my cg.f.8r.w7zvd l l2b*0vdyGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 ;j ,wpd.ca)j(ma+ oecdistance for the four largest moons of Jupit+mj;aw)o,j(ac .c dpeer (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Eafp. ;. yzl/; po7wjv14vimqa orth from the known period and distance of the Moon. fvap/ y;p4mo.i;.q7 vlwjzo1    $\times 10^{24}$

  Determine the mean distan 5)xasz;gj0 . qlqi;;gh)f cnlce from Jupiter for each of Jupiter’s moons, using Kepler’s thirdil5n;.ajq) lf;cqg;)xszhg 0 law. Use the distance of 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 8rnj5.8nw h yxmany fragments (which some space scientists think came from a planet that once orbited the Sun but w.nn 5yxr8jh8was 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 art6:e1brx7ht4j bk/gkp ll63 jqificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where i6:e47p k1 xb/l6b 3jgtljrkqht 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 mu pg8i-dc:c( gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a forc8iucp:- mg(d ce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surfay g*3 ,hjmd6iace will the acceleration of gravity be half what it ismi g dja,*yh63 on the surface?    $\times 10^6$

  On an ice rink, two skaters of zru(i- +xg5yj 6tl,7v;h f+ lz iee2tkequal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms,ze+zugvy e 5iixjfr+-h7 2 (;tt llk6 are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent a y 4rznn3nvl :e0.rd5xcceleration of gravity at the eq . d543lxzn :0yrrvnenuator is slightly less than 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 Earth will a spacecraft traveling k3zw2a e;i/0guz 5 whadirectly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite / ug;h5aw w2iz0eaz k3forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathro:* mb8jivhofsold; 7 *-x+jz5aa.vemom scale in an elevator, it says your mass is 82 kg. What is the acceleration of md*o-s8ave*: bxfavhjli. m5j;+ o7zthe elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about r24ozz,1pt ,4e)tywc wmzpv 8 its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. Wp42o8w )pcrztz 41mvt ze,yw,hat must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a p/n+ 16gjlrcrn6lld/ 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 planet in terms of its radius r, the acc,ui /.; bccgq. yjf0lx7uo 2vpeleration due to gravity at its surface and the gravitational constap/cglbo; y,jf0 ixqvc. 27u .unt G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by ae) a4+wxj;koft 9r6r5 tz8g ran anglek+arex o8tr; 6g wj5)4t9fr za $\theta$ 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*ffk:-qm .g6+y kyz)gsmu3d.ua lcz2 is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a cyad:+zk g63s.*mkfugu2f m.ly cz)-qar safely handle the curve?

  How long would a day be if the Earth were rotating so fastqvp oeh*yt 5fho)6 *+s that objects at the equator were apparently weightless?otf po v+*eqs 6)hh5*y    $\times 10^3$s

  Two equal-mass stars maxfpfraj0tj* x)3mp (n8r pr;2intain 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 curve of radius 235 m.:osqdf9bt +6t-bi()i ggj /gt A lamp suspended from the ceils-/tg b :idg()i + ottj6fgb9qing 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 as the Earth. Thus, it has been:ne6 g kddtd n.210iuk claimed that a person would be crushed by the force of gravity on a planet the sizdnnukd6e.i: 1t2gd k0e 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 deduced the presence o5wz ;xgi r+es+f an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gax 5;ewris+g+z s 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 sph:sl rgc d12-25tsmumeed as it traverses the hill and valley shown in rd25u-ss l:hcg 1t m2mFig. 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 the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gv pzd2y7db6yl4vi b2. roup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satebd 224b7yvd iz6lpy. vllites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 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 ,t +6ffqdgpnzm:;qm /.1 billion km, is meant to orbit the asteroid Eros at a heighq,mg;tfp :mq d/zn+6 ft 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 sae95wanz 82 .k eu5f 3ua/cwtdztellite in need of repair. You are in a circular orbit of the same radius as the sateza32 wewt8zun59k5 ueafc/d. llite (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 z,s1 wq f8xk0we+7kyb1bx, ec years. (a) What is its mean distance fr1f0,kkyb+w e, x7qcb e8zxw 1som the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if youuvh9zid9c kgnepc6m*+ 9o v; wk912d r could actually "feel" yoursecw2 dez6ocd v*9+99 19k hvmi pknur;glf 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 Milky Way Galaxy x;0;bu1mfihzu. eb8ww2o;w )s ;os lh/dhy8y (Fig. 5-46) at a distance of about 30,000 liez; u duw)b8xbh;w8ymfio.;h/os 2 w 1;hyl s0ght-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the cornu;cbrye0aj:bk :q 8(cers 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 0 r e(cjaq;:k8u:ybcbplaced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits th5q. mu).gzj svo6n,f re 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-c-x.8tuqe qy.ym -xc77h + majmm-long sweep second hand 7j ythuxxyq.q-m+.-mm7 ae c8on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start tbutzp4:g, i 3d+v)r tko swing a sinker weight around in a circleit: , dbzgk 4vrpu)+3t 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 the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highw,i a+hasu3zj 04 bfm6ks h;i+aay is designed so that a car traveling at spekz; fuah0bj,smi6+ a +hia43 sed $ 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 k dce/ gc0765oyqa1 kqtilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The 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 spee 1eydo70k qqcc k5a6/gd 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.$\approx$    $\times 10^2$