Sometimes people say that water is remo fby)/b+3p05 ygi mnnyved from clothes in a spin dryer by centrifugal force thrgpif mbnyb) 0+y5 y3/nowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp 4 lm/tr0zg 1m6: jmxcccurve at a constant 60 km/h as when r0m4tclg:/6 xzc1j mm it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed al oqty63 g+lrorep i uzwypv;4t)23;y/ong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top ofqyl2v3i3 4 /)w po ;t+gzyr;tyeo6rup 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-got lr6,tpt*t 2k/*xl pq-round. Which of these forces provides the centripetal accelerat6xptt rp2qlkl/t, t **ion of the child?

A bucket of water can be whirled in a vertical circle dbdky:6t hdpjq1 )mlg 6 89p9pmj.+wewithout the water spilling out, even at the top of the circle when the bucket is upsidep9t8 djd jy .+:1lqhpp bgkw9d6)emm6 down. Explain.

How many “accelerators” do you 2z- s5h;a/ gz7nfdaxrhave in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produc-f7z5 zgxsdran2 h;a/ e?

A child on a sled comes flying over the crest of a small hill, as showd j3rhqpz:w 8,n 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 hqwr ,d:pz3j8he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at highi6oz(g slom( 1 speed?

Why do airplanes bank when they tuv t/g8qg0 xg-frn? How would you compute the banking angle given it-g vf 0x/g8gqts speed and radius of the turn?

A girl is whirling a ball on a string around her head x j1sfc13qb2nsi-a q 5in 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 strqqf 51-xsas1j3 i2nbcing?

Does an apple exert a grw pisua3,tkq 6ut; 0s0avitational force on the Earth? If so, how large a force? Considet6si;pt0q, 0asuuk3 wr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whahzimz9yespdv6;ov,rmw:*n 2gs / 3 * ct it is, in what ways would the Moon’s orbit be differe3ye,vm*c h 9/i wsd2rzvoz sn:*m gp;6nt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon sb*/k4 1nqd.eqto rt.on the Earth? Which acceler*bo q.ten rdqk/1s 4.tates more?

The Sun's gravitational pull on the Earth is )b osd05lpqg 4much 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 t4s l05obp) gdqo the other.]

Will an object weigh more at the equator or at the poles? What two effectd jkcs.8t 14u/nfo+hys are at work? kcyj148/su dn+fh .otDo they oppose each other?

The gravitational force on the Moon due to theor4u-,q6z3 em) cdli :zkgl6e Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eo kz, ml6iqu634cl: rgez)e-darth?

Is the centripetal acceleration of Marsg: ixpv6vz w90dy yn). in its orbit around the Sun larger or smaller than the centripetai:0 y ) xdyvz9wv6p.gnl acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or,fmzewq( ;pu/ (b) toward the west? Consider the Eaf mze;qp/wu( ,rth’s rotation direction.

When will your apparent cmz(g+y4j : vaweight be 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 upward at constant speed? In which case would your weight be the least? When would it be the same as when y:zj 4vycgm+ a(ou are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer spacer3 oow+; uc *bj-do4eq could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical 4bje c *qooruo w-;+3dshell 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 experiences “free fall” or “apparent weightlessness” beqx+0f 87bsxr0 en: o-hnhddd)twee q)o-xh7+ed:8x0s nbfnr hd 0dn steps.

The Earth moves faster in its orbit around the Sun in Januap +hx 4e+th,z2reh4uhry than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the mhh2xzte++ hhr,eu 4p4ain 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 discovered t4hwn1 8 ob:wxro have a moon. Explain how this discovery e 8:hwwnboxr1 4nabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. keu4xup+yt* q3 lao s: wh46b+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 kol*ab+xw 6 h4 puty:43euqs+ 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 195rhz a4mam.f 880 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetaitg 4+ 7p+k lzmui/ .jq;b0lz81zhmuhl acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radz+qumu/mp4+70hg81 it zl khi;z .lbj ius 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 2.0b8waz,wq4*b8 lopwn 4-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed o ,88qplnwzwab *4 wbo4f the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and+ aeg;fs;g)-qf qe3w p circles the Earth about once every 90 minutes. Find thef;f esq g;pe)3 aw-+qg 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 clay on the edge 1xcp2r-ekq,x(8l wkcof a potter’s wheel turning at 45 rpm (revolu1l 2wp8erxx q( -kkcc,tions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a key ;yz23sk9guniform rate in a vertical circle of radius 72.0 cm 2zek s9;gk y3y, 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 c;urml: oj;(iv an 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 ind(;io:uv lmr; jependent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and t s3 my9l,qn1ckvuji7 9he road if a car is to 19cin j9,lsmy q37vukround a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet 8 ;ic2 mj9iw67rpd0 ckfp f-wrfighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times cfpkifrmjd ir609-wp; 72wc8 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 tu-+o* 1wbmeb +wl lnw5mhqy)n8rntable 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 the coin and the turntaw *1+ho8 en-bb w) +nw5yqmllmble?   

  At what minimum speed must a roller coaster l6toq)zu3h;6mtb dp .bi j/2fbe traveling when upside down at the top b; 2f.ob)zitmpqhlt 6 63jud/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 (yrs)o,b(1 d v l2jjg)rx h0ym6including the driver) crosses the rounded top of a hill (radius =sl0r v,6gho(jy r)xm dyb2j)1 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 15o* me.dv,y;a8wc-tam -m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the toco;e , wa*-ma.tydm8 vpmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius:4; xcx6nmqj+sqil mt;// 6t jpcv: kb 1.10 m. At the lowest point of its motion the te:ci4 xcbt: 6s6j qq v;+nmm;// tkxpljnsion 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 rotaten/n/k j48movl if a particle 9.00 cm from the axis of rotation is to exp nvl4/nmok8j/ erience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in ayjmyi,1 6m lh8 cylindrically walled "room." (See Fi8 m,6yylji1 mhg. 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 circsa9cuf,b.c p, 8vg1z zle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m bupc,z ca.f1v98 szg, ) 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 time, bydd4a3 w r/ e,6pdhswt7 not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnea/pd,36d wt hwr7 d4situde 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 wn c-wpab*2*y9. fvsc 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 masses7bfd4v u1f6kr $ 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 3qjv-oc: 6+)2::.u sbgspk zh1 d tkrht10 $\mathrm{~m} / \mathrm{s}$ . 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 componenvj,xqo jzr78/ts of the net force exerted on the car (by the ground) in Example 5-8 v xoj7z,j /r8qwhen its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly fo(b5j jiqdy+- rom 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 betwe (jd 5i-bqyo+jen the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle i: 9i gmk7ha7qof radius 2.90 m . At a particular instant, its accelera7 i: qghi79maktion 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 Ef8mu5tjrv8p. arth radii) above the u 5j .tfm8vr8pEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hz1c3s3iqo7fp/(9 ( ufk 0wwzbnu z /oaas a magnitude of 12 m/zwuf71 n3 i(apo/ ocuz0zb fsk39 w/(qs$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1.74yvqq;8m *qez 4qzq ym4 v*8eq; $\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 3pj savzo3u .1has the same mass. What is the acceleration due to gravity near its su.pzoaj3us1 v3rface?   

  A hypothetical planet has a masq hc4 j;sdf3+xs 1.66 times that of Earth, but the same radius. What is g nea xsf+3jd4c hq;r its surface?   

  Two objects attract each other gravitationally wit mmz k oydk;dq0j+o )60dndn4;9v-cj nh 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 effectivay*gitbw0e ntry1 0 fk3vki329u,-yke value of g , the acceleration of gravity, at (a) 3200 mvfe1kny 0-k 39r3iiuty atb* ,yw2 0gk    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center a,jb jo2,oz9q to a point outside the Earth where thegravitational acceleration due to the , 2azo,jqo b9jEarth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a lo7al ;m*t r9isphere about 10 km in radius. Estimate the surface gram ;l*t9o7arl ivity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our rn; 3 fb ul:8q,lu7cfnSun but is now in the last stage of its evolution, is the size of our Moon but has thelnf8ru qu7, bn l;c3f: mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlesu3t3/3lq8:ups 9-tuoj stz/psqg5fss while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so f:pgstj5u83qu-s/ z q9 /t 3sost 3ulpby calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locatedv,5o()dhlbb o *h zoc1 at the corners of a square of side 0.60 m. Calculate the magnitude and direction of thehh b,bloo1(oz 5)cdv* total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most .6gif1z(tc.2 zk51x ex -t kfqnes3de of 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 t( .1. eftzki3 g6 sz-qnxde51kcf2xea 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 of gravity at the surface88 7v(wkxmp vidvvp)5 of Mars is 0.38 of what it is on Ear i)mw kv(8x8d5v p7vpvth, 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 r mig0* uf28flperiod of the Earth and its distance from the Sun. [No flg*0mu8fr2ite: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving3,0y0o qnu r k(p-gupi in a stable circular orbit about the Earth at a height kp0yo0uu,-gqi3(rp n of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a aa0ar49za qt* circular orbit 650 km above the Earth. How fast must the shuttle be moving (relativq a9r aa*0a4tze to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricalj.s au+ xxr7 h2av47ic spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give ax7hsij .car7v+u2x 4your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eacmbu;8+rk -7rzwx 1vj3el9 id0p vmy2rth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of 9 yjz 7m012kredxmpwvl 8c-i +;uv3brthe satellite?    s ~    min

  At what horizontal velocity would a satellite ha q.2,d l i+j /tk0bsdn0gj4:icemz mh;ve to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? bs:gql/m2j+; .nid 0tij,zhkd4cm 0e   

  During an Apollo lunar landing m9xwme qeo:dl )* d8:epission, the command module continued to orbit the Moon at an altitude of about 100wexqod )p 8*m:e:9led km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit thlaensw l+/m40 e planet. The inner radius of the rings is 73,00m4l a/e0wsl +n0 $\mathrm{~km}$ , 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 i7 .( 5(lrbysqj*vc3/kp dy xuln diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to h(kv(r d* j7q5yc3/ubsxl ypl. er real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astsgp-92a4vj yd ronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocid-yg94 js vpa2ty,     ----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 tb, 8a673bcr9yddv7g6 kgtj8f xi6inh wo stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Eadg68vj9a ncri 6fk8, b 7gib7h63xtd yrth 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 weighggj *, b84glaat of a 55-kg woman in an elevator that moj*a,lbg4gg a8ves
(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 elevator. dy 1, sjy2yehkvb:e6)The cord can withstand a tension of 220 N and 2)skd1v:ej6 ehb ,yy ybreaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near thelmat(j 9.c q:na+y ;;xb f/cajoavq*, surface of a planet with period T , tja+acax ;(otj.fbm9y c;nq/* l, aq: vhe 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 Moonb/90umajq8 78 fdjpk 0g4rj3d*duwxu (27.4 d) to determine the period of an artificial axuw d p30 8kqfbj90j udjg74*rdu/8msatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitk7n5 .f cmtl q3k.grd9s the Sun like the planets. Its perig.lkt9c r.7 f3 mqkd5nod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average5qwke3diyzpf d-*-kgau;l; )- zs 3r m distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes z - o)9gkml-mc0pt eb-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-9l-k 0)zctgbm-mpo e? [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 Gal 0,pm+ptup3w6c/e7k+f.u7kt q pyzmpwaf 2 ,laxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 forv v3i xd.b.zvamk63-x the four largest moons of Jupiter (those discovereb-k vdi..v xxzm63 a3vd by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth flp /gdkz.5x,h rom the known period and distance of the Moon. gp5lhk/z,d.x    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usg1 wd5 i*s/ye u5mzv4oing Kepler’s third law. Use the distance of Io a*5uyg iz/mw1oedv45 snd the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frag(o7: (azb5it t2yxexx ments (which some space sye5:x t7ati(zx b (2oxcientists 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 talq 1v /yrnjm1v;e describes an artificial "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 this sun is exactly like our own,ny/jr v1mq;1v 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 n:d:oojcnm :w y5z/9w6zri h( gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 140m dn:nzj(z6 w:y5/woi o:chr9 0 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 surface will the acceleration or(9qrq.+euyq(*c at yf gravity be half what ict qrye.(* r(+q9ay uqt is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands ansy94o j(uw r1/buk0cu q.a xf1d spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and(u sc yqrbu uxaokwj/41f901. 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 apparenx;p9e w1k /avvt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effec9kav pe/;vwx1t. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from th q3iwz4vxxd br16r. t)e Earth to the Moon experience zero net force because the Earth and Mo.r q6 t13xrw 4vdi)xbzon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but n rr9x ,ck4(bpwhen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which drpx(r,kb9c4n irection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube th.a 7,dx0i(kfv)zez hqat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by 0qzv) akie 7,( hxd.fzthe tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraf;v c e1s* 5iahtlfv0(/7 wqyjm s,yao.t 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 g7mng m+g3gc pw5vd qii,i5dr9g1)v 7ba8 z6nplanet in terms of its radius r, the acceleration due to gg7,wg)5iv+1m9nc5nd3i6 abz 8migrqvdgg p7ravity at its surface and the gravitational constant G.

A plumb bob (a mass m hangi2c7r(4c9f5k q pbv4x8evq (ai vpj/d fng on a string) is deflected from the vertical by an angle(v2fvk9ria4 xbccf /7je4 v8p 5d(qqp $\theta$ 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 coeffime6v- h*)y ;pa2ocaimgkc)b-cient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the;yg mbe-6mcica- )kop *h)2va curve?

  How long would a day be if thts g:c t/ka)f0. i8g 2qlt4u dd+qi0gpe Earth were rotating so fast that objects at the equator werl8. qgt2g gk+cid4 ptu/q fa t:i)d0s0e apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8 29q n5*qlyg i.2)o+akpnxp zq.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 speedk1/j rd3o *oq bgfk74m rounds a curve of radius 235 m. A lamp suspended frommjqr4 *oo 3k /bdg7fk1 the ceiling 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 claimed ma: p ho-i6f0e73 xkanthat a person6 ak0ei xhm7:3n-pa fo would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: 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 deducbr3 s.n 3r, gs osk)l+,vuf)0nzk rxc+ed the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of co b.))n0xnklgsr+r3vu,, +s3fr skz 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 hill8.+n.lx2: gkq pamz+gu )xjhv and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go withou qx).n2h +xlm z:ak.gp jg+uv8t losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites oe e/mo9:pbc tdyl2*,g rbiting 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 Eartyeg,9*e/lpd2m co : bth, 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 Rendezvouss(i, h yj otn h((bz;4cm5pl:l (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros i4lnh ( lthb5, ym(;c:ipsj(ozs roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need og h7m93ja cv:8k,b/a +gvn4bcbw o5fzf repair. You are in a circul h3bmbn/k+8f ajcg5ovc wab94, :g7vzar orbit of 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) Whavars 2c2a+.tm +fbz;v t is its mean distance from thec+vf b; 2tv 2zmaasr.+ 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 g3nciz.rn7dl x ki/ma217ok6 :q5v tu need to be if you could actually "feel" yourself gravitationn/ tql3r.7i voa2cdk61 nm7ki 5zugx:ally 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 Gr38g7p t 1tqxkz 0vl4+qjq:xl:l wd4z alaxy (Fig. 5-46) at a distance of about 30,000 light-years from the c4:g4:lp tqr x1 zkl7q+ztlqdw0jv x83enter $ \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 ;opco0 wt+o: oo/m6(( u q9ld-oncamzof a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the squu( o ao/ p mwnt-do0mco69;(oo:q+c lzare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits n h1uzwy:skc1rh9 0x 6the 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 sweep secoejtw 0ag 553z -7gjkfvnd hand on your wrawj vj7-05f3t zgkge 5ist watch?    $\times 10^{-4}$

  While fishing, you get bo6cem gb(d ;/nmtl7i g7s4lj k-red and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a 6ns/b(dij 7lc 7kl-gtm eg m;4complete 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 highway is designed so that a car travel5mqg z k,l0,x nkjf*q) anesjok019n/ing at sf,9 n, asnk jq1k lk0mn/jo)*x05egqzpeed $ 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, utilizee*ap e-xe k8s*layj++ fi8c6is tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Considexlic8a-e aiesk 6ey*+pf+8j*r 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.$\approx$    $\times 10^2$