Sometimes people say that water is removed from clothes in a spin dryer by ce f9j1w:u vqz*zxzldpoy412 t0+mjs -b ntrifugal force throwing the water outward. What is wrong with this statement?-sz1tzj4 *+w:q 2m9jpuydl z f0boxv1

Will the acceleration of a cna / -,xdt2 xvdjav44war be the same when the car travels around a sharp curve at a constant 60 km/h as when it trd2xn a4a-w/xv, j vd4tavels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alo dh n)/duc- z2lxnv22+cud7 cong 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 n7zucvl) 2nho+2cd-/2xd u cddip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a coum:m xlr; s-61po- lchild riding a horse on a merry-go-round. Which of these forces provides the centripetal am-lxo:1mc- 6lpo u ;rscceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spml*z2kay tp pj-dv 66.ty14p lilling out,d6a t2t y 1* jz.4pmyll-v6ppk even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? T wa/hg9 b3gp-s6nvca ,here are at least three controls in the car wa6a3nb hgv spgc w9/-,hich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comesjrc v5*6 1rzdmo9styd*/ig .z flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feelort5s6**/1gd crmz9 .diyz jvs 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 lean ixp8xhab9a7 q(my,.frl12lnig /ls i2nward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you cof5lc-wheh yfni t 809:i:o ts*mpute the banking angle given its speed and radi8i0 sn e:t- wlyofhih*9f c5:tus of the turn?

A girl is whirling a ball on a string around her heau ;i/d+q:3h)fa tda bxd in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other sid; 3fqa dah:x/u+dit)be of the yard. When should she let go of the string?

Does an apple exert a gravi+uc /4 ta rxdxc:4t,xntational force on the Earth? If so, how large a force? Consider ax,d atu:c4x +tcnr/4 xn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were anul71q :)z (kdxs rvl:33 ze0up2mphdouble what it is, in what ways would the Moon’s orbit be differpkru s 1am2hnl03:3)xp7 zv :lduq (zeent?

Which pulls harder gravitationally, tr6i c:vkj,u7l l7u;1zdd( rtbhe Earth on the Moon, or the Moon on the Earth?:dlu, t7lbc z 1r(i 7rd;uv6jk Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yoxw(ujx-h36m i gz pb6 ;kbi/(et the Moon's is wo(b- ( x;zi66 3/mgp xbujihkmainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects . uq+bc zpm5jg vu5k,.are at work? Do they oppose each other?kzmgu+ qc5.5.pv,jb u

The gravitational force on the Moon due to the Earth is only abou8ql , o07npt*1tbefpn. 7zf uht half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the t ,7h 1*ebfzu8popnlnft .0q7Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger orm9m+go)+ yn bu smaller than the centripeo)+mg+n9 yu mbtal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward thm ) di31j:niu iv)rc6ke east or (b) toward the west?vdii)cinj1 r:6)kmu 3 Consider the Earth’s rotation direction.

When will your apparent weight be the *ibdbu.0g .9sn hxnn -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 weighd*g .h0ubx -nni9 bsn.t 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 adverselyssz pl kbfek2 h*ytqq9biodq ,;.u2)kx+y7,3 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). Ex7*xesi fq)qy2tql. z,, db3so;hpk +k9b 2yu kplain 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 runnervqrbq(4)f4a n ;9bn9pchq j:a experiences “free fall” or “apparent weightlessness” betweennb):nr 4(qqv9af apch;j 9 4qb steps.

The Earth moves faster in its orbit around the Sun in Jan4hwd / 0cs-;uzw/z vrcuary than in July. Is the Earth closer to the Sun in Januar uwhcv/crszwz/d4 - 0;y, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explc)4k ez6s (udyain how this discoys )zu(dk 64ecvery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's m urziyqf+ :sh(yj934. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center ofyyzmrj+9:sfq4( i 3hu 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 7o/uc/sva8zz 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripe*g lb slda+c55tal acceleration of the Earth in its orbit around the Sun, and the net forcea5sg+dc* bl l5 exerted 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 rotates uny:60leovk mcjhzs/1 ,2jj t9 giformly in a horizontal circle (at arm’s length) of re m0lz , :h/jjjy s2votk196cgadius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cirp848u:pbm0o x z2tiaa cles the Earth ab8pix a0 pz:ua4o8bt2 mout once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude qxn gi4dtj60+of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter6gt nqdj i4x0+ is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical :t,th t:hbfu.(n sg01 y9rapfcircle of radius 72.0 cm , as shown in Fig. 5-33. If itsfy:0h r,a(tpht.b9tg f 1 :nus 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 carpn3g/k8yuni / 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 of the mass of the car 8gni//u3nkp y?   

  How large must the coefficient of sta;se 0xik+cfkj bd uc(; flf2+-sg :nd6tic friction be between the tires and the road if a car is to round a level curve of radius 8(k c26d;xck;s-f+edsl f0f+b:u j i ng5 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed top fr8n,ktsi1la3+b(;o-a yfm) q kac- rotate a trainee in a horizontal l-syocmb)q ;kaira8, (anf+pkf3 t 1- 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 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 ro9oic.b;n) ebl tating turntable of variable speed. When the speed of the turntable is slowly in9l.in;bo c) ebcreased, 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 turntable?   

  At what minimum speed must a rchee,sgmx.; q- jy k em-dc.76oller coaster be traveling when upside down at the top of a circl hecmc6j-y,.7-g. ;mkqesex de
(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 manero,c g6 e-qn s3)za7ss 950 kg (including the driver) crosses the rounded top of ao6 -)g3ane,qze 7nrsc 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 d-xj 0:.jogwmwould a 15-m-diameter Ferris wheel need to make for the passengers to fedj0ox-.wm: jg el “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ver y+h-z mw0xt *h-3alrytical circle of radius 1.10 m. At the lowest point of its motion the tensioh3y+w x ml0- zaytrh-*n 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 particle 9.00 cm f l3rx .a xwmwdd1 28w,6y/imfkrom the axis of rotxk,2.wwlxm w3m 6/d drai8fy1ation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindriuf 2z9(dieai(j h:c w.cally walled "room." (See Fig.h(j.i 9uzdc: fie w2(a 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:dl rti5 ni nkk,cv258 rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig.c28rl : tk5knnii, d5v 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)q. ibb*pr ,4fm u*hakd,ww4g c vqw4lh2 0p8b, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mq4*hpm8)b a,bgd24 pcf r*wwkqi 0 u,.vw4lh bagnitude 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 car l47;wr n0h )0(f wk2eantywgjtraveling 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 massebz9j 5 m fuq6;e3ks4nis $ 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 31z9 yb ekvk,7.u0 $\mathrm{~m} / \mathrm{s}$ . 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 componentsaez/-4 l,fy o8do ;prc of the net force exerted on the car (by the ground) in Example 5 / o o-ad;z8r4ecfpy,l-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area,svae67 b - jsu0yp0q7y 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 tangen s0y yabje07spq u-7v6tial 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 horizontal cir6uy v y,7kdf(fcle of radius 2.90 m . At a particular instant, its acceleration is 1.0 uvfk 6(yf,7yd5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 o7c v/ bc( w8j*)t*80/9m fnni vagczebi:jgpif Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is c c*j*tiegn f:i 8/) nm9/8pj0iza bgcv(bwv71350 kg.   

  At the surface of a certain planet, the gravitational acceleration gkrys 8i83( mtqu7v4lp has a magnitude of 1lt3(rp84vk my78us qi2 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 dzh/c(;vr3llq ue to gravity on the Moon. The Moon's radius is 1.7/h3clv;rql( z4 $\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 the saa(d +*1v sm z+8od pddmkrb:2rme mass. What is the acceleration due to gravity 8d*rdk avodsr1 p+:2db+mz( m near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,yemr*vtp( (d-+5 nu+0gi(fu ax7heyk but the same radius. What is g nearpkx uvgdumeanh-ye(i0f*5r(( 7 yt++ its surface?   

  Two objects attract each other gravitat9fkfnn 2os c 9ms/0z+iionally 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 ,evl: fr(py l fw7w+gv9n60f dvalue of g , the acceleration of gravity, at (a) 3200 m epffvl0w+:lg,6yrd 7vwf9 n(   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eab sp)(m8m/4inv4 wsvf rth’s center to a point outside the Earth where thegravitational acce84(/bw vp n)fsmvim4sleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star c 7o360ra : a: h4swypa33fi3pjl e1ryakn5ydhas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimat3srpep: 315 3 hyao0ajya ci76w nr:fakldy43e the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf -lmq 9edb7un3 star, which once was 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 surn7 me3- 9bqlduface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightu+ 0f2hcpffy3less while orbiting in the space shuttle. Your uff+3yc2fp 0h friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the cort9wyg:4b js7p6pbw d:ners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on onebbp t79:6gdpjyws4w : sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yeo spt4ugl:m+ ;ars most 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 inm:4so +u;gtl p 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 of gravity at the surface of Mars is 0.:w3 d3jkt58e5z tmfcg38 of what it is on Earth, and that Marsdgfmt8t5 cjkze 353:w ’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th xynp7(m hd; .h9dtzd/e period of the Earth and its dd.(;hndym7hp9 td xz/istance from 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 moving in a stable circular orbit about 3gw:cea *:5t8kkwej ithe Earth w* wtcega5 8:ki 3j:ekat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above t5* r 5lq5zwzifhe Earth. How fast must the shuttle be moving (relative to Earth)iwq5 z5 zrf5*l when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are too0h)4ztks 7bw-9;o z.lip k u/q5 swqq experience simulated gravity of 0.60 9w.us;z)5qs zhq4p/7ot-q bwkl0o ik g? Assume the spaceship’s diameter 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 satellite to orbit the Earth in a circlr5 7d(+x:vkt xtdc;o ular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whi5c k r:7xdd +tvot;x(lch 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 velocitya8h: 7kerx . hdl:jvje /6w,xbm3f1 jf would a satellite have to be launched from the top of Mt. Everest to be placedheebj6x /wd j:l,a 7j: xrfk.f3h18vm in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modulgki5z8 ujy*( le continued to orbit the Moon at an altitude of about 100 km. How long did it take to go arounkzu58(* yjl igd the Moon once?    s

  The rings of Saturn are composed of chunks of ice tha *c5:l*zkun zc-m rbtw7r8d x6t orbit the planet. The inner radius of the rings is 73,00rzw rb8c7:ltd -6*zk xnum5 c*0 $\mathrm{~km}$ , 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 rotat;a xbxb w(vxl0l*alu ,j: t40fes once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her reu:04b; ta xbalx, (l wflx*0jval weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wenf .dx3fkpb*8ohek( bm1z p;0ight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at consta03bxp1 dfep nb.(f; hmzo*8k knt 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 0jnpszh bgi(b /; wn9x1wgx1 2system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yen9 0 z b ;gbp1xg1js2iwn/(xhwars to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kgw-5c0j bc 45iry3a8i h)nolj f woman in an elevator that moves y3cr8j0ciojwab55h) li4fn-
(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. Th/j-t o .m9jrwte cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (matwrjo-./jtm 9 gnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planetqm35e x1s hr 2ktstw.j.d7h;o with period T , the density (mass/volume) of the planettoe 2wkxs 1;dr .73hq5t.mhsj 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 Monf*k 5nf8 , 92uxyakk x nxuu57jrcn34on (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surjnx *3u 5cnnk9raf54kx8xn fyu2k7u,face.    s

  The asteroid Icarus, though only a few hundred meters d/jlq5 d0/z raodp0b )across, orbits the Sun like the planets. Its period is 410 d. Whlb)/q/jp0 d0oddazr 5 at is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 ic r s.vv/9k9 , uljqse lz-sq,+c e92j*wei2q$\times 10^{9} \mathrm{~km}$ 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 evert;sc b/jx w67vlj,+k sy 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 thir6tlj;s /kj +7vs,bxwc d 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 Galax4naj e(qgw0 tg5 q7np8y $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,m k eik092jr.etr9;l a and mean distance for the four largest moons of Jupiter (those discovered by Galilek ejm;29e ra.tkr l0i9o in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known periocw.:fbaex )* od and distance of the Moon. wo.b) *:caxf e   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter/nbfam ,,u- gn’s moons, using Kepler’s third law. Use the distance of Io and the perio/m,-,anu ng fbds 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 fragmaql ea5 ,voj+3ents (which some space scientists think came from a planet that once orbited the Sun but wa a3,v+ lj5eoaqs destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band copc4r;w.cg aaho-nv1 a/69 85 1.slytdv xnzhumpletely encircling a sun (Fig. 5-40). The inhabitapgu4d.y naxhr9;c oa1c lstvvz6awn 51 8/h .-nts live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in 4w8j1xhdr, *c :yv egfan arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he4dxv1* hr ,cyeg j8wf: 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 aooi (gee32m -j0yl bb0cceleration of gravity be half what eme2g(00ib- yl o3job it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin biv: 6dr;bx2z in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on on ;ivrzb6dxb:2e another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent axhr2mo,n:n (za0onu9qk q.o4 cceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rot0:qn no4m kq.r,(hnz92oouaxate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a s/m0h oxydzf/5 n-+bcspacecraft traveling directly from the Earth to the Moon experience zero net force because f5mxc /y-z d/ns+ 0hobthe Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,scv6um,t,73p zltdht / ta+c, but when you stand on a bathroom scale in an elevator, it says youvs,t6+ta 3cc7tlmdz h t/p u,,r mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tha z/iu,5x de5x69 abxlqt will rotate about its center (like a tubular bicycle tire du/x9i e5lx5a6xzb,q ) (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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his ,uxz)x ezno*rr /nof n+15f4 md7ndn+aircraft 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 planet in terms of its radius 67be1enklkhg n 6m:t 17smx4shx/f2cr, the acceleration due to gravity at its surface and the gravitational ch sk x6nhsbe6/cm:17m4 1tlx7fk2engonstant G.

A plumb bob (a mass m hanging on a string) is defl;ap 5vs3utvxjx-r6v 4 ected from the vertical by an anglev65ur a4jt v3p xs-;xv $\theta$ 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 f m)s :f7tg9wnfor a design speed of If the coefficient of static friction tf) nsm 9g:7wfis 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating sey b nohl:/mkh m1:h2(o fast that objects at the equator were apparently hy el(b:hoh:k21 nm m/weightless?    $\times 10^3$s

  Two equal-mass stars maintain a const m,g(a/;g ahsb9j nd0nant 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 ro6i bzddo *9 s30dg2aszunds a curve of radius 235 m. A lamp suspended idd69*a20sgzz 3osbd from 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, i-)ycbqs n7/ a u5sdxs7t has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the f7bs)xans s7 /u5dyqc-ollowing 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 presence91-1zggc u nwoi/h h,c.92iitg xcrr) of an extremely massive coro2g1 c91hw g)n c/iu9cg ,rh rtz.-ixie 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 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 constan tbl6;o)xbw,-u .)f9qn dlmgprt-p 7ft speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the 9f ;u7g6r-)qob)tpp-.bf,m wnlxd ltnormal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satel5snpa9n e .c2u*g1 cgxlites 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 altitude of approximately 11,000 a gc.2 1*us5n ngpcex9nautical 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. px2 h9e8dhlr traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly hphed8 xrl. 2940 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 sa in,p vlkpt4is ,f th6m) e9m5lfrwpz28+c,s. tellite in need of repair. You are in a circu tc6+rpew5,pis .sk8 4p hvzlmfnlim9 2t)f, ,lar 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 gw5*wr ffon +0mb,oay; ;zse;f tm+pl3)to0o3000 years. (a) What is its mean distance from the Sun? ;w meftn;+o o+ 0;aflgftrw) 5zomy03,*opbs   
(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 you coul0kx hde,gdtb8 lw7. t-d actually "feel" yourself gravx0h 8-7tb ekgd.lwtd ,itationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the dlr.5 9vkr,gn center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 3dr9l5nr ,v.kg 0,000 light-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 rds;: kpwwyqnch4q t526 w;,lcl)bz :2c gz-pcorners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg ma ),l;w cqywq24cph2nzzp5g:tc:sb k6;ld -w rss placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitqi 2r p3w;3jb76xav qzs 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 tq ; oeh)6m*gfdls a,3fip of the 1.5-cm-long sweep second hand on your wrdg,hl;foqe*a s6m) f3ist watch?    $\times 10^{-4}$

  While fishing, you get bo-rf0( gvz w1 ;k)co7y2 2ij)ouoohiiered and start to swing a sinker weight around in a circle below u)zoroieo; o-0cghi1 (ki vf72w yj)2you 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 hig7mh73 mq3 -msdw+2rwa:hzy ybhway is designed so that a car traveling at spe- wymmdh327s3m y+wrzha 7bq :ed $ 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 tra8nl fzol8w2d lc68nx7in, the Acela, utilizes 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. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the frictio8l2 owld7 nz6xc8l 8fnn 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.$\approx$    $\times 10^2$