Sometimes people say that water is removed f8uh8gx0u/ebo54v wgz 4 olpr 5rom clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong wi/ x 48b45r5zg8ouv0g el wophuth this statement?

Will the acceleration of a car be the same when the car travels arou/jp u ynp,8h ndj9/hy9nd a sharp cnj9phdn9/8, yup/y hjurve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road p 0ptl9n7oj-sl(m yd,. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on amt j 9sp-d,opnl7l0(y level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rjw96 br y,9ep3jltlhvbs ky+99 oji +um6-9svound. Which of these forces provides the centripetal accelerju o9jy+-9l6v6 shi+ rl9m3yp w9 bjse9bkt,vation of the child?

A bucket of water can be whirled in a verv.ya -)m xu8 pagg+a4etical circle without the water spilling out, even at the top of the circle whe8mu+exvaa. p y agg4-)n the bucket is upside down. Explain.

How many “accelerators” do you have in +a-t.+rijb s 6guuyy,your car? There are at least three controlsrua gj .u+,6+yi-btsy in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes fly(z9(mysl gw(bj:+cj king over the crest of a small hill, as shown in Fig. 5–31.j9zykm:jb((+l sw (cg His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounddlh xnl; h-nyg4ew(y.-+yg wr,9 ;b zhing a curve at high speed?

Why do airplanes bank when they turnssz,5 sl05 c)n;vpghb? How would you compute the banking angle given its sp,snsv)gchbp 5sz; 50leed and radius of the turn?

A girl is whirling a ball on a string around her head in abrv ym4w(g 1(y horizontal plane. She wants to let go at precisely the right tgy4b(y1 (w vmrime 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 gravitationaa dfm7 c3 +/kr(xu*tts2 p9t8zh opk*bl force on the Earth? If so, how large a force? Consider an aphp+*fpomtr9x/u (tkt*dbs7 a kz8 c23ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the s()a c;okcb;w Moon’s orbit be different?wk(;bs ) c;cao

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thw(:h j75i8jsif3m jjfe Earth? Which acmf (fij7jh s 8wjj:53icelerates more?

The Sun's gravitational pull on the m yv;vd)km,m8 i-z ko0Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatii ;,m-okv mvkdz80m) yonal pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two ea:s/f 1a e,9 eyfjql6effects are at work? Do they 1e:fy,jsqa/ alf9e6e oppose each other?

The gravitational force on the Moon due to the1 . sb2g9zie m-rurv/k Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the m r.9uzvsr1ibg/2 -keEarth?

Is the centripetal acceleration of Mars in its orbit around the Su xt.uv)q5u*qt+hxqt/ n larger or smaller than the centripetal a./ +t xq)v5q *txuthuqcceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east *+o;8tiefx wtg*- g xqor (b) toward the west? Consider the Eaqxget-g o8t f+*w *xi;rth’s rotation direction.

When will your apparent weight be the greatest, as measured by a k9i rqo2iu 50zkg, ig-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 wokqog5kgui0 ,-9 ii2 rzuld 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 axfwq+sc,a (xfjk e+22w4 g n4hdversely 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). Explain how this simulates gravity. Con kh,jfac ngw(2f 44++qes2wxxsider (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 wei ocerifrp3:.cbs t rz*75v9h0ghtlessness” between st.*9z sei:br7rrfc30p c5o vtheps.

The Earth moves faster in its orbit around the Sun in January thapel:66iai ch 7-wi2c en 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 main factorc 2ciwl7 i6h:e e6-ipa 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 me w1qgexfwrm xe15:- eglb54( oon. Explain how this discovery engrf1e4w 5leqex5g1:bx(m -w eabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mo bsx5 so(49xercfx tj7bo61l,on's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A chbts fs ,e64oxc1 x59x r7ojl(bild 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 19.he8 9+ rtqq (piq7ldz80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 its orbit aot) z * 9f j3jr3abp1oimq9-6qknb f9kround the Sun, and the net force exerted on the Earth. What exerts this force on theb33) p tknqo jz9 i96rqaf-*b91fjkmo 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 exerted3qmff ul u/rzry)*0x 5 on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radrqu5l) rz3xyf 0*m/ufius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from theb o;*r, gxjxvlw-x 0q) Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express x- 0 q, xjbxlowgr;v)*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 ds 6fcub/9fn -speck of clay on the edge of a potter’s wheel turning at 45 6b f/-d9sunfc rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is re , 7ujnjt7q ytegyjp2j (-,kg5volved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its n7jg pjtyj7t5, (q- gy u2kje,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 roundx7g.uhr6xs n; a turn of radius 77 m on a flat rog6sr;.h nx7 uxad if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tir*l5wk bv3a /:x;cfk/,+dizubz7 q ayyes and the road if a car b/b:i5flu z+x,vak; 7ykwq/cz 3dy* ais to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pbw1lo7-2 rp . ur;b3cwc b*vbgmp 9l/dilots 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 7bogw/ 3uc.lcb*dl7b b-9p pw21rvm;r.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of varia0v hw-1r mk ol9:1hk .cmmxzsfse2 w)-ble speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpkhw :-hk1v-0m l. sx 92fmzcos)1mwrem 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 coaster be traveling when upside down at a(bm lk u 6w47f.v-rczthe top of a circlkvrwu7 -zbamfl.c( 46e
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roundekv3.9-q)ka ec r*n/a*byp de hd top of a hill (rae9.ac ave* *3y nbkpqd)h-k /rdius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need j2e2p5xwupuok .ho* )to make f.oj2u ppxo kh5 euw*)2or the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At tqqk,grvd.bz ,,,wu1l he lowe,1,rdbv .kuqqlwg, z,st point of its motion the tension 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 cv )aw-hh7 lf7z8j3wrsm from the axis of rotation is to -wrs783lzwv7h ah )fjexperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyli930bay48zhxrpkora 96;wzcnh: - xf wndrically walled "r ; h8axn:ra3 rzw9-b4x6fy zowh0k9cp oom." (See 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 c-ow2wnqe8ue inq5/ /air-hockey tabletop, an w5/wcn 2 oeqn/-iuq8ed is held in 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 time, by not ignoring the weight of the bawd t1oae)105 nd;( (lf4cfxye 9mchett 6jq4mll which revolves on a string 0.600 m long. In particular, find the mf4 t)59n6ca df0;4tjw( tcl(y1ee dqom mehx1agnitude 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 forllnkli./taz :0sp fw 1d o3o;6 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 masse6s .lndvc-.eb4br r *z68k0ln vto;xks $ 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 ued3v(z4lmo i.bs/mj a.g 5 ppu;m o55evasive maneuver by diving 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 of t91754mlm yl;p njdwns t0yy5ohe net force exerted on the car (by the n0s ypd;4o175 jwtm9yll my5nground) 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 500 accelerates uniformly from the pit area, goinf z)t 4c*,lpmge* khl.g 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 t4p)g lfc.hl em*z,k* it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontsp4d7g/k*rk uc8c x0 xal circle of radius 2.90 m . At a particular in7c4 s g0pru/cdkkx8x* stant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,zl 4:ed, cr;4xr6rrb c800 km (2 Earth radii) above the Earth; b4 e rlzrrdr46xc:c,’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration t5gxt-5n /b kcg has a magnitu-kb55 tc /nxtgde 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 graadc 9 nx3)iw(ppx*,iw:f dy i;vity on the Moon. The Moon's radius is 1.74w ;9dny,( iifd:c3p *ai xpxw) $\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 ths ;n:xov rxhj2(ypd0o/c:o: k e same mass. What is the a(: px2cy;h/sj ok rn0:vo:doxcceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.6i8dcv*-3br0a ua+di a6 times that of Earth, but the same radius. What is g83a*i-uda0d bc vra i+ near its surface?   

  Two objects attract each other gravitationally with a fa b11q *t+cpqad7. rwjorce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of 5 m08eem2jdhsegt( u6 g , the acceleration of gravity, at (a) 3200 m m(5ue26 emht0s8 ejgd    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earnndpzz a z l462wn3hudp7(v8;th where thegravitational acceleration due to the Ea3nnn4wz7 dp lvd(z8p; 6a 2hzurth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ourt w(bii8ft))w1gzy1nvpx /o4d x:0vy Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thiow (xp1 n0/fzdxty1i y gw48v i))tvb:s monster.    $\times10^12$

  A typical white-dwarj f*4-m2,p3cfqj/v 0kj. qwt;qbyzemf star, which once was an average star like our Sun but is now in the last stage of its evolution, is th;,qb3k*fqj/ve0mq2m4c pj tyzfw .j-e size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in thetdt kdl48b71 y space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it 4ybt7lt kd18disn’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 corn6r6 u.sq ( rb)rz9f(-obsfsms ers of a square of side 0.60 m. Calculate the magn.sb6 (9rf()mr6qu osf s bzrs-itude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets l q jh)h:*pqo*pine up on the same side of the Sun.pqh pq:j h*o)* Calculate the total force on the Earth due to Venus, Jupiter, 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 of k 5jbmfw;yu e sq+j3u1t9ty7ofb )wn6g0,zr ;gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ bytrt)o;kg,j;q 5unm31 b67w9ews fyu j0zf+ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valx*8 hg.*f7gxs xf:do pue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtainegp.* x8:xxod hsg7* ffd using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite ml5x+yc mqyf,c2 ) nqhrw,4k-wa * u5igoving in a stable circular orbit about the Earth at a height of 3600 km+ 5-m),hn,wyafkcxu5i y4q g lrq *wc2.    $\times 10^3$

  The space shuttle relex3 .k1v tch6l418fjtx;hqe ps ases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when thej c tk1;e8pxthhv.f 3l46xqs 1 release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiencpsr2dald8q 1031qg wue simulated l qqspw1d2aug r8130d gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it mmus:zi2xq :)takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above qxmm: s)i:u2z the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from sowbi1qb8v90s3m eg6 the top of Mt. Everest to be placed in a circular orbit around th31q 0gvssib 86embwo 9e Earth?   

  During an Apollo lunar landing mib0z1 jurxhs 5xr** j*c;t2 csxssion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once? x0x21*zrjx sh c*5crb u;j*st   s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Thex q :4g*brdge49 tl )paha9gr6 inner radius of the rings i*:lbhpr9 qg 4e4d96ra) gtagxs 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig.uj ce/; cd0y5u 5–9). What is the ratio of a person’s apparent weight to her real weighuc;uce5/y 0djt (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrhn4 0fhpp- t x nh0:mh/phft+:onaut 4200 km from the center of the Earth's Moon in a xh:nftp4ph hhh+ p/ 0-0 nm:ftspace 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 equal mas1lyj(fs + clw3s. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit abwlfljc(1s3+y out a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the wwlfb/ -v/eb4 weight of a 55-kg woman in an elevator that m-4w/ blbw e/fvoves
(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 fro-) a.zpjsn78dp 7confm the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevatorpj7fcna pd8.7o)n - zs accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very neafvn3 8jb7yi/v:hh j;tr the surface of a planet with period T , the density (mass/volume) of thebjf it7h;j n:h8 v3v/y 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 o* aj pfqs/t1i5f the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfas ip/5qj1* tface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sie++20a3 2 ,h,xjfrlcl* dhf)pa effqun like the planets. Its period is 410 d. hrj0f)if cd+,x 3q,lh +lpa* aeff2e2What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of3 vi c7d 6:d5-)wp 3wpunfwewar+un1b.e:w rv 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. 8r i-x9tw dgr,e7433b9 crp;o6mitfthh /gz dIt comes very close to the surface of the Sun on its closest ap d 9gcb;6,t i/3d hprt4z -i fh8xgw7or3m9terproach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates abou tt4dt oj5mt*-5/h2hrb+vraa t the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons ob7kyef,pd lybu f+50 z93j 1edf Jupiter (those discovere910 jed+efdb yp3y75lu f,zk bd 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 from the known period and distancepz +)ef ul/vo 8zalh6: of the Moon. pv z:8)elo /+ha6zlfu    $\times 10^{24}$

  Determine the mean distance from Jupiter -muc.psqu;h-3 xrbl 348aqb ufor each of Jupiter’s moons, using Kepler’s th34h 8r 3mu;- lb pxqb.asu-ucqird 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 5-3+w ig hn:cnpn5buuconsists of many fragments (which some space scientists think came from a planet that once orbited the Sun but 3u-p 5c: u5nnn+hwbigwas destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describe/ sfi 3ug nqy95lyx.)ys 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 alwl9g /3yy5fuxs)in.yq ays 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 02gpu(e-euo .jvip h7swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the.h(gu0pe- p u 27eovij 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 1.w5 g9c;cjne u+afssthe acceleration of gravity be half what it isw. 5s1+fjs cnc9u ga;e on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands a np7d o;umo,gu:2 azzfc ;-m:4vi *ocfnd spin 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 4,7zf ::i2-ocvod ;ponug m *;czfu amkg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotat txv pbc:ecvuz;a0 (..es once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if thuv a;x.zb:v0ct. (pcee Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earthxml/fn: m.: wa will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the mw::m . anfx/lEarth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, butnb x9jvrb.b ;8 when you stand on a bathroom scale in an elevator, it bb8x j.rbvn 9;says your 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 that wogimkykvhl1*y bg /289hgz21ill rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per dayo 1ig/1*ky2hbm2hz g9kyv 8 lg) 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 vnpl c -7cibsn* y,ga9-ertical 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 radiu0.iyw:,2 x1 qxhih erxs r, the acceleration due to gravity ,q .xx12 h i:xheriyw0at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) ) xqnj7u :vakbg5:0k dis deflected from the vertical by an angua0:kbj 7: kg5)vxq ndle $\theta$ 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 u( .-zwf)rpcz*k pnm0b:x:wodesign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curvf: wpb( z)zkrc onm-0pux:.w*e?

  How long would a day be iwg9bu yr1 e*:mpa v+v/f the Earth were rotating so fast that objects at the eqa+b* v:g /wveum y1pr9uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di+y50 evj5vd6x6eta hestance 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 cosokg45 g*12l xwtgz/u nstant speed rounds a curve of radius 235 m. A lamp suspelo25t4*g sk1 xzgg/w unded 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, i6 bwq x2rj:x4xt 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 4 2x6xjbwqrx: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 presenvb*gizxc* 11 nce of an extremely massive core in the distant galaxy M87, xc *n*i1vzgb1so 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 constant speed as it traverses the hill and vzw04+x5rrnqzxpojn .ct 1 .r r,3uh)qalley 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, r3q.h1 cr)w u xnt znrqj45o,rx.0z p+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 )5auw. i gmx 9*yf3jk,6za nayoya)n0(GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each sai6wny*x a j.moa z3 a,a5y)fg)0 yk9nutellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvo,* +vb+jjppgxus (NEAR), after traveling 2.1 billion km, is meant to orbit the aspg*pj+b x jv,+teroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the sdm-zf3 wa18wcpace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the sat8mzc1w fa 3w-dellite (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 peraowv 2 bd +c3,zq64fb) 2seuzw2xyu,kiod of 3000 years. (a) What is its mean distance fro,2o)e46yk qxau23wbwu , fcvz+dz2 sbm 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 (*fw ;( chcx rfuii;a )49csem would need to be if you could actually "feel" yourself gravitatio(i wa9shf c i)c*4xu;m;fce(rnally 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 Gala.8m c(feyydf xr0w.o2xy (Fig. 5-46) at a distance of about 30,000 light-years fro.2(8cdo0f exwy.ryf m m 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 au *7bn,1 c owlglzjq8s y-1r)vt the corners of a square 0.50 m on each side. Find the magnitude and directibus c-y8nogjw 7,)l1l*1qvr zon of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth5cjmv ,98aa if $ \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-lon. 1:o v9jpemh v,au- jk:4xmamg sweep second hand on your wri, 4v:e j.:mmx9 jmohp-aav uk1st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a; og.squ5rc3x circle below you on a 0.25-m piece q 5.3gxsu;rcoof 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 highway is designed so that a calr ;h2y,oo7bb*xri 1er traveling aty bbohri1*or2,l7;ex speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cag bf u87cb1 l*m3i:gs-o f8y3nji6dl cd 2e6wbrs 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 radi1wdcd*bg6gue88mn ob2 lf6y 3s -j7il:f3cbius 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.$\approx$    $\times 10^2$