Sometimes people say that water is rw n 6wpxxr/3vih gq4l5 lg4/fq67(ouiemoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrongqgu (xhql7i prfw64/x64ni 5lo/v3wg with this statement?

Will the acceleration ofwueudw 1u79 5k a car be the same when the car travels around a sharp curve at a con1d 7e5uw9 ukuwstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant spej0jn q53s2uiqed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a ns20 qjj3ui5 qhill?

Describe all the forces acting on a child riding a horse on a mh; s j*,qkw:hserry-go-round. Which of these forces proq:wh;s kh,s *jvides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without th(7d gn ivby:c, gh/gufr-5, qhe water spilling out, even at the top of the circle when the bucket is upside downhd c-gy, ,7fv(ur:b5qhig/n g . Explain.

How many “accelerators” do you have in your car? There are at least three cone/o)r1l)m yxa trols in the car which can r))xe /lmaoy 1be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over t yw876s)z nb2c4ipo emm 0tqeyzbg51:he 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 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. 0z6:p ig2sw8 mc1e7 my)5 zbt4eb ynqo

Why do bicycle riders lean inward when jqshtrkx,6ltk(m,- cf -s *i 8rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankiy tu)r-nlaj :)mko 8+fx:veu 6ng angle given its speed and radmok:)va 8fe xt nu+u-y:)j6rlius of the turn?

A girl is whirling a ball on aq 0zj7 jv0zv7g string around her head 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 side of the yard. When should she let go of the string?70jg0 z qvz7jv

Does an apple exert a gravitational force on the Earion6i. gosl4/3sf/m hth? If so, how large a force? Considni6lh ./s3mf/ o4giso er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what:klr2g,u0 ig.bdraebj s2vnf2f ;, 5r ways would the Moon’s orbit be dif rfrflba2;,:rsegv 2d bj n,0 u.g2ik5ferent?

Which pulls harder gravitationally, the Earth on the Moon, or thet505jhk xj)*rn9w+ries yy y/ Moon on the Earth? Which accelerates moy) /re xtyj9k0wi h ry*5s5n+jre?

The Sun's gravitational pull on the Earth is much larger than the Mnqq6:z4 lyp tz q9al/7oon's. Yet the Moon's is mainly responsible fz6yt aq:9lpq/l qn74z or 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 pbq4m* ga v*.nloles? What two effects are at work? Do they oppomla*q v*b4n.g se each other?

The gravitational force on the Moon due to hyu 1.06htp ely*oygi jet (;ygfg,/3the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from j.(h; p*,e ft3i6yylu ygt1y/0 hogegthe Earth?

Is the centripetal acceleration of Mars in its orbit +vesyjl73 y*/ xakuc2around the Sun larger or smallerly+* k jys2/ue3c7vxa than the centripetal acceleration of the Earth?

Would it require less speedi)5t,i i qzey+n(j3a w to launch a satellite (a) toward the east or (b) toward the west? Cona3i izqy,w itj)n( e5+sider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a s+q ;p awo81e0b mavpf/,ed2dscale 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 af ape ;vm8dop0q 1w2,d+se/ bthe 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 adversely affectedx pg 3s-(gn 7m: pcg-yyld*h;w by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, wi;ph :sgy(x3lg*-mw - gny7p cdth 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 experiencesd / mj1:xvve f.qy1x7q xuwg7 te9:5jy “free fall” or “apparent weightlessness” between /v5u ef.gxq97xqxtyweyd 7jj1vm 1 ::steps.

The Earth moves faster in its o,u*vh.wg/7z ogcbn c )rbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbivou).7/cgzngw*c h, b t.]

The mass of Pluto was not known until it was discovered to h z)qyfymc t98)ave a moon. Explain how this discovery )9 yz ymc)tfq8enabled an estimate of Pluto’s mass.

  The Sun's gravitational pu pj7f 9 b2xj g7:abcqb6xl5m93 .jps2rqqei v.ll on the Earth is much larger than the Moon's. Yet the Moon's is:37fjpvqbp. xg 2a7 c26mb e9irsq9.x5jjqlb 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 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 travelin2uk8-h/kl o+j*q3a gyb huok,g 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 centripetal acceleration of c1tr 5 cfbd01othe 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 a05t 1cf r1dbco 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 u69 rhsoc1.ppit rotates uniformly in a horizontal circle (at arm’s length) of radius 0hur6 9sc.p1 po.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 45m(hdo3.yyemb 3 s b2y00 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in termym h(2bye3 smby3d. o5s 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;pwu8 fa 7j0+ vg8tgob the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 c;f0+7uog8vtpgw ab 8 jm?   

  A ball on the end of a string is revol.;/vni ,5uv8jf tch deved at a uniform rate in a vertical circle of radius 72.0 cm , as ,uf d/h5 tv.j ev8in;cshown 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 witheb; fv*z989w ihd rc.g55ywl c which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass orlydccgi89 v5 w. 5fw*h9zb ;ef the car?   

  How large must the coefficient of static friction be between the tires an a2r mf,qv ;sj*ew2pki7l83 jtd the road if a car is to round a level curve of radius 85 m at a s j2e rwafspi3,qjlm;2t8v 7*kpeed of 95km/h ?   

  A device for training astronaua7ovy,h m 7h.:jd9yqd a0fwz j;uf,s-ts and jet fighter 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 her own weight, how fast is sd, z.m-hujo,ay;9:qd yavhwj 7 7 0ffshe 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 at: ro cj2-jjkmyqla ncd5 .5d- ,qve,2xis of a rotating turntable 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 turntaq.l2 :q-jyv-ekdr5 n2,cctamo,jj d5ble?   

  At what minimum speed must a roller coaster be20y(kt x; zvxwz:oov* traveling when upside down at the top of a circle (:0o zz2kvxo xv;t*wy
(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 kgnr7eb)t i:af) (including the driver) crosses the rounded top of arnt): ae7b) if 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 we6 xe3p+tx8t:geoul km0 w 8,uould a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” u8:l o 0xw63mtk,e+ugtxp8 eeat the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circl45 yxf36)avri w4 qx3mhyecu) e of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N3x)h 4vm5a yrqfieu6y3w)4xc.
(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 from 4c( kj)fd 2+ oyg+nmcq(3ocerthe axis of rotation is to experience a j3coc o+k+4mq(e( crn)yf2gdn acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at sn :ubr-:rfp ;vb3j4ma carnival, people are rotated in a cylindrically walled "room." (See :pf3 ;n4r:sbbv-jmru 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 air-h7v ok-akw/:ileluk- ov9 5sk6 ockey tabletop, and is held in this: /kis- v l-e975kkvokuw ol6a 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 9edpuy9+pqo . not ignoring the weight of the ball which revolves on a string 0.600 m long. In d . 9upoyeq+9pparticular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radi6.io 4 qpbavn7us of 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 masseif,nn 2zsh-q/c86d0jnp7 g w50vv rv k/qa)dvs $ 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 evasinq9cfp*xjj tf29h*6wvt dt45kp+.bwg9f lq 1ve 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 o/m)b+:b 5jatpr tcj8q1t( qmh f the net force exerted on the car (by ttt/ (pa)j + 8b h:tqq1bm5rjcmhe ground) 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 accvob*c xjzc s;-a h,;b -m0(vypelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceler;;-,ybzhxc ab(vp o m0s-*c vjation with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m ps;.pi5bz3 j u2 unen9cb je95. At a particular instant, itebs9.nep b9p 5 3cin5u;j u2zjs 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 spacecr r +a c5/bayyjvc--u+xaft 12,800 km (2 Earth radii) above the Earth’s surface if its- a+-acx5 rb/ jycvy+u mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a t4rb1cequ;. y-c b lb; aezf86magnitude of 12;lc-.;f6 zubr 1bqa 4tycbee8 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon')cjk3vlm3 s m/5w as:ts radius is 1.74 s kvs3j:3)waml m5 ct/$\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 samx:7-v21m af8rayr0(p, lyx p eetoo3ae mass. What is the acceleration due to gr0o3px em2 :laaxy7 -,r ryvaeotp(f18avity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,/1hf w:4.zd(yf thefy but the same radius. What is g near its szf1y d(h. htf4e w:f/yurface?   

  Two objects attract kn6 o,g4k9y pfeach other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, atpe0 poka-v-f ) (a) 3200 mkp--epvo af)0    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth ya 0 5xvkka0nkg3avuq8l 000 dwhere thegravitational a3y uqdn5g0k kk0xl avv8000aacceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pack* ;g/m z:tzanued into a sphere about 10m*;/ atgzunz: km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average wk7tl c :4cn6ue/6t*yqo)uyqstar like our Sun but is now in the last stage of its evolution, is the size of our Moon but has yq )4*n etl:6uuqko6/c7 tcwy 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 k lydvaj8 3kl0ncl5*q82 - tytthe space shuttle. Your friends respond that they thought *5-dqtynkcjtv0l8 lkl2 3 8 yagravity 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 atg vshrl2( 48 )j.jfuds the corners of a square of side 0.60 m. Calculh)2lf(v r .gss4udj 8jate the magnitude 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 line up on the same42l lj6nj-*v h5ey;vy5jpfe v side of the Sun. Calculah j4vv 5;l*eeylnj2yp 65vf-jte 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 gravity at ;;9 w zz*m; )rjr afe7jvmlca3oi9z4*k xpwr6the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, detlr ajvoam)x6je7z*w ;micwz3;;r 9 49 rpf*zk ermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knj 6 yks-p* ksx*sal-k.own value for the period of the Earth and its distance from the Sun. [Note: Com.j6yas*--k* ks plx kspare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving hm5d.: qma fm v(q.au0in a stable circular orbit about the Earth at 5q:.um (0d mmq vaafh.a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km at7* hfd-f wyrmf- t6v:6uxwy8bove the Earth. How fast must the shxt6ywfydwhur f *t8 f7--6:vm uttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotatfj*v k5rh7: lqe if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed h7q*5vrfjkl: for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular /qi 5ab tf99;b/oevltjp(l,q “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whi/;,f t95aejl( b9qplovbti/q ch 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 wou52*gv 4nj(pdoh2 xp bwld a satellite have to be launched from the top of Mt. Everest to be placed in a circular oo5bdhw *p42 vnpx(gj2 rbit around the Earth?   

  During an Apollo lunar lan6;oeksrty*9ml ( lx v/ding mission, the command module continued to orbit the Moon a*vtks/ 6 lml oe(9;yxrt an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice tha d6eno1zig6 0vt orbit the planet. The inne6eno1zdvi06g r radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Wz x 7o 6mj*npej*;l9hehat is the ratio of a person’s apparent weight to her real weight *z;x oej 6*n79hejmpl(a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg ausz oh,10 n*.irsmc a,stronaut 4200 km from the center of the Earao, ,u1*r s0izmhn.csth's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consis 0yt1:nqtqos 7ts of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a po0:qs 1y7qnttoint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a i( .801/:5 ctr;oemsmx-n g5 e*hnvojkejisa55-kg woman in an elevator that nh/iec(s0k1mg vo*;rt mji:ex5-. js oae5 8nmoves
(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 sulijzk a v+ 1 nsp(9o*z5gonntb;v-4i9spended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude zvn1+ai9zl osb gv *o;5k pnnij4t (9-and direction)? a =   

Show that if a satellite orbits very near the sumb+/a2( t4ufmwx6t.qps do j +rface of a planet with period T , the density (mas / +sm4buf6.tta(j dowm+ p2xqs/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 oziw4q4 8byb1 zg lx;l:f the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near b;x:zyg84wli1b lq4 zthe Earth’s surface.    s

  The asteroid Icarus, though only a few hundreqjs w4y +3dib8d meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance frojy84sdq ib3+w m the Sun?    $\times 10^{11}$

  Neptune is an average distanc r lzl-y0nq(z. g 5,kl4a29fwzqbevo,e 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 Su 1f bc+m7liup2n roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when 7lup m2+cbif1it 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 about cxwq/4 nbs zaa4f(5l65 .fyvi 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 l -eb 5edau jcwq4fc6jk4s7+ 7jargest moons of Jusf 5q 7ja- b4u6 cjejkcew+47dpiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earnyas7/e hs/r+8.5om hsn;w rnth from the known period and distance of the Moon. +n/.hssmw8yoa s;nn7r5hr /e    $\times 10^{24}$

  Determine the mean distance f9q 4(ee6d ;0gnhjp;z s(ai5.i1a kvobln/n hl rom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io andan e (n1 0n 5i e4ko;l;djs9/(bhih6a.zp lqvg 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 fragments (whb ymy :c;/ v/gq7fov/,mpl;qr ich some space scientists think came from a planet that once orbited the Sun bmv//;o;y bqpf, 7vgy mlrqc:/ut 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 tale describes an artificial "planet" in the form of a ba mgqn8hww/o8w, w2xw.nd 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 ow/o8w mxh,2ww .qn8wgur 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 croswq *t s.b-y7ot-rz6tk- 9rqzgs a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a toz* t-6 7qtr9w- ry z-k.qsgbforce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will u+d etrx aoo8-yr89r5the acceleration of gravity be half what it is on the surfacoryo9d5e+rxr 8 8t- uae?    $\times 10^6$

  On an ice rink, two skaters of equal ma65:lmfx j aj 0l)j)dsdjgrvt 13:dr.ess grab hands and spin in a mutual circle once every 2.5 s. If we assume 0mj)gdfve j3) l trxr6d5:j1: lajs.dtheir arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatmiwng.;.1e/:;tz(b b hpcubzes once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is t.b1i .c g;e/bwut:mb pz n(;hzhis?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direct*l3c 7b dhiy,gxk43h3vzu8qbly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite for hydh,lvcu *i3b4zg78x3 qkb3ces?    $\times 10^8$

  You know your mass is 65 kg, sb :t (+ngw5 (8onboqmwv-3be but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is-8q+wonb btsnv: b mw(5e3g(o the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboualq/ka e2l(b3xk+4w9dunj t ;t 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 dat+nd4k (3x/l2w uj 9a;b eqlkay) 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 vertical loop (Fig. 5–43).x yfszy.b1,:y n**h3yf 9ze yb
(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 aj+* ps1fsh*z*b7kkda25ur.g+ l mq qu planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constant u k*skdqsfhm5 pql2zr7a j1bu.+* + g*G.

A plumb bob (a mass m hanging on a string) is defmrlv--)-k.j e*w 0ga efbdccx)+ ,sf zlected from the vertical by an a-),bmz rgee*f0wf- .cc )xdk vl+s- jangle $\theta$ 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 speedu2d8e2goy fqn2/a7 n y of If the coefficient of static friction is 0.30 (wet pavement)fa uq72n 8y2 nyed/2og, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating9pq8ks*.z w2p1t gbem so fast that objects at the equator were appa8bw.pes* kp29zg qm1t rently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a const5 qxa*ydi27 .+n/f.ndkzf q peant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp10pucl d i:4j*d sr)pk suspended*u i4 dp kp1:sd)j0rcl 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 masknrny7*: mc 0dsive as the Earth. Thus, it 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 exmcrn 0n7yk*:dperience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the pre 5lwpjpo(s 5x5sence 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 bs( o5pw5pl5 jxy 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 sp5+27rvu zn sc04pxstoeed 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 normal forces acting on the car at A,tp s +5z20x r7uoc4nvs 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 Sys;9z0si 6 ouonitem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver o ni9ous;zo06in the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion k59y vff 1ikw(yd*57xx)n lc ojm, is meant to orbit the asteroid Eros atyifjdk no17x9 fxlywv *c5)(5 a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite+w.amr u.i co x+2zw un2brg2w0i3dc/ in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but3o 2zabiw.gx2 wwui./r+rmd2uc+n 0c 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 k7 egu,aso derl5w:/2b4c+8 muk9y:au yy2wv) What is its mean distance from the Sun? 722ra5s8: kwo : bcu9mgyey 4,/+kluvweyua d  
(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 th71fkojv*u3if you could actually "feel" yourself gravitationally attractvhfuk*13 o7 tjed to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a *1nk,q0 cpq2twm ha a:jlry9(distance of about 30,000 light-years ftkqwnmrcah,p2qa* 9:10l j(y rom 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 corners orau( kx0l8:- 0oib ar-pheme7 f a square 0.50 m on each side. Find the magnitude and dire:e7bolmx a- 0up ek8( -ira0rhction 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 kguvx04h.ciy4z -3-zvbuvyr 2*ag q ej. orbits 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 byspu.6 es 8p-xt the tip of the 1.5-cm-long sweep second hand on your wrist ws6 eps-u8pxt .atch?    $\times 10^{-4}$

  While fishing, you get bored and star daclue1efiiwuoglnu++s1 r50pw (x9 .3 *h:st to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.] a+nwfwd + 9u5:oechlix.i1su pe0 3(u* gl sr1   $^{\circ}$

A circular curve of radius R in a new highway is designed so that bjqyb9c 7/04vlo-d aba car traveling at sp9djva 7cq lb0/4ybo- beed $ 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, thw o)hxcl j n)o6.ajys5o7e2d+e Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on thcood)nl yh+s72)w65jj ax oe. e 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 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.$\approx$    $\times 10^2$