Sometimes people say that water is removed from clothes in a spin dryer by centr8nxs0v 4p tb6frbxkz85q 40hoifugal force throwing the water outward. What is wrong with this stateme npkqzxt4v r84b 8650h0b foxsnt?

Will the acceleration of a car be the same when the car travels around y6tzk 5t-w:by uh: 8uult:.wpa sharp curve at a constant 60 km/h as when it travy bt:.tuput-::568zlkyw wuh els around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car nzel-1d9.k -5kp y uajexert 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 1 5an-zeyup-.jlk d9kof a hill?

Describe all the forces acting on a child riding a horse on)jq7:2n)ioqyvfqg3iy p(qp ; a merry-go-round. Which of these forces provides the centripetaly q27nq f):)3( giqivp ypq;oj acceleration of the child?

A bucket of water can be whirled in a vertical circle without the war0rqb,0 tovm/e 5ofzy226 dz.l e gd1ln,si4kter spilling out, even at the top of the6d5r 2zze0rl14i/ .f2e sdlkvn,ob g,moqyt0 circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are f3qkb vwd 7r,r4 0cy;jat least three controls in the car which can be used to cause the car to accelerate. What are they? What accele;wd vqr0,c fkrj 3y7b4rations do they produce?

A child on a sled comes flying over the crvfpp53o* sgi0sl9 af+ est 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 decrv3s gf 9poia lfs5p*0+ease using Newton’s second law.

Why do bicycle riders lea8ubnc yl jc0 4/146gzrxcpw 2yn inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking rf*+ l48 /4gnnx2ge qdggod.uangle given its speed and x/dgnfrguqe d.og nl82g 44 *+radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.au7d sg9m4+ rb 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 s4 9u b+rag7msdhe let go of the string?

Does an apple exert a gravitational force on the Earth-+8mfn- vuubpc0vd-6 d,k agr? If so, how large a force? Consideg 6 kn8v, ruu-p0f c+--mdbdavr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s o+2atwr1uu2n2* olaj)3k x oo ozr)-a yrbit zkaouou t12woa)3 -rrn*xy)loj22 a+be different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on 9x+dkwa/q jcd: aei 45the Earth? Which ke:c+ i5/qwaa4 d9 djxaccelerates more?

The Sun's gravitational pull on the Earth is mhj4+fc;.hgn pu wv65* t6gsis uch larger than the Moon's. Yet the Moon';h j66t . s5+s4fg p*hngciwuvs is mainly 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 equatorcan3h dt+bft, /:i pqh8r ni*/f-1lkw or at the poles? What two effects are at work? Do they8rf3 n/+-tcibf* a ki/1:hptn qhdwl, oppose each other?

The gravitational force on the Moon due to the Earth is only about half *)mr tkw9mbo1 the force on the Moon due to the Sun. Why isn’t the Moon pulled away mt)r1 k 9mbw*ofrom the Earth?

Is the centripetal acceleration of Mars in its orbit around e7yu0ylwhz m/ j. t0q9the Sun larger or smaller than y9zuetmy q00hj 7l/w.the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towarii 60bm7hma6 rd the east or (b) toward tm6b6hai7r m0i he west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as meam**l1 wp2 s uf8pxc;wgsured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the grou8**w1xw ugpc2p;m lf snd?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods2vc ).ndj1sd4nk9 swf in outer space could be adversely 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 hs12.knwfn vd9 4)dcsjow 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 experiekh v3 3nxbhf9.k27h pmnces “free fall” or “apparent weightlessness” betweembkh339xh27. p vfhn kn steps.

The Earth moves faster in its orbit arob7k ,dzysgv4-qpc6 ;e und 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 thp 7y4ekq, 6sdv-;b cgze tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discove zop3rs9 hz/;fred to have a moon. Explain how this discovery enabled an estimate f z/93 pz;rohsof Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the ea4a6h256,u9w v b orgksj8us Moon's. Yet the Moon's is mainly responsible for the tidesu,s jsk hgor9u42ewv b6a6a58. 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 travelingour- . dn+rb1b 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 centrim8ti8 ,r.q pk4x bzwb n)gy.,mpetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this fory.mq8 kxiw)b rg.,8n,bp t4m zce 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-t 3rrk,6aif k3r 0xdn.kg discus as it rotates uniformly in a horizontn3rrfa,x03 6r itdkk.al circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surff .4 p dlx/cq.6uqqrv;e)t ww(ace, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational accelerawc uqltvr(q6. )dx/ ewq;p4f.tion at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on thk oagusc( .54be edge of a potter’s wheel turning at 45 rpm (revol4 s(kugoc ba5.utions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circlw/cgi+phh u5t; j /th7e of radius 72.0 t/+j57pg/hwi h;c u thcm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can 93fetq12sd hf*3zk me round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and r etshq f921k*z f3md3eoad is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the we3h5wovl 9yf6z:l3jtires and the r6wef 3z39hlvw lyo5:joad if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronau6fftq u:;i a;ufbsd2: hkad0 2ts 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 7.0h:2:6ud skatbda;u f;i f2fq85 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 axi,+zicw p)qdp, s 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 copd iwp,) cq,+zefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when qcgfxf 3sf,e 0 3edz 8gj2yf.+upside down at the top of a circlqye exdjzf+0g33g., f8 f2scf e
(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 roundebp ny+lyr45fe*z t* 0bd top of a hill (radius =9 5nby +4bf0tle*y*pzr5$ \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 z0q5e66(e1 dzo.sh kp-d dgepwould a 15-m-diameter Ferris wheel need to make for the p.p6zz51-h s6dkdq(oe gedep 0assengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.0 wu tpydht ,bk+ *u.nx*k1;,py0 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportingbkt,. +1,d pwh*p txu*;ykyn u 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 from the axis o96+don wrv28zdl) ycpf rotation is to experience an acceleration of dz9cv2) +r w8l6ynopd 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cqtpm8)*et6qf)f e0a rjg1*+x8xjp ti arnival, people are rotated in a cylindrically walled "room.ai t1q jme+t8fp)eq8f*xtx*) 6grj0p " (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 ak8+lfg ;i hox l/u1k z9aky*m3 circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blocloxiy;u *kl/hk agf+mk z1389 k (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 thmrcq/8ryo db7qp0bf, z. ;l.fis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find thfd,ymlq b.o8 r7c0f./r p ;bzqe 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 radius of 88 m is perfes5pptyvp .jpe5+-5 vzctly 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 massess57b/8l0dxp nkgdo)cho2 5 ih jsw:k + $ 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 dii:bb3gw7 8 4g t5k 9x5zqyjkowving 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 the net force exerted 2l qlc/au56iaon the car (by the grlca/5 2luqi6aound) 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 th 5afvkh:3lr;;wfb to 8e pit area, going from rest to 320km/h in a semicircular arc withal5bkf o8;h:t;f3rvw 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 acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partich,b jyjm:j4iu.a:7lxd. :hb m ular instant, its accelerat:7l. :4 ,y:ja.mj hb udjhibxmion 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 4)ylf z yg9iwx2gj/:atlae 7* gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if it/ 7jz)t *w:llae yx9f2a igg4ys mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratio-9d4nex h9zzq/uk phi1rgm;7 n g has a magni/ze1mqhixd4-zk;9u 9 7pngh rtude 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 grav3g 9k1bf:ic ovity on the Moon. The Moon's radius is 1.7413k vcbo9ifg: $\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 mzg7r10u wu(srzwt;et.c ( 3xEarth, but has the same mastwtw.71gzs3(z(x 0m c;ur ur es. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of E8- 6l d 4u1bs3mf:qmk3eqxcxq arth, but the same radius. What is g near1 :xsqmu-km3qx4d6 lqce3bf8 its surface?   

  Two objects attract each other gravitationally with a forb2i/5 o yaor3k 7fv+vxce 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 accels6cld4 - hmy2ceration of gravity, at (a) 3200 m 4 smhl6-2cdyc   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from t yyn0qv kz-(g1cry i,(he Earth’s center to a point outside the Earth where thegravitational acceleration du-1ycnqyiv0z ( ygk( r,e to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivrq)z8 ysg)6pse times the mass of our Sun packed into a sphere about 10 km in rad6 ) pzsg8rqy)sius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an aan.; r i*(ipawverage 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*;rpi(a n.aiw the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiti./ fx pm 34qpuyg,ow4c- (cskfng in the space shuttlm4,p/ cw(43kffsox qpy cgu-.e. Your 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 corners of a square of side cr/u j( rja2j.2jup 2-1ltif 1)xmmdl0.60 m. Calculate the magnitude and directionm2r(1p2ll jcr-imfj ju )1tadx2u /.j 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 sz. b8h2bx 4eyb-vd :elame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets leb dvxe2y.z -:hb8b4are 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 gravitydb6 +, j7+d h/yj)wk,uwbjwuo at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determineuy+bj ,dwj w d+b7/6,wjo k)uh the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for thzp)(k sjkbv:ah )agm3 tgb4;2e period of the Earth and its distance frok ;)3k gat)bbm(p4j: hg v2zsam 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 abok /m3o. w:xnk(uabf9 vut the Earth at a height of 3600 kmw9v:k3m ao.uf b(xnk /.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km a09nqu+h+ trbe-njd1uwo2 8v 13 yolvpbove the Earth. How fast must the shuttle be monu20l+o b1 -y j8uwntpvv+qrh oe39d1 ving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if ocd h n)-7mrfs9p3qa4gj o)9eqb cupants are to experience simulated gravity of 0.60 g? Assume the spaceshi 9f934jsqh pro edm-)7 qbg)anp’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 circular “d; ast*d dm (ey fq)*itry*2j7near-Earth” *d d;j aseq r7t(i*ym2*dyft )orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to b*lle d8zh9) )t+ojoebe launched from the top of Mt. Everest to be placed in o*eob+ 8)9elz) dhjtla circular orbit around the Earth?   

  During an Apollo lunar landing misq n+4um n5y:yesion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take :qyne y+ un54mto go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the1qny zdj-;p u- planet. The inner radiu-p y-qz ;u1jdns 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.y/v yc-9qrf wz*e q+8q 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bott/w yz9r8yqq f+ecqv-*om?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of the ,egc-m na* uw/yda7h(Earth's Moon in a space veaa /,dmycun *h -e(w7ghicle (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 kruehe.i):d rq d(20v equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What i2ruk(eir d:v eh) dq.0s the mass of each?    $\times 10^{29}$

  What will a spring scale (ulw5yp8m1pgud r5;* xos x7u read for the weight of a 55-kg woman in an elevator that mu*7 p 1pusw5;(yru xg85lodxmoves
(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 elevato+jqhd 3v/9gzcr. Thechjvz3/d9 q g+ cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet withope051 ry9bynn ;es;h2qg 2kl period T , thee 1ny2 o0kng he p;5y;q9bslr2 density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine ttael;b4 3c.yurf7 o 7ihe period of an artificial satellite orbitin37utlr7cbe4. iya of;g very near the Earth’s surface.    s

  The asteroid Icarus, though onl-p4 js gg5c3vwy a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from thepc-g4v jw gs53 Sun?    $\times 10^{11}$

  Neptune is an average diofn, 2 (aw5x xs*yozq)stance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun v)yd(kd:rmel5. sqz: 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 it is out there? [Hint: The mean distance s in Kep( vqd z:5.mderlky:s)ler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about th+cktr+2r0s.yb)m 3jq 8+q alw 0nhvjw4q xwu,e 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 me+glssy5( o p2s8 .zurpan distance for the four largest moons of Jupiter (those discov ps zy8p (os5.sg+ur2lered 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 fuksl5*v 0:* lfaxjt 48a4xwo urom the known period and distance of the Moon. fs0:txwv ua8ka4ol*5jlx4*u    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,yd.- *sw psey2 using Kepler’s third law. Use the distance of Io and the pes*2w-des. yypriods 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 consiak. m5 rz f dpx,q.nb53/1wpdqr.ez0usts of many fragments (which some space scientists think caw0qpp31k ,n/rb dzex5a r.5f. zmd. uqme from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in tiwjt7+ )0 f;v8fhrzfthe form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distancezj);t0 v78rihf +fwt f 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 s9j i1d v-, qbzidq eodm,+v(nfe 55op;winging 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 max-(q5e+ o5bfdi, zvqmen;1od9pj,ivd imum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration ofuho)po gg)6 b. 4i,k: lbsavki*ty).a gravity be half what it is on the4 o:6 l b)t)giubiyov.,g.ka ps )kha* surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab :yaq x 4rqu+,gbe* p0rhands and spin in a mutual circle once every 2yb4u,rrep x*qg:qa0+ .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 one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accvhz:c r1fmx. j:hw,x)eleration 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 this? :h.hj,cwm1 rvzxfx):   $\times 10^{-1}$

  At what distance from the Earth w topyjsy2s k:qu.b44 7gj7:ze pxzg:0ill a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pj.2 u4jbz: q:0gp7s g:py4se xz yot7kull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an lrfgrq74fhrbgh7u*.0 w:i e. elevator, it says your mass is 82 kg. What is the acceleration of the e.eu:r*gl b4fhi7fr7.g0 hq rwlevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abourvjelch:* * ,wt 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 day) if an effect equal to gravity at the surface of the Earth (1.0 g) isv, rl:*cweh* j to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lob5zt r 2)w1t6vcca)n yop (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 hv 19/:z wvlxvthe mass of a planet in terms of its radius r, the acceleration due xv/w19:v vl zhto gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on4(+(tyuw(xbthy xoj *4f itf oj ;gv819dsq5z a string) is deflected from the vertical by anyqoy4fhifo(jsv(w;5+ u t* gx(x4t8 t 9zd 1jb angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coy:o(l uk (hz3v-en1t . tnks3yefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle 13(:u lso .yytvtk-3n (nzhkethe curve?

  How long would a day be if the Earth were rgkgt;w9 n;aq2asb6/ qotating so fast that objects at the equator were apparently we nt;9 /bs6ag wk;qqa2gightless?    $\times 10^3$s

  Two equal-mass stars maintabnpfp*rtt waeb m1 /d89 ,o;a:in a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve 9ldxxvzcw) / lp2*8sg, g3:ird)d dz jof radius 235 m. A lamp suspended from the ceiling swingwg)9j:v83/xdg* lpil czds , x2d)zdrs 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. Thr) 4fp hls,.cvg,w f8+hhj6acus, 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 ths6,rw+hhg h fpc,.j )lv4c8 afe number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced th*j h 7kylt**lojv/ -phe presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (froh**k* -tljpvyj 7 hl/om 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 vallel o.x wum0o,(vy shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact,ovm ow.x(lu0 with the road at A?

  The Navstar Global Positioj d-zas32tgk .ning System (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 satell 3sgztj 2-.akdites 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)b 4xp6s* jw,xz, after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros x*pwj6sbx,4z 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 pz2 l8ls5uj+gsatellite in need of repair. You are in a circular orbit of tus 8 j2+gllpz5he 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 (*nf/jivzw2 pm:.ldg 3000 years. (a) What is its mean distance froiv *m jfnd:/(pw.2glzm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuallu+h+pdqko,x, g5jxk979es, rftwr x7 y "feel" yourself gravitationally attracted to someone near x 77+,,tds9xkwfj+xk,gu5q9heo r pryou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cezis.5n7uy 3ronter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the s yiu3on5. 7zrcenter $ \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 of a square n zh ce0d. 9li(c*a1th0.50 m on each side. Find l(at0d9hhiezc .1*nc the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits/n1ghwu 6hia ()zx9x s 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 byfm j:x ((y9;h4 m5ckrr/bn bxu the tip of the 1.5-cm-long sweep second hand on your wristcuxx(b4mr5b9/r y:m n(hk jf; watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around inva 0dmn,76mn z a circle below you on a 0.25-m piece of fishing line. The zda7nm,v60mn 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 carkpa; 2gxc*+g t traveling at speed ;g pt c*axk2+g$ 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 Acelu .-:3njveca7+ykd lea, 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 e evjc.l ea-du3 :n7yk+xperience 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.$\approx$    $\times 10^2$