Sometimes people say that water is removed from clouh34p8m6vxj sclg cj0)thdes;+ s9,bthes in a spin dryer by centrifugal force throwing the water outward. What is wrong withvxsc s 9em 3dhu+tj6 4cg p,0b;8shj)l this statement?

Will the acceleration of a car be the shljfdym0( fxa*(d 5f 3ame when the car travels around a sharp curve at ( l (*f0f 3mh5yfxajdda constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves ab paqz.k9f(7f4en 0d et constant speed along a hilly road. Where does the car exert the greatest and .f9 eked7 qab(fp0nz4least 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 hill?

Describe all the forces acting on a child riding a horse on a merry-go-rou3u:jix y4ye5fqw yzzf7 01z/l nd. Which of these forces provides the centripetal acceleration of tz1z q04zu7l5x ijwy3e/yy f :fhe child?

A bucket of water can be whirled in a vertical cinp4 -g,a+( hueuqpx lhf -q-3io ua15srcle without the water spilling out, even at the top of the circle when the bucket is upside down. Expla+h-naxg 14ip3qepoql( 5hf -,- uusa uin.

How many “accelerators” do you hinxlf )or3w ;ff3r32have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What ax3 ff33)no;r hr fl2wiccelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig.y;2.zo0cqmgf:3 uat n 5–31. His sled does not leave the ground (he does not achieve “2qnogmayf ;0:3c.zu tair”), 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 rounding a curve at high spe jysy923g8xd ied?

Why do airplanes bank when they turn? How would you compute the baw.ag nb8uw7j /sk3p5 irj5fu m *n;h1jnking angle gifwu/mj5ubsnjn7j*a1r83 w .k; pi g5 hven its speed and radius of the turn?

A girl is whirling a ball on a strgya/ y/zo m;y2 2 aveirmy46m(ing 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 ofm ;6i224emao ( ym/v y/yayzrg the string?

Does an apple exert a gravitational force on the Earth -m3vyuv0( rdy? If so, how large a force? Consider an app 0myr-yv d(3vule
(a) attached to a tree, and (b) falling.

If the Earth’s mass wk jpwdqpopv 1,v k5a4)**l ;nzere double what it is, in what ways would the Moon’s orbit be 1p pv, plqad*j w)ok* k45nzv;different?

Which pulls harder gravitationalbmqe3ls3lu1l ; ;s/jcopn ow5ex.* watr4a2.ly, the Earth on the Moon, or the Moon on the Earth? Which1ls* .3l;smpaca5 /;tbr w 4.wu jexq en2o3ol accelerates more?

The Sun's gravitationalhc d9f;meg3b) pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the hm gf9;be dc3)other.]

Will an object weigh more at the equator or at the poles? What two effects aw (,mxt-winr-d;cl h20 s:e iqre at work? Do they oppose erq -, s;n:edwimxw2(ilcth0 - ach other?

The gravitational force on the Moon due to the Earth is only about half the forcds2z 3ge 7k5 wb+ohy8ce on the Moon due to t3wsd+7eh2kob gc5yz 8he Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleray/ tanfb) kv:(9gbb0 rtion of Mars in its orbit around the Sun larger or smaller than the centripetal t :ya90bk()rbgb/ vnf acceleration of the Earth?

Would it require less speed to launch a satellip5 n fd0nw8g-chux /c aky *rabf2. ,oy9-d7rkte (a) toward the east or (b) towarxryn *kkda 802.o7 ,cw--uabyfrgfdc pn /95hd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measosi7bgy8pz;8 f a945rdmspg3ured by a scale in a moving elevator: when the elevatopap84m8db7fzo 5rgg9; yi 3ssr (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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely rn3x1qe)84 kc7 8pwgvxe ly9haffected by weightl3gx rl84cex h1ypn8vq )w9e7kessness. 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. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessn5 byo qi8(f)m j9y8 d fmkn u,dk(g1cx5rlzp):ess” between steps.,x f5pnb8 f(d)kmzqmlcu(d1y:5ryio 9j8)kg

The Earth moves faster in its orbit a ccuj8i-fjh1l z/3fc9+oknb8round 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 c89 h3+-loz8j /fcucnik fbj1axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moo64 sr lwm5z*upn. Explain how this discovery enabled an estimate of Pluto’s m6ursw4*l z 5pmass.

  The Sun's gravitational pull on the Earth is m kf 8,6+ bv*wquw,xnoluch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain.8+*,uvk6 lfw w xb,onq [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 traveling bclpia.+ yvm1z.k5- zxfs)r 61980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 arog7)5acd0ul bcund the Sun, and the net force exerted on the Earth. Wha0d )u7b lac5cgt exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it2*cjx. )* ryb+)cy4miawqpf4nfo7v r rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the v2iyayr *)b)crm4nq w .+fj 7*cof4px discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth'sab)tw dga 8,zg44sw q1 surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer wa 4 zg gt8s4wq,)1badin terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a po/x40smpg4oxd bwta 8+ te s:i8tter m8 ge4d8xtpw+:x ab4i /os0ts’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratz1s1 (w kw /ceae+puh7d,.6d e2 irqele in a vertical circle of radi e klde e6he1qw/i.cw21r pa,zus7d(+us 72.0 cm , 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 wwn* aa-:a4pqjith which a 1050-kg car can round a turn of radius 77 m on a flat road ifaq4paa:j n*- w 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 frictilq9 jxf;e.q3r .amc6 ron be between the tires and the road if a car is to round a level curvelex9r.;3qam . jc6rfq of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fi(23g le69*verfz gxke .q wd,gghter pilots is designed to rotate a trainee in a horizontal circle of rag(fl9e 6e rdzk,*3eg 2wq.vxg dius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of varia-wuu.q2l (l ;qczbj i e,v3gh9ble 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 turntaij.cu;g23 lh(z,-vl w9 uqb eqble?   

  At what minimum speed must a roller coaster be traveling when upside down o qr dyl4xo./6at the top of a ciroy /qxrl6do4.cle
(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 dr8 /p 0e7(4lnjcvi.qugsjdt g2iver) crosses the rounded top of a j(dcusgv jqile0 g. 7p/842tnhill (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 d*s54g z l6pkeminute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weighglpdzk4s6e5* tless” at the topmost point?    rpm

  A bucket of mass 2.00 kg ct(ffe89y zs2bet z;r*sa* 8 ois whirled in a vertical circle of radius 1.10 m. At the lowest po8r;os(eeztf *y2*8fzc 9sat bint 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 rotate6vxrapi( t( j.)dr-fm if a particle 9.00 cm from the axis of rotation is i)(j6xvr r f.t( -padmto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopleqf ;vs39hqh 0q are rotated in a cylindrically walled "roomqq;hs93 hv0 qf." (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 o; 0gsggwzrr 4/y 7c3nrotated in a circle on a frictionless air-hockey table0gngr;zwco3s y4r /g7top, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 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 ignorr.w 8 :a(j okkvn1tor0aoi*j;ing the weight of the ball which revolves on aai 0*o1k;or r vn o:kjt8a.wj( string 0.600 m long. In particular, 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 radius of 88 m is perfectly banked for a cankjim)r- /3du r 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 masses 5 ;hio*wr sr0qbii30x2m ql9al3zi0 r $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 3pus ucj+a;0pyhq) y6 .10 $\mathrm{~m} / \mathrm{s}$ . 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 onm hp* 0.cvkwk1m+gjqx(,;okrb 5 i( rv the car (by the ground) in Ex 5(j+rmm*, kbiwkc(;q. 0vph1 orgxkvample 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 uniforml/qopkg uw)yot,i;h,mv: b*r(0er 7 lry 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 acceleration with no slir*lm i/wt) :er7yqo;o vr,hb0(k, pugpping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular i6:gxvq r3f k;enstant, its6eq3;g xv:rf k 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 gravkjkn p*bwat .2h*u,rzj)1r3 ay- t) odity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 k*3)*oka, 1yn kp.hu2rj -b)zdrjwtat g.   

  At the surface of a certain planet, thyeh ekpei-t:w *vk o/;wd ;3i3e gravitational acceleration g has a magnitude of 13;ywvt /-:keie i 3edh;pk w*o2 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 accelerawfa1e ayn.k8sj/i u *5wj a8z45zqc6l tion due to gravity on the Moon. The Moon's radius is 1.74 .a iln* 8jw f1csa ka8uzjw/y4565qez$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hauov) vn b4d34 )f:g fuyel0jk2s a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to grav vv o gnkdf0u2 :ufby)4)j43elity near its surface?   

  A hypothetical planet has al20vwg y;pd( ml5b+zm mass 1.66 times that of Earth, but the same radius. lp+0 gzvw dblm5;my2( What is g near its surface?   

  Two objects attract each other gravitationally with a force of we95q nce: m2uv4wdgmz5 1d a02.5$ \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 32jk3thdse1 *ej* f82ukl tihvalue of g , the acceleration of gravity, at (a) 3200 mj t* ehtule8k*ihfk1s2233jd    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’ u2)f74gsfxgw p/1fol vw/zi2 s center to a point outside the Earth where thegravitational acceleration due)w7 uflv2 4/so 2gff/xpi1z wg to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the masv hmz)u9 6eri0s of our Sun packed into a sphere about 10 km in radius. Estimate the surface )u9m 6vire0hzgravity on this monster.    $\times10^12$

  A typical white-dwarf star, whicqd .hjt8g;wp+ xrl (1jh once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surf gj pw+l(dxh1r.t8;qjace gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbit6:lq/cr 6fz sg 5ao5e7tpjdx 2ing in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calcu5o/pldsj:6t gq fr 7zce a265xlating 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 pj4c. ib;02)pc jcg ngweb c wq57i6s+of a square of side 0.60 m. Calculate the magnitude and direction of the total gravita.jwb cwbp;pc465 n)0q + g7cegcs iji2tional 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 same side of hyj t+b q p.8j-vg)/althe Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assum+l 8y-)pbht g.jq/vja ing 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 a)31wi*d ujjdd t the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 340ijd) w1u3d dj*0 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eartdk4q/ :aqgg hxn2dr46h and its distance from the Sun. [Note: Comp4g6 4rkqh2dndxa:g q/ are your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stablm9 8eagl /bbj;vasd//e circular orbit about the Earth at a height of 3/sj8;b /ab9lamegd/v600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abo( l.1ayw7m4 am-gr/ 4xtpo znpve the Earth. How fast must the sm 1/ wp44n -pxlmgr 7to.aza(yhuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceqdz7(vw 8u zme45 4kd. 3jilrvship rotate 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 t zj8v 3d7vliwd z5 u4q(4kmre.ime needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes fs)5sj nwu es6mpl0.)for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth)s)s0 w5.e6mu f jsnlp 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 the (s8rw x)g 0bj(, yspkqtop of Mt. Everest w (bry0p8 ks)j ,qx(gsto be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module coa7 ;4czyz rbb5ntinued to orbit the Moon at an albz75 a z4bc;rytitude 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 that orbit the planfqhni u a0anj7 e974q8et. The inner radius of tf984quji7nq 0anhe 7ahe 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 F:w,1epcft- x aig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) c efwptx:1a,-at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centejvz7+f u dh3g9r of the Earth's Moon in a space vehicle (a) moving7jgfu9zv h +d3 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 u7scfv-c+) : 5 gqidwptwo stars of 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 is the m psgc:7f-v5wcu+ iq)dass of each?    $\times 10^{29}$

  What will a spring scale read for the (obz(z sro7+0 6)ubgqi9ug qpb ex96a weight of a 55-kg woman in an elevator thatpsb( q6 uxz +7ob9(q0a6be i9zrogu)g moves
(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 el*pj7m oma47mx evator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates.7*4ammjo7 mx p What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfacbzlx9c 3 v/oknw/4w+ je of a planet with period T , the density (mass/volume) of txwv/+4/3ojw 9lzb n kche 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 (ic) +m*wcs vx nk oze3v)f22r;j9 )ieexc +;bs27.4 d) to determine the period of an artificial satellitevec2i3fzxs9s* )ee vcjbx rwk nim)2c+;+ )o; orbiting very near the Earth’s surface.    s

  The asteroid Icarus,)4yn6svjjz2p8ja ktq; 7 gyf 8 though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fqtjv jj psn2ak48zyg6f7)8y; rom the Sun?    $\times 10^{11}$

  Neptune is an average distanck.mv*( kufl7p -xoq: xv4h qzvu w163*vy:wmye of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. Ibs95cnf m. r7yt comes very close to the surface of the Sun on its clbf5ysm9 rnc7.osest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about;7iongi,x 2t n 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, peri) n4rjb303kzdj7rm k tod, and mean distance for the four largest moons of Jupiter (those kb3krdtz)mjn43r7 j 0discovered 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 ofawim-(ldv r6r kyc,a64pt70 h the Earth from the known period and distance of the Moon. ly (kacdv7ar0w,ti 4- 6rpmh 6   $\times 10^{24}$

  Determine the mean distance from Jupiter for ea6l)n;hek-ls er(4h v h 8ikf,tch of Jupiter’s moons, using Kepler-k)hi864n v l skltrhf,(ee ;h’s third 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 consists of many fragments (whicqta)b ;ro+z/ oh some space scientists think came from a planet that once orbited the Sun but was dqoz b/)ot+;ar estroyed).
(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 "plazye1l2qit g3yx1v*,2k:e / ag vowv:tnet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants li:vzy *ltgeva:/ ,wv2qy12 itex3gko1 ve on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging issd2 - :+fcz 6jhjbnq,n 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 lowest point of his swing? His mass is 80 kg, s2dz :6,sqjc+j - hbfnand the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratqk5 u5*hq9xi(h ,dks tqi(0mj ion of gravity be half what it is on the surfac50d*5mhui,k qhtkq((9q ij xse?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spivv3/;hy ktkozb q .ah,mh+4 (zhpu)(rn in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m arzy(h3m)/zpk b4 v;ho+hh kvtqu,. (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 apparentk79 zgf56je +qkjgc(k acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude ofqkjg(e6+ 5 fgzjkc7 k9 this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly v7 uolg h*5fsn)tzlw6kd *w 0;from the Earth to the Moo*w7n;wlvdt)gso5*6lhuf zk 0n experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass isw;2o mpapv/r 3 65 kg, but when you stand on a bathroom scale in an elevator, it says you;rvp /w23ap omr mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statioyqn.ds7c.q )cn consists of a circular tube that will 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 day) if an .ccyn q.d 7qs)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/ wj, ko7:lllk kjeas-d( 9s4x. 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 ra .q3kmiq05pho dius r, the acceleration due to gravity at its surface and the gravitational coqhk3q0mo5p .i nstant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical b)e k-do4.wpcy y aeypc-d .wo )k4n 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 fo/hjj: irfb k,3id;84yplc bk a-)a1v nr a design speed of If the coefficient of stapj8kr b i3y-;cbhj/lk,4 :ifa vn1)datic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth werj4pfi a47q7ll e rotating so fast that objects at the equator were apparentlyf7qjp4l4 7l ai weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of y5/uan (*m95 sqpdqslvar( gorhub v2w 1s)/4 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 rsq4okwvy4)4 o b n0zw7-b/vg2xsq ye2adius 235 m. A lamp suspended frb442 e -/nyws7zxovokvs q0 4gbwq )y2om 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 ,cbv2asbmtq6r t9y de1w wd10*l-9pa the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupitq619l1 wdsc m9pv debw2b*ta 0a,-yrter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Span(qy( f3fanwu 7/ yto +cs*;ifce Telescope deduced the presence of an extremely massive core in the3fsc iqnf7o(ntu y/yf;*+( wa distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as vzh 0f(l9e l-pit traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) H p9-(lezl0fvh ow 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 with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a grlk1(bn*;x szdec6dng* y/;gbp 9qnm1 oup 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 n q;ynbm9gbd*l xn;d1*s1c/gz k6e (pcentimeters. 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 8 kyx+fq*nxn. Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abouty q8x k+nx.nf* 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 pursu(u4y,*u ke;v .hkismh ing a satellite in need of repair. You are in a circular orbit of the same radius as the sak(*.e, 4h;vk mu iyhsutellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance 2 rr; anr6c: vkcwc*g5from the Sun? r n; :crk5 *vcrg6cw2a  
(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 coul7/6io2xf ta jn9u.k oud actually "feel" yourself gravitationally attracted to uxtjno. 2u6 9afkoi7/ 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 dist:j5 7bduyek)* ppoc0lance of about 30,000 light-years from the cec*pyblo0:p jk d5)e7u nter $ \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 0.50 m on e8mj hua ha6 z/h*pts09ach side. Find the magnitude and direction of the gravitational force o9j tp6mza h 80/hsa*hun 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 yo*halec5 n: *the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5n3vnw uzu *(9aqgo*d(-cm-long sweep second hand on your wrist 3 *(z*aqu 9wn(vngodu watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circcw/7i ,e gyqllj8 qu**le below you on a7ywcqu leqj*l ig 8,/* 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is hwqt:ye zhv 3elco-+2g(d7h)designed so that a car traveling awg- zce qeth+hvo:l ) (hy372dt 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.xr w ;kcqjwo88;yim8 of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force ne.mo i8cxw8 8y;qrwj; keded 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.$\approx$    $\times 10^2$