Sometimes people say that water is5vldsvgmlha * 1fu,e v-7n7p4 removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stateme54e*n vvll ,-vup7d7msf ga1h nt?

Will the acceleration of a car be the same whe bsbi, **ly96av4 w :hqyxlea4n the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at thehe b:6yw *sily4b,* v9aalx4q same speed? Explain.

Suppose a car moves at cons thwh l4c z7gpa9a0bh2f h;0t8tant speed along a hilly road. Where does the car exert the greatest and lh 97afpt ;40 hacw8bglt2h0hzeast 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 h. ,(lym g8 zm08somyfrorse on a merry-go-round. Which,.ry8lf m0m8 ms z(ogy of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle witho3n;qhx;kt6p5s- u )cv .tmafwut the water spilling out, even at the top of the circle wh n3wvf kc 6.tmh ;;q5)st-xuapen the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at eq*6qi-ap7eq tl:i o.xcln0yzu 2t1,least three controls in the car which can be used to cause the car to accelerate. What. ,u0ai1l:7tyqz6e -x*onep q2 itcl q are they? What accelerations do they produce?

A child on a sled comes flying ouy rdaa2wh,g 2c *58hxver the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force * h8ayxdwuah,c2g2 5rbetween 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 a6u6g; rpzm1pix z whx4u9d o /x5jwu3sc 234upt high speed?

Why do airplanes bank whe(ap 1jhc8mlbi7j: f*h n they turn? How would you compute the banking angle given its speed and radiuj7 hl:fj1bm* 8cphai (s of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.o y4h caq ;-g)crlhka1q// vn* She wants to let go at precisely the right time so that tnqchrhov;k /1l4g-y/ *a caq)he ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitati)9yv s tc-+alional force on the Earth? If so, how large a force? Consider an applva )tc-+ i9syle
(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 orbi pj qaak4nhsg d ;,o0d87oq4n-t be differen oja kd748pshnqgq-; dao0 n,4t?

Which pulls harder gravitationally, the Earth on the Moon, or thp 0jhveh b.50,i h rvdfh/jn2)e Moon on the Earth? Which acceleratfrhhbj0nh2/p5ivv , 0h. d)ej es more?

The Sun's gravitational pull on the Earth is much larger than t.hxzn ;g7muxrd418iy he Moon's. Yet the Moon's is mainly 8g;1yi7xu4. rxnmzh d 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 equ+ i dxea5wkn+2x*)rimator or at the poles? What two effects are at work? Do they oppose eachadn)2i +i*xkxmr+ we5 other?

The gravitational force on the Moon due to tnf2*q o-5 tpaohe Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the -5fqoo npta2 *Earth?

Is the centripetal acceleration of ba(wi:wxr. wt+oz)8,do;s rnMars in its orbit around the Sun larger or smaller than to:(ab )nrdw . oxztwiw r,s+8;he centripetal acceleration of the Earth?

Would it require les txlq;jj)dl-; s speed to launch a satellite (a) toward the east or (b) toward the west? Consider the xtq;-ljdlj ;) Earth’s rotation direction.

When will your apparent weight e,y bayy -m(5mbe the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In whi,-ay5 ebmm y(ych 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 spaczsgcj9beb rx;2al/2 )e 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 bjzc9g;xbr )2lea/2 s 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 “freeyp r( o9rnib2u9jk 4o5d;k;jm fall” or “apparent weightlessness” between sb9kj2 kr; 54umoiony( dp ;9rjteps.

The Earth moves faster in its orbit around the Sun in January than in July. Is .zo* nu;wl*rn the Earth closer to the Sun in January, or in July? Explain o.u;zrnw*l*n . [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovesv 3 74zpqw g-g3htz1gred to have a moon. Explain how this discovery enabled an es43 7h 13v- wgqgzspgzttimate of Pluto’s mass.

  The Sun's gravitational pull on the qt*g)wg j)ft+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 other.]A child sitting 1.10 m from tfqgt )) *wtg+jhe 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 1980o)z cr:;na z3y $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripe gmill )ne-8qko7b 2r8tal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this forc8k q-i27 erlogbnm)l8e 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 di 10,r23yij o;asxm*dh8ea ilpscus as it rotates uniformly ; al21hosm i3*ad8jy erx ,i0pin a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbitwohg 5v5y0qrc 46)4 k g;mu ecbcbs4*i 400 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 terms of g , the gravitck5* ym 64r;u5 goq0cgbw h)bciev44sational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of thqk+8 f)/-dhhlf fk(d6nf+ :7frve ekhe acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per mel(f rfnf fk:vh +) 6+k8f/hdkdqe-h7inute) 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*7defo wr+0el circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4+*7fwe dle ro0.00 $\mathrm{~m} / \mathrm{s}$ 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 mmg30jhv2 jf c: )ppe,b02tj1yvibt 3round a turn of radius 77 m on a fly2b)jj0e3pctgm2ft0 h3, i:mp v1b vjat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static /1szys5o g ybg8m. lspbnc2uv3:o;p 5friction be between the tires and the road if a car is to round a lu ;s3mb28pygsypo./o sn51 c:zbl5 v gevel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilsr* .htko.783j5:rtozln sf91zs u qsvi/c . vots 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 sh9izv1f:8to./jhcq7vur ss5s tzokl.. s3 n*re 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 variabl n4,c3.zvo::vb opaco 9o8ex le 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 aze3:ox4c 89nv l,ovc bo.pao :nd the turntable?   

  At what minimum speed must a roller coas6/lotjyk f*bqd4 wxj k,fc+/3ter be traveling when upside down at the top of a circl x4j,l+bkf 3 jk*ycw //q6odtfe
(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 (includ4-b, pq /hrdnding the driver) crosses the rounded top of a h,4 nrh pd-bqd/ill (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 would a 15-m-diameter Feo 0.l,92ror yovy ndc yd; 2+9i(sjchtrris wheel need to make for the passengers to feel “weightless” at the;.2t9lds,o n vdccr 2jyyhiy+0o9r (o topmost point?    rpm

  A bucket of mass 2.00 kg is whirled i(btxbs* bzvv4f,y h w7r2 ,2yhn a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 Nhtz4yh,vv2 ,rybbfw sb(2 x7*.
(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 particl3gx5 tz)6( vgyxti1c ke 9.00 cm from the axis of royx1tgt6k3gz xc)v(5i tation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotag z.vb2s)6nxjtg+h1 gted in a cylindrically walled "room." (See F )v tsj1ngxbh 62z.gg+ig. 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 cvvy,,f6fp e5zog 8c(d:bd)ag mla)d*ircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as sho,gz*d)b6fdy:fvpecd8 l m oaa5v,g) (wn 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 ignor*p y+*p8je4fcp km+a4mmpt8ljx r); sing the weight of the ball which revolves on a string 0.600 m long. jx4pk+js;mmp8 a *e4t+ f8pmc rly )p*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 trj, :o3uw+sj88 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 masse-)ndmg j7byh 1yqhn1b0 vu;,es $ 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 manwlt2-e8fi1. kk doq tie(zsu d71bg*6euver 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 a :cy4zdu:: wt-bfhx9cnd centripetal components of the net force exerted on the car (bch x9u4czf -:b:w dy:ty the 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 Indianapoli;4i n p35z-k6rml)srr t eb)kzs 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Drk se nmt-zzk4);)6l pb3i r5retermine 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 mpi5m5hv-)ha9 *r0 lsmebfv6 2.90 m . At a particular instant, its acceleration is 1mbli*6 -h5pa9evv)mhf0 s5m r .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 efv(+e:o 4a0mt s-f tu2f o.-vrxupj*of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass isr*ve -j -fmavxt(u4 :op+2f.uo ts0fe 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration j(wg :-a x69dpb if-u7 tvxu4ug has a magnitude of xbai ( g ut-9:-j pw7f6xu4dvu12 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's radius is 1.7d u/k*07ucfs+6m dhi ccxb 4b04 /c4uud0 c7 f6id +*bkch0xmsb$\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 has09x3,2kg2 6 reww. 6 brfou oftrro.ef the same mass. What is t69gr,2xwr2ft owo3 er.rubk 06.of fehe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that ord2 f(u i +rzrwd(a5+ff Earth, but the same radius. What is g 5frrz( dar +w2(ufd+i near its surface?   

  Two objects attract each other gravit .d.3 vv84x fcbktzak/ationally 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 effectii s 2*mg+hpq,kve value of g , the acceleration of gravity, at (a) 3200 mhi+m 2sg*qpk ,    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from thsbd md j8 3ii;;ln(y,hwfe+v 8e Earth’s center to a point outside the Earth where thegravitational acceleratii ji8 bvy;wh8+3nem(lsdf;, don due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five tru 1xl p4r33ytimes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surr33lry1 uxpt4face gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sta4s;:vp * s 1+tungx9rnbs wsk(r like our Sun but is now in the last stage of its evolution, is the size of outnsu* x p91sbsv:n+ ( swrg4;kr Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlm:(e(i(h9 xpkwc7g9una r 7jyess while orbiting 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 calculating the acceleration of gravity 250 km above the Earth’s surface in termsgx7pn i:uy( e9k9(mjawr h7(c of g.   

  Four 9.5-kg spheres are l*5x+z g*xs)v bflxca7.pw xh4*daqx5ocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exervsxq4xc + g**dh5a xpfxl*z )a5 7.xwbted 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 tt6g .l-a7ewpje bp3w: z4i6lon the same side of the Sun. Calculate the total force on the Earth due to Venus,ga bp:. zp6wt4t7j-e lewil63 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 the surfaiym.0aga; bj2ce of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of M;jg0m.aiyab 2ars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of thvx ,d+r( f ji8-s9 29zwfyabvme Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.] 9v d2 -j(iz smy8f,rxvwf9a +b   $\times 10^{30}$

  Calculate the speed of a satellite mo4t46a,ui +k *:qkrvzrv ug ns.ving in a stable circular orbit about the Earth at a height of 3600 km. qr 6 4kni :4a uz.kvtug*rv,+s   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ea rsgpij 4emlqj 4-5;9*dnx*crrth. How fast must tg p4*msjxijldr9c4q;*5- er nhe shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate ifm8 c72/whzlla2 u)p no,p: yfk occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answ7ol:cz ua) /p2m8nhf,y lk 2wper as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a svb41 x.u c q8euwo)jf1atellite 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 which is very small compared to the radius of the Earth. Does your result depend on the mass of the satwej1vu.)8xoc1ufq 4b ellite?    s ~    min

  At what horizontal velocity would a satellite hapi /w-x /)l)4cz)tt vfvrh mv9ve to be launched from the top of Mt. Everest to be placed in a cir hv )/-v4mirftztplw9v )c/x)cular orbit around the Earth?   

  During an Apollo lunfaq sc8knq, 34dh e(1o63k f;nxberz5ar landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go aroundeq8 3(; a3hxn6of qczs1r bf ,ken45kd the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The i:vjq.g):snna, 9y eysnnya.:n,g )evsynjs9q :er 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 3wkjse7es-kbv1 c7 l/gi,gc4 rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s 3gs,ve7sl g 4kw/ij- 7kcc e1bapparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 vykki);;o8zvln :q1dct0b2 dkm from the center of the Earth's Moon in a space vehicle (a) moving at vt:y 1k8bnc 0 ;;viqzdo2 kd)lconstant 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 s;jup fjl3z., ywhtkz1a :v3o ,tars of equal mass. They are observed to be separated by 360 million km and take 5.7 E lzo.yzkaht 3pfjj:uv3, , 1w;arth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale rei0 ;/d 2rkityy5 /zpkr,1wc 4mz zqo,kad for the weight of a 55-kg woman in an elevator that1 w;zkrdc z4zk yiqm /ry2t,,/0o kp5i 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 cor c3s 5(vtx+tatd suspended 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 accele3a5ts +xvtc(tration (magnitude and direction)? a =   

Show that if a satellite orbit3ug7/x0oulz2te8 lo a 61hrngs very near the surface of a planet with period T , the density (mass/volume) of the planet it lzauorl360g u/8xe 217gh nos $\rho=m / V=3 \pi / G T^{2}$ .
(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 the pewh+f0yz, 0cq 4mr di.iriod of an artificial siimcfh yw,d0q+z. 40ratellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, oplrr63)fhpek5q ,0gx; m 1mbsy u(em 7rbits the Sun like the planets. Its period is 410 d. What ig 0mup6k7pe)f( h;lxm rmy s,eq35r1bs its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanx3(d5/v*nr./jtxa gmhu e p)ice 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 ro :zrc3 wq+5.frkgx*ikughly 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 mw. *+rzi3kkc5gr:xqfean 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 the center 15y; y4w 1,rck/ aos edy z*lvxyfq5s6of 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 dista ;;oo; t zkv-am/angzw+obd8)nce for the four largest moons of Jupiter (those discokn/ wzbdoz; 8)a -; tgoo;vma+vered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period o9:rghb +lal*and distance of the Moon. hbr:l +lg9 o*a   $\times 10^{24}$

  Determine the mean distance from Jupiter fm*.(ct czqh/r70thhd or each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to htm c0h7dqz.r(c*/th 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 cono8zqau d;m,,6ar1 k basists of many fragments (which some space scientists think came from a planet that once orbited the Sun m81 6kq,bra;auz dao, 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 the form of a b- *he*q o3lkghand 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 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 q*o 3gh keh*-lrevolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinginy*q :a,o3edct 7qa 0dntz5ae (g in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of hiqdq* anoa dca7 ,y(3t5e:t0ezs swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hal,i5 r;y( ,zkxbvlzdcbfw an+4fmbb8 :( gb 4f,f what it n,b4(f wmb ;(g:bzcdb,v ff4z 8b a,5xliry+kis on the surface?    $\times 10^6$

  On an ice rink, two skate, xa, hi:6iqxngt.v 8ers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0, ,xgni ahxvq 6i.8e:t.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 accele7,ugthwv7s y51d:mw, p3nnio ration of gravity at the equator is slightly less than it would be if the Earth didn’t rotatw ,hg :nyu,mi5tspn137 7ovwde. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spack;msr og i0.s-u 60drrfkv48zecraft traveling directly from the Earth to the Moon experience zero net force beor8dkz40g6r kir0;msuvs-f . cause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sca-tpl :ppmm hi;dzj4*1 le in an elevator, it says youp p;1*mz pmidj:4th-lr mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate y 4cjokrbl rb4k+5*a) 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 anokya 4l) r4cb*k +5rbj 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 aio0spnev 8k v+ndm +7l(2wbh 0mrcraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for th yun (1q0z0prte mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitationalt1(0n ruyzpq0 constant G.

A plumb bob (a mass m hanging on a string) is * oqyc8yt:v.n*v - ullgp k4p4deflected from the vertical by an angle * tno8q:v g4kvuplpcyy-l.4 *$\theta$ 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 the8q 7v4 sdwq.lu coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car saf7q4. qsld uv8wely handle the curve?

  How long would a day be if the Earth m48 akguv.5vb were rotating so fast that objects at the equator were appgv .kvb84au5m arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.02,s wm x(f7lxt $\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 ra b p*7tgtf3f;kdius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.bf;3k 7 ft*gpt5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 x h1k .qoycc, :rwq68:m ,,xge ulqe,mnt-f:otimes as massive as the Earth. Thus, it has been claimed that a person would be crushed brho:q qu1 m,,6 l ccygow.km:xeft-ne8,:, xq y the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the 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 9w :2slpuk ;fhe1m ddx1d743fhqg7o q deduced the presence of an extremely massive core in the distant galp;d kh f79 h172do 1 uqgsxdfl4:ewmq3axy 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 io 8k;b riq:5bst 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, B, and C compare? (Which is :bbr8k5;s qoilargest? 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 lj az-g*7pqw7e0 .8xnewy9 mugroup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude ogjl-*z7aun9 w m0exq87 .e wypf 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 km, 4 b2p3t(0e)bul12c+zln s getjf;rhf is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 4fl1tb3b4+ nefsj2cph; g 0et2() rlzu0 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 in8+yuis))o ctnny(ny 8 need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Eayscno(u)t ) n8y+n8yirth), 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) Wh0+luea4e ;p jkat is its mean distance frol;+a kj4 epeu0m 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 actually "fet g),rw6kd-wdn.9 mof u1wlesxw0u7.f)qo 8lel" yourself gravitationally attracted to someone near y)8 lunwkxgf.01e t7sf,o rmq-w.)wodd9u6w lou. 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)on;ywhs jl02( at a distance of about 30,000 light-years f;0 (o wjhsny2lrom 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 of a square 0.50 m on each si49z ./t 89ksnjemlrgide. Find the magnitude and direction of the gravitation nr.kg8s/z4m9j eli9 tal 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 /4(kpvoj7g o0pm , irbkg 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 by the ti nkyn:i26 *y-rweoy n;p of the 1.5-cm-long sweep second h-eyn *r iw; :n2yykno6and on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored a1mb rehnafs 5 kmo+(qu j)rpw 03)9kr5nd start to swing a sinker weight around in a circle below you on a 0.25-m piecemw5bk m+9(j5us0 rk)hr1neqrao p3)f 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 designed so rht49 jwc4+;;nde)tdg: 3 mazn ;ekxuthat a car traveling at speed cuz+h;tk9;mn 4 :rexn34)tg jd awe;d$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cvo jv, g/3sp4vars 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 frictiov3j sv/p, 4vogn 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.$\approx$    $\times 10^2$