Sometimes people say that water is .qdz,1rmnfa + removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong witma+zdq .rn,1 fh this statement?

Will the acceleration of a ce -je + tk9yd.4s*fuxmar be the same when the car travels around a sharp curve at a constant 60xj +*se4t 9k- ydf.meu km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed al7c 0zkynsz+y6b0c)4 . vu hguvong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch ne zv 7z vc0u.kbhyg6+ s4n)0uycar the bottom of a hill?

Describe all the forces acting on a child ridicg(g+ d/4781uhtjsklt ty4fd dbo(9jng a horse on a merry-go-round. Which of the4tsc( bd jtg d yo1htl(dj/ g+8kfu479se forces provides the centripetal acceleration of the child?

A bucket of water can be6:n 2n 8ww5tsmnq-gcu whirled in a vertical circle without the water spilling out, even at the top of the circl-su5wnc2t g6m:q 8n wne when the bucket is upside down. Explain.

How many “accelerators” do you have in yo*oyxmw4veqoin *pn59 *a))nr ur car? There are at least three controls in the car which caowp eay5)**xnn4on mi *v)q 9rn be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a s baq8, mt/7+tt ey9jsvmall 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 d mttta/qv 89,s yb+7ejecrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwa, bid3x(8gsujrd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you q h7pn-pt 4*kjcompute the banking angle given its speed and radius of j74*qphtpn- k the turn?

A girl is whirling a baltdes10fy ue;yylkeq/)* 2 h h*l on a string around her head in a horizontal plane. She wa eyhueyhq1y0edt* s2f)*l/k ;nts to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth?2;cn ew5 /f ,yj nuorc80n2a3mjh+ivq If so, how large a force? Consider an apple /ni cvharmu,+n5q2e won0cyj3 jf82;
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what 2i scpp+,r9mxways would the Moon’s orbit be +iscxr ,m9p2 pdifferent?

Which pulls harder gravitationally, the Earth on the Moon, b cuv.-n -/bicor the Moon on the Earth? Wi vcu-. /b-cbnhich accelerates more?

The Sun's gravitational r ubjg5 g2rktwf* ,7vr 3b06wzpull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consid7wbrz6 0w2 ,rfg*utj bvgk5r3er the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator o 3dw1zet2y1iob3+l wtr at the poles? What two effects are at work? Do they oppose each other?b2eliw zt+ woy3d 113t

The gravitational force 29y83sz wqw n5dob)b1 wt: ftbon the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled awa b2n51t)wq9bf3oyws:dwztb8 y from the Earth?

Is the centripetal acceleration of Mars in its orbit around thedf 04:i2ubtfr Sun larger or smaller than the centripetal acceleratior2 fif:bu04d tn of the Earth?

Would it require less speed to launch a satellite (a) towards mmh+); y0 q+rnaz;vd the east or (b) toward the west?qvzn0;dy; ) am m+h+sr Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured 9de vji-jgr4. 0nmlu)by a scale in a moving elevator: when the elevator (a) accelerate4g09ujdm i -) lvrnje.s 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 perioq qb*5uc:f--ve)qi phm b :w4gds in outer space could be adversely affected by weh):q q*fic 5--w bp4b:mgeuvqightlessness. 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 “appare .,vd+ bx23x-c) bhmj la0sawwnt weightlessness” between stemlxj)da a2c,w.b-hv xb w0s +3ps.

The Earth moves faster in its orbit arou n nfi;zv3 /5napvb2f(c-ey(z3:lkqnnd the Sun in January than in July. Is the Earth closer to the Sun in January, or in ny2l3: 5nz fb;fq/e ( pkz-nvnca3(v iJuly? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovereds g,zs *,eat4n to have a moon. Explain how this discovery enabled an estimate of Pl,*t szn ,ges4auto’s mass.

  The Sun's gravitational pull on the Earth is mucc+v,0v sak*u qh larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider thqkvuacv,+ 0s* e 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 198eh hffjmd6(au 5 p7,s20 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripets6b6yftmsq4) q7a x2cal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orxc2q6 fyt bsq6)4a sm7bit 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 2en7m(adl3 p;gjp3 3 jzs11aw0t yrx ha 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calc rgj1;x wtj1pe 70(d3zymp33n2a hlsaulate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km zuxfz;s8-y 38ho- sslfrom 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 gravitational acceleration at the Ear sl;hxfzs3z -os-88 yuth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of j ,cm 0uz8wd)*sfrs- pa potter’s wheel turning at 45 rpm (revolutions per minute) if thrs )0-sj d z,wp*ucf8me wheel’s diameter is 32 cm?   

  A ball on the end of a string is rigqh*qbl5( p1evolved at a uniform rate in a vertical circle of radiusb hgpiql51*q( 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 w+/;aq 2;a0zudp zkpm4ng4l sfith which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this ra; u+pgldzp2;q4n /fz0mkas 4 esult independent of the mass of the car?   

  How large must the coefficient of static friction be between trpmm1x b .z*sqq8 6,v*7ipsnlhe tires and the road if a car is to round a level curve of radius 85 m at a speed of 95kmpvs* *q16 q sl z8r.ip,b7mxnm/h ?   

  A device for training astrjq2/ d 9:ygyn1rokw;sonauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 time /2:q r nsokjyw9g1yd;s 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 ax0cu-5y rm u/kpsvbl 4e:03 af hf/oxb/is of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable u :/ox4kfepfa5b0s /ycb3 r h/m-lu0 vuntil a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a ros1nu,0que 1vp h1ob4nller coaster be traveling when upside down at the top ofn11ne uhpv10q 4,obsu a circle
(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 pvvo nt 5su9y .5-upyx4*iiw5 950 kg (including the driver) crosses the rounded top of 5xop spi ti *n-v95yu5w4vyu.a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Fe q:o.3d;euzm15wc8i hbv ozw4rris wheel need to make for the passengers to feel “weight h uw381cw5z4 z.bmidq ;:ovoeless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirwss.w5o 0 -.jen/:o )o oqnagvp w,3rnled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket in.qj:5os ng.wwrs ,ep0-o v/ao)3o wn s 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 patwyw :y4u5v6sebxz pq79 e sbx8*0c a/rticle 9.00 cm from the axis of rotation is to experience an acceleration of 115yevuxzx p 8c9bw 0ysq65e/ 7a4:tb*sw,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated irg7s9(o u t 469hognozn a cylindrically walled "room." (See Fig. g (9g6tz 497ru onoosh5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tab j rzlxau7-ob1puk / ofc1*/v1letop, and is held in this orbit by a light cord connected to a dangling block -o/ up7zjrox1c1fu *ba /lkv1 (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 , preci:glepcn 9 )1o hg7bk1asely this time, by not ignoring the weight of the ball which revolves on a string 0.6e91ocnlg hkgb1p) a7:00 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 bankkx(shn* y ue fgi;)(r3ed 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 masses j 2 xh8d(g ziu-9rn1bm$ 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 ve9a;oerju))fygbok 7atuev . 5(y p)m) rtically 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)pw7n5fzi*44 wisk vbb*d u 8d and centripetal components of the net force exerted on the car (by the ground) iwi5 w8kvbdnb4u4d f i *)spz7*n Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit areaxu.fsewk e-- grd; ehqv8.;m; , 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 te fs;-.;gexd ;r ekq.h8-vwum he road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circcgj vqxjk;*w2 :8ble3. 3juolle of radius 2.90 m . At a particular inse jbx 83qjo2v *g.lu3ljwk;c:tant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force ofgnr0/.h)g ay 2b)yve j48czpt Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its n/).)0pzc8begy4t hgy rva j2mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a ma7 3 /3jjred5lcgbxg6 b+kbt0ngnitude 5lgbcrb3 /d+nj0t bgk763jx eof 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 acceler(i 9) 7v 0iosrx(gsrination due to gravity on the Moon. The Moon's radius is 1.7rx7iisg ( )vi9s (rno04 $\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, but8v x4jto6t jwhm*aki* :pp7 (z has the same mass. What is the accelekjvw:4zot ( px7hi*mj*a 6tp8 ration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66tu . sa k7rtz(be6z((g times that of Earth, but the same radius. What is g near its(zt6kure 7(atg b(.sz surface?   

  Two objects attract each other gravitationally with a force zp 1u2xgakc20pfj k;8 of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, f6b u0+ wvz qpc0;cp9eat (a) 3200 m u 6cqcb0e 0+wzvpf p9;   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cynwe(y3j9e gm6zm* 9s enter to a point outside the Earth where thegravitational acceleration due to tnmsjeywg96y e( 3 *9mzhe Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fih:(b,w 2vjeiy ve times the mass of our Sun packed into a sphere about 10 kvie: wb jh2(y,m in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is ohy3go6vu84 cp1 s)nvnow in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is th sv84 )up6c1nvhooyg 3e surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in m/nr)irqq/ 5athe 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 th qnrm 5ri)q//ae 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 0.60 m. Calc8)udt +f tcwp8ulate the magnitude and direction of the total gravitational force exerwd8pc)fut8 +t ted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mo n,gpvh;f /e8xst of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and;x vhf/n,gp8 e 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 surface of Mars is 0.38 of gg tb;/aabty4:9sso3 what it is on Earth, and that Mars’ radius is 3400 km, detoa bg/s:9 st 4;g3bytaermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using t86/8fu q,qt*sp i ed4jz6khaghe known value for the period of the Earth andez / pq s6*tk8q,gd4j8uhi6af its distance from 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 9*e9c kn ih2by)z k.aya stable circular orbit about the Earth at a height of kc.*nh2) eyzik 9by a93600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 6vnxul ww5i l8yfh xw2q0m-3)650 km above the Earth. How fast must the shuttle0ym)h3nv-uf l68 qwxwli x25w be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to exm*9f9zffifvhsa1 (; hperience simulated gravity of 0.6vh9if1f( f h9a;*mzfs0 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eaao zfszi0x2++lky, u 1rth 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 youl+fo1s,yix2 u k+0azz r result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the i66:u1jeymk s top oi se6muy:j61k f Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the comman7i6y4 brvqq0k g(s3 5 eax4btrd module continued to orbit the Moon at an altitude of about 100 km 7(r q5kq63 yervbag 44ibx0st. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of icf3ra j)0ca;g7,vkpm(o h3 8dk8qe b *tf4xkzce that orbit the planet. The inner radius of the ri;,) za 7 krk04qef(m 8hbcgk*fxvop3atd3jc8ngs is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9).bs4:sakw+vt;a 83 yy o What is the ratio of a person’s apparent weight to her real weight (a) at the top, av8ot4yaa :;b kssyw3+ nd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 420sbu.sm8u n4 k*0 km from the center of the Earth's Moon in a space vehicle (a) moving at cs48n.k*s muubonstant 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 - rkg8t6r+p ng /txn,fu:lrj6stars of equal mass. They are observed to be separated by 360 milu r,lx6+g rkf8:/ -gjnrttpn6 lion km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for te0dhlkci 3 7+lhe weight of a 55-kg woman in an elevator that mov03kil le+hc7d es
(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 ob5pw2mo8ni+,g.k m o-d al,va cord suspended from the ceiling of an elevator. The cord can wo+p 5bl a,dom8 oig m,n-.kv2withstand 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+2 6(l zotiq8trzputg::az p( a planet with period T , the density (mass/volume) ofipt t+(pztzulzag q(:6r8 2: o 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 th ;ojv a6wakxg;0c )(nfe period of an artificial satellite orbitin x(6;0oa njf kc;)gavwg very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundre7k4. a4l4p+:sjcc,khljqi c gzfr 39wd meters across, orbits the Sun like the planets. I4,3lj4+c7kcpsg jqk al rif4h9czw:.ts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average difo/-l mf(/hqp+;shk d rw1*dbstance 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. It comes very,l-c sl rikb 2569 c9lcpariv* close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatescp2ck5asi i6brc ll,-v9 l r*9t 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 thk+7i. n1pxra fe 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 m,hcj8 sjbwzq32 t/xi6ean distance for the four largest moons of Jupiter (those discover wbjj qcizts2x/8,h63ed 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(wp78l.o bo em and distance of the Moon. pbmo w e(l.78o   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usindar.8u..15 ky/l ws4aodhg mrg Kepler’s third law. Use the distance of Io and the arl/os81.ag4dum kd.rh w y.5periods 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 betf3xhlzaehwd4 w *,m4d) aa;2j(wr.th ween Mars and Jupiter consists of many fragments (which some space scientists think came frhwt )x.(aa*dderj2 h44 fh,z;wwm la3 om 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 the form of a band w yh*r h9j /-hsceeszk8m69 0mcompletely 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 *czr0 9/yhmseh-wmh9s6 e8 kj will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc nk tc(9vv9cfq (gf0l: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, and thec 0(clffnk vg(tv:q 99 vine is 5.5 m long.   

  How far above the Earth’s surface wilwe*k,z: ; i;smh 2bneel the acceleration of gravity be half what it is on the surfacehb:ez2;* s ime;en,k w?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin i- kznrtzbw01ml)3kl, n a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses wz0 - k kn3l1blrtz)m,are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotn 9icorvf o r7.mg5.2xates once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotar7.5 o2m ofn cx.i9rvgte. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from k lc71;l.lnqwtpjw*vc;95:g ke.x rpthe Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and ox.l. ;;7 jqwt5c9lk:l*1pewvk prngcpposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a 64wsue/d g -xyyzu8* rbathroom scale in an elevator, it says your mayd yzus 4e/u8 -w6xg*rss is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists ofbc7k9e.a y- ej;0 dznh8t/ast 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 diamete8;cn0aez .a 7ytt9-shke dj/br 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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft iok x;qn.mfu4t44 a3 p mrfm b9*hpq*2dn 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 the mass of a planlh) xfmz:65d1e0qd22 dbrdrf et in terms of its radius r, the acceleration due to gravity at its surface and the gravitational consta5d1f2 zddhfe0qbm6 lr:)rd2xnt G.

A plumb bob (a mass m hanging on a strik-/ ;ix ,i+, mkjbg vv*dtm-lsng) is deflected from the vertical by an angle mv-bi,k ;k,l-/tsvx md i*jg+$\theta$ 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 banke/ 6qigqerw6l)d for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle te rl 6w)6/giqqhe curve?

  How long would a day be if the Earth were rotating so fast thatufy 2 qvxl7t4xq 1m4 qcym+e-; objects at the equator were apparentlqqc2mxxyv u-4 mf4+1ylqt;7ey weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apaf 8n)xe zpqhnus862fj;(b6(i i uyct6rt of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp sua2-v3xli4 hp4j(q bsrspended from th3ix 4hb2( -ra 4qsjvple ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 time*npzrkg*w,11h-1ta gx b3s:gp)p y zbs as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of 1pga3g1*b)yt :wsz-pnbh kzgxp,*1rJupiter 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 deduced the(s+edg zx/( ez presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the co(s xz+e/degz( re 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 vato 78pr7v( *otyms9tvlley 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 7vs(7t tmvprot*8 y 9othe 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 am 3iusp0 m nls,uy4mh).2yt7f 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, allow ,f3ss74 0i)y mmutyumn.lp 2hing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traw rktix +;u-lh:5ny-nl.c4aaveling 2.1 billion km, is meant to orbit the asteroid Eros atuc: yaal+4 -l. k-n5wrh;ixt n a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space sh:po9a9vrwy s7uttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellp 99savo7yr:wite (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)/tmql +5 eyh)p What is its mean distance from the Seml)qh/tp +y5un?   
(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 cowlc:+da mmr xo8d 87(muld actually "feel" yourself gravitationally attracted to someone near you. Make reasona8cxald m(drwm: 8+7moble assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy q mubw..:bef:(Fig. 5-46) at a distance of about 30,000 light-years fre:fb w m:.bu.qom 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 o ;hv,j,c/h7jubb fu9:xz fi) rf a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed aj, ;h czbb :)jvf9,hxiuf7u r/t the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartd6 ofxi rijk/- he;.nk2 ak79th $ \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 tk6-f gc :n-h+fvipj2ohe 1.5-cm-long sweep second hf+6vcikohfj n2- :g-p and on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker eig y)8h6zxy/dk1 y 63xggd- gweight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete gx-dg 3 6k6 )1yeyz/ixgh8dgycircle 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 i; ttt3tn cac;wt50xg/*2aq u0 hhs:7(sujf o that a car traveling at speed s0/ch ;50ft ti73 at:hja*tuwc x nug;qots2($ 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, utilji)96ev:jw iv 2z 8ji.kvq(l nizes 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 experience less friction force against the seat, q)eki 28z:( 9jlni v wj6i.vvjthus 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.$\approx$    $\times 10^2$