Sometimes people say that water is removed fro ul zc4cwp;6+dm clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this s4;c +wp cd6zlutatement?

Will the acceleration of a car be the same when tvd hv2u3q x4x (ge44sihe car travels around a sharp curve at a cx(x3 44 gdviqv uh2s4eonstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant s v6m 7tg) ml,jdc7tqi4peed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at l,)7tq ji m7dtm4g6vca 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 honj9sliw88jd gw fw 8m0c5w:)erse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chilw5 )wwe8:m9sw i8 dflnjc8j g0d?

A bucket of water can be w5n6z bo.*nlfc e(nh4chirled in a vertical circle without the water spilling out, even at the top o lznc56.nc ef(noh4b *f the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There aty4xfx)sr(a3x( l411*3ds:xu vqmo omfp dt4re at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelexs ()1daqod3 up:txmx *l4f1oxf ymvsr4 43(trations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Figmfods: ).bf2 a. 5sf:d) .o b2amf–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hirht*3 y y g n4t+4y71teb)mczogh speed?

Why do airplanes bank when they turn? How would you compute the banking angamljylh+d *)4le given its speed and radius of the yj4+l adml*h) turn?

A girl is whirling a ba (vw1ufz,b +osll on a string around her head in a horizontal plane. She 1o(f+zswbv u ,wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If soxq;nw6 , *lz+tq *zv19ks m or+fyikl3, how large a force? Consqz*sw1 i znvrlqok 9x,*k t;6y3+ lf+mider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tfl+, h;mnrir/e y1f*bhe Moon’s orbit be different i yrerb/h,+nf 1fm;l*?

Which pulls harder gravitationally, the Earth on the Mooahyn:rt9)gp 9 n, or the Moon on the Earth? Which accelerates mg)h9yrntp:9 aore?

The Sun's gravitational pull on the Earth is much larger sym; ;i1 . :0n;l0d7khbifpzqz5npq ots g/5 xthan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravixk1/i5q;:;y0z.d bfpmzhsl0g7 s; iqpot n 5ntational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two, fddwz/o/yq; effects are at work; /q/wdyz,f od? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only ak9yv4ixx f-i5 bout half the force on the Moo i9vfx4 k-5yxin due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accelerationo+yd3e bh *c0f of Mars in its orbit around the Sun larger or smaller than th e boyh*0dc3f+e centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) tgpx8/383 3n rs8seg fd pl7fsjoward the west? Consider the Earth’s rotation dix f g e8l/sd3ss3fgj8p87nr p3rection.

When will your apparent wyp fxsr6/yi60 akpr o/ 4d1gp8eight be 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 which case would your weight be the least? When would it be the same as when you ar kf pd/x6 yyo a86i/r4g1s0ppre on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could x,tp q/jhy-cuiv48-u qu(yf .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 how this simulates gravity. Consider (a) how objects fall, (t(-4yujf8hu , /-pqqivxy .c ub) 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” orkxwl t/nj (8o* “apparent weightlessness” betwee8*/ ntolw kxj(n steps.

The Earth moves faster in its orbit around the Sun in Ja3l3jlw i9qut:3h;7wafzl)l dnuary 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 al9fw3d:;tw j)hzu 3ll3li q7axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expl4llu u5b o+l-fs5q 8reain how this discovery enabled an estimatelq5 ofl u-b84re5lsu+ of Pluto’s mass.

  The Sun's gravitationg3ro*8 m81mt x3z r2bge fjop,al pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides.1xm3,rjr8mopt gz o eb8 3*fg2 Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19h 9-luq p4ehd680 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 tpdld:fp 48:,rouz c:h he Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that theoz:f udcrpld8:4p:, h 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 it rotates unifor;t et)8jw9bxe3/l lvayjwq.- hv3 5iomly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. vt o 3-9beehj.xal 8twyiq;w35jv)/ l  

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and m3:,im b9 vvdwcircles 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 accelerat,3 bwmv i:9vdmion at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of ff)5undnlf mzq y w o-eno04y/8,6i+ia speck of clay on the edge of a pottzl-d6f4efi 8 myo+o5wq 0infny n,/u)er’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 rate in a verticl;zy: z 5lnq7lal circle of radius 72.0 cq:75 zzll;yln m , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of ranrf,2lrmd4e1 dius 77 m on a flat road if the coefficient of static friction between tires and road is d2 enr4mfl,r1 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betwee3 e qr-tzpgw4rkp6 (gdu3r/ sxfc)p 32n the tires and the road if a car is to round a level cur33-qg4w2ufxgpd(rp k6/z3)t rcsep rve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rw jtfo60v5m sj8;g:b;ih tm *m. klbp+7d1zljotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 j.i+st0vb j hw 6b *tjlk7 dfl 8;1mz;pmo:m5gtimes 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 turn2 :9* ewxvyvonf*hxr)table of variable speed. When the speed of the turntable is slowly increased, the coin remains fixox9h2eyxw nv :** rf)ved 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 turntable?   

  At what minimum speed must a roller coaster be traveling when94,mrun2v tpm upside down at the top of m,pnutv2 m 4r9a 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 950 kg (includigin m/uc qcx 1cec i6.+r+6fi.ng the driver) crosses the rounded top of a hill (re+c6.cfcm6c i iu+g 1i/x.nrqadius =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 Ferris wheelqn li5vfmv4 /6 need to make for the passen6i5nv4 mf/lvqgers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a veu2vw wwks*a 7*rtical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0**w2wu wv 7kas 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 xy e1i0 ifbq2uo+2q-s a particle 9.00 cm from the axis of rotation is to experience an acceleratiosq0ue-bxqio2y 2f1i+ n of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people arerv.q18mewo8mtg z9h: rotated in a cylindrically walled "room." (See Fig. 5-35.)m :91q.8trmozv8 h gew
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-hock9k 3y w4mrca/qey tabletop, and is held in this orbit by a light cord connected to a dangling blm39/awkr 4ycq ock (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 timy3gj *b:d3n. -u pf7vh6guh ate, by not ignoring the weight of the ball whi-bdtavu36f 7 g 3hygp: jnu*h.ch revolves on a 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 banke-3t- ib:zckqmqw,/ dpd 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 massesz *8)ji5fltex $ 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 maneuve1 wtb igs ;ol+lx)zk+wb:/c1or by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components y8 13 gfjldma,pa4w4k of the net force exerted on the car (by the ground) in Example 5-8 when 8 jm1,3ag4kay w4pdfl 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 uniformlyal4*fqr j s/xiaa s+;8 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 *aala+ f/ sj ;si8rxq4when 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 kgrbx)/xc).ia (d+i-s l0l oi radius 2.90 m . At a particular instant, i.ci-0xskxri ) oadgib/ ll()+ts acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecra l 9rrw91saus9ft 12,800 km (2 Earth radii) above th9asuw19ls 9rr e Earth’s surface if its mass is 1350 kg.   

  At the surface of a p w-e-/)bvu)d -8fptxxg sk y:certain planet, the gravitational acceleration g has a magnitude of 12 -pwxp/svg --8btyd e fk):)xum/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 Mndu*5c+ lqw j3oon. The Moon's radius is 1.74q*n 35dljw c+u $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a b) qdsj*- yp+rf d18htradius 1.5 times that of Earth, but has the same mass. What is the acceleration 8qbrh+t-y)sdfd jp* 1 due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earthn ye7q rntpm+eg3 wh6h9d88s1, but the same radius. What is g near ith8eyng sm 8673hnw+ rq9e tpd1s surface?   

  Two objects attract each other gravitationally with a force of lzigz3vm,:v(wc9o 9f 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, at (a) 3200tk.b33yo5*i1hfh gbwghq4+x j0 8wwo mof4 y3h.t38g1wbq5o kxbh+ ww *0jgih    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the bd -mpgn3 m47jfx0j:pEarth where thegravitational jgxnpb4d0f :mm37 j-pacceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere3e1md9dq ezwn 4nv2 a8 about 10 km in radius. Estimate the surface gravity on this monster.wedqn d 4m3a1nev28 9z    $\times10^12$

  A typical white-dwarf star, whic98pc5 96tb nzwg-v diah once was an average star like our Sun but is now in the last stage of its evolution, is the s iap 9v9z cntg58d6-bwize of our 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 weig cm j )7mno2dlt 7ouh8,q++iathtless while orbiting in the space sh2) c7 n7a+ +ihtolmdmo,qu t8juttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located oc,pdc,jtb2 e w my*, 2xzx(6vat the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total g dczy*pbeow26x2x,cjt, v,( mravitational 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 lin-o42 fuqcuaj)q: dz 5te16eud:c gc- fe up on the same side of the Sun. Calculate ez:g) cdq f5 :ej4tfu2--u6dqc1 aoucthe total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfaasr(w5g: 2x 5z+tiezgup0 c/y ce of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine t/c: pxzui5tewar25z sg0gy+(he mass of Mars.    $\times 10^{23}$

  Determine the mass of the Su.)iks pteoc(10mtk1 9nww4udqw*u c6n using the known value for the period of the Earth and its distance from the Sun. [Note: Compare youru90 ik)64nt m1spkw.cdqu1 oc*(eww t answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular9tlw vht7 4/sc orbit about the Earth at tst4/79l wvhca height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbin5 5q0h8nd xykj3anf3,a+x blt 650 km above the Earth. How fast must the shuttle be moving (rexq5+x,3d a0fa53 lh jnkny8nblative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spacesh e4q8uo)2b m2lebnuj 1ip rotate if occupants are to experience simulated gravity of 0.60 nu1bel82 2qbj)uo4m eg? 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 fhzlb7o/pvk)eaz5.sd ,(ks. (51n lg 6ltr rzaor a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” ozd5o,naz5e1l s)h gpr6bskr zv t7l/..ka((lrbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launchlwudk .sob t15j,5o:red from the top of Mt. Everest to be placed in a circular lo 5,o.tjru b:w 1d5skorbit around the Earth?   

  During an Apollo lunar ls31xl qs8out- anding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it tts-3o 18 lusxqake to go around the Moon once?    s

  The rings of Saturn are composed of chunks ofg,c8s 6h 8fhvce;)inn ice that orbit the planet. The inner radius of the rings is 73,nsic; cv 8,8 ehh6gn)f000 $\mathrm{~km}$ , 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 8j* kfn;kek* evhj;y8 Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and eek88jjkyv*;f * ;hkn (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 6w r-t bedg;ae*n+e k:75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movin :dekrtbe*g;6-a +ewng 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 binar oz2j t(ui-hx;y-star system consists of two stars of equal mass. They are observed to be sejuoi( x h2t;z-parated by 360 million 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 forh7wzga b/r;fk47-6 nfvno7jf the weight of a 55-kg woman in an elevator that moves vzf kh7n o-74wnfr7j; 6a/f bg
(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 ceilin12w/ ( l;tfo mrr-kvsog of an elevator. The cord can withstand a tensio m/lsfov- k(2ot;1rwrn 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 surfae ;t8 jyhzyc;2t2 sm/dce of a planet with period T , the density (mass/volume) of the planet j y;ytmhe2s8 ;t/zdc2is $\rho=m / V=3 \pi / G T^{2}$ .
(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 p;0lr6) g +gtwme7fcu of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near 67+ lmuwt)gg;re cp0fthe Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acronu3s; 5ti6xpt ss, orbits the Sun like the planets. Its period ixt53;6tpsn ius 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dismrulltw 9p3;y s*x ..u xey.yol+v52utance 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 Sir* ,i lgo3h;pun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “r3,g*pi hol;i 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 abouybvt2rx 7 8;szt the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons o1 zb(,h j:c hp-cc0kotf Jupiter (those discovered by Galileo in 160obc cz ,-1chk0:ph (jt9).
(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 the15 /,u0y (a sn/0oesgrcaqnwf*q pr0j Earth from the known period and distance of the Moon. qsyawfjc1,nusr * 0p 5/g00rqa/ no(e    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s m 7p,:s o-vqjfloons, using Kepler’s third law. Use the distance of Io and theopj7- :,fsq lv 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 8y ssy1 6v7cg9q pbcfsu* 4s*ofragments (which some space scientiufgsy4sy *7*69s1 os8c cqpbv sts think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planetehuciw lo 2s5ye/c * o;+l)g8z" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), a5+)wl8clz2oe/ sce* gi hu;y ond 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 in an arc from a hanging/ufcb1x9re f- ewc:j5 vine (Fig. 5–41). If his arms are capable of exerting a force of 140wjc5r9 f:- xebfeu/1c0 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratihr6a s6 3xqii-on of gravity be half what it is on the sur3 isi-aq6h6 rxface?    $\times 10^6$

  On an ice rink, two skaters of equal ma tmrmf 48wz:r6ss grab hands and spin in a mutual circle ot: r r46fmz8wmnce every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratio2gh7: )cwi94j gv negrf 8 kzo3zzed8wd90 m/qn of gravity at the equator is slightly less than it would gfdgow9e43 j0nig7c k8v/2:hw dz8 z)rz9qembe if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from tis5wu8:x; mb khe Earth to the Moon experience zero net force because the Earth and Moon pull iubms; w:kx5 8with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom1-grqsfb* y) b:guej3 scale in an elevator, it says your mass is 82 kg.1ub g3f:r - seby)qjg* What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consi/b0. a-7ct3garwn)e5/pbk2 be j oh lgsts 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 daca/.7/ th-e o lbg5bag2e3jn b0rpk)w y) 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 aircraf47mhz.fw ,gv6urf 3dyt 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 the mass of a planet in terms of itrje nywk. (ngy nq4+93qkdb)7klv0x 0s radius r, the acceleration due to gravity at its surface and 0vqnx 0jkl 7 r (kykbye9.+n3qnd4)wgthe gravitational constant G.

A plumb bob (a mass m hanging on a stri 58fqt5;jpge 6w8bumd ng) is deflected from the vertical by an ajw6dp5bq;fe5tg m8 u8ngle $\theta$ 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 bant4hwe+.i 7ro mx* 9fwhked 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 hme94 *ho7t rw+ w.fihxandle the curve?

  How long would a day be if the Earth were rotatin-ithz)/ 0j1 atc )rsgag so fast that objects at the equator were appar h1j)g )c/ia-s ta0rtzently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance ap/ ;.*cor4l0sjtgla3yq, u - 1pvtkaszart 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 lampq:h e a(bfk:)h q/f3ru suspended from the ceiling swings out to an angle of:ah/)q r(:b 3hkueqff 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claz81r wgu1ld0quvs2 1kimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of gw21 uq10vkg81ur sz ld '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 presence-fid oxxqcil+b 971nr0zxe 7 ) of an extremely massive core in the distant galaxy M87, so dense that it couldr7 lxo1+ )0iqi c-edbf xx7zn9 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 iv+xv51.(l jxw zdu*mm z7har(t 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 x zv+rudhl(.(zjw5*a vm 1m7xacting 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 Systemq0 pim, (;u msqkvs.2b (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in eachvibs( 2q q;pm 0u.mk,s of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 b-4mtvm eh*6tp +0/ z tl:krwwkillion km, is meant to orbit the asteroid Eros at a height of about 15 km . E e0: k*ttvtw zmh m6-k4+rpl/wros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in 1m-vrxi)2hpo7 e/i t mneed of repair. You are in a circular orbit of the same radius aso x/)2 17ri-mvt hpemi the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp hp,0 ij/1ryxjrf1x3 owas a period of 3000 years. (a) What is its mean distance from the Suro1x/p 0yi xjrj3f, w1n?   
(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 actualltk ) .2vvp(meyy "feel" yourself gravitationally attrpv ev.tm)2ky( acted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cak, 6, u1kko)n woiue2enter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from o 1),ue2k,k nako6uw ithe 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 + 2z25d .-tdumyirvd4zda8iza square 0.50 m on each side. Find the magnitude and directiozzd md2i25t uz+r4a -d.8viy dn of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits t *y3*4vgrq ftc iwpxn5*e3 f3ehe 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 1.5-cm-long sweep335m2 ewo.i ce8 oeviy second hand on your wrist watch?w358iv e 2e .yemc3ioo    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight -ofydffmhs. bd7-* b8.rc xc) around in a circle below you on a 0-8cxf7*d dhrfm.by.s - )bc fo.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 designed so that a car i2bkkm9( bbok-39fcnh* o o7 itraveliik-fobo3n(b m9o kc9*hb2k 7 ing at 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 w5 ,i a:wjuddyv(z,7lAcela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does nojww iddyvaz5 7: (,,ult 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.$\approx$    $\times 10^2$