Sometimes people say that water is removed from clothes in a spin pt e( 9);wxhbq;n6avzdryer by centrifugal force throwing the water ou);p9atn b6w qe;h( vxztward. What is wrong with this statement?

Will the acceleration of a car be the same when )mh3m mj)o5zlthe car travels around a sharp curve at a constant 60 km/h as 5l3mmojz) )m hwhen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does)hb1z8 8n ix*t(g lzfc the car exert the greatest and least forces on the road: (a) at the top ohx z* f88zgb(1cli)tn f a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round.y (j,vsxsshne:j16l2 Which s21x:jjlv s(h,6 nys eof these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the4-2* gprr3 t sbscds.jpalz08 water spilling out, even at the top of the circle when the bucket is upside downrctg203szp -psld bs4.8r *aj. Explain.

How many “accelerators” do you have in your car? There are at leg m e,60q9 kyp,ivn7vrast three controls in the car which can be used to cause the car to accelerate. What are they? What acciv ,ye,pg06 kr9qvm 7nelerations do they produce?

A child on a sled comq3.qz6:5o+gpidd la i.yl 7 dves flying over 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 between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s seco.i:yldz gdpv.53o qq+l6 adi7nd law.

Why do bicycle riders lean inward when roundin*z gkocu. z3;yg a curve at high speed?

Why do airplanes bank when they turn? How would you com8e,e)esmmfr y 5wwa;t 2yn8(wpute the banking angle given its spee)weyerf8s,wem5 8;2yam tw(nd and radius of the turn?

A girl is whirling a ball on a string arour-yx h kaux32w 8-ggl6nd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of thxky-6 lug8g2wx ra-3he yard. When should she let go of the string?

Does an apple exert a w wjbsjw) g087gravitational force on the Earth? If so, how large a force? Considerw j8w0 swgbj)7 an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbi37x) xnkeg e (obj3(kunm/4ott be difn3x73 g( e bt/k4nk(mojxo)euferent?

Which pulls harder gravitationally, the Earth on t.xql 1;de6 ru( 0o8altz(lr chhe Moon, or the Moon on the Earth? Which accelerz e0rl61xh;t8. rcoqdl a(( ulates more?

The Sun's gravitational pull on the Earth is much larger thal;ofppfq ./i1j1qn n.9 9 ocgmn the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differeniln po gn./911q p.f9q jf;ocmce in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or a45oaj jtgyp9b8 8cf4q t the poles? What two effects are at work? Do theyp4j jyqtg58f98cob4a oppose each other?

The gravitational force on the Moon due to the Earth is only about half the1bt;i8(vufq4 q. lapu+ra*d l force on the Moon due to the Sun. Why isn’t the Moon pulled away from thp rvb(.i8a4 qq *ftdll+ ;uau1e Earth?

Is the centripetal acceaoia6**6a n+ 4bgzcw tleration of Mars in its orbit around the Sun larger or sm+ ab nwacz 4a66tgo*i*aller than the centripetal acceleration of the Earth?

Would it require less speed to launch a s(7maneo 9l35d sz68tey.tk fnatellite (a) toward the east or (b) toward the west8k7 6z fm.td5yt3oe(ean nl9 s? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, dh8tf-hsc-0 ly3* vek4m5tv z as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c)3mthd -vh t0ec z-8*5 k4fvlys 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 qk;o)n gffnrrgsc07+n4 q8m 5long periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on tg8m s7) n4ffqnqkr+ nrcg05 ;ohe 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” l913b izo;5em:uiprr 2sf:nnor “apparent weightlessness” between step;:r:zif5rib op3m1lus2 n9 n es.

The Earth moves faster in its orbit around the Sun in January than in July. Is tu qc8pt6/6cvvp0ex ) 7pb:sg fhe 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 axbc) p0p qtv78 upegfsxv/: 66cis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expla6px9f7gbqu4ip0 iqu j x3hn yq6it2(3 in how this discovery enabled an ey9qqp7qi6 xg ubj hn3t 4x0u( pif263istimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger dgjq0u542r1tl*ehw(fiol p. 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 the center of a merry-go-round moves with a speed ofj2dti el5.w1g h04qu(rofp*l 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 e/,h/ ,lo wunu 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Eartp1;n lr c;gi9my8o2qvh in its orbit around the Sun, and the net force exerted on the Earth. What exert c29;nq;iprvo18glmy s this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rm*0 )asnzm ,oiotates uniformly in a horizontal circle (at arm’s length) of 0o *)am imz,snradius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 40phtt;;lw dzrsg2k u-3(hae;: c9kjl +0 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 oh l pud;k2jel-a: r( +3h9gs;;twtzk cf g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acce) b lllhk.k;j9leration of a speck of clay on the edge of a pottk9.hbl);l kjl 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 w7iw:r 8d:i t flnw,p5:op6j na uniform rate in a vertical circle of radius 72.0 cm , as:to :w 8jwp n, 7dn:w6fr5lpii 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 withv4l h+ y/mcem1 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?1ly/ +cevh 4mm Is this result independent of the mass of the car?   

  How large must the coefficient of static friction t)o.etwnc q/,ip41g, *9buzcqg z vjn 8oq() ibe between the tires and the road if a car is to round a level curve of rw8cuz,/*qnv), j ooq (z qnt4ie9g gb)ic.t1p adius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fightsg1a l1m 6 jmm6f6k)rder 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 times r)ga 6jmm6f6s 1mdl1kher 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 aing15wbl3 m9 bxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate o nwb9lg3i1 5bmf 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 t:m4sth: qy lgz,j0h/qraveling when upside down at the top of a circle ythq:mz/ g, :lh4sjq 0
(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 (in;c;;jgvbmo 6*p ucv/r; 3cz jucluding the driver) crosses the rounded top of a hill (ug;c/6;p;v;c bz rjo*3m vjcuradius =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 wheel need to m;2 f*p,p5p;d r qsr)dnzlhj .fake for the passljp qz f hd;2n ;rf.pprsd*5),engers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg iswx5ev* +foo. lhwx8o6 whirled in a vertical circle of radius 1.10 m. At the lowest point of oxoeflh +wov*w.8 6x5its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle cqw0toy xd )o22 j2 ;gax2q-h(q qdlv79.00 cm from the axis of x t2 wj22-qyg70c(xd )qo;vhq d2alqorotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rob6( m1fuskwmv-;9g o3(klkyztated in a cylindrically walled "room." (See Fig. 5oylk9wkk m6z( m1b; v(3f-u sg-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 ioe9 t83 ;nkop gnao3u4:fez .frictionless air-hockey tabletop, and is held in t uzpo4n g:3.t3 8o9e;k enoaifhis orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely thdzwtgeotm ;dc +)3 (p:is time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitud(dte) tp: 3o ;dcz+wgme of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 759/gq91wpl x. uqu* z; u5va;y+p, x jgbqqh9ea $\mathrm{~km} / \mathrm{h}$ , 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 masses9o1fyl1 t.i yq $ 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 th2-ou6hr p4 bmaneuver 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 co*c aq vbv3khw;)kh/e* mponents of the net force exerted on the car (by the ground) i)qc *kk vbawhv*e h/;3n 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 Indianampswlxe19m .rrk0* n . yewm(0polis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were10err m9*m(k x .p0lsymwew.n 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 radiu2w h rdq7d7m7cs 2.90 m . At a particular instant, its 72 dm7 cqd7hrwacceleration 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 o n 8/89cx*crlo1eak grf Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above l kx18*/cg c9naero 8rthe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certaiyyzz9w,d;2 oin planet, the gravitational acceleration g has a magnitude of 12 md ;z2 yoy9,wzi/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 isr9gxj *q0r hml4 5gfwkzd5( (s 1.74 w(0(gzjrmqk s*9hglx 45rf 5d $\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 has the 9ply -)+ytkez)rtp) gsame mass. What is the acceleration due to graykp )9)r) ye+t-ptlgzvity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. )xkxfln + hqiw-j7n (-f;xn*aWhat is g nea(l+nnx i-7jqf fw n;kha )*-xxr its surface?   

  Two objects attract eaw h5f-y xvgz()ch other gravitationally 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 effective value of g , the acceleration of gravity, at 9m+f5ckb 6geywu q3x6 (a) 3200 m ewmq6 k+g63 fbyc ux59   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point o7*mb*)w6 s:) dvqddw*vlj izputside the Earth where thegradd*z7*jwdvp6: qm)* sivb wl)vitational acceleration 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 ma a5mff j40br6tss of our Sun packed into a sphere about 10 km in radius. Estimate the surfatmj6f 0af45r bce gravity on this monster.    $\times10^12$

  A typical white-dwarf sb ,o4tp+emw2fk +y)n+ctx8zetar, which once was an average star like our Sun but is now in the last stage +k 28 mw++ )z4xtteb p,enoyfcof its evolution, is the size 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 a7sskmoa(jla j33g h6 -stronauts feel weightless while orbiting in the space shuttle. Yh 7jljo-aas36m g sk(3our 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 locagno 4pyluxw ::wsx ,4(ted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on onx,wl (:wygpsn:xou 44 e sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thegd b7m,bv2 :ma planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are inmm:2b g,av7bd 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 what kcm7gu o0v8 7dw5+c1;ja jqwoit is on Earth, and t+ oo8v;w7cm70g5u 1kcw daqjjhat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kvev-7y; bmq5k9 64nf8wunc xunown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawu c-y x8uq9ev4 kn;6mn 7wvf5bs, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cqoj :) 5tkjz)y+qkv c6ircular orbit about the Earth at a height of 3600 kmzqv) kqy)kj+5o6 j:tc.    $\times 10^3$

  The space shuttle releases a satellite into a 1h3 x8y.1;b+(ef svns7ysbq:hmmubxcircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occ:xf bv +bqyhbs8x31m ; sh.nmuey17(s urs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupant6l w.u dp:c+k kv23mvps are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and givl+kw.:ud3m pvv k2 c6pe your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to ok6vc/sy7bk6ic9)lj 6dftz p, rbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earb/p 96z 6tkisjf,)dlcvc6 k7yth 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 woul()yje90odm s f2l tzm+ho+er)0-v ic id a satellite have to be launched from the top of Mt. Everest to be placed in a l92) ( f +oi0 hj-oimsrey+ztmde vc)0circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command ub5uzedil mis)7. gyu-/k0 t2 module continued to orbit the Moon at an altitude of about 100 km. How long dbmlu.275yg )s-/u z td ieu0ikid it take to go around the Moon once?    s

  The rings of Saturn are compose-vl fpmqzxyitzn l;;n+5- 7o, d of chunks of ice that orbit the planet. The inner radius of the rings is 73,,nqzxy-vtill-f; ;+nm5p 7 o z000 $\mathrm{~km}$ , 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/oxrn srjx(e.6p, 4h l. 5–9). What is the rati /. 4n6hje(rxr,lsopxo of a person’s apparent 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 astronau-9,z vzm(93xq1aydb hvi*igct 4200 km from the center of the Earth's Moon in a space vehicle gc139zmv(9,xhzdyi * -vibaq(a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star systc7iis +bw4j d*em consists of two stars of equal mass. They are obser c di*w+bj4si7ved to be separated 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 for the weigh3 mrn1gynt.5:sib, vxt of a 55-kg woman in an elevator that mxrv13nt:is,nm 5gy .b oves
(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 sk 1ka yh*ww.i48sta v(uspended from the ceiling of an elevator. The cord can withstand a tension of 220 N .4*hai1yw8w (tkvk s aand breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period m ,pnqhrxyciadyt2y) w ao:y9m; /+ q3sw29l 0T , the density (mass/vr y9:x02htyq9 3d/ w nmya,pml+y2iscqa w);oolume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d)upo);tt*k nfv *ovno)iar 1 14 to determine the period of an artificial satellite or r;unpfat *on)oo1* v14vkt i)biting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundrea4) df7kuxmfyv n:s8i)n*o 0pd meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distancfxonf8 d yn)ka7pu :0imvs)4*e from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 uvajlkmj wzr.7/7s(tv3e b. f. /z uz;$\times 10^{9} \mathrm{~km}$ 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 1/;sut f stk y*ycqhjmx2.z. ,every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distmzy .suyqkfc.1*; 2/ ttsx jh,ance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of/), agor9/u2s hgjncn 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 m 4sln sr (p;xg-d2dxh+ass, period, and mean distance for the four largest moons of Jupiter (those discovered(npl+s s2 xgh-d;xdr4 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 and dista jn x,y;l*rjk*xqoe52 nce of the Moon. 2yj k o5*jl,qr *nx;ex   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usingydj,ixcy +: +b Kepler’s third law. Use the distance of Io and the periods given in Table 5–3.i +,+xydyj bc: 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 Jupiaw q0h(:op j)18me /fcww :qriter consists of many fragments (which some space scientists think came from a planet)q qf(pro01w acje:8w/w him: 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 3x4c ,hcbt, vs 8zwmh7form 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), and that the ring rotates quickly enough to produce an apparent gravity of 3c4 bhc mv,wxh7sz,t 8 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 vine (Figwry1v:q44vg3 h8qfjpa v68 m6e4s*lxty,i gd. 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 i x ayi vf4egr: 4hmtj 1q8dv3l, 4vsp*ywq686gs 80 kg, and the vine is 5.5 m long.   

  How far above the Eart(zbq 7j)yd:pq h’s surface will the acceleration of gravity be half what it is on z(ypqjqb ):d7the surface?    $\times 10^6$

  On an ice rink, two sk1aq9gj,* l8y )ttogdy aters of equal mass grab hands and spin in a mutual circle once 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 argtjt)*g9 yolyd1 a,8qe they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accele45k68b6boz0znfw79 f m* tfbyes m,dc.)yqe eration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimkob4e9smy te, b 0z5.fq6z nbwcd )ef867*yfmate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eartd+ osoi+(uv1 sh will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal aov(i+ds sou+1 nd opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on o)uevyoo 0h/;z84lfq a bathroom scale in an elevator, it q0y/evl) ozou; 4hof8 says your 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 k1k1 79r6fxooek 9 uvdrotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diametex o1 61rvde9kkofuk79 r 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 in a vertical loop (Fi m6;erf)w j6xmg. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accja4qs372 po;p iohs2deleration due to gravity at its surface and the gravitational constant ;2sj h72odoq3aisp4 pG.

A plumb bob (a mass m hanging on a string) is deflected frp0 4e5h,b spi.ujf9hn ,gk h:eom the vertical by an angle 9ih:,gknbhh,suf5jpe 0 p.e 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 desig 6fd5 ;bsh5cegn speed of If the coefficient of static friction is 0.30 (wet pavement), at wha5hf c; 6dsb5get range of speeds can a car safely handle the curve?

  How long would a day be if1uiti44 *s5 rfsmvy(j 0a a: gyocf;m0 the Earth were rotating so fast that objects at the equator were apparently weightlevimssy 00m af4: tci1oyu*( f5 rgja;4ss?    $\times 10^3$s

  Two equal-mass stars maintain a constay 38c,/3 wpeuoc.klsn nt distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radiz/t nltiy7; 2(,iz7vepl 0megus 235 m. A lamp suspended from the ceiling swing ;lm ze07p(7 i, /zyltnigvte2s out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as theei0(ov byp-kh cd: :e4 Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equatoro:ky vep bh:di-e(c04 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 thekhnl h*,p m1y, Hubble Space Telescope deduced the 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 oh,*1hkyp m, nlrbiting 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 consthit 7y *2g0spkant speed as it 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 largest? Smallesti py g*s7h02kt?) 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 grouu8wx2 v7v;tw op 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 altittvw;u2 xo 8vw7ude 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.t (ogyp )0zslw n,i6z51 billion km, is meant to orbit the asteroid Eros at a height of abolg0pi,(ts w y5)zn oz6ut 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 p a0dtp1w gh9h0-7(f ghwilo9shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behidp1olh(a7gpt0- figh 9h0w9 wnd 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 perioda:r*odp9wh 1wn tsxx2 *oqp..w5 nj w- of 3000 years. (a) What is its mean distance fro1w*j.pop wt5 wr -. a9n q:dh2won*sxxm 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 wolgjct ;)t0.ls uld need to be if you could actually "feel" yourself gravitationagt0t;ll). cs jlly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5z) ujqapmx 8w vbvc:w,z h*2-3-46) at a distance of about 30,000 light-p*wj-h xzu 8a32qv:czwmv,b )years from 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 locatedqg gv1ub 4kvtd;e, 9j94s2yvpiiwc / 9 at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg m29y ie4d tk1pq9c;wv j,vvu4g 9bigs/ass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5 cn)*28nwjtib 500 kg 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 tip of the 1.5-cm-long sweep go-c5*eu rur* second hand co*5- urgru*eon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cih0a gr:2mc0ws5h/vitrcle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. :0vachrm iwg ts2/0h 5What 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 nfc/bz ;2h7)r 3hzoe usew highway is designed so that a car traveling ath3/oz fzre2cu;)hbs7 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;+3 5(aanc luj:w jepe Acela, 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 thej;a cwae+5(enl: u j3p 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 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.$\approx$    $\times 10^2$