Sometimes people say that water is removed from clothes in iwn 1bp .h iibz)5j66ga spin dryer by centrifugal force throwing the water 1 p5w zbinhi6).jb6i goutward. What is wrong with this statement?

Will the acceleration of a cv5pr)k4jna l +ar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels ar+kr5 l4an)jp vound a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alon;* lqcy j2mc;yg 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 stre*y;;lcm2 j cqytch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go 08)/ qvelhso tnj2j witpq(k9) 6s9ee-round. Which of these forces provides the centripetal acceleration of the childn tse0i9le8kthj2q/ v poq(9 j)6 s)we?

A bucket of water can be whirled in a vertical circlo/u/d eyz3t(y e without the water spilling out, even at the top of the circle when the bucket is upside down./ez(td/ ouy3y Explain.

How many “accelerators” do you have in your car? T4e;rplrrn5q k*dw.o . q:ou g2here are at least three controls in the car which can be used to ca:erqu.od5ol pr; .g rnkw2*q4use the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of aq:xy.nn6.*3 r izqas l e7a1gt 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 second .t a y:*qr6.sex niz1ag7nl 3qlaw.

Why do bicycle riders lean inward when rounding a curve at high s*nv0er lskw nra/p)2 ,peed?

Why do airplanes bank when they turn? s i4n1 gvd4gg-ut*uxc :47cznHow would you compute the banking angle given its speed and radius of4nv4g-d*cug4tx :cg s7i nz 1u the turn?

A girl is whirling a ball lpm e5ankk6+: sdu8 a2fpq:m+on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target+kdepf6s5a p2a8q m+:k nl mu: 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 so, how large /gs0dcv+ hs5ja force? Consider 0cgh5jd+v ss/an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would t a90bflc 2l p+8covxehd(b,7dhe Moon’s orbit be difffbe,(0c b7oa2l v 8x+pcd hl9derent?

Which pulls harder gravitationally, the Earth on tl fhr6f*g ,vzz7kbodw;3k6 t(he Moon, or the Moon on the Earth? Whiczhdfrofk66(g 7b lv ;wtk* ,z3h accelerates more?

The Sun's gravitational pull on the Earth is much larger n,k)p/t t +dhqthan the Moon's. Yet the Moon's iqk dt+, t/np)hs mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the pc 3vywwm(s ;-kdr8;qooles? What two effects are at work? Do they opmw8 rd (ky3s- wocq;;vpose each other?

The gravitational force on the Moon due to the Earth is only about hag */gy6 ijpbm d6nkz62oa;lk)lf the force on the Mgb6kg2p /kjz ldi; aomn* 6)6yoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or svknz,s 4cf9crb4:; rk maller than the centripetal acceleration of t9,kf4:rsbzrk 4 ccnv; he Earth?

Would it require less speed to launc *-*oko-qt3pb k n4,qla0 f+rq;yw/-x xnhjkr h a satellite (a) toward the east or (b) toward the west? Consid/y *kw3q oo,klxa-4nt0h-rnk; bqj*xf r+q-per the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movi* 7ks20cl h 2wcfrwowgy /qg;s. 6l6upng 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? Wh pl 2w g7wfgu ckhl/. 6cs*syr6w;0oq2en would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affewb f95j .ck +r.k3qgfocted by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the insidk .wgkr5f+cj. 9qofb3e surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnesn0zfhoe0tkq +.hjff36hmje x4 e9:r: s” between0fntez:fh.h0oqhj +63 mjke4x9er : f steps.

The Earth moves faster in its orbbta 2y)yko8l 5it around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the m lo852ytbyk)aain 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 discovered to havic 3bxeq m747eq ate.+e a moon. Explain how this discovery enabled an q maxq3+ec b7e.ite 47estimate of Pluto’s mass.

  The Sun's gravitational pull on the y. igw(pdw 1)wEarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sittingdgwp.(yi1) w w 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 198h 0cq2mb1d o22kwtf7r 0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit aro fz(aify / .nh79pumi;ya l,8r16pnatund the Sun, and the net force exerted on the Earth. What exerts this force on the Earth?nipua,ym/ z .yfpi8a7fla6t;1rn9h( 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 ex1wmory6f -xun6mz c7o d)s 60verted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lengt-0mc uzs)v66y1 f7mnd6rxwoo h) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fj 5vt kt/,bdz tg1s/xes7 9;w:xyf*hc rom the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space zcf d s,9wtst/htj1k:v/ b57;ygxex*shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of cl2qac;o v 4.ymha7 2cfzay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) i27v4 a.ofa cq2;hcmy zf the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verticalm :de ol7y961ic 7qbj+gs7 vfg circle of r: 9 +c1yb fvmqi7gd6sj lo7eg7adius 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 with which a 1050-kg car can round a turn of radiuso .a10/xql swm 77 m on a flat ro wslxo/q1m. 0aad if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frict q7buc: gqhu7 t;si* bra,/g6iion be between the tires and the road if a car is to round a level curve of radius 85 m at a speeri,c hbqub;st:*776 ui gg/aqd of 95km/h ?   

  A device for training astrong13wyj ,7zkor auts and jet fighter pilots is designed to rotate a trainee in a hor1gjykw,3roz 7izontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is 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 rotatint10 jyyc jb;k/g turntable of variable speed. When theb;tj jy/ yck10 speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsidcd 7:6ye lz2*8fb7m2i; dpazu- dwbdee down at the28d di e7 bfzy zlu-;:7c 2dp6m*wdabe top of 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 950 kc a,r micmuu6 *x;/3dxg (including the driver) crosses the rounded top 3cxx*6,/a druu;im cmof 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 Ferris wheelev 3pp1c:tsn a7xo/o2 need to make for the passengers to fee2 etx:vcap1sp 7/3 nool “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg 6: iu )ia;nh*n8 a7m pbol/bfzpz(*tq is whirled in a vertical circle of radius 1.10 m. At the lowest ;6l:78u*)aafq*ptzzn /b n i(bi hm oppoint of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifu14;v iwp o2v)kjs;rv rge rotate if a particle 9.00 cm from the axis of rotation rv oijvvr4;2w;pk 1)s is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylq..iowq nug by3 8)/,m si 4g9scxt*kbindrically walled "room." (See Fig. 5-35.)b b/8gg,uws qix3i .4oq nt*. sy)m9ck
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 1f75ybum/yh;z ; edgx ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cenbx7fgu z/dmy1 e ;hy;5tral hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignt a++h h1lqdt+oring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mag +hqdhtt++a1lnitude 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 radbar -5emqxizr+q4t2e(3 0 xilius of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses o-.h x y.h(l4qquca5a$ 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 jxo3pz 318 csrdiving 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 of thrvpz*gp; 3dt 0q)l (ike net force exerted on the car (by the ground) in Example 5-8 when zlg;pd q)kt(rp 30v*i 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 t mic7ev .x b7mg2b6m7hhe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static frii . g7mb 7bm6xce27hvmction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horly t*2 x,fh*/cd6opzm7 9zf yrizontal circle of radius 2.90 m . At a particular instant, its accelera9mcz6,pylftozd hx fy2/r *7*tion 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 spacecraft 12,800 km (2 Eirx )vv- 3hco1 e,ie5gvqo9 t3arth radii) above the Earth’s suri x vvi,9ve3horqoe35c1)g-tface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational ;pbhss pkv 4df02h7y4acceleration g has a magnitu7vybh ppk 2s4s04fhd ;de of 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 acceleration due to gravity on the Moon. The Moon's rak- gk1 8 b2 /wqlnym ,ds.5ag+xy2cchcdius is 1.74 +2ws8 ny1l /h xg5.c2 dq-agyccb,kkm$\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 Ea1xm 2p ,s:qzdirth, but has the same mass. What is the acceleration dues:m p,zx12qd i to gravity near its surface?   

  A hypothetical planet has a mass 1n7 wl/3kwldv 7.66 times that of Earth, but the same radius. What in l7kvw/ 3ldw7s g near its surface?   

  Two objects attract each other gravit txqh8xkm-8 7iationally 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 gravitys4x:pg 3n;sde, at (a) 3200 me;4xpg: sdsn3    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fr//d+oz;bvq r6 k+ edcuom the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earkv6/rud ed czo;/+b q+th 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 inum4 ;t -pn+ ibu2 tw*1xqlqp,nto a sphere about 10 km in radius.*tpn; mwbi+p4u ut-xn 2 ,l1qq Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whicp56gj bli2 gve8d, z3gzx x*ws+2 yyk,h once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has *ebg,2 j 6sp3 yxy5kvi+w,ggzxzl d28the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting ina8py+p3lbzi00 om+ya 2k*b c z the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. C m80yc2bz bo+l*pza+3ya0p ik onvince 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 locatedju0,wyroc5znwg t tuulze4 7+91:*lq at the corners of a square of side 0.60 m. Calculateq7 1eoc rzt+yu,zwn4 tgwll j950 u:u* the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sun.k 680):iufllly5 3qe5ypviwa Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses arvll)qauf5kp:iew53y 086 iyle $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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+ +naajw sp0d;ao,:k ea3ee)ti5-jwk at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deonjaa iwe 5)te;0:wpj,3dk+ ks+a- e atermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of/uc6fx8 ghylrth jfi; q5)42z the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–8hctu ) ilz6f fhxrjyq/;52g4 16.]    $\times 10^{30}$

  Calculate the speed of a jc .t8oa rwqst2l8g+: satellite moving in a stable circular orbit about the Earth at a height of 3600 k+ tjg28 q8c.rstl oaw:m.    $\times 10^3$

  The space shuttle relhxe s*njt+2r5 0sm)ls qunu g+mp;i30eases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be ;mi mj5s3u 2 hs0nu ng+sxleq0pt)*+r moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupa2h8taj )gf1 egp ) jzk(qd-hxq gl(7c3nts are to experience g g (he)7tq-8123ga(fjdx jkzh c )plqsimulated gravity of 0.60 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 goszr 2f 5tq)y+5 :bgjEarth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is 2 f)tr55:+jzbyqs ggo 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 k4gj3kn +qr1xhave to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? qrk1+ j4xk3ng  

  During an Apollo lunar landing mission, the commann1+t lte,c7r )7okk -mudp 9ybd module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go ar- ly79tu oeb kr7mk+1dnt, c)pound the Moon once?    s

  The rings of Saturn are composed of chu3a +mrayg1m-o v; 1vvunks of ice that orbit the planet. The inner radius of the rings is 73,000gymavr1au 1mo;-+ 3vv $\mathrm{~km}$ , 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. 560pg4qnf3nmk(ek2 z zg4q7 uz–9). What is the ratio of a person’s appar7u4ezz20qg kmnq(63zgkf 4n pent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weisn:mkd( yp .hk6:bhz8ght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at nhk (mk.hd6p:yb:s8zconstant 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-sc*qv7a .r- - eiswurxmi;5dd9tar system consists of two stars of equal mass. They are observed to be sexvd;7 swc i9riu *5a--r.q emdparated 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 fc 6wilw-ur9tx.y4p(dor the weight of a 55-kg woman in an elevator thau49 w xw(-pt.rd6cyilt moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling )6:zcb dd 9sjuof an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and diresdd6 u c):jzb9ction)? a =   

Show that if a satellite orbits very near the surface of a planet i4 dm7pk,e m7fwith period T , the dens, m4ef7m i7pdkity (mass/volume) 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) to determinezp,l q r t+wxu/wx/x/+ the period of an artificial s /p +x/lzr,u/+xxtqwwatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thoughj9z cqs 4u87w779hcwb wl)idl only a few hundred meters across, orbits the Sun like the planetjz99ws)i wwc qb77u8 l4h cdl7s. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of vw)/v32d bkb v6q 8man 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 t. fmr5 w7rhz6av;f oi9he Sun 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 “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in K;a rih.ov5rf7 m9f 6zwepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of tw8btkfxv w1 ei(pew8b:*n 6f z.t-)cche 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 dis ;7(qn8k kwbvytance for the four largest moons of Jupiter (those discovered bqkny (w ;k7vb8y 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 f qzyz. 9 -l1c9yxjufd:rom the known period and distance of the Moon. 1y- zq9 dzuf:9yl.jcx   $\times 10^{24}$

  Determine the mean distan jzu3i9o4:g 92k.fh gzk 7qpszce from Jupiter for each of Jupiter’s moons, using Kepler’s third l 3h:oz s4zj.97qgz ip2gf9ukk aw. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consistw/8+jx. x fwdas of many fragments (which some .8 dxaxf wj+/wspace scientists 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 de:n3)njkaw o8wnjtrd ) i;4)io scribes an artificial "planet" 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 samw; rowati):id8) n3onn k4jj) e as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. mw ba42:p te8c5–41). If his arms are caawemb8cp: 42tpable 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 the vine is 5.5 m long.   

  How far above the Earz ap 7-c;f3 2hcx(decfth’s surface will the acceleration of gravity be half what it is on the surfa fzpc2-( cf ;7a3dcxehce?    $\times 10^6$

  On an ice rink, two skaters of e)isb xo3,m 0s9e1b7c cffr:kequal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m l9os1k70mc3:exs br c ibf )fe,ong 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 ;hdwk0uv*; isapparent acceleration of gravity at the equator is slightly less than it would be if the Earth diddkuis; *wh; v0n’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 spacecr/i9-edl ;2ddvxyw8ffaft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposivw 8dlfdf9i; 2/xeyd- te forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scalyyk 6e-k6 ,xiqe in an elevator, it says your mass is 82 kg. What iskx ,k y66ye-iq the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of :cppgwb 0t8,g za+e8 ka circular tube that will rotate about its center (like p+gk08ctb:e8 z ,aw pga tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an 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 verticmks6cg ri e9fva +86y;al 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 forejgacs+j)u )- ywd( p7 the mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational conjw+uc)a e p7s-y d()gjstant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical b s:2vpy9zrxtwn o 5p432c t8*bfku1uoy an anglnvf:1w4ztcbrotupy 59xu*p328 ks2o e $\theta$ 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 fm+rcpk yd4qkf/.ws4/ 1 e2 a /-nevhmdor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at / /mw/phreavfyd24k dse4mnc1k. -q +what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rota1echr hu:magh /n3 ey0:0rk4qting so fast that objects at the equator were apparently weightless? /egnhh3r :ue1y 4mq0h0ak rc:   $\times 10^3$s

  Two equal-mass stars maintai )xss-.apqd j 8.z;domn a constant 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 radius 235h ( gg f)7fkrmgg6g5uy+x5ab1 m. A lamp suspended from the ceiling swings ouyx 5g6rgg7gf b(uh fg a1+m)k5t 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 the Earthcu*aj9d)hts ial,xs47n5g5 n. 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 equator of such a planet. Use the fol a9i5 j* s7lu)t5sd 4ncanh,gxlowing 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 Huf-vb8(b2 t7 eypjq0 nwbble 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 pjb70qy2ft v-8 (bew nspeed 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 it travezz;e cp*lj365 mqx g)erses the hill and valley shown in Fig. 5–45. Both the hill)m;j zc 36 gz*leqpe5x 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 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 group o7 be7 ho rnl5j8ro:l5cf 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can bl8o7 coj: hl rn55r7bee determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude 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 Rendbi r3rlg* -mt 8,8rrjbezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eroslr bij-r, mtgbr38* r8 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 i.rbenn()k4u jn need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25kre bn(j.u)4 n 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 yeeo btun 2(o)q3ars. (a) What is its mean distance from the e)bun2q3oo t( Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could ac kvu1tky+eh)9tually "feel" yourself gravitatiu1ye +kv) 9khtonally 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. 5-46) at a dist. j.4w dwm-qxtance of about 3. wjwq4 t.dxm-0,000 light-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 located at the corners of a s/5..mkr n s a.dj2ecmiquare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the . ac.e d/rskni5mjm.2midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the :*ydbz)x 4hy/wam* ayuwr,c1Earth $ \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 ofpnmfk( q;tmtw yu:o5 4y w)x:1 the 1.5-cm-long sweep second hand ot154)w mfy; nxtuwpym qo:: k(n your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and szjgy .zf c2:rfl7 be23tart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing b.ej2z:2g7z3fly r cf 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 traxd. 59qk dbpaau,44 ufveling at speed .4p4xd59, qkadf ubua$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars wh7 4o+xdpmp+ peen negotiating curves. The angle of tilt is adjusted so that the main force exem4ppe7d+ +oxprted 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 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.$\approx$    $\times 10^2$