Sometimes people say that water is removed from clothes i rsn)gf6* 4wizn a spin dryer by centrifugal force throwing the water outward. What is wrong with thisrn*6 ig4swzf ) statement?

Will the acceleration of a car be the same when the car tragk15h gxhir hfio7 ++1vels around a sharp cuk+ 7hrh1i+gfxgho i51rve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alon.azh f;5)7ruuyp g y-kg a hilly road. Where does the car exert the grearh)pz.;7u5yay g u-fktest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridin0 0.bypdzlx mcx370 urg a horse on a merry-go-round. Which of these rb 73x.0yxcz u00l mpdforces provides the centripetal acceleration of the child?

A bucket of water can be whihrs o 797;ykj (1y z p.dsz9f/xurwhu8rled in a vertical circle without the water spilling out, even at the top of the circle whhz ryxuy81 owu99zf/h 7.ks;j7dsp(r en the bucket is upside down. Explain.

How many “accelerators” do you have 76-:jcjgnj* uto:1 ao)ns,fo6bj x s din your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they j): : foos6dnjtb-1cnj67xgo *,sjuaproduce?

A child on a sled comes flying over the crest of a small hillwiisi cu5s:*; ; nxd/x, 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 decreaswii;/xs ux5 c* ;:snide using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve a2jjik eoqwt g5 nk 6jl2p74la*3ei3z*+kk e 5lt high speed?

Why do airplanes bank when they turn? drx t7:+ihyi:obtx6/ How would you compute the banking angle given its speed and i r/toh :y:xb+d7i6x tradius of the turn?

A girl is whirling a ball on a string 1hyzi w +3spc(around her head in a horizontal plane. She wa1c (izhp3yw +snts 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 so, h 8it( /h liliz :ann,9pjy+-xbow large a force? h- l8 , /nlbzi:ta(9ipj nx+iyConsider 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 xri-:cn4:d aj2ooajv /8;vor’s orbit be dif::8n jioa;dvc axro 42- /vjroferent?

Which pulls harder gravitationally, the Earth on the Moon, or thr6p*74t tilkr e Moon on the Earth? Wh *lrt6tkr 47ipich accelerates more?

The Sun's gravitational pull on the Earr jp.n2)r by:hth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diffe yjn):pbrr2.hrence in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What tw 85w):vwac tfyo effects are at work? Do they oppose ea8wytacv5 :wf)ch other?

The gravitational force on the Moon due to the Earth is only about half the fdgbl0o+5 69;och k n u,mxv1w,ruun+force on the Moon due t , 6b+u, u;vwdunf1xml gr0on9o5+c hko the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in 4qmu s d2ce,e2cu, xn2ywkmwu4e h;:0its orbit around the Sun larger or smaller than the centripetawu 02cchm,m2ye uku e2:qsd4 xw;en,4 l acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or 6; ygu(:s tr/;vrfzpks7w n 8n(b) toward the west? Consider the Earth’s ryrnwk sg7s6tzuvf (/r8; : np;otation direction.

When will your apparent weight be the greatest, as measured by xw8y;0 m8cg-6s eywyna scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant spee;8s-mngc e 6y0wywy8x d? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer spac*a n:ah4fa7/ff hxs1ue could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and7f n ha:1uff4/aash*x (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightkhs/m *qc)7t elessness” between sts* ) eq7m/hckteps.

The Earth moves faster in it 1z :b- 4byebp1(5d/dbjvxejus orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? 511xeduyj bd -/b4e:zpjb(v bExplain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not kn/kt lxe./5/nij tip 9nown until it was discovered to have a moon. Explain howjip5te/ k/tnxni9 .l/ this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the;/hmvfv v ytw9,3(mwq Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differwvhm m93(v,/w tvyfq ;ence 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 1)(dfk:5d lh uq980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ap)hyk lp)xuqze4g6( 2*xj*wthe Earth in its orbit around the Sun, and the net force exerted on the Earth. Whaa)g kqwe**(lu6phjy 24z px x)t exerts 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-ksu 9td yx2 /ofs2fo+0rg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cso9 2 t fx0u/s+ryfdo2alculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surw/t sjq-v3 k5fface, and circles the Earth about once every 90 mi/j5wf tq s-k3vnutes. Find the centripetal acceleration of the space 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 s vef+m6z1u b3cpeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter bf+ ev1cmu36zis 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a/euvn9xfr;pxnzfrq0 p10 8eux :*.h o vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If nnup9e xqr:1vr0 0e zof*xf/hpx.u; 8its 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 g.i()):vdcnsd2qbmg8 s5v firound a turn of radius 77 m on g).5dv(gi2 vsb8f :qdimscn)a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between t *k8g* zcs6oimhe tires and the road i ms*c oi8kz*6gf a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designeb:delg l.qdkf7-x 9c3ck j wa7 j;kz6-d to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by thexlc-w jeddz:7kbjcl a63 .qg7fk9;k - 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 rotating tzr7aok e 15pqrbqow ,: 0zdf62urntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntablez r7arq, k 2w6 bp:odez0f5oq1?   

  At what minimum speed must a roller coastfd * q8hrdkk8l2 +he7ner be traveling when upside down at the topf*2hdh8 ldk7eq n8 +rk 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 masu0zfkpa , 3lqe4*uk 4i4f cnu3s 950 kg (including the driver) crosses the rounded top of a hill (radiusnqekac0fl u3f,4pzku4 3i*u4 =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 wo93rrmfeu np .w585cq i8+ ofxt)gwo-suld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at t)u5m5wosni9-prf + r f3.8woge8c tqxhe topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical (1aixys *gibtws)p ) z0ek-*ccircle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucke*t (x)0gypw-c)1ab szs* iiket 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 w rq5b 6cxf.s6;xttg,a particle 9.00 cm from the axis of rotation is to e5 sx6tgfbxt cq ;r.6,wxperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a caiev;8 m4gjc: xrnival, people are rotated in a cylindrically walled "room." (See Fig. igm4:v;xc 8ej5-35.)
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 inc/:0ct9;tetv 7 qlcs/nh)p mi 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 c htv q;tl// tnpi9)sme07cc: ) 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 timj qb.2iyarx5 a-r:-bte, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnityta:2r-b r-x. ia qj5bude 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 travelinga0g j *yvsx,v2jcw3r4 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 a*0sdg4oq .uqg50 (,oc d zxzo$ 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 maneuve.fuvlz k6/8 o:jv--jo( lalvyr 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 centrip5 0fp) veyh-n2oppx b oe0/n7aetal components of the net force exerted on the car (by the ground) in Example bnp 5f2naop h0/ eve)oy0-px7 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapoli gvhk17w:n1 tvs 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 were flat, what would the coefficient of static friction have to be between the tires and the road to provide this vhtk1 7: wvg1nacceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a payeey0 .0fcvz9rticular instant, its .vc0yfe 0ezy 9acceleration 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 gravityr/(nd j**,5l glsobig on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass rl(os*gjilgb,/5d n* is 1350 kg.   

  At the surface of a certain planet, the gravitational accelera4w a dyapos3m+up73ip8 ;+dsk tion g has a magnitude of 12 m/s ypsmpk +o+33 da7uiaw;8sd4p $^2$ 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 ona4 z/ 3 9oun*c1z8l(pjollb qn the Moon. The Moon's radius is 1.74lol/a 348(uc*1zplbqnzn 9jo $\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 thapbo8+u 4wg*8f/p dppvt of Earth, but has the same mass. What is o vbppdpu p4w8f+*/ g8the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bx q-(yn+ nyhm;-n 8vucut the same radius. What 8mncvx+yh; (y-n-u q nis g near its surface?   

  Two objects attract each other gravitationapu pd,hr; )xx3lly 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 e 7stsgrg c:g5y8 gu4tq37e *n ,h*znnvalue of g , the acceleration of gravity, at (a) 3200 m s8tqcgueey ,h n z*s7tg7ng 4 n*r5g3:   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from th+;r9q mqn j 88n0nadwqe Earth’s center to a point outside the Earth where thegravitational acceleratr;nn+qjd q880wa9 nm qion 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 sphere x/y90ap(qabhr .w6s w:j +gmuv0 fxu 1about 10 km in radius/6y0jhxw u0ua(msr p+9gqvx1bw:f .a . Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun butg.xe*ym.-zeubon2 2o kfa87. ln8twp is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravxb.8ze. e l gwkuo .tny7 f2pa2-o*m8nity on this star?    $\times 10^7$

  You are explaining why astronauts feel weigekwa n5jnt2( /htless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km abowjnen t5ak2/( ve the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcu4md91 jho:pxxnc(liew *1vi*late the magnitude and direction of the total gravitational force exerted p(1*eldxim*:ho4 jn9c1w ixvon 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 Sq;z-ijw bv 7b6un. Calculate the total fo6 i-vbzq;jb 7wrce 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 surface of Mars is t- 7:xb*jq-n(hnkcgz oq(p (u 0.38 of what it c kznoqnx( q:-7(h-up(* jgbtis on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period t*3)aei 7wfkzof the Earth and its distance from the Sun. [Note: Ctwafz*7 e)i3kompare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit ar w5/ formkn.v;lco b*5ef., pb /ki3vbout the Earth at a heigwfkvoic/l e/ r vrk.*mbf5,o5n.;b3p ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a ct +i2b41*i0yle- 4ughyy hpi iircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) ghlhbeit yiy p-0*i142 i4y+uwhen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to e)m 1yg+9wi fp+vl-pabvgjc7 /xperience simulated 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 1v+w cgplp)jyvbf +iga /-97m–32.)   

  Determine the time it takes forf. cz(rwnjr (*cxc7.x a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the ma.c wnrc7 xjcz( *.f(rxss of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top ox(,d mc 2py8ff8fch)*jitwz .f Mt. Everest to be plac )xc dy,fh(c8.f8z2jwmfp i* ted in a circular orbit around the Earth?   

  During an Apollo luna,-dsdqjn;ct;g u nl)4r landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around th dj,cqndt)u4n;; lg-se Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.kp7il,w aen8bi+w1h5 The inner radiu7ai8+w1w kp ihl ,5bens of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in ae0a1 35enlh6u1 wva3i edl+ zdiameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent ad113+ea ev03 ew ullzh6ia 5nweight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut ;pu.8x -e zk6: ;hljbxiqc( sb4200 km from the center of the Earth's Moon in ac-6 .( spjx bhu8;elz kq:ib;x space vehicle (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 system consist n9 f/8mnapfa 3;vrpogvwt412 s of two stars of equal mass. They are observed to be separated by 360 million km and tn3w m ra91g2vf /4;n pvap8otfake 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 weig 2g 2bmy5.gntt+ +ctuwht of a 55-kg woman in an elevator that moves +.y+ nt5cb2umtw2gg t
(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 of an elevvavgxs:q 05dn13f f )g x+tm(cator. The cord can withstand a tension of 220 N and gg (d0xfm+ )c 3t5s:ax1fqnvv 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 k:q(,jw)ae kj ( wyl6ms0xx, eT , the den,,6ejqak:m ws(x0lekywx () j sity (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 determine the perio) v6kdb*ya w6c.g4 3q)suf lvid of an artificial satellite orbiting very near the Earth’uv63vaf *s)qgiky.wl)4 6c dbs surface.    s

  The asteroid Icarus, though only a few hundred meters a6t r cykioc5toi 4nv19p i70 2;gjbgz:cross, orbits the Sun like the planets. Its period is 410 d. What is its mean di2ig ob5i4j tkv o9zp 67cc:yrng1i;t 0stance from the Sun?    $\times 10^{11}$

  Neptune is an average dikh0r)x- dapvw v r+w89stance 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 66jnrn-f o*c:vr/nkajc 8.am6 s e(to the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closjo6:a. nvjn *fccstk r-mena 66r8/( oest 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 distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center h fsb.o)s(bpscm (( 7cof 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 distan*8xaszmj( r:gl ro;.4 j:rn lxce for the four largest moons of Jupiter (those discoj so 8 ;:x*4jza:m lxgrlr.nr(vered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the egio/bobq+: 89kh41 us6 lx rsEarth from the known period and distance of the Moon. o+ gru hb/x9o6k48 sl1: eqbsi   $\times 10^{24}$

  Determine the mean distance from Jupiter dp8 vbkwpbr4l;c ,oj8b: hvv:t,q :)h for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in thevk vl:j:obd p8:rq c ;t,bpv,84wh )bh Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betwee:f,c7f)9 gfzrq s q2/klfyas3 n Mars and Jupiter consists of many fragments (which some space scientists think came from zf)s k9r,clf/fsg:3f27q y qaa 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 artificiali(grf2jv5e: 1zdtg+d "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 same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be t jvdeg:g2(dz1t5i +frhe period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from *+nzv u1ztl6) vuw4 pva hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vtn*u1)+4zwuvvpz 6l vine is 5.5 m long.   

  How far above the Earth’s surface will the ac8z,dz*q:yfvp2ku+ll vb /-gtceleration of gravity be half what it is on thp+l,:u g- qzzvf/v82y*tlkbd e surface?    $\times 10^6$

  On an ice rink, two skatery+.i(rutsrnvbu .9pu snj7;t zo) 8a-s of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we ass; .ir(9bua unnst r st+8uvp.j7z)o-yume 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 o) j/z)8v ri6zj atj nnii9nc xnmy.4+)nce per day, the apparent acceleration of gravity at the equator za/ v4cntni i9 z)8yxj)nnir 6mj.)j+is slightly less than it would be 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 s vazco: a6 5r)bu;i+oax gwkk9+ ph6-zpacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull wi xo;)b- 6z+azc v oawrk9k6:up 5ahg+ith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, b 8 kuufs6dat 8x8.y7oimm rm,1ut when you stand on a bathroom scale in an elevator, it says m6a8ot,x1y7i 8 du kmsfmu.r 8your 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 1qsk*g2o3g s: u. mykra circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle fo3 g.sqrug1: k2ok*smyrmed 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 vertical loop (Fig. 5–43). k8k 7dbmjx o8y ;r0zk+
(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 termzh4lfur 4v8k, a7y8c xcvu - k)y4)h.e,twbkms of its radius r, the acceleration duey8u mazwccl8he)kru., k74yt f4v)bvh ,-4kx to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fromo 9ugi5bd)+ee b)wq 9v zi, u,8yvn0vr the vertical by an angle ree 8uvw5vdq zui+9ig 0b,ny)v9,o)b $\theta$ 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 bankg tqeg)yi8 5 0q8ot2kced for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle 2)tt o8g ckqi e085yqgthe curve?

  How long would a day be if the Earth were rotating so fast that objects at 5t-6ihemim(mau 6(u7m1fm g zthe emfg1u aimm5e(hmi u76-t( mz6quator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanzq;9 q i7a /dy1v3sp7wa ;zsblce 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 curv 4*om2ayie+ aue of radius 235 m. A lamp suspended from the ceiling swings out to an angleeua2m+iy*4 oa of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as tpz .r,9rvw*wqnwgo- 6he 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 equator of such a planet. Use the following data for Jupiter: maqg-pzww96n*,ro rv.wss =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 k: y2 d0m0upj9xt i5gxc.qz3b 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 escapesui:3 j2ytdzg59k xpxm 00qb.c). 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 it trave5ny 5m stj0t5erses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvatue55sn5mtj ty0 re 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 Pos;wkgqkl,9 ,6txhs* w;u-cd jhitioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on tgtwjkxq-k * ;s;,h ,dclu 9wh6he Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude 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), a,qhny1 +qq. (lu.d +gdadd 6nffter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height ofl.q f +u.yq+ndgnda 1qhd6d(, about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttiwhav mk6++1 lsv: p3qle pursuing a satellite in need of repair. You are in a circular orbit of the same 1+sihvq+vapm 3k :6wl radius as 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 has a period of 3000 years. (a) What is its 8.qt/ij 9moc n)lv g(tmean distance from t/t)v9cqt8gl.omin j( he 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 valuzgme3 u( u4qx9e of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable ax g(u3 m9quze4ssumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center r29ef7 smn*2x e;aiurof the Milky Way Galaxy (Fig. 5-46) at a distance of about 9u7nx ;ree2rsfia2 m*30,000 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 the9wohv fuky+ p;0 ctr-wn oj0 -;dx+i/q 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 mass placed at the midpvdwtjoh-oir y0x q w9c/u0;k f;+ -pn+oint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Et ou34+g,r qzxp8egw;arth $ \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 s1j5 8pwae rjj-weep second hand on your wri-pw jrjea5j8 1st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker auv323+z-kx *ie5on lw 4ljywweight 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 line makes with the vertical? v53wy no w4ljz x23eu-*ikla+[Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R inynlkeo;/;g9x(jxq 5s a new highway is designed so that a car traveling at spek ;x/xq ;esj(y5lngo9 ed $ 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 *9 wkx ;*qk4 yvl5ubrecars 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, tl4u w k*qbv9*rexyk5;hus 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.$\approx$    $\times 10^2$