Sometimes people say that water is removed from clothes in a spin d7 v.4,dbwkvq bryer by centrifuga d47w,vbqbk v.l force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when thex-ek2jc, djyaxn:o-9 5x4 qyq car travels around a sharp curve at a constant 60 km/h as when it travels a249-e d, x qq5ya xyckxn-:ojjround a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doa.,fas6 bn*3 t bpt8jnes the car exert the greatest and least forces on the road: (a) at the top of a hill, j3b.s6, t*bntna8fap(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 0vmt* doio89i a horse on a merry-go-round. Whicdv8 *0omt9 iioh of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without th/fi8ocad rm9 +e water spilling out, even at the top ocmdfo98/ ar+i f the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? o8hijhob ,cvo1 6-f,rqwk: x+There are at least three controls in the car which can be usx q8+, iobkfjh-1rvc,ho o: 6wed to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hilx b-fqtm3i3jr,i+dj( uu6q7zl, 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 hi3iq+fujmjt( bz-637rq xdu, ill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve aty5vd)af:roii ngabmz76 l:/9 high speed?

Why do airplanes bank when they tuq9.t9my b6xosrn? How would you compute the banking angle given 6q os9tmy 9.xbits speed and radius of the turn?

A girl is whirling a ball on a s d.(5hdayx nb7 uvwjp 5(qar(m8uer,i:l pf 02tring around her head in a horizontal plane. She wants to lvp, uipm(h nrl2bxur:daf5a( .y je87 50 dq(wet 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, how large a forc+ztb*wf -y8d)vjyw (o e? Consider an apple w8j* v fw+yy(ozb )dt-
(a) attached to a tree, and (b) falling.

If the Earth’s mass weremctnz p3*,//ap6 rmlg; rqg2u double what it is, in what ways would the Moon’s orbit beg; lctnu*/m6 p/amp, g3zq2rr different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon oldcyk1o 7.i y(+)z7b qtdtnh8n the Earth? Whichyttz o7ycdn l qd.)k 7b1hi(+8 accelerates more?

The Sun's gravitational pull on the Earth v6*j89rwy t 3e0 r9wh vtrdxa,is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravi8y6*xarrjt w e,vt3vrw9 90h dtational pull from one side of the Earth to the other.]

Will an object weigh more at the equatoylw),yq6hb id omsa1uz0e(5 3r or at the poles? What two effects are at work? Do they oppose ea0b6q 3 h,ywi(la1u5d )emoy szch other?

The gravitational force on the Moon due to the Earth is only abou*2uz /aezk4oa 4h+ns ut half the force on the Moon due to the Sun. u+42 / s4a*uk ohaeznzWhy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or s ae. dll3v+z3imaller than the centripetal acceleration o vl+d3 ai3l.ezf the Earth?

Would it require less speed to launch a satellite (a) toward the east nq()m;fp d3 ovor (b) toward the west? Consider the Earth’smqv) ;3np( dof rotation direction.

When will your apparent weight be thvhl(563ijg qj e greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the sam6gqj v(3ij5l he as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spendkmi juo+fu)kz/41 1zn long 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 the inside surkf1ziuu+oz)1nm/jk4 face (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 experienc).pb.ov x br9*pmdt8p es “free fall” or “apparent weightlessness” between stepsr.8p x *)m.vd obbtp9p.

The Earth moves faster in its orbit around the Sun in Januaryztp 3*dvoj8-9gst rx4 than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor isdj 3 49-trpsxzv8t* og the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was disco 4 4uj*(hg(r(xcnq izsvered to have a moon. Explain h(h(( ns4q* g rjxcz4uiow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mucs0 (ocm6vk+vbc 3 d1crh larger than the Moon's. Yet thk1vv0c3(dc+os6 c rbme 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 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 1980 dvefermtm7 t5( *jd815nx wu+$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ii o)*1:4,r7 ltem(s , rrgjeox ini(jxts orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle (ol:e(r1xism4* jnxi rji,,r)e 7got 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 l 5ruc)i 3nv2v8.sy8j4nqdi1 ukmm1k exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radinn2)5v s18vk3 1 umlujqrmyi.kc8d4 ius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circx;c:rta3k5d c) ;mrsmles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleratik53r :r m;ccs)xamd; ton at the Earth's surface. $\approx$    g

  What is the magnitude of thxms g-td:zm c490s,r ue acceleration of a speck of clay on the edge of a potter’s wheel turning at tds9 zmc-u4 :,rxmg s045 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertip*3xg b)sz 0ru+yi c3jcal circle of radius 72.0b*r3z0 ucx)s+3gy jip 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 rp2/tz m1tokg4 5:n nfwhich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of/2tf1gn 5rtkmpz:o4 n the mass of the car?   

  How large must the coefficient of static friction be between l m m+ggf16+bc;b dhv:the tires and the road if a car is tomg1+ghmb6vc:f b+ ;dl round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts a0 (jkz/fht+b5b zvc+znd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her bac +bh5z0(f +kczvjzt b/k 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 f)mycu/lb:5 tc rom the axis 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 of 36 rpm is reached and the coin slides off. What is the coefficient of static fricticcb5)m t/uyl :on between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling 7(sxbs n08ura when upside down at the top of a circle 0(8xursab sn7
(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 (including the driver) crosses th ;v.9psf1uox(q iow5j e rounded top of a hill (raxs9iwu op .1(qf;ovj5dius =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 Ferrisnqddmxt2 t3h 2pa(o ti7z04z) wheel need to make for the pass4ti(d2azpnh xt7zoq d2 mt30) engers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00tmf6z)5/ws kt kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion thezs/ )tft6k5mw 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 9.00 cm from the axis oy la16)cs*txd f rotation is to experience an acceleratald 61y*x c)stion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c9ai1 lp3g e/sdylindrically walled "room."dlps1a/9eg 3i (See Fig. 5-35.)
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 rotaidtqua17pw9zo4 (g e7 ted 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 gw d e oaqt4i91pzu7(7 m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this ti;(tvri(q )lxqua 8m1d me, by not ignoring the weight of the ball which revolves on a string 0.600 ma (qm ;vd8tui1qr(x) l long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 1ky y38g 9cinw9o1b kn88 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 massej 0 18pokv)r* czvy0ehs $ 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 evasnii)4i x4mvp;zkq y3ko1 1f7 4nlllh 7ive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exer5u -ljr7icu 8 pp+t5fited on the car (by the ground) in Example 5-8 when its stpi+5j ul7 ic-p8f5rupeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformlo 2s*8j vqrr im*6g /sjmrk7oo:o:cg )y from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Deterggm s scjkorro*:/moi27q8o6:j)*rv mine 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 acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a p ; (qextgcz5msqrqe m10,m+(y cqya 7*articular instant, its accel5xm ;1+t0qzy,a7 yq *q mecgmrs (eqc(eration 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 g jru1qw7+( g-ythk;wj5d5d tb ravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass55d kty- udb+(t ;h1qwjwgj7r is 1350 kg.   

  At the surface of a certa hc+9*x2fow goa:dyb.)vy sj5in planet, the gravitational acceleration g has a magnitude of 12 mv.*xo:agcy)h 92 oyj5 w+bsfd /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 accelernik*x .zv7( qfpz- v:cation due to gravity on the Moon. The Moon's radius is 1.74 x qc.v7zf:z ip*(vkn- $\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 thatu151 ftg8ax9un(:q2g a laegp of Earth, but has the same mass. What is the accel2l 8n(a5u9g eq:fxg1a u1tgpaeration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times th,w)1q4l dy n2b-;,hi gti7hj bh 5kxrtonea-0at of Earth, but the same radius. What is g near its surfaxjh-)b7-0,e1tq2 b5 hlrgd; wi nn ,ah4ioytkce?   

  Two objects attract each other grau2zq -p -:bhvemout; 7vitationally 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 wn l0qwxwu(z05e-3;ipnu7 aj of g , the acceleration of gravity, at (a) 3200 m ;7j0zi we3xuw5(n l0p q-a nwu   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pointvt3fie 5h :p3gpz)( iov(ea mkk v495j outside the Earth where thegravitational accehto )k5v ek3((p z :9pieivfg3va m4j5leration 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 sphe;(mause gn7; 7jupl0s re about 10 km in ra jsgsuluem(pn707a; ; dius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which b* 4msj o jl60ten.:cs*t.h izonce 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 the mass of our Sun. What i .blchjtsnemz06o:.4j*ts * is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fhd97wam g2t +i 4ze4bbeel weightless 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 calculatm4ezd7ag9 h2+b4w i bting the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are l stcn/+va )z:uq0 dvff/8zd7tocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the tota)f0z t q:zfvu dsn//87cv a+tdl 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 s)gxwjw+*(y; s ifmis hm2z+ 3pame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38).z ; +mf()mp*iwxjgss3 2iyh+w 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 )wv b k)q2)ur6qpd2)1hpzfeo is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine th2ubfr)qphdk )pq)z1 wv e6o2 )e mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the p 3ut*z zj/nav2n* ) m3pgc/vpyeriod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s la 3gmzt *y2)nvvpz/j n*uc/a3 pws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellitdmdhf*n,( y( ze moving in a stable circular orbit about the Earth at a hef n(hmz( d*d,yight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the E+ (9dgxnjlw oi49v z0karth. How fast must the shuttle be moving (z9j vlix (w +dg40n9okrelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occ eb0/g9molu ;1yuswx1upants are to experience simulated gravity of 0.60 g;xeub0 1g1lw umo9ys/ ? 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 o5b1 gzopaf1w9 gj5.tb rbit the Earth in a circular “near-Earth” orbitpaw5oz .b 1j5g 9tgf1b. 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 mass of the satellite?    s ~    min

  At what horizontal velocity woyqjblqz tjk 36w*800x uld a satellite have to be launched from the top of Mt. Everest to be placed i j0k8* lxb03q6q jwztyn a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to or 2i)6.gr s.0hhgwt hxwbit the Moon at an altitude of about 100 km. How long did it take to go around theghs gw. )ri hw6.20txh Moon once?    s

  The rings of Saturn are co 4nud.ohqo)5w434sk ouft n) umposed of chunks of ice that orbit the planet. The inner radius of the rq3f.)dhw44ok) ouo5s unn4 utings 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 dia*)uui1 2ateiqn.ef( b meter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’b qi(e.at*u) efn21ius 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 astron f/xu,rvtqyhf 7io0y8yeoc7i2 :4fn,aut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant ohfc8io 72, :/,e4fi fux 7vynrt0qy yvelocity,     ----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 binaryz;hc6bibff,bzk(:y k(m3v p+ -star system consists of two stars of equal mass. They are observed to be sezbi v+pc3( kkf,b:fz( ;myhb6 parated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale reaisrs8m6q/8j 1myj6)gati:tz d for the weight of a 55-kg woman in an elevator thatimz agj/18t: 6t)srjiy 8q ms6 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 suln yav;-r6 )yuspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elr6vyu )lan y-;evator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfacx v +b.6lxxg,,kaw7wadh(fw+e of a planet with period T , the density +, w(xbw6d,aka+7 wgx.hx flv(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 periodfw5z4 ghm3a* o of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’h4 *fmz3og5w as surface.    s

  The asteroid Icarus, tio/7f+xwrv wc4c ny9r+lugrk 9/ 0 ;cfhough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from thenxlc/r 0i+7w9yu4g9;c+ vffo r/kcwr Sun?    $\times 10^{11}$

  Neptune is an average dist( 0ir ;luek9liance 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 w: n,zb2ud7 tnthe 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 Kepler’s third law iubd, zw:tn n27s half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of tz2ts)3*uo w2c* xgu tthe 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 meann pyqrj/q+,h gn/x -1p distance for the four largest moons of Jupiter (those discovered by Galileo in 1609pqnhxn/y/-q ,1p+rg j).
(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 distance ofc:1fdl ed l7b)4eah1 y the Moon. 4 dh lfe1 )lb1e7ayd:c   $\times 10^{24}$

  Determine the mean distance from Jupit)up;j x;cx-t eer 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 the Tabl-;pj x xte)c;ue.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betwezj -:e9nlql s)en Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but ) :jn-e9qslzlwas 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 ta eestc:qz9fgm*v 809xalr, p2le describes 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 same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent c8029lt*,asrv :9fzxe gmpeqgravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorg k 8q+zkq5ley-mdi /y1e by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the ld+ q15k8yze liqkm- y/owest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravityupnsh ,fw2t9 9 be half what it is on the surface?2fu ,wnp 9sht9    $\times 10^6$

  On an ice rink, two skaters gv8*vr on2pc4of 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 are they pulling ogvp82onv *rc 4n one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravi//: h)jy moc6gwoict;ty at the equator is slightly less than it would be if the Earth :o)hm;yc g / wtcj6i/odidn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from5 i/d*m 9doz+97orx s3 dfu59bubal bb the Earth to the Moon experience zero net force because the Er9u95*d59o73asbzb+ mfdlou bbd i x/arth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on ae- raqljigh- y3/ek*b 0 :.jna bathroom scale in an elevator, it says your mass is 82 kg. What is:eia bghej0*rn/qj -y a3. lk- the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about.6r 1gvf tdxb/mdt82a its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions p x mg6tr21d.f/tavbd 8er 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). b bhsh3q3f/m9
(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 radi g7cil,g+u p77tl)exa9q;h q lus r, the acceleration due to gravity at itscgp7 +l)qqig lluhx ,eat7;97 surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is nvd9nr7j .- dvdeflected from the vertical by an angle7dv .dn9jnv- r $\theta$ 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 design speed of If the ch4xy;hei-9 lkh; ,jojoefficient of s;4,y-h le9ji hoh ;jkxtatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were u0c)gpy q; w)yrotating so fast that objects at the equator were apparently weightless?)pwy) ycug 0;q    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8d+spn41o 9qm9ybc/n n.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 c8 nzf7tir6 ,myurve of radius 235 m. A lamp suspended from i my,8nz6r7tf the ceiling swings 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 the Earth. Thpyva;ik kt ;+i++aav,us, 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. Calk +a;kvti+;aia ,vyp+ culate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of adpv8w 6.of e:iojcd36n extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which nodf.vwio 6oce d:p683j light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley show1rkyt a3/qx((5gca wan in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast ak 1wa /(qt3ga5xc(yr can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gr5rm s8 oti9z m/c iinfo;d245voup 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 aroun58 9fii54so inczvmm/t2 ;odrd 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), afs(q9ik (a2pw mvf1a:t ter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a h9a2v(pft(sqw: kai1m eight of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of cjio y x .pcddh*/4t3/repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 34dj. /dxc*hc/yto pikm 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) Wha 6 /qckf9havp1sc*,;pv.l(czcsg hw) t is its mean distance from thev .6; pfk( c h)qcga/svscw,hzcl*91p 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 coul 5e.hhy4b:(wejzs si6d actually "feel" yourself gravitati( sb yj5e64wsh:he.z ionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ofnq0c9o urb aq v6c48+z the Milky Way Galaxy (Fig. 5-46) at a distance of8qna6o bu4cvcq 09+rz about 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 the corners of a square 0.50 m on each sg//*ehx(zc m*mb vrr;k ge2j+ ide. Find the magnitude and directionc*h/v2/z;bgem x +m(ej r gkr* of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 55004i. h(x2r:zon yvaee2 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 tikyun p() s6/rgue:(ejp of the 1.5-cm-long sweep second hand o(/ru6)ke(e uyjn gp:sn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to u ea4q1v +vw4obb/wm:swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight ma/b:e4 vmovuaw+bw 4 1qkes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a carzgez gh6we+ .gqh6 )6x traveli+ge.h gg x66z)6w eqzhng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes ti cs zkhha8e:/- j/azk7lt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela tra7/ezzak:j h/ c-h8k asin 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.$\approx$    $\times 10^2$