Sometimes people say that water is removed from clothes in a spin dryer uqawp5, nhy9ee)l0s+by centrifugal force throwing the water outward. What is wrong0e,asl penwh 5 q+y)u9 with this statement?

Will the acceleration of a car be the 2kgvp-t2u)z k same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the sa2g ku-zp2k)v tme speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wb+ b)*tdk-rl bf(xy v:here does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip betweenr-b+(y *fbxkd) blvt : two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse oztw0kp.)hjy 3n a merry-go-round. Which of thesep3h0)jzwk .ty forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withoutst )+hl uy1dmnk3hl:5ddp2 t5)e* bfq5 v6ubs the water spilling out, even at the top of the circle when the bucket is upsivl15u dbu5fbdpk+ld6*)q35 e) hsy:smt tn2hde down. Explain.

How many “accelerators” do you have in your car? There are at least three co.t9 wlnfyqzu-0k87c;da.y9tusj -qz ntrols in the car which can be used to cause the car to accelerate.lw0tqf.s9.d 7ut- zqynky-98 c j;uza What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small h9; l vze*ve :wjek.6pcill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), butevevke.;wp: zj6 *cl9 he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lex bg3pl/x(:u gan inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you 8 z15-gqwbv sdcompute the banking angle given 1qbv8zwgd5 -sits speed and radius of the turn?

A girl is whirling a ball on ap qwcim+z.b* r.3p) ob string around her head in a horizontal plane. She wants to let go at pr biwr.+q c p3z.mo*bp)ecisely 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 gr96 8bzg kqz7pg k3ic)vavitational force on the Earth? If so, how large a force? Consider an apz76zi ck8pggq9 3 bvk)ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what waysige. l7j;g q.xy rsj)/ would the Moon’s orbit be differ.)/q ei;ggxy l jr7.sjent?

Which pulls harder gravitationj d0cf.0rcix,ally, the Earth on the Moon, or the Moon on the Earth? Which accelerates m,jrd0c0 cf.x iore?

The Sun's gravitational pull on the Earth.n4hm b-e:n 7o8kep hp is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Considerme.ho4p k7 hnn:p8-e b the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator ;3qe rpl7 mlnl.z4iyp u:4j)ror at the poles? What two effects are at work? Do they oppose each e y7mq l pz;4l)rj4u:.n3il prother?

The gravitational force on the Moon due to the Earth is only 4zwfv xei fpj l(4u,f e04a 31:fgq0jhabout half the force on the Moonzjv0wg xfe:pq(4afl44 1,3ffh0 j u ei due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit a3gpo *eukm18g round the Sun larger or smaller than the centripetal acceleration of the Earth*3gku8 pomeg 1?

Would it require less speed to launch a satellite (a) toward th- r/y/aw*k-y a8tqbpayp3c 2r e east or (b) toward the west? Const/a8/pycpw bak-* q 2ary3-yrider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movi3h,;,f13zye b9dhzvh6t rr zong elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? I 6 tro 9e;,zhyz1hb,dzrhf3v3n 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 lmu4-ltb e ;e9space could be adversely affected by weightlessness. One way to simulate gravity is to- ebl l4ute9;m 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, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparenqy 0saijw-gxmis4r 9y :g6c8.t weightlessness” between stepsgw cxs4ayqm.j0yr-i g96s:8 i .

The Earth moves faster in its c:+l1kr( ji;gsl -ecdorbit 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 seasoncs cr;j1e l(-dilg +k:s — the main 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 dismt(nz3 ug *ji0r7h4 g95crssh covered to have a moon. Explain how (h0* rc3ju4mgg9rsznst i7 h5this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than 1;; pka6(er60zy x wf x4luzmtthe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a spee;a6 weftx06zz1p (m ;lr4x kyud 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 19y 7-um7g 9a4*njo lhif80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ine b;kqmp p*6q(dpkl 7 21m 1m;ogdt:sp its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on thel1eqdm7pot2s;kgb 1q ;mmp*p dp k:(6 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 2st 4-z(/ numgj.0-kg discus as it rotates uniformly in a horizontal cir /-(ugjzsmt 4ncle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbz*8:/z/ yq.zs gobetfit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravita :*z/gzt yzbqs .8ef/otional acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accel6gyrhf 8.h/n m 3.(i; slk evtq/ddzk8eration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revihg tk ;d l en/sm3dq8(6rkfv/z..yh8olutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved acw v86essxqfd.:j . eqdpuj.: 8ucr0,t a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0,: jr:euqp0wcssc 8x8.de d6j vf q..u0 $\mathrm{~m} / \mathrm{s}$ 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 ovqv,pf;cjd ;+ 1 u ;1tl4rq-c7qusuevd s2p6uf radius 77 m on a flat road if the cov;4q q,u+;qlcrs pse cdv2 u u61;uvf t1dpj7-efficient 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)4ggtmy9e o w( of static friction be between the tires and the roaot) y4gg9e wm(d if 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 fighx h2e*qad w9e2ter pilots is designed to rotate a trainee in a 22a9wx*q ehde horizontal 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 f44o ttp+rplsmq2 9x :brom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin r2btm x st:9pqprlo44+emains 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 tra9fp g: b6v: oz rl ;hfuhcvq4f3.1jqu9veling when upside down at the top of a circl:c4o.f h9g6 fqj 3vh:vfp;1 lu bzqru9e
(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) f(lgbg f-j2t/crosses the rounded top of a hgt-fb2g j l(f/ill (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 Ferl6j tkx4c f4* )ux;9fs7) mgcgokiz/zris wheel need to make for the passengers to feel “weightless” at the topmost point?sf; of t/9k mjxg)ug 4zkxz47l6)*cic    rpm

  A bucket of mass 2.00 kg is whirled igg8 h-w moyf,47k*d syv) cvd,n a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the s kydw*,gv8h)-gy d74o vc,mfbucket 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 particl1wja j50t-qbn4 lz5zme 9.00 cm from the axis of rotation is to experience an acceleratj5a bjzmt-ln z54q0w 1ion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyli1 +xzvkzz)hf5 93wim lndrically walled "room."h xz+1vfmk3l5)z i9z w (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 rotated in a circle on a frictionless ao- uf;3 jbv693oqr njq9q0nnuir-hockey tabletop, and is held in 93q njju9u6ofn 0 oqv qr3;-nbthis orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring 9q-wbxt,57r akm m0pethe weight of the ball which revolves on a string 0 x0pkmr7b9m, wq-t5 ea.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a cxr u31ohtngrbel o71,ey 0ot7n-i68 uar 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 p 8 vfxjz.:*pvk2ckzcw6bm 31 $ 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 diving vertically at w u/mkgngkc;f)kh*rt7gb: ) t)3bwr;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 exerted )0is;hj9/t5 veb; eid3bc yzhrv8g8m on the car (by the ground) in Example 5-8 when its s/er5v )is;8ct3 jhdbv ;bhmz0 e8yig9peed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indiana.n7ps 6bbdb2+ozk5+d8vm kaj ba;lr- polis 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 acceleration with no slippin+za;+ v8b7 56bo mrk2kpl bbadnjd-.sg or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Atf(vs5knh1 6m o a particular instant, its acceleration is 1.06fh51v(kmno s 5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 spacecr5uhf+u7tam7g/ gn. rv 0eo(qv aft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 o/7va5+ u(unvf 7mq h.rgt e0gkg.   

  At the surface of a certain planet, the gravitational acceleration g has agl(s,;m(pz rk(l4d jtu hh.4jfg,- q z magnitude os-pk(fzhg,jl q;rg (zulj(mh 4d4., t f 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 rm/l7auiryot(+dfy)ti 82ah4 9a xgh7adius is 1.74 (4gixm arotaiy+2ht7)uad 78ly9f/h $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiut7:sqjs+bhcu(z a wtuf91.f,s 1.5 times that of Earth, but has the same mass. What 9t +uza f.ju,sbwqh c7t1f:(s is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thykq0 i3)rq lr v6s1m/ce same radius. What m/ ycr6isl r0q1 q)3kvis g near its surface?   

  Two objects attract each other gravitationally withbl( 3hx9mpm8 t a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3alz1;bu nvj( -200 m j-lbvanz(1;u    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to )9r o-cpe ytd,e2+f4 zvk1clze3z3 ega point outside the Earth where thegravitational accelerak + zoe pltr) cez3-9,3cf1dey4gz2vetion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star haa 3ez g5n-wcbkig: dc*v 84pi(s five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate*ni e- c3dk5:cw g4vpg (a8izb the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but mh2 dmg/7i8n4 .uzkd)h jvf+dis now in the last stage of its evolution, is the size of ourd m.7zh2)/ghvu nk 8+dd4jm fi Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitin3f (mlusj t+qv:k+4rdg 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(ksut rd:l34mvf jq++ km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of av l 60znut1ejede06.d/e qs2z square of side 0.60 m. Calculate the magnitude and direction of s/t.eq6v00j ede2ezn 16 l uzdthe 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 qs cc8eny o t39(seww10)/5tq7 xlxapSun. Calculate the total force on the Earth due to Venus, Jupiter, xs qy(x8tns)ta el01 37/owec cpw95q 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 it9pgk +w,zr9td+ hkz8s 0.38 of what it is on Earth, and that tgwdzz9+kr8kt +9,h p 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 of the Earthmcdbok -00 afjc4m 3hfo409 mj and its distance from the Sun. [Note: Compare your answer to that obtained fh 4o 9c00fok0mdj3 -j4 cbmmausing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the E.g6xzateux 49t nr8 a1ro ,m6zar4r8 nrou6gxae, 6x1 .ttza9m zth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65dfhs:yc 4 rv.10 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the r:h1vscfd4 .yrelease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to6 fwgbjv*o u l/)kq-n* experience 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, F/-u**gw6 lq)konfv bjig 5–32.)   

  Determine the time it take 6/bzd7m m.n7fzd2iyz s for 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 mass of t/zd. fi7nmz27y6mb z dhe satellite?    s ~    min

  At what horizontal velocity would a satellite have +ym5pznsz.e5 to be launched from the top of Mt. Everest to be placed in a circular orbit around the 55zp +esnz ym.Earth?   

  During an Apollo lunar landing missig6fd. 3ei/j zy+8wiut on, the command module continued to orbit the Moon at an altitude of .ei3ig6+jfy u z8/tdw about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks o.,*ckv.b1mq3us hbjb f ice that orbit the planet. The inner radius of the rings b1u.3hqsk jbv*.mbc, 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 diameter rotates once every 15.5 s (seeq(m h+w;z-d y* fhax6n Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at h+ 6n;yqh -a(fx*mzdwthe top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cent-ocae h6o ll8,er of the Earth's Moon in a space6l8-colh e,ao 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 consists of two stars y m h:le,lzps6ius+ h1o+os8/fno 9i+of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years ss+f/+e:8oul1 omn +z hi96yph sl,oito orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevuen* yipi3g)4p1f y;dxrk/ v8ator that mov/n*eiy4f)rg 1 dpup8xiy k;v3es
(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 u3gut8me d;w6vche, z 3zx- i*v1;gqxa cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator;8ivw3mxcx;uhqe , zugve d1 3*-zg6t ’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planeen6/muwy5j 4uo ,vtg ce) 5hl fd-(xo-t with period T , the density (mass/volume) ov )5d mxt olw--eu,g/co (yjn4he5u6ff 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 Moojqs0k :e)w ue+n (27.4 d) to determine the period of anw0sejk):e+q u artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbit+o 8wfks6x*s cs the Sun like the planets. Its period is so swxf+k*86c410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagh*jtq4ck du 78e distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It 0vbbctf+ 66: akfle 4pcomes 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 third6apbl e4+v0 : ffbt6kc law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce) xq/zun;*)tx0tdvas if bp70nter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance foragjkfd9)o40co hrsrw +37 tb/ the four largest moons of Jupiteb+j/ ak)w3cot4 9dr0s7fhrgor (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distanuk.tf l3 iy6x m7lvc2zbmg.5,ce of the Moon. kib.uxt6cl 5mf3 2zy v.m7lg,   $\times 10^{24}$

  Determine the mean distance from Jupitelb76/pkhyyur3t/ 5d j r for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the b5//h7t 63jyrdu ylpkperiods 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 bet vyi-afb1 h(7jchm471 v3vw mm9xlvp :ween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun butca (i3vv7j9wx 1fm bh17lv:mmy p 4h-v was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "px)y u3eum *+k m26wflklanet" 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 the period of revolution, this planet's year, in Eartuk+x flykmm 26w)*e3uh days?   

  Tarzan plans to cross a gorge y 99gfporaaenqa)4+ 1 by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting +n9 aa) ro4a qep9fy1ga 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 Earth’s surface wills1wh q6,5wok c the acceleration of gravity be half what it is o1sc,w6 qw5khon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands9*a-va etb/j.uc 4bean6;y t j and spin in a mutual circle once every 2.5 s. If ab9;ye4/ b 6.nuaca* jtte-vjwe assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth ro32t c;g6gk;yy skwwi4 s .sk.7qt( wastates once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t gww(.kts3a4i yk.; 7ks gs tcs6 yqw2;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 tra jxe32per)m-5 ld9 /oumyfx6mgm i. g.veling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite fo)mjlxg635ogyi . x2 puf-r. dem/mm e9rces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand;ob 0h9v5bd arji3mw1 on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevib h wvb d50ja9m3or1;ator, and in which direction?     ----待选择----upwartddown 

  A projected space station consisggu ;0l9 h5pao t,,bx 0v.lhtgts of a circular tube that will rotate about its center (like a tubgg9otxat0 pl 0 hbhgvu,,.;5lular 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 vertical loop (Fig. 5mk0w nx(u98ak )lisf/–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for th.-xq+hgya2nzy4n3 zr/ p/lx ;/h wsz xe mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constant Gp3y; n/zzl- g hq2//x xhn+rx.swz4ay.

A plumb bob (a mass m hangingjmm,10vleh 9v on a string) is deflected from the vertical by ah ev 1vj,m9lm0n angle $\theta$ 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 coefficient g( a1k.w . 83vt6c+gnm+kekaad- t yboof static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the cur.(k3ovwt n1ga -a.8+gm a y+dbk kcet6ve?

  How long would a day be if the 2mb;hscqm23sp gm0ew9g8u(kwosm 6( Earth were rotating so fast that objects at the equator were apparently weigh82mhpwsm3ome g(gb 9(k m c0; s2ws6uqtless?    $\times 10^3$s

  Two equal-mass stars maintain a cfgg a+mxtvgzk2xd;1mt 3g+8 h5/)w cuonstant 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 235 m. A lamp sus yb :5i83se fbcs.7hvkpended from the ceil8f5ecys 3bvikb.7s:hing 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 Ea:w4xs fjd2f.irth. 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 survf4s2wi jf.x d:ive 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: 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 Telx02m*dgvhq;n escope 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 speedxn2qdv0h; m *g 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 8e(hlp)xnvrbh1-p/apa5r q 7the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (h(/hx 1q baprep lp58n7 arv-)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) utilijy pr9al)w x6zk9 6vmw ++e)ppzes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately emkz)9)+ 6p6ppyvj9 wrx+wa l11,000 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), afte vw (wcc9ga89sr traveling 2.1 billion km, is meant to orbit the aw8c swva9g( 9csteroid Eros at a height 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 mklrmyran r.,iw*7 ((k)vj7r of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind ik7a7nrkmyw* (, vmr l. )(jrrit.
(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 pfv mwl6v0hm6f137siweriod of 3000 years. (a) What is its mean distance from the Sun? 3wvm hf6lsv1i60f7mw   
(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 actuaqitl7 ,a:mm ,.z c,lctlly "feel" yourself gravitationally clzt,t 7,lq,m. mac:i attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around tht 2*sgorxj 7de+03d: zf)gfeze center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fr r7tg*z3xdj+0go)de2e: s zff om 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 atypdf(u q.q1itwc3m; , the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of theu;c m.fiqp(d3t,q1yw bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 k0yme t d5,wq+sg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5my2 ,xz+z/copz,d 1 5.bccmzz,d ani. -cm-long sweep second hand on y zmo 1ddz,+ic x.,pa2/b.y5 nzzm,czcour wrist watch?    $\times 10^{-4}$

  While fishing, you get bo y 9 x6mp4 oik+obv47ecrc;zd:red and start 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 line makes with the vertical? [Hint: See Fiz49d mr4c y76e:xi;kbo ovpc+g. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that ,.or dufw.0g x:vvqhd68i- cma car traveling at sq d.u.vog8mifh w:vd- xc6 ,r0peed $ 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 when negotiatu n6x l 1yer0yg9r*o7ling curves. The angle of tiltl*no y9xe lu7gr 1ry60 is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does 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.$\approx$    $\times 10^2$