Sometimes people say tha .cc,y /kx4m3vyfeb )et water is removed from clothes in a spin dryer by centrifugal fyx./,y)c cev3 fbe 4mkorce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when thbwv-voa: xh:u 9qj 4i2e car travels around a sharp curve at a constant 60 km/h as when it travels arou4i:bwo -v :xau29 hjqvnd a gentle curve at the same speed? Explain.

Suppose a car moves at cwi**ep+ zlx*e d81 sqkonstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) z ie ql1xpe*+*d*wsk 8on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. W;ipj4y ,zl3xchich of these forj43lz;xpciy, ces provides the centripetal acceleration of the child?

A bucket of water can be whk8bp(g, w n99uh jw5(kfqa1g+ jiv0fvirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaing5gubia998j 1 (k(n wfh0kjw,v qpvf+.

How many “accelerators” do you have in your car? There are at least three co bacpz*fw14ma80i v c2(f7gdantrols in the car which can be used to cause the car to accelerate. What are t8dpw 702zi bgacaffvma41c *(hey? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. s1rgas1 z rh)65–31. His sled does nor)ha g16sszr 1t leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at me fv/p)a oz)0high speed?

Why do airplanes bank when they turn? How we5 k -j (p4efcq)lyye.ould you compute the banking angle given its spe5 ejce.feyk4 - y(lq)ped and radius of the turn?

A girl is whirling a ball on a string around her head x t(ozjk:.zff8 -7raxin a horizontal plane. She wants to let go at precisely the right tiz 7x-f(z tkf.rja:o8xme 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 tf dvsz; tsy: )syez,10(1o/ub/wx pwd he Earth? If so, how large a force? / )zy(/sxb , 1d1w0es :uodtf;vwzpsyConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wou4a+0 t05s*tsde fwla i7cz0qy o mo,3ald the Moon’s orbit be differentw o0 cdztt+me70f,a3ya*soi0l 5s4a q?

Which pulls harder gravitationally, the Eaw17qql(s mf/ 1vc ua9orth on the Moon, or the Moon on the Earth? Wh7qq l1 wusmf1c (o/v9aich accelerates more?

The Sun's gravitational pull on the Earth is much l4a5u.2 .j r)kdtx qy hk-nxgp;arger than the Moon's. Yet the Moonntkx.k5 a2d-x; ) .quphryjg4's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects ara m fca8-jenj;n4-wh0 e at work? Do they oppose each othen8cj;ma4ajh0-w- f enr?

The gravitational force on 8k0+uk rgpe toc 54s*wthe Moon due to the Earth is only about half the force on the Moon due to the Su0 g+8kkr o5 eu4swt*pcn. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun n ls(k9j 1 hza;kt8 ypnwoubo dd dr1,4b1*)s9larger or smaller than the centripetal accelerationb*ok1n,p b 8d9ya) d9ldu zn4tsjr1khwo(; 1 s of the Earth?

Would it require less speed to;wjrfaq *j+ w5fg zaup((3,il launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation p (g*z(wj 3wfa,;5r uijalfq+direction.

When will your apparent weight be the greatest, as measur -qwdph/ut:o(s aveyn8*f( 9ied 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 y /:huo8fwnsv -iptq9ad ((e *the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversequ j08x h,z08;cmecjo ly 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, and (c) any other aspeo0cjj,8hq z0muc ;ex8cts of gravity you can think of.

Explain how a runner experiences “free fall” or “appauccobcw12s8 0 rent weightlessness” between stepc2 0 uccwbso18s.

The Earth moves faster ie0 k42r lvs2xfn its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is theelrxf0 s2 2vk4 tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have+ 3/p*gem-sgnskbzn. a moon. Explain how thiskg m.s-/n sz+e3 gbn*p discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largerl 2qchyaim,)u3/xg) p than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a spee2m i3 )/ )cxa,pgqyuhld 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 8 bx/*4wah vl-kqy)oi 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the E4t* r0 2yhqilkuzb0xg z7 :1ttarth in its 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 ci ht kt0 zrzb721yq:lux*4i0 tgrcle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotadngop55 uh,f( tes uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. o u(fp5, h5ndg  

  Suppose the space shuttle i4v 7m:nq jdat9gqp 3.ns in orbit 400 km from the Earth's surface, and circles the Earth aqq v t 9d:anjgmp.3n74bout once every 90 minutes. 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 a2 vjr:lpdn ) qu/cx9s*dez 04occeleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (drv9:j2 p*n4xz ) 0suoqdlec/ revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a su;4ax o0qjz f9o)(b auniform rate in a vertical circle of radius 72.0 cm , as showfauo)40 x9;j q(sa bzon in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 10ziq5hpl n3g5550-kg car can round a turn of radius 77 m on a flat road if the coefficient of statihin53 l55qpg zc friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefftcii w;mjv l- 0nxp124icient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95k;4 i21ptm -n0jwi vxlcm/h ?   

  A device for training astronautsvje5d53: /zv 2n*rrv nyxm bl: and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If 2zyrb:rn5:5ej dl xnvmv*v3/the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating t+m xz xig5ib ,(m+ly+zurntable of variable speed. When the speed of the turntable is slowly increased,(zy+ +mgxb mix+i5l,z the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tguqivc+s (a3p px(y 34i t:6y5w,k twfraveling when upside down at the top of a circlgqy6k ypaw:u+ v34 3tispx(f(,w5ic te
(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 yp8lqbyifq6x;y) tj .v) i2a7the driver) crosses the rounded top of a hill xqaq7 by)6pt v.yl8)f;i2yji(radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need toxr9wgo0y v4;h make 9 ovgyx h0rw4;for the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. +;l6v lojq7itAt the loweq j+ilo6vl;t7st point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a pa7/o6 ut y)dgg t2kvn;hrticle 9.00 cm from the axis of rotation is to experience an acceleration of 115,vggn6o/)hk t ;7u2ytd000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walli5v t wr2/z,eved "room." (r wv/it5 2v,ezSee 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 ai+d8/ p*ujk*zcsf g nd:r-hockey tabletop, and is held in this orbit by a ku8 *p+nj fsdd/zgc*: 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 the weight of the b6 rw:ex7um iouiicig;ct0 /3:i;/xpm all which revolves on a string 0.600 m long. In3it gc/0u/iui:ix7pmwroxi;m6 ec; : 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 car tm tu3ieti *11uqsf30jraveling 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 1;s7an- buzwi $ 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 dzlc 2+jw /zbk8iving 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 f ljk(s2 kk5y7; uusts3c 6al2lorce exerted on the car (by thj s 6u72salk ly;c(2uklk 53ste ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the (s bksz,np; o1s.0xgapit 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 cusx0. ;snkzsb1, pa og(rve 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 pac-yc+yj v4di f400s 7uri*zhzrticular instant, its acceleration is 1.jrh0i*si7 ycz4c uy4 d-+0vf z05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 grav*cufc0)csl *,x n0 sevity on a spacecraft 12,800 km (2 Earth radii) ab*nfcxcl), sesu0*v0c ove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, tx7zkyuxto)j;(b 6lq - he gravitational acceleration g has a magnit bl6)x-t(jy kzoux7 q;ude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravitym k6/8f0hjx ta on the Moon. The Moon's radius is 1.74 mxfh/t860kj a $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timlsd juwee,071 es that of Earth, but has the same mass. W07 le,dsw1u ejhat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.e+cth4 53uyk 8qkuf7l66 times that of Earth, but the same radius. What is g near lfe 8ku5u +ykhtqc3 74its surface?   

  Two objects attract each other gravitationally with a force ofuib4s-ks:1c.6o 5 sm8 evkr dg 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, at9txfae 01b y8lpp (xc5 (a) 3200 m ya8 5xp01 x p(9lefbct   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earbas0*wo -fl -h 5qt3rzth’s center to a point outside the Earth where thegravitational acceleration duel w tos*3 za0bfq5hr-- to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times them6vz 6l2ee *ovd zq(+e mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfacezv6ev6*d+2 lmoe( zq e gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a6 ntd; rxljb dz( k1i)dzx)8j3n 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 ourz))dk;t8i x(dj1 xzbd n63lj r Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in y iy:j e3s4e1jel/c7wm,tj.x the space shuttle. Your friends respond that they thought gravity was j14j.isceeyt 3jwm:x e ly/,7just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are wqh4d 3-kn:ol n9ys9rlocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thrrlwk949osdn q-3hy:n ee.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Su c3ri1ic 9pc6vyde.;n n. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planet13yr.c 9 ;cienc dv6ips 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 ;8-p fepg8s.b1xbqvg hxp6 e4z 8gtw*r-:hla of Mars is 0.38 of what it is on Earth, and that Mars’ radlg8-s ;eh:.g6heva b r-*gx wpp8ft41xb8pzq ius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fes1jhdz+b ;. mor the period of the Earth and its distance from the Sun. [Note: Compare your answer to;jbs1m+h ed .z that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellifpy 3 pcuf;qi1+k6i lr+pp79ete moving in a stable circular orbit about the Earth at a height of 36elif;kp1u3fi7++yp9q 6rcp p00 km.    $\times 10^3$

  The space shuttle releasel(/d h0l gltd3s a satellite into a circular orbit 650 km above the Earth. How fast must tdl3ldh(t0l/g he shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expz )j.lx. mo0rserience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed . s).z jxrm0olfor one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “ne olqfi (6+bpob+ 3xku/ar-i +fxq+ub (6o/opbl 3kEarth” 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 the satellite?    s ~    min

  At what horizontal velocity would a satellite n86k(b ty;j:qf5kyp rhave to be launched from the top of Mt. Everest to be placed in a circular orbikbky; p q5 8jfry:nt(6t around the Earth?   

  During an Apollo lunar landing mission;deizm*j1. 2,ias zz y, the command module continued to orbit the Moon at an altitude of about 100 2z* z,smdi1yi; e jz.akm. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice thaiokz/ n8 2qvo+gwz 0tgt, 9h9ht orbit the planet. The inner radius of the rings i, h k+h0z nw8ivtz99to/ogqg2s 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 0qh 2(mp - 4ll-dsqft6)w bblionce every 15.5 s (see Fig. 5–9). What it24wb bhs()fq -0mp-6 lq dllis the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km xk o u3uobia6*dq,.kaw6w5r ;from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, wkwk,qa ao6d3 bu ;ru*x6i5 .o    ----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 of equal mass. They4p*kdf dmp/g)l-kp m9mp4t6 i are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midw k6pdpi t4)9k/mg lfp*4mmpd-ay between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the wg) jm o3(n.znb2 6g fiirb4nd(eight of a 55-kg woman in an elevator that movergf6b(zn4 bdo3 nji(.ign2)ms
(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 c0dlu3x o6tgz( eiling of an elevator. The cord can withstand a ten xzt3 gud0l6o(sion of 220 N and 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 0ekflht -2 )1nnv pu/j7ua;zmwith period T , the density (mass/volume) of thenm/2ju7az k;flu 0p)vt e-1h n 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 ;ty 1wdvq:kk*y,.d ro g5) pqcdetermine the period of an artificial ykgr,q15;q:yo dkt* cp d)vw.satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits thm r2m: nkvg(gkon79 z3e Sun like the planets. Its period is 410 d. What is its m2gkon:kvr 3m z7gn9m(ean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4o i+,4 tic:plk.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 ro,ngxp(,o ag p;;yk:m dughly 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 oyp,d; (ap;o,xm:g gnk f 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 c nrh)i )) /2hww/puwfdenter 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 for the four : mrbbvq7le h9w0n0ijg ,k80elargest moons of Jupiter (those discovered by Grjw0egq hivn,087 :m l0be k9balileo 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 kn7dbs;vf 7 1flnown period and distance of the Moon. fv177 dsbn;fl    $\times 10^{24}$

  Determine the mean distrk5yxf *2 rux -lgy;n,ance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tabkrgl xuyr*n fy;x, 52-le 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which som-4zdw pk xcg7+e space scientists think came from 4+gdz wxp- k7ca 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 art1j t:y:d q1ywd b t2 z)c2clj5fv0zu;jificial "planet" in the form of a band completely encircling a s5dt1 ::vjcdc)j fy qz1l02 ztujb; y2wun (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 Earth days?   

  Tarzan plans to cross a gorge by swinging innxou7k:us7az7,uf t5 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 c,7zu 7oauf :7s5kun txan 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 willn omib.azf0zj .a.2)x5abr(sv26ry a the acceleration of gravity be half what it is on the subfs2ora0yai6 m za 25).vz.(aj.xrn brface?    $\times 10^6$

  On an ice rink, two skater c9v l-vd/qf.zs of equal mass grab hands and spin in a mutual circle once every 2.5 s. I- dzvfc.9vl /qf we 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 rotates once per day, the apparent acceles1j1p)wy rqrteq0 h3za q-c1.ration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Es3ap)rs wy zh0qj11q c.e-r1 tqtimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direct hp-77ntgnk +b bps.h*ly from the Earth to the Moon experience zero net force becbk gp*7. 7+tbsnp-nhhause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but whenz2 8hw5zv2 ftf mmk1 yt 3te3c+sw9,2ntvj/vr you stand on a bathroom scale in an elevator, it says your mass ishe 3+ nvy1/mr cwt9,vzzk3m52t2 v 8jtwf sft2 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stynj8nyd7 0d o wvzb16mzi8j 63lq2fh2ation consists of a circular tube that will rotate about 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 per day) if an eff12zbwlhmfzn2yq0yjd83 j6n7 vo 8 d6 iect 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 iz6n fc2f xngw3(g7s*zn a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, c-rui22zt kelhy. n3 s6k y/.)c7bndg the acceleration due to gravity at its surface and the gravitatizt6uknl- /2 rsce7gbi.3ndk.c2 ) yhyonal constant G.

A plumb bob (a mass m hatg)e4r 0btzfi8b ob5nuz v(3 *nging on a string) is deflected from the vertical by an 3r*t8vub fbe5i n0og zt4z(b)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 ,zzm0e )a*8acpf en:wa design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curvew8 zzp:e,0a mcfena *)?

  How long would a day be f9e 3)1pse7 f(ece: xxws0ir gif the Earth were rotating so fast that objects at the equator were apparee(fg97rx0 3 cs: se)ep1fiewx ntly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a q /z t9x3 kvc0i. x2nj0vqzh7econstant 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 cu,,nch . uo;cvonstant speed rounds a curve of radius 235 m. A lamp suspendedv, c; unho.cu, from 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. Thus, it has been clai(az4m7q wayz* he k0*xu0y3cqmed that a person would be crushed by the force of gravity on a planet t 0q*e0u cayqwh3zy4xm( 7kaz *he 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: 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 Hubblel;f:gj ic9p e9 Space Telescope deduced the presence of an extremely massive cip9eg j9l: f;core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds 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 constanmx70ha: ;e grut speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is lm:g;e ra07hu xargest? 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 Posu1/twu:,(o p hwmr0wpva cs*. itioning 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 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 “fixem1p *wcu(ruo, vtaw/w:sp .0hs.” 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 Ren0u5agd 2* *ye 0nwrkqrdezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is ro eduagk *y5r02rwq0n *ughly 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 r(6 kr 86p6fqcsozof. ckc/ 5din the space shuttle pursuing a satellite in need of repair. You are in a circular orbit cqk6r.odc(68r5fspok / c6zfof the same 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 off8/z1 4vo,br1 ml; wfbxdf4k t 3000 years. (a) What is its mean distance from thew/4fb tfmdr flv4xb ;1k8z 1o, 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 valuetpfe60zh ngp p;.(uhk.wq-* j of G would need to be if you could actually "feel" yourself gravitationally attracted to so-pkp*.nh; g0. wz j(uqphef6t meone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of (x3)fm; kxoyua1j; fothe Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center ;mk)1ojfxof (xuy ; a3$ \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 locatedtrgkd1:gs,d* at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth k1std d,g:gr*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 5500 kg h;t) nt9lmm c)3m(vgv+pw3k oorbits 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 experiencd -ur*.ihe5sved by the tip of the 1.5-cm-long sweep second han.r v dhu5*ie-sd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start ghz5+ o f0hvyv+gv/r6to swing a sinker weight around in a circle below you vf/zy+06horhg+vgv 5on 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 Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a v iu4:-sj6m69.hdw 0ba vmzypcar travel0: bh.6v d9w zsa6-v4mipmyujing 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 tilt of the cars when negotiati8r lgyv wv06er7xl;m- ng 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 l8 x7r-m;ywelv6g v0rcomfortable. 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.$\approx$    $\times 10^2$