Sometimes people say i eo:tkpub9 .z+f8y;kxwh- *c6 ,u8 anrir4l ithat water is removed from clothes in a spin dryer by centrifugal fornh46c;r,+a8ipbf9i.rz t -u:l k*i8ew yuxk oce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels ar rq58nrop9r9 d0snn-pound a sharp curve at a constant 60 km/h as when it t-q 8nordnpsr09r9p 5nravels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the cqen)5 jud*cv 62rvh;lar exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch *;vud)evqnl 2jhrc 56near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wh/2xuzx,9lu47ms 5yan/xu dm5 rgna 6f ich of these forces provides the centripetal acceleration ofm//ldfyr,mag n 467 xsu25u9zn5u x ax the child?

A bucket of water can be whirled in a vertical circle without the water spillinkqpudix,,.irhc,g(-: k b6chsq)4x 5 d; gk ykg out, even at the top of the circle when the bucket is upside down. Expla (s,hkgqch- i.g xxk ,;ruy6:dkk)c,i4p 5 bqdin.

How many “accelerators” do you have in your car? There are ai1zhlz f2. nhvn83o4z/ rfrab7b1me9t least three controls in the car which can be used to cause the car to accelerate. What are hzn/ ezvzoln112.897hfi 4fra3mbb r they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as- lggghwi /wwd*lq-98 shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this dec-i/9wqhwgdlg-gl*w 8 rease using Newton’s second law.

Why do bicycle rider/(klv a fihn9/s lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angzby*k;5 zi:t vle given its *:k zv5yb;tiz speed and radius of the turn?

A girl is whirling a ballw ;,6,yrz bj04 rbebep on a string around her head in a horizontal plane. She , bbp6z r; e0wbj4,eyrwants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Eaf*knc2b;1p-pzx q /gprth? If so, how large a force? Consider a 1gfqkn x p;bpc-2pz*/n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit6 v2y.xui7 vtc betyv cxi672uv. different?

Which pulls harder gravitationally, the* kdp(hi *d,hj Earth on the Moon, or the Moon on the Earth? Which accelera,*d*p(ki hhdjtes more?

The Sun's gravitational pull on t /k*ecaoang+9jl ma;2he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravcgm;on *ake aa+/ 2jl9itational pull from one side of the Earth to the other.]

Will an object weigh more/rl(1r ;maz et at the equator or at the poles? What two effects are atr1e rl/az( tm; work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half thj8pcl*rjp t2gl c gio4q ;,sas487ou/e force on the Moon due to the Sun. Why is/8,g7;8p po lqoju rlj*c4ct4s i2 gasn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largy 2v)r +j(a .yitne;mger or smallev;teymi.a2)gj r y(n+ r than the centripetal acceleration of the Earth?

Would it require less spee t24jl2v2c1y/hobq7ai px2yi 1xajt9d to launch a satellite (a) toward the east or (b) toward the west? Consider the Eara1yqho/tai22bi9j7l4 cxv x1yptj 2 2th’s rotation direction.

When will your apparent w y ta1gj22vv 6*gcikz 2e82gmseight be the 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 same asi 6*j vkvg2sa8y2t cgmz2 ge21 when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer s kiuf,(+hfm w6khp6b 3pace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity m,f(6k6ipuh+k 3 hbfwyou can think of.

Explain how a runner experiences “free falla v5kyoxh 3i*(” or “apparent weightlessness” between stv ykh(53xoa* ieps.

The Earth moves faster ibk,0orv e fdzdr q1zna782q:hpp g:;5 n 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 facr;kvpzgo dn187:5zq,q r0b:fpd2eah tor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known uns.gqk.is/ cew 0 v;6mftil it was discovered to have a moon. Explain how this di s v/f .qsem.6gck;0iwscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the wx2 2s ro f2i*wl4m3i+e4nj7 3 mvwcsrEarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the dxir*+4vnrf 4we2mo3s3jwi 7 2s2lmcwifference 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-*)ioonwa(lq j7w/nbv9ks7 q $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arouz/4kvbm/ d 65 5ddajtyow ph, *z2oo:k l8hha;nd the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Ev ,/do;zhot amdw*/j86 l5dh5ho 4y:z2kkabparth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates c)j9uu(o/uss uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate th(/uo suc)9usje speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfacg cs./ li:v.tuy1; jscnn ,ub9e, 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 , thn1 ls,/jy:vn. .9s iu; gbuctce gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of9 dz7sfd,v 2ry mqc53r a potter’s wheel turning at 45 rpm (revolu7qfz 3dryd m5 ,r2csv9tions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stri 0ixsg4)k0nga ng is revolved at a uniform rate in a vertical circle of radius 72.0 cm , kg0)40axsig n as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius 7sr8 + 2sr:ugfj7 m on a flat road if the coefficient of sta8s+j ursr fg2:tic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be p7 s;- ezi59old:,-f aciamdmbetween the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/s9imlm ;ope d57-,ca azfi:d- h ?   

  A device for training astronauts and jetyq l ao8r+l08p fighter pilots is designed to rotate a trainee in a horizontal circlq8p0ylr+a 8loe of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a/(. iz qgrrdpqnkq96) rotating turntable of variable speed. When the speed of the turntable is s.gkzq6prdn (/9irq) q lowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speea,) rxp fgz*m8d must a roller coaster be traveling when upside down at the top of a gz*apr) ,xfm8 circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 9)i;i xjnih //*cs+ zdu50 kg (including the driver) crosses the rounded top x//c;i d z *inhsu+)jiof a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheeokfpax 6e((dls 8m ++3jx7 bxel need to make for the passengers to feel “weightless” at the topmost posx38k( e+ lpx (mjax7+bfedo6int?    rpm

  A bucket of mass 2.07fgeikzc +rw75z9+ ovyc2w9 p0 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2wzrf92pgkw+795c c v7zeo+y i 5.0 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 roqft3isd)b8bp 7 uuc,, 3mf)jlo kmo+)tate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of mu7i3)cm,38u )f, kqftj b dl)o+opsb115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walr orzt(ex;wkza .i;)3led "room." (Seoz).;r (t3;wzxk eiare 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 cir(p0s5ic ql7 an5g68uzt3/4f7ru-j jevddg yxcle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) thr3a(dr/ce y4jqp77jx vin585g sfl-tug u dz60ough 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 teo;ma *7 kad5- kg8yjchis time, by not ignoring the weight of the ball whi 5k87doag*;- aeky cmjch revolves on a string 0.600 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 wc i+a3q23ujgbanked 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 massesvihz6d-;g8q ;rhi5m y $ 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 pil*j4/wsa0/k p1eqh 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 centr+*jnm +q-tvp4q0l 3s6w lx1jun o2 sspipetal components of the net force exerted on the car (by the ground) in Exa3+ j-ns s41 pwsn 2 +p0*tuqlxolm6vqjmple 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 unifzj ot46 i95d27jstwhb ormly 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 slipping o2w 7j6zs otbjh5 i4d9tr skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particularbyqu/ 9x.qu;n k6 iwgy*.sl: v instant, its acceleration is 1.05x u yqnu: .;/sk q6byli9*vw.g $\mathrm{~m} / \mathrm{s}^{2}$ , 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 gravityc nxu;6xg2v/ lg kbp ydlnw4c2+:(o,c on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surg :bl+ ;4gwvxkc( d2o/ plnxcn2uy,6 cface if its mass is 1350 kg.   

  At the surface of a certain planet, the o2g v8f1pi jj, qpwa/7gravitational acceleration g has a magnitude p/wfjo2,g j a8v ip17qof 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 g)r7ua-ior3d, dco1 l hravity on the Moon. The Moon's radius is 1.713r,i)d lorh od 7uc-a4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has h5cqkto p4cq k*35bw(l:2e u othe same mass. What is the acceleration due to gravity near its kwutcoh :q kpo53b5el2q4( *csurface?   

  A hypothetical planet has a mass 1.66 times )7q)au li6 kff k )c18xarhm,jthat of Earth, but the same radius. What is g near its surjqlmr8), 1) a7ahk)ck ffuix6face?   

  Two objects attract each other gravitamqmzb 1.+09wp prj,d mtionally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acc t4p7nib/ix i14lapn4ivh ;*teleration of gravity, at (a) 3200 m l 7/iatipv1in*i; bhp4x t4n4   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fr 4gfcpal ag0pb,:6b6z8v. kw rbbav88om the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Eaa,a6rpbbvp:bc8gvb4a8.6 8gw zkl 0 f rth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mar0*e/gnske* v ,pm v-oss of our Sun packed into a sphere about 10 k,pekge v *m-v/so0rn*m in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star,ygz-( +a h/wz) vglt,h which once was an average star like our Sun but is now in the last stage of its evolution, is the size of ouz+gyz-a(v,h)tw / hglr 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 orbiting in the spvple* 6mw8*a-/w pm ;cyy/zyn ace 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 gravitl6*w - m8 ypvcn/;m*pyye/ awzy 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of p:t(db5jx r 8hside 0.60 m. Calculate the magnitude and direction of the total gravitatibr j 5:ht(pd8xonal 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 w/u;cl. .vue-wm:dao line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuom ue;.-. ldwcwau /v:ming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what ww9k 83a5yn bnd(wv7sit is on Earth, and that Mars’ radius859kaww(b3n vy wd7 sn is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period ofu xy- 4 olpcjbc0-8;cu the Earth and its distance from the Sun. [Note: Compare your answer toypj- 0c -l4cu8oc;xu b that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a-i js16 l*8d6uodpnjp stable circular orbit about the Earth at a height ofp -njlj6ui* pd1do6s8 3600 km.    $\times 10^3$

  The space shuttle releasesmt )w(62l 7tlovs85ikwv6 pjq a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Ealw2qmo) it pv 667kt( w8slvj5rth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantsh o /-4bcdbp,m are to experience simulated gravity of 0.60 g? Assume the spaceship’s diamebp 4dcho/,- mbter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takesm v /9n5cz6:j2q 26 nwchvewuv 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 oe2q6c/c6z w2 9uvhnv:vwn m5j f the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fr,ws gl+ +wb q.ic6huls/8i.s som the top of Mt. Elsu / s.+, lbcg8wwiiq6h+ .ssverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the co g7ju);n,o6x vqzatp yxe,4y9mmand module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon ge x qpoytx, 4uv)n7z96y;a,j once?    s

  The rings of Saturn are composed of chun)5xd+ ckon4csq8jgu4j ,7j.y knz wl4ks of ice that orbit the planet. The inner radius of the rings is 7cqu7+nyzk d 4cj l ox8,.5sjwkj4 n)g43,000 $\mathrm{~km}$ , 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 evera jvrnxp. 6p5,h0e )avv49q bqy 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real jev, bpna 0v 9hx5aqvp.6qr)4weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cenbdwm5k hk lan; r;t-i:y076cfter of the Earth's Moon in a space veh tbc06a 5ykn;k;wm:r-f hi ld7icle (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 of equal mass. They ar1du6yfbi,g37n7 ocveh f t13 pe observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point dbip7e1u t3 h,vcg 713nof yf6midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of )h)bxea+/zhr a 55-kg woman in an elevator that mov)xr/e hhza )+bes
(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 hangqa :u 5 sdgh(/i+xuws5 jhqsd373u (jws from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accel(q s:7 5usw d+g(33ids qhha/wxuu jj5erates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surffdr/f6fe/ yv7h(kc j 7;j( dheace of a planet with period T , the density (mass/volume) of the planet i(7hf f 7ve e rkhc(dj;df6y//js $\rho=m / V=3 \pi / G T^{2}$ .
(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 oupwxc,,s/j g, 8 9bsq(o9 jvxqf the Moon (27.4 d) to determine the period of an artificial satellite orbiting very neaps 9,b 8ujswx/o, qgqx cj(v9,r the Earth’s surface.    s

  The asteroid Icarus, though only a few hu. tapt55x;exok d wx2hq(r*)lndred meters across, orbits the Sun like the planets. Its period isx. wtdrptk hqx x25*leo)a 5(; 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o+3jshdrj : 1t +f(3 -qks.cgx*amrj alf 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. Itdg; pe l.v x+sa3oau /qey4;1v comes very close to the surface of the Sun on its closest approach (Fig. 5–39). E;l vgeoe+/p asy;v 1d.x4 3uqastimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centh eijsvh3w2f*r473 vper 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, sj vv4gh21x:nperiod, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609). g4 1xvhn:sjv 2
(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 Eartd)gfqq 4f0 2 w +lc.je6c9jlpfh from the known period and distance of the Moon. 29 cfgq jq6jpl.f 4)fecdw0+l   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moonep tc:+ n;l xit:h;:pz2xr+jsvg w 8kk0.x f)hs, using Kepler’s third law. Use the distance ofx+ehzt: xsckr2fgi:x :. ; wn8p0vkh+ p);ljt Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists o06yq vsp rp+4bf many fragments (which some space scientists think came from a planet that once orbited thq6ps0 y rv4pb+e 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 der *-oyj lfgxlg+,n l/(nxwy7, scribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that ty,gxlow +xj y*lg,(/l n7rn-fhis 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 az 1da+-.f4:,ic wfswdnu30 r ynz ap(y gorge 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 lowest podc 4 f0nd(ywpz-r1 :,w+ ayu.i fnsz3aint 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 g5 vkpqv1 k1m6l2not .dravity be half what it is on 16 dplq5ko k2v.ntmv1the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hanum;5st4qh s :pl7iu9lds and spin in a mutual circle once ev h;tup4s7q s 59:iumllery 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 on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerm n)98il.;g/g ukhvbw ation of gravity at the equator is slighv8mg)l;hng9iu .k b/wtly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelingl4ewu92 dyr1) wem(+y j5j uvm directly from the Earth to the Moon experience zero net fou) ly j2u5ymjem ww e1+94rv(drce because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bzyh0jozoy-tg5q d,e(b7b ,0 but when you stand on a bathroom scale in an elevator, it s t bqz50g,b07oe dyy (objh,z-ays your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate a( psuyw:a3b z5bout 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 effect equal to gravity at the surface of the Earth (1.0 g) is to (pa by5: s3wzube felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertikxux:bwn ;t0s1n(i s5cal 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 rqsm7h- c4lm. xadius r, the acceleration ds-lm74mc.hq x ue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertiq8,sic)cuo+gx e 0 t(gcal by an angl,0ucge )s 8 oxqgt(+ice $\theta$ 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 mn x6o ,:tjs6d;x (ont If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car saxo6 od:t;6ts(mj , xnnfely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects .zb9cs gzjn/uabd(/ j ()fd pa,rd)x /at the equator were apparently weightx/ z/src.(fg9) dbd) azjap/ ,bnju( dless?    $\times 10^3$s

  Two equal-mass stars maintai-l d0 cpfjbp;9n a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a cur sa 2wt6twd;p jdmw0iq,5+4bive of radius 235 m. A lamp suspended 4;tw wsi 2dtm56,0+qwiab pdj 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. Tb9ya0 o rr2*bfhus, it has been claimed that a person would be crushed by the force of gravity on a planet the si * a0yborb2f9rze 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 Hubble Space Telescopetvt8n)9cd) jw. lo- y smw,)5simi+jz deduced the presence of an extremely massive core in the distant galaxy M87, so dense that ,jtvoinjt -csw5.8m d+ls9i ))w zy)m 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 constant speed ;*6,xcl9nh f.y vu6gi32fmtb wm kp/has it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvatgnyw mpu bhmhlcv f96x. 36k*/,;f2iture R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (xhd158w+.ptp u-o,jd0 p-t+rge gnfx 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 satellitesr+ +t p o 1tw-jnfd g,peghu-x5x.d80p 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), after traveling 2.1pb0 idfi k vc9/nh*7+y billion km, is meant tohpb v7 cyfi0 /kdi+*n9 orbit the asteroid 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 v7/k q/ 4 umumbrd1/ob mq,/lkneed of repair. You are in a circular orbit of th/um 7q ml ko/v1rbd u//b,k4qme 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 of 3000 years. (a) What is its mean ao8 (op8k3m80x6yb cx7fvmuo distance from the(x x f mvb8 ou8cm6po0k3yo78a Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feojvuw 9cf*cac( (jp+2w kh1g3 el" yourself gravitationally attracted to v2((g j3faoccp 1*k9juwhw+c someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) atv 2lxk+ au9/nv a distance of about 30,000 liukln/+2av x9 vght-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 3p1a,x zl-oq6u o+rwj0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at t qj +1a,wulpzxoro6-3 he midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5 b*rqi ,ed/nl5500 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 tip of the nh ijdsv.7o w3cx9,*u 1.5-cm-long sweep second hand on yds* 7ui,xj.v 3hconw9our wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and ljc8 /: 2huwl0kl-vmfstart to swing a sinker weight around in a circle below you on a 0.25-m 8v-clll 0/ ujmk :wh2fpiece 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 car trave5 m 8j7mxjwyk/ling at spej58mykmw 7j /xed $ 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, the7 l-sy,gxl/ga Acela, utilizes tilt 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 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 tray,g a- ll/sx7gck 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.$\approx$    $\times 10^2$