Sometimes people say that water is removed from clothes in a ngqev2(/hy4k8-ch easpin dryer by centrifugal force throw nh-y g2ae48/q khe(vcing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car trave5 :wycw;b2ghkls around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spe:h5kb wg yc2;wed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car e y/m:5k/w ,ggwphoit9 n(zxygdy rx4hl b ,*94xert 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 near the bottomnbr,yy9xz4wk: h9g4 /iw/,pm dtg 5 ogyh (xl* of a hill?

Describe all the forces acting 9f 5trvm+2xin7dnor yfw*qy8-h /f)eon a child riding a horse on a merry-go-round. Which of thesn /) dfynf+v-i fh rx7wr9eo82 t5*qmye forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wim6f n*nkedwa tk8;jzs2ujx-f;2 )tk0thout the water spilling out, even at the top of the ciruf8f s-t2e26x wj)dk an0j*z; m;ntkkcle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three contrq 6g7gsc o+k/easm5 y3ols in the car which can be used to cause the car tog5ea6m oc/k7ss3q+g y accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cr cmsjfj* 2-7vhest of a small hill, as shown in Fig. 5–31. His sled does not leave the mjhj2c*s7f -vground (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 rouf9uv u utpi47:nding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking aippeg4 -v u3 o)uq50skngle given its spegeuus-)i 3qo4v5 p0pked and radius of the turn?

A girl is whirling a ball on a.;6 3pgqxogahc iofl:nv8gwy9** jg 2 string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the x9:gig nfj2gg*c hla w;6py83.q oov*other side of the yard. When should she let go of the string?

Does an apple exert a gramzfuom3al)z7 c (xdeh280 t8 dvitational force on the Earth? If so, how large a force? Consiuamo8 e( 3 xc07 2ldzd8)ftzmhder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbiz bx2r 2ml)dds9+9zal nqm70jt b2l ln djbx0r+ 2az9qs9m7mdz) e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on bs6its6m;d4.zle0y z -(cuwythe Earth? Which accelerates mobmwu .0t;d-6siz(6sze lc4 yyre?

The Sun's gravitational pull on the Earth is muc 4:;o0yw9m-oa xa5u zq,ancagh larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider thmq -,xocoy zw4u0a5g 9 :;aaane difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at az 7x 59u+wrkothe equator or at the poles? What two effects are at work9owz uxk +7ar5? Do they oppose each other?

The gravitational force on the Moon kh71ksan;l *ol3 , wdfdue to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fk3loaw d7,; fs*n hk1lrom the Earth?

Is the centripetal acceleration of Mars in its orbit around ther7k t k4uro9th8nt j; xp/tx6( Sun larger or smaller than the centripe7 ok6txnhpt;4rxku tjr9t8 / (tal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east/i gm5,yo e5x hb+6j7on ut6jo or (b) toward the b/65iojgtuy+,jon hx 5 m7oe6 west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measurln5vbgfk-3u em b: d *z9n23vzed 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 as when 5v:nf-zk l 3 v9z*n2ubg3mbdeyou are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer srhkmw 5 nts;q4ck;r96pace could be adversely affected by weightlessness. One way to simucsntk6rw59;; hm kqr4 late 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 you can think of.

Explain how a runner experiences “free fall” or “apparent( i l+ca q0ym(mduo1:k weightlessness” between steul1 i0m( a( qcmyd:k+ops.

The Earth moves faster in its orbizq +8ol.n6as.n lc v;tt 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 facqnzol+ at6v. ;.nsl8ctor 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 until it was discovered1)f yb ybras 1xr48s3jrfhjo92 h,w y6 to have a moon. Explain how this discovery enabled an estimate of Pobryyf a j1b jwrh)642h38sf91, rsxyluto’s mass.

  The Sun's gravitational pull on the Earth is much largb l34j6aef,sdw +*u7a tht .qmer 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 *fwtba, tq. 7us 6ahm4+3dj elwith 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 v bojv+.2ur 0o p2hh)ujg7t3x 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 thg/8, l55kcpuvnq2bfse Earth 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 orbi ufps/25cvbk ln85qg,t 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 exerte 31r6v1tbe)yhat/zsix hrjc f:) hy16 d on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) tt rh6x :v1 irhyfbjehc )az1 /y61s3)of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in om1t:jre9i,2(f 5,sexmtik w *yu wz 1qk p1h9wrbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the kjf h11r251p :*y i9w9miut, ,qx ewz(mtswk espace 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 ofn5: -wpfg. 3c ;c4po1adeb hmm the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revoluta:. wm1n mp3pb4e f-oc5c ghd;ions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in +a5rtivtkl rmvjo9354: -cowzw 5 qb,a vertical circle of radius 72mtbt ww5io vr9 oa,:5jk3rv+ -4 qlc5z.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of ralh 7*,go+rwb idius 77 m on a flat road if the coefficient of static friction bgi,wl*r+7oh between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and g jr mi3dt k48/su4q9xthe road if a car is to roundjtx4guk qs 483d/ir9m a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jqk/ua : ,ui/ruet fighter pilots is designed to rotate a trainee in a horizontal circle of radius i,r ukaqu:u// 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 fr po) p2s*kn,5t/ss2p/nnx hdlom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable? l ) 5oktnsdp/2psx*n n2/h,ps   

  At what minimum speed must a roller coaster bdvs4a* od 2 +c/gepqod0j* v8ue traveling when upside down at the top*vo/aucs o p82e+j40dqd d *vg of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top 1.s/h; eenbvp( )z9bv ds7kgoof a hill (radv vbzg po/7)19h; (ks .bnesedius =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,qgo, alu*)hk-m-diameter Ferris wheel need to make for the passengers to feel “weightless” a *lao ,g)kquh,t the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle olg1kc0cq(q 34by; bwof radius 1.10 m. At the lowestw( yclqog4bk;q c01 b3 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 particle 9.00 cm from ti;hupt)q v8)gdp b:y*he axis of r*pg)8bvqu:pi hy;td) otation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a z;i5mnj12c,8ccmzqxcylindrically walled "room."z,cx j2mzc 5cq8 in1;m (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 frictionleee8. fer(l r84ayddx4zb- iy5ss air-hockey tabletop, and is held in this orbit by a light cord connected to a danglina.e lb i4fd x dy8-8(ereyr54zg 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, byk :v-coewf/ +wf5nz8e1f*ffp not ignoring the weight of the ball which revolves on a str- 81wn k* evf/5ffw:+fcp efozing 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 gxse.uy 648ct m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses9xm .t zr -y(zlxqfv- 3l*e9bz $ 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 maneuve0tp;mw2q:l zvu1o)4c nax z9dr by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the n; 1kh*os -nj)vy/ir. wf yrz/zet force exerted on the car (byrsi ; nv- .jfr yz)*oz1ky/h/w the 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 uniformofb4nlw (,8up f6pn, qly 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. qn o4, ffp ,(8ulb6pwnIf the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 4 iwl;, 8ubbuwm . At a particular instant, its acceleration is 1.uw;4builbw8 , 05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,us*u.h qy,druk ()hei*,jo6 d800 km (2 Earth radii) above the Earth’s surface if its mass is uhdy * je.h6sudi* ou)rq,k(,1350 kg.   

  At the surface of a certain planet, the gravitational accel:edbo ylx0, xf*x (h8ueration g has a magnitude b ,*hx: xo08u(exydfl 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 gravity on the Moon. The Moon's radius is 1.7klj mgsm:ctu8,17 ol wtw-m7 44luo tw74: wmkm ctmg17-j,8 ls $\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 thad9 eilgb+l(qdz:0 o3w*v1q z 5rqslavhw89g2 t of Earth, but has the same mass. What is the accehv(wlq:d qgge198l32d 9bq+lvao5z* z w0r sileration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but,j)2 byfqa ool3 :m fp,wn0pl; the same radius. What is g near its surface? ,f:lwlnfjqo;,a0 3)m opp by2   

  Two objects attract each other gravitationally with a fo85c 2l6x puut re+xak6rce 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) 3rfg x 9c93y;sg200 mcr9 3sfyxg9 g;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fro -vymex41: ehnm the Earth’s center to a point outside the Earth where thegravitational acceleration due to m: ey1nvh-ex4 the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere aoz fd8lso 90n7bout 10 km in radi9zofo8n7l 0dsus. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averqhb29 d7t*fwt h( m0pcage star like our Sun but is now in the lastpt9qh * h0bd(mwft c72 stage of its evolution, is the size of our 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 orbinq42/e a.b8ft; jbfchoc- g .pting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yo;.efjtq8 gb o2cc/p.nh b -4afurself 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 located at the corners of a square of side 0.60 m. v9xv9.q * cpcjq h:sr*Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othevr*9:9 *q hpxsqc.jvcr three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on ty.eat8w68 eg. ic fm(d.sc)pp a/me8yhe same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assumind csgy .tew i).mcpamepf .86e(88ya /g 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 i0te.t5ws*vgy+i h d0 wt is on Earth, and that Mars’ radius ett wyw0*g. +si5hvd0is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for(c ; qebzi;eep6y 3v1l the period of the Earth and its distance from the Sun. [Note: Compare your answer e(eyv3el z;6b i;1 cpqto that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbi)c.rhn-7veisz/vzs7 t about the Earth at a height of-s)7 n.ihzcv v7zrse / 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abo gs l6pf(ndsv.w/m(fl; 2f ve.ve the Earth. How fast must the shutfmle( ;dls6vf.(wgsn2 p . vf/tle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experi0cfre l5 3aj m;wm55daence simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and c;3a5f j0m5l5rda mew give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “n mck.-4 z,qyejear-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 the satellite?m4ke ,jqc. yz-    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top oibx/ypd2 f 1c05u. uba4etuo0 f Mt. Everest to be placed in a circular ba2ueyt0u i p0.bd4uo5/1cxf orbit around the Earth?   

  During an Apollo lunar landin;fq1 g7xjnev,:7jwwk g mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around t:k1xjgn ewvj 7q7 ,w;fhe Moon once?    s

  The rings of Saturn ar2t((*jzz/*bcyetg f ie composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,2f*gz*t ( eij(/btcy z000 $\mathrm{~km}$ , 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 (ssp /4 r8/rhrfoee Fig. 5–9). What ir8for4ps// r hs 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 from the cenc4+q)moj3m7k t ) qg nph)o v0(xubit2ter of the Earth's Moon )+o tqoi v37mk4mu)n0q)btxhcp(2g jin a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star sys/p(-/lv0by42 b mtrx hee-boh ::gnp5ax7c g ftem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Eaehygbrx:g2pf7tlh0o (cv e -/ xbamb 5:-pn /4rth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the we7s72 dksx-nnfe7vys v*2p) ga ight of a 55-kg woman in an elevator thatnyxsgv7kd pf-sn7* aev 72s2) moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ce2 st7dww wlei 0w8daa;;ubi (;iling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration 07iwdbtwl;w ;d8s 2 uei(; waa(magnitude and direction)? a =   

Show that if a satellite orbits very near the sh yiucm awxt63c( **a:urface of a planet with period T , the density (mass/volume) of the:cu*a3i c*xywhat( m6 planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period y+8 9l;aoq u8u.8lbm +ssgxfv of an artificial satellite orbiting very near u9xlm+l+ b gq8. s8ao8vu; yfsthe Earth’s surface.    s

  The asteroid Icarus, though only a feyg +wi5tov t2.w hundred meters across, orbits the Sun like the planets. Its period is 410 d. What isgt+ow .25ivt y its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan .dj31y2mlyv m9tjoa+)ywy1 u ce 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 yp/ldsn(l3t w0, ki o/eears. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it o0 (/kltd psw/i,nle3is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of nya r5mma2i;s 1z g2i8the 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, perio wf cm68fzbe45d, and mean distance for the four largest moons of Jupitfem fw8bc45 z6er (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 peri o2 d orj:a,d+qg)qps3od and distance of the Moon. 2odajs:gp+r) oqd3,q   $\times 10^{24}$

  Determine the mean distpay9+lec9wg1mm g ).y ance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use th)e wagy1y+m9pc lgm9.e distance of 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 of many fragments (which s3 vf (*y/ 8-kg:ualuhk5 wsro:zlvs w.ome space scientists think came from a planet that once orbit3 l -uoavl(/uyv* hfw :wks:5rs. 8kzged 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 artificial "planet" in m.ek2tfo w7y, 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 tempom7wk. f,ye2 terate), 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 5qg -0kfql0rk.jh kt- 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 lf - qh.t j5q0lkg0-kkrowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity bb1swvp 5j 2ls236oe hie half what it is on the surfa1p2ej vs 25o 6lbhisw3ce?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and sphup ;zseu 9v27in in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 v huzp9;72u sem 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 datdd:q / :.o0xhv(mx4qpl6nccq 76ksby, the apparent acceleration of gravity at the equato.o d:x7l6v sxqntqq6 0ccbm 4k(h/pd:r is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wiovfrl9 :jp /:gll a spacecraft traveling directly from the Earth to the Moon experience zero net force because f/ pgo:l v9jr:the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in yvna34q xh)tf2axy*51oz 9 fean elevator, it says your mass is 82 kg. What is the acceleration of)naexzf fy2o4 v51h*xt39ayq the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate ab 3;qka8*b xammt :f;chout its center (like a tubular;cahfm3 *;8 mbt: kqxa 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 sr.j9gngqzzzf17hne) vw h0,e,vcf7i.x86 m 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 apaxrb9 kfl,yccy :l2 d,) -u3c planet in terms of its radius r, the acceleration due to gravity at its su)y -3fr k9 lxb2dc,alpccu:y,rface and the gravitational constant G.

A plumb bob (a mass m hanging onae u5 -3okgm(c a string) is deflected from the vertical by an anglekm-g 5 c(uo3ae $\theta$ 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 fl+ p+biy) o65o1ezcv z12dlbc or a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curv+2l 6y1olbvp)cobdi 5e+z cz1e?

  How long would a day be if the Earth were rotating so fast that objcyyzy 7upl f3x)/t7 eph6buq15)) p ktects at the equator were apppy7)) zl1bctyfuq ypk5/x 3)ht pe76uarently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart /k+ ym:znn1pzof 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 co +azxjg7 7ib8instant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angg87a7ixz+bi jle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive asf+ ,ack, tvv ue-o*gv: the Earth. Thus, it has been claimed that a person ,t- efav :v uv*c,gok+would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: 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 Te:b6 ks b7:budvlescope 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 speed of gas cloudsbb 7kbsu6 :dv: 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 av)ou-ap zbqbwp fwo6r,a 2;2mx*9nurz) ke6 * s 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 largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losingxmoero pz9bkwbf)ap nr*6,v2 qwz;2* a6u)u- contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24s9/w68mz knm e 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 satellizw 6s/8 mmken9tes 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 2.1 billion9bwe1c ty-(p;vffc (a km, is mean 1tyec9acb(;-v wf pf(t to 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 satellfrcn8j)- kbj6ite in need of repair. You are in a circular orbit of the same radius as then8jj-)cb 6r kf 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 yezr6+x og(-x -e,dyvld ars. (a) What is its mean distance from the Sun?--loxg ydv dex+ (,r6z   
(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 "feel" yr-c* okm0weq* ol:w/ d1sd;hyourself gravitationally attracted to someone near you. Make reasonable/odwmowqceh 1sr: *dk*0y l -; assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky W;n ctuno;s)o* e )p2qbay Galaxy (Fig. 5-46) at a distance of abouc) pb)sn n*;et 2qo;out 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50z39 2ri, 4jlaqja 3vlp m on each side. Find the magnitude and direction of the gravitational force on a fift2j,4 393a rlpzavqjilh 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 kai9.e egnz)2 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 acceleration7 0 epi8ucqjh7 experienced by the tip of the 1.5-cm-long sweep second hand on yop7 7uhq c0eij8ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and s5c/xuy cgup) l/ 6kx0kkmbxfcs6 i.6* tart 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 mak l*0mb6ykux /csg .kk5ucx6cfp/) xi 6es 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 tc u.)usr -ly2rjc*ej:h wbd 9t 0cl9:iraveling at spe:cyhwc9bi- d9t)sr 2. *julu0c:el jr ed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed 7 ixdbp f8 jln5lh2ym+h .q.(gtrain, the 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(+fl i7lh qx2n.8ygj p.bh 5md 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.$\approx$    $\times 10^2$