Sometimes people say that water is removed from clothes in a spin dryefi1 fipc t)i60r by centrifugal force throwing 1 iif6p0 )ctfithe water outward. What is wrong with this statement?

Will the acceleration of a car be thet(czq3: 3rkzc same when the car travels around a sharp curve at a constant 60 km3cc : kz(rz3tq/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hrtsxb86vcs/ h mz,ra5vvq q,r 800-xnilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dmh,v58 tr cra xrbs, vx86 -qn/vsz0q0ip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a 49a / vfwfdsf,merry-go-round. Which of these forces provides the centripetal acceleratio,fawsf 94vf/dn of the child?

A bucket of water can be qaez2 v/ )d11b gkg;gro;1 xsjwhirled in a vertical circle without the water spilling out, even at the top of the circle when the bucketg1r )/dx bokge;;jv1gs2a1z q is upside down. Explain.

How many “accelerators” do y/)au/mht i;c+puvld z4 lt 5,xou have in your car? There are at least three controls in ,/)xll ;m +/d5t4tauucz v hipthe car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill,g. vw6mcbqpy2/ hf45 e as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but gy qvm5/c b.26p4fwhehe 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 ln,j0 :cggvo( dean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bank )w1ty*vvox9+ xx s+ 0t (rhn:i2utfmring angle given its speedi*omuv(s+9 rh) +2wx:t t0 xnx rf1yvt and radius of the turn?

A girl is whirling a b 2)z/jlq yz (zroac+/uw 9nlv-all on a string around her head in a horizontal plane. She wants talz/w+)9 -zl/c( z v ro2nyjuqo 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 Earth? If so, how lar 10/onhpn 8cv7jt nmg25l7nhm ge a force?mnpnm028 vn5h7l1goht /n7jc Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is1zui9u:fp8 y n, in what ways would the Moon’s orbit be diy :nu1z89ifu pfferent?

Which pulls harder gravitationally, the Earth on the Moon,sn/0:6,rvu r9 cpud 0ufp p1ta or the Moon on the Earth? W/u f0sr0p d1,p6ucpr ntuv:9ahich accelerates more?

The Sun's gravitational pull on the Ej0 ae,l6,ww-l.3+x k olpkj;dm7iboj arth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference inkw3-bx,.e6,o kj pdj;+ im ajll0l7wo gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or3ist1,2k1had xv hjy : at the poles? What two effects are at work? Do they oppose ea1h yk3 xi1,s:avhdt2j ch other?

The gravitational force on the Moon due to the Eart::f 3x ia fb+oht5y5xnh is only about half the force on the Moon due to the Sun. Why isn’t the 5xtox bh +3f:fyi:5a nMoon pulled away from the Earth?

Is the centripetal accelerajoioq ;9 s,igm j3hjr4i;e v.1tion of Mars in its orbit around the Sun larger or smaller than thej; e.r34;,gimos io1hij v 9jq centripetal acceleration of the Earth?

Would it require less spi +crz;+10t;c zzv l/mbc4zzheed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotati c z +v c1c;lzm;r0t+hzb4/zzion direction.

When will your apparo0 x xy*u:p+ugent weight 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 le:xg+ ux*0p ouyast? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely al ldy(4a34phaffected 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 gr4al4d h(pl3ay avity you can think of.

Explain how a runner experiences “free falw (uiszfwsv2 gn)h)54l” or “apparent weightlessness” between ssu)ns2 wifgw)z54v(hteps.

The Earth moves faster in its orbit around the Sun in Janua)+xvemlb)h3t we ri /0ry 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 ) 0er+wh xtlmbiv)3/e— the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was ngnmo :s6vt-x 2a o90zhot known until it was discovered to have a moon. Explain ho:oh agvo 6 s9x0ztm2-nw this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'9qjjug1r p ;5os. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in grjp9o5;g1q ju ravitational 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 190g4dggb y2 h+.*7g0m xubhpe c80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 around the Srg m3m- u sa7s9/*pokfun, and the net force exerted on the Earth. What exerts this force mak-rgo7/sm p fu*93 son the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a)sv8ovu3-p2 swde*i3f:nbf) gb. eob 2.0-kg discus as it rotates uniformly in a horizontal circle (f8g u2o*3f vo)p3n-e v:ib.ebs sb)dwat arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 kmo6i -5rtxw4ondi1xeq 7cm3 ton 2o.l: from the Earth's surface, and circlwdmc5itn .r26oq3x7ixol: o -4ten 1oes the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceler,m/,a ej0zezration of a speck of clay on the edge of a potter’s wheel turning at,,z0 jzmeea/ r 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ra cqnhv3b.ks0gl c16h sk:jo+.te in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spcjhnl3 6.0bsvg+ ksoq1hk. c:eed 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 turnaq)l(qlip t (gv4 x e800cch,z of radius 77 m on a flat road if the coefficient of static friction beta ql 4ipcv8e g0qthl x)(,cz0(ween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient ofgec f8jn v2: )xa/i6kt static friction be between the tires and the road if a car is to round a level curve of rajv)k:nf /at2xc8ie 6 gdius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pij uy - iez/7v*;r6auxulots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . I6jeu r -;u7uv xzai/y*f 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 ofw w/d xrq:jvo /wtvs4/5bg1y0vm-f9 b 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 ryvvwv:wt/w b 49-//5m1x0o j rqfsd gbpm 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 traveling when upside down at 5utunyf46u8 x2abc 6du) rxai y.q(r/the topf4c ya r268d)b/uriat (65u.nxu yqux 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 1 0wl,u2(wz yog hu55qc g 8mnje48lbhdriver) crosses the rounded top of a hill (radiuswuo4, (hgl88ng52qb1 mlz jewc 0y5uh =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 to gwk6 veg+m2 vk;g2:uqxnuc2: 15 xxxhmake for the passengers k 2n:x h2xkgqx6m+ 2vg 1u5v :;gxucweto feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled intj; 1p who 7-nwjvvr35 a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in w7w vj- tn3h p;jv15rothe 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 y(o )egpsrs *+xb*c2mm: ylm 9a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000 lx2mb mp* )g y*r(m:os9 +ecys$\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricall /c jzavz/5j*adkeuotk/5o. ,y walled "room.kozj 5ezaoukv,5aj// c. /td*" (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 rotat1/5r2f emv--kljfzi 94dkmg ted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling k5efj1t/fdm4iv2r9 m -k -lgzblock (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 i ddb /( rmrw:b.f+a4mcgnoring the weight of the ball which revolves on a string 0.600 m long. In particular+madb 4crd/ (f. b:mwr, 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 traveling.39cy1 jgehu x 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 z i y30oap a36nrrh/g .p6p)zv$ 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 mane0z7 kxf5z5fiz8jqbd+ uver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted on v kgs ob8jc.i;s.,.tyo1 3yrnthe car (by the ground) in Example 5-8 when its speed iy. , cgt.b3.rvk; os1yi8nsjos 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 theuym , wmc6)4hp pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangent,6p )ywu 4mhmcial and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a ho2o- zinuo-+ (u7ujzrt rizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.0 i - jtnz(uuu2+o7z-or5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 spaceqo. oh -*yi)5pe*ymkgcraft 12,800 km (2 Earth radii) above the Eq* g. ipmoe*)5yh ky-oarth’s surface if its mass is 1350 kg.   

  At the surface of a certain pl2 i ea3i4l1fwwbcl-h,anet, the gravitational acceleration g has a magnithl4i ba,2wwi-3 c l1feude 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's00 r2rh m7e .ej6 z5/dizkspti radius is 1.740mtr k 65 ijzes h7ez0p.2/idr $\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 the same m j/bqzhct8hs f33z,.y ass. What is the acceleration due to gravity near its surface? f,h8c s/hj .yzz tbq33  

  A hypothetical planet has a mass 1.66 times :oepwuh.d /d jyha0. *that of Earth, but the same radius. What is g near hwu p:*d .h.yjdo/ ea0its surface?   

  Two objects attract each otherxw.h; +bb m;yg gravitationally 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 val dm/nr (pxn+oh-m :/apue of g , the acceleration of gravity, at (a) 3200 mmm-:/a(pn xh o+prn/d    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Ear: hos .r+s*fk i//;jczbq xt6oth’s center to a point outside the Earth where thegjs*o z.xq;:k /r ofchsit/6 +bravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun*ady 3/ xqfwwa 5( e+tsvm mqeziz(3/4 packed into a sphere about 10 km in radius. Esti/ avmi3e3z*( w mqsyt4(5 zefaq+w/dxmate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average av;m;t r ev fnc)jyn))14rzn bd15b. cstar like our Sun but is now in the last stage of its evolution, is the size of our M t. z)a mc n1nn1bfvyd4;b);rjrv)c5eoon 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 orbiscpwl( :jq7 pjxo2x ygtjk4-3f 3l 24fting in the space shuttle. Your friends r3-xyxsqjj72o4fgp l 3ljwtp:4 fc2 ( kespond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a s 0ki96+h hcii7-w yqmk,esc 8;x0gytkquare of side 0.60 m. Calculate the magnitude and direction of th70yy i8+hc si- w kmcek9;x,0gqith6 ke total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same siq8g q+etvdsuv13 0k em/1 o9hlde of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets qho0lv3gdket 89 /+1muv1eqsare 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 isz h -et3xbo kva*x.h06 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, detee6 ozx0thv. hb-x*k3armine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usintc+ j0. k:xpmnds(tks jrrv6,r-7 o74p 1szohg the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answerxhk .rm-7pocp(s +rkt s d,74vo 6sjn0 rjzt1: to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the /r4 hxo;q+lq yEarth at a height of h/ yl qxq4o+r;3600 km.    $\times 10^3$

  The space shuttle releases a satellitev)mq1kbx+yro l ,yi +. into a circular orbit 650 km above the Earth. How ) qxbl 1y+.mriyvk ,o+fast must the 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 exgs 1w* e r8s;ohgs3jy)t)r/hjperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your jgs/)w )hr3 esoytg*;h1js8r answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a t z8ww8*egv b9satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of98b 8zw w*tegv 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 s4p ym h8h7cw0mt9 x:nqatellite have to be launched from the top of Mt. Everest to be placed in a p 0y8hx mct:97qhn4wmcircular orbit around the Earth?   

  During an Apollo lunar l9k xd7l4mc1p fanding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it tac14x df 7kl9mpke to go around the Moon once?    s

  The rings of Saturn are composed of chunks of iceqezkyg-x k:tv 6 zhk6,mc56 7v that orbit the planet. The inner radius of thek6hky6m, k 5t6eqcvgxz7:z v - rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 79i x6kozxs 1t5–9). What is the ratio of a person’s appas7 6o1zxti9xk rent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent we-km3z*9q;:jx4koy+dsw/wxt oj qu e(ight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocomsqtkw*xq-j9u w3dj/4kyz+ : (xo ;eity,     ----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 twos. wld k(.+n70us+iphn ylq9a stars of equal mass. They are observed to be separated by 360 million km ana0l+qw9ulnh ( p .y7i.+ks sndd take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elev3ndo to,dl,.bd k70 koator that movdo7okol.b30 t, d, kdnes
(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 ceili da3i;esz)w, png of an elevator. The cord can withstand a tension of 220 N and bre,iea p) w3dzs;aks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfac7j2w)k r(o oexe of a planet with period T , the density (mw j r(o)e2kx7oass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of theksi0xr./q .d i Moon (27.4 d) to determine the period of an artificial satellitri/ 0..dqxski e orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thougfpkctci18m sp9gk/ 7s0z(m/ r h only a few hundred meters across, orbits the Sun like the planets. Its period is 410 dcgzk8s09 i 1f(pkrspt/ 7m /mc. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average ddq (ygpw0 nr.gq9rw3 /istance 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 yej.13, dkismz )7y(ab-u admdhars. 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 )m (d 7yj.,d-d baikuhm z3s1astill “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 czz6*;mcm 3sm q+g93rzvu 3mu center 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 disty5 aibros79 ( vf0iem:ance for the four largest moons of (7:y 9sam5evfb ioi0r Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period an oqo,, kq89bszd distance of the Moon. 8q9kszqbo ,,o   $\times 10^{24}$

  Determine the mean dista0d7hbg,v ih.rnce from Jupiter for each of Jupiter’s moons, using Kepler’s thi ,hgi0.dvbrh7 rd law. Use the 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 betwk39),q ysv7lnbcm ;h ween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was7 b sc)9kn3lhy;m,wq v 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 art;2 om(cmht5b: ss;ynpificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent grhyco2 s;(:5b;tmpns mavity 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 sh:rr*bl k jyk96)zet ,28do xwo2hqg3winging 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 bdwtoho9g3k ,kqh :)r82*2zryj e6xllowest 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 py,6:otoaipa k48iw 8 the acceleration of gravity be half what itaoipk oyt a 8wp6,4i8: is on the surface?    $\times 10^6$

  On an ice rink, two 5 r )ck/hhru6y;1 77 x;rqeisbbim0 yvskaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anotb;i kb1xrym;q /u5hhev0cr)7 i rs76yher?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra xq0k7.5n +xmb)lcolsvity at the equator i7b k lxsqoc l)0.+mnx5s 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 will a spacecraft traveling direc752)rk9wbx1ql)hoyp ;n : azh)gdrhqtly from the Earth;z bhq 1rkxw9l) gp)h)25noya7d: hrq to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is wfzq 3 b92dp9mpfpaw-1+j p)b65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of b 9ppqjf13 9w )+dp2-fwzmbpa the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statipby 3*vz -7vtnon consists of a circular tube that will rotate about its center (btp 7y*-v3zvnlike 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 be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lc lf0sgz4:q*n oop (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 7ty rn .jf(w:/xqe f )r 1w4nzl/kh3,tryd*xba planet in terms of its radius r, the accelerationxzjr ,wktt b 4hdrf.f:y3(/rxl1w/qy *7 )nn e due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verti7 uvghis8:/. nfake4(m be5m fcal by an angle nbm vk ag7:u.i em5(sf4 hef/8 $\theta$ 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 67unypwm/3zj- ;g-si c) m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safelyy)n-s w ujzic m;-/g3p handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at -0eekyde:x* e the equator were aey e-x*ek ed0:pparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di7 c (xdshu-;ptstance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A la ej*2xa ip+v4smp suspended from the ceiling sxj v4 a2*espi+wings 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. 7cw:8r.l 11 nu/k ho6ee8xnv6x3pri tr8cxuy Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't 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: m61v6 krxi8n:c x .uch /prtxnee7ol u188yr 3wass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremecyba ;s2o 3v-tusp .c 08x9tqwhdj: )mly massive c3a 0qw -8y o)d.xpmsbvsc;t2hu9j c:tore 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 constant speed as it traverses the hill and va0 4i4 /i6fqpbbbb1w fplley 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. (bfbp bb4i i406w /b1pqf) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes aof ij7zb 7jk08 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 accuraziboj70kj 8f 7cy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 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 (N4aawg hm8umo;4j s4(kEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . E484hkms 4guawja m ;o(ros 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 satelli0s evykoy ;amf:2 e;,bte in need of repair. You are in a circular orbit of themb ,aev ykf;0 ey;:so2 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 * z rikyx88sppc ,m6w3of 3000 years. (a) What is its mean distance fromrwpp6z8*8s yc3 mx, ik the 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 2rmsp8g2byxb y;btx x820.kt*k/ no o G would need to be if you could actually "feel" yourself gravitationally aky tk;0bb8p s 2 mrb28xo/ox2. *gxytnttracted to 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 Gacf*0g ch2t3:uyi g8wu /ok xu1laxy (Fig. 5-46) at a distance of about 30,000 light-year02utuuh /c yf i:gk8g*wco1x3s from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on m5 v) ypwza6 v94k.ubxeach side. Find the magnitude and direction of theaw p.5y u) xv9k46mvbz gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg oz8.fa u5qp-xr rbits 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 th w gpf5o8.0* ea+e2hdkgw5 vuke tip of the 1.5-cm-long sweep second hand on+ kwag2f oewd8 eughk*5v5p0 . your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a 4l,jp (rz pw6xcircle below you on a 0.25-m piece of fishing line. The weight makes a compj4,p zxl(6prwlete 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 tha:wbu 3ydd azq0 :v+)hl p(nq6st a car traveling atndulqwpa vbz)q ::+d3 h60s(y 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 ca)o+q9zn eys( frs 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 track is not bae ()y+9 osnzqfnked 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.$\approx$    $\times 10^2$