Sometimes people say that water is removed from clothes in a spihgn05 l-pkpn :n dryer by centrifugal force throwing the water outward. What is wrong with thighkp- l:p5 nn0s statement?

Will the acceleration of a caxb 6eqr-go* 4mr be the same when the car travels around a sharp curve at a constant 60 km/h as whem-g4e*oq b 6xrn it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at consfq3gs8 x,cpn2 h 4k nh:hm15eetant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hieq3c 2x4e,hg:1 mkh8snpnf5h ll?

Describe all the forces acting on a child riding a horse on a merry-go-rjg18zhrv9)j9 i.h j5e trgke7 ound. Which of these forces provides the centripett gh.j71j kirer9v8j hg59z)eal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water shnxm)-vdsxj q 6,7l *gpilling out, even at the top of the cin*d)lx-6hm,jq xv 7gs rcle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are sie1ioxxl /))xl(kw 8 at least three controls in the car which can be used to cause the car to accelerw )(e)x/ li1ikx8osl xate. What are they? What accelerations do they produce?

A child on a sled comes flying over the creste,m( txc75tqs of a small hill, as shown in Fig. 5–31. His sled does not leave th,xs 5qtt7e (cme ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riderso4s -bf c2k5uko nx8e/h-v8qd lean inward when rounding a curve at high speed?

Why do airplanes bank w(4p: ;k t -2xmjxmzafzhen they turn? How would you compute the banking angle given its speed and radius of the turk mtm(zzxj:;4pf -a2 xn?

A girl is whirling a ball on a string around her head in a horizont )q:44x4kwq w8dpmufv al plane. She wqpwd v48q ):u mkx4f4wants 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 thi+;fc1 n-5kmhxp wf+ ye Earth? If so, how large a force? Consider an app; nwykf5h-cf++ mxip 1le
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what w q1dexk 34tzi1cm, r0:h,z)zrvy nh a:ays would the Moon’s orbit be difimzzhe 3c0:xkr,dt h:zn1r, 1 vq) y4aferent?

Which pulls harder gravitationally, the Earth ofvqk-:p0 fs 3ln the Moon, or the Moon on the Earth? Which accelfv:qskp3 -lf0 erates more?

The Sun's gravitational pull on the Earth is much large2whtoc7echp/f) l 6+yt ;rl.qr than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull frorlpe2c7;t+ ) qth.yhl/foc6w m one side of the Earth to the other.]

Will an object weighg utd:o 64nd0)bi qw ;83ifvwx more at the equator or at the poles? What two effects are at work? Do they oppose each otheri d 0q:wdo 64bv)x u8fngt;i3w?

The gravitational force on the Moon due to the Earth is only(yr* ew+mn fxv2/ )ijx)mdhck):k -xf about half the force on the Moon due to the S/)xn: edwf k-(j )xy *hfi kxc)m2mv+run. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars itxp esxy/6 lz9p.m:be7 4hi 5p8bw8 zen its orbit around the Sun larger or sma p5 h:z98wtb/e pe 4xepml7.6zxsy8ibller than the centripetal acceleration of the Earth?

Would it require less speed to launqshi/q- *)cf3 xemo2izz :i-b ch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dioc: )2s3 -iqmzf x/bzeqi- h*irection.

When will your apparent weight be the greatest, as measured by a scale in abti.ujq vglgu57: 82e 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 asj.i vlugb:eg82t5 uq7 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 affectecnfclb 5j7a )*d 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 aspefcl )n cb75*jacts of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent 6e;0qrn vm2aq*k5iz , sz+krzweightlessness” between stepsesq 0krr+vaz kzq6i*,;nm52z .

The Earth moves faster in its orbit around the Sun in January than in Julel:an kz7+1jy y. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane y7kjena z+:l1of its orbit.]

The mass of Pluto was not known until it was discvp, xjo ,(cl/hovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass.l,jcx,(/hv op

  The Sun's gravitational pull on the Earth is much larger than the22h.dsd y69ewck/r /y uf,ohv 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 sc h,vehd2 yw9 6o2u.rd y/fk/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 19,juv 0ta*i(-pdq ow-k 80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerati.a7tk6gs5sla + 5fliuon of the 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 orbit is a circl+ils 5t65fs.ukla ag7e 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 oj tv-8h)n,; hsnroq;y n a 2.0-kg discus as it rotates uniformly in a horizonthvyo;,- sqtjr n;n)h8 al circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 kmry0,csjpms/ n +*f7w t hi6 bx*-tun)t from the Earth's surface, and circles the Earth about once every 90 minutewn* s*/ j typ-0,nim+ sttrx6)uc 7fhbs. 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 accelerati03+fner()w 7z dv2lyhi 3affqm n t ;ifie.a11on of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions pre1q 07h dv 3ztfm2)1a;f( yaii+wnffeli.n3 er minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is re9 ) jm818-mlj inav gfyld5er3volved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If it 3a8)y ei59mfnr mgl-v8l1j djs 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 , 6);y)bzh fn7yhs eesturn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent besn,)y)s6yhe7fh ;z of the mass of the car?   

  How large must the coefficient of smu gcs/hc +umve5wzj)05x o0eg1 :. uctatic friction be between the tires and the road if vg+u oxc55u0./w 1c):mcgmze suehj 0 a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training 782g v6vnbqwcastronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of raqcv7b6ng 2w8 vdius 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 axiv m4nb.9w+y-jnj n-whs of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the w+b mnjjnhy9-w -v4 .ncoin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travel/r3ag vl7o ml:ing when upside down at the top of al/r7 3lmo:agv 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) cxn:1co -nib7 rx3vtf 8rosses the rounded top of a hilx7i fbt 18nnox3c-rv:l (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 minb3dxav67 ooy0q8 ictv bqz4: jq:-.bxute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at th ox6.aq8by0c-z 3 idqb vqo7t:jvb4x:e topmost point?    rpm

  A bucket of mass 2.017 tw*mwju,,is8bq il0 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the t,1t*ww , u7 qmijsl8ibension 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) musi1r 0wg cjnv,z.b 6r7st a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelerat1vz nc 06 r,wb.7rgijsion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walledbzct 7 tfx45*n "room." (See Fig. 5-3 7bf t4n5z*xct5.)
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 circ-g4ysmt0xwt)y/ vu (ele on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown ixg /stty m( e4-y0uw)vn Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precivr/ wh5ga1 -fisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of af 15vwigr/-h $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 ca 8/njv r h ; qgful6/94y4,mdq(tyyrtfa0 )zmpr traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses h6ff6mpy9bxh(,35-mlvm9 ) n w seuxs $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 94 gcupu9ksig e3ls476r 2svz 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 aa6lxpwk0- k-g0 -fnagdsdfv3;8esv8 nd centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when i0sxfv g0k-p 8a6e - -dg3akwdf8svln;ts speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 5) u zblp hl+++s6-c5mchu85 +epvaebj00 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when5jc+h 8uumll)ecp+hp ev +5 b+-sb6a z 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 horizontal circle of radiusa0, q2sup ,ovs9)bb gn 2.90 m . At a particular instanup9)ns qg0b,s2b v,a ot, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 gravw,0kkx2og mz9i5r )dsity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfac wzdkr 92kg,m50sx)oi e if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitaes*r9( guxvi6sj0i ng ex8klp9cu/9 ) tional acceleration g has a magnitude oxu*(slee8gx c9gn ii9r9j 0kpv 6/)suf 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 rabf-ulvp4rx* 59z croo5i*3ipdius is 1.7iz*9*ir45-xu 3fpo vb rp5clo 4 $\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 svrf+9j.iu x r4ame mass. What is the acceleratiui9vr4.xf j+ron due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timewf3 b*a h 79 ofb2ga-64lxkbwes that of Earth, but the same radius. What is g neabaf-*ghf2a 9kbowbx4wel367r its surface?   

  Two objects attract each other gravitationally with a force of 2bjy/s3eslki- 3m8vq0.5$ \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) 3a; kawb7pz* 20nis(ep 200 m p;w72 0zpik a*bnas(e   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the E,lshj4a5uq rlz8jh 2, arth where thegravitational acr ,jlq 2z,8hl5h4jus aceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fiv7aws1nd8p .n se times the mass of our Sun packed into a sphere abnpds sw.a781nout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a y 6w-u4bj d )mkm/+he1m)f*yquqy5jcsho l)(n average star like our Sun but is now in the last stage of its evolution, is the size of our + hf m(ey*bqmyl) 51 u/)so6qjc w uhmdjk4)y-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 whik3i, jqc4 hkydw5z fns9.is00 le orbiting in the space shuttle. Your friends respond that they thoughtyf i,.nqsk5h 9 j0c i4z30dksw 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 3l-a5u,egw p ls0un*iof a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sl5n* le-pgw0a,ius u 3phere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the sbw*wu1f2 e;:h9 na tcname side of the Sun. Calcutwbu n1f *a9 c;2:nwehlate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the accelerationb1gdu(ru*r gj,7-x5v*2g rqu uw 1 mbz of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Marsvz5m* wu,uur7ru1g grb(j -dg1xq2*b .    $\times 10^{23}$

  Determine the mass of the Sun using tjf8+p: s 2oxpu7wn,ynha ngi ( d-t6m)he known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtoua,pg 2ityj8swnhn6)m x+nd:-( f7 pained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving s +ltr w5* puhji3.j4hbl2r2sin a stable circular orbit about the Earth at a height o llhi h r +p.23jwj45trs2*bsuf 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbittdch.2s1k.r ofv* 7bi 650 km above the Earth. How fast must the shkh.dbo vi2t1s*.7cfruttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to gmflh4:l+ij4 experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.g4mj:l +4f hli)   

  Determine the time it takes for a satellite to orbit the Earth in azk04z84i k5h ce.dhh u circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of tkd ue4.i5 zz8k0chh4h he Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launche7.*;73ci jhrz:wbaar nj0jejd from the top of Mt. Everest to be placed in a circular orbit around the Erenh b:*aijcj;0wzj .a3jr77 arth?   

  During an Apollo lunar landing mission, the command modulem3;cm9)y6cgin ;c fhi continued to orbit the Moon at an altitude of about 100 km. c3 6yicmg icf)mn9; ;hHow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that vfq;4 vz:as 6f7x.xsqd1) sewzs xv34 orbit the planet. The inner radius of the rings is 73,000q7z ) xq awsvv3x:vs ;.4fx4zd1e6ssf $\mathrm{~km}$ , 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 onc: -i ldnn pn(ce/:p5yse every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent -5( :cnlp:ypd insen/ weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight :wx1qu*d(+n c jcqh: wof a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving ahq 1xw*wu: n: +jc(qdct 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 syspq5kle hk0r5t();hxztem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is tr th5lk(hp05;z)e x qkhe mass of each?    $\times 10^{29}$

  What will a spring scale read.j k/cxdentl p06(y:t for the weight of a 55-kg woman in an elevator that 6n: lycxkp/ detj.(t 0moves
(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 ceiling of axjxyb() tgf pyl3d 7)y-et) 3qn elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a = ytqyj -)xfe )d3xgpy( 3b7t)l  

Show that if a satellite orbits very nei 4i 2m)162h n ;q.mfxv/lqnpernbu,yar the surface of a planet with period T , the density (mass/volume) of the plah ln;ipq rbv, nqy416m)2xi/ unf e2.mnet 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 ( 86td :pzepdb(27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface. b:t68z(dpep d   s

  The asteroid Icarus, thy (jpzar, v c8vgidx)h/x: 9k,ough only a few hundred meters across, orbits the Sun like k z/(cdvayhj:,i ) gr xxv9p,8the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance )1in;ym.sy uyo c 2(ne b+:ri7 xgycj/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 roug sx (4hw :o:b eqd*tv3gbjb6;p)d5hmahly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearev34wobgs*b5xh(edtd:p ;:6b )aqmj hst 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 center of 0h61izgm y-iq-q)w2x phemewa f73f : 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 dici8r5l i1 lx8:c ugn2t xn vw;amw)0c;stance for the four largest moons of Jupiter (those discoveredac1 mc;5lclunvxi0t;irg n8)w: xw 28 by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of th.vli 1jov , :.3dabpqfe Moon. qd.vl, f3i1pbaoj.:v   $\times 10^{24}$

  Determine the mean distance l//5 * vtfrbjlfrom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tabletv lf/r/5jb* l 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 (whichc0b(((dsct-t djwu0g some space scientists think came from a planet that once orbited the Sun but was destro(cgu0dw dbtc -0(t(js yed).
(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 "planet2a*cn5l)r 3y3qhmkdc b ynr6:" 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 rimydnqc)3c hryban*r632 :k l5ng rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hangingw uip0 ck9.zx60 a12jbiyhq0,x zjll 5 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 toleratejx 6 l9pi 500 uw2x.1z bl,0qkicjyhaz at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gra 1jn :r lpdnaa92j,qgk, ll.3avity be half what it is on the 2kad9j,nl 1,j 3:ap.larnlqg surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grabcau l6 :aevj)) 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 hvj:lc a)e 6ua)ard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration0c/+wqi4p smi of gravity at th spmc04i qw+/ie equator 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 will a spacecraft traveling directly fr)6jr r;w4,i: zwxir7zxld0lrom the Earth to the Moon experience zero net force because the Earth and Moonwz740: r)zl6ixir;lxrj d w r, pull with equal and opposite forces?    $\times 10^8$

  You know your mass iy 3os1es 1*gbrs 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. W3r*es 1y s1bgohat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stateg* yl 8fgpi:*6klo-fion consists of a circular tube that will rotate about its center (like a tubular bifl6lfg*8eg -*k o:ypicycle 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 +fum8z1b*x )op/0bj1yzb.k , uyn nir vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its rhepbv w ,jh+ zzqezj* l0-f;gq8p-gs(o8:p :nadius r, the acceleration due to gravity at its surface and the gravitational constangb*88f qzj(hp,no e gel-s:; wz- hj0pz+:qpvt G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by aoclchnmxoo ottba :4-t76j87 w9*z7sn ango- 4* n98mlx tca7tcozwo6j 7:s hb7tole $\theta$ 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 23ze8fcyo 7b;x vt twx: b(/maa design speed of If the coefficient of static friction is 0.30 (wet pavement), at whato:t/v(m x;7zcwaeb 2yb8f x 3t range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatinga n1pl )csji8 p(yg 7wks;4k+u so fast that objects at the equator werlicp8wg1p ) kn;4(7sjyuks+a e apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintl8/9i8ei.ggnie ulr*fd b9h( ain 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 curve of radiu;, bty8*bfnuko /7wfbpq6hfd/mf7 )p s 235 m. A lamp suspended from the ceiling swings out tok)f bpfywf6/m;on/ 7,b hq b7u8 *fpdt an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimjgus ,,u-fw- m+odc2ved that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't su,, 2j gws-u-fduomv+c rvive 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 Tele(qlr l7ou w-j*+005op ugn rvpscope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it l jnro-r u o+q57lp0(w pu*vg0could 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 spewx ekk 2q,6+bced as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valle ek2bkq+w6x,cy 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 losing contact with the road at A?

  The Navstar Global Po/*f w 6xerisz 7*l/b.og(ah6a quroj (sitioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbq *whj6/slaooi.z /e *(f(ugar67x br its, 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 tr4ts;e te(32oy y ./obq1zkl8rmyt+lmaveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly bqto (m1 +l y43ytre2.e mzls8tok;y/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 satelli4qvzc9 )vm roph.t;jl8xr)g0te in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abo rrjhv0)gt.qvml8)zpx9 co;4 ve 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 300 g)q:t+vs0 p2qous3yft(c3wi0 years. (a) What is its mean distance from tcqy 2wu +v:fgss(i 0 po33)qtthe 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 ifi ol goqz;(a:ds vcag33m e7:y1en7f/ you could actually "feel" yourself s l(gaa/yf7e371i: m nodv ec gq3o;z:gravitationally attracted 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 Wandi4ax s+vhy.-k2bz; nhd.*f y Galaxy (Fig. 5-46) at a distance of about 30,000 lh k-s.;2 d vdnixb4+z *nay.fhight-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 cornersk u p*xyql4 fs80vqqa3v 5df+- of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of th3u *8q x0d av-v5flf+ps4kyqqe square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass -:b) t,mhz bg,qm(c pk5500 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 tipbz3a n7li8vy: of the 1.5-cm-long sweep second hand on your wrist wat8n:a ybziv 73lch?    $\times 10^{-4}$

  While fishing, you get bored and faj1.j,d uh. ustart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makesd. u u1fh,a.jj 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 highwayfp5twxlu xnt8 .c e*76z2x y8y is designed so that a car traveliw2e x.l7 t85tuxpzc 6yfxyn*8ng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatingac0t6ko :v 2om curves. The angle of tilt is adjusted so that the main force exerted on c:t2kmoa ov6 0the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$