Sometimes people say that water is removed from clothes in a spin dryer byvkn) hw of8b,yv/ld*fp7b-:o7v q*c y centrifugal force throwing the water outward. What is wrong with this statementnvcv*q*8: d,lok)-yf b h7p7fowyb/v ?

Will the acceleration of a car be the same when the car travels aro2*riw,.(p qpmnz 9m2 sk*ikbaw*2hv u und a sharp curve at a constant 60 km/h as when it travewa *ii( m2n p2*zm p*hkqwv2sb r9u.k,ls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hil7 gg/yzh9o pg(ly road. Where does the car exert the greatest and least/oh y(9 ggz7pg 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 hill?

Describe all the forces acting on a child riding z+h2j)bft u.e a horse on a merry-go-round. Which of these forces provides the centripetal ac)hetf z 2+ujb.celeration of the child?

A bucket of water can be whirled in a vertus 4u0akug+/ryr ; 7sqfpgl86ical circle without the water spilling out, even at the top of the circlesgas y;fl/76rgu uq84pk+ ru0 when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at lexbldq;24e t9 +qk 9z(( umomo+rjtn-j ast three controls in the car which can be used to cause the car to accelerate. What are thedo;2jl+ rzbqm9ne kju4(t o (9qmxt -+y? What accelerations do they produce?

A child on a sled comes flying ovg/;ix4 7 c1qw21t ccncbk1r xler the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’47r;wn/ 11cqc txcblxci 21gks second law.

Why do bicycle riders lean inward when roundinm69 o7d-d+y2:kk3rz nyb+ j7wbdh o tag a curve at high speed?

Why do airplanes bank when they turn? How would you compute the sv ,r3t(ndv:.e bstt/banking angle given itevbtdvtsn , /t.s:r3(s speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horti9pri vc, lw/*;glp0i 6 5z i5akwq;jizontal plane. She wants to let go aviircg5ki i * w ,ll0/z5wp;a;t9qpj6t 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 l(z74;9 kwm bdj y1 7mjubvj9kt :hl-yxarge a force? Cons:ujxkvz dw4j ;hm7ylk(9 9m 7jyt-1bb ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wencwdm03ai 84q re double what it is, in what ways would the Moon’s orbit be 3dmncwiq 40a8different?

Which pulls harder grqf4xj6sc 4ia /avitationally, the Earth on the Moon, or the Moon on the Earthx4ja f6isq/4c? Which accelerates more?

The Sun's gravitational pull on the Ea7hrq sl6 d-/.gkgguv9 rth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitation gd./ 9grlugkv7sqh6-al pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at4 mp i8b9zb9zn the poles? What two effects are at worizm9pz 8bbn4 9k? Do they oppose each other?

The gravitational force on the Moon due to the Earth is nxom9aix9x2h *1lv4v3n pdh4only about half the force on the Moon due to the Sun. Why isn’t the Moon pulll n 4dv93a* xovxmx9ih2phn41ed away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the S,h d,*ft3s n af7(oku8o2mfnwun larger or smaller than the centripetal acceleration of the 8*d ot ,fnak7sm3o(, f hf2wnuEarth?

Would it require less speed to launch ats ibcdai8ls8k)ytd(u738 a*)ujj. o satellite (a) toward the east or (b) toward the west? Consider the Earth’s 8y7tasij)*8.c(adk d lj)o u8tb3iusrotation direction.

When will your apparen d hwv,aj76*imt weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a),i hw7a m*dvj6 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 you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend loni(bus+ oh-aj .g periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a)j suo(+ .iha-b 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 “h)kg 9i hf3ak+apparent weightlessness” between stepsf3k9gk a)ihh+.

The Earth moves faster in its orbit around the Sun in January than in July.qdi v o(w2,+aejc7f;(tag p)k Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is 2aitfpv;(+g k7 cw a)de,o(qjnot much of a factor 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 w2byzzo a( 57xfas discovered to have a moon. Explain how this discovery enabled an estimate of Playb7(x5z2f z outo’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet3qe df34 tqc3al9-vw1cm;urp 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 theu ;wqparl-4cefm1d3 3t93 qcv 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 o5spbik+1 bg9ks, xq2wb w 3(7czc j.d1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centrip;+mmw2p axeo h:b,zxodk(t/*rdp 8yxc* 4 -bcetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. Whatp +xdh*m ( b ewb ot8,4;:cop*- k/m2ydzcxarx exerts this force on 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 2.0- a4f0:xh gg4; za5smplkg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calg; lag40hx4p:zfs5am culate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface,p-azj rqjb,+ 9fjntfx6e- k:/ and circles the Earth about once every 90 minutes. Find the centripetal acceleration of -f9nb / e,jqj6 tjarzkf+:-xpthe 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 acceleration of a speck of clay on the7rc5h +. mu ea1mn)dfz edge of a potter’s wheel turning 7famz+)5rh uc d ne.1mat 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 rr o):z*b;ug aoate in a vertical circle of radius 72.0 cm , as shown in Fig. 5- *goabz ;uro:)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 with4 x0pgru,8 g0ip*h xxg which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road8g4rx0*xpggh ui,0 px is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fric/ .4i t):* sa+gjl2ra yehgqjytion be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95g rieaajg2/*j.h:tyqyl+s )4km/h ?   

  A device for training astronauts and jet fighter pilots is designed to k)ncd j1ywd,q( v,lt7rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is shk(c ,)vyw,7d1j ntdlqe rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.e84ew a+) wqz* qc(m.6jxkkl e0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntableq e)w .jm eck+we 86l*ax(z4kq 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 traveling when upsidn(kbov*m56-d4 plhme e down at the top of a cirevl-m5 (pbo*hm6n4kd cle
(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 (includr6cw 0i, v0ifplb q05ding the driver) crosses the rounded top of a l5r bv60,c i0wdp fiq0hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to mayhawrwto9h- m -s e38,ke for the passenger,w em3h8h-awo9 y rs-ts to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Avov:xu(3nk-w 3s-s p pg7fl;ot the lowest point of its motion the te3-xpku3gnv 7s;vlos - fwp:(onsion 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 rotabhcz7*o o5h .ete if a particle 9.00 cm from the axis of rotation is to experience an acceleratihch*5oeo 7z b.on of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatedty:ed6y45wgy4j y;txy *p olxme2;y- in a cylindrically walled "room." (See Fig. 5-35.)4yeyed;-p6yygx; o5wyl:y4x 2tm *t j
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless ai+f/3ub4ab fnxi 3.+m ckfag+ mr-hockey tabletop, and is held in this orbit by a light 4x 3c+b /b+ f.kffigmna3m+uacord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisnpsi49lqdl5:n+q er -ely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find thenq4 i ldnpr+5e q-s:l9 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 bps1r5tfq1 -w aanked 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 masses zw .pn ewl)i/;bs;f3oa-lwl* $ 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 verticallyzphv hmkc -ocrzsjqxo*/)9( o 6.1* hv 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 foo0 0a zu *6ntmi+uw:vdrce exerted on the ov6an 0 u dit+m*u0z:wcar (by 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 accelewuoshhw9 hlhp :2d5;5rates 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 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?lw9hu:h d po;5wh5h s2 $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . 3vkq6n( .mbcjAt a particular instant, its acceleration is 1.0b3mk6j q. nv(c5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 ok4 p wgapa-f ea3--yo4f Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s s4 pa- fagw-oaey34 k-purface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitati/n 06mkoqz9m3j cowqvdkpbv 75-* nb:onal acceleration g has a magni7k3q o m kj0m:6*dvv/bzc9no5 -qwnpbtude 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'e4 ++fy lk :puyq9x8p1 pc.s:xq,xa ysln+,q ds radius is 1.7 syxea+yl,9:pxx8 n. csdppqy+l1uqk:+fq 4,4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet p3:udcm lv xao/,2vr h:, 5puzga:e1fhas a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravit,c ahax3 ,lzfep:/pgud om5v12: rv:uy near its surface?   

  A hypothetical planet has a mass 1.66 times that g2:/4neifoona9 io1v of Earth, but the same radius. What is g near its soo fnv9go/ 1 e2in:ai4urface?   

  Two objects attract each other gravl 7i7pdrh.7bc itationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g 9 br(ep00rx02jemypg , the acceleration of gravity, at (a) 3200 m xeg9 0jberp 0y(p r02m   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth s)f-c /wb3odbj8 /4ddn-il3vgtxz- crp4zb4where thegravitar/x 33l wb z-fpn4-oj4 dcid-v4dtz )g/8 bscbtional 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 *ci0(v 6nqeuc the mass of our Sun packed into a sphere about 10*iev0cu6 cn( q km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star pj* kw5xh/h36fy)bhxw 0zp 1r like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. kphhj/rb) wf5*01z xp6y3 wxhWhat is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightltkq9z /kyhfii9oh;;5 k95wqa ess while orbiting in the space shuttle. Your friends respond that they thought gr k9ykhtak;o;9qhwfq 5i9z / i5avity 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 aicxpn2ci, 33bt the corners of a square of side 0.60 m. Calculate the magnitude n i ic2cx3bp,3and direction of the 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 thysy4 tun 9jv+;e same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). v9+4sy;jnu ty 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+5e,d(ir/dh kji 2i;zdh6hm o surface of Mars is 0.38 of what it is on Earth, and that Mars’r o2/edji+hhh;z6 mkd5i(id , radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usin ja) r ijge7n;jjt +/i,l(+ocjg the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to oir g)l ja +(+i/,tn7ejjjc;jthat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sft;f(2c ku( g amr0w)tatellite moving in a stable circular orbit about the Earth at a height of 360(c); r tua(gk2ftmwf 00 km.    $\times 10^3$

  The space shuttle releases a satellite into a cij m53-ohra)e /.zfka frcular orbit 650 km above the Earth. How fast must the shuttle be )fke3mr -/f.z aah j5omoving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experie2wsa* r; ,r:esaep 9kdnce simulated gravity of 0.60 g? Assume the spaceship’s diameter isesdr,ar 2apw*sk9 ;:e 32 m, and 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 orbitl e*qnkl:sq0yk ,)8tc the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the y :,e)csnlk8t *q0ql kradius 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 launch5y j2 8sz(d58)njmsbjj3;i ft( owwzeed from the top of Mt. Everwd)yw 5(3 zbe2n sjs8j8ztfi; j(o5mj est to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contiyk j14oql6f 5cnued to orbit the Moon at an altitude of aboutcy j46oql51f k 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of ch ddtm it)j;-m 2-zeu0eunks of ice that orbit the planet. The inner radius of the rings is )mztt-j2e0ue;dm i d- 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 onc cworq: x(38gdgjp0 )be every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to hewgqc )0jprbog(d :3x8r real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kght4w2 2tc3cawpu blob *8( i3r astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velowp4t3 * wh2o 3cbtlr8ibau(2ccity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars9)ufsvi,m( i6k g8jnr of equal mass. They are observed to be separated by mvii9 kn 6(jf8grs)u,360 million km and 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 q i7eoj: 4tgweer6 8sj,c*8xc-kg woman in an elevator that m76s :rjoeti8ceeg 4 xcq,j* w8oves
(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 an elevi-wt n+ mq2s+k: fddmk2/ld.d;m80kg nx v8lpator. The cord can withstand a tension of 220 N and breaks as the elevator accelera8lvi+tqk2s/dm:; -n knwlxd p.d+m 08mfgk d 2tes. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits v z3hcaz1 m :(gzge3-jrery near the surface of a planet with period Ta 13mg3 zz:grcj e(-zh , the density (mass/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 the Moon (27.4 d) to determine thekgu:uftq0v;1 bybw8y7cj 7mx2 ;x7wo period of an arti7uby2:1 x0ubwmqv;gj8 ko7yxc;f w7tficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred msv9/* hszwx yift2sfe3*u(.ieters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance frofifh * u2issy/*9tv3wse z(.x m the Sun?    $\times 10^{11}$

  Neptune is an average distance+ygtldg.53ilr* . xth 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 years8wulaq,8)js iml 3fq 0. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distanlf3 wm8a)l,qujq08s ice of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G5p vumo 7sa7.dooa.+xalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four larges+gfet,: ze)gk9sut,68ffn zgeg k8l(t moons of Jupiter (those discovered bn,zgkge8g+l,8t( :f)efgu szt6e k 9fy 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 dym- 18q c8,d jp4rzbnyistance of the Moon. c,p8q m j-4d1ybzny8 r   $\times 10^{24}$

  Determine the mean distance frzgm er1yo/1i)h2.e)p c 3*w2 vhljoru om Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the disuvih 1lo gr2e1*cw 2yh mep/))o.jrz3tance 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 nmw fh;5tzahp0b 3k38jal* o- fragments (which some space scizaw03o3l -b h;tknp8hma5 f*jentists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in thexhb 47w c81ic+aw/u vl 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 db+4u wv8x1 c/iwlc7h aistance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine*d ;l)zez9ewxb 3 lzlei-h(ad,3 zyb 4 (Fig. 5–41). If his arms are capable of exerting a force of zh9-ed)lbi4z3axzel;d e w3 z b*l (y,1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will tptea. --z7/8r -q)q ccqz;dsctaesf-he acceleration of gravity be half what it is onpztzqt- crfcac7s -e eds)-8.aqq -;/ the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsne ycao v* :q./puuql7b 3j:22pdzzo( 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 hl3nj2uu7v p*eac 2o:pd/ :qb. ( zzqyoard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratio3nls*sv bzr8 7n of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the 3vs 7rs8nz*lbmagnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrafs uad *bo5ln-uu n8:uay e* 92qx(t)ekt traveling directly from the Earth to the Moon experience zero xbuae(5 e)n2utlqs*- :you kn a8u*9dnet force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 61v hjw2e9x2;cz1 q-+hjred x r5 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, wdr- v;rh cz 1jexexj+21q9 2hand in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abbm6vom-ij: h+hh-v2t1f y0ntout its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has-6tbn:ivv mfh0hyh 1j -2t+om 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 aircrcc5;pf o (f fa4ldq/-taft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the a+jmh3m)u)a1ptdme ;g cceleration d1 pm;u+tg ad)h3jme) mue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strid/ ijf2 rq5 qh)sbts)0ng) is deflected from the vertical by anq dsi)qsb0tr)fj/2 h5 angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design spe+ akysxai2 *cjjrx,(1 ed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the cy * c(1ja +xsj,kxai2rurve?

  How long would a day v ieywc;8;-p/ ajqq :ibe if the Earth were rotating so fast that objects at the equator were apparen:cp- ;ywi avqjqe8i;/tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant0mjfbi7no8oyrr(cb wc 6ik :h66 *lz9 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 radius 23u)) krlni pu6 (dlgy+45 m. A lamp suspended from the cer6)4y+dnlg)lu kp i(uiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massi4ith3tey w238pin 5zbve as the Earth. 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 b tez wint5 yh8i3243pdata 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 Telescope dedu2yslc */qe,w u4flu e;y/a,h njk3(h dced the presence of an extremel2l3(a w4dh/*cuhe u,kyfyj; e,l/s qny 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 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 traveyaw6vjj(uq2- rses 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(a 6vqjy2j -uw. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites o,2h ern-.) g ebj*xqkzrbiting 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 satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite. *kxbzqe.n ), gj er2-h   $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travel k h1;o*-)zga1nfy pehing 2.1 billion km, is meant to orbit the asteroid Eros at a height of abo ;y e1gf1*)nh-azkp hout 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 spa0fwc1:10 v m0jtiohllek1pa ( ce shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), buva:1 k1t0f0ip l ml0 e1woh(cjt 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dist .zq +b +rvi) ogcwv.m61k1 jrh 5*)qqp,gbmwpance frpvqq p wr1.65gigbcrkhj m1,q++)m* ).o wzbvom 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 -j, ul-qxlh;1e ydw(tof G would need to be if you could actually "feel" yourself j ,1ewh xtd l-(u;ylq-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 Way Galaxy (Fis4js/qugon .6 g. 5-46) at a distance of about 30,000 light-yearsj6 nq4u .sogs/ 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 eac/htv x*jk mr8)h side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint ofkm)8vxhjt* /r the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orxf(ab w xs4i m;m-xv98bits 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 tz o8q0v:fl(fp8o3*c) llrg6 oadr 3epip of the 1.5-cm-long sweep second hand on yf6 3vd)cp f(8o q03grl 8azprol:l *oeour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weighb ( mrz4;kgk)mt 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 makes with the vek);mr(kb gz4mrtical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a ctra 0m)fk*z7 far traveling at speedf)rfamz 0 7k*t $ 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 yon r*u19g +xku1d:*rm zm d4owhen 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. Tmu+o zn *:k1mdg19*4o ryrdxuhe 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.$\approx$    $\times 10^2$