Sometimes people say that water is removed from clothes in .wq96zfo ,-r5 aovqewa spin dryer by centrifv,o5f69q w ew a.rq-zougal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be th/t:ek4z x7z nue same when the car travels around a sharp curve at a constant 60 km/h as wz 7:x zukne4/then it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hillysaq2 x 3hpas/1*t).pve q wly3 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 y)a t.xq2*v aq psh/33s1lw pea level stretch near the bottom of a hill?

Describe all the forces acting on a child ridinvy* ;y9( ctye(hufo+y g a horse on a merry-go-round. Which of these forces provides the centr(;yvfcth( oy y9+y *euipetal acceleration of the child?

A bucket of water can be whirled iy7k h0 5+s ,kr3gxw0 ;jtkvir,db pes8n a vertical circle without the water spilling out, even at the top of the circle when t kjspr0kh x,i ,0b8ks egr7y5;d3v+wthe bucket is upside down. Explain.

How many “accelerato oij12que8slf e3s;+ nhxv(z3 rs” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acuee2zl3h 3n(8+vj1;xf io q sscelerations do they produce?

A child on a sled comes flying over the creqe rj ,l1 fe988bcnxwq5)n4mest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels51 br mc8 jf,ene 4wq8)qnxe9l the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high sp7pmlb: pq v(7l ;gvqw;eed?

Why do airplanes bank when they turn? How)*bafwp)6 b )ksp;a50gmr asb would you compute the banking angle gi6)g b;)s0wamfba *kpp5)bs arven its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Sqd iirie8e elfv 9g d,u /;n7z2a*mb1(he wants 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 le l*e,i9a8fdbz/e1e r imdq 2ui;(7g vnt go of the string?

Does an apple exert a gravitational forg j*zd 1d u;6mht/m2znce on the Earth? If so, how large a force? Consider an a1;hm*ntud2/z m6jg d zpple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would(zg ;s,+68to jnz rwci the Moon’s orbit be dif+gzn; r8i(w,soctz j6ferent?

Which pulls harder gravitational7 -;(inq qysfnly, the Earth on the Moon, or the Moon on the Earth? Which accelera;sqn-q7iynf (tes more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet thjhz3u f;;0 8qvyfe g10qly cci-mv:3 pe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diff;0gqc ff j-hyp i cy l1m38veuq0vz:;3erence in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the imdz +x gvi fxf1s +u8)2v09vpequator or at the poles? What two effects are at work? Do they oppose each otgffiump vxxs1d90)+ z2iv+8v her?

The gravitational force on the Moon due to the Earth is 2j:wdvgj6 ;zstw) og3 only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away frgwdsjw):;2z v goj36tom the Earth?

Is the centripetal acceleration of Mars in its orb trbzlj+m01py xfz-9ys, t+n.it around the Sun larger or smaller t+l.n1fm-yp rzz xbj0s ,y9tt +han the centripetal acceleration of the Earth?

Would it require less spee ) +z(;ae4fne 0y.hba+lf2fcycidpi.d to launch a satellite (a) toward the east or (b) toward t z ffi.4ahci+dy)e.fpl2 yb;a+nce(0 he west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scj xi.ld( .m2. fs8gxfwale in a moving elevator: when the elevator (a) accelew8m( xsdig ..ffjx.2lrates 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 long periods in outer spajn*j +rl6s)fw ce could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you j6 wl)j+sn*r fcan think of.

Explain how a runner experiences “free fall” or “apparent weig +s 7p rzw6;iks8/nzvthtlessness” between str z/;+7pzsn k6i wstv8eps.

The Earth moves faster in its orbit around the Sun in January th/ 3ijh mrfncy(v9p .y0an in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factorhiy./0jpcr f3(ny 9vm 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 )h pxuf g*z+5cwas discovered to have a moon. Explain how thiu) czp fh+xg5*s discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lu,3v9 koc8 eov.m :v,.hfsnuaarger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting3.fva uv,vm eo9 k:s.no8c, hu 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 19+/ o 5app1cnvs j3f. gi,ou4pr80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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++ec,mlue : l q bv0k+yhh,h4g the Sun, and the net force exerted on the Earth. What exer+h u qv ,gh em,+0by:4clhk+elts 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 ouh6 04p xiniy*n a 2.0-kg discus as it rotates uniformly in a horizonnhy4xi06 uip *tal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, andd6aus;hwn k y+h89sy d(, vz6t circles the Earth about ony6 hd9+8utyw,sk(a; 6snhvdz ce 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 acceleration of a speckvu85jts 7 pcp5 of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per m55scp jtv78up inute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revg - 4bprebu6o;;8bann olved at a uniform rate in a vertical circle bebn-8o;6gpnrua ;4bof radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with whichy h0ky/ 2g2 aponiy8w/im+ h:j a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static 0yg/poynk 2ijym8 2+:iha hw/friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be b// *k + .)tldrmclazsuetween the tires and the road if a car is to round a level curve*m/ /+)ta r s.llckzud of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed c)g wm9*qb)wjmm0tl1 to rotate a trainee in a horizontal circm c)mwtj 1mg9q*0)wbl le of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the ap,jqd )e y;d.dxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of;yj. qpded)d, static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be m /4x:ukk0gxf: 8xghytraveling when upside down at the top of a circxugxfkx :/0m4 g8:ykhle
(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 drivv*9-ql wc/6 b+zbsczb t/q0bb9vfio 1er) crosses the rounded top offs1/v b 9qbzbiw*-0q6l cbt /zv9bc +o a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diametewt sqpoj0o6u3aoh - 61r Ferris wheel need to make for the passengers to feel “weightless o-1jaqp toohu6s360 w” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At thaa6-f-.4 bnff hrn7uje lowest point of its motion the tension in thhf f- anf4-6abn7.ruje 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 ovexq./ + ud,b4jv ho(rotate if a particle 9.00 cm from the axis of rotation is to exper.v e+4 d/oh(jqbovux ,ience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are .p .f 6llddh: vv3+qgdrotated in a cylindrically walled "room." (See Fig. 5-+vdd.:lf36lhg. qdv p35.)
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 air-hockex7v,rui 6gxl 4y tabletop, and is held in this orbr 4x7x,vg i6ulit by a light cord 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 , precisetd:2td* vb ge-/z(ws cinr1o4ly this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In t(dw:r 1cvz*-n4ig 2 s obdte/particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car x*ku 3i:vo(0cvfoo8 ptraveling 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 vpzzz 0k 1clb)3 wz1c+$ 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 arn-:s* igfwo2:ko5 cs od:n ;yt 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 centripen.mg q :7nsv/qtal components of the net force exerted on the car (bv :.sqn/g mn7qy the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit arb xr -yd0g d.wucr;4v)dc8q*nea, 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 fl c-d0)w4r xyc r.*q 8ddg;ubvnat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At 9,cy ,w rx-ba xkh+qt5a particular instant, a+t9 ,-5xr,hyqkwcx b 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 Earthd omqnv-qm+ 8*eyx )2j’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Eartxo nj+em*2my)d- 8qq vh’s surface if its mass is 1350 kg.   

  At the surface of a certain plg oge ; 0jl;9:*jbd+cv 8gaikranet, the gravitational acceleration g has a magnitude of jk9or ce;i:jg+ d; vbga gl08*12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius 8n/8fo+ge1 02kjg 7e-vpoa uk qxpdm; is 1.74 o/j ;ugv2-18 pdo7 qma8gep+k fk0xne$\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 Earthf 9grnv3(r:yc k z*(mm9p7kfo . w5awr, but has the same mass. What is the acceleration due to vraw cm5(k9nzw*3fr(r9go f:yk .pm7 gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rai,rnnuvv q23)se**ym qs 39f adius. What is g near i, y9 v*2nusve*33s amqnq)ifrts surface?   

  Two objects attract each other gravit1 xoi-is9 f9zhationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of graix56mq(z h3p *3 e tt4;qjpj49tcgvjlvity, at (a) 3200 mq;( jj 9gc6itlz34jvtq3ppm 4*hx e5t    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a po 1.ec:x .gky, jfqx k -vvus4/cy.9aqmint outside the Earth where tha9ve-qx .cmgy ..4, cx kj1q/:fy uvskegravitational 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 S p187yf 14rth0ql1:wdwb emn zun packed into a sphere about 10 km in radius. Eh0d wfw: yb 471nrt1e8lzq1m pstimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like o4kq b c..v vkkcdv3v93ur Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is thevqkckc3kdvv. b943 . v surface gravity on this star?    $\times 10^7$

  You are explaining why h5aubqcomoi10r j r2eh*i4s x a74y09astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Coy2qb0591mri0a4*4o7s j oa ch reuxh invince 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 sq6bxy w8b i,x*luare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othey x6bwbx8,*lir three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on tw (;h k,b,gi:fw8gqcthe same side of the Sun. Calculate the to;wicq,k:g 8bw(f ,t ghtal 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 acceleration of gravity at the surface of Mars is f*/o u. wlmaim5lkf 810.38 of what it alof.*im5l uw f8 km/1is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass o da2-+u*kxpwssbc/* q f the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, 2*psdsb/qwa-+ x cu*kExample 5–16.]    $\times 10^{30}$

  Calculate the speed o: 6 /wnjl:uxukf a satellite moving in a stable circular orbit about the Enu :/jx6uk:wlarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into i3484ckvfxcz a circular orbit 650 km above the Earth. How fast must the shuttle bkxfz434v ci8c e moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experi6ysr gggve )0p31fe0rence 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 5–32.1r)306g ee rsvygfgp0)   

  Determine the time igz7e/,cci7o/zbt hcgd j6 m .gr;-4uk t takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface rbg;g c-.6uc4mz,jtick /7go 7 /edzh of 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 satellite have to be launched from the top/x2htw0/u c 4ovf(rg/1av jy nm 6vlj: of Mt. Everest to be placed in a circular orul0ngfwxj/1 v:(jva4/ h2c6otv y /mrbit around the Earth?   

  During an Apollo lunar landing mission, the command module contindtbxzghng9w+z7n8ly4)o0 f- ued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Mf + ggdlwx-nz7tny4oz9h 0 b8)oon once?    s

  The rings of Saturn are composed of chunt+1:ddy yj8a rks of ice that orbit the planet. The inner radius o8r: 1+adtjdy yf the 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. k 6b j fklvnz 6i:8cuhv21c-3f5–9). What is the ratio of a person’s apparent weight to her real wen1v8jb2cf h:6 u3 zlcf6ikk -vight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg a,0moid; +oq ejstronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constan+e dji 0m,ooq;t velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists oauo 0tl /k 7lbsb zp1qchw4h9 c/o9*e,szb0: lf 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 9*9kuqo/hez a pwlb0t bsco b 0/l4:cs, l7zh1between them. What is the mass of each?    $\times 10^{29}$

  What will a spring shyd-sm cd8 lw7 8bzj. q/m0vn+cale read for the weight of a 55-kg woman in an elevator that movl h8c. /d8vy z+ w0b-7mdjsnmqes
(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;bj j(jd1 hrwp al5 );:btdjr8 from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? alhj j8;brjr:d 1a) j(tw bpd5; =   

Show that if a satellite orbits very near;rzi 5 up93y9tkun9 xa the surface of a planet with period T , the density (mass/volume) of the ;r9yznuupxit99 ka 5 3planet 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) tq7 /cxc, f9w/. ufbh-r6dcjaq o determine the period of an artificial satellite orbiting vej-/dc7fcq r6/uq.bwxc,fa9 hry near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbyfctt:cqgx+c yqg45 co/ fv2,c ( xc4/bi:c:fits the Sun like the planets t o /4xg2fff :ygccxc+cicc5t :( /ycb:qq4v,. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of dn:-t6ydi* kz 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comesmreo-.1wi) g z very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet )iwmz-e or 1.gfrom 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 aboutncy* -kh c(j)b the 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 distance for the four largest mooh0xg29 vmr, e)spc)jans of Jupiter (those discovered9m2egvhx )p0csa r ,)j 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 tj)3cs5 u 3gig ug7l7ldhe Earth from the known period and distance of the Moon. 3dl j7)5sgl7 cuig3gu    $\times 10^{24}$

  Determine the mean distancf,anxj-h n4 pr5sp3x / b9afi9e from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periodpfxjan9/ hfbapn x 5sri 34-,9s 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 consistma: qsxvnvl+1g3c vn+xam:/3 s of many fragments (which some space nvagv :mx1 +c m3axv:+nl sq/3scientists 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 the forqiu 2:z,esgo)m of a band completely encircling a sunqz u:2is e),go (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 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 amwv vyvv0wng1xss ,3m-:68 6mderq/ qn arc from a hanging vine (Fig. 5–41). If his r w-qvx3my/g,1dmv8:06s qvm nwvse6 arms are capable of exerting a force of 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 the acceleration of gravity bejif 0z5s7sqj * d.9twj3yvid9 half what it is on the surface 7095i.ddjyzs f3wjv it*qjs 9?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inqxr ko4v0cu*0 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 kx0 rou*kq40c vg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent y,q9ex; xgt 6q:tsp-/y w*gtdg: w; bgacceleration of gravity at the equator is slightly less w ,x6sxgqe9wt dg;qp*-yt; g:bt/y :g 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 spac 3ini6m7yao ufhu1e9/* ik9k -ey+emaecraft traveling directly from the Earth to the Moon experience zero net force because the Eartk9e6 oeuiia/n* 3y9ku ie-m 17 hafym+h and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is p5mm p c+h,+syl )lsb*65 kg, but when you stand on a bathroom scale in an elevator, it says yourmyl pph+*l ,)m+bs5s c mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stasv.c ()8:ck k6fop czdtion consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (8z.cfksc vc6do:(k)p 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 loop (7f koce8ijgg:fkn o2+k77)r/*jjw m sFig. 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 i; /syb2:.oq (g8be0vjbvcii jts radius r, the acceleration due to gravity at its surface and the gravitational consti(; oj/bcj0. eiv2ysbvq8: g bant G.

A plumb bob (a mass m hanging on a string)pvf u7 -k1s 1hyhy5l .)8dsm4fw nh9co is deflected from the vertical by afpnu c7sv4kw851ld9h hsf . m)y-oyh1n 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 zm8: y,lv rsq1speed of If the coefficient of static friction is 0.30 (wet pavement), at w:1rm,zq svy8 lhat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so f ,/ had,mkwvu;ast that objects at the equator were apparentlyak hw v/,d;,um weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constantecsi(gd/5 8-x yvo 1qj 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 23: rqe4dkz/p p3vo6/ dg5 m. A lamp suspended from the ceiling swings out to an angle of 17.5:gved4dq3 /o k6pr/pz$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the E9/fiq uyl jl8-wsqgc65(m5xxarth. Thus, it has been claimed that a person would be crushed by the force of g89ifqmus-5cxgjw l/ ( 5l6yxqravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescogzk0 aw-(p5 ycpe deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a blackzyw cpka0 -(g5 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 constacp*myh+ wj40 c/mu4sc nt speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature Rc4wmsh 0m+j/ucyp4 *c. (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 Posit5w) dhnuj./ ebbtc)+ yioning 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 orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximate)end5c/h.) bbyj+wut ly 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 Rendezvn *1l3i)s ypjo;vzr p5f;-yfqous (NEAR), after traveling 2.1 billion km, is meant to*)qyo jifpy f;n-z13r;pv5ls orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pu2xxt tuk3yuoct 5+.k /rsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (2tc+ /tx3ukkx5uo.t y400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance fr( wxenbnuwo -;h4z3 +lz5fo6r om the S 6ur3ln o-4nf5 ozwwxh(+eb z;un?   
(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 needtiy sqr7z6 u29k, :1zsp hvdk/ to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, tdz29i:6hsvyk/ps z7 qkru1 ,like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the 0ze33 0 wv x2pkrk61jzdqhc )yMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light vyd13kzep rjkx0 2zh) 3q6cw0-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a -paizu;2m+:awz vm i2square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed atmv: 2i+ ia-;pzmz2uw a the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitsuea 31y7v n5hx ,6zbcu 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 tivm i1wi *.sghy57vgx fv p4(0sp of the 1.5-cm-long sweep second hand on your wristh1xvws vf(ivm 7g y*.0isg45p watch?    $\times 10^{-4}$

  While fishing, you get bored and s nsyx)o4r+h x( chvy m to15u-2g2tns2tart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle ever2+215)hso-g uth strym2xv y(onc4n x y 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 n(ek,0db hjd/kf) p.l R in a new highway is designed so that a car traveling at se)lf(/0 jn. h bk,kpddpeed $ 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 psmoms3 t zp1y360vv :tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass s3mop6v 3 styz1p0: mv75 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.$\approx$    $\times 10^2$