Sometimes people say that water is removed from clothi0h/q 1a2am) n9lohzles in a spin dryer by centrifugal force throwing the waten 2a1ol09mh/q ) hilazr outward. What is wrong with this statement?

Will the acceleration of(ob2pbq+ w8d, 1 parxr a car be the same when the car travels around a sharp curve atd8opq(x21rbw +r ap ,b a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves ar*nc787ylniy i 4unoox z-1 la1 (kt8dt constant 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 17xn( urol8lia c4-kty z7nidy 81n *oof a hill?

Describe all the forces acting c8ap67a1 ix:c8 jqyf1r2yhw eon a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration oh fyq87e :c182i cp61ywaar jxf the child?

A bucket of water can be whirled in a verty 8-ivkig 5-uwzm k;3yical circle without the water spilling out, even at the top of th5kzgvmy 3i-uyw;-ki8 e circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? o r265i-5cobhm utxc7There are at least three controls in the cauotx5ci -26bm oc75r hr which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled come(bwo ) 9gye (,c2dvfvxs flying over 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 vweb cv)(9o(g,2xfd ychest 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 sp0j;cuc/ )y85q k kd9 adiqyo2jeed?

Why do airplanes bank when they turn? How would you compute t +urab+;oceopp(: dmz / :3suvhe banking angle given its speed ars: 3+ce ubo;+dz ( /povmaup:nd radius of the turn?

A girl is whirling a ball on a strmfe7z7 ibwe co)v3/ .jing around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the omew.f 7ez j7/b3)cvio ther side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the El7a1t z,e x47 mt yg3d-svsrk2arth? If so, how large a force? Consider an7stt smgr1yx2,z3-da4lev7k apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double w lgzxf: arq.dl, ti;1)hat it is, in what ways would the Moon’s orbit be differentlz,r)d: taxl 1q;i g.f?

Which pulls harder gravitationally, the Earth on the Moofzo90gsc y 9m0n, or the Moon on the Eacsf9 zg 9m0yo0rth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than tf5hnpx0 y k (bpnecemt)0-07uhe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side )ehecuxbt0n nyfk-( p p05m70of the Earth to the other.]

Will an object weigh more at the equator or at t.h-uarv zdb /jka mb7gx65) (a1ezd(the poles? What two effects are at work? Do the a1(u-b(trx) vezhj5ma6 ak.z7g/ b ddy oppose each other?

The gravitational force on the v z /jbjww41)x1nrz )prmomh (m*ogo*d6 ,1xyMoon due to the Earth is only about half the force on the Moonmdp j o,*or)m1h4v*yx o 1mz)zg n6(r wbwx/1j due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its + (gmd6wyxiu v (al8y4orbit around the Sun larger or smaller than the cem((ugdx6 wyi+ a4ylv 8ntripetal acceleration of the Earth?

Would it require less speed to la mx+r(;ya twb3unch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rm 3(yxr;+a btwotation direction.

When will your apparent weight be the greatest, as measured by a scale(5 )1m th5 n iol82xxeun8ubhx in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least?h (x)u h1nmxel52ix8 ot5nb 8u 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 periobmw 4el4w.w8g ds in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a c m.84w wbwe4lgylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “a7wdi;+jkw h6r;s m+e upparent weightlessness” between s;si6wdhj7w um+;+rke teps.

The Earth moves faster in its orbit around the Sun in787 0ctnbwzxxb1j1 b m January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the n71x1 87 bcbmjtwx0zb Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to havmlo b ug+o+; e soov7rnw7p(z)s.(;hpe a moon. Explain how this discovery enabled h+;+wp7 7lvoo (emsr .z()bp; ougsonan estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ear rdx4y xbvi4/ :c.r7w)ler8vfth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a 7) / i4ryfbr.revv8 c:w d4xxlmerry-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 167iolo oqz x62980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Sj:,juc6 gfz9 q23tnm y2cym8xmc vh+9un, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle 6j2fnjqm:8+uc, gmyt2z9cm3vx9y c hof 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 exed5si kjthya;o6 ;sf/ 1rted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calt has;/5 kjfy1 i;ods6culate the speed of the discus.   

  Suppose the space shutt62v(yrjw ,w .:yq 5oxiviww+z le is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripeta62.zwvjywwi,+rq:(o5i wxy v l 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 m-p z.+ljx97nzd 9edfacceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the whe.jzexmdd-979f lp + znel’s diameter is 32 cm?   

  A ball on the end of a strinq 6:flpe*7uh -d9n5 ho9xzsycg is revolved at a uniform rate in a vertical circled-he 6ulpq cf:9xs 9z57yh n*o of 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 which a 1050-kg car c(aw5b c,nkgxi8;1gr/1 zaj npan round a turn 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 of th1g ; (nzkxibrcn,j1/58 pwa gae mass of the car?   

  How large must the coefficient oj j,g3gf:wvc.f static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a jv:3w jg,gf.cspeed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to q:fd1zjc v9f8bto4,u rotate 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 8fo9j1:cv bfq uzd, t4own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotas,j*3g,b hkdc bxlt23 ting turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntablds blgh,jc2tk *xb,33e 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 upside 1 /a* jxarqfr:3bijf3down at the top oj /rxq fia3b3ar 1f:j*f a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses ty4-a vb pvo-9ox .7kf0b exy.lhe rounded top -y0xbve9. .-yxlk4 bv p7 ofoaof 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 wou8t,jud)-fldilu0bfm cwe/, f,d / vk6ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmosmi0f fd,8 ,)j,bulcdtd- 6w/lve/kfu t point?    rpm

  A bucket of mass 2.00 kg is whirled in a 4tz2jw6 sxto ;.g(h 5nt hbps6tw8:emvertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket 8 .h(nt6otsxpms 2w4g;e6t: bzwht5 jis 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 cent8bwn +jfk 3m7lrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience mw bfln+ 783kjan acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are/ vrq:84q gslc rotated in a cylindrically walled "room."gq /:8r4svc ql (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a f aq.( 8i/vh.2 c0;6i) uddyugxr fciynnc0.ivrictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centrc6u0in.uy).2ch (xq n iiv8df0;ac yig vrd./al hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely wbr9 p5e0*8fjq6lqt 3ez(8okbh8fx ;v m.oh mthis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude o3. e8 hm;6xbeqr*fwo8 vfm tz0 9l8bj5 qopk(hf $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 4 bll xlz9bfgp2i 2wyfuu m26k-+0mxu;-jg( b75 $\mathrm{~km} / \mathrm{h}$ , 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 t1qd *dj5,n cm$ 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 eapxz,9il2v9(lgbd w r))u( l f 5vghe/pwf8 1vvasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal comp bu b*t, 5x4dv ;jmq2pa9ug5hlonents of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15,adj*pg5v b b5xqm9u u;2tlh4$ \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 area, going4 4gvbaq.t gw6 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, gqagt.6v4w 4b 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 horizonte5mtt) g/yvs72 cls ,tal circle of radius 2.90 m . At a particular instant, its acceleratio, y75et2tvtg mlss/)cn 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 gc2q ws 6-s,he/gb8 th,di p3dmravity on a spacecraft 12,800 km (2 Earth radii) above the Eaih2d83q d, t6,swehsp-b/g cm rth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationah y;k2 vrm 4qi 1drm/2on2b-ydl acceleration g has a magnitude ;2 oyymd2hin- 4q/ bdrr2v 1mkof 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 cpi, y(80 cqecwca3- vis 1.743ca0 8vqwi,p (c ce-cy $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same f i)hgmln( jdtn )iwybjhf1r 084e 22.mass. What is the acceleration due to gravity ne w)dlj .t4ny81fr2hi n g 0fe2bh)(mijar its surface?   

  A hypothetical planet has a mass 1.66 times thhm-amu /ab io0lo6. f/at of Earth, but the same radius. What is g near its surfo//.mof0 l-b6 mhiau aace?   

  Two objects attract each other gr.ru,ckv (,ghb.agx1nb 6q wmd/vyt8.avitationally 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 ;fl:c/ i6g xi3k(toshof g , the acceleration of gravity, at (a) 3200 mxfi s3:/tloc;i (6kh g    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poi, 5a(bazj,eora+trut3;o-yint outside the Earth where thegravitational acceleration due to th , i3a+r-e ;zj(tb5o,rauoayte Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star ha * r,)bhflydub.4lw; ls five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfaclry;lb ,4 lbh*d u.)fwe gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an ay2jks (82,q2 ej4ayc;qa pl zuverage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of oe;u yc4q8 pa22( az qkjly2sj,ur Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in t -i) k g jz/k+am0ro*i*g:o*zvfuq;drhe space shuttle. Your friends respond that they thougquo *gakrfjgm )/ **:ivdo- i0kr;zz+ ht 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 locate4,oyn( i/szbtd at the corners of a square of side 0.60 m. Calculate4,siyt(on /b z the magnitude and 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 1cjq;a: tn;tqmh3x zcn6n(,y line up on the 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. 5n ;t3n6y:tx,q ahm(c;z1ncjq-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 surc:suh0 y of4m3face of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determifo sc0umh4y 3:ne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuepmm s:u72ch1j for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using mscm1:2 7phju Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about thwh 0umq (pm5j5e Ea0jmm5 wp5uhq( rth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satep/izpr37 zvw1q+v q:st4(fo kllite into a circular orbit 650 km above the Earth. How fasti/ot+qf qp7r:wz1kzv4vp 3 (s must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a *t y:x/;zsmoorvt((v/s n9 ft cylindrical spaceship rotate if occupants are to experience simulated gravity of *zot:(ssvtnx ;fv9 mt/(o r/y 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.)   

  Determine the time it takeatgva :spj0xhi4m :w8c)3 nv- s 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 of the Earth which is very small compared to the radius of thx a s-t4amw:vig p8vhj: )3n0ce Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would(yjfjxht ;azrh.i *14 a satellite have to be launched from the top of Mt. Everh;( .1yjzj4rax fiht* est to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landinmyy f0pc5f/hw;a po/ 0g mission, the command module continued to orbit the Moon at an altitude of about f/ oy0ympa5p f;c/hw0100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are nz97wo 1 4yomrcomposed of chunks of ice that orbit the planet. The inn7y4monz wo91 rer radius of 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 e.n.m rq 7xnl2ou )pg*cvery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b).* l2 pmqxngo.nc7r) u at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the ,x(u:rwmyrz3 v2 b2 ejha9(mqcenter of the Earth's Moon in a space vehicle (a) moving at constant velocitj2erm uq(z9r2hwx: a m vy3b(,y,     ----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 stars of eru70j2wkyt6p dz5 tn+ qual mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a poy6t7 kd 0zjut 5+prn2wint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the 08o,wp(ag. rzca6f57ohga.wt 4 fd ofweight of a 55-kg woman in an elevator that 7o(fwgt zoa6d48gaca ,.rw 5fo.0fp hmoves
(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 th889*8 hekfslf tz*e zve ceiling of an elevator. The cord can withstand a es9 lk*z*vfe8t 8z h8ftension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite niv +k3w y6zktb2w) l;orbits very near the surface of a planet with period T , the density (mass/volbw+ 6 2t3nylw;zi)vk kume) 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 periodz8h (vzas5vp ob6(z3k of the Moon (27.4 d) to determine the period of an artificial satellite op( az68 zvshbok5vz3( rbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters6nufn5+uv 0v cp hps3j .z-qo. across, orbits the Sun like the pnfc qv osp3-u.uz+.6 vhn5j p0lanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of h o4w0b ek6az6q* kf8c 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 comes v8qiwfp oilt+ny5wzx //-n0 a 5ery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest ofzi+l ay npxwt in/ 50-58/wqdistance from the Sun.]    $\times 10^6$

  Our Sun rotates about th*kj 1vkzn9 zl/g 6dq6ve 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 largesj74s lg3gcg-st moons of Jupiter (those discovered by Galileo in 1g s3g7 cl-s4jg609).
(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 periozyy 26 ,: eilq5-nghwbd and distance of the Moon. 2y bh 6eiq-w5lyg,n:z   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s qal/m444 ty 9y;vvjjdmoons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valuesqy4/l m y t4dja4v9jv; 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 cons g( 6hv,rx1+z5h1a fg gr;lnp.mwma w-ists of many fragments (which some space scientists think came from a planet tha;aa l.1+n- gwz mhfpxg 1v,6(mrh5gwr t 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 des 77 g1mw6va81xk jaqd5 u4hluhcribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climateava7u 4km8 ljx5h d 7qg11uw6h 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 hangin5a/ lh)3 knko jx0ut4hg vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine i0/xhka5h )3 luo4 ktnjs 5.5 m long.   

  How far above the Earth’s subaeg 5vb 0dhe(1qd p(vl+bm(*rface will the acceleration of gravity be half what it is bahel5 bqd1+ e*pb( vd(gv0(m on the surface?    $\times 10^6$

  On an ice rink, two skat(zc9wv;*t: qvibe2a kers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual mavbwa2; 9qezt vi(c*k:sses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparentpr /vqsa:sca10) (n yp acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of thi/c )vpa nsy(qr1a:sp0s effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a.u,pw2- se na5lacvh; spacecraft traveling directly from the Earth to the Moon experiene ;hupna2-a. v5,lswcce zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in fyn t xlehk(,-z-9c3 kan elevator, it says your mass is 82 kg. What is the acceleration of ztcfek(9ylh 3,kn-- xthe elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulgo6uh 9at v6-bar tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle 9bgva-6ut6 ohformed 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 vertica; o y 6lzq;f0f)imda0mww4l4a l 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 planmns.xi;jzp.gi ec94h .p t2.4coj ) wret in terms of its radius r, the acceleration due to.4njsr9w; gep.mo.2)ijthxpci z4 . c gravity at its surface and the gravitational constant G.

A plumb bob (a mass mgr )c2 ui-:)jsfzb a9g hanging on a string) is deflected from the vertical by an angle2zjcb9)gr aigs:u) f- $\theta$ 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 i5l ..pcx749 m qkqxgnm is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what ran kxq.qc9 il.np5mgx4 7ge of speeds can a car safely handle the curve?

  How long would a day be if the Earth wer1e uqm+2 pfur-m.ibh5e rotating so fast that objects at the equator were apparen5h b1r+me qum2 u.-ifptly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant jul l,ti5/dq6distance 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 radiuw19c 41hsxpc vs 235 m. A lamp suspended f9c1svp h1cx 4wrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times v-yvfftz )tew 0 e, 3zvfce*.2as massive 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 w ctfe)z, *v0 .evfzwv-e23tfyould 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 Tewkz 5les6lc1r2 .bk0a lescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could bl z6l a21e0kcb5w.srke a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown inir8xh30 gi hl5 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 c 3h5gir ihl0x8ompare? (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 Positioning Sqhs3v-bczbn1 t3et i(8* ck.iystem (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 evet i3vz-ict3skqcn1 (* be.b h8nly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is mes :yn 9t(wv5vnant to orbit the asteroid Eros at a y95wnv(: snvt 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 spacr46i x0qfanv) e shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above in fv0x raq)64the 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) fai 7npq/,5oovw 1pg 4j je 9g-ws0-jvWhat is its mean distance from the Sun? qn os/74- jj,9fip5jvag pgoew0-w1v  
(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 f co*(x9ar.ui of G would need to be if you could actually "feel" yourself iu* or(ax.9cf gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around th eulla+fth+zprx1 - 31e center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,hu 13le f+p+tr1axzl-000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each so6qbostds iv(ge *5mzx /p.b6nign:ri. d9-5 ide. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the mi*s iv:-6zi n9.6gpnx/dbesm qd(ib5o rgot.5dpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 wpt66zvl3/f fkg 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 tip of the 1.5-exo 02 s dnp8f,tgc;m-cm-long sweep second gnt- x2sco;08e d ,pmfhand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start eb1rv9a t;4o) +bnsq)w cbh*0qp -n2sxvmd3u to swing a sinker weight around in a circle below you on a 0.25-m piece of fishin9ap* mnsb)tehu24 o-b 1)q +cbxvq;0sv rd3wng line. The weight makes 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 highw8ini+n4o hu-gay is designed so that a car traveli+h4nii 8n- ogung 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 negoezmr9-; lsz;r tiating curves. The angle of t-l rrz;9e s;zmilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not 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.$\approx$    $\times 10^2$