Sometimes people say tdq;gs3 e7.lya9 jyma7hat water is removed from clothes in a spin dryer by centrifugal force throwing the waj7 3mga7.l;9se dqy yater outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharplyr811 b,8u9(3qxbo j f jlxap curve at a constant 60 km/h as when it travels ar83lyx9bbf(uja qo181lj r,px ound a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wheey0tx .c* br9wre does the car exert the greatest and least forces on thyx *0cwtbe.r9 e 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 chfhn68)eyzva q hc 57-jild riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the zyf-e qv8j 76hc)a5 nhchild?

A bucket of water can be whirled in a vertical circle without th kf6.l2v z7 qxwexd/1ge water spilling out, even at the top of theq/d zx1w.7v6e gx lkf2 circle when the bucket is upside down. Explain.

How many “accelerators” do y7qyigr 3+y; ,oxsb l1;owkx flg8c (x2ou have in your car? There are at least three controls in the car which can be used to cau3qy7 (1cxk;y8 gxbw2if ollx;or g,+sse the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying ovrt5psnw6 2ic/tn 47pcer 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 ptw7i c4trs 5pnc n26/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 spragauks kz1j83ho+3 + tb/*vpeed?

Why do airplanes bank when they turn? How would you compute the baey0ay*+lhji7n*ara 5k4 vzn3nking angle given its s+jni4 l5n r* yy7kah0*zaea 3vpeed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pl )yvji,pz p,e 3a /+w0oz 9wza)hyccl,ane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard/,z,v a l3yp9w wa)ce0+,hiz)jzcy op. When should she let go of the string?

Does an apple exert a gravitational :quufes -32uj force on the Earth? If so, how large a force? Cf3eujs -q u2:uonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double wha ,:6xyw+xxw jct it is, in what ways would the Moon’s orbit be difj6x+ cwxx,w:yferent?

Which pulls harder gravitationally, the Earth on the+hj n5f9p l5ae,ckhm0lgwc .7 Moon, or the Moon on the Earth? Which acceh 0 wcaf j95cmk7l h,ng.lp+5elerates more?

The Sun's gravitational pull on the Earth is much larger oh/kepo6j 59m/iv:jw than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hin9mkehp /:iw 6ooj/5vj t: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whatz(/t0uceb *)hq 9vift two effects are at work? Do they o( uqe9/*t)bth 0zficvppose each other?

The gravitational force on the Moon due to the Earth is only about h 1 1-dq bj,9e8yvoepuualf the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eart y,dueq-p j 8b19voue1h?

Is the centripetal accelerat33uay u,o;tabgufu 76;tgx4y ion of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Ear,u; auobt y6ag3g;3 u47x tyufth?

Would it require less speed to launch a satellite (a) toward ilvc;xueq( lhs.94 x+ the east or (b) toward the west? Consider the Earth’s x qe+hcv4l;.u l9xsi( rotation direction.

When will your apparent we)r*cge:wge ,vight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case we*wr :gveg )c,ould 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 perioa 1y7b.kg oxw ohy2q35ds 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 thisx23ah gqwok5.y7b o1y 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 “apparent weightlesuqqlh ;gr 8y w/)ji*)vm9jaap5r9fu1sness” between steprw;/mjuv9p) q h9j1 qra 5l*uya8g )ifs.

The Earth moves faster in its orbit around the Sun in January t2bh9gua6r w8cv6uq(jhan 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 Earth’s axis relative to the plane our 8wg6qvbahj6u9c2 (f its orbit.]

The mass of Pluto was not known until it was 0i3 dm4vq9 v9nda1nr *+vgcy mdiscovered to have a moon. Explain howndc qgv9*vyva4rmi 09+3d1m n this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on th jetg zqd11l i*u8)l7yhw k38ne Earth is much larger than the Moon's. Yet the tnh1qz187 wg3ikll yu8*jd)e Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round 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 198mpj,. rbrocy+ i x+c)u cyan 6l5x27s30 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Sf8fizsd ,mq49uw,bzlh1p ; +iun, and the net force exerted on the Earth. What exephmus,il8 , fb4z9dfz +wiq1;rts 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-kg discus as it rotates unifom1v sspw0u) 7k y(*ywarmly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcuy( 01mpkvw 7syu)ws* alate the speed of the discus.   

  Suppose the space shuttle isptkz 8qdgjt+haxo5dm a/ 57 ( jnj3c1: in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centrit5/zjhka p8 x(+ntj3am 57q gd o:dcj1petal 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 accelerz:mc . l/ g2hf2l8kmkuation of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dl.8km z/gul:f m khc22iameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertica-e; ym/fo7.7w2spmx vyx) pte-rgm)pl circle of radius 72.0 cm , as shown in Fi y2.m;gymv t-o- e e)/7pxp7 rpmwxsf)g. 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 can round a turn of radi6*;q* gofye leus 77 m on a flat road if the coefficient of static friction between tires and road is 0; oe6ylq* *egf.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the +i 0v yjsdgqe)2 d:hu2road if a car is to round a level curve of radius 85 m at a speed of qh :id y s2e+g20u)jdv95km/h ?   

  A device for training astronauts and jet fighter pilots in:ih mw5h3 *7d2iq9lg6abwzl 89lr t qs designed to 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 timw2ma8 nh * gi6w9 blqh759lzril3q d:tes her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable op*sr 68mz5mfxf variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a r68psmmf x5zr* ate 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 down at t.8q36q -ngmqw un 0/fnzqva5ohe top of a circln5f zvg0 qm .q6 8an/owq3nuq-e
(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 the r ctxg9x4c sx*6ounded top of a h xg9cxt6c 4x*sill (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 F p n(w rik :n+1ev6e-h2cag3vverris wheel need to make for the passengers to feel “weightless” at the topnvk+1hgre new v6pa:-i(v 23cmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. 2wykg 4 hfeq/fz my5sskc66*5At the lowest point oq g fym 6c2s5f6e45w/kyshk*zf its motion the tension 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 rotate if1svfw(2 vii2 f a particle 9.00 cm from the axis of rotation is to experienvvf2w f2ii(s 1ce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a j*;i ,of s-r(6ruy 6kc,kc:;eyv irekcarnival, people are rotated in a cylindrically walled "room." :y-ukecf ys6kjk irc, r(,re; 6;*o iv(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 fricti5(q4gdykos v6/3i f lzw.bn:zonless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5- n kl(y4sz.zo6/g 5 wdqv3b:if
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignorirkj4 0k*sq()),xgq ad igf -cxng the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitud,*k kircx-(4agd0)fjqq sx )ge 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 t8ru,l+e8boj sbqm857 pu3ql n raveling 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 massesxinz: k01 q,nd $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310awk1z:nmn*ube3 sy.:i n)k 5 h $\mathrm{~m} / \mathrm{s}$ . 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;8z;ru8ymup4g8fbs3ppz 7 si onents of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15 ybzizmup7834s;rp8sgf8 up; $ \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 pi;zpd ;t8pf0am t 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 tif;pm z0 t8pad;res and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horiz8yh n+q/mi1d wontal circle of radius 2.90 m . At a particular instant, its acceld1qnh8w/ y+imeration 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 gravity on a spacecraf)5jg*).ppjj )/g oem skiy a8dt 12,800 km (2 Earth radii) above thegji )dmj)pkosj )8 5e*.p g/ay Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceg6;;pdpy k0 y/wvrk-tleration g has a magnitude of 12 m/sv-0/ry;ptg pkk y;dw6$^2$ 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',m:sipk h zw04kjvb+bkd.s 0)4q9r hts radius is 1.7p4 zbv,4qkhjs b+smh)w0:0kk.dri 9t4 $\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 Eadtr+didk0x4 ) rth, but has the same mass. What is the acceleration dut +0iddk)dx4re to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times tha mcsm86: zcacw b8ont a-u)8v5t of Earth, but the same radius. )t8cc -mnw6ab:mo asuvcz885What is g near its surface?   

  Two objects attract each other gravitatievnl+o 4 hgws3rfo t5(xrk8ku-6 ;ws-onally 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 zpghmu ;fq;2cl8 y67r8l4v tfof g , the acceleration of gravity, at (a) 3200 m g88ft mc; 6fvuhz7;p ll42q ry   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to abo4yk 13yg2*pi ;vsnn point outside the Earth where thegravitationay*np ; gv1nyk2 4sio3bl acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spx4/w ky/ x+inwfn te04here about 10 km in radius. Estimat 4x0f/kyxietn/4+nwwe the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, w0 ; gopl591jajwjxr 9ihich once was an average 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 our Sun. What is the surface gravity on thijaipj;l95gjr9o x1 w 0s star?    $\times 10^7$

  You are explaining why astronauts feel weighto-)sl r-:/a*m l/qd1byv zmb cless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker dq-/cybmzl:sl*m) /r v -a 1boup 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 a an m;8aj+v,zlocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the tomj,8vzaa +a; ntal 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 uanp32wftt/ltvocp*9*j f : ;p p 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. 5-38). T f3/t*patto;j lcw*p2vn:p9f he 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 0.38 thd p koj6*9 o3b:z,m awqph5*of what it is on Earth, and that z*6t3 5,hajhpop*wb : mkd9oqMars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the wld:, b urh0hy86m ;0 elzfft+known value for the period of the Earth and its distance from the Sun. [Note: Compare u lzwbr fym06h0f;el8:+hdt,your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a say9dgo 9e4 4sv80phaeatellite moving in a stable circular orbit about the Earth at a h8 vegp4oa9 4y9aehd0s eight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abov r* o,rh9atqh9o -r,i g;epn:ze the Earth. How fast ;qariron9:hg r ,ep9oh*-t z,must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical si ij;u;tbw9*u es t33-q2kiv bpaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your ansuqwi;sb;tiu23b*- vj9te k i3wer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit thekz ndm1buau )zx*f9*.9gw8v(p glon, 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 the Earth. Does your result depend on the mass of the satelli ,nwguaof)b8znu9*ml* d( x z kvgp.19te?    s ~    min

  At what horizontal velocity would a satel,i 1-ecqqg c87*mbjjfc 9yc;xlite have to be launched from the top of Mt. Everest to be placed in a circular orbi 8e1cgy c9*x j;ij,qb-7cqcm ft around the Earth?   

  During an Apollo lunar landing mission, the command module continued tof l:mczw).gq/ orbit the Moon at an altitude of about 100 km.wg. mf lcq/:)z How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks oft zurr gnfk6;1z mv;-0 ice that orbit the planet. The inner radius of the rings is 73,0n;tg vmrzzr - 10u6fk;00 $\mathrm{~km}$ , 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 rota0m b7,)slko 7vaebt;mh )bbsq /1cl.jtes once every 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, lb,a)jl ho mmq0ss7c.tkv/) 1b;b b e7and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of thytj qo-a;qg//e Earth's Moon in a space vehicle (a) moving at constantoqatjyg/ /-;q 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 syst5an9aplg *i,3l qsc x+em consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a cax5p +*,ll 3sq9iang point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg jh834h3 5wu ng8 kruq 0l1xrrdwoman in an elevator thau3 q0l r4xdh8k35wnrgru8hj1 t moves
(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 dkpz7)u3+sd 1hh ox o:suspended 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 directi7 odkp+ )h3sohdu:1xzon)? a =   

Show that if a satellite orbits very near the suhlu),*u eo3a yrface of a planet with period T , the density (mass/volume) of the planet is ,h 3eo l)yau*u$\rho=m / V=3 \pi / G T^{2}$ .
(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 x6v f8ffm lmzp6-g3*r- ce+cz.4 d) to determine the period of an artificiall -6+3fmefx8c*c-6 zg fvzpmr satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrossn(ewz y :t1wx)dkr;x:, orbits the Sun like tz:1w(; dwn)et:xy rxk he planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance i8.sk ni,im)x 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 thehssbey n6p,ln2i *nlk)f o ;,d.j)h p**dnzc 1 Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “iisds2nzpnb,h j) 1 )6*n;ny pc,fdll*eo k*.hn” 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 Gala1b6 tvd tyu+0lxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 masfk k /:7cq7yea) 9ioafs* v9igs, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 16ffo9yi iq/7v:*cka askge7)9 09).
(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 d z5b1y mpui yh.;g;p*xistance of the Moon. ;miyp*b phu 1;.5xz gy   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usingl io(vqo:t)4w Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tabq:i lo)4tv (owle.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of mfkq( q2m8fk2many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyekq 2(m8ff2q mkd).
(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 form of a bx/ u7n .m)u-bbq-fu bth6w7yuand completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun btbu7y -7mwnu .ufxh/ - bu)6qis 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 b/et kpukskya+;f w+2v yif fe5;hy l(bm977h 9y swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolb 9k+ feyysvhf9p k /5+ l kuh2;mt(i7aw;ef7yerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Eartuk*cf xcd:c*w gx 7b8 *-zm:wyh’s surface will the acceleration of gravity be half what it isdy:xc*k-cw x*bf ugmc: w8z*7 on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua,e4kypku5c9h l circle once every 2.5 s. If we assume the, yu pkh9ck45eir arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent adguy8q3phy 7km*/f 7gz5gk y /cceleration of gravity at the equator is slightly less than it 5 y*8/guykyf/73pgzkd mhgq7 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)bpl)2:( 9sg0v w m i-wdjldyw))pqzw Earth will a spacecraft traveling directly from the Earth toww l9dv0gd:)ziywj w(b p2s- l)mpq)) the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a ba s8s )u5u nke9j2j6bsjthroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the j2bjjs kn9 u)u65s8se elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboi cx iy r861f/;zvn6xout its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by tr;/i68xf oyi 61cvnxzhe 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 (Fig. 5–43). 64k fk7-s)v9hul zrnj
(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,yc.r t-3d ;*hhdfwe;t the acceleration due to gravity at its surface *.t-;y hhe w3dd;rtfc and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is de: 9(d0qmw*eg sno: q7l:q4f)pxsprpm flected from the vertical by an angle0l4:se*:pwf9m mr(:xpgnsd)q op 7q q $\theta$ 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 speed of If the coeffico-t eh+ 2sj,xyient of static friction is 0j 2 osyht+ex-,.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating soif2l3jb5n uu+ fast that objects at the equator w2 j+l3 u5bnuifere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cons .k.;2ocg/o facoyhn5tant 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 235 m. A l+niem80iv x *aamp suspended from the ceiling swmi8*xeav0i + nings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320bukdn . ul6) b)wm-y6vbab)p . times as 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 ab p.)l buvd by))u6.bk-w6amn 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 Telescope de ( 39m zqnn4/nvqdg;nbduced the presence of an extremely 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 cl/n q 4mg(b ;dnv93znnqouds 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 hilyc7e-/crc ev9z fm- m7(y u.ynz0f9sml 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? Se- 9fncz9e0(7srmm m-fy.7yz u yvcc/ mallest?) 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 System (GPS) u6((wepd8 z fiwtilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the68 d(wwifz( pe 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.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travelin+ 1sbzt/3h unig 2.1 billion km, is mean1/+ub z3nthsit to 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 f2 e8 o6bc,hhzpursuing a satellite in need of repair. You are in a circular orbit of the same ra2b8,ch zfh6o edius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance n8mm2p68.i .ta+ qb8d9ecb w4jm2 y gr3yefcm from dpgebymj4+8rm 9ic 6bm.2.m3 n2cf8ya eq 8wtthe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "levvii11k0b0r o gt8( feel" yourself gravitationally attracted to someone 1(ikl8vrtevi0 bog10 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 (Fig. 5-,7uydc3 kd4zxy0+ qx n46) at a distance of about 30,000 light-years from the nk , 7y4zddxc yxq+u30center $ \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 0.5 qe 4:1od5zdwa0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom 1q dd5e :4awozside of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits th ,jvm hm*4un+fy) ) fwpx nhr7d1ot8s6e 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 1ec8j.iye ix/a8y5 ie/.5-cm-long sweep second hand on your 8/.8 yi iaeiec/j e5yxwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkerjryph vf) )7+k i+)ecd weight 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 th)+e h7k)cpdirjyf+ v) e vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that m(v)pa7i- nqc q/4zhekzyl+ ,a car traveling at speeak(,7hz4nyv +c q qlzi-pm/ e)d $ 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 negotiaxg .t:ay3e8h is2s rc-+mu2tjting 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 otxush+a set3c2:jr 2-8 g.mi yf 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.$\approx$    $\times 10^2$