Sometimes people say that water isx3q l im+m:mt; removed from clothes in a spin dryer by centrifugal force throwing the water outwam+;l:iq mtmx3rd. What is wrong with this statement?

Will the acceleration of a car be the same when the car trn fth q3knu+pyk0 x*/)avels around a sharp cu/ky 0)nxh3+qf*tpn kurve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whek sxgu u+u-;g1re 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 neg ;+1 skuguux-ar the bottom of a hill?

Describe all the forces acting on adm4swzor e4y9x* 9r+3bvwl w5 child riding a horse on a merry-go-round. Which orw+ 9y35oels4w 4dz9bvwx*mr f these forces provides the centripetal acceleration of the child?

A bucket of water can be whirs ;hr kb7+ef*pled in a vertical circle without the water spilling out, even at the top+h*7e fp ks;br of the circle when the bucket is upside down. Explain.

How many “accelerato4/3f5a- vxpe(bfo xpt rs” do you have in your car? There are at least three controls ibt /faxp5f3epvo x-4(n the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Figd xt bld- ;v( *7hecnj o0*od,zid2hw4. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s seconld-hdd42h*c( vi70own b; z oxd*te j,d law.

Why do bicycle riders lean inzkgc+) t hn42 4 l5me2b4wibsvward when rounding a curve at high speed?

Why do airplanes bank when they turn? How wouljop iqqnz hfc0f 6*/)-xl)my. d you compute the banking angle given its speed and radius -q*z6h .)nyc/p fifmq0)xjloof the turn?

A girl is whirling a ball on a st wdv5ioivgq f2 ge v ;4.--wbmtf406hnring 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 other side of the yard. When should she let bvqii 6gvdohfm5t4-g2 e wn; -fw. 4v0go of the string?

Does an apple exert a gravitational force on the Earth? Ifqr r/4kp1bw ov5/ j a9i;d)vzp so, how large a force? Consider an appl1b/or4/v)q ;d9rajpz5 viwk pe
(a) attached to a tree, and (b) falling.

If the Earth’s mass weru e g p,/idu6v8lt7*jle double what it is, in what ways would the Moon’s orbit be different?ellg,pu d6i ut7/ v8j*

Which pulls harder g0sj. 2qk fypx7gh m;/cravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more. qfxp7y/mh kjgc;2s0?

The Sun's gravitational pull on the Earth is much larger than thib8sw)i* g/e+jk6hdne 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 Eakbh+djwig6s)/i e*8n rth to the other.]

Will an object weigh more at t vlly)mgb7/j/gn ra)e:o/ j,w,s4md che equator or at the poles? What two effects are at wos,ml,b)d/ ylc) r/7w j/jamev:n4gg ork? Do they oppose each other?

The gravitational force on the Moon due to the Eartz* o6qob e*7sdvy,4fh h is only about half the force on the Moon duoq6 ve*7z*fhos4b dy, e to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its)n2 8 xf*sv7)ase9q( ujguy cr orbit around the Sun larger or smaller than the centripetal acceleration of the 8s f(sxr)vc 927)u qa ejgy*unEarth?

Would it require less speed6 ;ibxt2wwnt am;3mgh-6a5w d to launch a satellite (a) toward the east or (b) toward the wesw nt;2i5aa63xm wd;-bh w tgm6t? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest(+y-sj-y hjk 6 hs 0imjmyd0mf6i; d7w, 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 would your weight be6j 6wsdj0dj sym -yhiyki+0m-f7;mh( 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 fp1 iy/8pm0i obsc .l.space could be adversely affected by weightlessness. One way to simumol .p1is y8bpf. c0/ilate 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 can think of.

Explain how a runner experiences “free fall” o -xvpv y*y (n7s os4d:2nbol)or “apparent weightlessness” between step xovn- o:42yssyo) (n7l*bvpds.

The Earth moves faster in its orbit around the Sun in January than in Julg+m*rver-vs* d +w0spkvm ,o3y. Is the mrswoer *vvkv+g0+s-,d* m3pEarth 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 of its orbit.]

The mass of Pluto was 6jcr6u4px+f d not known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Plutou+ c66j rxfd4p’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet t08cagru2vd* fy4 2khf he 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 u ckar80f42 f2dvhg*y-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) se motgmdzw) :rw -(8vv 4y2r+ qt57linpp4v 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 El6 ,2yh+v;scof f rzx)arth in its orbit around the Sun, and the net force exerted on the Earth. What exerts thi of )hv;2,rsc+lxzf6ys 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 rof( ybsvab6)9p0 mup/ ugt18 oltates uniformly in a horizontal circle (at arm’s length) of ru1y0f pt pouv 98()abglmsb/6 adius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shutv1n 8n+ibmu0db/ *kskgpr1 h8 tle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the g/ hb8gkiv8sd*k n1 mn +b01rupravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitudehv0-/ky 7 utoz of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter iszt-k7 0huovy/ 32 cm?   

  A ball on the end of a string is revolved at a uniform rate immbto b (l3zi+ /6c +ucf:;vgcn a vertical circle of radius 72.0 cm , as shozc+3b+ugi;mc(l 6tmbvc :o /f wn 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 spevqrearqzxc 9b p )49-)vg*n-zed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepen4ep-q n-)g avrr)xvb9cz9q*zdent of the mass of the car?   

  How large must the coeffv3b3x:/m, 0dgmo droi icient of static friction be between the tires and the road if a car is to round a level curve of radiusr3m0 o gbv:di,/ 3moxd 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter piljrjxpwcg). ch((/vkms j2j9+ ots is 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 times her own weight, how fast is she roj(pj9 /(w mk2c . hxvsjcj)+rgtating?    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 fro dy-ws9ny+ezp2r( he5woo g 2g 251rl;zm)fn cm the axis 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 static frictlwmrwg -2g;12o+2c (denz5pyhzs enf9 ry)5o ion between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsnzay:1f m08efide down at the top of a cima 1 0f8nfzey:rcle
(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 4x0)ch iyaus.(including the driver) crosses the rounded top of a hill0)iy.ah x4 csu (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-dihx5d- n; sh9vgameter Ferris wheel need to make for the passengers to feel “weightlhd5 g sn;9-hvxess” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical czl1yyst;s9 szdk4e: cr,( zf )ircle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporte,4 zt; )z yyr csd:fzskl19s(ing 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 am6vc8t w *oq s)/bz7hj centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelbmjcw*6svh) z/qt7 o8eration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyl.v y(,ldl 70o5dtmfynurs5 t9 indrically walled "roy dy vol5d.r70f mltu59s tn(,om." (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 frictionless air-hockey tpk.c7o1 bu8u -frpe9 kabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fp1f987k.-ueo rc bpku ig. 5-
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 ignoring the weight of the 0o.x/ee1x:t w un2rkl d9pn1 wball which revolves on a string 0.60txwr0kenl w/p1ed1x n2.9: ou0 m long. In 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 c;kly-npc ud* d9v iqy3q 3,9syar traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massesb4xvm2t+y6:fxljx p m.v*n/ypuk7u .y43oij $ 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 e9cfiu+ /i/ nhavasive 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 components of the net f+u06luktib9 wyi3 p3(as6i cxorce exerted on the car (by the groupi3ukli ytix0 w6(9s a+bc6u3nd) 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 area, goioo;rs9 u c.yq*q3jba 98 q0ejing from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car wheo8yqj 3;b o9j cr0a.q*i9suqen it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rav.37crsy4j gmp0t e.m dius 2.90 m . At a particular instant, its .jmgt3.0vp7y r4mes cacceleration 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 spaa4q2/iyw q -w):uvxr n9vns .zcecraft 12,800 km (2 Earth radii) above the Enw9 ayz2vwurns):/v q4-q.ixarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a ml;2 f g.iu(ovz : r;getuw*4boagnitude of 12wl(bv2:uu;. t;goofriz* e4 g 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 ;2neoy;/ s.;sb jwo -qgquy+p due to gravity on the Moon. The Moon's radius is 1.74 s. +qyg;n ob s;-yw;2 puoe/qj$\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 h 9 2f-fp(k(lgs nn1tcfnyg84was the same mass. What is the acceleration dup((1nw2 9gfcnlnfs k8ft-4 gye to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rad2v 30hdxriy7ig pwz m 2g7c2vf8v46ddius. What is g near its 722dpf2v xh3wdci yrgz74vgmvd08i 6 surface?   

  Two objects attract each other gravitationae6i xrxlul ,:65.o4 ol,hmnsdlly 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 gravity, at (a) m1 /b hjsytdv8ui .f3uqi* u9*3200 mu mq*u9ti. *vsy3hfui 1j8 bd/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a .d, xrrw8pk4*uny g t rtl+bp ) /f503slodil0point outside the Earth where thegravitational acceleration due to the E3k5* wtxpu b4yg0/sl)ltdnp 08d.lo,ri+ rfrarth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thk8k:mn4y pv5uksx ,1ge mass of our Sun packed into a sphere about 10 km in radi: sn85kv,4mg ykx u1kpus. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likl iu,h5t80mzowk 9v n,e 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 ,mziok,95h n8 wlv0utis the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weighd6n ;kmz(ba14 d6o. e0ju* cgzhhrel1tless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself th d6(c;ej1on4r.dg1 hlm0ea h*zk b6zuat 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 squara:hi*hmb - 9qje of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on haim-*:9h qbjone sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most o-iknlwi99 5hao z+il 5f the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assumingkiih9 59i zl-owla 5+n 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 accel )x lceqnvc(vdn, u170eration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine0q,c )lnexc(7vduv1n the mass of Mars.    $\times 10^{23}$

  Determine the mass of thyq7c / ka0tnytl( z5b/e Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained ustn/ t/kz(yb0l7aqc5ying Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit ab v)ekh (auq.8njwpa57out the Earth e5) a7 8qkvnp( jauh.wat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the E0o3.p i)snuq p h6pl1yarth. How fast must the shuttle be moving (relative to Earth) when th.puqo)0 pyp n1hi3ls6 e release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experien v- x.gmra/dw:9gcmh7 ce 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 Quesc:mxv9a 7 mdhw-.ggr /tion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orb+ 10v6; hmvlbs5v1w i uhgmbp(f qm0g:it 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 the Earth. Does your result depend on the mass of the satv sm h gbmguhw50mi+1f1 0l6p qb:vv;(ellite?    s ~    min

  At what horizontal velocity would a satelliteu -643 o7x1prvdcersz have to be launched from the top of Mt. Everest z7 -oedp1x6s3rrvuc4 to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contin ppw9)rtgj;s8ued to orbit the Moot)jrp; sw p98gn at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orydh o1ly, 5uqesfsd8 /pu. o3.bit the planet. The inner radius of.uu/s phyeq1f8o. ls 35odd ,y 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 Figjtc( jsw5g-s;zl+avy+3t/ul . 5–9). What is the+watts uc/lsz(+ 3v -jj5y ;gl ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg c c d9bxja8s7tb b9g1)astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant jxgcb8s9t1bc )7 b9davelocity,     ----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 equal e- 1x/ectomuz(m g2l* mass. They are observed to be sep1c*o e(m2ezl- xu/g tmarated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scalewp+za(zy /ugbv 42pyzi.w h .7 read for the weight of a 55-kg woman in an elevator thatg wyiz p(yz./w 2b4azh.7p+u v 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 suspended from the ceiling of an ez lgdy1 u7b*t8zg e81mlevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Wha8bgz18utl yzdg e7m* 1t was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periodm fbu1aixf5: 2 T , the density (mass/volume) fa5u12: fmxbi 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 periojo*2 nduhrg e7 emu5*: pgv/v etw6:)md of the Moon (27.4 d) to determine the period of an artificial satellite orbitgouvme n:vm72/w5jetu h* reg :*6d)ping very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundeu pxw) 3 z6j8sh4x34k0f jezm. lu9uxv6;hbpred meters across, orbits the Sun like the planets. Its period is 410 d. Whath3keb6f 3)l 9sxpu x6u ejuz8.jxm0zh 44vp;w is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distaw1tvj5.h4dx/ ljg um6nce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once eveq6:6b5q rz yd zlyc;9qry 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 “iqqb;z5y 6rld z96qcy:n” 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/34 86)rgr,jgeovxpen 7 p lhe 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 moon :ntx 8ceuxa+;s of Jupiter (those discoveau xt8;+ xne:cred by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and diec2luk 1 ,;yjgstance of the Moon. lk;c g21eju y,   $\times 10^{24}$

  Determine the mean dista5pk72a0g u 5ak ihssh)nce from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tabkagsh5su)52 i hpk7a0 le.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between16w./jwajo,d vj 1i cd Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun butjdv6ww1jao./ ij dc,1 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 deaavbf*91d9 9la nzz1ep0 jfg,z *4cczscribes 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 climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. Whj a9pzz 0,e n*1vag *fa1c4zd9bfzlc9at will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging 9fi(r:ens 2mnvine (Fig. 5–41). If his arms are capable of exerting rnnm if(2e9s: 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 acu wo *eec.iad 01j0.xuogso(:celeration of gravity be half what it is on theoa0w:jeu.uo*x oe0(c sgi 1 d. surface?    $\times 10^6$

  On an ice rink, two skaters of equal massn/.t ;y0ai1tf7aa j xp/lxa:e 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 masses are 60.0 kg, how hard are they pulling on one ano1na jaixt 0ay ;:afe.xl /7pt/ther?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acce 9pfd,+ vbc3gz4.2rdig(o bi eleration of gravity at the equator is slightly less than it would be if the Earth didn’t rorgdivfp.(d4zb2 g3i,bc+9e otate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft j 9ne -ix1mtk7p .v2hk/gcx 3ptraveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equac3ihk-p7xx g9tjp.k mn21 ve/l and opposite forces?    $\times 10^8$

  You know your mass isl1;6*tk o /ggb8hj t;dq5tyir 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is gt*yjth r5gt /d;6;l8qib 1okthe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo4cu3ypv v) nqh 2rk)u3ut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diauvq3 hy2kc 4)3vupn)r meter 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 hisoe4;. hmyb ma- e grrr8a k+0.hkq4m0et fl+r; aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a +zv672 bwyu8 rzcdj1dplanet in terms of its radius r, the acceleration due to gravity at its surface21dzdywz 7 r8 ucbv6+j and the gravitational constant G.

A plumb bob (a mass m haxnse7t 1j07+xjr-by o nging on a string) is deflected from the vertical by a 7 1xn0tjr+xb7eojsy-n 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 speed of If the coefficienrdt u 5)gcj8.7.j/orfbe y7pct of stat5/7r eub8pyjj c.tdf7g)rc. oic friction is 0.30 (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 so fast that objects acd8z )dd5 .9eh 9 s1omv z7sv.h hm+resr-9xset the equavmhdx+8r7)sd99 e.zh5ec- o.9h sm r1dszev stor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a co-1uqow5fan9k; ,mdgznstant 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 speeyhcugj5 ,0i a/og:1 zfd rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out tou:zojg ,5yac1 /h0gif an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as lj:cyd-vp;edg a 8y6m.u2s1u the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of :pdmv2 u c.ej yudga6l y;8-1sJupiter 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 Telescope deduced the presence of an extremel vypn9 zaiycypetm2p /48/3-s zd/1tly massive core in the distant galaxy M87, so densyein8/3am1pd9-s pzy4/ yzt/ vcptl2 e that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown in,m8c5y 2iyexwde7vxfuj6fc8 26u tp2 Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact w82t82vmejd,2ueiy667c cxy w5fpx fuith the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites o j2itm0)*tfu 9n gei6zrbiting 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, witzij0nf ) t69utim2*egh 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), afte4qqzeh f3u:6tr traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height:eh u6ztq qf34 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 pursuing a saq36unl4 r+so htellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind itq+4h o nulrs63.
(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 yea5ue36fab):* j tlffb5a sdso-rs. (a) What is its mean distance froms ef5 abaj3 )5u :flbtfd6so*- the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G *x lc2a 8bzey+ wy56umy0c(sewould need to be if you could actually "feel" yourself gravitationally attracted to someone near y8 eyce lsm2*y(b0z5wucy + xa6ou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy+m. x pq;8s akdqaag3- (Fig. 5-46) at a distance of about 30,000 light-years from q a3.8g-;xd +qsampka 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 tpkpzi )2xu5o7e: + c/fcknqw7he corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at f)/:z5p ckuk7nq+ce7i xow2 p the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbiy xlf2t-gt j.squ5m:sxr4ims89 2f:t ts 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 tipxq,yr 7 n0;tz4oqdcy6 of the 1.5-cm-long sweep second hand on your w,z n7x64 oq0 rycq;ytdrist watch?    $\times 10^{-4}$

  While fishing, you g-205ethbxsj; )ga up iet bored and start to swing a sinker weight around in a circle below you on a 0.2 e)iabg2t;jp- xsu h505-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius 2, 7afgrz4w fnR in a new highway is designed so that a car traveling at sp,2 zfa7n4r wgfeed $ 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 ofjjob4lt 2tr+. 3;xu cj the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the b3.rj+c4u lxjttoj 2;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.$\approx$    $\times 10^2$