Sometimes people say that water is removed from clothes in a spigtm)nz5+rju) vm + ma1n dryer by centrifugal force throwing the water outward. What n t +gzj5am)m)1urv+mis wrong with this statement?

Will the acceleration of qn,s5e kqw 7y+pm1/a-cl:q gr a car be the same when the car travels around a sharp curve at a constant 60 17aqepq:k q cls5w r/,n+m- ygkm/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed aloe7)bmmvqgj yqnr +*i( ae)( .ung a hilly road. Where does the car exert the grm ) eaie ).v+nu7ym((qr*jgqbeatest 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 of a hill?

Describe all the forces acting on a child rilg ( /r/)/zj0ikl:f (ugeoj tlding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chi lfrok i/gl//j:tjg z(e) 0l(uld?

A bucket of water can be whirled in a vertical circle without the wv0yw7it9:fjlxz7mj . ater spilling out, even at the top of the circle when the bucket is jlm:7f 09zxjy 7 v.iwtupside down. Explain.

How many “accelerators” do you have in your car? There are at least three 5daeoj7+z7dlbrl 6g 0h2 3fjd controls r 5be0+737oljjz 2hlddf6 d agin 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 cresax vmi5tefev k(7 u71*ap 29cot of a small hill, as shown in Fig. 5–31. His sled doesum* oe 21f 7cka9pv7t xveai(5 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 second law.

Why do bicycle riders lean inward wheymjrd), e24nmn rounding a curve at high speed?

Why do airplanes bank when they tuz*qb4 + pv2 ns gxch7:dwa/k+lrn? How would you compute the banking angle given its speed and radius of thed + b7/xgzn*2apqv+k:l sc hw4 turn?

A girl is whirling a ball on a string around her head in a h7 ncwuk mmmy d(i5nf z-:9 g(m )rb-xv/l*8sqyorizontal 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 go of mm5dgnq/ nb 9 mmrw)*7ckl8zsyu(v-: i(-xfythe string?

Does an apple exert a gravitational force on the Earth?alp, kd a-y.u4 If so, how large a force? Consider an appley, ua.a-kdlp 4
(a) attached to a tree, and (b) falling.

If the Earth’s mass were0 2 copdwmog0) double what it is, in what ways would the Moon’s orbit be di 2pom0w)dco 0gfferent?

Which pulls harder gravitationally, the Earth on the Moon,sf.zv/3 wv*sjx1ur 2q or the Moon on the Earth? Which accelerates more1qx.rf3vj szvu /*w2s?

The Sun's gravitational pull on the Earth is much largerx3vm ihi6fj 9z( q v+h3wte8.j 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 z .hf3vh ijqit3( 9v6+xmwj8e Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are zdy:.k + fw0qn5t9iz: jgy,kwat work? Do5 wq +kzd,z:0: f.j9ignytykw they oppose each other?

The gravitational force on the Moon due to the Earth is only about hatt -2lyk (vmr+lf the force on the Moon due to thy2+trkm(t- v le Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around m6lfefitg)3xtz baazv8 7/xs : (v4z+the Sun larger or smaller than the cezt sm/ 8+gxzeb:f ax(f)l67ivv 4 az3tntripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eafk 7me1nw9;lqpu1q6oo:1q o ef 5d e.ast or (b) toward the west? Consider the Earth’s rone ak p 7of5. 1med9qo;loqqwu:16f1etation direction.

When will your apparent weight be the greatest, as measured by a st:yq lr6oo5 +dcale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at condrql to5+o:y6stant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer soz3w6ml4 h rs0pace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) h6zrm4slowh0 3ow 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 weightlessness” 8 m/l4c .v7xmkux.f rkp)z:a: cdwrg)between stepspk4gu7 kfl.cx)/.ax:) c8 rdz:mv mrw.

The Earth moves faster in its orbit around the Sun in Ja40eg ;k:b;hjvydqah7 nuary 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 Ear g4 0ahqy;j k7;ebh:dvth’s axis relative to the plane of its orbit.]

The mass of Pluto was not kno 7 n2 o4ii-b).r9 cloii5 g*3)lkijgblxxotu4wn until it was discovered to have a moon. Explain how nlil *otucixkgo3 xl.42rj74i9i-b)gi b o)5this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than 1z-m .csnvmd8the 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 centez1m8 - cs.ndvmr 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 19805rk14 / .chs/ fa9rtkfyhap2k $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thxa5 u h-a sg*wgz(mmb)z x653oe Sun, and the net force exea3bz u6m5xgm5g*)a (hw- xzos rted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniforgp8uoe-e fd 3hgq3km 0 7)1yftmly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the dipefd o-)ku 31tfge g0qmh 7y38scus.   

  Suppose the space shuttle is incw);d3do rki5 orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal accelerak5 ;)od idwrc3tion 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 accab p3zr6oqrsmw,cx0m./p1 yb .4xt: p eleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpx:t3ros0. zb,mcb 1.p ym /aqr46xpwpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rat1*d btu3jd )rqe in a vertical circle of radius 72.0 cm , as shown in Frj*udb)3 qt 1dig. 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 afpoe3)r9c fvlou) h pzb:lx,1-/ov g7 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction betpfvx31oo,g p/lrzoc f)lv9 )7:- uhbeween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betweepvw,n:*6+s,ljhu tb0 wdc bv: n the tires and the road if a car is t,s+6b jt :p v:cdb hn,*w0wvulo round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astron:j-ja9uie ,xg:a4zqjfxr gh 006 ,kvhauts and jet fighter pilots 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 owr g9, jaq0z:j-:egf,vuhx ja6x4i0k hn 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 rot5x b/n3 zyhix:ating 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 friction between the coin 3zx:5/xi bnhyand the turntable?   

  At what minimum speed must a roller coaster be traveling when upside d7zb2ci9z(2d eqgq4p .l7 bsmmown at the top ogi9l.cs q7 zpe 274db(mqmz2bf 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 9+x9btc).zr;4nnt fi 4qexta750 kg (including the driver) crosses the rounded top of a hill (radius 9tfrt+ e).nxitba 44czxn q;7=95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to m6rjsxeh; -wm1.y; kf99bf2 cvv4oou l ake for the passengers to feel “weightless” at the to4;ou6se. mf hyvlbkcwv 2f;1rx9o9-jpmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vert 3kudyp n-uq1zw8*.phical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting theh ud*k-z. qwpy3 n18up 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 w a kix 4432)6 w+alfyt3ncqkxrotate if a particle 9.00 cm from the axis of rotation is to experience anf t+43)k4ax6 yw3ci xw lkq2an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindr68xkeqr b x.i4ically walled "room." (See Fige kr8x.biq x64. 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 f0q; xfos+t + c0x;4vce(*nen qm3smg how 5x9irictionless air-hockey tabletop, and is held in this es 5;xfe+nqc0 moxwq3 oxm0*4sv+t;(hig 9n c orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the v)fc etz6, ivv95tc0w rg9oh .weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of 5w9hvgittvf9,)ce6o v.rcz0 $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 *k1 ke04c;pw1 peoriv k1zni3-xb g l9for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse6y n1a e6iz,yns $ 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 maneuverd+o6b top z(q8 g s0smu0n24xw 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 cocem8.dhqa q 0v*64pg dmponents of the net force exerted on the car (by the ground) in Example*cad6h8.gq0d pq 4mev 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 Indianapow juqaxws,5b(6d,,q kb; *osm lis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceler(dk,5us xjbqq a w s6b*owm,,;ation with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circzn tzth.) r(x b.e+wlwdz ,s5.le of radius 2.90 m . At a particular instant, its acceleratbztd)(re.z w, .htlnx5ws+ z.ion 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 Eartkpxp )(mm*ibt;9-d l;pj m-kmh’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kp; (ki-tmldp) -mx*kpm j ;mb9g.   

  At the surface of a certain planet, the gravitational acceleration g has a magn.zx-i* 3h ykeaitude. -yk 3hz*xiea of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is c2eij96f uuh5 nu:9oicy4a 2h1.7u aef yo96u njci4ihh25:uc294 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hasm k(j2 z3 h2htv5au 8kmsy7-o0 l0utie a radius 1.5 times that of Earth, but has the same mass. What is the acce 00kejlvamt5u(2t3i y2mh7su-z8 ohkleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times o:j;ujch u.:6t/du-e v0l vslthat of Earth, but the same radius. What is g d ju v. luv:o;u6ch/e0stl-:j near its surface?   

  Two objects attract each other gravitationc,je;an /kj5;+mwu4lnygu g 74u,fa kally 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 of1gv2 wlt h(7h mt+e8nf g , the acceleration of gravity, at (a) 3200 m 8he7hgt m 1wfnt2(v+l   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Ew .,ph;d 1d;tapm9cqy *scja)xgv5) parth’s center to a point outside the Earth where theghy9)s1 * 5;aj gqta cvx,ddc p.m;ppw)ravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five 7h6 k tg y+imn1oj/0 ttp+4bso*.)wonaqxqu0 times the mass of our Sun packed into a sphere about 1nhpqm+ a 46 t*wjy.) /xbktguosot0q+n io7010 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wi:k:1g;cw:hxk 63 vul jvsnz ,as an average star like our Sun but is now in the last stage of its evolution, is tiu,1v:ckgxn: vw;:lzk j3 h 6she size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting iy85lgw8jmk), +ub5w jxl fhh0n a7*hj n the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration xhl5ayjbw +f*wu5j 8n,07 gj khh8ml)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 squ9bre o m81ofm7are of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted oe 7 8ofmo19rmbn one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planydspvo5 wz )qu7;l*a )ets 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 planla)7 pq dv*us )woz;y5ets 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 accelerap))3da 3j vvt9nrz9rytion of gravity at the surface of Mars is 0.38 of what it is on Earth, and ty9z a3rpvnj)rv)td93hat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of thek) cz ezbde:u.iekkyx x*-6(vdu)f28 Sun using the known value for the period of the Earth and its distance kude26 * e dxk)ev-.(k byi8 )fzxz:ucfrom the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sa*an49jcsa; eb tellite moving in a stable circular orbit about the Earth at a height of b;a * 4ea9cjns3600 km.    $\times 10^3$

  The space shuttle releases a satellite intoa lb.up;p;ui0izyth0 51x+z -oz6q lg a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rel 5ilpupazz y0ht;zig- ;qo0+ xl1 bu.6ease occurs?    $\times 10^3$

  At what rate must a cyl8uf 1fn0lt xv/indrical spaceship rotate if occupants are to experience simulanf/ f8xt10v ulted gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular v2a+acry/,s)q y zm(u “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 resula2, my(v)s uq+zycar/t depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top m-fcl bq ow)j3a9+t0 bof Mt. Everest to be placed in a circular orbit aroundtb+wobl) a9qj0 m c3f- the Earth?   

  During an Apollo lunar landing missi,mft:s ni,j,y 71bcsb-znrs/on, the command module continued to orbit the Moon at an altitude of about 100 k,- :bmc t, 7,isnjs/1 szfyrbnm. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chuc1:dfzhy5 s 7x)qwvwxh9g b*+ ie(n- cnks of ice that orbit the planet. The inne7- hxz(x+5:yv1ci swb)hqfen9wg c*dr 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 diameterpp v38 d5obwpq j )l0d- c)b:1mcym3ln rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a)o3180j p3:vnpllwbd) y 5 cmmp)bc-dq at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of6 ,2ge zca /mmmmheq:2 a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moa2e2cgq m,/mmz:e h6mving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consist.z8xkq. dub. dxme- ecm:0m/ xs of two stars of equal mass. They are observed to be separadx.umkzmcd-xx/e 8q.e . bm0:ted 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 scale read for the weight of a 55-ko: inn2j- ai;qg woman in an elevator that movn-iaqo:n 2;i jes
(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 cej3e4fz) e/l0:s)cyxd hf d tr+iling 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 dir y/l)ecsdj 4h:t)zf0x +redf 3ection)? a =   

Show that if a satellite orbits very near 1xc:v aj0o o8miy*lo.the surface of a planet with period T , the de: *mlox8ojv c0.ioa1ynsity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the periodj9 .ibyj ).cj2q;dxx p of an artificial bcq2 .dpxx y.;j9)jij satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus,,euuhgd, y:.2spc i1p though only a few hundred meters across, orbits the Sun like the planets. h isgu.ep,1cuy2:d ,pIts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average* nelusicj4ju 8*/b hhz 97hx: distance 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 Sun8 ddj-g 6cpy3u 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 “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’sc6 8jyg3p-d du third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates abouty/8; (e f nyz6z.mlooo the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the maz8:sv0ksh z,l 5aww;xcy ,b.pss, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo y:a;w 5w, bzs,hlcz.px8ksv0in 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 twk ,zza58pbc+5j0 i0jmqx7 anhe Earth from the known period and distance of the Moon. 75p0 0jmia j8nqkzx ,5awzcb+   $\times 10^{24}$

  Determine the mean distance from Jupiterhx2k8 xk0i q ,l-ss6nf 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 6 0nklshf 8xxs2 iqk-,the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmentsj farz.z,-83insqc g ; (which some space sic;anf3.zr, -8 q gzjscientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale dbfutm-6 -7 w-avqia4cescribes 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 temperab -amwa7i -t4vq6-fucte), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fil .o(fkuqi ) o;x8:jung. 5–41). If his arms are capable of eooufkquln() i8xj :;.xerting 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 sw:5 lac.2i-xl2lka in urface will the acceleration of gravity be half what it is on the surfa iawll2c.-nk il:25axce?    $\times 10^6$

  On an ice rink, two skaters of equal m.ab hz5i,i(m iass 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 indm i,i(5 bhaiz.ividual 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 acceleration o:hy5a2hbyob5uwvk9+fr 0 cf s9, nm2f,kyuq 3f gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the mhk2,0q:fhb 3nu5 a,9bcf2 o5 s y9wy+krvumyfagnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trave g11ghy8+ p4pwgv7f duling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal andduw g+gg7hpvf41p1 y8 opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale inth, 5m 7m*tjml an elevator, it says your mass is 82 kg. What is the acceleration m*t75jh m,tmlof the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube :)cu2s0lf5w umll/r b7zbrn.that will rotate about its center (like a tubular bicycl0 nfl2:ws7 rlmur5. cl)bu z/be tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertic,f4 *af p2nxf)zwjgv -al loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accelere+it/vn)oi a7 ation due to gravity at its surface and the grtni a+ o/v)ie7avitational constant G.

A plumb bob (a mass m hanging on a string) is d7wokl)c 3v 8 ;nobzm7beflected from the vertical by an anglon7c k oblv)mw;b837z e $\theta$ 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 coefficient kc by92ml;rz9*m8l mrof static friction is 0.30 (wet pavement), at what range of speeds *r r9mb ylm;czm82l9kcan a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects c p-f2o8q,u(xh8kqq b ykh x-:at the equator weyk:qf (qc-xb8x h puh q-ko82,re apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apap nk4 2 9p0hnv97mhyixm;dk3wrt 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 q 88hy( ccfo4nf /s4ilrounds a curve of radius 235 m. A lamp suspended from the ceilingc(s8fn/oh4q 8f lciy 4 swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it d 4 fcf jg-g4ulpglg h; cp 6b4uf;/0.4jaxc0rhas 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 jplh46-d4 . bpg0j/ul;0;guc 4fxa4g cgffcr 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 anoufz2rj *f: 9hhgs))e-pq l c8 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 clouds orbitiff8 2 pgc *)jo u-qhhrs9ze)l:ng 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 2fa.inz1 ilwgd8ns,go+i18t * mlo; eit traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largesi1dlnls1 ;z +no2w8m.oitae*ig, f g8t? 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 System (GPS) utilizes a group of 24 sate0.pdsc t5 jeu5d8qk0s llites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellitesqt.0s5 kjded5p c8us 0 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), ad2knj7edz8z d20ze s 3fter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . z2dzzed7j2des0 k8n 3Eros 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 thf*e6 hri (bc2eldi d elv1:fbwl)43 t*e space shuttle pursuing a satellite in need of repair. You are in a cir1d* f 26(welltilve43hf)*debrcbi :cular orbit of the same radius 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 itsf yhd* +sao)i7 mean distance froyd *7f+hs) oiam 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 rp frk63qxy.+would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumr6f+ pqxr3 .ykptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46)bzxs ;zjbj0 *n+52t:jp nilo7i7qv(b()e sl a at a distance of about 30,000 lisn7 z2sa l q)lbn(xpjjz(b vo;j0:ii* 7et 5+bght-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 0.4ebkk.4s ja f550 m on each side. Find the magnitude and direction of the gravika4k5sb4f. ejtational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 c6p: poyp3 ;o44qvokrkg 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-cm-long sweryo7vxvb(. 9fep second hand on your wribvf.7r(9 oxyv st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight akjruawsq )3.r/c(bo qns22 *xround in a circle below you on a 0.25-m piece of fishing line. The weight mabans2sqwo /r3qj c 2()k rxu*.kes 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 highway0xutj f7no2hw c9xh1, is designed so that a car traveling at speed9hw u2 f1,0hn txjx7co $ 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:xr .qlxeqswlvqy4q c9y*p.52lu2*t Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a4sq .rx9.qq5q :yv*l xull ptc*wy2 2e 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.$\approx$    $\times 10^2$