Sometimes people say that water is re5(4 b95vkbs jkrh i:kfmoved from clothes in a spin dryer by centrivhrsk b 45if: jb(95kkfugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car buligj*:azu* n57uh2b cyh . g9e the same when the car travels around a sharp curve at a constant 60 km/h as when it travels hulinua5.u**h 2cy:g 9b7gzj around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whpjq2 e0684xzce etsp+ere does the car exert the greatest and least forces on the road: (a) at the top of a hill, p6e z+e0j2s4qtpec 8 x(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 riding a horse on a merry-gpr 2b-kbm,8fk o-round. Which of these forces provides the centrip28k fkmb,-pr betal acceleration of the child?

A bucket of water can bx(fo(o/2u 6z:okzs lge whirled in a vertical circle without the water spilling out, even at the top of the circleok/s((oofuxl2 :g 6z z when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Th2 yx8+lbuh8bmxxx+axx5 :kulcb5+4fte. v h4ere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prf5 b xy8hx2+4ual x. ubv5kxxhcmb84+ xel+:toduce?

A child on a sled comes flying ovtfdi cmo:n u2lo4wrxws 3rx+-: 2d4 h+er the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the uricdxhdn tl-+434 s2 ::xw+wrom2o fground (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 when rounding a curve at high spekok)qff1tfi 0ii( o15ed?

Why do airplanes bank when they turn? How would you compute the banpj,85rk 5afbb vs9q37il vy9 iking angle given its spkj ,yip 99355avsvi rfbb ql78eed and radius of the turn?

A girl is whirling a ball on a string around nj0cwasi,-malpy+ 5 b pq*u3 0her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a targeijb-up m0, y0a*p+n3a cq slw5t on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Ea aalku/ mqpooq1u ,:)(,kvnp0 4 3mtftrth? If so, how large a force? Consid,akp a/t(q :qu4f 1ulo0 p3mt,mno)vker an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wxyt(u zs w14 jqgs25+eould the Moon’s orbit bex1 2 4ge5wt(yzus+jqs different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on t: 8v 6zslws9irhe Earth? Which acce 8izwv sl:sr69lerates more?

The Sun's gravitational 5: nn ea0g/lkgb.7bmypull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]mb lgk0a7 :egnb/n5y.

Will an object weigh more at the equator or at the pol69 dcdzkd4b0 ies? What two effects are at work? Do they oppose eac9c z6d 4kdbid0h other?

The gravitational force on the Moon due c f;au6qgsvzc7ns0:wgw2 6m6f+qh-i to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earthfu aifwg76 v+6 scn-cszq 6mhqg;w 0:2?

Is the centripetal acceleration of Mars in is7l pz cry.*d5r+qb5its orbit around the Sun larger or smaller than the centripetal acceleration o5r* b lrsq +.5pdyizc7f the Earth?

Would it require less *ukwd0j1 9bko y) yns5speed to launch a satellite (a) toward the east or (b) toward the west? Consi5 *bw9kkjo 0ny)uy1d sder the Earth’s rotation direction.

When will your apparent weight be l/a vytre4 4pyda/9 6dthe 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 9vy4 t/p lary/ae6 dd4would 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 space could be advers403 mmoluqd inx5oe 1 ;5km*-do; noxfely 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). Exi3 xmonm 45oe0ddxkuf* onmo 5;l1- ;qplain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightl*c80np ez+kk 5ncd1 dk;ws6/hut f ,lzessness” between stepsdhfs68 nktlz*knk;c,zup+ 1ce5 wd 0/.

The Earth moves faster in its orbit around the Sun ovkpd / (iainlp919,m in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor ilop/ 99vnip, mi a1(dkn producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known unt +yfg +nr*7npn3ln;f lil it was discovered to have a moon. Explain how this discovery enabled an estimat+*7f3ngpnrn ly+l;nf e of Pluto’s mass.

  The Sun's gravitational pull on the Earth is m k5nmwbck8/i- p n8l )*-ypqqiuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diffem kc8qp )n-bl np/-wikyq*8 5irence 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 travelin9 h4sq2 ;mcstj4nzbb1 g 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 acce ,zo0r7ah.dksnu3 jx,leration of the Earth in its orbit around the Sun, and the net force exerted onsjh d,7zon.r0k3x,au 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: za 0nwq2sri z4;60wi t/ rhedis0u(m is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of rri zs/tei60usr2iz;04d0w (hmqan w : adius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cirvkk-6i wm f:p 9)bmsj1cles 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 , thek p1ks -mj v96bw):imf gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the 7: 5-jgdj ha gio8nt6cr xfb,6edge of a potter’s wheel turning at 45 rpm (revolutions per minute) n-:58j6 7j6 grcgxh dbof,iatif the wheel’s diameter is 32 cm?   

  A ball on the end of a string is reih 5x:kuf3ad/tc;mq5 volved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33dx /3c:auqtk5h m; 5if. 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 speedms7c5 alj0p0l with which a 1050-kg car can round a turn of radius 77 m on a flatl0calp 7m50js road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of statvk,*5dzd7h dk-tvvnfm*c2 la4+t c, tic friction be between the tires and the road if a car is to hta2ckdt,m cdl fdk t*5 4zv+*nv-,v7 round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotacnn+ic sd,e m9 l28qegi5izkp-kb2,445 shwjte a trainee in a horizontal circle of radius 12.0 m . If the dzwch-5 4ek g89 pcmik4jsi sqien2n,b5l+, 2 force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable spne/hw4wd52sypefv 91 eed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntabwp2 s9 4e/n whfd5ey1vle until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed musthy)mkg-ax 0ae 2 ex-a5 a roller coaster be traveling when upside down at the top of a circay-x0h xee)a a-k2gm5 le
(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) crossjb9ay j 214wskes the rounded top of a hjkjy 2w9abs41 ill (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-pyc 1v7 k/y;pi9 *t xonq.7:5l wycxrzm-diameter Ferris wheel need to make for the passengers to feel “weightley :yqi 5.w cpvlyo71c/k;p7rz9x*tnxss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circc k/wum-j m2k dxyr480le of radius 1.10 m. At the lowest point of its motion the tensionjc/u yw-rx m20k8kmd4 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 if a particle 9.00 cm froma ) c5ki/.+xyl9 n1t9mqp*ny 7ojfsb z the axis of rotation is to experience f1nz9atys957bp+ oq*lxky./cmn )ji an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricallypw: n,e:/uw)i/ d*mwvta p)v n walled "room." (See ta )puv),/eni:w :nm* dw/wpvFig. 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 tabl. uw;buep ;j4yetop, and is held in this orbit by a light cord connected to a dangling blockw.be 4yu; ;pju (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 weight of the balll a. xuc+daxs;2 v;owri* tv3- which revolve; ;i+vtxvxu* .l2 cawars3d-os on a string 0.600 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 )(rfi4sh.2 wzhs mia/for 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 masses rxti z5fh7fed4*)ffhn2g94jh6qp7e ;mo /v g $ 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 maneuvef0jr6e 7kr0z*eg9lz cv cn+ /or 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 o*pnsy n3-r qm7gkv 47zf the net force exerted on the34 q7pz-r7vkm *nynsg car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from thegikglfb(dc*,3 r2aq6s z n 2y,w 27gwu 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 accelerati 6*agig 3dfw bk lzgu(,2 qsw7yc,n2r2on with no slipping or skidding? $\approx$   

  A particle revolves in a horizs+tbe92m5dq*aa04i ok a+ xddontal circle of radius 2.90 m . At a particular instant, its ka0d2+oad5 +sa49eiqb td *xmacceleration 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 gravix ice n mk8/9 r8sq 7nj*r3amwba,,ak8ty on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mmnrxkkn,i,rs3e7mw 8c 9q8a*b /8a aj ass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelere/i2jn8vvuk; 81w so kg: koo-ation g has a magnitude :k ve;oj8 uow/ 2in81o-vkgskof 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 1.7whw*3 j,xgw hoq7/*nz4 73nhwwxz w, joq g**h/$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical plane-,iboc fu:s;jc8pl xxjr5u40t has a radius 1.5 times that of Earth, but has the same mass. Whuf0 4jlu -pcc:x8o ij,bxs5r; at is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sa 5ph: r;fo5upr5ig qm-jta v+ jk33/awme radius. What is g nearia kw3upmp:5a55/-jjovq 3fhr +g;rt its surface?   

  Two objects attract each other gray* so.elc46n1f qgsf)vitationally 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, a n+ktxt95qu5e b2k vb8t (a) 3200 m e8 9v52quxttb knkb+5   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s at a8.k6 tub ;k(,c w+ fy+h7tmsy8aeukb(4jpcenter to a point outside the Earth where thegravitational acceleration due to the Earthjf k y,ub+aek8uatyhsa7t4(;8w( 6t b.p +ckm is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hej;ve1 r0vl 6xz 7yey)as five times the mass of our Sun packed into a sphere aboutvz7)0y j6 ve1yreelx; 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sha 3szhue*gz g6b, ujs u91.,gtar like our Sun but is now in the last stage of its evolut se bah3s 9g 6h1guzuzj*,,.ugion, is the 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 in the space mtqr)e y(moiy70 ctjt m/6 ,(mshuttle. 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 of gravity 250 km above the Earth’s sur,q yyec t) t0(ijmmr(tm67o/mface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squa(9)tvnv-kzwnk 9,ugh4ruo3y re of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thr,ng (nkk)ovh-9 9 u wzy4t3urvee.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets linctzm;x(d.5 9fl tu q;ze up on the same side of the Sun. Calculate the total force on the Earth d;.tzc5 qf l9( xtumz;due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravi9(k -y bjd.xymtw( gr,ty at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, 9wbrx (. yj,dtk-gym( determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the pe9 7r nl+xy n2g)ijel2triod of the Earth and its distance from the Sun. [Note: Compare your answer to that obxnn2yg9ei)trl l7j2+ tained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cizb)vq(jf ulxhj o:39 1rcular orbit about the Earth at a height of 36:3q) bj1lv( uj9zhxof00 km.    $\times 10^3$

  The space shuttle releases ar +cfo:v.ia 2vujno.: satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be movin:f v.:n uvo. 2+acojrig (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occuwj5t qccm+ le;l g 3yu;z9b kmx-pr440pants are to experience simulated gravity of 0.;lwp- k guc+rjt;x4c l5ez94bm3 0y qm60 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 ou,ad*,6z 2g ld rfm,qzrbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbu2*6qm,ldaf gz dr,z,it 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 satellite?    s ~    min

  At what horizontal velocity would a satellite have to be laun,al27yg*uy 3vud)z hbched from the top of Mt. Everest tlbvz,ugh* 3a7y y)d u2o be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit2;- hkj * :dnjhicy7 e fnxekie)t)k1( the Moon at an altitude of about 100 km. How long ddkty j xkhje(iin 7:c21 )e-ef;n*h)kid it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the paml7az(7lqoal x6e29 lanet. The inner x6malea9z7al(l o72q radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. -.usniiwtgi 4- 7a:7lkx )*hl,gcn m c5–9). Whati*kai gc7tgxcln)n,7 --u :wmli. sh 4 is the 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 astronaut 4200 km from the center of th vnx ,dikb d bi*x,59p(7ystz z6i/:eme Earth's Moon in a space vehicle/7kbsn(tivi96ey* x zz:,id x 5,pmd b (a) moving 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 consists of two sgu2 kd+l 01nhcug6w: wtars of equal mass. They are obsg kh 0c+u:26lww u1gnderved to be separated 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 oh3h4f 2 w-l);msj aavsuac n/:f a 55-kg woman in an elevator thasmaav2-jacn :lsf h43/h)w u;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 susp 0 3b xvwxaxi(h+oe72qended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction) 2x v3oex0qhb 7+xiwa(? a =   

Show that if a satellite orbigfnc 3 2fg8o /u,x1atbts very near the surface of a planet with period T , the density (mass/volume) of the planet is f ft1c/bgn8a3 2ougx,$\rho=m / V=3 \pi / G T^{2}$ .
(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 themi+ *sni5wy gj.nj *z: Moon (27.4 d) to determine the period of an n.s5nw iz ji*+*g:m yjartificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acroyc d+xeb,ime;+3a/gi t*e h*8 uwxad (ss, orbits the Sun like the planets. Its period is 410 d. What is + d a ea3ig,ticm*dy*x x(hub+w ;8ee/its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancx9: bpy7rqja )e 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 p-ly1z3l r-f 4k nx6dgsoy* 2conce every 76 years. It comes very close to the surface of the Sun on its closest appk r-1cf23zn s64 dyyp gllx-o*roach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

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

  Table 5–3 gives the mass, period, and mean distance for thh4b1n-grhw/, ; elj mse four largest moons of Jupiter (those sbr,l;1- nemw4g/ hjhdiscovered 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 q;6*vf2xs* pz*)wbk qs tgj ,vknown period and distance of the Moon. gk*vjq),qp sz;*s *fxtwb26v   $\times 10^{24}$

  Determine the mean distance frog(aj1s n4( oram 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 t(a(nos 1agrj4 o the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whicb fh;fo-g*e:80 c ylgwh some space scientists think came from a planet that once orbcl8;y b wefgogf0*h:-ited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the fo9f :eyy+tg /6c3thwgk rm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always no:ttc3 k6fyy+g e/9gwhon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arcd l:j7z ljf q6mc6-sr2 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 tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is2lq :rj lcz66js7dmf- 5.5 m long.   

  How far above the Earth’s surface will:fcr bjsc(2 l5rr a.c/ the acceleration of gravity be half what it :c.j5b2fr(c ca / lrsris on the surface?    $\times 10^6$

  On an ice rink, two skaters of x 67pun yq/i-wequal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pullinn q6u7/w-pyx ig on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparentzromr, h9ty(8v y*o7r acceleration of gravity at the equ(t ,y7 ozrry9 rhvm*8oator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a sp2fy 1m ihg7r6uacecraft traveling directly from the Earth to the Moon experience zero net force because thmyfhgr2 6u17 ie Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wheuy6 if o+wnf-re i2,x-n you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accel-y6 -i rofw+, uif2xeneration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consist(uhidz ykr7h ms/:6 4fs of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–44i 6hd7 h/k:fsz(yurm2). 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 aircrafte v lx2ji4d9wn xw)u*;9a9ds q 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 pxp(z2 *7n7 f(lskfhzp8rr y y5x1p;aa lanet in terms of its radius r, the acceleratiz1(zkxy7rp 8hp7r5 y laf( ns;pa*x2f on due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) .;mn8bk9w kxb is deflected from the vertical by an n;b8kxwkb9m . 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 *8w9mn z3ugcj a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds 9m8wg3ju *zcn can a car safely handle the curve?

  How long would a day be 1;: ,b*doo5n ncxog xlif the Earth were rotating so fast that objects at the equator were apparently weightcxngbx;lo5do*,1 :o nless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of- b7znkx549u tjluw3 r 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. A3 pphtyur/ o*1 lamp suspended from the ceiling swit3r* uh yp/o1pngs 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 td h6a2 *kljis,h3uu6 )l7nua 0hns(vj he Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a 7v2ljj(shu6, *nu6anal)usdhi kh3 0 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 eky44qui2 t 8xk q. gu)vif0/su/oo4fmxtremely massive core in the distant galaxy M87, so dense tk/u)42g/ 8 xkiys m4 qfvo4tqf0uui.ohat 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 k2rou/7kzl 6z 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? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the kzuzo2l76kr /road at A?

  The Navstar Global Positioning System (GPS)a*hc;x .g e /i 5ba.pyxd*5fee utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, wit5pca.*x5ea;xedg ie /hbf.y *h four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, iu 3a5.. n5i 2ctmzzhnns meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughlyun2 n5in ..ach5 3mtzz 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 satellite in need of repaiw) dxqd4jr hnecwk 9.6;fga**e bt.n;r. You are in a circular orbixea)r;nhfd*kb.w tc4 9wd* nj6 g;qe.t 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) Wha pew3lqae+9bk,w x/u86jb9u rt is its mean distance from axle3bbkeu +jr9/8wu6w 9,qp 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 would neetmqef4co0hz ,-q7p(lb/c4)*w ch fi q d to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make,t-c0q()*hqe/ h zqw4i7c f fblm4ocp reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dista::(tbwt7ai 1uhu0 n dknce of about 30,000 lightbi dn0tu1k7 wta:(h: u-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 locatedqxvc kj0 tfk(:cy4p39oe 1 n3 uetyt(2 at the 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 mvqye(x0j3 koy :( uecn1k2t94t f3pctass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg m2.q0towd 8qn sm 4poo/4cxi 9m1sft g;9,xbborbits 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 bi(d)l; yoz :*)) fjwk ruit dyx3yfyg../l ,qwy the tip of the 1.5-cm-long sweep second hand on yo iy.* id3 ,wlgyl))uyjyd:tf q/.k(r wf)oxz;ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start tomnhc,o nnmv9ulzl516c0fw3( swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the z5,u6cm3w(lnv 9 nn10flcmo hvertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desig 3pc3ctbs+6ho ned so that a car traveling at speedb3s h co6c3+pt $ 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 crl;/zx9vnbup9zy8,e ars 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 againz/8 vnbe,yxuprl; 9z9st 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.$\approx$    $\times 10^2$