Sometimes people say that water is removed from clothes in ay8lwf 5woqf 0hd0un cn8+x +d2 spin dryer by centrifugal force throwing the water outward. What is wrong with this stat h8 ff+on wunddx28+0 lw50ycqement?

Will the acceleration of a c/3qc/ ,qwq hzlar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same,qqz/ ch3ql /w speed? Explain.

Suppose a car moves at constant speed i5by-efj b)gngv.o f;+06ddq along a hilly road. Where does the car exert the greatest and least forces on the road;y.+q )bgfofd-0gn b idve6j5: (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 riding a hoa2xu(+ m07yszxwoq7 ;lfj l4e rse on a merry-go-round. Which of theswf0oz7+ 4ualj xxe(q7 ym2l;se forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle fn-k g6vi6a9 wwithout the water spilling out, even at the top of tfwi66a-v g9nk he circle when the bucket is upside down. Explain.

How many “accelerato qemp9:l )5a 1/sgiyeyrs” do you have in your car? There 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 prod)eayisqg /59ml pe 1y:uce?

A child on a sled comes flying over the crest of a small hill, as showni: olvgv3 dq-;m9j8 pw in Fig. 5–319 wqvo j mlv8g;-p3di:. 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 second law.

Why do bicycle riders lean inward when rounding a curve at high speed?7h4( i l(hb 3tvmfal+f

Why do airplanes bank when iv:1gm. 8 r icq+csdplb33 eu6they turn? How would you compute the banking angle given smv 3+bu1c83rlc 6.eqidi p:gits speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plp*c6kwc um :e:ane. She wants to let go at precisely the right time so that the ball will hit a target on6 : wku:mpec*c the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If soxq2qj+ zeb6k;.qjmu2is -lpo.1di) n , how large a force? Consider an ao ).2z kp-xeiqqu+q sj2.n6i;mjl b1d pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways ip0zh 88mtn)bwould the Moon’s orbit be di88tnpbhz 0 )mifferent?

Which pulls harder gravitationally, the Earth on the Moon, wc xyz:keh ;w6d 76ehw0j) f 7cdd47beor the Moon on the Eacyzewk6h6fx hed7b 4w w:;d7e d7j0) crth? Which accelerates more?

The Sun's gravitational pull on the Earth is much large5 fvo,,bds8 xh6c v-tir than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differencebx-vo,f8d is6,hvtc5 in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator d5wop:q l+ :a/5 ps)j erl8xnaor at the poles? What two effects are at work? Do they oppose sqe: 8lrax: jnpo d5la 5w+p/)each other?

The gravitational force on the Moon due to the Earth g c5u k y0s,+tobg((qbis only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the y0 g(u,5bscogq(kbt +Earth?

Is the centripetal acceleration of Mars in its or7 p7qn sqb3pkr cn-.u:)m/ .xilr0v tfbit around the Sun larger or small fru/v.xi-tsqr30knp7.pl ):n bmc7qer than the centripetal acceleration of the Earth?

Would it require less imt) .4yi:dek speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Ead) i.k4t iy:merth’s rotation direction.

When will your apparent weight be the greatest, ajh v x;xm:y* rcqe-r*6s measured by a scale in a moving elevator: when the elevator (a) accelr cv-j* xx6:e ry*;hqmerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant 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 *x:c96tq5 wo wg+oau yin outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) thoc5t+u:y*aqw w9 g6 xoe force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner expey2l dljws0s*69c(cxe wf,d r* riences “free fall” or “apparent weightlessness” between steps( sy6lwrd0*d*9, s e2fjccxwl .

The Earth moves faster in its orbit around the( efm y9xsmk/ 3a80lrq7 ot7rl Sun in January than in July. Is the l0 yor/397m ( ktqf8exmrsla 7Earth 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 not kex-h 3xqj h:(l40)v zdev94wuzwl2g qnown until it was discovered to have a moon. Explain how this discovery uvex 940e(lhlq: zv3qxz 4w 2wh)j-dg enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much l) 5c hswp/mpk(w5d)j targer than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Co p)ht)w p/jcwk5s5 dm(nsider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelingi *g)udxs3zp: rz ,jkg9vq9mok s3i38 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 +b:ghll1n+ .tsq/wqrEarth in its orbit around the Sun, and the net force exerted on the Earth. What exerts thisqq nbl/sr1+.h+w: tgl 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 uno84ms , m 7njd8j1f:alp4hrih iformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate theho 7p,msa :jm8j448 r1nhilfd speed of the discus.   

  Suppose the space shuttlu l1,1ho c:zwme 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 spacec1omu:1zh lw, 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 accpp 7b.sxh:i)gy4k v:feleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpfh4p s.: ):vxbpgik7 ym (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rateb wx6i k)hacka*u5d;htau45yk2i --y in a vertical circle of radius 72.0 cm , as shown -2h d 5ab4kwc-5;6)akytua*yikx uih in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed re1e6afoos m9lp*/-f4b tq g0with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient- g 9m aebolqpe6*4fo /01stfr 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 static frictio)p.mj :yjppv x-taw;)8- qorin be between the tires and the road if a car )p;i-)poay vj-r.tjx8 pw:qm is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pil,rn s)8puf1ix/m v7 ev wl..wuots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her v.8s ww7 ui e,rpn.um1x) v/lfback 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 hvozbz h-a9i 8+: xaq:*n vh9mov8*eu7n3hsx the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remaie ioavq7:9*vu* z+hhnb89h:oxzx a 3 8m nv-shns 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 and the turntable?   

  At what minimum speed must a roller coaster zhzjybrr7 q -c*55 y5c:yefrr jl5 /4rbe traveling when upside down at the top of a ciz 7frrybyy-cqc /* 4j lj :erhrzr5555rcle
(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 950fvh zh1:.znny b6u:7 a kg (including the driver) crosses the rounded top of a hill (nhv nuhaz1z7y:6.:f bradius =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 mwi3ac8u 6fxr2b/ 4pvry; x fw-inute would a 15-m-diameter Ferris wheel need to make for x-ry;3if/2xrfa vwb8w pc 46 uthe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kgc4tv:jphk 9cu;z */ uq is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope su; c:j/p4tc z9 uv*kquhpporting 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 frb.qs4 5asf8h, hjmblem7kg81 om the axis of rotation is to experience an acceleration of sb5.1 al488hh s kmg j,f7qemb115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopov/f6j kk/(k ku yl.zapjvv.5nzd9,.le are rotated in a cylindrically walled "room.z(/aopnlyuvj.v.jdk 6 v/fzkk,k 5.9 " (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 w7xk5ei+ 6m zya circle on a frictionless air-hockey tabletop, and is held in this orbitwzk56x + eym7i 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 ignoringtdmy8( i;eq jm5gq1r9 the weight of the ball whict;mj mi( 1e9qgyd5rq8 h revolves 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 for a car travqwik: te8z )3o7xuau47 hu1x qeling 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 masses0npz6a j4yr zi5ssa*i2y .uh; $ 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 ma1q)wvwhuwz54* s5 c sq v3q9zpneuver 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 centripexcoet2dkew(u u*am0f:4gh x n5;6zs7tal components of the net force exerted on the car uodse:7g ezh *wm0 (n;56xtk4xu a2fc (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 tf9q ue73y0a d2 yg3*vq5zgyyche 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 betwefgv* e0yc3a2gq 957zyqy u3dyen the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in ab sketgv k4a:s 9.r lk,zb,u*x8gw1(l horizontal circle of radius 2.90 m . At a particular instant, its acceleration i ,:4eaxbkg .*lsvwt g8b rk1z (lku,9ss 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 spacecraft 12,800 km (2 Earth radi 4jiog.7 xvii8i) above vo4ig8xi . i7jthe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain plane,bkl .prkgiy,14u;as)p hbzi bt8)7v t, the gravitational acceleration g has a magniay)b)h 18l,i7, kpsvr ut;gb4p b.ziktude 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. Ther20yqou,j+mze i).u x Moon's radius is 1.7jxmzo .)y,eu20 ruqi +4 $\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,t 9 lvsx,f8tj 9ly78fv but has the same mass. What isy7v tl9t89ff lsjx,v 8 the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sahn,t4sl .8, eeah8cq;r z y4 )ssn*4yx ktk/knme radius. What is gr , ).t ltsky*n48;shann eey4cks,xz k4h8q/ near its surface?   

  Two objects attract each other gravitationally with a forctb3u 8: h*aiu/ odp2f dxo-z;fe 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) 3200foa* 2nfa 1q * zukpg;22xh xknnkl7 g(-,9yok m21nnx9 hon*fx -l kkoukg*qkazf 2,y 2( 7ag;p    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance f1ok 32vujeav; rom the Earth’s center to a point outside the Earth where thegravitationajo2kev; 3u a1vl acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed i)kr*-l/b sn: utctx 1 ega(,zfnto a sphere about 10 km in radius. Estimate the surface gravity on this monstert(g -/cnzl:f*es,1bu ) rtxka .    $\times10^12$

  A typical white-dwarf star, which once was an avemv ql0mn4u6 )xrage star like our Sun but is now in the lasqm 4uvlx )60mnt stage of its evolution, 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 w421 3cp ykxv -)+3dfda vdvrfqhile orbiting in the space shuttle. Your friends respod1rf3pvdv3x a )+ fyvdqkc42-nd 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 surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squ5obaccn hznc9 a1y0 )/are of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted o09 zcb/1nnocha 5acy) n one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the platea 1 nf/4k fq8t+xjdk+/df*dnets line up on the same side of the Sun. Calculate the +xk n/*ddf f/ 1kt8qja e+fdt4total force on the Earth 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 gravity at mrung3)wr l:;v,- dis the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars. u;lrvnsd mir:-wg)3,    $\times 10^{23}$

  Determine the mass of the Sun using the k)gw/wph56v/zphf + vf h1e 8/vc1ygajzkt m/,nown value for the period of the Earth and its dista+/ m1tz6kpw 1p / fh5vwjch8,fvhga)z /e/ygvnce from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movd*ztr0w +q 12fhoiv:p+h) x3i s.dezoing in a stable circular orbit about the Earth at a height op d+wfsh)de.q i3xv :zo* t1zh r+o2i0f 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbdc86wj3 z zcpuk6n5-4jaj vzgqm- 2j*it 650 km above the Earth. How fast must the shuttle be moving (relatpa3mcuj nj-z6zqvgz64 kdc 5w2- * j8jive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupant)tan4h)cyl:wa4o :x, 6r zpqrs are to experience simulated:,oqry w4 )pca4x:)rn6z ah tl 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 cjjnd: 2w6 cnylt -b3-a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of thlc2ydc3j-btw j6n n:- e satellite?    s ~    min

  At what horizontal velocityk v:- zkr5pza6 would a satellite have to be launched from the top of Mt. Everest to be:pk65av - zzrk placed in a circular orbit around the Earth?   

  During an Apollo lun+g s,wcwt12c yar landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How lon2+ts1y ,ccw wgg did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet-el.vu b5fzn 8mm33nc. The inner radius of the rings is -zmn8vl. 3cu 5fen b3m 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 (solr).mar ,7y8 xutz(jee Fig. 5–9). What is the ratio of a po)(r 7t,m a8r.xzj ulyerson’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 k pfqb6mnn 2 hw( 7ryke01+4unfm from the center of the Earth's Moon in a space vey4b0+u7hwn 2m n( frk16fnqpehicle (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 stars of equ4k,d+nu)ndi, c wppmcl p +1i0al mass. They are observed to be separated by 360 m d++,k id,n cnlcppui)p0w m14illion 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-kg woman in an elevatoay(wrhb80 ,o9e 61jdr syg0oor that moves d9o 8aoh60owb e10srrgy( j ,y
(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 cen5mdt -b,/(bmorh3 dlw u 4tq.iling of an elevator. The cord can withstand a tension of 220 N an-dl 4tbq.bn 5u mmw3/dtrho(,d breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very nh* plga-6z9d y 7pwp812nkubwear the surface of a planet with period T , the de lb61 u-zp8 *npp9 ww27khaygdnsity (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 determicx7dwh.e bq 0u +a/1zrn0jze -ne the period of an artificial sate-j w0rndu/qecz0b+ azh1 7 .xellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred met4 0txeh)4mgh ders across, orbits the Sun like the planets. Its period is 410 d. What is its mean di40xdt) 4 gehmhstance from the Sun?    $\times 10^{11}$

  Neptune is an average distancg(* n w tr*vvh6c3qm8we 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 ekpl)/ l;i ej4tvery 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”l4pi)et/ kjl ; the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G 4oj5bwicze1ixp;dc*j*g- :c alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 oyiy8t*g,p -.: 6 oixwwe pi.afour largest moons of Jupiter (those discovered by Galileo in 160p.-o. gw 68xi i*t:peaoyiyw,9).
(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 periodqm(piurfa*s5lis ,(q.8f i 7tf 9mb-m and distance of the Moon. 7(ftfmi(sqa* bi,p u l m58.i s-frmq9   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupi ztq;ce0 7 plfes,* n:vgmn*0fter’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 pnl et;mf0, 7 n*cfe:0g* qzsvthe 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(kow13fi1/v +fylt zr consists of many fragments (which some yt3/+ ofkv(rf 11lizw space scientists 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 descnoufud3k j+k -py6)7 cribes 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 climay6jn cd7k+ -u3)uok pfte temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from b+d:ip w;)nzy 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 y wdbzn )+:p;iat 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 wvlw;e/ge8h2 xill the acceleration of gravity be half what it is on the suvx2e/l;8 ehgwrface?    $\times 10^6$

  On an ice rink, two skaters of equalzsbve, e5luphh28)* m 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 individuabe 5,h28pmhs*l) veuz l 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 of gra48;4nh 3fbb m np9j(xuiv x8rvvity at the equator is sfb4 vjirh(nm 8;8 n b9x3pu4vxlightly 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 spacecraft traveli6w ++gkwzb eq+o4o e:zng directly from the Earth to the Moon experiencz+ zwe: oo4bw qk6++ege zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scjx j1 zi r ye0nyi.st6fa5h11-ale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevai -e zxj.n1 ts 5ryyi1fjh60a1tor, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tha hzoe47fyx d 9u(jv;n,t will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. Wvxz ndho4y7fuj,; e9 (hat 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 ekcw,8x (hk;0expi5va 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 th9pi+ lm5 i*2q:8 7jdkrfueg eie mass of a planet in terms of its radius r, the acceleraqe m 8l9j*i:2p eg5i7uk+ rfdition due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vert3ep:g s gjmm 4pt q431vc2is9jical by an a:cs3vmpijs g24 tgm931q 4epj ngle $\theta$ 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 1 vejo dhr/h9;the coefficient of static friction is 0.30 (wet pavement), at wharhdoje h9/; 1vt range of speeds can a car safely handle the curve?

  How long would a dayyphf 1ce95w.nyt apbw78mm : 4 be if the Earth were rotating so fast that objects at the equator were a.wan5f 4w8eh71 :yc9y b mpmtppparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart l(blhs.05 atwem / at.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 roundpjfk- elbc4f,4 7 kd,ds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an anlf,dd 4 -4cfk,pkj7 begle 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 has been cl i;ee-,m2.v kkyxl;fb aimed that a person would be crushed by the force of gravity-;;k e2fvb ,xeky.iml on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person 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 extremelh s uzu;ixko2ea:: 3ak7jv62y1 +bswny massive core in the distant galaxy M87, so dense that it could be a black hole (from which no ligh wy v a3kza;os+xu12kue: 7nshj2 b:6it 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 spepw-q:r4ynk y wza)stgh 9w, xv f41*1qed as it 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 largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact wi k4w1-r pyqhtwz 4*fq:vgwysx)n,9a1 th the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satb.m7tyopx(v* *o t4xl ellites 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 centime tbt7oxx*lp(y .mo v*4ters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR)va:- ax2kl4bxk rht19, after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . -49t2 xkb1lavhax kr: 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 satellite in need o x4o dkv4pn (bfp2jglk( 7zz79f repair. You are in a o92xf4 pzbpj7((v7k4zlndgk circular 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 :,9vox( sj wuagl+ef7its mean distance from the+ s(gfae7xv:o j,ul w9 Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuah/j23e3jdcy 4 ep.uwblly "feel" yourself gravitationally /e y3.4h 3b j2cupdwjeattracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of +9u ul+kzpzi: the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 p+uzl +uiz9: klight-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 wm1v-vj 8g9eyof a square 0.50 m on each side. Find the magnitude and direction of the gravj1w8vv9 yg-em itational 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 kg orbfx 9vhlm (2ygp-i- ,iiits 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 o86o5 f9ywgdq b-gyyb yx,bj 61f the 1.5-cm-long sweep second y -bb5xgb6yyo1 w6fdg89 yqj,hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cirrmwh -rt2ne7myy:5 wi-x)4 kycle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.5m7-:yr i) w45thy xmrynw e2k-0 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 highway is desigvf (sec4eu2z 3ned so that a car traveling at sc3v4fz(e ue2 speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilize9vvqqkl9z4fgr q 8 ,2rs 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 passen9lq9q vr vgqrk8,z2 f4gers 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.$\approx$    $\times 10^2$