Sometimes people say that water is removed frol:il v1z+ko q6rw8w4ydnzg m(h5poke hq2 *-2m clothes in a spin dryer by centrifugal fo hlo4e5ol *kq6 zwri yvnkm+(w2phg1z-d8q:2rce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car 5 qb;f1ioh5xpbe 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 speed? Explain.i x5f5q1h bo;p

Suppose a car moves at constant speed along a hilly road. Where does the car tsa/* hv h a0da)0i0ynexert the greatest and least forces on the road: (a) at the top of a hill, (b) at a diy *00nat )/hd0 svahaip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child rml+fh: : k ),lcikl8g)g8d dhtiding a horse on a merry-go-round. Which of these forces provides the centripetal acce8ht+:d:ckm g,lfd)kl)g8ihl leration of the child?

A bucket of water can beafd t )2tnt7+ b0.cvss2lixr:+re cw6 whirled in a vertical circle without the water spilling out, even at the top o+t6l rvswdecctxfsa7.)+:ti n0 2 br2f the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your cvtz)r5koa g(r- cd0k v-)kx /far? There are at least three controls in the car w0av5rkz/trx-c k ) (dgo)k-v fhich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in 2pe6a p5va+e/xe:dpu o7qp2 tFig. ae t72ee/apu5q:pp p xd+62vo5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lo-qpjubqmj f9 45 slexz41c*4rr a.-k ean inward when rounding a curve at high speed?

Why do airplanes bank when theyg)nn b t,bkopm:pj.vf 1 3e2*z turn? How would you compute the banking angle given its e,npvfpz1* gb jm:b2 .3)toknspeed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane9u* (3mcoczetiu* m +a. 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 m mztiuou+9c(3eac* * let go of the string?

Does an apple exert a gravitational force on the 3cjnn4i.,up4l l2ybl Earth? If so, how large a force? Consider an applnn32ylul,.cp bl4 4jie
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s of qg7-cu9 3ltwrbit be differenc l7gtu3-wq 9ft?

Which pulls harder gravitationally, tv9ar - uw)upu: 7)javs2um 3ukhe Earth on the Moon, or the Moon on the Earth? Which accelerates more:uv2u)wpva r mj7ka u3-) 9suu?

The Sun's gravitational pull on the Earth is much larger than the Moohk7bnj6 6*p;ajh fcm/c::y hs n's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationa6b cn:mahc;k/j :*f7h y6psh jl pull from one side of the Earth to the other.]

Will an object weigh more atb lp 2jwd6zxm0fu,1v ; the equator or at the poles? What two effects are at work? Do they oppose each 02 lbfz6mwxu1d v,jp; other?

The gravitational force on the Moos c7(,* 5j9jsfrbplpwn due to the Earth is only about half the force on the Moon due to the Sun. Why is5j* bfs(pl,cp j 7rw9sn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or sm ldo 18cgcep49aller than the centripetal accele1 8eg4c9opc ldration of the Earth?

Would it require less speed to launch a satellite (a) toward the eas kvowc/z2m*5 65vxfpf t or (b) toward the west? Consider the Earvw of52mc/56fz* v kpxth’s rotation direction.

When will your apparent weight be the greatest, as measured by e47lj kz7uyk3a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight b 7ky4u3kj 7zlee 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 beu,iee7d.i a4 j lrrt(e47twz 12d l*la 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 sii ee,2 4 zlur4l*7j(.7 wedirtlt1 adamulates 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 weightlessness” betweex-c wdu *7(uki9 (poolc(lrb7n stekid(7r(lw ocb- oxl97cpuu* (ps.

The Earth moves faster in its orbit around the Sun in January than in July. w76f4ftw5h , t st+*asjpm(xi, s9 p9fsg q-haIs the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s9 (wf,sqgxfwi s67 tspthmh -*ft54pj a,as9+ axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hateq1)1l t3e9- foenqe tywuc:; )6utsve a moon. Explain how this discovery enabled -y)wte)euu eteqfl ;3t 6c11qt9 s:n oan estimate of Pluto’s mass.

  The Sun's gravitational pull on the pohb:a),lkmra-ax13 9 5m uaz 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.]A child la5xm1)oarau3 mk- azb ph :9,sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1 ee4 3u;hrig8w980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ouu0idc96ny f uw;8awd3. z+ duf the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radiw6+iy 0;u ad3duc9 .fdw n8uzuus 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 avp(v02owmhnnhk3g4 7f8 sr8 w s it rotates uniformly in a horizontal circle wpw 7s ko2vhg(mh4n8 0n83vfr(at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's +mbr3vsx*dk56m , lmxsurface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitatikl,xmmbvd m3*s5 x+r6 onal acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a sp cje jismu3prx-16i z q:q:h:k -+e/zzeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32i1e jzqrcihk+jz q:6x s -u: :pe3m/-z cm?   

  A ball on the end of a string is revolved at a unizz (0ev 35cwqo.abcs9form rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sp5cq3wa 0 vzec( sz.9boeed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius 7mv gjun:jtgm7* *gjhss) - 8z97 m on a flat road if the coefficient of static friction between tires andj- 8: mms79jn* zv*ggut)jhsg road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficien lg(ame4-s .u e80gazdvo73qrt of static friction be between the tires and the road if a car is to round a level curve of radius- .lg am8 s( rdge0ov7z3eua4q 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designpuife-vjmblrt9s2k4 6 ya+ 42ed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trai4vbpe9f ut2 6y is2l-+rk4mja nee 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 rotatingkk25 u4x3 ,pzgggn92 fjcn,ef 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 af5z enkxjc43,n 9p22gg gk f,und the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down bqkrsez3 gj.2(k3/- 3h hpxqfnixz-3at the top of a circle 33i-kfz2jepq-rk (h 3z.3xqb/gnxs h
(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 (includimd1zi c59m0c gng the driver) crosses the rounded top of a hill (radius =9m09 m gidc51zc5$ \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 to1yd nb 5-5djda make for the passengers to feel “weightless” at the topmost poiban dj-551ddynt?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ra-oc7x4*, ycmmr42 onjwwj7:car xo 4 rdius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buc,xr mw4r77ooac jjyw2x om*4-c4n: rcket 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 cenb ljiowp,)m78sj2 zb ;trifuge rotate if a particle 9.00 cm from the axis of rotation is to experijjz o78bi l)w2bmps ,;ence an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival,ys;,t -z/4c2v flgobj people are rotated in a cylindrically walled "room." (See Fig. 5-35 - 4by t;c,/jlgfzvs2o.)
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-hluiuh nzn++b h x-0;.lockey tabletop, an u u++zlnbin- hl0h.;xd is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
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 jb39ry0g1m aqball which revolves on a string qrm903 gb1jya0.600 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 caryj7m 5,yxd+w(nm 8valwfvg 15 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 k9*s5 d wgy0pc$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver bc9dgm(mm fv68*5pkj s y 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 tangentia. h.pp: *e-dqs kdqa(fl and centripetal components of the net force exerted on the car.:eash(*.pkq -d qf pd (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 acfwm/cv. wy4 ;s.0ycgbcelerates 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 thrs 4 yw. y.bgcv/cfw;m0ough the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle)1./*zwong1mff xqv e of radius 2.90 m . At a particular instant, its acceleration is 1.0 xewqf/ov).1 *zfn 1mg5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 gravityi0pz 3am 47e8(0xck wwjzg0fa9 mg:nl on a spacecraft 12,800 km (2 Earth radii) above the E gmiw:jam0xgzl( pf74w e0 08kc39znaarth’s surface if its mass is 1350 kg.   

  At the surface of a certain pnb:b9c9 t3gnu lanet, the gravitational acceleration g has a magnituducb9g :t9nbn 3e 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':wguu+*aqk gokxm5/4 s radius is 1.7gxq*u4 gkou+:/m5w k a4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has q )z1wo w1*u tm-mf)fe fsm/*bthe same mass. What is the acceleration due to gravity neo1umq)fm )*/f mt1fsww-*ebz ar its surface?   

  A hypothetical planet has a mass 1.66 time0+.f hoy n dn(m;7+fcegui6pj s that of Earth, but the same radius. What + f0i 6 gcfd.;y+(n7 hnjmoepuis g near its surface?   

  Two objects attract each ot*-c 8-jbdjbxther gravitationally 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 vall8y 6 itj0j/i*:0w c mrm:dc7bvv(olzue of g , the acceleration of gravity, at (a) 3200 m6 wm0jcivldc7 t 0yrvjli:/ :ob( m*z8    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E-6foy4giys 0b1x(; tx gfzd2 pech3*larth’s center to a point outside the Earth where thegravitational acceleration due t xzyx py*tb4; c 2ioghgl-d(fe6f1s 03o 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 bxal;my fp75ei 15 a5iinto a sphere about 10 km in radius. Estimatbf1iaix 7m y5;p5la e5e the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncekcg1v e-;vdeqzd2s5h jo /*-j was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravizg 2d*o5c1 --;ekvsjdj/qe vh ty on this star?    $\times 10^7$

  You are explaining why astronauts fee+hg 7 oseen-j.wrffx:52j uv7l weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yow g+v27 euox- ref5fs.nj7jh:urself 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 square fzizw0+ uu6r9 8kbg3bis0t/7:h n-s9ja ysoc of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by th387i:n sr6c0s/f9zuiz0au- jowhk+bg 9 stybe other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on t2q nun/gvno x5z+ n2hh;l+.tw he same side of the Sun. Calculate the total force on the Earth due t5 hvhng+nxnnlu; /wz.t22 +qo o 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 gravityjb3 z.j8.qpzk at the surface of Mars is 0.38 of what it is on k3p j8bzjq. .zEarth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known vac :e3qopxzg.4 lue for the period of the Earth and its distance from the Sun. [Note: Comparec:zo. x43eqp g your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a sta4rbi0 1 6xk can7h okc(/puzr -zc* xnc/q3ui8ble circular orbit about the Earth at a height of 3608pah/zz-0oi3 n crx1icccn(uxkq7 * u/6 4krb0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circ/) fst3uj m2rfular orbit 650 km above the Earth. How fast must the shuttle sf/3)2t rjmfu be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan6hinvazu + s/)n i3n:gts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revu 3ng i/nn)ish: v+az6olution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the*vx l( l1f,d4ba-vinw 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 co *vdxal4,l v w1f(-binmpared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity;h /c1)po;vwo0 v gnkz would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth ;wvpvcg0z/1o o) hn;k?   

  During an Apollo lunar landing mission, the com0xoi770bqfpx2fr00ej tq l/h8 1 jmasmand module continued to orbit the Moon at/020oe j qp01l q m8ah0stjx7i fxrfb7 an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pli:*:chmx aa)w,/jkr8sx-yb 7 u gyp-c anet. The inner radius of the rings is 7)abx7-,sc:x* upgikw- ymac :yh8 /rj 3,000 $\mathrm{~km}$ , 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 ;h p fhnly-nmv8n4 nkl6w :gr0c62)gj every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the ; m 0vc8gpn-gfrlhkjn6n4h w6 y:nl2)bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of,t40e chanvj(imk 18a7e;sc6:e fb6q lu) knv the Earth's Moe66ekncclb)4htn fei j( 7q;u18s a:mv0v,kaon in a space vehicle (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 equa(batmnxp b0. nie: ;x h0sy92el mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway bxs x0h 0y.9:ea;emn it bpn2b(etween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wom8 iq.m1efl,3at-ba:m*8a fro r5abfr an in an elevator thaael omr3.i*fmq ra:,85ab f t ba8rf1-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 suspended from the ceiling of an elev 6lcr) 0+t)a i)kkhltqator. The cord can withstand a tension of 220 N and 6)ithkl)kla t0)q+cr breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period 5t t+rg*hc1ogv1-b r)+cqm ssT , the density (mass/volu+s*vg -sh)qmccr5t 1 1g o+rtbme) 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.ug 3f2 lpn7qp)t7mx;r4 d) to determine the period of an artificial )q2t ;m fu73pxn gl7rpsatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though5g812(ef- mwvs-gq p md o(ctv only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distac5gfv-m1q g 8 mvtowes((d2p -nce from the Sun?    $\times 10^{11}$

  Neptune is an average(oydi: j7olz sm9 z2*c 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 Sun roughly once every 76 yeari f6yd etm-u47s. 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’s third law is half the sum of the nearest and farthest distance fr 7efd umty64-iom the Sun.]    $\times 10^6$

  Our Sun rotates about the zt9o.-+zc fei 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 the four largestx c(nho0e: w6jgn+ i k )pw.-tfdj*jq1 moons of Jupiter (those discovered bgd1jq*wop w jf h njnek)6x(:ti.+0c- y Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance ofublt.3u n3u3ebv v y24 the Moon. vbb3v3.2ylet uu3 n4u    $\times 10^{24}$

  Determine the mean distance from Jupiter for each yjo yluth0u-ihy6li3h2a3-y o 9.x 9o of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3 l6hi93ou.x3l9j20 o yy- htauhoyyi-. Compare to 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 fxc;cur, 1k2 jJupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed)jkr f,c12cx; u.
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form qu2t9ud*(vc jc0 yq;yof 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 qqdt( 9 c0;c*2yujyu vband 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 (l(wp nv -lft;hya2. 5qprfb+in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of hi- l 2lfqfnb( 5.hp;(av+pwtrys swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acc0-e n dw t4bg1kaz jnb3+iqcv z5 ,cq0;)6ggoleleration of gravity be half what it is on the s n60gg5qct zb+vj1)cn;ed o0, awq4kl-zgi3 burface?    $\times 10^6$

  On an ice rink, two skaters of equ-pqjvc3qj n/.al 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 m/qp-q.c jvnj 3asses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent al7r7u 5vmh)) el ar9cwcceleration of gravity at the equator is slightly u )5erwlmc 7rvl7)ha 9less 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 traveling directly fr.3e-bwadl /.zme xq0nom the Earth to xl/dqw-zam n 3 .e0b.ethe Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathro +tzn;1 wf hl9s lnynburw/7f+:ua34yom scale in an elevator, it says your mass is 82 kg. What is the acceleratinw:9s3tl/un 4ra hfy byw+1znf7u ;l +on of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station cosh 2wbr - m0hg hh*6)5bsls:ejnsists of a circular tube that 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. What must be the rotation speed (revolutions per 2g-jsw0mbsh )b5h6h:s l*r h eday) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. pfq5-wirz a74 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 47d 3qj djo9f82ldrby radius r, the acceleration due to gravity at its su2j7drlo4 93d yqf8bjd rface and the gravitational constant G.

A plumb bob (a mass m hanging ydkq2uk).:a1b wc; 6cllt1 a eon a string) is deflected from the vertical by an angl11abk c ;cy.uladwltq2:)6e ke $\theta$ 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 coefficient6wtgdy 8op4zpm i4 h,5 of staticzi gmoy 86t,p4pw5h d4 friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that ob w +b:)j;0kasjs0yiopjects at the equator were apparently sw 0jok +i;y)jps: b0aweightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8 ;7 yu,4si20vixnqajp .0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lampaqvb.y1usue ;:xa / .g suspended from the ceiling swings out tous.ya aq.;vbeu 1 /g:x 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. Td(eo742xej4lu mjtz86hn o,o hus, 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 person would experience at the equator of such a planet. Use z(24 8jhometdxe,luno6 o74j 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 Te7czfo pa6c3 y+br4yt). vks3nlescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this va p 33krcny)t4cz7o+by. fs 6by 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 co4b, 8 +ilkbxstnstant speed 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 +x4l b isb,t8kfast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizespfwdze,n z4/: ;,l xkc 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. T4lzx fd;,:c wenkp /,zhe 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 (h2dzt/y1 m tw76g9qdxNEAR), after traveling 2.1 billion km, is meant to orbit tht7t/h 2 z g1yxdm69qwde asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle jx9tmed -i c y-fz4 f/)drrd*8pursuing a satellite in need of repair. You are in a circular orbit of the same radius fd)dr* 84mdxc -ifze9-jtr/ yas the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distu-7j lj:c:6mqy* bs7fln5crnance from the :rlnuyjbmlq 6cs-7f 7:c * n5jSun?   
(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 siyk sg/0sm+/w+4wta7pmqj .*jhm o4 need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, likp0 +jaj4o+*.m/i gwq/ss sktymhw m74e F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) , *; qqrzwdkq-at a distance of about 30,0*,dq zrk;q-qw00 light-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 0.50 m on each sida-:3qd (uxgdu3 lz(wkpc4 l:e2 whc1ce. Find the ml dwu3c3:l-cd(qwa:cuk ph( 1z 2gex4agnitude and direction of the gravitational 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 orbits lad njek: g15swwr4v+3.y8rl 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-c wu-b0dilb53qm-long sweep second hand on youdbqi5b w03-l ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swingwsu; 8wh2i5;8p 5 ysv k2ndlia a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circlwnk8u 58sda2l2; wpihi5ys v;e 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 hig)a e203gwt f i7gtym 2)fsb78g urek2mhway is designed so that a car travelingw)fggt t3y7mk8)a2gmr 0s2e bfi2 7e u at 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, uj9 xn* mjkk3p7r wyc7z+c9+u: blbm, 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+cm9y7nwl+:3zkbku, 9*7p rubj j cxm the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$