Sometimes people say that water is removed from clothes in a s2yj u+6 4n(dp tvq u:ddjzg6a-pin dryer by centrifugal force throwing the water outward. What is wrong with this sa+juj:t2d- n66 ypv dz(du4qg tatement?

Will the acceleration of a car be the same when /lqtzy zx1bxem.0 2e-the car travels around a sharp curve at a constant 60 km/h as when i -lz teyexb0mzq.1 /2xt travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a h 9v,jx+tkyqut fjgkx).4 ) w)dilly road. Where does the car exert the great))g j .kwx94xtjkft)u, v+ qydest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the force9*eym pcoh b k8 5);(et2ad qdzj+i8mjs acting on a child riding a horse on a merry-go-round. Which of theseez )i dj8ay2cht;mp bkd5qeo9(*+8mj forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a ver9 /x wgv n/ix( gpse3u8ub w+in. j3ztx5.gxj(tical circle without the water spilling out, even at the top of the circle when thegx/ bxnns 3+.9/wj(3xueptw i v8z uj.gi(g5x bucket is upside down. Explain.

How many “accelerators” do you 55.dz:* idag,gm qfyw have in your car? There are at least three controls in the car which can be used to cause the car tdq:fdz gg*.i 55y ,mawo 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*f aaq9i;jbx*-p; cxud ar;:f Fig. 5–31. His sled does not leave the ground (he doedxuf:9i *a ; b;r- qpcjfxa;a*s 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 cure 7 niw;gv2s1we4:bf bve at high speed?

Why do airplanes bank when they turn? How would you cmt tou:l+ s 8x.6a.dgbompute the banking angle given its speed an t+db6xulgt : asm.o.8d radius of the turn?

A girl is whirling a ball 5 qmi1c5 (nyfaug-v1iq .ria 6on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she letqq(5ncaif5m.vi 1iug ya- 6r1 go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a force/ j qv4n+8uzpz? Consuqp/+jn4z8 v zider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would theg7j8k 3 fe+pm h5o,hdj Moon’s orbit be differeeojd j,8g3 +kp7h m5fhnt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on w 9rl6c hu9b8)yyio ue.du8 c3the Earth? l98r6buu.cycuh)e 3dio9w8y Which accelerates more?

The Sun's gravitational pull on the Earth is muquvg(s8zb, uj/r,yc+ch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hin b(,cyg,/ vu8j z+sruqt: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mo(u f u+;xiq4ihqa7+u;mqcok7 re at the equator or at the poles? What two effects are at work? Do they oppose each oqa uimhcu7q;;+o uk4x(7f+ q ither?

The gravitational force on the Moon due to the Earth is og la1w5g.c zd*nly about half the force on the Moon due to the Sun. Why isn’l1*wgc z.d ga5t the Moon pulled away from the Earth?

Is the centripetal accelerationhzg3yezr*+eel+ 5m1p of Mars in its orbit around the Sun larger or sma+h+ye3z 5pzeelm*1gr ller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the ejhps 52o )v*)+h0yj +nj/ z3sbwvkzjdast or (b) toward the west? Consider the Earthzj 2zwjhv)svn+ky 5)hd/ps3joj+0 * b’s rotation direction.

When will your apparent weight be the greatest, as measiv,) c(ah8o9k lacb) uured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upw )h, (c)uvc8oila9kabard 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 in outer space could be adversely affeoa)0 9m2rqceitv tfz,++u : gtcted by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rottez,0t:+qa+v r 2tm9uog)ifc ates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessne 8guwbw,,1f)jw j7x fzss” between sjw ,7f1wzb g) fx,u8wjteps.

The Earth moves faster in its orbit around the Sun in January than in ,klst -9g -p* rjfpmx-July. Is the Earth closer t-pm,rf-k*9gtpx ljs- o 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 knx hf9ee30,+hmhol .vyo n e5/gp /9rngown until it was discovered to have a moon. Explain how.eeyr +3/x90 hhmnleg of/h nv op9,5g this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull quy2gi1o*0 ox9ko q-z 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.]A child sitting 1.10 m from oug2o -*1q9zi0x o qykthe 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 1980 hu;-*3xw bti/-pyf t.lit. l c$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 En:1 m:fx s gz;5do8airarth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earta:g;fxs581z mnd roi :h'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 210q:lm :su9 :hg6/0eg x8qa cyjp N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at armxg9gjq h: pc0y mq:/:8u es6al’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 surfacerlfihewhf5k0 /b 86k d*k1yq 0, 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 gravitational acck6 8dhb0i0flk1rk5wh y/ e f*qeleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a jpt;1i;+ 3bn auymcfex4 2joc,4ob 3w speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute)y oej3;nx m32wbp +bac,i1 ut4c4 jof; if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circ*qe r1 2v5hwks1ek6km77 fxv hle of radius 72.0 cm , as shown in Fig. 5-3*1 h7e1vsk7 kwh5mvkqfr x6 2e3. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-d*.0gb:fa ev9dp lr9hu(hv i q524 vfzq-r 1slkg car can round a turn of radius 77 *d:p0-rvg4 l9iq ah vv(q 1ld.uzhr2ef5fb9sm on a flat 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 sn a wumfb2+k2 65f qhwe8)gkb/ hnh/os6e+;vctatic friction be between the tires and the road if a car is to round a level curve of rade/k2gnev mk+6hhb h6 cb+ os)qa/25 fwn8fu;w ius 85 m at a speed of 95km/h ?   

  A device for training ;uc;ot8lw ,l h8c 4sjyastronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weig4ltywc,8 uj;8olch; sht, 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 variac:vmq2 uy5c;able speed. When cq ; u5:cy2avmthe 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 and the turntable?   

  At what minimum speed must s: 0let6py33(e.; ofk ddkpspa roller coaster be traveling when upside down at the tot kdf 63 3s.kop;d0lse(yp :epp of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including t 1l8k hsr0wk7reaka u- y4/ca7he driver) crosses the rounded top of a hill (r suk8-ra0/arh7lk1 wya7 k4ecadius =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 minutmg( yh6j i:8m+, yclrve would a 15-m-diameter Ferris wheel need to make for the passengers to f:(6 yvjrhgl+i, 8mm cyeel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ra4tneo.rs g .d2 cp4vz3dius 1.10 m. At the lowest point of its motion the tension in the rope suppo.s 2cgt.34dzop4nr ev rting 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 froz8 uknd:z; rq6m the axis of rotation is to experience an accelera;kr:6zqd zun8 tion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnwp 08w2l82ie, ksy-v kvxb c6h,vvb9xival, people are rotated in a cylindrically walled "room.,x0v9 -28e kk wbb x82,yvlwh6ivvcp s" (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 lg l*eaq9 5n(rq s) *m o7c+h4dv:qnkec-e ee8in a circle on a frictionless air-hockey tabletop, and is held in this oc+* vman-e* ) e :(d47rl8qsecqhenk5o lg9qerbit 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 ba q/-szndd/f z;cq xbo93ik9k8ll which revolves on a string 0.ckzf-i okdx ds9/bq q3z9n;8 /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 t h- vzx4(u(gamraveling 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)s.zui 0nnizl7 a synz7qd38 0 $ 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 by diving vj e)ppv)-8 y (ukphb4pertically 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 centrij9 bg ;br5wd kvg,q)lt+ipkggh+*8 b9petal components of the net force exerted on the car (by the ground) in Examg w+jp;qrk gbgti*5,hv + b8k9dlg9b )ple 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 unifo/3edk3hg 3osc rmly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential accoksghdc 3 3/e3eleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a fu0)t( m2vc xwparticular insta2tu0mvcw)fx (nt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12 2pfoc8m:r7qdtpp 8b6,800 km (2 Earth radii) above the Earth’s surface o2 f: mtcp b8d8p7qrp6if its mass is 1350 kg.   

  At the surface of a certain planet, th s.xqgxlq9-3uy )z (qve gravitational acceleration g has a magnitude of 12 mx(u qsl-.qvx9q3 )ygz/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 b w4pque1ap.(3dm k5dgravity on the Moon. The Moon's radius is 1.7pmb1w 4pqe .u(35kdda 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 Ear 9uojnu n4.s :8p f sjxu9y/kosl2)c5zth, but has the same mass. Wh/z k 5pus:l9n8xjcnu 2su9fs)ojy 4.oat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rn16yi )mva7u t) boki sq(o8p-adius. What is g near i6its-op18kmn()vqby u) ai 7ots surface?   

  Two objects attract each omjkyvp::t 14uh9 a2 5jd(nslu ther 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 value of g , the ayxi, -:ckwh/uv vu3*dcceleration of gravity, at (a) 3200 m v3*hiw-uu: v,/cdykx    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s ce*bcfot(jl 427+5grzv f zejaut/6kh* nter to a point outside the Earth where thegravitational acceleratiooz*hlcj5t/ej( g2vaut6 f7z r*+fbk4n 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 ofeqnuog4c6t -8j;ho l0 our Sun packed into a sphere about 10 km in radius. Estimate thog4qeho n- luj80;c6 te surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which; : aywfgn-4rf once 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 gravity on this s-fwf 4;n gra:ytar?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space sjb(,oa fr)3dzhuttle. Your friends respond thatj )arzb 3od,(f 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 squ2y l2wf5.i 7yts))nokb 2lnixare of side 0.60 m. Calculate the magnitude and direction of the total gravitational forcn nyif22 w) 2xlt)yki7bl s5.oe exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same s/ 9eh92rl 0vlb w8 d tnle+k(ohghka-,ide of the Sun. Calculate the totalw(henkd,+ l- havtgrle/b 09 8h ko29l 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 the si3knt u 9-6 w,x/z,xwpwm1yxuurface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the1i z-wt93uux6 ,/wym, wkxxn p mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the know aea162 yi9xr4amy3so6b 4egwn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s 1i43maea24y6 ar6x e o wgsb9ylaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about therug61m)u8l0 tzt . gft Earth al01g ur. 6zgmft ttu8)t a height of 3600 km.    $\times 10^3$

  The space shuttle releases a 7qwd0g 3l (y9j mjocsu*e p8b*satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relativcp7ogds*wmj*3 (j 9 qeu08ybl e to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshil.ssxywki.w)i )p(k,9vg 2m f p rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diametew9pmykswf)2 isi(. )lg .,xkv r is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth j/w i:sx pr.5cmk c7cbz62 a6vin a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satesc6rc:2v/7z wmx aib.jcp 6k5llite?    s ~    min

  At what horizontal velocity37x/mhg : 7 j9qnfe l,6mtnuip would a satellite have to be launched from the top of Mt. Everest to be placed in a circula7qj pe t6hi:xmmln/7fg,u 9 n3r orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit thgleur( p(+4h t.w6 jnbe Moon at an altitude of about 10 rgt.nbj4 l(u6w+p h(e0 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice thid*fah- j;nw;x dck1swi m0,;at orbit the planet. The inner ran1kmd ,;swi;-f0ix cjh ;*dawdius 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 (i -fkz .5q ux2xoewg*,see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight-g ou . ,k25*exzfxiqw (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 omuo0la ,mbh -+f the Earth's Moon in a space vehicle (a) moving at constant velohm 0+l,mbuo- acity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. The du5drejiu*7- 1,lglank4(r n+fs+k u y are observed to be separated by 3u n57krg,d1da*jlfie-4( +lunk+ rus60 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 mi9gy zkiep(r ,4o2)zp. e v9othe weight of a 55-kg woman in an elevator that 9zgve)r42 .yo,op ikpmzie(9 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 ceilipoe-tx is fy7)1*; giong of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’siyfto )e*7ixg-o1ps; minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfe+na o6vqo-yr:h6lj9tn . 9uvace of a planet with period T , the dv ae6utoq6n9j9l-ryov n.h +:ensity (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 pew*03 tk *cvdkgriod of the Moon (27.4 d) to determine the period of a0kt *c *vgk3wdn artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, o7q/p dd*ii /uejj oy-:rbits the Sun like the pla*u/i:eq ijy-/ j7pod dnets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanw)k+6cifad4td ql 2)o59rfy mce 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 years. It )5wq ghq j9+b qy*)ple q9+wtccomes 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 distanc9 qet gqw)p)q b+95+ywcqjh *le 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 cents0p lv *,dgl1ek/cj4t er 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, o+i k4 xh:hz+mand mean distance for the four largest moons of Jupiti: +4oxzmh k+her (those discovered 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 jc hpmy;sttf 3uxq,4pnrb4pz ,j) (70known period and distance of the Moon. rt4 4ypz0t7p,su,xb) 3fcq; m(j jphn   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of1auc)( wrt:j;utm0l h Jupiter’s moons, using Kepler’s thw)1j:tc;( u 0thuarlm ird law. Use the distance of Io and the periods given in Table 5–3. 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 Jupiter consists of many fragmen*xhsic 1 -shypa x /thm:n() lp.9zc8gts (which some space scientists think came from a planet that once orbited the Suhsx hg/z1: m nc (yp) psxlh-.8ai9ct*n 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 fv-jl5 1vtl9yx57. im hzigx+ yorm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's ye-+t7lm ig 5yixy. 9lv hxz5j1var, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a had apz tsbr5e6 jh,bq/: 5b02ie y)c2uwnging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what qb:0,rs) ab 26e u/5hdpyi tzwj 2c5ebis the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratio:gaoq62ta r vstj o-7dep +*e3n of gravity be half what it is on the sur7raodt+os eg:qj-a3 * tev6p2face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circluwhnr br / *z)mvrg;yh+-x)b*e once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 gb rx+nm;)ruw*)r/ y h *vzbh-kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day,f y+6lv(ehz*g tofds;m xgspg5v,g v,h1 ,0+i the apparent acceleration of gravity at the equatfexhogpvgt *vzhfd 5i, ls;,(0g6+sg v+1my,or 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 spacecraft tr m9b( amm8 tga3;-24lm aediim7.kpuhaveling directly from the Earth to the Moon experience zero net force because theim;bi ka8- .mp4 3eltammahg2(9d 7um Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stay;da 2g vq txk1avyfkk226( 5rnd on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directiq(;1 v262 kyxf5adrv ya2ktkgon?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thatpx96* e grsn2) ru*qov+qrs,k5 wr p*r 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 rotat2r wsso* rn9e)*prxk*,q6rg5qr+v upion speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loobxm9s :fl 8hgqqsa+2,p (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accelpwss-re1 g k0w*vf3 -ra e:f.leration due to gravity at ia v:pr grw-efs1 *w0s fe3-l.kts surface and the gravitational constant G.

A plumb bob (a mass m hanging on a stri o pdw.npk8,p*pc+b)zib.x s +ng) is deflected from the vertical by an angpbpwd xo+,psn.+)c zbpi *k.8le $\theta$ 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 1 g 8j24twpczka design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a capc 1zktwj8 g24r safely handle the curve?

  How long would a day be if the Earth were rotating so fast thlylqr p9j 2 ,u0d3o.v/ohri8cat objects at the equator wedhl3 i,v r9q 2.oo8urp0/j ylcre apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constane 2z 2*/jhewirt distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a coj e.;v r( rbhc t;gf*,v4xoaj/nstant speed rounds a curve of radius 235 m. A lamp suspended from the ceioe. (,vjth*r/ r;bgc;vajxf4 ling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Tw m8try w8nex;qtsk 5ui9k-: q,ay*p/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 ';x wmyy9q un5t-t8rpwi,s/ q* k8ek:as. 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 dedu0m;qwcqu1n x7ced 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 dqq7x1uc;mn0w id 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 ito 4zam) .s7cyv63 ycmc 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? Smallv6c )o 7azmc.yc3ys4m est?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a i ct+ y:;1ozkfgroup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be deter:c+1ofy;iz kt mined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The 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 Asteroid9ilbryysz1+ (i nf2:le/phtt(r h 48 i Rendezvous (NEAR), after traveling 2.1 billion km, is meant to or(i bny/he+ 9rz (sifth rtip1:y24ll 8bit the 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 thhzut ( ;dr)lbhf5zkzc+fc(8 :e space shuttle pursuing a satellite in need of repair. You are in athfz k+ 5dhr() 8l;bzc:z(uf c 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)ve:9 awz,bj.3zoy:7mc vp 1 a hqey(v9 What is its mean distance from tc1z:9v vw o:pv y9ab e,hzem73.aj( yqhe 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 yoz.b ge 2ws8g6vt0o mueut5j):u could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptio 6.ggtzj 0umo8tv2 5wse :)beuns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wa-vdo+x n vkm2,df:o;cm *v; fxy Galaxy (Fig. 5-46) at a distance of about 30,000 light-years v ;x *cmdd,;- fmo2:kvoxvnf+ 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 om fm6vq1ncy) tiaf7b 2db11 djb7 ,l)the corners of a square 0.50 m on each side. Find the c6vf2f 7bin ayo1m,dqm11bdb) tj)l7 magnitude 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 the Eartw: ,9rwn4qmp zh $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep seconidz)0)t5 b:k an hbqhefod) * yt:g/;yd hand on your wrist watch? b) oyi;g5 )taz/yf:bd* q:thdekh 0n)    $\times 10^{-4}$

  While fishing, you get bored and start to sohns wi3.5kzj jnl+k x0z9+7cwing a sinker weight around in a circle below n.+5zzlj3 o 7k9wxnckjis +0h 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 vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a ne;x;dip.in:(rk b:y cdw highway is designed so that a car traveling at spbd:i:;cd. ri;x (p ynkeed $ 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 cars c 0p49umvcz* x 2ccf.swhen negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal ac2mpsxc v9f04c z.c u*cceleration, 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.$\approx$    $\times 10^2$