Sometimes people say that water is removed from clothes in a spin dryer by i3vj9u ;rfn/ncentrifugal force throwing the water outward. What is wrong with thisv/nfi3u 9jn;r statement?

Will the acceleration of a car be the same* to,-az au:xi 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 speedt :a-ixo u,*za? Explain.

Suppose a car moves at constant speed along a hilly road. Where doejl482rvycvqc2yts/-3pb 5 i gs the car exert the greatest 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 o-4jypc q3tsgcl2v5/v 8 2byirf a hill?

Describe all the forces acting on a child riding a horse on a merrym2s.ls b f3/x cr 6/j fv9+ju,qy)dlle-go-round. Which of these forces provides the centripetal acceleration of the ch)+r lc3d.je,sv/qf ljlyx/f269sumb ild?

A bucket of water can be whirled in a vertical cirq27flcxvv;7)swhjr :sq drox./f 8t,cle without the water spilling out, even at the top of the circle when the bucket qc )rs jxf:2ovlvd wf7.hst 8rq/x ;7,is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three con9htd :/c be7iotrols in the car which can be used to c/ebdt9:i7 ochause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a sm- +km yvxggn04s58q nzall hill, as shown in Fig. 5–31. 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 hen-8vzs k qm0ngg+y4x 5 goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hii,bbtew b)4plp:61dt gh speed?

Why do airplanes bank when they turn? How would you compute the banking angle giaw04+,sn vwb6ik1yrx gr4ku; ven its bw kynvugrxa41 06rw ,;+ i4skspeed and radius of the turn?

A girl is whirling a ball on a s))d,h:cpcxm8 7hndb dtring 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. Whd 7bm c8nd:x )h)dp,chen should she let go of the string?

Does an apple exert a gravitationa,ltn2d jvoni-c+ w7;kl force on the Earth? If so, how large a force? Consider an apple2d t;n+v jk- io7lncw,
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what waysef7:xjp jim,/bbxpz,. 9gq8j would the Moon’s orbit be differenpqjbz.jmi,7gf:,p j8 x9x e/b t?

Which pulls harder gravitationally, the Earth on the Mj+gezf )s8ybsy +7bb;oon, or the Moon on the Earth? Which accelerates more fz+;bs)sgj8 eb+ 7yyb?

The Sun's gravitational pull on the Ecm/tq kvmt+hvoe ;mx).6qy .2arth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [. xq;/y6tocm mqt)2kh.+vemvHint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What to-w ej )4gmjtwrv7kj-9k ;*njwo effects are at work? Do they oppose eachvjw 9 jnwm4-kk-*j;g t7)roe j other?

The gravitational force on the Moon due to the Earth is only yz,k j2rm2d3dabout half the force on thedd,z2m2kry 3 j Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Marsb7nzn8 )/f 8 brctb0hc in its orbit around the Sun larger or smaller than)bzc7h/0 tbbnrfc8 n8 the centripetal acceleration of the Earth?

Would it require less speed to launch a sate,h+tv*4g 9v0n (rqdbb deo bm1llite (a) toward the east or (b) tow 04bgd9mt r +nqb,(1 v*dobvehard the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a iu*s 8qry/ ;ji w6txn iw .9.dpe6wrc5moving 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 be the least? Wheuriqx9p;rd es66*5 yt8wj /w ici. .nwn 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 adversely9n zg)cda2p9z 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 surfaca2z9pczd ng 9)e (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 l63jlpm zz 1-9fm6wog“free fall” or “apparent weightlessness” between stlmo6 9 l-wzp1 z3gm6jfeps.

The Earth moves faster in its orbit around the Sun iuhgv t;l241h nn January than in July. Is the Earth closer n4u1tg2v;hhl 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 known untir ji( -d uqrr(2vq ej-xues/;)l it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’suvr ;x/q 2-jru e(e()idjqs-r mass.

  The Sun's gravitational pull on the Earth is much larger than t8fjvsg2j,2n pp;tvf 8 he Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with ,vv 8 gn2f8;sp 2jtjfpa 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 ,6 xsjnb pow+3y*e,s d 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 accz .xnclmv 9l.8reh/ t1eleration of 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 of9xv.m/tl. z ecn lh81r 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 onxig/9t;rmszb:a/f xoj:ad5 / a 2.0-kg discus as it rotates uniformly in a horizontal circle (at amjia/r:d9 a/5x f ;ot:x/bsz grm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ear :u1w2ar b8-deg.yth .kpxn -,3lgqys th's surface, 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 gravitationa-k 1: g.nux.bgwe-y,qp 2dr8 h3aslytl acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the -egfdf yaajfaa6 v6nzq+(s 1z:/ kl0w7xa5 f:acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diaa+gaje:fzyv aqfa s7wx(n: f1-ld/5 6afz06kmeter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in ;3yih bf(sim*:iys s3 )pnben 9 67mwza vertical circle of radius 72.0 cm ,ep bmnsiw )z (fy6smyh3bs3;i7n:9i* as shown 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 with which a 1050-kg car can round a turn e1;q3is jdo5x- oh;vyo,cc k3of radius 77 m on a flat road if the co c xd;yk,1 qios3cev3;h -o5joefficient 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 static8ee4c m58yr*7 :nh4ucg ledfs friction be between the tires and the roa 88d eym hcersnf*45u :el7gc4d if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rokz6jbi 1+c.mk a:oa.etate 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 .oe+k:j ck.baza61imown weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable dlpr4p o 04o6ew8n2 naspeed 404ro w6neo2dnlp8ap . 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 and the turntable?   

  At what minimum speed must a roller coaster beyux6ir g)c3g( oie+(t traveling when upside down at the top of a circle36(oy)rg ige+c(ui tx
(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, xcquvb fe0gf/c 28v. the driver) crosses the rounded top of a hill .g c0vfxvc2q,ufb e8/(radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutionsms,*:v.q .x h ppfgo9bhz cli(, w2;ek per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlezqg(hck9lxmh bp. pe:v ,f *o2s.,wi ;ss” at the topmost point?    rpm

  A bucket of mass 2.0lr5/8yo / e3w q:rlotz0 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supp5 3 otrye/z8wllqr :o/orting 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 centrifug9t 4z:f 6eft vqg3 bblwd+te1-e rotate if a particle 9.00 cm from the axis of rotation is to ee tg qfe34t6v:19t-b+lzwd b fxperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people arqwfjy0vrbv7lx;p8 w75/a ny 1 e rotated in a cylindrically walled "room." (See Fig. 5f7vwyyl;pb8vq 01rwxj/na7 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-l upw1i1fyfqzq ;9m2/hockey tabletop, and is held in this orbit by a light cord connected to a dangling block ;ymfp q1 wluiq 21/fz9(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 igfg93 sneo v 8 0cn,.e(ohos0ahnoring the weight of the ball which revolves on a string 0.600 m cesf eh8,0nv0(3ohg o .9nosalong. 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 rada 2hxvrb4 u mx/6i-k5 av/td*qgx -v(wius of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse/ki8qu kq)w u7s $ 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 manig dws9pn6l9yf *nt :56t)mhi euver 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 centrijy g d4,3jp3 1hrvid7bdj9g *hpetal components of the net force exerted on the car (by the ground) in Example gg7d vryip hj 3,bdjd1h*j4395-8 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 the pit area, going fro*p;k txyv2)fqs:.bwvz 5-x ht m 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 thezhx tf: );v.txkys-q2pbv*5 w 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 it *um4s /maeha po98e0 v0mew,n a horizontal circle of radius 2.90 m . At a particular instant, its accelerat vswa 0etpaeo4 h9me8mu/*0m, ion is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraf zsw 1arxr0t-9 b/ply3t 12,800 km (2 Earth radii) above the Earth’ 3a1/ps0 wl9rtrz-bxy s surface if its mass is 1350 kg.   

  At the surface of a certain planet, thxh85g fij25wpy d3ts(cmq g5;e gravitational acceleration g has a magnitude h5wdggq(p5xj2si;8 f5c3ty mof 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;wtzum5 auj-(ay7wy(c j1t3: h r5jki on the Moon. The Moon's radius is 1.7hj3cru-j mza 7 t(1;5witj 5(uy:a wky4 $\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 the satzp it-,-e 9xome mass. What is the acceleration due to gravity near itsx ,ip-zote 9t- surface?   

  A hypothetical planet has a mas6hjx5zy; 0tw*m+ ie3x nqf,bjs 1.66 times that of Earth, but the same radius. W*0jxqh nftb5 3 z,;mxj+ 6eyiwhat is g near its surface?   

  Two objects attract each other gri01)xienn+i- pjba 7nu4+t gm eg*rg4 avitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration o c va3 4rbgp..dof.o;x v,6rtpf gravity, at (a) 3200 mo.x grdrv p;4 ,.b t.pco3fv6a    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a p/yd m9jp+wt;r 0nr* bloint outside the Earth where thegravitatiot*n 09 bmpd/y wr+r;jlnal 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 (n+1qdx h1o7be vja29-w s ocxkx 5m-nthe mass of our Sun packed into a sphere about 10 km in radhd-mxk-b cq w7os5 2xjvo 9+x 1a1en(nius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an g3brhr0g+nvjxc( 7clv0 g5b , average star like our Sun but is now in the last stage of its evolution, is tglgb 3+g(,rnxh0cc5b jrv 0v7he 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 weightles6mu9 fd8cc ek;s while orbiting in the space shuttle. Your friends respond that theu6c;fd9ck em 8y 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 square of side 0.60 m. Calcuty -+ajqjb- u;late the magnitude and direction of the total gravitational force exerted on on-+; ujjayt-qb e 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 i kuag-o3qnntq8j.5 6side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are qotaquk-ni3gj.5n86 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 surface of Mars i- t t0kacg, tfdv(ia26s 0.38 of what it ,t a6tdvfati2 -c(0 kgis on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period o m;;f-5 .id*vg-h cbesuyg7bgf the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examp; hu fc.*-yg-5 e i7vdgbs;gbmle 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circ m hrl4 drr+t0m4px:jrkc+,7sular orbit about the Earthmjm:407 x kd+,rtrslrp+ hr c4 at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite in ukb:/ jnptgnfd;2r/*to a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Eartt unrbkn2g* : dfp//j;h) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupakg eet+2;mqk,nts 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;mq +ktkeg2, e revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes gxsm2: g6zcq- 5.p )crcdsmg6 for a satellite to orbit the Earth in a circular “near-Eart.mr2g :sp5)-cxg c md66z csgqh” 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 satellite?    s ~    min

  At what horizontal velocity wihdeyjva//r6b8 d1:w p xe,g;bs9+0r x8 gmbhould a satellite have to be launched from the top of Mt. Everest to be pbig+xxg 8p/be6yw0a d9vbrr1e m/; d sh,8j:hlaced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continue s7 nbkptqgtp0+lp56ld5u uov /:u:9qd to orbit the Moon at an altitudopk055sq +udqu::g/v6l n9but 7tpple 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 or5 bw:zrsp22n6duhzhn0 h 0-wtbit the planet. The inner radiu uwbs060:hnzdnw hr 5 thp-z22s of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig ga fvyjc ((9f2pt.f5zle(f5x . 5–9). What is the ratio of a person’s apparent weight to her real texg5(a( vlf(f9 p25jcffy.zweight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from z5sibui66)n:d lo h7gthe center of the Earth's Moon in a space vehicle (a) moving at constant velocit7b)d:zol65iisu 6nghy,     ----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 concjool i6 rmt4w 89,3xz9m hb9vsists of two stars of equal mass. They are observed to be separated by 360 miox8z 9699 bmhi,o4l wjtrv cm3llion 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 weigg8 vmu8a6k6gsroyc2sqjn4faes 2+rp b :; /,mht of a 55-kg woman in an elevator that moves j8 ,ram: ss/y+q g6g4 6m nv2poraef;2cs8 ukb
(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 fro5*z te 3;f)rd rc)ekf/kio/wkm a cord suspended from the ceiling of an elevator. The cord can withstan5ewt))ki k 3f/*e krr ;zdfc/od a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite or gv +0-p6 .x xfort1-yy)ttw)tlcjxs9bits very near the surface of a planet with period T , the density (mass/volume) of txtw t-9-ty6+sxrtl .)cp) yjvxg1f 0ohe planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the periodz;hjl m857ru v of an artificial satellite or jlu57mh8v ;zrbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only 6ksahmagou+wv x-f- fc ,0u+gij ,0 h7 -if)wya few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What76u), , +uc+fk0 famhg-as-ywv- j iwfx 0ihgo is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5mrc,y1u*x jbe f74l,n $\times 10^{9} \mathrm{~km}$ 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 comes xp5x(res ruc(*0um ;nou 7w* qqnq/4rvery 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 from the Sun.] rnxp7qqx0(* 4 usu;r m *o(/wn5 cerqu    $\times 10^6$

  Our Sun rotates about8gd 5wz/s3b:3dn kbro the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distanc wxuz- i4+0ej01sj x)yw z8pige for the four largest moons of Jupiter (those discovp sii z84+ej gzx0 1wuy0)wx-jered 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 known period and distanc 6h ,mwpz g0b)0s0mbger 8hl4te of the Moon. hze4 860 hrgbmwgmb slp,0t 0)   $\times 10^{24}$

  Determine the mean distance from Jh; u+h4x+n ovbupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods hho4+vn+u;bx 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 fragmentf;4 /jn9 tf6 hvis09piiwsry */.lxuss (which some space scientists think;s 9rf x.l/ti hv6inywsj/sf* u9p40i 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 describes hebl6v4zym0vj1)f fym : :b 3ypv71iban 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 thf yylp6jf v1i 0vb:4bm yv)3h:zbem71e Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig.a fgraykl2gd 5+z7s- 85zuel sf4f1;p 5–41). If his arms are capable of exerting a force of 1zzaf ; f2s-r1k8gp gyfe 5sad 4l5+7lu400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s sud/x2s alrp+-x rface will the acceleration of gravity be half what it is on the s2p a+rs/dxl-xurface?    $\times 10^6$

  On an ice rink, two skaters of equal ma/xref 5ssj-n0ss grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 se5 jfsx/0-nrkg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratio vnxpw:70pvqv 20;vvqzanw94n of gravity at the equator is sli07 a0vq2pz nvvvwqp9 :w x;n4vghtly 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 wil,fj mcuu3a 59ec 8z6rbl a spacecraft traveling directly from the Earth mu, 9c5 arcu6bfe8 z3jto the 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 bathroomkw01zgy ;2co v scale in an elevator, it says your mass is 8kvyo 2zgc0;1w2 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space sta,*cij0e dqa 8wl8twa.jm;,wk tion consists 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 diame;,*cja8.tl0m wk we8a ijdqw,ter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircrafr2(ndoo9 y*0 z;fx scjt in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its y. df*r6m e0ho0xt7c7 ;njxzklchc) 3 radius r, the acceleration due to gravity at its surface and the g 3*zlc0ch0;7j r7x dyecohmk)nxt 6. fravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from t r,gq5pa7q5 zl*md8c2yis -ajt4u; d dhe vertical by a cgya5d 548 tim*2ljp;d- zqr7q,sudan angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of 0el qhty13zx; If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely0t;qe 3 yh1lzx handle the curve?

  How long would a day be if the Earth were rotating so fast that objectsv+; 5 :ppjvkqbe /e6vr at the equator were apparently wvj;kv:qp 5 e6/ v+perbeightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aa:gzwask uu ch-6a;.6+6ahtewu ;we6part 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 rounds a curve of radius 235 -h l.bk8ylhn(44xp gh m. A lamp suspended from the ceiling swih bx(g4p8nl 4.y lk-hhngs 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 dd9y 1(qn * /xee6kig1dc/z- po/j oabthe Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a dn1p(e /xi1yzdb/ / ec9- o*qokjagd6planet 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 Telescoc /)a:x+:k(kb+l il t0n 4+pgxkp xpsupe 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 4 gk+/s0 )aiulk+blp xtx ::+pknxc(p light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill an7m7- ejz z4t 0i( sf*cq7avmkgd valley shown in Fig. 5–45. Both the hill and valley have a radius of curv 0-f* (7i7kc4qszjz t7g mamevature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utianjpr:itbp;y ,2 x. :glizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the:byg :.t ni,x2r;ppja position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The 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 t:kaep- xu+r2 Rendezvous (NEAR), after traveling 2.1 billion km, is meant turt-2x:eak +p o orbit 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 the space shuttle pursuing a satellite in 0xrc gt)6p;k +)gp 9dmwgv1+qc qpuf -need of repair. You are in a circular orbit of the same rap 1 tm +)p6)r;gkx +-f9w 0uqqcgpdcvgdius 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. (amjo ;vs7 v/q(xpffr5, ) What is its mean distance from;5(mv o fsf7qj,x/ vpr the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would nex1k92grlezb*pw luo cz k0;6w;5glr 9ed to be if you could actually "feel" yourself gravitationally attracted x 01*rz9w pzc6;5r9ol webl2 ;gugkkl to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a distn awgs2/fz-.gance fsnw/.azg- g2of about 30,000 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 squj *a+nxc8oxl:f 3k.vvn3 rxt g-8r+iyare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifao3t . r-+jv8nxi ykx8g*fv:x3nlr+c th 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 orbit 6actv,h;ox un8d -/i(v3vlnu s 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 ow*w :mx70md ttip of the 1.5-cm-long sweep second hawmt7o :dwx*m0 nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to 0*a8q9d hu0rpjww t q(-u 9ydfswing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.ud( wpf0-w qa r90*jut d8hq9y50 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 designed mh5u+ ;b1r 0k;i2rd03nco thd jl 4yceso that a car traveling at;hu cc1ont302hb i5rk ;y+4mlj d0rde 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, utilizes tilt of the44phsc r *. r79t a zycyxaee,+j8iq;e cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Conside,ech .;c4pqiyz* y9 saa 7eext4jrr 8+r 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.$\approx$    $\times 10^2$