Sometimes people say that water is removed from clothes in a spin dcr*g6ladw+o 7qb +a8iryer by centrifugal force throwing *ad+8a o q7bi+grwc6lthe water outward. What is wrong with this statement?

Will the acceleration of a car be the same whe8.mbpfur n 2z.x 7f7pg +zd0cln the car travels around a sharp curve at a constant 60 km/h as wh72 fdzur7n+p 0.gc8zmf lp xb.en it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car z w6wt4d-v47 v6mbbwp-c p 2ug3o(ujf exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hillsvu4m(-jvd42f6t- 6wc bwzp bwogp73 u, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridi,)f(q(9t )t bvw dwlpbng a horse on a merry-go-round. Wh bpdfvwq((),lt 9wt b)ich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wij/ n 1wyt8dko*0gu;9(f*- pp kfmunuethout the water spilling out, even at the top of the circle when tht;f8 u k*y/-nk0um(upjonpg*d wf19e e bucket is upside down. Explain.

How many “accelerato ( b1 e ,iv9sli:uscv.ek;gx3mrs” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. s.1vx eg;bvi9sk(: ce i3m,lu 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 Fig.v2 t w::wmo mci mur;c66ootn::zae.9 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 he goes over the h;or:mo mn6izc2 6: wocwem:tv9a.tu:ill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at dn- ;4oit 7bytaqq0.rhigh speed?

Why do airplanes bank when they turn? How would you compute the banking angley7buzkx,de 5*jxjgxc/+byjc. 7 ou0- given its speed and radius of the tu7xyeux.57o *,+-c y0gxdu bjjczkj / brn?

A girl is whirling a ball on vq 32gp-6ml* r8ctnnj a string around her head in a horizontal plane. She wants to let go at precisely thegq63mn*p8 -tvr 2 njlc right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on tb8ug3x t8q/;*f yunuthe Earth? If so, how large a force? 3 t8*x/g yq;8fuubu ntConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouldbfs 7ocg7 o(ror6;:ws the Moon’s orbit be 7bwc( o:os rg7 ;fs6ordifferent?

Which pulls harder gravitationally, the Earth on the 16sq -juyz* qbsq op*:Moon, or the Moon on the Earth? Which accelerates 6jqq*1q-osybuzsp : *more?

The Sun's gravitational pull on the8v.c 2t (3kc6 uqrmdkm Earth is much larger than the Moon's. Yet the Moon's is main8vm cq (6.dcrtumk23kly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mtfrv2+x /tb0nore at the equator or at the poles? What two effects are at work? Do they oppose ea x/ t0b2rnvft+ch other?

The gravitational force on th;gihee,z+hj up uu 38,e Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the u,; eu+8 uh p,jgz3ehiEarth?

Is the centripetal accelerap xe.x*; i3oh l3kfh-xtion of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of;px xk*-hx3if leo .3h the Earth?

Would it require less skrgz6s2tg)0/ ue c, 6jfk9huk peed to launch a satellite (a) toward the east or (b) toward the west? Consider ts2g6t)k9 z jhe kucgf/0ru6k,he Earth’s rotation direction.

When will your apparent d9ixr5f cz3z3weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?zxci r9f53z3d

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space coue ahclw*y8u45ld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, wel *ayh5w84cu ith 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 “awh99xv d*bp9t pparent weightlessness” between stehxbpw *v9t9d 9ps.

The Earth moves faster in its orbit around the Sun in January than iss2y, hxg6g(mn July. Is 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’s axis relative to the plane of gm(s2x6sgh, y its orbit.]

The mass of Pluto was not known until it was discoverz-x 8*d+dsxyt ed to have a moon. Explain how this discovery enabled an estimate of +-x8*zs xydtd Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th.0q 0zxk jxu5/ew+yontg31nbe 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-roun1+ g/.uqy 0e5b xnoxzn0k3twjd 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 bwrtiau d0m1ln2 z8771 sbj c2 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 centripetal0(.6cf)aj bell; ssk7z- ulvb acceleration 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 oflu;sj6(azk0 fsb- 7vcbl l.e) radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.6c x368us lh(j -zssga0-kg discus as it rotates uniformly in a horizontal circlegc shx8ssuz jl(36a 6- (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 surface, an q -z/hbcspo**d circles the Earth about once every 90 minutes. Find the centqzp-bohc** s/ ripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay sb,ysi16(ocnxt tw us8sc2ln;/1 l7j on the edge of a potter’s wheel turning at 45 rpm8s1jssoln 2wt yn i67,tbc/ (u1l;cxs (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is re3m;ymxfpaz2b2s dafhg4 q: u. -;(tawvolved at a uniform rate in a vertical circle of ra; .:fwm4d-q x3p(ayh azu2a 2ms;bgtfdius 72.0 cm , 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 be*v4k72 v9n*hsg+,wh 3 lxh;s hprhy round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent ofhes 9+gh ph*ns;bl3 ,kvyhxr2h4v*7w the mass of the car?   

  How large must the coefficient of static friction be fxckd4u(io , 3pkyfvnrt 1 005between the tires and the road if a car is to round a le puy5 nc104kko,0rivf3 (ftdx vel curve of radius 85 m at a speed of 95km/h ?   

  A device for training ;9 .5ap-bs g,x eiwkfu.wyeg)astronauts 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 7.5ewyu.egawx, ;s-g p)if 9bk.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variazt88 /cr(-glep -a oujvl.pj+n)acm/ble speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reajl( -/pjz g/p t-.ou8e vlaccma8rn+) ched 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 be trav1zwj5* 8p cp(xjiqi,- ly/mm leling when upside down at the top of a circle 1-y 8,(pxl / cm*w zmpliqij5j
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top1uay-r l-h.txn+ tn 4rbr l)ph1 6;sd9ja*ehs of a hill (radi1rnt h4rhan-p jlx; 9 d *sh+ul6tsr e)-1b.yaus =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to mak t7k tyq6d ;bzxfk237qe for the passengers to feel “weightless” at the topmost point? k d7;xk7q3q b62 yttfz   rpm

  A bucket of mass 2.00 kg is whirled in a vertical ci 74k+xdvfhz ,vq+2redr+sbb2 rcle of radius 1.10 m. At the lowest point of its motion the tension in the rope supp7xz ++b 2fddes hvb 4rrvkq2,+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 cenml lizmvn,zzv q z5f)-h a+40y (7apy(trifuge rotate if a particle 9.00 cm from the axis of rotation is th7i(q(vaf)zall,m+y zpy 4 zm-5nzv0o experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wall h me9x;bw*u,zed "room." (See Fig. 5-35.) , zemhx w;*bu9
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-hb z2jf).+ 5 ).)iykjlohajd bep-*vqu ockey tableto*)5)z .yv ajqkulhop. ib-+)d jfj2bep, and 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 ignor3grhd-.g*.qg 7 yyjfh w* 5lpring the weight of the ball which revolves on a string 0.600 m long. In partigph*gr f-3yl5* dywj. 7qrhg. cular, 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 ranqk.g4qtz 7-eh s r(zd7*9pc,vuso3ndius 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 masses o, rj 77c6envb+ldg p,$ 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 evas2ogq b mioqw2 u7-o,ljt,s: 8 -ef+qlwive maneuver 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 tangenticbkl 9vmih6(js 82xv5 al and centripetal components of the net force exerted on the car (by the groun9(vik6mvhjx 2b8cl 5 sd) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates un:lclw78hl4., kmge ux iformly 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 acceleration. If the curve weree,w8 m.:c gxh7lku4ll 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 2.902 nf zqyz6j *+ o.w/fwj7ffd.d m . At a particular instant, its acceleration is 1f.*o/qwf jy f 67+j dzwn2.fdz.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 k:rj2 ;e21 shm c1/t 89gbmpcefo8wr xxm (2 Earth radii) above the Earth’s surface if its mass iwb:rxx c92 ;eofrjstm 1p8c2 h8/g1e ms 1350 kg.   

  At the surface of a certain planet, the gravita ihbblj4 2 +2t wx38pel5hiz4jtional acceleration g has a magnith z+4 th 48ljj2x32pbwii5lbeude 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 k gxg/t)-:znlei. v; (xfzls4j6t)ok Moon. The Moon's radius is 1.74 f/( -tz vte.k :zgliolnj;)) g46xx ks$\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 f5ub)j9cnyp )th, but has the same mass. What is the acceleration duepyf )jb 5n)u9c to gravity near its surface?   

  A hypothetical planet has am 8:9xpyyr l0d mass 1.66 times that of Earth, but the same radius. What is g near its surfad 8mxpl:0yy9rce?   

  Two objects attract each other gravitationally with a force ofg(+,gam;rhhuj+ipig 5 /ovw/r ,bz/ g 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 valu/gt+z, c-lmdwqmlq.i,j f 2x+e of g , the acceleration of gravity, at (a) 3200 m-dj,g clx,wq q+.m2mi/tz l+f    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to .giqc5e 2 .ru:oxf/naa point outside the Earth where thegravitc..u:g ef5 2o xn/qraiational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass gcvxcl4ffw9/e1. w h9 of our Sun packed into a sphere about 10 km in radius1.efwcv/ wgf9lhx49 c . Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf sz wxp:3 enq*k/tar, which once was an average star like our Sun but is now in the 3k/z pxe:*qnw 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 star?    $\times 10^7$

  You are explaining why astronauts feel weightless while 9zas 9xsv t0e4orbiting in the space shuttle. Your friends respond tz9esa9s tx4 0vhat 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 95d)xaw4ksak;ilp. jkw(u )ua square of side 0.60 m. Calculate t .w xu4)(du ;sk5jpilakkw )9ahe magnitude and direction of the total gravitational force 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 si(zmb ob0o9km 7rd8/x2jn+ekyde of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are 2oen9k/ 0 j7+8mz yoxrdbb(mk$M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 is 05uif1- s gf8 w- s7jgdl-oyou;.38 of what it is on Earth, and that Mars’ radius is 3400 km, determlw;s-oiod-ff1jg-5u7u8g y s ine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fohzsp qsh* ,1y)r the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obt sqhs)y pz1,*hained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cix4ub+h. e,i r1kypnt8w r )w+yrcular orbit about the Earth at a height of 3600 km.ikw4htw )u ynx.1y r++p ebr8,    $\times 10^3$

  The space shuttle releases a satellite :y;+m m +gbwocd. +ixvinto a circular orbit 650 km above the Earth. How fast must th.xo+d ;vmm cbg+:y+w ie shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship f/9nzwk(kv aogp8 0y0ft ;ah+rotate if occupants 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 kga9pwn zfoavf/+0(; hkty08 revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satelgp3/al p:umi)lite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your resul:i)gm p ap/lu3t depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from theea nemfe k )v5qknx5e/)q,/sd x/c;9 o top of Mt. Everest to be placed in a circularoefkc)k5/,)5ve;nm qn s/ 9/ eqxeax d orbit around the Earth?   

  During an Apollo lunar landing mission,bn;eyc : / 0eb.st0hfp the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Mooncpsn y:e0;0befh/ . tb once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. T.qocte ,ny49ars9 4 l i wlh ;8pfood-em240nuhe inner radius of the rings is qdoo4uf9 lse 4ole9ih2r 8.;a ,mt4nnw0 -pyc 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 )z ow) a z nns-nsznnl4.w9)0mrotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real)-)snz 4onlz9sn) m0a w.z wnn weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut d ckoq)pw u9/l5wv 36t4200 km from the center of the Earth's Moon in a space vewu cotq6v kl3/dw) p59hicle (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 e sf a5si1lpx/-yi (d0of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 E 1sid ap50ixsyl(-/fearth 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 weightqzcsltcnbmmh9jz z6 (x16(66 of a 55-kg woman in an elevator that mozcz1 cb6h 9q6ms j(zt6(nlxm6 ves
(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 elevator.wr:m )(pxm+p 6z3/inoym v1 qn The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’rmq/imp (1n :y+o6vx)n pz3m ws minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periodm6, ypc+nxb5x T , the density (mam ,pb5xc6+ ynxss/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon m 3dj9p9he1(;hc cjfvy gs53w6 lghe3 (27.4 d) to determine the period of a m1w 3p3h; 6j9(gye vcf h3egd59shcljn artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few h 3us30c5zhofrr :9l7sol sf0hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from thes 330 or5 ous07l:f9zhh lsrcf Sun?    $\times 10^{11}$

  Neptune is an average d tpxs*i s+:4,j)xzhx you92ug istance 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 comes very ( 4skwa:v *y7rmrw;klclose 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.] r ;kvw*awr4 s(:kmy 7l    $\times 10^6$

  Our Sun rotates about the centagbzwnq,lu( mq +v5*j7pe3 rm (; h9ueer 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,z upf ozi /3 xg0et5c8tvx*m9-r.6yeh. 3nyev period, and mean distance for the four largest moons of Juon t.z6c/tu*y0i 5x 3z3g.eyvem xfh9ervp- 8piter (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 known period and distance of th86qo09+m qgr8tax8p8 fq cyx ue Moon. xo9c8 x+8q0gupqqa 88yfm 6rt   $\times 10^{24}$

  Determine the mean distance from Jupitwxf nfkwe 5504er for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5fw e45w0nfkx5–3. 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 Mayqf *(;f8p5 qnwywzy.2hyzat ppy.; ;rs and Jupiter consists of many fragments (which some spac 5;n qyy82 (ywypzp. f;ztf;w.*phy aqe scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the jz+ic22mu41 w.twj yk form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as owuk 41mi j.twj22zc y+n 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 vineu,/:h:twf argp/9ty c (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swingu hf/rwaytc:t9/p g, :? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accr4eg.f:okan r8- 9fo jeleration of gravity be half what i o9f nekfr 8g:ja4r-.ot is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equx53i( rc1c4. xnhc*nek3z a5cpu + awoal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 ace+ nxa3*xh.rkznow p 1 5c(ic53cu 4kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acy7w ukr4 qbar94a5: tfceleration of gravity at the 9kaay rtu7 5q4b4:rfw equator 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 traveling directly f 3,j3089qrvm y . ilbzarwdydue+w85from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal lwr8 35+mj e, qfb8i3d d yv0uwra9.yzand opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand onmaosl b4, t vl5*n./je a bathroom scale in an elevator, it says your mass is 82 kg. Whatb5esa4j,l *tmnvl/. o is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular xu2.::w4 werzuu8k i3fs4ayf +sdi0g 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 day) if an ik4 :40wrf:gwsa e uuf82sdyiz +x3.ueffect 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 vert( f9mb qcv s(wfzkgs,vu(+ d35ical 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 radius r, the acceler1m w d+o6e1oys-bj9,tsc-ft c aw-d-cce1s9+s o,1j bmt fo y6ttion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string(6tl og2ze y-j pr/za;) is deflected from the vertical by an angle yzzg ;r-ao el(p j6/2t $\theta$ 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 designsozqo) v*e ;i5 speed of If the coefficient of staosi) ;v5e* zqotic 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 objects 8mbhdtrl; l2i 7d9pn)dc31la at the equator were apparently weight;idclp8 l 2ah1 )t9 rldbdn3m7less?    $\times 10^3$s

  Two equal-mass stars maintain a constant distan kn2w*;7cmk xace 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 constant speed rounds a curve of radius 235 m. A laml3 n,hw -rbhc)p suspended from the ceiling swings hn,h3)w -rblcout to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timc --u r-44yffsmzt+ux 6jb+cwes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the nub-f-j urcf m yz6-+tucx4s 4w+mber 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 Ho(6fmc0gyd;d3sh zu dty o00 9ubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be aouzf3h0d ysdo096my 0(g tc ;d black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speem gr qx384alif/qxa- yo1.ij*d 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. .y 4qrimjxaiaq13l8 /fg ox*-(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 group of 24 satellites orsif7 tw sgr1yjt3prvued*j1+e. *k74biv*y7 dsus 7 4ekr1t ej +jfpwg3r*.ti1ting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travelit qlu 8kz.xv x;)gv)m.ng 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Ero8 utvzv. xm);xlk. )gqs 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 :lrf715unraz uph)1m in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earthar711u f h5lu pmzn)r:), 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 iv 1jk zini eig4mfu4b7g48s 4*k(n1c rs its mean distance from the S vz sjiu(m8b14r7* 4kn4geigf1cik 4nun?   
(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 ne :p uu d+tfk/a.si.* 0xnn)dpaed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumx ki:*.atn)ud.n0udpa+ /pf s ptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the c-w w9nqh(3: m)l1b yrl2gqlpld .+p txenter of the Milky Way Galaxy (Fig. 5-46) at a distancemw 3ln p dpql1q.w9 hxgrb 2l+l)t-(:y of 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 axjkqxrh:kcvq55if)72cv tz;bi 7. g*re located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force oc.;f)57:gzkjcr kqx v7q *x5 h2ibtiv n 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 5);fgee w, sb+ f.imrwb, p3hu*500 kg orbits 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 +m e pxj4b) a;lkde6j n5-sinj7w5lo) 1.5-cm-long sweep second hand on yoj7s;wajjd6lm kxlep +5-o ne54 )b)inur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weigcpaq2 1c *1j p.ono/vvht around in a circle below you on a 0.25-m pi1p1 *./pqvjoa2 oncc vece 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 new highway is+;x o,n4 g)vogsib ioa8kl si(:3r.sm designed so that a car traveling at spea3b;ir)( ig.io xso : svk+gm ,l8sn4oed $ 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 when negotix-s cg4eglq: o.jmk) ) eg.4uiating 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. 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 traixq :cmgkuej)o e.s.-lgi)4 g4 n 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.$\approx$    $\times 10^2$