Sometimes people say that water ezf60kjrju4e2;l *t p is removed from clothes in a spin dryer by centrifugal force throwing the watere ;uj6 jft0l 2kz*pre4 outward. What is wrong with this statement?

Will the acceleration of a car be the same whe51+qgpn.0 bj u,izo ban the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentlei.pb 5 jg1abn,+ 0oqzu curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wherea4 iv0r b 5x33m2ixya3(j tice does 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 s0r4m33 3 iac2ji t5x(xiaebyvtretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go*jniu0a; 1rodff rq(h;yte/ 1 g t(ou9-round. Which of these forces provides the centripeto jgeq1(ifhdr9no (;t/u u1faty;*r 0al acceleration of the child?

A bucket of water can be whirled in qg. /s r sw:0j0dhppp3.yti*ya vertical circle without the water spilling out, even at the top of the circle when the bp*jsp 0hr3y pdqi: .wgt/0ys .ucket is upside down. Explain.

How many “accelerators” do you have in yourqr*knqqw 1i( / car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accel1wq* qr(k qi/nerations do they produce?

A child on a sled comes flying over the crest ht /cc,j 42tc1)boenu of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normae)n4 ojcb /2 httcu1c,l force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hi/.vf r*7 ehfuvgh speed?

Why do airplanes bank when they turn? How would you compute the ban*;* 2 z)jy7 v-ghani fqkgfc6rking angle given its speed and radius of the tur7zh cjvy)*-6raif*2g f;gkn qn?

A girl is whirling a ball on a string arouyc/9p7n621,q da*lh myi sgy und her head in a horizontal plane. She wants to letg*c 6di2s9lm/1py qh a7yu,n y go at precisely the 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 the Earth? If so, how large a4 uz 1mu.b. ala;3ifrc force? Ccmubf4zu. ri1ala;3 .onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Mot+usqieih/o.o - y8; 4kib7ya on’s orbit he-uoia;ob8y i. qit4 +7/k sybe different?

Which pulls harder gravitationally,; l5bs-y e/h; py;x jf6dd)owu the Earth on the Moon, or the Moon on the Earth? Which ac6;lpsy-/e;;x o hy )bjddufw5celerates more?

The Sun's gravitational pull on the Earth is m ocb83w,j,oi7iyjp nzuq;o9kfwa. /8uch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in guof ozn bjo/kwawi3p8 c,8j .,97i;yqravitational pull from one side of the Earth to the other.]

Will an object weigh mhe)wh0:s vy 1yore at the equator or at the poles? What two effects are at work? Do sh)h wv:yy 1e0they oppose each other?

The gravitational force on the Moon due to the Earth is only aggamr z b)i/;4bout half the force on the Moon due to the Sun. Why isn’r agz)g/;m bi4t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largj.a ,fzivpuo 1 /vzn 4myd zx*-ji8.a7er or smaller than the centripetal acceleration of thez ajz1x. apyfnjozdum,v./* i 7i-8v4 Earth?

Would it require less speed to launch a satellite (a) t5m hw m kvo;c(+dia +i;:icvj)oward the east or (b) toward the west? Consider the Ewo5am; :i(;divm + k )+jcchivarth’s rotation direction.

When will your apparent w 3sn97cxykh ag:kl3 r 45vk)xceight 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 thkx 7 a4glks cryvc3k35:hn x9)e 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 affectex- ngxrqtefs;n(b0f2l 5z rx8z/j7,fd by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravitl rr -qt5zx/fz xgj7x0n,ebf f;n 8s2(y. 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 weightles*wypj,qvw-d7xl q9 8bsness” between ste q7-pj,vy9l qwbd*x8w ps.

The Earth moves faster in its orbit around the Sun in January than in wao,s2 q*l9m+ f2l.jesxi dk 9July. 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 oflljmsqx* wd.sak e+f29oi92 , its orbit.]

The mass of Pluto was not known until it was discovered to have a moonam.qvdc5c y 13. Explain how this discovery enabled an estimat3dcaqv .y1cm5 e of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mo (d6v v,grhqiu m8pj.,on's. Yet the Moon's is mainly respom,8id qgr6( ,hvvp. ujnsible 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 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 ygh1+i ;dm;l :mfba,c5sko5 g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arounj8 0kr4mg7i1z lx3gc kd the Sun, and the net force exerte cg8m kz4k3 1rg07ixjld on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted oncob1m :gajhxi2c+ n. ayty97 * a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.mih2c.y:tyn9joa*b x1g 7ac +   

  Suppose the space shuttle is in orbit 400 km from the Eart5d0on,ef lf /yh's surface, and circles the Ear5eff/yl0 o d,nth 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 acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the ed ng(:z.yz:jrx ge of a potter’s wheel turning at 45 rpm (revolutioj:nzg y( r.z:xns per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revo tabkng(d8r(3 lved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in ( ar8dk3n(bgt 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 clj +5)d +skkuzar can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Isj+d+5kkl) u sz this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and tt 3e zs-;ge2 :r;1dmdrx)w vhzhe roa rhr 2z1t;e xze 3m)-:g;svddwd 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 rotate ar m 2es*5c*k. c*nydik trainee in a horizontal *nc2rms *ceiydkk .5* circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis gjb ) 5 ix4jm*l9*wvtcuil;k8of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coeffic;c jwu vgl9x*lk i4i)bm* tj85ient of static friction between the coin and the turntable?   

  At what minimum speei9 xom0ckwj8m:i (k d1d must a roller coaster be traveling when upside down at the to xc(om90ji:kk8 dw m1ip 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 (includzrob8h6 h7l44yn got+ing the driver) crosses the rounded top of a hill (radius =484og r zb7n6holy+ th95$ \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 to15wjb,r6d+wb 0ya lx s make for the passengers to feel “weightless” at the topmostwb aly6jx5,s 0br+w 1d point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circlez:+8cb 1p kn37f 3k/2u3pw g3jqzrsjmb w9htg of radius 1.10 m. At the lowest point of its motion the tension in the rope supptw z+3upfrbpgk: 387j bw3cgznjq1 39 hksm/ 2orting 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 from the axis kz/6pyf* fcv 8 v,k m.yjl-u)fof rotation is to experience an acce6j-*.l czfk,y)y8vum /vk fpf leration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylijw- z:s+q1si g)hia65vp2cno +5 pe hendrically walled "room." (pswjeiz5p c1)6+ e novs+h qa25h-ig :See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circlla:7fb xqbij9q);nqh,t i8s3 e on a frictionless air-hockey tabletop, and is heldqnqf9ih8, :i7xlbb )sj3 q ;at in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring th pd 7z7d,ifr4i-e5 viplyzs52e weight of the ball which dz2v7i ,yezlsp-iidp 45r7 f5 revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveliywe/z yp ;y*x,ng 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 massep;lt4r y /lq ), y3ugx85q;w0rt npuxas $ 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-n o+ caywj1l( 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 aa7-sk9t 4xwbg0( mneznd centripetal components of the net force exerted on the car (by0znxat -s bk(m9g4e w7 the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformlr0- j68 ylnu/rvbod mj 0i2t2f/gwy2hy 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 accelerationo2i2/ly h6r u y82jg/-t jdwf m0v0nbr of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal cm4iv:xp :xy)i94wge w k4ah 9h z5phm2ircle of radius 2.90 m . At a particular instant, its acceleri:gz5) mx 4p:k9v 2 py a4wmhheiw9xh4ation 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’ a m1 hr3afa5e+22j6 j7z-rypcfvkhg:s gravity on a spacecraft 12,800 km (2 Earth radii) above the eah1rya zr 2mg: kc256j-jh+7ap3ff vEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain poomc e-xspg 1-k,7o1vqi 04 pblanet, the gravitational acceleration g has a magnitude ovexmk04 cop7bi- -1s1 qopog,f 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1.7v/ykxe* 1g+pzg rx(e)4 kr/)z egvx1( * ey+xpg$\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 Ear2c:l8 ;d k3akkh dgw3n*k6oc ith, but has the same mass. What is the acceleration due to grl hdd c;g33:kckk*2ikwno86 aavity near its surface?   

  A hypothetical planet has a 0k;ahyb,e 5+sk ht:6 o nv;crlmass 1.66 times that of Earth, but the same radius. What ot60 k s5; ebh,kr;+anylvch:is g near its surface?   

  Two objects attract each other graviu9.n1mgdz(c7 hdvlm.; i gf6 rtationally 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 ch;*n+/8 d:b jx ,pnahrlovw/, the acceleration of gravity, at (a) 3200 mro+,:nj / b8/;aw nhc* pvhxdl    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthec.ut :9 tj8yc7za5sf where thegr j:sucfc5t 98.ezy7taavitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five ti pnmc*4 ucb5g,mes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on gnccb m*,up4 5this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average c 5mtvhx o-(3v3x 2jxx.oczv6star like our Sun but is now in the last stagexmxh v. ( jzxov5c-x32otc6 v3 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 weightl85s c8su -fhbless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calcub8sh8-csul 5 flating 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 side1c .+m )jc wc9z4ijzshr2jf0a 0.60 m. Calculate the magnitude and direction of the total gravitati+zchi4rc29 j1) jz .fm scjaw0onal 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 on9l hlg4hzr*x2ejez)o;) n4h7(a wo i ksue( 1s the same side of the Sun. Calculate the total force on the Earth due to Veg;es4u1 l4())j2sel nok(e*7wzrioa 9hhzxhnus, 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 surface of Mars is 0.38 0q iajs uu r(,5a)0lmxof what it is on Earth, and that Mars’ radius is 3400 km, determine the a0u sl5m,ia(xu)j0r qmass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using tzdrwuy)4wo5itew)fq+86) za l )w .q rhe known value for the period of the Earth and its distancqo5f)rww+z d4)ytl a w )eu i.)zw6q8re from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circuli+ fzrk1jng4p z89p5qar orbit about the Eaj5i1g8pp f4+kz r9znqrth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circu2d l5f3 ytxh.rkwj0 )wlar orbit 650 km above the Earth. Howkj d w)yx.3hwl0 5t2rf fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupal5(wqep q:8v a (y6qzpnts 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 revolution. (See Questie: w(v ly(6zpp5qq 8aqon 21, Fig 5–32.)   

  Determine the time it takes for a satellite,8*puxj6ey yh 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 euhp y y6x,*j8result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a s;u c kwf;5lz7vatellite have to be launched from the top of Mt. Everest to be placed in a cirwl;7kuv 5;fczcular orbit around the Earth?   

  During an Apollo lunar landin4a e 8km jxr3 h,q rsg/lqxsn*w0.pv*8g mission, the command module continued to orbit the Moon at an altitude of about 100 km. / *83epj.q*x h qvm4 ,slsr0ak8nwgxrHow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The i; hv/1nxd/wd mnner radius of xmh/v ;wd /1ndthe 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. 5–9). gnp ),/ fm1ymwWhat )wy1,ng/mfpm is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight ogxj;i7ys 91z3r 2 +eimdm-jscsoj+ 0nf a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movingm3mjc sjn9;-i 7ds+s1 ie0rx yjz+ 2og 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 cons9h 0gf;pn (q9 k ,rb48:p 1fhjlbqcqhgists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of(9c 9 qqjnrf :gp;1ghhh0plb 8kq,4 fb each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman ib7sj 7a.a*h mbn an elevator that mob b .hmaa7j*s7ves
(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 hangs38j9r5tfom1c wkj,z usi w7 1k from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directi tww1zs3 m1jkcro8kj597 u,ifon)? a =   

Show that if a satellite orbits very near the surface of a7 f dasfrcr2b)ysy 82: planet with period T , the density (mass/volume) of the planetsr2ya:r2 cdf87)by f s 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 thtvni9f)i4az ;uy :ks 9e period of an artifi v)9z:ka f yi9stn;4iucial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,101r8f;; t wsjsd0vsxfja 1ue orbits the Sun like0xr ;jffse1 s;u1awv 81dt0sj the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofcb y5d 24v/p3,wedn ro 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 ihdpyl539 sa9v4wjv44j3 mczcomes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.] 94hmyjcpis54 4l 3j9zwvvad 3    $\times 10^6$

  Our Sun rotates about the center of the jaazk2h; 9e 9oj(mx i0Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for t07v rj bwq+:wu4k-bqphe four largest moons of Jupiter (those discovervb0qwr: k j4-qwp7b+ued 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 distanckh,s/o: l,sb1zjb di7 e of the Moon. b1ssokhi: 7bd,lzj, /   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Keplgv)gs*brm)f nl*c m4x*-q i9u) r)n9gl *sxu*-mmf4qgbic * ver’s third 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 fragments (whi q :am ph4ndhfx3:,*z f1cr8ppch some space scientists think came from a planet that once orbited the Sun but was destroyed). 3 p* f:rp4xzd8qc h:amhnp, 1f
(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 artificialt5k v je ml3,sb:t(xox1s53 ju "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), 3t ( xveljoxut5 ks3j5s1:, mband 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 -.4 jh )1obgr+ulxkgh from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine,b+k.lh x1hrgo- )ug4j 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 surface will the acceleration of gravity be hkjlock+g4 hi4soz9 ol)a.u.y 2fta ): alf what it is on the surfaco.)cl4uaaik.t2 :l ogf4j h +skozy9)e?    $\times 10^6$

  On an ice rink, two skaters of equal massft+.o pav3m4e grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.8.to3ve+m ap 4f0 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration0 sto7(b ygfab(g12m bkls5( 3led*xx of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What frosyfxks g l270lgd(31*tb(mbae bx5( action of g is this?    $\times 10^{-1}$

  At what distance fromt k 8ui)hcy16q,f sr31 -zqjxc the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite ur6-k f1qxsy 31c,8qhjiz c)tforces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an5vm.zko k:* k9*m;v g ih,tdph elevator, it says your mass is 82 kg. What is the accelerationi:v;mozvkgpht,m *h*9dk .5k of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistk0 (y*pyq;+ 4lzcupic s of a circular tube that will rotate about its center (like a tubular bicycle t;lzk y+( p uycpq4*ci0ire) (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 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 lo/v7 o 5dkqdkef6sxky +ya88c6 t ua+p2op (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 ptr.n*i-tr5slg p3ls 1lanet in terms of its radius r, the acceleration due to gravity at its surface and thei-t llt*gsr rns1p. 35 gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verti.of.sc1ba;kjm z.i c -cal by an az.-omb1 ci j;s..fack ngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed ofz 2+jfk*iaja - If the coefficient of static friction is 0.30 (wet pavement),j i*faj 2ka+-z at what range of speeds can a car safely handle the curve?

  How long would a day be if th.ncz kvl m6bb ad(e-7(e Earth were rotating so fast that objects at the equator were apparently weidne-6z vm alb7.c (k(bghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distshg0trbitb*/zfh e+.xpb: 0 : ance 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 248u:tm6) x smaskvre(35 m. A lamp suspended from the ceiling swings out to an a)m 8mr u:xav6kes4s( tngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mq duw bu4,nxm jc:x7++assive 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 number of g 's a person would ec7+b jn+xu,4d m wuxq:xperience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced there3j 2vv11sjt presence of an extremely massive core irv2j 1 svte31jn the distant galaxy M87, so dense that it could be a 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 speed as it traverses the hill and valley sg; gtl) p1uf.whown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal tw)flgu gp1;. 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 (G2g.xths o9dzz+ )-gc jzx:n o*PS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on thejnd *og oztz) +xgh9cxs2z: .- 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 (Ngrdjv7-.ch;f x(xk 2rEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros isrr2. h7g(;vfjck x-d x 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 pu exsw m::;8vdzh: 1dxvrsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite : zx1wdvdhev8m:x:s ;(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) W6iag(9xig l w1hat is its mean distance fromlg 61xi(aw9 gi 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 need to be if you could actualld:qe: 3fvg2yb y "feel" yourself gravitatidg:v3 :y2q bfeonally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milg7lf d.kcd:i +0llr(gw4(j zs ky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the +lijfkw.0:csdzl dg rl ( g(47center $ \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 squar,wk l gw: r(: fnw,epe(b)mx9ie 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of theekfrp,:wm((g,:b 9 )ilwnwex square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ear; xr t,a0is vzgobz+3.th $ \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 th1w/ex su r fe)7qjounj9hc8 s 3/k1x0oe 1.5-cm-long sweep second hand oj qocfuj/hs xo)k1e w37r8/9 0s1 nuexn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start t ()o:tyv1 zl1igdk4yoo swing 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 0.50 s. What is the angle that the fisv( yy ido11 gk4ozt)l:hing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of fwet k,0n p:/ ;gkoa4xradius R in a new highway is designed so that a car travelp4 eaktx,fn;wo 0 gk:/ing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when netcfzeb 7h pfr,k4(uz 9ze6g(( gotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the nor b ,ree6kf79z(uzh cp 4(tgzf(mal 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.$\approx$    $\times 10^2$