Sometimes people say that water is remod-,f )a j;evphved from clothes in a spin dryer by centrife,- hfp;a v)djugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car /bkfrh 7)t9+w;vm b0 efnpi*otravels around a sharp curve at a constant 60 km/h as when it tr/9e kf)*f +oiptmbnw7 h;0vbravels around a gentle curve at the same speed? Explain.

Suppose a car moves at (ta0 j, b i-clwvphi.g w,.*yrconstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip bet*rg, -i(ba0 cpw. jvw.,ilhty ween two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child rwqd/mnnae*:) hn/0 8qwfv n,kiding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratiade* /08nwnw , q)nvn/:mfqkhon of the child?

A bucket of water can be whirled in a vertical circle without the water s6+ejds y89tx5pvhq 2 dpilling out, even at the top of the circle when the buck2+ tv5jqhd8sey 9p6xd et is upside down. Explain.

How many “accelerators” do you have inch).2k9 frq;mh t6u zh your car? There are at least three controls in the car which can be used to cause the car to acceleramh6kf) r2uch . zhtq9;te. What are they? What accelerations do they produce?

A child on a sled comes flying over the cqd)f6jg avi)bxhdyt30 - 2j0zrest 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 normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s s qj)h 0vyaidgtj)3zdx -62bf0econd law.

Why do bicycle riders lean inward when rounding a curve at high spee uphj2a) tyz ct*r./*id?

Why do airplanes ban; u 5wvqbd5luk7-s bpm.oyy/6k when they turn? How would you compute the banking angle given its speky -bvu lb 6m;qw/7.ds55oyu ped and radius of the turn?

A girl is whirling a ball on a string around her hea3-ug ;e8+*8q .tp dqlwczyw jqd in a horizontal plane. She wants to let go at precisely tq88z3qe l-. +upcg q*w d;jwythe 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 yy *gf+wfqr 8/z 3xfu-on the Earth? If so, how large a force? Consider an appleqy *3y+f-u8gf f/wrxz
(a) attached to a tree, and (b) falling.

If the Earth’s mass .nb8hr. g e2).jsz(dajoyi k3were double what it is, in what ways would the Moon’s orbit be dibajn)(82 .zridj.yh3e.o gks fferent?

Which pulls harder gravitational5 kmn25.gpnud ly, the Earth on the Moon, or the Moon on the Earth? Which accelerates mokmn5d2 ugn.p 5re?

The Sun's gravitational pulpwfz(b*o*ye27 k ink: l on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to t2ipow**(bzkf: ky ne7he other.]

Will an object weigh more at the equator or at tq:d5rq0/w0 6; e/lzwqyxnxzche poles? What two effects are at // ldqzx qw zry;exnq65w:0c0 work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half tz.4 e1;ddh l(+boxtq4 :fksxy38rb u dhe force on the Moon due to the Sun. Why isn’t the Moon pulledtzqdso:l 84d.x+byb(1fkdeu xh 4 3; r away from the Earth?

Is the centripetal acceleration of Mars in its orbe4r+jqs s2p;fit around the Sun larger or smaller than the centripetal accele+e 4js;2qrpsf ration of the Earth?

Would it require less speed to launch a satellite (a)do,yt 9yqmd+zh/4 dl6f(h w )t toward the east or (b) toward the west? dd)t(tfz+y hm 6dhlw4qoy9 ,/Consider the Earth’s rotation direction.

When will your apparent we:uf* blgmd/.ng06mhua5d-vjzh( . c81ymnxz ight be the greatest, as measured by a scale in a moving elevator: when the elevad d51gfg mmxvz/a0u.z(n * myclujhhn.68b:-tor (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?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adveud*c.;jjjv+ yuoagj4 fmne 2q a, ,z-*rsely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, witmad ,gf,vou2ae;j *z- jyjuc j 4+qn.*h 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” o9r)mrcj1y1 8aimy y7ur “apparent weightlessness” between sty u) m8yr1r mc1ayi7j9eps.

The Earth moves faster in its orbit around the Sun in January tht3iwgj d) g,-neg20kj an in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in,t)3 0d2kj gni -gwegj 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 until l hnidg(z8)4ceyz624g ir/qcit was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mas lh e4rdqigz(n826z 4)/icygcs.

  The Sun's gravitational pull on the r xcg6+*3(kaza 4kptzt9ruhr2yh4;f m xz3/lEarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravkxt mlhh *azkfc3r4upr 3rt;2zyz+9(xg /46a itational 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 1xs(-,dtlnnac+ n2 6g7mstdf 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 aro:hjgy(k o hew299uv v6und the Sun, and the net force exerted on the Earth. What exerts this force on t( wvh 6e9ho9k g2jyuv:he 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 on a 2.0-kg discus as it 05c0 mvfkjuw wc8 )c8d/fr sk(rotates uniformly in a horizontal circle (at arm’s length) of rad dvjc)wu( 0rffm8/ks80ck5 w cius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in or/1ymqrdida:/rtuix a4c 0n; 8bit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acced nar xq/m;a8dyc:iu 4t/ 10irleration 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 ond1vj(8 b j)smk the edge of a potter’s wheel turning at 45 rb8jk m(dvs)j1 pm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uni;re y0 vg9b,ytform rate in a vertical circle of radius 72,t b;vge90y yr.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 round a turn of radiuix:qaf d+tyc g:; uz 6hu8,2ous 77 m on a flat r iyh o8g u:26uta,qzx+ud;fc:oad if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and tuz7u 4( (jetiuqae62 khe road if a car is to round e e24ukit (u6j 7a(uzqa level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and (ik bzi1yie+ n-fn6: z)j fsb-jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times herfn -i i-s+z(yj1 nib 6:)ebkfz 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 tudyv8gv c86o*i rntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction betwec88vo d* 6yigven the coin and the turntable?   

  At what minimum speed must a rollmg3we69*;xc0 hcqzzz er coaster be traveling when upside down at the top of a c3czze xcq hg*w z690;mircle
(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) cross1.de(3s5gsdmwc: b)zdg zbq3es the rounded top of a hill (rad5g wdse) qd( gmbs3z31zcd.: bius =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-dia2ettf j)at 3;d4qjx3xh .ro;a meter Ferris wheel need to make for the passengers to feel “weightless” at taxxe;t)2rt33 ;hqd.j o4at jfhe topmost point?    rpm

  A bucket of mass 2.00 kg is whiri4z7pr2w ah, gled in a vertical circle of radius 1.10 m. At the lowest poi7igzwr 2a4 hp,nt of its motion the tension in the rope supporting 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 n upn *,ji 1uswhrl arkfsy:0+g:u:i7 v1+og+cm from the axis of rotation is to exov+h r ,k ugssw+:n lpfi+*ayn0uiu :1:r 1g7jperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricswk3iz vm0( lwh4xpn)t8+7beally walled "room." (See Fig. 53 )h7 iw+xzkmst0 l(be nwvp84-35.)
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 frictwt0x3 eo0pz1 mionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block p0 x1t3omwe z0(mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of t/ia-h5ze( ebfjol5h c4 *lv,t he ball which revolves on a string 0.600-5h*/5f(ble,e4lvztcioj h a 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 travelir.xs/+2nl td:q /ublqng 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 fv+nk8 /eq4vo $ 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 52j3 q h++ppfpbgv,yf 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 centri + d+e9*oj;kgc hgrr4ipetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 1g;i4r e9+ j*rdh+kcgo5$ \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 3 06f+ iem lu)my77yn-s itc:l,gvptfpit 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 were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acug 7il)mf lciv e06ttyfy3sm- 7+np,:celeration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.4bunagox7.wx2j4 c9a 90 m . At a particular instant, its accelerationobacnga. xw4uj 2x749 is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Eax 5js,- /k.x9a ysugbfrth radii) above the Earth’s surface if its mass is 13bx9 ay-,5x.fss k/ ugj50 kg.   

  At the surface of a certain planet, thes;:dd ;h4qudk gravitational acceleration g has a magnitude of 12 mq4dk;:;dsu h d/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 radiu 3q45,bha dh-f wpd(aghs2 rjkh*2k.r s is 1.74 ws2kqgd2 354 hkprhja *.(fbha-rd,h$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planetb+myp:q x1zx xz0e *hvdm1w60 fz8w-q has a radius 1.5 times that of Earth, but has the same mass. wxh1pqevy- fwm +6zz z81qd:0x *m0 xbWhat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same jvz 5tw9k;c,h*:8i4jvzzk u qradius. What is g;tc:5qhk 8z v*kw9u4ijz vz,j near its surface?   

  Two objects attract each other gravitationally with 1 oiiml pyqy, d,6ah32a 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 af f(0b.f+hzkg , the acceleration of gravity, at (a) 3200 m k0 .f(f+fah bz   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where.*o5) oj/7hacc kn-p xtmgxi 8 thegravitational acceleration due to the Earth ia m 8o)nxcxi7 -p5tgc j.h*ko/s $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed iqz0+oeaom z4 8nto a sphere about 10 km in radius. Estimmo84qoa z0 z+eate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star z(e:jqq2jttau86z: x like our Sun but is now in8jqt(ez: ax:j 6zq2tu the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feueu.mzi.. g6 f:r*o og63q bunel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lo6:gn g. e.io*uu m 63zobf.qrut 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 sideuvqw -w)t5r 4p 0.60 m. Calculate the magnitudw-r p)w5qtuv4e 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 yearbxjsb+/zws ik:4vc2+ s most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, J24 ikbsz+: cb/ vwxj+supiter, 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.k /9h3eemm/bj38 of what it is on Earth, and that Mars’ radius is 3400 km, determi bk3/emhe /m9jne the mass of Mars.    $\times 10^{23}$

  Determine the mass o ea 4/ sjdgsa:j: thnz(v-4ey+f the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s :d sa e a/jzhy:eg4+j(sn-t v4laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satel;y:mh8n0x glelite moving in a stable circular orbit about the Earth a8lgy:e0x;hn m t a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above tjst2q /z*d lq:he Earth. How fast must the shuttle be moving (relatjqld :z*q 2/stive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate 8b8 h+/hl1p myiy xj.wa 0lym+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 revol+ 1l.whilymm/0pby x+h88jayution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to p )al5pci36tjqd9p ki-0l upnu44 4q lorbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is qk5iq04ud t ucil-pl3 nplp6)pja449one 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 would a satellite have to be launched from trht. jbda wr/9h8w *c;he top of Mt. Everest jacb8; d.whhrt/9w *rto be placed in a circular orbit around the Earth?   

  During an Apollo lun*qc6x; s-abs bar landing mission, the command module continued to orbit the Moon at an altitude of about 100 ka* bx s6c;-bqsm. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of 3ts*re onpa4l( krk7 .chunks of ice that orbit the planet. The inner radius of the rings is 7s. n(*tr3 po lk7eakr43,000 $\mathrm{~km}$ , 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 p;kp3p 9lvgog 6; 5nlus (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight ( v6p9 oklppug;;3gl n5a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg .uekyq 4)djgju9h ;gg;5 a5tw astronaut 4200 km from the center of the Earth's Moon in a space9g5) d4a hwkgte5 ;uj ugjy.;q vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal 2xciij a9ct2m3(gw1h mass. They are observed to be separated by 360 million km and take 5.7 Eart hct2i3w9ga i(xc1jm2h 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 weight of a 55-kg -/ow k +j8r ys/eet+tzwoman in an elevator thazk/er -jweyts8t /+o+ t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspendj m,hoh4 uqg+dbe /7+eed from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevatorm,bdhj++eo/g7 uh q4e accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very nea,d 0be l. v62u1 hfbucecx60 *zn5jkour the surface of a planet with period T , the n .ec50e,coub v12uf0b*6j xhdzlk6 udensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (i 3 2gl1m*,fz7sacdaz 27.4 d) to determine the period of an artificial satellite orbiting very near t31 a*cl,z2 zfd7igsma he Earth’s surface.    s

  The asteroid Icarus, though only a few hundre0 8tb) o py(2eiae3fqbd meters across, orbits the Sun like the planets. 8eo fab(3y0b2)qepi t Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of x:ggb.4.hrs zbg( /v x4.5 $\times 10^{9} \mathrm{~km}$ 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 yez+ rlq;-u, qlqars. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbq, -uqrq llz+;it 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.]    $\times 10^6$

  Our Sun rotates about thee yt+:c s5imw2 center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moonhi8 l+um+zsfs d8 ;;bd,opg *os of Jupiter (thodb,lf sm+*h;dg8i opo 8;zs+use 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 know j::vgh)whsxf/ /4saxn period and distance of the Moon. )sh/:hvxfj ag/w4 s:x   $\times 10^{24}$

  Determine the mean dist z7( wdh/f/lfsance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the dist/ swd/ (7ffzhlance 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 ard9,.l -t5tfl 2j kqt8os xo3npy2gw) nd Jupiter consists of many fragments (which some space scient w2- ttsx)kyl,gq89oftpd3j25.n l r oists 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 form of a band cha*hb)0 1cfne82okq nompletely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period0q*8e2bhcnh 1 a)nkf o of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an ar 7y1lyf /by fy7f hjf./e9n.tcc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His massffh9jbyfn 7f.y/t 17e yc /.yl is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface7;vh7ee mtoejo/iw ( 1 will the acceleration of gravity be half what it is on h t(o1;w eei7oemj/7v the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab han4gs8y iv0p1ix(i7jc dds 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 mas(idipj0 v48c1 sgyxi7ses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerationo/nwx kp91wu+ of gravity at the equator is slightly less than it kxn9/ow+ u1wp 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 dire 8nfl2qm, x.vjctly from the Earth to the Moon experience zero net force because the Earth j.mf,8 2lxq vnand Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathros.mzn n3bd96;b1jf e1snh+nwom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in w 9mn h3. 1snnef6zbn+;1 swbdjhich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abolb8wp 5 qvg.wd gpr+93ut its center (like a.p3+9g 8brpvwgq 5l dw 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 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 0 z.x4x6b pmn(djitk:aircraft 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 ofomxf2j u6 r,+il,7yg-ml k+ef its radius r, the acceleration due to gravity at its surface and the gravitatioil+, x2o-u6rmfykj+emf 7 g,lnal constant G.

A plumb bob (a mass m hanging on a string) is deflected fro2hmc2s ah67 wmm the vertical by an angle mh2wsh62ca 7m $\theta$ 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 *uovsz.8 jzl( qns/ya ev 5);qof If the coefficient of static friction is 0.30 (wet pavement), at what range of speedsy/;zvos8*e( )lauznjv5 s. qq can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obj h jrc4c9 )2mpsim* gb.vb+8qtects at the eq4it ph29b cg*mv)8+.mqrscbjuator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars s0h;2 dw (e ohsz+u7m+-mx6fo3ieyw cmaintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed)xmg-z8ab8pt381wgkqp pj s/d za:(h rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to ahkws / 18 g(zpxgqtabdzp-8): mja8p3n angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mzki,i +yn +o- p)uz.jo:bw299jub gtkm o*/ubassive 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 experience at the equator of such a planet. Use the followiby):u9 wgk b*nmi+ 2kiu.-zjoo ztu j+ob, 9p/ng 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 the pre j1o4ini.w.i gsence of an extremely massive core in the distant galaxy M87, so dense that it could be gnwj4i oi.i .1a 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 hih)9z u*a 3hfdo3nx/1kyh mj5oll 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?) Eu/h3 9km)fh* h51o3 onxaz ydjxplain. (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) ui6o f q019 da64tcoaactilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” ctq9adoi a0 6of61a4c 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 Rendezd)hxt :s iqpas) ;q,ldy8x2rmy61ie9vous (NEAR), after traveling 2.1 billion km, is meant to orbit t) yidi 2p a 9eh),xqm6xls1r:;tyds q8he 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 pursuia sf 7ise:+z)dng a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 ds 7f:+sz)i aekm 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 perioy0;x7 n9k iwkb u(1ujiyg82pid of 3000 years. (a) What is its mean distance from the Sunby;kxn0 juy( w1 k7ugi9ii82 p?   
(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 woulwy9)7vc(h -a ucq0kaed need to be if you could actually "feel" yourself gravitationally attracted to ) wcaq-a( 0y9cuvh7ke 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.+aqkg ihy* (cw+jwx9 Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center qycj 9akiw*.h+xgw(+ $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.5ql g-8tn376vic -ttvm0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kglc gm8-t -tiqtn3 v7v6 mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth)ew8(ycnqsp2*y ua/*h;wxb7d rs(bu $ \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 accelera -v+zn :79zirr bovxzm(fuf,/eh3 wy4 tion experienced by the tip of the 1.5-cm-long sweep second haumofz f(bxz/7ivhv9ry -nr: +,w4 e3znd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to s x2l4 8x5lguq 0gt3ajtg0(pliwing a sinker weight around in a circle below you on a 0.2x8xit l20agpql 0lj t5ugg43( 5-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that ds1qi; (1 3i j;g3 vooajt-iygzp6hf+a car traveling;t+3giiazp 3di6yojs(- ;1 q ofvhg1j 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, pak:7ra c 1te.+7ocv x3 jl9ekthe Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to prove37cea9k .cvp:1rl7k o t x+ajide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$