Sometimes people say that water is removed from clothes in a spin drynws0 -mc q6w*yer by centrifugal force throwing the water s0-*qcw n6mwyoutward. What is wrong with this statement?

Will the acceleration of a car be the same when the cardw i: 38.f,mkhqi (wom travels around a sharp curve at a constant.8w,ofw(m mkq3 hi:d i 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant spp9 1x+u ci, x:;nrd:s8wlfmlz eed 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 between two hills, (wn 81:9p:xszcm +id ;x,fll ruc) on a level stretch near the bottom of a hill?

Describe all the forces acting on a c)- pp8a5ltms uhild riding a horse on a merry-go-round. Which of these forces p u-t lsa8pm5)provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci3ir6nxhg.zte z 5a;xlm-- mxcv.3 i2 prcle without the water spilling out, even at the top of the circle when th -mxe l5-tiz.vzhn2g;6c.px3maxr3 ie bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leasb zbeu2856 jo- mtn3yupy;xmfn+es*6t three controls in the carme*sp263m+ t6 5;b nbxuf-zyeyn ju8o which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small him8 /m*bae74g.-xmhghtvn 1ibll, as shown in Fig. 5–31. His sled does not leave the grx-ag17*ehm /g.8mth 4bnvmb iound (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 second law.

Why do bicycle riders lean inward when rounding a curve 6 ruy4wm,kf8gx mtj :,at high speed?

Why do airplanes bank when they turn? How would yoakl0u + pdgk66en-rrr su4 55xu compute the banking angle given its speed an5a6uk6s- rp5 0 kel4+rungxdrd radius of the turn?

A girl is whirling a ball on ao 8 *- /jue*xhao / abriydm3m:9+kowe string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the a m* /o3-i w+k a/r8 eouyjxom9bd*e:hyard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a force xpl8hghb (pdrjo)u-cyb 69(7byo cu8 gb-(pj 96( h7)hlxprd? Consider 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 Moon’s orbivh8) 6vg b.9gk,atrgxt be differek)gg v.t,9 gxha8rvb6nt?

Which pulls harder gravit8vep( r3da8/ek/ qu zqationally, the Earth on the Moon, or the Moon on the Earth? Which acceq(r du/ezev38/p kq8 alerates more?

The Sun's gravitational,qvu (i m9tn pe6t+: tx8*jzbd pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.ibj9t 6m8zuex+* :,tq(dtpn v ]

Will an object weigh more av0 n55ytdnx y6t the equator or at the poles? What two effects are at work? Do they oppose each other5ty 5xvnn60dy ?

The gravitational force on the n)c x2ppe8 8d2uy .splMoon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the u epd2n)p2 88.lpxscy Moon pulled away from the Earth?

Is the centripetal acca5q6g) mek f*heleration of Mars in its orbit around the Sun larger or smaller than the centripetal acce *6)fmga5hq keleration of the Earth?

Would it require less speed to launch a satellit8i* yvycr,x- s,di;c se (a) toward the east or (b) toward the west? Consider the Earth’s rotation dyi*s - cv;,c xs,8irdyirection.

When will your apparent weight be the greatest, as measured6d tab:6fp/e b by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free apt ebdbf6:/6fall, (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 lcav: m6ro g4ki1y+8yjong periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, w8ijyg4ockr ma16:y+vith 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 falwi76u l p 37rnh:azu4naryp68l” or “apparent weightlessness” between stpr3hal n6 i7w z4uun:8p6 a7ryeps.

The Earth moves faster in its orbit around the Sun in January than iuu :5ola703s ya2r rac2j8)+qw ykqtx n 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 relatiwco+q r2kaq: )uaur8y5xj37l 2a0 ystve to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expla0a; ,cnd b2gqyin how adnc,;gybq20 this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larg r*s ;2jypvke1;j8mksi v c-y4er than the Moon's. Yet the Moon's is mainly responsible for the tides. Exy rjv j2;kism;s1*4 vck8 pye-plain. [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 travelinp,9spd w j teyj/k*93rg 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 acceleratiodk(p ,ef: i7frn of the Earth in its orbit around the Sun, and r :,ek7pf (ifdthe net force exerted 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 21fsq,mjzoo: 5ee7; 7)gwuik h: 0 N is exerted on a 2.0-kg discus as it rotates uniformly in a ho5ei mj: of:gh;zqoue7w,7sk)rizontal circle (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 y oejvdt;si2;se7:5h d circles ;7ei d2s:h eso;t j5yvthe Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the ehw94a sxn;*nydge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm? ;4xysn9hn a *w  

  A ball on the end of a string is revolved at a 6 25ram2azcyruniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.2c aamr5 yz2r600 $\mathrm{~m} / \mathrm{s}$ 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 ckmi/ gn ln9y5hs8a as+zz* a.e5kf86turn of radius 77 m on a flat road if the coefficient of static friction between tires a6. 8f+yanncgkks5lez*a8s 5ma i9h/ znd road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be be4+oa 7yf vpy+w 5hoe:hutic-9tween the tires and the road if a car is to round a level curve oiapyt4 o:uch+5 y9v -wf7+h eof radius 85 m at a speed of 95km/h ?   

  A device for training asy3v6wgokf sx 6jy8ll c- (:kxza/1wiy30u3am tronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If th3kixvso8 f muj/l3 a66 -1z3w:ca (0ykglwxyye 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 axis3wywzl gfis7 2u3l/ 3v of 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 coefficient of static friction between i fl7 2zw3vu sy33wlg/the coin and the turntable?   

  At what minimum speed mustc gn:2i sp 3y0c72xlyr a roller coaster be traveling when upside down at the to0n 3lycp2girx cs :y27p of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driverl n8k wwrpo7w/b449rt o;sra;) crosses the rounded top of w knpa wr;48;t4wsobrl o/7r9a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel neediew.xzkon0-tp: gh+;syxw6e 1i81fzi ltv/3 to make for the passengersiileeznp;z +s/ v wt.g- 6 tixxo:h13yk81wf0 to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiusupjdl,z j+43hj ldnymt16vwmm t* * *8 1.10 m. At the lowestj8+1ydpmtl wudlz3hj 4 m* v*6j,mn* t point 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 rotat)u be.,hu1xzr)aip 6ve if a particle 9.00 cm from the axis of rotation is to experience an acvr 6h a.xbpi1ezu ,)u)celeration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people fw8wlyya4:d ; 5to /skare rotated in a cylindrically walled "room." (See Fig. s4kywfy5 tdwa:8l/ o;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 ro 29i yc 8+zo8ivne8ohztated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danglin+e88v zozn8i2 cyo 9hig 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 , precisel +dq a7po6vtj 2fln18 (rkj0em:og5jts dj u,2y this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mdaen+ ,o7k(ltj:j 8juvo0qd 2g15t s 2r6jm fpagnitude 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 forjo.n ks*x6vkkif 8alpfc2p) h9w6x07 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*447h +w jx;x orf9ofn5 djkvq $ 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 evabs:n zldz (3w4sive 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 tangentijl mdf+y,5v zh-c8vq-al and centripetal components of the net force exerted on the car (by the grohz d5yv f8,qlm+- jv-cund) 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 uniformly from the pit area, goi4lwe-: xwzsd b+z :ql;ng 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 wol+:s x- zd;bqwl4 wez:uld 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 /)hc tbfa0o)o circle of radius 2.90 m . At a particular instant, its accelerati/cft) )o0aoh bon 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 gr3cf95o*y-a dw jyvgw9avity on a spacecraft 12,800 km (2 Earth radii) above the Earth’9j9 *- a ywgfcwody35vs surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitatio xga16cy)e41 ;yue oyfnal acceleration g has a magnitude of 12 gyco6a41y u y1ef );xem/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 cz.ue6d;e 6(9qqz dfmys +2wc Moon. The Moon's radius is 1.7ycq scfwu;9 z6 6edm d(.z+eq24 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but u 29f l23jtfnqhas the same mass. What is the acceleratio 9t 22nfjfuq3ln due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times thb5x e1+5lhyunat of Earth, but the same radius. What is g b5h5x1eul+ y nnear its surface?   

  Two objects attract each other b 4h;d8cspf/s gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , tcaqcjz,7,1)jp f fxlgaj5h 0*he acceleration of gravity, at (a) 3200 m q xc ,fp5* ) ,0g7ahfjcjza1jl   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earths4,j .+ arfe p;.lmosq’s center to a point outside the Earth where thj.ss.mf p4 e;ar,lq o+egravitational 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 of our Sun packed into hw(uw.7qa 8bo moc;q-,uypu.q d3u z3a sphere about 10 km in radiuq 7w3- u .8yqqou. ,p;zubm3wc aodh(us. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an qaxr/: c eo ee+u4l:*taverage star like our Sun but is now in the last stage of its :qoxle /e+* u4 ca:terevolution, 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 astronau khyy8u4vstb7 z 9-jv4ts feel weightless 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 calculatin84 y ubvkjty-s9 7h4zvg 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--d +0hk:rczm9, vq7bne*xsls1uev p square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force e-m:7k x,r*sqsz1 +elnv d- 9ecbp0hvu xerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thec:oj6 ygto) o: a1oy7e planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are i67a g oto:y1:ec j)ooyn 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 ofrzw0(((.l) ncbj 7 wda4nlg dk Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the ma ngcda(wl wz)db(lk4.0r 7 jn(ss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the ;qs7:4fo /hymxo y )0 mrc*snpperiod of the Earth and its distance fromxs/ : *o yfmmo4p ;y)qhns70rc 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 movi)( s llj emin/ ybtjbg-0bewo(u:r:9) ng in a stable circular orbit about the Earth at a height of 3600m:nitllryeb0oj/) :(eb 9 w (bsju )g- km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit -a m*jo-31 -aom:kgewd ,mojv 650 km above the Earth. How fast must the shuttle be moving (relative to Eart-k3 oadj-g1 ,vm w-mj :oam*oeh) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants1,zjf tpk2r 1n are to experience simulated gravity of 0.60 g? Assume the sp,tj fr2z kp11naceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satelliu xtjs 6kf 4nkf89 :p-ngk7cu6te 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 -7n9cu gj8fk kunfx :6s46t kpEarth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the to /fh zmpd6i g0u4ll.i.v*5aor* r*i tlp of Mt. Everest to be placed in a circular orbit arou r*v0*iz lt*. riim.al46/ hgfpu dlo5nd the Earth?   

  During an Apollo lunar landing mission, the command module contw vjez2ta/9a 3inued to orbit tht29eja zwa/3ve Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The in lngid+g*g)3-pmyis 8ner radius of the rings is 73,00l -+dg p*iysm ng8ig3)0 $\mathrm{~km}$ , 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 jeh)ue8v,z(n diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a )je(, ehuv8n zperson’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of 3bb 0*3 bes hagasi72ia 75-kg astronaut 4200 km from the center of the Earth's Moon in aebas0*bgi3ahi3 s7b2 space 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 stas p, q gn-s+:b:uax/yvrs 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 /n:vbp+ygsxs uaq -: ,each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an enwtv i0zgj0 1.6h8hjmlevator that moven0wt6g8h.1h0mz ivjj s
(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. Tl y0llg36 48z p+imwpqhe cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directioi gp8l4mqpw36 zyl+0 ln)? a =   

Show that if a satellite orbits very near the surface of a s7+6ka xysky;planet with period T , the density (m;yy6x7k s+sakass/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 thedl8s) to; xk7t period of the Moon (27.4 d) to determine the period of an artificial satellite o8sdk7x; t) ltorbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only aj6* vn2jvzyb (yd w8)t few hundred meters across, orbits the Sun like the planets. Its perioy)2z nd8* y(vjbtwjv6 d is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distl rm yco5qr9v .b;n,d,ance 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 clov,kr*luk 3c94 i/ hfnyse 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 mean3/y *hvulf kic k,49rn 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 the center of the Gg n 19 o9m(czlk 7bgcbh2uk17clg7 rf:alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, periov-)l 6.im awktd, and mean distance for the four largest moons of Jupiter (those diskt-v lwi.)6 macovered 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 peu buuy:h57* 5 gze ry20at,o5jxjah3 ,d+tsssriod and distance of the Moon. tb5sojyg5hr*5 x 0ye+ uuuh,zs7jat:2s 3d a,   $\times 10^{24}$

  Determine the mean dist7zf1z1xi3w*yp 3gvlb ance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tapy wlvf 133x*gi71zbzble.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists ojw; ffp*k;t t78uryk4 f many fragments (which some space scientists think came from a planet that once orbited the ;w4 *;kpjftr7f 8ykutSun 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 fop9 c5-9/ ovzbyz+ 33acjbnlu srm 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 prub ln9o3a+3 5/vczpb- jsy zc9oduce 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 ez s5+6 jjc;krzqse;6 by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force oqerj;s+ej 5s c z66k;zf 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity b)zdk in 5+evj:. ut*wze half what it is ezdj)t+ v5 .n:izu* kwon the surface?    $\times 10^6$

  On an ice rink, two skatek4d8- emz ge9k5zk1e3wvijk (rs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assuwik(8kkd 9ej3 ve4-zzg 1m5keme their arms are each 0.80 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 dayc4o-z 28k/ujseza( (n4j xlu g, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earthjx(s/enz -u lz4ukj4o(acg8 2 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 fp s amvb*z:p5:rom the Earth to the Moon experience zero net force because:pa zp*5b:sm v the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, buwx)5e-pe 96on 6haiaut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which on h6)auwea6- 5ie xp9direction?     ----待选择----upwartddown 

  A projected space station consistq s:py9bg6d1lmdb+e z 9,7eq ts of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must sz6q 1,y9 7mdee9ldbtgpb:+qbe 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 ,/*4(fyds(dn sv rjcg6yt v/;rvpt .up;vkz -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 accelef*oh f p6)l6irj 4sic5gzqa 4(rati5pi)ls4crih(*gz q 4jo6ff6 a on due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from2 oeb up8olb g1+2 92kzk yk;gznpj5z+ the vertical by an anglugzgbkp1+ ok;y2p9znkzo25 jl+b 28e e $\theta$ 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 sb3mdzmr( -/x2lz; f ezpeed of If the coefficient of sf3z(l - m;dzmrx/bz2etatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a dayrfi8f-vrcj)a:2*oi.3bzjjbg,b+ rpj bf2p7 be if the Earth were rotating so fast that objects at the equator were apparently weightles3.vjabfr ro p,j:27bp i+*r2 igj8z)fbc j-fbs?    $\times 10^3$s

  Two equal-mass stars maintain a conspm6z(6v (n37cgi,yumh ngp8m tant 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 rounds j0+xi3irimz 2 a curve of radius 235 m. A lamp suspended from the ceiling swings out to an ang ixr0i i3+2jzmle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been e c0zix3/htl5claimed that a person would be crushed by the force of gravity on ac x3 lz5i/teh0 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 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 Telesrcam7phn7vu, 9 jt6*bp*v xq ;cope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whihxbq 7,;*ac9 m7tpnurp vv6*j ch 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 travebp*dij e(a+k8se e( 6drses the hill and valley shown in Fig. 5–45. Boebd(6j8a (sekipe d+*th 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. (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 amqkdi*9kkc2+ j5hvq + 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 a+k2 kk +dc 59q*hviqjmre 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 traveling 2.1 billion 3/;zx *ohcvucc ntu.jr.e kdm6d7i55 km, is meant to orbit theht 5 czv;uo ckm c6.ux5/n3r*id7.jde asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repair qwg0f5dnyzde 7 teeasia/j-,1z,u3 -. You are in a circular orbit of the same radius as t,-f/0yge wt7 a3,-s1aezi5qun ez d djhe satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a .xf wi 94ehtoyup--v2;hdv. mperiod of 3000 years. (a) What is its mean distance from tp .w-.-i24myuhoe;h 9fxvvtdhe 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 couldb 1 od2ca(ue4 yq-c-yibj6 wi, actually "feel" yourself gravitationally attracted to someone near yob--u, bq (wy c614ojc eiayi2du. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) 1a e. anx a -/qi3oswk*,;zxntat a distance oezaat n*q/k w-so,x3;.axn 1if about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at fuo1 l.0 a58hbscq4gtthe corners of a square 0.50 m on each side. Find th1u0 .at cqosl 548fbghe magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5dw ra (r4v tlcx5 2whlhw76+8i500 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 1.5-cm-long 6cld(15 vs5gw8gwweg 1fw gq/0s.wlw sweep second hand on your wrist watch? ws1ls g1 w.glw56dfgw/g5 (w8 0qvc we   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around o1 eci)7kox,wpw/6 eq qo;r5w l1ewv(in a circle below you on a 0.25-m piece of fishing line. The weight makes a ocvw;)1p6r woo(kw7l q5i,q w/ exe1ecomplete 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 newh:w 9f1qr9 essnunt3*m) n h;t highway is designed so that a car traveling a9srh3n h)fnqum;we ttn* : 91st 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, u9ky6t 4*jlvva tilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the fk9ayv jv*lt 46riction 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.$\approx$    $\times 10^2$