Sometimes people say thcl50.dz,cul rat water is removed from clothes in a spin dryer by centrifugal force throwing the water out0 , d5cluc.rlzward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a shar pc t b5d92im0nc,js2f3op6 pvp curve at a constant 60 km/h as when it travels c 9sbo5p2pc3 tn imd0 fpj26v,around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along dzspb8bv *0: 83nchpla hilly road. Where does the car exert the greatest ab08sp *dhb8 3:lpcn zvnd least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forcess ci81fg4fgpep +w44u acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration opu+gp sfi e 4c48w14fgf the child?

A bucket of water can be whirled inxnm+yvvjh. 3ysd. ; pq5b9u +n a vertical circle without the water spillingbn+5+ x3;9y jvm.pqh.vyn ud s out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” d f pgeg-lvk)+6ih3gdjpiq3( fj ,q*0r o you have in your car? There are at least three controls inqk3j dvlh,)j+p rq063fgi(i-eg f * pg the car 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 hill, as shown in Fig.plll8tv;zf -(k0;0, rp 4dzxy hidf(q 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 Newtonpt;rv08(;z q4 x (-pi,fldyhlldzkf0 ’s second law.

Why do bicycle riders lean inward whey2zwprjkd 9q +ysidj, m0k 7,9n rounding a curve at high speed?

Why do airplanes bank when they turn? How w tef(i1 yjcl8cej2s0 gi4;+suould you compute the banking angle given its speed anl2u ityf (4;ecj ij+sec 0g1s8d radius of the turn?

A girl is whirling a ball on a string around her head in a hofqo f5lgt-r8 1+*qmgtr8go ;x rizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the t m-gxq*18r8fot fq5l+ggro ;other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force of*bq )8 lc: s9 lro0lj43aocpjn the Earth? If so, how large a force? s* 4 lbrj9l )ccq:8lpfoo3aj0Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wao ,qx be*.we0xys would the Moon’s orbit be differen e xoexq,wb.0*t?

Which pulls harder gravitationally,lfzw9 .(nm a5k the Earth on the Moon, or the Moon on the Earth? Which accelerates 9.akmwz n(5lfmore?

The Sun's gravitational pull on the Eg q)*:zb xbzk2arth 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 th*bkgz:qx2 z )be other.]

Will an object weigh more at the equator or at the poles? What two effects ared j4c93pbadj mo1m5oe0w *wa2 at work? Do they oppose each othe3jcpowa*bwd52da 9eom 0m 41jr?

The gravitational force onb219 zmoh: xihel .+kr the Moon due to the Earth is only about half the force on the Moon do1z2 i hxe9m+.klh: brue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in z3,zbx*jw ;y1w dvn9vits orbit around the Sun larger or smad3zxw z ;nyj,w*bv1v9 ller than the centripetal acceleration of the Earth?

Would it require less speed toi3amed7/z.a 7t* cecl launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directionce7*c t3amile a7/ z.d.

When will your apparent weight be the greatest, as measured by a scale in a msd6dky7mx c (mdq)k+ (oving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fsm)k7d+x cy( mdqdk6(all, (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 adversely affected by6cdw(edi:vh+ weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts vidd 6+(we hc: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/oz e7u9n-da2x ge k,x fall” or “apparent weightlessness” between steps,9 o2xzgnx-/kee a du7.

The Earth moves faster in its orbit around the Sun in January thap 4wp4i m,qb8pn in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in p pi,84b4pqmpwroducing 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 it was discovere3h:qzs;+ 8afw d2ipwpd to have a moon. Explain how thiwh+ w:f2; 8sapidz 3qps discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largerji1/ :hccpdn vg( 6 6e)e92 mgfdjpr3b 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 th ec(jn )9c hpjdg/vedi: r6mb62fp 31ge 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 19pgt6xf0d+3z58e tu jx80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eamh ,hxwg bu.jk2.v:2q. ;dverrth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this fo:. jr2gwuh vq2kbme;d.,.xv h rce 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 on a 2.0-kg disc8tbzzzsp oj2o 8t74d8n od6oxo (5bl4us as it rotates uniformly in a horizontal circle (at arm’snzo ood888sltbb (44poj6 tox 7z2z 5d 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, mc9lm 3b*i1myand circles the Earth about once every 90 minutesyml i 3cm1b9*m. 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 edge of a r.u45vmal7 b-m cmw+rpotter’s wheel turning at 45u .lrw45mmar-vc +7b m rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a-o2 6geoo)t-zz 0wo/ tr t3bdk string is revolved at a uniform rate in a vertical circle of rad0d) et6t wok-ob3z2/to- zgro ius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can vo6 ;m kul-9:*ipoqx. ;ppihyround a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mam.h;l vixo;i6pu-9k:ypo*q p ss of the car?   

  How large must the coefficient of static friction 2ra* tdt xa ew4t7jw98/-ywksbe between the tires and the road if a car is to round a level curve of radius 85 m at a speed 4*9wd-rej8wy a2asw/ tkttx7 of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed re 4h- njzo/r 10edw4ato 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 her own weight, how fast is she rotating?e 40hj4w1a/-r no ezrd    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 ro,gahz 00a6paz,5d woog*k9e ts)/ lwftating turntable of variable speed. When the speed of te0 )o/agdl56wpah s,gw zzf* at0o9k,he turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down ath9 s f,r e9uccrayfv 1i59a(8g the to,(9 eu 9haa51vrfgfy s 9c8crip 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 dv e+:p4y)rde j59oahiriver) crosses the rounded top of a oj)+dphyer iv ea954: 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 aio go6 d/l 8jqbv6pr,f2ux5+h 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the torgvb xplj2/6fu +o oq56,dih8pmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.hz6(b 6 vvoe(r j456yzimnvfua5e*+k 10 m. At the lowest point of its motion the tension in the rope supportv(*ozye f54v66vk in6+rh5mjezba( uing 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 cennj9 j 9*wms3 ,tzx3dydt:*htz trifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of,n9 tjhtdzzm3*d yw9 x:js t3* 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnq-rr :x (a 4z(p91pw) pyobqjbival, people are rotated in a cylindrically walled "room." (See Fig pparb (oq-b9 qzwpr()x4y:1j. 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 bb2nm/o01vpv ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (man b1/op 20vbvmss 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 , precisi:f 9sxdvz -9j8vaj9nely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. Ijnax 9v- jvdz9:98sifn 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 travelinye/,pw9c7;liizku wbx* -z/q g 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 massesx5t 7uzjz m36n9of2w t $ 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 vert tujlm1. zte::ically 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 tangenti59 1o zyp 5emn/5sg/ m r0nenbyld7oc/al and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when // gsy505mo 5nye1drn l9e ncb 7m/zopits 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 pitc. jg ql2vjt)+ area, going from rest to 320km/h in a semicircular arc with a radius of 220 m+)gtvc j 2q.jl. 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 acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a hor1uvw m)0d-wzr izontal circle of radius 2.90 m . At a particular instant, it r)1zw- uv0dwms acceleration 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 g-ofnkvu a+dw 94c. (ksp4.j tvravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s vp4 ndo.(-j9takfwv .k u4cs+surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g ha2q r f;-d -s(gnddzcm;a6 9mips a magnitud sf;(p m 9rgzn-6-d;caq2id dme of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravi/aed* svn 1i,p/g0j 1zhn ssp7+t5hraty on the Moon. The Moon's radius is 1.74 ,pt n 5zea*s s+ng/ d0hshi7vpja/11r$\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 has5mqe9nl /afjq:zx zgm4 0gk4cm7v8 p : the same mass. What is the acceleration due to gravity near its s q0m a/ keqvngx :4f5zm897pc:l4jgzmurface?   

  A hypothetical planet has a mass 1.66 times thathhgez,6* 7xvj(xccry o8 /oy4 of Earth, but the same radius. What (j4* h,vcyh8 /ozgc76yoxexris g near its surface?   

  Two objects attract each other grukggk kq 6d(ku w*40g;avitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accytt . c;wtpj/4eleration of gravity, at (a) 3200 mw/jy t4;.cp tt    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from thjbos//clp ,,i8 oag *ee Earth’s center to a point outside the Earth where thegravitational acceleration due to the E,l a*8i/ ooebs/,pjc garth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times th6kanagftg+ l,) fg: /ve mass of our Sun packed into a sphere about 10 km in radius. Estaa/ fg:6k ),flg n+tgvimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf s.6zrzouj m rq;+r,eu:tar, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface grav;r.u e:6r+z jumqoz,rity on this star?    $\times 10^7$

  You are explaining why astronauts feej4w8g7a7 :czkb2nkmsp jj gic- ,13xql weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker upg n24skwg ji8ka1cm7,-3zxjp 7b cq j: 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 locatmt0fi3 (b n ypzc/hb9(ed at the corners of a square of side 0.60 m. Calculate the magnitude and b9/hz3pbmnic(y(f t 0direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the a7zvb- -9duvv Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38)9u--vv azvb7d . 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 gravityn/x6a r*w+4 ii 4x68vz fqjjka at the surface of Mars is 0.38 of what it is4jqvi xjz*rk4w6 /8a n6ixf+a on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value a24ol ;zyj;n ;d2cumwfor the period of the Earth and its distance from the Sun. [Note: Compand;;uw2;o m4cla y2 jzre 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 circular o +4vl+jegqvbh/p q ;5irbit about the Earth at a / j4qe hq5++vblig; vpheight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above th ptr;zb5f e zf/ /ru0x8m1ilq7e Earth. How fast must the shuttle be moviz 85ei1f0qb/mr x;f7u/rltpz ng (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience yv:ya;*lv 9dyd82)tsd05 /yl ww jlyisimulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution2 sl t5 0wli*ywv yayjyy:d d9d)8/;vl. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to or8z4qg3c42uhxh/nl h+ ebn t4jbit 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 result depend on the mass x/h4ech2n 8 4thnzql+3g b4juof the satellite?    s ~    min

  At what horizontal velocity would a satellite hav3i4p3islfwv wj.d.3d vg xm* 2e to be launched from the top of Mt. Everest to be vf3 2d.wip*iw 3x4 gmvs .dj3lplaced in a circular orbit around the Earth?   

  During an Apollo lunar landing .tt9.yuep:n28 yn4xzdpbn 1 p mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Mopby..1de9nnn2y 4ux z tppt8:on once?    s

  The rings of Saturn are composed of chunks ofymi2wfo+26;kn z mfvc77ou0 a ice that orbit the planet. The inner radius of the rings is 73,000f cm22iw7yu k0o anmo6zv;+f7 $\mathrm{~km}$ , 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. *bfmb9 r xxbrz+xf(/s /v-to45–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, an /xsrmr o9v* b/fbx-tb4x+( fzd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cofga+; ;v vt+wenter of the Earth's Moon in a ovfgv+wa t;+;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 star 3pnk u5p1by-nh+cp- as 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 b+13p-p -uk5nn bpyh caetween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale reaz*+fr 2qz8sr3h5: / 3ltiwdt)iz+-u vxdmai yd for the weight of a 55-kg woman in an elevator that m)r*st /hwl-3 f +xd+mai 2z 8u3yirzdz5vqi:toves
(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 elev- c)kx2.n ea+iw x a;nvgr64t 6un8osyator. The cord can withstand a tensisgta 8 n) nwx6ecr.k iu-26ny+ovxa4; on of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periodt-b;(9 qyo uec :f:ckv T , the density (mass/volum e:yut vok:c9bf -(;cqe) 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 o z0qx; cs/v mdl;7fw0ahjd+m,f the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near theddaml ,x vwm/h ;jc0s0;f 7zq+ Earth’s surface.    s

  The asteroid Icarus, though oscer :j) o-7ahnly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its meaer:a)-oj7cs hn distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of gilvlbceu tk*0 -;e ryc -1d:74.5 $\times 10^{9} \mathrm{~km}$ 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 eytd8kkg5f xr3-9s pbi,xo(y, very 76 years. 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 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 fab8y,is f-yx tkgx 5k(d9 po3,rrthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gogkns+ 8i8d;aalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 fouzssxmz 5k * *e;k-yzqi ofjo;3qj0(8ar largest moons of Jupiter (those dij(z qxa3o - 0z ;;eyosqmjzs*kf85*ik scovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon. -qaan;wg.v xyx)sms 50lmoyz )t/6h 5 -gy x nv05;a x mq)ao/.myh56s wst)lz   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kelx5c:qq/ ecu0 +z e:5biyxs( kpler’s tc lq5cxb:5qi key0+(u :s xez/hird 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 x+d8 l bfzcftck)i28g-o.ys: and Jupiter consists of many fragments (which some space scientists think y. t:zff- 8k xb2+) lcsigc8odcame 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 9f rs6oxqk+2wform 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 t69xfo kq 2r+swhe 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 period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc frommgv:xnckp2* id+ fl :b(2cv ;b a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is thncdxm+cbli:vp b (:k;f2v 2g *e 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 half whu/x/w3h7bwkqs .tz x1at it is on the surface 1 wqb.3/7hwtskzxx/u?    $\times 10^6$

  On an ice rink, two skaters o6:e xl;ywann,5 uy4ss* l )q x57btcvmf equal mass grab hands and spin in a mutual circle once em:6xayt4,nl*5y ucex5;)swnsq 7 b lv very 2.5 s. If we assume 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 day, the aex 7,t ma m42dk1b/vbvpparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t ro /12mmva, 4vbe kx7bdttate. 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 fromdtdkx.h* , efgph7e t 9/ok4o) the Earth to the Moon experience zero net force because the Earth and4p/)t7dtk,k xg9eho d* .efoh Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathror-yb;l -w+s d07b kwdwom scale in an elevator, it say s+bd;k-7 -ywrb lww0ds your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate t7f5 si h iafy3mjd412about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of th dm1is2fi3y7h a f5jt4e Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft 4c (3c4odp+nzsr rdk* 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 t9 lnpk w(hni rt.(b;2a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitan.9(tt kwln(iph; 2rbtional constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by abs5 l ka0cmg2r/jj- n1nrb5l - k j10g2scjm/an angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for ayo8r9se oei. + design speed of If the coefficient of stats.e8 i9ero+yo ic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the eer,mzk qc 63-r*b.f nuquatoe-f3 .br*mqcu6 ,krznr were apparently weightless?    $\times 10^3$s

  Two equal-mass stars may (ne/dr mrz*5z-xj8bintain 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 rounds a curve of radius 235 m. A lamp syypi c tno,yyk34s) 10uspended from the ceiling swings outikt cyop)1n y ,30y4sy to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Ear fn:rv0mf9zq3 th. 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 :f9vr fnzmq3 0the 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 deducjwta r dlm:ck ih37;;4ed the presence of an extremely massive core in the 7 tl 34m:kcdarj;i;hw 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 kr 0isp5, v adi1fd/+:mcuttr;e-sb; as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a: r;tp0 e;+ssv,ki itaud 5-f/dbmr1c 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 (GPc cldrfwzdc;c,i0-/42x xe6kt 3kt,u S) utilizes a group of 24 satellites orbiting the Earth. Usi/4 fldc20c tkdcwut,ir3k ze6-,;xcx ng “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), m-3p ax4jwp ;pafter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a heigxp3-wm pp4ja ;ht 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,)d/n;ii.j ; hf zlpua need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth),fn/i a .dup;)lji;,zh 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 4v1e euss8,gj period of 3000 years. (a) What is its mean distance from ujeseg 1,48s vthe 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 actually "feel"ji;qf*u k iw fojozwd-;ibj+t ,0,: q* yours, : 0uwi j+o;qbzjiik-*tj;fdo q *,fwelf gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the08gybbb b asc 9y4xc7v89o)ve center of the Milky Way Galaxy (Fig. 5-46) at a distance v4c9 9yogsea7b 0)bvx8bb8ycof about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners-9inua-/mn ;jt )pb hsyz r0(l of a square 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 trpm)z9( t-nn-b0 ja/ uyslih ;he square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg oqh9ud r* z3m5crbits 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 sweep secondo8.7st6m agla hand on your wrist watch? s go7l6m8.ata    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around *7tey(pmh jw )in a circle below you on a 0.25-m piece tj w(*ym)h 7epof 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 a car trave)q mxelwrw-0z*pajo z;/+v q+lin;rmzej +xw/*qwlp )a -qvo0 z+g 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 Ab /izy* 9- tsyyyuk3ns;d1zg*cela, utilizes tilt of the cars when negotiating curves. The angle of tilt is ad 9n g* zkdt ;yi1/yub-ss*yzy3justed so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the 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.$\approx$    $\times 10^2$