Sometimes people say that water is res;nbvxe)m9( imoved from clothes in a spin dryer by centrifugal force throwmixneb)9( ; sving the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around q ./sy4 uml0bba sharp curve at a constant 60 km/h as when it travels arou4us q0bym ./lbnd a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed altp)t3)ozq +g;r tfq8 fb/ , tx9kfze-jong 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, (c) onqztg )ftf;+tzbore83) ,/tkj - pqxf9 a level stretch near the bottom of a hill?

Describe all the forces acting on )w: l1nm9 jpjha child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of jh )9l jn1:wmpthe child?

A bucket of water can be whirled in a j8/s3oc)ly 95e;x;ve m 8zlrsdrqun 4vertical circle without the water spilling out, even at the sy3uzloc /l 5qvedjm ;4s) x;8r89rentop of the circle when the bucket is upside down. Explain.

How many “accelerators” )icifvu,5: ka do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produccfk5i :aiuv, )e?

A child on a sled comes flying over the crest of a small hill, as shown in Fwz;v ;mu.ifgl hd:.b7ig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force bevhlif.z;.g 7b;u:dwmtween his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hit)9peyepyv1xp: em- 2k( -hk bgh speed?

Why do airplanes bank when they turn? How would you compute the banki*;i 3owl*w ro8vgcr 1hng angle given its speed andhrg wl*o;iv81o*3wr c radius of the turn?

A girl is whirling a b /k.jitnx9c89ei) ie(xid ( nlall on a string around her head in a horizontal plane. She wants to let go at precise . elc(ii(j9 d9/ixkt8)nenxily the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force o;i qamnr r91xz i,v/,sn the Earth? If so, how large a force? Consivs n;rrm,1 z,iia9x/q der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what ityj m pta3zs*m7e:00 jc is, in what ways would the Moon’s orbit be sjje:pa7c m30 0zt ym*different?

Which pulls harder gravitationally, the Earth on the Moon, ck;x8tlf ra8kn7-vl6x8 h9izor the Moon on the Earth? Which accelerax79-hr;nt8v6 k la8 zkcf8 ilxtes more?

The Sun's gravitational pufqqc4 :9 q:kn4*q1iidoqd cuq 0 )ei,fll on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diiuq,eq4 *) ff91d4 qq0:ko nicqqdi:cfference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects ar3-aiy.f2ib t we at work? D 3 wifa-yb.t2io they oppose each other?

The gravitational force on thee ft85-c+)gw gveeax; Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fromxwetgeac+ ge f;85-v ) the Earth?

Is the centripetal acceleration of Mars in i6u. 5xfpslmf4ozrws6( (8f h sts orbit around the Sun larger or smaller than the centripetal acceleration of the Earzop5((f6ru lw. fsm468 sh xsfth?

Would it require less speed to launch a satellite (a) toward the eayi d40) xulf,uwqw06tuotkrb 0,/o:nz1 dn ,ost or (b) tow,t0nfu0)1do b,dr6w/o u:i,nl outwqk4x 0 yzard the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as j +8ctu; :4a0ukx vqiemeasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free ft:+x icku 8au0;4v qejall, (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 dh)e w y(d( lfhwqe454by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet,5hwl((w4f yde 4 )qdeh and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent wg dqx75yyav/3)yv8fg)d, sma dx1nh5eightlessness” between,syx)m7gdn5vy8)a fyv/5 g3 xha 1q dd steps.

The Earth moves faster in its orbit around the Sun in January than in Ju y0(r(b9ldrvp: p. bggxo(f5u ly. 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 g 9:frobbp(rly pdv5u (.gx(0relative to the plane of its orbit.]

The mass of Pluto was not known 4u5e g6 jlyoelfi9 /-bxzg+n6 until it was discovered to have a moon. Explain how this discovery enabled an estimatx bg5oe-+9i/4n6lj fy zge6ul e of Pluto’s mass.

  The Sun's gravitational pull on the* qj/;lfiov;i Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Considerjl;/i *viqo; f 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 travelin0,.nl(s bml/ zo.8pw3zrkyv faf8kk-g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earl7. r 9yfzrp)dth in its orbit around the Sun, and the net force exerterz.r)pfdly7 9d on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it ru3-wq xd(yzx oi z75n)otates uniformly in a horizontal circlwzn-iy 5 3x(d7qoz ux)e (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 sug3.*lu mwuaeh o0i:p j)k (m,jrface, and circles the Earth about once every 90 minutes. Find thejoew aml:)ih*3,0ugu m jk (.p 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 k,0ery ize1x /,kj +br96ngnp clay on the edge of a potter’s wheel i+bz9 egn6 p,jy r1krex/0n,k turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circle s5i bpct(bf2* of radius 72.0 cm , as shown in Fig. 5-33pf sb(ct b5i*2. 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 radius 77z we( u -cjnt3(wfz.k( m on a flat road if n3 u f(wzkz(.t(-wecjthe 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 fmn0c r .np*sd.riction be between the tires and the road if a car is to round a level curve of radius0cd.rn s* n.mp 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is duet1ds,m:z q +fs 0ig3esigned to rotate a trainee in a horizontalmifgu e:d,q + 3sz01ts circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis o*:3l hc/ep w1qclrgj3f a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a raw3j 31h:epcg l*cr /qlte 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 at the86,r( 4ttb mst6:.ji kcwmqpx s qxm tt:p( 6ik46,wc8tm.br j top 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 driver) crosses tft-;0xax+htbxk7k: x7k f+c lhe rounded top of a hill cf:xt habk ;+- x7+fl7txkk0 x(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 r tmbt/w xr 9mfe.uwcd+ok: ,wo +p )+c;g6sv7need to make for the passengers to feel “weightles+roms+k;vp gm) fow7+cxc,.r6:t bd wte/9 wus” at the topmost point?    rpm

  A bucket of mass 2.00 kg2vbzb;89 1 2 j ivx3igbu;mnns is whirled in a vertical circle of radius 1.10 m. At the lowes3jvnbvi2 812; u mizsbb9n ;gxt 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 centrifugut 3frl gg.y45e rotate if a particle 9.00 cm from the axis of rotation is to experience an acutfy lr53g .g4celeration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are z so+(.s5 x2vuup 5ct (mgr:wlrotated in a cylindrically walled "room." (See Fig. 5-35.sz5uvtc2r o(gs:.u p(l+5mx w)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tabi 4 dx0xbn ie fx6w34:qavv8b,letop, and is held in this orbidexwxq8 i6v3a4 :4,nf vx0b bit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by noua,+ u 4b/nxtpvqp9b,py:o6 gt ignoring the weight of the ball which revolves on a stripp/txuyu:vb pbngo4,9+q6a , ng 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radi,cqg cehjwnv . 5 p9pvw;6(1jyus of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massefq.lbyq b5)jw9l 87je s $ 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 ves/jb4i5qpacg 5z5 m7i ) -wkzcrtically 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 centr;q 43ldq) 7xfemilq;wipetal components of the net force exerted on the car (by the ground) in Example 5-8 when it;7qfd4qil; )3m qw xels speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates6 ffmqjo9+8u9fa8rcvp g3e (r uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, q+e389fomacrr ( 9gup8jv ff6assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circlhrr 8*hihnt4:h-s z+2i edwc/e of radius 2.90 m . At a particular inshte hih4sr:i/ hzr +2dn*c8w- tant, its 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 gravity on a spacecraft 12,nom ixtoa(d rr( g54j3 70gc,x800 km (2 Earth radii) above the Earth’sr0x3 rmx(od4 g ontiaj(7gc5, surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravit0a /:rm iq2wcf* rnd(tational acceleration g has a magnitude :02n(q* wrdi fracm/tof 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon' p dxwk+o:xm8toygvn1960 g.qs radius is 1.74 6o:+ x dq810mopv. kggyxt9n w$\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, -sonplzk( *2 jj*v49hdt1 ttb but has the same mass. What is the acceleration due 4*hskjt* p9 vdtlo-nbt (1 z2jto gravity near its surface?   

  A hypothetical planet hasexu;bsyb7yw7v 2 )eb4,rv(am a mass 1.66 times that of Earth, but the same radius. What is,ybwx); um(re2 b 74evvyb7 as g near its surface?   

  Two objects attract each other gravitationally with akp2ha8ky**nvmdl -k: 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 acceleration of gravjc,,jl;xu; as;jd 39kin:gw fity, at (a) 3200 m ,u,n gd jf3l;i:wk; j;a c9xjs   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eax obc8.5rpn2hrth where thegravitat.n2 obxc8rp5h ional 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 ,pi olm pv esrb* 9/przc8/-/linto a sphere about 10 km in radiu/bcl ,mzr*/sipplrop 8/ v-e9 s. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average stujh glrl 5;i06ar like our Sun but is now in the last stage of its evolution, is ther 6j5l;h0 glui size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weigdn6wie m/sq:f,2ig7g a*z vk* htless 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 itg:zwm*6 *kngq i2efd vs/,7ai 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 side 0.60 m.ltdzp +-dt 3 2qybco+0 Calculate the magnitude and direction of the total gravitational force exerted on one +p y0lt3dc-qb+oztd2 sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most ox1q df*) lc5uif the 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 in a line (Fig. 5-38). The masses ar 5 dxf*1lqu)ice $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of whx;ms/top xs;0at it is on Earth, and that Mars’ r0x so;x p/;tmsadius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value 7+khfj6durdy yf6v/d+.m0zm for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using K.hf+7u d0my6 +6zdk/mdy v jfrepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable *n oc6g;/hh*yquz60g if7cjw circular orbit about the Ear /7fc6w ;zoyi6 *njchghuq*g0th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular 7ktiry v+b-i1orbit 650 km above the Earth. How fast must the shuttle be moving (relative totybk+r17i -iv Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotaapc+4/k5j yn zte 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 revolution. (See Question n cjak+/zy5p4 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cir m0 lq g+vd42o,8anp9jqgxy(rx cfk9 2cular “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 radiusv+p20lonq8 9xam9yg2 x(dq,rg f kjc4 of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hab isum.3y/ p /dqps/t;ve to be launched from the top of Mt. Everest to be placed in a cirip/stsm b//;yupqd 3. cular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cons/ 7hvx*:plsqtinued to orbit the Moon at an altitude of about 1: vl*sxp/h7qs 00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chv uh *l)mkru( u()+jpzunks of ice that orbit the planet. The inner radius of the rings ipur v+ hujl ((k)*)zmus 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once 8hi4 h)cpyl;rkl/)t o every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real)h hc8k pl)l4yo/ itr; weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centeru1.ce 8ksks1pc2en)t x:7ah h of the Earxteh.1n):1cu cs h7k8s pe2kath's Moon in a 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 stars of equal mass. They arty*nxgn:5n b 18 ; skb,io(wese observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is thnxsn b in(:18bgwo*sk5 te;y ,e mass of each?    $\times 10^{29}$

  What will a spring scale read for the weia/ * s4mmo,xmefc3ql 7ght of a 55-kg woman in an elevator tha * qmmelmo,3xf74s/ac 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 suspended from the ceiling of an +y;h/mxffr p9elevator. The cord can withstand a tension of 220 N9pfxmf ;y+h /r 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 surfacejhuw )4f:fe 2n of a planet with period T , the:wnf)h4 j2 feu density (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 (27.4 d) to -omra+ fq./ye determine the period of an art+yfe- .aqmo/ rificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though onwkkz*g;.) jyely a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from theewjk;* y. z)gk Sun?    $\times 10^{11}$

  Neptune is an average distance of 4. 98dchjhjk3y:kp- ;hx,zgv+q 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 evtvi) ct)q c;f6ery 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)v6)ctfiq ; ct is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce 7e oczf,rxo;(z0 xp4snter 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 m zepd0ea; -l a vy)4*ram0fb,rean distance for the four largest moons of Jupiter (those discovered b -4a;elfre ard0p )bam0y,z*vy 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 mzqdh9n2 li0 *period and distance of the Moon. m*0hi2q nd9lz   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’(uii ppyq,4+6ps7 a.zdjqb8p s moons, using Kepler’s third law. Use the distan.su47z6(+ b a8pjippd i yp,qqce 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 Movz ;t9l ..8w.ohyf va wqhqt f192l:,tsdt1tars and Jupiter consists of many fragments (which some space scientists think came from a planet that once 1lv:sq wfzo,.8; .do 2yv t9lt fhh w1.9qttatorbited 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 artificia:2f:it iseb/prnx 85 5d+npfnl "planet" in the form of a band completely encircling a sun (Fig. 55/8n rn:p 2ifx+5e dtsbpi n:f-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 period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gor5 r6q4ryny0a 1z(qxhcge by swinging in an arc from a hanging vine (Fig. 5–41). If his armq y (r1x0y4 hz56naqrcs 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 mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the aii: isxj/lp9brom.i+ g v58f3cceleration of gravity be half what it is on the sx+9 fg ioj mivpl8b3/r5.:i siurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsby,fwforovs6511 jr7 rvo 6 /f and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, h 6j/yb rf11o,56orfrswf 7vvoow hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates onls2 .u tv3+nyhce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractv3+n h.s2uyltion of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling d5b6m s0iqk )beirectly from the Earth to the Moon ex5i6e bbkm)sq 0perience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand ( ;qbuphs8y1l on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of ;q ys(1publh8the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tubehp74uxl zzi0a+pvw dpo 0jzjws;,b c+5 (0* gp that will rotate about its center (like a tubular bicycle tire) (Fig. 5–4szagwib*pu7j;zp0l0 + 0wd(z4 vp5ohc j,xp+2). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loo5*wymbr,ye + pp (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 acceler5 u,;qlq 4w(dv:lcavnation due to gravl;4lq:a5u(wcd v ,v nqity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is den s sqe-b6vyl5 .20:d;n hwma.n*lebs)pvt f1flected from the vertical by an angle .ta5eqv.-1fmvlnb; sbp e* s0nw6:n dy l2s)h $\theta$ 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 kgok1h()b6f 0 siamn*of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handl1i a(gm )s* kf0h6nobke the curve?

  How long would a day be if theng-iep1 kht6 1 Earth were rotating so fast that objects at the equator p1ikhtge6 1n- were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintainl h 21ls:n+vmy 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 ofh *re l7+v pyi+0sevswdpo k:9mx6s81 radius 235 m. A lamp suspended from the ceiling swings out to an angp9wsh*kv +yo d+:8ml s eer0ipsv761xle 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 claimed *pj5q4ogp r(b 8 no:y 2cz,fijthat a pp4j,z:i8fgpq 2 rcy5*nbjo( oerson 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 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 )j -:op wg3)g)jahz(;:ex (ea emigr fSpace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no lre3)m::oejgx w-fh( )ez( ga;ga p j)iight escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shf6 f -*v:ggvv lb,8lkiown in Fig. 5–45l8li*g k-fv,v : 6fgbv. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (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 (GPn0pe zj6r b2+.lwxg+rS) utilizes 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.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determinezpg 0bjw e .x6++n2rrl 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 km, is h( pbb9r0rif lo2)(iumeant to orbit the asteroid Erou)i (bph( frb9 2il0ros 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 repaig5 njtmmo)42) iwgb0qr. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), )gg bimq05mj t)o24nwbut 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance +ek.ug )0* spkm /fwmaq2f s6ltyh.w1from f/.6e1fs) 2u. gtm +kasw wym klph*q0the 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 actul4a 8h7)6hwzjqxlrgz xem3 ( (ally "feel" yourself gravitationally attracted to someone near you. Make reasonable assumph78)gx zlaqz ( wr6me4(hl3xjtions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mjw* /hm s2uu1s-6ynuremi( u2ilky Way Galaxy (Fig. 5-46) at a distance of about 30,000y2*u/sn-irm6(sewm uu1 uj 2h 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 atr 8,2 kp)bsg /xc7nwap the corners of a square 0.50 m on each side. Find the magnitude and direction of th8rs/ gpxp2b,w7 ck)ane 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 5500 kg orbits th8t0+ ,s9c,pz ulmcpv0yqk x,zj2s gm 5e 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 07 maht cy; n mc;k;5)(fyz e0izzom4yby the tip of the 1.5-cm-long sweep second hand on your wrist aezm;cyy(h);mcimo07 zzk 5ft4;0ny watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weig nf 9wtuc8h0v5ht around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle hnu t0f59 wc8vthat 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 travel1djeq *x4ylargkl u 4.n0vy19ing at s9.4 llg0d4 vae u1ynqrkx1*yj peed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when 4 fx gq0h:; rb/m k3ezds8ya,ynegotiating 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 fricg,0yb8yxrmk/a h3fd4z s; eq:tion 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.$\approx$    $\times 10^2$