Sometimes people say that water is removed from clothes in a spinz ac.4k18-wt ugm8 ufc0)e niq dryer by centrifugal force throwing ne0ict1.ucw4f u m-g8)8ak qzthe water outward. What is wrong with this statement?

Will the acceleration of a car be thexklk da; 4tk2ps)dki0l+h4 i8 same when the car travels around a sharp c80adksihk l; kl4t+kp)4id2xurve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where:+mhv fyuxo0/198k:;5ndkgqxlg xaj does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level s/lv +yu9qkj:fxo1hg; 8:dxk gn5max0tretch near the bottom of a hill?

Describe all the forces acting on kgjv 4 bb1w7q:4yd*pka child riding a horse on a merry-go-round. Which of these forces provides the centripe4gd1wqp4*y bj7 :kkbvtal acceleration of the child?

A bucket of water can be whirled in a verz*ms ihu xbg802wtsp(5og+7ip,4g x rtical circle without the water spilling out, even at the top of thgz*7p, ig8b4 hsw(oti+ mg0u25rs pxxe circle when the bucket is upside down. Explain.

How many “accelerators” do you haj fy ,v-iw7 *8y6bni/jntki-a ve 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 accelebjyt ni 7-vainjik6y -w8,*/frations do they produce?

A child on a sled comes flying over the crest of a small hill, as sh;xa7 bi:f g:c+( lu(yfbr etm4own in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his cb+;4(u:( b gta: ef7m ylcixfrhest 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 ath5 +.znjfmio2 k4shmkt(q,yl b /h1-i high speed?

Why do airplanes bank when they turn? How would you comput*mhml r h q+j9ha;x pwzw.-k1.e the banking angle given its speed and radius o hahx1*h9lzk w.p r;w.jm-q +mf the turn?

A girl is whirling a ball on a string around her head in a paa:i l7s h-(l3dnx +fhorizontal plane. She wantd+l - lsp fxhi7a(3:nas to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational f cql/-w4x va/q +o-(ucoe,lydorce on the Earth? If so, how large a force? Consider owl qxedq,uvc(o/--yacl /4+ an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whatak7-u1mydtmnp s.3+x ways would the Moon’s orbit be diff m ux.1ady7mnt3-kps+erent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon oynb j,c922 kjxh+j.o3eola qbzis:d(*.+p cd n the Earth? Whichh ckj+(3di2n*+eqso p.c,x:9aojb zj by.l2 d accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet :-7na 9vfgn9kxgm3 a-r g3ypb ,esq6pthe Moon's is mainly respokg ,mapbf9 36ap:s9gq ne v-ngx7r -y3nsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more atfgc7 3pt/sy* pj63)ln9b heg t the equator or at the poles? What two effects are at work? Do they oppose each other?py3ge)n/fgs3cpt 6lj7b*th 9

The gravitational force on the Moon due to the Earth is only about q)0r ah*,5 r-miukual half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fkq u-hau,mr r5ali0*)rom the Earth?

Is the centripetal acci+k l+fqtdn45 b98k2pscgxd7-2o l b44lgryreleration of Mars in its orbit around the Sun larger or smr ki2d9s gd -2ofn l4c +t+7pgy4q4xkrbl5 l8baller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) t f8(a9ev*ma -yd jvff/oward the west? Consider the Earth’s rotafdvv9*aa-(jy8m/ f fetion direction.

When will your apparent weight be the greateq4ed h 8occg./st, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the sac 8c /4hgqo.deme as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in oute .b)5ffw rsj( c4/jekvr space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Conside f c.4rb/jsvj5we) k(fr (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” o9 u,hb+fgtvfcn0 oj1 3r “apparent weightlessness” betwee j19,h ffu3c+b0t ngovn steps.

The Earth moves faster in its orbit adjza2 c8m3vhuu+;l,pau+2ygy.,b e r round the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain.j2 ydb+.3a 2cy+mr8ph; ,lua,zgeuuv [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to ha scpqk dvm*k4yj12)2qve a moon. Explain how this discovery enabled an estimate of Pluto’s mjc4y1kps2*d k q2 qm)vass.

  The Sun's gravitational pull on the Eaub 0x ni 0*j5ywiz-wc*rth 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.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed iw5-* *ci w0xj0yunzb 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 1/ae2i76uq n mg)bqb: u980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth iz)q8psx +z(oa15zy wrn its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Eaaz )8xzqo1z wp5s(+ryrth? 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 rotabbq *3 ;wb2zhktes uniformly in a horizontal circle (at arm’s lengw2h*3qbbk ;bz th) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfgw 3:7a p:r,/ -s-coj5x7zme,jpq0tfm xj u mpace, and circles tasm3jjjp- x7qwpmrox0,g,c7 f e/m: :- 5zupthe 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 edge of mp2ii ikqyc*x(7ix / m.i p;k1a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diametpxicp kkix (*iiq2 .1m7y/im;er is 32 cm?   

  A ball on the end of a string is revolvr4 u+m7a k3f, 0yzp vs/ay11g)cmh vcked at a uniform rate in a vertical circle of radius 7akk) zcc1s yr/mvp1+ ,gm yvaf4u370h 2.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round alg.mae (.d vsoy )dc ;)i)lwq( 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 mass of the carc (a )w ;ed(yso)gdlim)q..lv ?   

  How large must the coefficient of static friction be between the tires and the la 6a3hnyke-ah a9 ic2l f7.vbhv8;c9 road if a carhlck7vyaa;9he 6c n 89la2h-v a. bf3i is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet f0dfsa 01 tgj;gdg6ri9 ighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, howigf r gsd 091jt0d;g6a fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of )e+sa81eoqs5wzoj s ;variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable u)j zs;eew qa8+s1o5sontil 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 at th)uc eby1pc e13 4htz;ee top of a circl1cbe tu4 p3z 1eyhe;c)e
(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 (includ q/x*63wodu3/9sergaa -inpt h ,l3 oping the driver) crosses the rounded top of a hil9n/aa* qd w3g-lxh/ o p6er3pu3o,i stl (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 r4sh3c3,x 5j yi9x vv- kpal9tper minute would a 15-m-diameter Ferris wheel need to make forctprxk 34v, ia9j39-y5lhsvx the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 ame sw:l1c4y0idmz 9o3, wiu,kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buck39c,:,1wi a0dz y4iu smwmeo let is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a part)o1s5 +by;bcnkco/+f dd3l*z xv*z jx icle 9.00 cm from the axis of roto**scvnbl f+ jxk)3c z51 z+xoy;/ dbdation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at 9/ c9hxb b q bk4n17omgaorb5*a carnival, people are rotated in a cylindrically walled "room." (See Fr4b9o7b 9*cka5/ bngx1bqmoh ig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictio g/*z(5linwo xs hq8 s+h*/jps4 j7cminless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole j5/4 wl+ipjsqmi 7*n8 s z*hs(o/cxgh as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not iupa vl.. r in9 xs0)ly4co..bfgnoring the weight of the ball which revolves on s.4r 9. nyu pv.xb)of.lcal0ia string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a co6 1 c;gv9z hcx(a5cvaar 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 xg-. kubbrz 1m jc-+8k6df8w8ee ysq*$ 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 evasiv,qht5ut+s mn1e 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 tangential and centripetal componentsnfu mae3ve 3d5;hj z0+ of the net force exerted on the car (by the ground) in Example 5-8 when its speed isevz3h;+m ef0djnau 53 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly fro50lj oze 1st*wzz;rd59uq* c dm 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, assuming constant tangential acceleration. If the curve were flat, what would the coefficient*odz u*5e0rt;jlws cz 1qzd59 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 circle of radius 2.90 m . At a particularj7i8e *xary ;b instant, its acceleration is 1.05* 87ayjr; iexb $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Eartq ut1gc dbo/hixn crg8j 6;:xmdu832*h radii) above the Earth’s s6u:nt 8dd/ bcjqg c*hum;o1xi8r23x g urface if its mass is 1350 kg.   

  At the surface of a certaiijks*rs f l(pqn:+n 6.6bhy o,n planet, the gravitational acceleration g has a magnitude of(* +pjiqs n,b:.ynlr sh6 fko6 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 Mooneskuq 8.(w)2anaarj ; l7ak(0 rk bdu3's radius is 1.74 7 uukna(w2;s) dr e3k rk(aa8aq0blj.$\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 thaiy+r/reyx2txba d;5h c+zq72 t of Earth, but has the same mass. What is the acceleration duxbeh yzr2xdy/q +;7t25r ai+ ce to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that ofn)4 hrk6+hpw3vndl2 i Earth, but the same radius. What is g near its hvd3ri26n+l w kp4)hn surface?   

  Two objects attract each other gravitationally with a force of 2lvlpy (8)wm1+ :+yqs fwgyp2i.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 gravity, at (a) 32 e-y* ahpbyxqc/hz(f a+93tg000 my(+ 9ghf3zx- ata0ecy b*phq/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whf ;0kh5r+(sleozudvv p94 w g6ere thegravitational acceleration d(9fklweg 4ods;06pr vhv +5uzue 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 a sphere a*e iitqmzn)hs1wb 3,/bout 10 kmh*/i 3qnsiwe,)mb 1tz in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sm;4qsgch. d611sp lxuh, s (4h9iqvmoun but is nuq;ih4,4cm .h d pl sq19ox (vhg6ssm1ow in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weigh kkkgkv04 f*jdf+j;;d2:2xs pwtz h ,ftless 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 calculating the acceleration of gravity 250 kk:+fdghk 0x4jpkv*f k;2,w; ftdjzs2 m above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at te8 2cn dzpx yefhmgyj.3 7ckz1:i 9)4rhe corners of a square of side 0.60 m. Calculate the magnitude and direction of the toz rci: fj3 p z78ge hy)c.1yx429dkenmtal 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 plaqvaq;tc; r5bmii l+. .k:cg:vnets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, a ;v .aivit cqk5r;lmq:gc .:+bnd Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mar18vpd z. m :k(9x- g2nqejpfwuf19:lt(zpc j ks is 0.38 of what it is on Earth,2:91.x p cv89 wtjp(qk-(e gufp1zz:jnk lfmd and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of thkm7v9gc p 0zuoj+: 6uge Sun using the known value for the period of the Earth and its distan guuvcgkj6+mo :097 pzce from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable2:b tiq*cp1mqri e k)0 circular orbit about the Earth at a height q0)kpr:i* etmbc2qi 1of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above th v g24u mo6s;u:ste9ozg35 rehe Earth. How fast musm t9gs oeuug;4o26v5 e sz3hr:t the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrica fpqgivn 82 6*7ywwrz3l spaceship rotate if occupants are to experience simulated gravity zf3 yq7 *n268wg rpivwof 0.60 g? Assume the spaceship’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 satellite to orbit the Earth in a circulas:)8mre y6ongr “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 depennrye 8o)g sm6:d on the mass of the satellite?    s ~    min

  At what horizontal velocity wop u+-fc6y)f wm l.yx/uuld a satellite have to be launched from the top of Mt. Everest to be placed iufy .cw-fuy)lx6 +p/mn a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continukizg1 ;*ts f)ped to orbit the Moon at an altitude of about 10gi)spkf ; *1zt0 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are co5ng wmz1qc6-lkcts8yy(1.m ef g-3 iemposed of chunks of ice that orbit the planet. The inner radius oeel 6-f .8ic1m 3gw- t(zygc5qmks yn1f the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whp 1:xathi xe,7z7zm i7at is the ratio of a person’s apparent weight to her real weight (a) ai:7p mz7eh1,txx iz7at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cnbnmn1 7g *kqc:.5a xlkamhfj;16: a wenter of the Earth's Moon in a space vehi l1m:h* 7aqk1a:5x.b f ng ca6;wkjnnmcle (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 ogcuj 3 klft*z49ej;6kve:n s9f two stars of equal mass. They are observed to be separated by 360 million km and tak ;6zj4ge:cltk*s 3kf9 jeu vn9e 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an el k3r8.t0tyw v -kyou)bevator that movebktw0ou3.y 8)-r tyvks
(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 co 9;osan 4oircq )fd71 6))rgxuvcgor5rd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eleva5r ro6; )r4)qcgi71d)xgosofcuav n9tor’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orx i,a64)upsfwbits very near the surface of a planet with period T , the density (mass/volume) of the planetw spua 4fxi),6 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 Murcdc1foge3,-1;j eiqa: hw vqt 8m* 3oon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface. -3a38mhq1*:ivcwj;gc feuorq1ed t,    s

  The asteroid Icarus, ry5rta+* ig 3gthough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What 3tgyr+ ag *r5iis its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofi ((wmi 4yftj7 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. Itvh2j8w6. 6ea- ii5bpkkz/k z hza4 eg. comes very close to the surface of the Sun on its closest approache-8z gb aia6kevz.wz.2h4/ pikk56jh (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cpopfo 4up ()t3enter 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, a(4jm4+ 8yviao4twms gnd mean distance for the four largest moons of Jupiter (thotmjs(ogy+a4v 48 m4wi se discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known perb-c w r93gei09e zwx;xiod and distance of the Moon. cx-irw e ez3gw9;0x9 b   $\times 10^{24}$

  Determine the mean distance from Jupit 4svuqj;dl4: apci)) ier for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Co vduc)jips4;q) 4a:ilmpare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments z37pq x/dtsb1) uuja7(which some space scia u7u3/71xztpb )d sjqentists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificiag *ppgv , twt* :tujr(xv9:r7tl "planet" in the form of a band completely encircling t ,t* u*:trvv w7g j:9gtxprp(a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an ar9nfwwh 0/ivz 9c from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg9wv9zfi0 h/ nw, and the vine is 5.5 m long.   

  How far above the Earthy8cr04l cb/gdotyn ,79w+a jy qcl3m *’s surface will the acceleration of gravity be half what it is 8clg* rt blno qc0/4m, yy+aj79dcwy3on the surface?    $\times 10^6$

  On an ice rink, two skater)w4s 2vm9s rcm h*w,jhs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m longhchm,w4vs2rw9 j s)*m and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra8 tq,adkwa29enug1 h2vity at au8n 1,2tw agk2 deh9qthe equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveli,* kh sqn gb5bmjs8+7bng directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppojhssbgn,* m 8+7 k5qbbsite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on .jje b3 3f9jmf0hf + owi)gxjghb48q*a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which di x3 fgm+qe9h*g8fjf0j4 w h)b.oj ijb3rection?     ----待选择----upwartddown 

  A projected space station consists of a circular tub3vpd+ti)e cd4 e that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42)+ 4e)p vdcdti3. 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 loop (Fig. 5–43). p8c qu-is)g9 h 5t5voh
(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 accelerv(vi.i4 xl u-vg f)*dy./eejj ation duee fjx.e/d)ijv v g*l(u.vi y4- to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string/ zoaz 6*y/v g6antk/ilc/ps; ) is deflected from the vertical by ao/g/ia c;yv6zpt*6 s alz k/n/n 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 a design speed of If the coefficient o+m6cic,1nr 4uxmo/3 fgx p(zof static friction is 0.30 (wet pavement), at what range of speeds can a car on,g6/x+3cf pmc zu4xm r(1oisafely handle the curve?

  How long would a day be if th-s b-e4q wgsuce-w)i7e Earth were rotating so fast that objects at the equator 7u )gwebi q4ec s---wswere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 pswzvzj s 6nf(/a4*xx5i:m,n $\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 curve2 pv6y:ll(algx5 2+cbc ;cf lu of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17clu:p ;cf v 62b5(llycx+g al2.5$^{\circ}$ 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 thhtr7kcvj:x/ wjei 9(/ at 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 pli erkh(c vw/ :tj7/9jxanet. 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 S*n/n mwg7x7 vig+ f/9t+lq utf 6lvza-pace 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 light escapes). They did this by measuringm6 ttfqvulg9xf+wlzn 77/ a- *+/gvni 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 (+kw)smccw 5,mp:bhi-:5 n kx2vhs i oas it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the :2s5c),ix5nocki:m(w +wh km-shbv p car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satell5q,jm/dz33diso+rn(b zly1lv j:y v 8ites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver,3 dj+jlvzr:8z vlmb(5yqsy3n1 ido/ 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)ikbja6,s 6c,(si0z f k, after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly sbci a66kz0 ,ik,fs j( 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 s cna,cc2 ;n4t,co5jrg huttle pursuing a satellite in need of repair. You a, j2no,;a5ccr tc4gncre in a circular orbit of the same radius as the 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 period of 3000 years. (a) What is its mean distanf )p4fnczv.j4r4q 9i /hb+a uace from the Suj4cqh+v uapra4z b.i/f49) nfn?   
(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 a/xlx ( x0o3 qgk9hg0.fbzh7fneed to be if you could actually "feel" yourself gra f.xhlog3h/ 7z9x 0gqk(fbx 0avitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroundv2126orgfw kopq fn27 the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30v rf27go261pqo2kw nf ,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 of a square 0.50 m on each 2ty q.me a de7873qkgjside. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg 7egaq t8e37.qm 2dkyj 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 orbik:22rb-* di fyprnox.ts 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 :*6whjf5wh:t/cvpy e the 1.5-cm-long sweep second hand on j :pwh hvf*w/e:56tcy your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker 6dq fwb( tyzfk1yp 9)a*mk 8:oweight around in a circle below you on a 0.25-m piece of fishmfz 6(otf *k:p ykwy1a) d9b8qing 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 o+c8 oldjjiyxc/5 u4i ys7c 24 in a new highway is designed so that a car travelin8ij4cj/s+ix o2 l 5y7o4u ccydg at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatingeod/rp* )o4fa curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration*od) 4/oera fp, 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.$\approx$    $\times 10^2$