Sometimes people say that water is removed from clothes in a spin *d4 qip30bafv dryer by centrifugal force throwing the water outward. What is wrong4v 3d q0pbf*ia with this statement?

Will the acceleration of a car be the same when the car travels around a7xg1g+fhrv*8,n s2 cna: p mxz sharp curve at a constant 60 km/h as when it travels around a gentle curve at thp82n v7x mz*g:,a h1gn+frsxc e same speed? Explain.

Suppose a car moves at constant speed av xvrs2jh0czxaac4+p* b 1o30 long 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 sbcax 4r vc 2p*0a+1jh03vxozhills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-grj9h -zzn1 j8ao-round. Which of these forces r j8n9-jz z1haprovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water -9j*s,p hl-vaq:x)rf ,euddq 0sy0zispilling out, even at the top of the circle when the bucket is upside down. Explrij, d -v: qhx-zu)y9pssd0 f*, eaq0lain.

How many “accelerators” do you have in your car? There are at least three con5 kceq6,.qqcmeuq+u 2trols in the car which can be used to cause the car to accelerate. What are the uc.q5 ue2cqk+e m,qq6y? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, il)wqbhd(ndb/b ,.h 2 as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decreah i,wbb l/dqhb2(n) d.se as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whey,gscxwa5x*q)btr ( cm:*3c cn rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking anglemv3:vy v ug,89a;mkir givr:ygi 9 8,a3vmk;umv ven its speed and radius of the turn?

A girl is whirling a ball on x.q-l3dh(rif3( benq a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of thebxnq3d(-fh( l .ir3qe yard. When should she let go of the string?

Does an apple exert a gravitational force onsj82il ( s:fhbc-*pxt the Earth? If so, how large a force? sb2l t-:i8 s(*xfp hcjConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would th60 mz4fz2gb (,yx ae. zgejfh2e Moon’s orbit be differefz ejg2ab(hm g xz042e6f.zy ,nt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thy;lmz39xq q p;e Earth? Which accele39q ;pxlqmz y;rates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's.u u+1; mpv 6hks,kwo0y 7/)dd:uts ain Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side6k on0kw utd1:7y,du;hpvu)+m/s ais of the Earth to the other.]

Will an object weigh more an06e ;h:aj0 wyjn 6mdtqmr/)c t the equator or at the poles? What two effects are at worknw:6;mtah/cedjn60 j0 rqy m) ? Do they oppose each other?

The gravitational force on the Moon due to the Earth is o rt7 kjuy6w7:xnly about half the force on the Moon rx6 7u:tjk7wydue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of M5jxp oiee+-:c7qair +ars in its orbit around the Sun larger or smaller than the centripet-7e+pq i:5jiroce x+ aal acceleration of the Earth?

Would it require less stgntzx( ( sj v6er w*g5c+o)m+(7g ftupeed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotajr(6c)g(smxtgz g f w5v++tt en(ou*7 tion direction.

When will your apparent weight be the z ug mo3i3rw0/(3hq /eno8 nlkgreatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerate0umrn/lh o/in3e owq383( kzgs upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lorg) )y: u-mdiu,nht/ yuv,vi2 ng periods in outer space could be adversely affected by weightlessness. One way to si,)uurht,ngiuvmyv 2 /)d:y -imulate 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, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appx mnzpg7/cg26; h(ea carent weightlessness” between steps.g/ gzp2hcme 6(;7c xna

The Earth moves faster in its 9r* qk )ee nhe6)ak)a tu6a5wfls )pm+orbit around the Sun in January than in July. Is the Earth closer to the Sun in January,)sw*a e96uaq) arm 6khf) kne+p)tl5e 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 relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovermn9uvvy:c)g*5 f dxk5ed to have a moon. Explain howk*c9mf):xnvd5u5 yv g this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's)wttl nw o6*p6 *xx*fdoh9i6s. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth tow*6n* *dps fiwx6 totlx6h)9o the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling r)ygb6g/5 y)tcte vrfa7/ tx2 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 acceler g*lop,puf0/ ad9zvs- pbl*p5ation of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Ezod*lppb vpau95* gl-fp0/, s arth'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 discuss81.s ub 89p+klp2ug/fxcdp i as it rotates uniformly in a horizontal circle (at arm’s length) sp9cf./uu2p g8ips1x8 k+lbd of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 3+ t-uqjlsmel;gz 7.1s lu+v akm from the Earth's surface, and circles the 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 accemu1v+ etjgz a7slqu- ;ll3+s.leration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay o)k )napp i;gr*u:kso esxr;6 .n the edge of a potter’s wheel turning at 45 rpm (revolutions per o)kp:i;;x 6 ep*nagru .)rsskminute) if the wheel’s diameter is 32 cm?   

  A ball on the end of axd4f+jy)l0 3 xigc9enfn;3ag string is revolved at a uniform rate in a vertical circle of radius 72.0 cm ,a3cf+y3ngn0xle9)fji d;gx4 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 speed5xrzzs .n0ypp 5)breevn7:3mf8jkf9 with which a 1050-kg car can round 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 indep:y55p z8mff90jrevs bzr )3.pxnek7n endent of the mass of the car?   

  How large must the coefficiento6ff;fpvdm* 9 of static friction be between the tires and the road if a car is to round a level curve of radius 8vp f*9 ;ofdf6m5 m at a speed of 95km/h ?   

  A device for training achm0 rwwy17pg:wl. 7 qstronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back w wqm.0w 1gylr:7cp7his 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 of a rotating turntable of variablu: ;4gxupq :k pj0q6kze speed. When the speed of the turntable is slowly k0pg6x 4;:p ujqz: qkuincreased, 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 at thev; md9hyz--no top of a circlenzy;9vo-hm d -
(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 the 84nwea(s* yprrounded top of a hill (n8ps aery*4(wradius =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 need to j bp3:x;xxhq; make for bx ;q;x :phj3xthe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad*opaib09 hg(jf vov:2ius 1.10 m. At the lowest point of its motion the tension in the rope supportinpo 9boaf* j(0vi2:ghvg the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rothimr rd17tpk*i4 + tl)ate if a particle 9.00 cm from the axis of rotation is to experience an acceli kp+imht4t 7dr )r*l1eration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rota09n pur (u5;bew+r zntted in a cylindrically walled "room." 5 twrnb9u0;pe uz(nr+ (See Fig. 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 frictionless air-how3jju-x 3tp1 .qef/gpckey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig.q3x1wf/ppt. u-g jj3 e 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this7 huh quea37:u time, by not ignoring the weight of the ball which revolvh u7e7qa h3uu:es on a 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 f5 / kl.bs)0pvsajg tl0or 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 masses2 .ozo9 a)+yn ywr(c2ofv:chb $ 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 vertica,i6 ryic:-u2(z7 lux ur;wfp z yo*a;olly 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 components of the net force exertear-ir1o5*n;iu aqgqa 1m6z g1d on the car (by the ground) in Example 5-8 when its speed is1*gurgi ;61 azao1qn5ra q-mi 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 pgc;y; *jci 3v.2jrdggit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. D2y. dcv* jj3gcg;i;g retermine 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 horizontal circle of radius 2.90 m . At a prd (3wm v2h4ad5iney*articular instant, its acceleration is 1.05 yh2dr *a 5iv3de4nmw($\mathrm{~m} / \mathrm{s}^{2}$ , 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’sa *x) c4sjh:.a)fjwkihw(un8kq 32d l gravity on a spacecraft 12,800 km (2 Earth radii) abowudhswj2) aj: )xfa h(lk qni.kc48 3*ve the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleraj-xnk,q/;dbeq khb)n . ba b.8tion g has a magnitude of 12a.h -q8,bk e) n/nk;j.bxb qdb 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 Me3ybcz qn5tzp,c18 f+ oon. The Moon's radius is 1.74 z 18bfzeyn5 c+,3qtpc$\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 oi 6u3 3vcy*mnahoo06if Earth, but has the same mass. What is the acceleration due to gravity near itn3imhiu y366voa0* ocs surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but th,k(nr5ps3o ve e same radius. What is g 3psr,kv (o5ennear its surface?   

  Two objects attract each other gravitationally ;w0bp ,he3 kc2kt/y0m3 jdfza 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 acceleration of gravity, at (a) 3200 qq9c(wfu3u-5wk f/xz m (qqzku59-wfw3f/ u xc   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poeg* gx zz;(/ywint outside the Earth where thegravitational acceleration due to (*;/eywgzg xz the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times t6p ss6e cy2a3vcsi;l :he mass of our Sun packed into a sphere about 10 km 6layvp ces32; :6icssin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which o;y0ivvuo.wzg p*e 9ik. : 7jef6xo.yw nce was an average star like our Sun but is now in the last stage of its evolution, is . 7uey:;.jgv 9viyfk 6oiw0z.woxep*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 weightw exya4* imt34less while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yoursm*34yt i wax4eelf that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side wi21nv 8co(;q /ondpfa : wfd10.60 m. Calculate the magnitude and direction of the total gravitational fo (1f2/i ap;qdnwwdo1nvf8:corce 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 sider0)r-l qzozx 9 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).z lo0q z9rx-r) 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 ofbbq4i s q-lf(10ik 3ib Mars is 0.38 of what it is on Earth, and that Maikq -b0s3b l14 (fbiqirs’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fombgr ,dbt8 76j.f+ iewr the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obt8g7ebbj 6df,.i+twm rained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abf ljxp8qhm.2b- lp-t0e5uagrf(8m,z out the Earth at a height of 3600 km. -p zpx0,qm ll u.(28h8e5 m j-gfbarft   $\times 10^3$

  The space shuttle releases a 0sii).ebch)q satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? i )h 0i.b)sceq    $\times 10^3$

  At what rate must a cylindrical spaceship j yi dd+zbao. hj-;2ou80p,q hrotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, ao-q8d.2,jpadohjz uh;0 y+bind give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellipmq4c01 vl *ntbw5 h0tte to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radith p1w cq*n5 l0tvm0b4us of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launchmaqexpk1cli6k,kg1;n8z r xgj 1p-6( ed from the top of Mt. Everest to be placed in a circulacmx8 pn61x;grk,61qzg (kp - 1eilkajr orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to omna h+7hq)k1 s2y,ocd rbit the Moon at an altitude of about 100 km. How long did it take to go around the M ,h1dac7qmso )+ky nh2oon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pp 1zyjg3/be k)lanet. The inner radius oy j1b e3kzpg/)f 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 m.ib7 qsfg +yfeh2w04once every 15.5 s (see Fig. 5–9). What is the ratio of a pers qf mi0yg7+2.w4hsbfeon’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrone hibnsql +xyd 2+m05/)g6ykgaut 4200 km from the center of the Earth's Moon in a space v gyex6q)+kn05sidh/2 bl+ gmyehicle (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 system9jx8djti/ x tw7b xogm4d0)ft 1m/p2j consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass oftp20i 47 xfbmdj ttjd/) xmo/x8 wg1j9 each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in -gl gux m+q6uv+ou3; dt)y ec:an elevator that moves ouuly:eucx ;g+g) m6-+3dtqv
(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 hangx*ab/ v cnn .cnysxw; *,lp8a7s from a cord 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 elevator’s minimum accelnxsp.vyb;8a/, cac* 7l w*nxneration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a 8cl 1wue,nl r3bra g89planet with period T , the density (mass/volume) of th38,8r wu lc el91nagrbe 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 t hf9lxv;mi7o69mfo;i dr gm:,he Moon (27.4 d) to determine the period of an artificial satellite orm g , vh9;o9oxif6l:7m dfri;mbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meterw77/pqubk6j v s across, orbits the Sun like the planets. Its period is v7 6kw /7pjbqu410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4rvi*qqw r:-sie e u1; 4v:o/nt.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comeszv8 3 ,dfo;qdxj1q+qcc; 8pwwdb jm6 2 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’ocz8;xdjq;,qvd df8bwwp j2m 6 13cq+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 abouii3. mt uiq/z(t the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fou0;z92flzb1b 8emd 4frw4 un gar largest moons of Jupla1 ; 8bn 424zrudfz wbe9mfg0iter (those 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 pekx49v/wmb *hn( po ;urriod and distance of the Moon. o 4;m(n rwkhpvbx9/*u    $\times 10^{24}$

  Determine the mean distance from Jupk cuc2py 1dp6(ff x.7tfj) bt9iter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values d)6 pyt.c x1 p ffju7tkb(fc29in 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 frage2+hnyy9kk0sr 4c tbmapt. 4;ments (which some space scientists think came from a planet that once tbt e;20kms4 .aycph4k9n ry+ 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 describecwi44a 4mb1pxo+ 5ppnjo4 1ivf5e y2js an artificial "planet" in the form of a band completely encirclpoi+ 4p fm4o1e41n b5j24vw5cajxpi ying 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 arc from a hang xxbth1.-cn)ypp.x4m ing vine (Fig. 5–41). -. ptxm) 14xx.hnbpycIf 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 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gra :n 5u/atls:qlvity be half what it isqnl::t/s u al5 on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and sp vmpnv3 634-t;qlj o,dqnh+7*w vrwakin 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 kdrw*pkwt+ aj3ov;vqv6n mh7,ql34 n- g, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the applb8 fs8k xl;nq(i8lw*arent acceleration of gravity at the equator is slightly less than it would be if s wilk ;n8blfl(8 x*8qthe 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 tlf jywo 67:y/xba,1 nyjvb 4m+raveling directly from the Earth to the Moon experience zero net force because the Eay xmn6:ob1ybj j +la 7vw/y,4frth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scald zj ag(2z(tpv w7lg:.e in an elevator, it says your mass is 82 kg. : ldz7(tzv.(pjga g 2wWhat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that willdq ih79 q7*t/g4s j0r,illetb rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if 97gj0 tie4 q,7dbiqsth*/ll ran 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 g 51bxaml5 ,3cr dglq+q/k:ehloop (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 maslz7ry4fz s.8plr(h ,v fs( za.os(7i ay3uf2 cs of a planet in terms of its radius r, the acceleration due to gravity at its surfos8ysv zf (us3a7rfl zprf ( 27a.,yc4lz.h i(ace and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecty+gaej+xf,go, :x h1f1llyg* ed from the vertical by an ang j+x gxh+*a1fe ly:gog1yf ,,lle $\theta$ 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 d uhw;z(ar,z7++okoj kcbh67 If the coefficient of static friction is 0.30 (wet pavement), at what (+,kbzj kw 6;hhz d7ro uc+o7arange of speeds can a car safely handle the curve?

  How long would a day be if the Earth wemuljd ar27c1*re rotating so fast that objects at the equator were apparently weightles27 *jrc alud1ms?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of isl36sg 7(llnjxnw;vf* *: we 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 nyte,l;3aj/z)k sh9, )nj beh of radius 235 m. A lamp suspended fraz9 l3kehy),j/te ,sj)nh nb; om the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as masfw1nns0+ba1j + vsn8:fv;f yfsive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the nsff0 fyb:1+nnaf8; jvvws+ n1umber of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the prese a4rmvgj0ik7e 2e+yu -b70b lg3ffty)nce 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 measuring the speed of gas clouds orbiting the core to bb ay t4r+-f kvj7)ilgy20b um0 7fgee3e 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 shown in (,:g y qbae f5oi+d0jqFig. 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) Hi0yo,gd: qfqaeb +5j(ow fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orzthu 3laq (89;c11j axhl7 glhbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determin9jq3lg1ha( ux a1l; czt7l8 hhed 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 Rendezvqmm r7t p))a6m29(qfhd4mxci ous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at7f ))cm(iq xd mm2t96a4hmp qr 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 astronauto5yw*qz *n3xg in the space shuttle pursuing a satellite in need of repair. You are in a circular o3 qw5nzxg* oy*rbit 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 distancz)o+f02r gi 6kvm;s y /jif6sne fromfn k+f2m;isso)z06ygjrv 6i/ the 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 coulv4,3 jp 0ldcetu2u+ yrd actually "feel" yourself gravitationally attracted to someone near you. Make reasonabl uvdujr 0tce y+p2,34le assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arou6(tf-hw e/c 6jiay4hind the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-t6hefjc(a6y/ih-4 w iyears 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 l s1j0hgh sz41g hx3c5 i:t/wr5i0tng yocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth04 h1wjxr1:hs 0g5 t5ni ct/gihgz3y s 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 orbi-j gark-gt e( 1h/pf0ots 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 bn4cnwbn (3v z+y the tip of the 1.5-cm-long sweep second hand on your( zwbn4nc v+3n wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker xc1)c*mctt q,9 :fbppweight around in a circle below you on a 0.2pccf:1p* ct9 xm t,qb)5-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that achf1*c62bf7x 3t0b e a z:aavj car traveling at s t:0j3bfxz2*ba6 7h1fcecavapeed $ 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, utilk:py/kytqq7 t v*h*j4i- r7 -bschv(yizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acctjq-sr*yhk47 *y tcb(vk /7 :ipyqh -veleration, 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.$\approx$    $\times 10^2$