Sometimes people say that water is r6yl ggcjygb5jv ;s7) .emoved from clothes in a spin dryer by centrifugal for56 . jb)ljg;c sgy7ygvce throwing the water outward. What is wrong with this statement?

Will the acceleration of ah0dv)gsb7d 7 bkp px0/+5a mcw car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aroun0 bgd5k )xc7dvb07/p+p shawm d a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where dofcbdk 7mf* h1;h; )tvhes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two 7bhf1k hvc; fd;mt*)hhills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse o3xe) iyl1n hk3n a merry-go-round. Which of these forces provides the centripet)kln 133hyiexal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spilling36i9 mf.w7ic5 snf6 jieplqfh1,dz. w out, even at the top of the circle when the bucket is upside .67ffqf9 w i,3i5iwc hzpdjsel 1n6.m down. Explain.

How many “acceleratorsz *z.)s8xd.n *ihnc n6j +jder” 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 produces hedn.jxi8cr6 d+j) zz**nn .?

A child on a sled comes flying over the crest of a small hill, as shown)cp u4pn 0sd)8hnd*rk in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but hn) n)dp 4rushd8 c0p*ke feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high2euy6uxw omdqe 0.t f i75*pyh6i9u 0p speed?

Why do airplanes bank when they turn? How wk tdg8xc.l6 *kould you compute the banking angle given its speed and8t6kck .*lxdg radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. She*b,jv ;2 1kit 184 * atbaow5 xc.syp9ayyoyms wants to let go at pr5,.yvk;1cs4yxmpbj ytao o a* 8ba yw9i*t21secisely 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 on the Earth? If so, how aai) *)jl:0.cu uv wmjlarge a force? Consi*).a uu:imjl wacv0j) der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, inbg42h:juv xx0dad (4hqa 3hn. what ways would the Moon’s orbit u d4x q:g2hn4a0vxabj .3h(dhbe different?

Which pulls harder gravitationally, the Eas:ol8 o-dv v 4nw jab2qg2i)1urth on the Moon, or the Moon on the Earth? Which 4j l2n :g182vvq oou-sb)iadwaccelerates more?

The Sun's gravitational pull on the Earth is v1 zezmnlrn(v2 6*c/q much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravi zvm1/ e(*nnqv 2czr6ltational 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 are atwe.1h 1eicv:sw:.erz d 0p-b t wori p1s0r:e:- wz1d eth. ebwc.vk? Do they oppose each other?

The gravitational force on the Moon due to the Earth i/m, ejg(+ks)y;dj h u7doj6u ht3 x1zp 9se-yks only about half the force on the Moon due to the Sun. Why isn’t thek/kjs9e6d yjyz;7-,+)uux t jg1 dpe3o(ms hh Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largbzfn2;k,y mx0 fd d::ger or smaller than 0d:,d:f zmfxy bkg;n2 the centripetal acceleration of the Earth?

Would it require less speed to launch a salyg h/t;8*9pb1)ft ncwrrp (atellite (a) toward the east or (b) toward the west*(c1tpyrrb gw9f n ;)8tpla h/? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured )v. tx)gac162r hwmty dla ,5cby 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 wei.ry)t taa,gdwl5 2vhc 16mx )cght 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;g. t z ngc qspr6- 6lr8(+wsvx9/datr 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 sx.tn;p9c g-6zdal q rwvrr t+(/sg86surface (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 experiz(8i ugd9(qan*rd k m;j1v5loences “free fall” or “apparent weightlessness” between8*o vmrlk i g(d d1nq5zja;(u9 steps.

The Earth moves faster in its orbit around the Sun in January than in July. Is hkcu2gg),dk,:zqe w *ov rm1- the Earth closer to the Sun in J,o)uc2 *kdkm1rg-e hg:wv,zqanuary, 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 4-gh: qmq9 x4)gadh cbuntil it was discovered to have a moon. Explain how this d)gg-d xq 4 h:mabqh9c4iscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Egv4- 68c8icl8vxkuk sarth 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 from8vv g8- 8lkk iusc64cx 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 seiq9fyz z 283 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 Earth in its o-) y ku thwsje5246lmznop:q(rbit around the Sun, an62zt)yn: j5(m4psl uhe o-kwqd the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exx t81u53kwj1y 2cyb* 4sid foterted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cxy1*bs81dujf 3wt2o 5c4tk iyalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surby(2 n gx 9g,c2r kqz.hkv+/6k cl(kblface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the spackv n, l.2(/h+(kbg9xq2 b glz6krcky ce 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 o* 4jt -2y78ljqcppuj uf a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s 4p7tu2jqlyup*c -8jj diameter is 32 cm?   

  A ball on the end of a string is revolved at awo+c+-(ehjcpb6gt 2 l uniform rate in a vertical circle of radipb++6 c 2cghj-wl e(tous 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kgun/pblic:l 3i ;-4ju g car can round a turn of radius 77 m on a flat road if the coefficb-j ;3l ncg i/u4p:uliient 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 friction be between the tires an ts 3/k 7 wauwh8cq2vni;t/ gx+sht-*hi9 d.gyd the road if a car is to round s7 ny;vcw+ qigsxaih*/.8ht/- ht29 gt3wkud a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fig;mrax, qs/p z3hter 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, how fast is she zqxsm/ap ; 3,rrotating?    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 rotatii( v3kvc s1(6usz: ,gsxe2hnhng turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntabls,kn(hci1 3xe(2v:hzs6s gv ue?   

  At what minimum speed must a roller coaster be traveling whe3wmg rd4,i rj1h9vaxcphk , o:,:i(pen upside down at the top of a circleho k aprcrij 9w ighp,,:d:1(m,4e xv3
(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 rhv8u bca iqe:u42(l , n;svj+7ye/db mounded top of av(j u7evcei2s/8nbbd; uq4 h:+mla, y hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute wou j;od*v-ukarffs 62a 1ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topfad2rf s6 uo j1va*k-;most point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticall( w8y4gszgfj6hm6iwl .8 vb/ circle of radius 1.10 m. At the lowest point of its motion the tension v sjwlb(g8i fmg6z.486yh/ lwin the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particlerct:feh5910 f )a yc qgzbp59w 9.00 cm from the axis of rotation is to expp1gyzbchrtf5 e9:c 0 )f a5qw9erience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carx ;qsd 2l nxr0* 2nyq.wuq-9zdnival, people are rotated in a cylindrically walled "room." (See Fig. d*29q wyqqz-0 sunx.rl;2 x nd5-35.)
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 ai 58r0hl2a6 -r cnhdt8sazlq9 fr-hockey 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. s 0chll6q2 fatdz5hr98r a8n-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 noxpftdfr)u4, 2on9;l i t ignoring the weight of the ball w)o 9f lxpn2ru ft;d,i4hich revolves 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 iwbw(lp ;. y8sfor 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 massesm1m 1.fgrpg 0h $ 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 evasivmo 9x x7cjkz6q91ip(r e 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 components of the net force exerted o2ulkh1q m0sw.x oife+0+1s 6 vhm *cobn the car (by the coo u 6v2qhx01w.m+01 k*flie hsbms+ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniforml+n, o zdcle,t73 rlm8oy 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, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have toozm 37rce+l,l,t8ndo 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 parennwdbd (wa1d (* (db2ticular inst dwn*adb1 (((ddwn e2bant, 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 spkc qg8oh3 1dh0acecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mas8khc ho 1gdq03s is 1350 kg.   

  At the surface of a certain planiw rt0 -u,v8qjuq/k2 iet, the gravitational acceleration g has a magnitudewi u8v kqr -t,uqji/20 of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moo63ol w(vcfq)bp7h v0ln's radius is 1.74c370 q) vhvob(l6l fpw $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but kd/6ai khjh)6 has the same mass. What is the acceleration duekhda)/6 jh 6ki to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same 7c 5 giqca9t;rradius. What is g near its sq; 79it 5rcagcurface?   

  Two objects attract each other g8hb; w50xpf6wlqcr *kravitationally 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 accelerathopu1:)jv obt lh y-(eo-- +vgozsw2 8ion of gravity, at (a) 3200 m h ovy hj2bs(og 8-:e+pzlu-t)owvo1-    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsiqkj d k0en9l 3ul4m7do3y;u: qde the Earth where thk49y q 0 u mnd:quldl3k73oej;egravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into hfq+h vb9pmse jz+ )hn;x8d8.i o+)pe a sphere about 10 km in radius. Estim z+m +nq9oh)v)h.8 pfx8peie;jbh + dsate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, j6xajp zd2 :c7q 1se-iwhich once was an average star like our Sun but is now in the last stage of its evolution, ie -2 ds 1zjjiqp:ac67xs 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 weightless while orp x(k2 3a7ntzibiting 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 km above the Earth’s supa7kt(xz3i 2 nrface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calqu .4le*q 1p(2m3z tk:.wr w1n wzsosmculate the magnitude and direction of the total gravitational fswl.e1tsm(zq 12zo.*npwwm :kurq 43 orce exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side 5t2lw+ a/yn/d90jytmna 1 yxg0n jjj/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 ma0n 0a x+w/naljytj j t//9mj2gyyd51nsses 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 accele3mhn szn5a7p+s33sdx rz a3 (mm+(xpj/tqi (mration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, detept mixn ns r735sm/( s+(hza33+ (ap3mzdqxm jrmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perhyrm-dvwdeus ,,0:jq v) . mz:e;pv 3niod of the Earth ar.u;,h,j 0m3dy:nvv -ved )pq:zewsm nd its distance 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 stfc27;c 1l72vobjw 2ed.r u eqzable circular orbit about the Earth at a heibrl c.122j ;qu7zwcfoee2d7 v ght of 3600 km.    $\times 10^3$

  The space shuttle releases a satd8d5 :m kibn e7xsf/u18cuegfc fku, 7j0)rt1 ellite into a circular orbit 650 km above the Eacxnk:edts rf /u fu1cu1,08mk)f gb5dj78 7eirth. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshicnpyhpgs lm 6a **5uzbz (jz3k/0 +a9zp rotate 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 Qul/0nk6c ymhas( z 9+*ajz*3ub gz5zppestion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the *d vxzvxl.x*c5jn6 b; Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depexbl ; *xnj*5dvxvc 6.znd on the mass of the satellite?    s ~    min

  At what horizontal vhw z b,9/zrn;zelocity would a satellite have to be launched from the top of Mt. Ever9zzr ;/, zbhwnest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuedpz3b q0b :8)kg6 ywm6 jyup.ks to orbit the Moon at an altitude of about 100 km. How long did it take to go ar p3b0 ywq6sm.z kb8j6uygp k):ound the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pj (ug1r v 19q+eighuz4lanet. The inner radius of the rings is 73 ih uqzuejg+ 19vr1(g4,000 $\mathrm{~km}$ , 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 diameter4p syrhudmqm0pnc1*u b/3 y6+ rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (bqum sny16ph4dr+ cub p3my*0/) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg:55sneesq-o q astronaut 4200 km from the center of the Earth's Moon in a space ees5nq: qs5-o 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. They8 vdaq2m d *jv3:n3p:)cxrokk are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between thj2 om8nk3*c dkp )avqdxr:3v:em. 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 elevator ylb3(eku-/ ax7 :anhv that mo(7 veha/ xkya :3nlu-bves
(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 ofna12()c8yn qqd /ezif an elevator. The cord can withstand a tension of 220 N and breaks as the elevator z cq1q iye/(8ad2)nf naccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface ofck7 qsmwrnn9 sc 9a 5pct1v4c,i6q*(u a planet with period T , the density (mass/vascn7 n14mr *wkt(vp ,cuqic59c6 9sq olume) 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 anfs)u5lz7 fn a3tf v6n4d the period of the Moon (27.4 d) to determine the period of an artificialsvl3t)fnn6 5 7fuzfa 4 satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters av tf2cx)pmyk8 zfq191 y,z8vjcross, orbits the Sun like the planets. Its periodx8v vq198p1kj,fyyz) zcf m2t is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distazy e:j:kh**qznce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close 2o,b1mut2 tof v.rw1 xto 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 1tt1u.rx ow22m vobf, third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about ( + 0s7 cc(l:l s4lf9*iec4wikq qatpmthe 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 y)g/zbcm/ bo h 47ejs+dy7t t6mass, period, and mean distance for the four largest moons of Jupiter (those discovered b7t7g b /y)ztm/sj6cohe4y db+ y Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Mooy.p8 1 r x-91sovt2e3jgl6pd oilu: sbn. u:yvel9og l2 o j xrs dbp618ts-ip1.3   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moo e*ua5bx l,27aizv7s p6t.mi hns, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the ves7mp6 .l via57uta zbx*,i2halues 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 (which soe8gi g -2nc /nal 87dngzg1cn5me space scientists think came from a planet that once orbited the Sun but ig1cgz8n an/d7g 8 2glc5-ennwas destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the forma; -mkf-mftmv28c zbg9,im 7+vflid0 of a band completiz--7avvmb 8i,g+m l 9 fdck mmf2tf0;ely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to 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 hn3w+l11fyi mi anging 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 massy1inw+i3m1l f is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s sur6lm 2-dcrfs +tface will the acceleration of gravity be half what it is on the surfa+m s ctd62-lrfce?    $\times 10^6$

  On an ice rink, two skaters of equal mass greqnyf tel+t91g7-h 8fab hands and spin in a mutual circle once everyhyf-gn ttf l1q8e +79e 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accel3 dsx5r;8vn ,y;ltvcleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate8ltxv ,vn dy;3rc5;sl. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a a *d9sr:gvc)gy y3gzh a;fu(:spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with eq9g)gayc zv *s d 3:;(ghru:ayfual and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wz* ewvv,e:6qvhen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wvqv,evz :6*ewhich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rota80vc pc 9+c aaf/vni wy4)*gb-lm rbe8te 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 an effect equal to gravity at the surfaa+ vpaiwg8)vc r* -ncb9lecy40f/m8bce 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).a s6jhg*oy c;,uei(:j
(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 accelehd 6dm s7gqq: sl)-,mvration due to gravity at its surfml76msqhg-:dvdsq ),ace and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectepl sjkxkv 4+2zlq+ o:na(f ,z2d from the vertical by an anglk 2n (lxzop, v slqk42:a+fzj+e $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design2vt fbjxb;0m+orlt+ 8tl7 sq6 speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of s6ttblmrvb8 0 ;x f+ot j7s2+qlpeeds can a car safely handle the curve?

  How long would a day be.x)kza d 6bznfyakqj)/7 vc8 s5ww0f7 if the Earth were rotating so fast that objects at the equator we8.)yz qw kba) k/7 f6xac7swjdn vfz50re apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.lgry0 t .c+v-mtbt 84vtq 1jq10 $\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 rot6f0)4 m:nezy,az/y mv9;6dqdgy y fio cv7 e;unds a curve of radius 235 m. A lamp suspended from the70f tiyzf9q;g c vd )v;e/nmemyoy4 :d,za6y6 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 massive as the E8hzt gw 862iowu0l y(oi rug 2u0lu(o+arth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of J0u2ltih o+ wo 6z(glu8(rogu0 u8y iw2upiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced tvlt;l oqd931khe 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 blov;t dk3l1q9 y 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 shown inh k83cv;0 hui1 dtipzv,nfb,) Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normauzcvnh;b ,10vfh 3dti,8pk)il forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) ugd9v6d)rk 2 sz7 asugsq;7(+ r+wiffvtilizes 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 si dz ( sss772dgv r9;)qgv+rkffu6ai+wx orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billionv5u*4ff g9 hch km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is 9fhfcv 4u gh5*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 rnh:gpjj5x quw6/a +d-epair. You are in a circular orbit of the same radius as the satellite (400 km above the Enj6 ug -hjqw/dp:5x+ aarth), 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 meax( ng v1vm;hx 8ri5u8kn distance from the i vrg;mn(85k1hxx u8 vSun?   
(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 cou*fxrymjx; u(;ld actually "feel" yourself gravitationally attracted to someone near you. Mrx;ufmjx ;y( *ake reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arounds576yor2 fp 5pehh.x21 fibcd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years frop7sx1h25o p.yrh2 fdfc ieb56m 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 corff85k *3pkdib; :lqstners of a square 0.50 m on each side. Find the magnitude and direction of the gravitatk5bt* q pl :ks8;df3fiional 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;w i www*)5e *bysg+x x1r-jjt orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm zxhnh77*9smanu05j f-long sweep second hand on your wrifz7*50 9ashm h7nnx just watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a; og vk1t4:xrg circle below yokrvx g; :t1g4ou on a 0.25-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 wujy8x26 aq qcnd2o*2highway is designed so that a car travelin8x*j2c uo22ad6q ynwqg 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:sl9l8;efl nu d7aob4 negotiating curve:9o lf4anu; s8le dlb7s. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the 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.$\approx$    $\times 10^2$