Sometimes people say that water is removed from .)5h/eb2 .dielwf vjzclothes in a spin dryer by centrifugal force throwing the wat.2hljeewf 5zdib /.v) er outward. What is wrong with this statement?

Will the acceleration of a car bignz0/ tlr -3 ss 2/2dtyzqj;je the same when the car travels around a sharp curve at a c/z /;ij-s32z jlngd02r ty tqsonstant 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. Whz(fv- ndh j( y5y37lv6 6ucszwere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip betwe fwydusyz5 vjn6( h7 6-l(zv3cen two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces 6owsc gcpb0:* acting on a child riding a horse on a merry-go-round. Which of these forces provides t:sc*6gw op 0cbhe centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the watefs y6cyr)s6lssxg6* j u ; an,v9a3-ier spilling out, even at the top of the circle wa,ync 69yrus -ie s3*gj;sa6v) s6f lxhen the bucket is upside down. Explain.

How many “accelerators” do you have i 2137lb; efw ww6ckwwpg/e+er n your car? There are at least three controls in the car which can be used to cause the car tww / w37lerebwf w+;cgp612keo accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyv ye,jrrw ajl;v.g4/p8iyulmq685eaf)z1 8 jing over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feee 88 rq5jv.y/ ju 4)rfel pim;61jawl8g zavy,ls 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 wh .sdm9t y:r)jlen rounding a curve at high speed?

Why do airplanes bank when they tura 5 ,thq1ltpt)sak,q1n? How would you compute the banking angle given its s5 tak1t,)qq1ahltps, peed and radius of the turn?

A girl is whirling a ball on a string around her head in a z+hbk9nu z7h+ horizontal plane. She wants to let go at precisely the right time zbu7zhk++hn9 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 fx f/,8tor0 i-2x3 dn6asiivce7fl o) force on the Earth? If so, how large a force? Cons3ieo f x,rs2oci 7f i l6dtvxa08n)f-/ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass we;zopf tgr14n7re double what it is, in what ways would the Moon’s orbit be differetf7z4 nro1 gp;nt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moop x9gl)vkhwa e*5vy os-;b-t.uo32 nsn on the Earth? Which;5buw ahe 3kl.xy o-n*2svstg-)9vpo accelerates more?

The Sun's gravitational pull on the Earth is much larger9tdoc uhxsc cw4h*g9eh1 5.p( 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 Eartewc 9 sgc(dht9 x 5hu.4ch1op*h to the other.]

Will an object weigh more at the equaa:e -x : t/mi8ec:zkoitor or at the poles? What two effects are at work? Do they oppose each ot k :e- :e8ixi:o/tmcazher?

The gravitational force on the Moon due to the Earth is only about half -1o3hhsr/e,f0w g zqethe force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Ear,s3 1 e0 g/efqzwro-hhth?

Is the centripetal acceleration of Mars in its orbit arwz*qf/k5( ijp ound the Sun larger or smaller than the centripetal acceleration zqk(5/j* wpfi of the Earth?

Would it require less speed to launch4 f3l6vbxoh91 8c;/uj (*aee abgvvph a satellite (a) toward the east or (b) toward the west? Conside9h uav x/8lhb1og4v (bf*6j3ea;c epvr the Earth’s rotation direction.

When will your apparent weight be the greatest, ad5).w ss1jupdg a tp+0s measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accd0 +)jp1 w5sput. gdaselerates 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 long periods in outer space could be ad(rsl 1yle89 zkmo7*to versely affected by weightlessness7zl(kt m1o9e lo r8*ys. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “fr fj.: c4r+9 fmz:wx loclrxc1trm7y e6mm c)+0ee fall” or “apparent weightlessness” between ccrt17:zmmmr:jl r4l.c+co690m+ fxf )w x e ysteps.

The Earth moves faster in its orbit around the Sun in January than in July. I6qb y:nvsnt m fu z+/r(87o9kas the Earth closer to the Sun in January, or in July? Explain. [Note: This is not mu+as98kvrufz/nn(7 6ytqbom: ch 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 discor *yezmuxj: g*k2+,gyvered to have a moon. Explain how this discovery uyg2e x*:,* zj+rm ykgenabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th 0gtljo d8o-bzf;5c l) 0dgrx;e 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 merr;l gz0gcd 0bof85)o-d ljrxt ;y-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 198w wix6z)+1wjx 0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbit around the g04 * mulch9htSun, and the net force exerted on the Earth. What exerts this force on thh40l9u tm* ghce Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0- zm 4(s4zim;cykg discus as it rotates uniformly in a horizontal circle (at arm’4i;m(z s mzc4ys length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sug70e 4r*rzzt , x5nbsdrface, and circles the Earth about once every 90 minutes. Find 0rtn e dzg7r *4zsx,b5the 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 oz 75*mbidog:jf the acceleration of a speck of clay on the edge of a potter’s m*5g7j iozd:b wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of ae3 kg6min)k, o7rad 8s string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as on ,as)g67e k3d kimr8shown 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 a turn of radius:*hd-h2rwg eh w+6usp 77 m on a flat road if the coefficient of static friction between tireshh+e2s*u-: dwp ghw6 r and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of statj9.x m 8jdd mg8+qbu 0vt9uop/ic friction be between the tires and the road if a car is to roun j9qg88duoj9uvp/bm 0x tmd.+ d a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to roty:c; bjc 3r2.:ugx azlate 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 rotx;:r2z c.yba:g3 l ujcating?    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 a54h(gsc vjzoz s3c 6z( rotating 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 reached4 s(ogjz3v5z 6hzsc( c 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 dow- +t(krp eg)wen at the top of a e+g -etpw) r(kcircle
(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 (inc+s22xw da4 s/hmjw o lkw,7ji.luding the driver) crosses the rounded top of a hill (radius =4a wj2,xksw7+/hjd il2smo. w95$ \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 maofnj5(h sj7* bke for the passengers to feel “weightl 7*nbjfsoh5j (ess” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirledq4 :f94dmgbsp wtut4 qjot 3;( in a vertical circle of radius 1.10 m. At the lowest point of its mo43u4fjow pq 4(msq9: tbt g;dttion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if wi2 gb ab / 3 4v26o6wqkctoo1.woc(vka particle 9.00 cm from the axis of rotation is to experience an acceleratiowio/6(wck1o b2g6otwv 4 a .qb ckv32on of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylinhh,d d gr4txrl n6ximp,*6z(r5 :sy g,drically walled "roo4 ,: rh,(6zrd p6dmixn g*r5ts,xghlym." (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 frictionlessfgc1b o12rj 2yz.5 w:ksy8l yi air-hockey tabletop, and is heldy8z ws2o1 g .1c:ljfk r2b5yiy in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ball fz -y+8 blv6.40i-yce h thffwwhich revolves on a string 0.600 m .c-fyeh8yfb6w hi-vf0lt z4+ 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 isp b7/f drm9wz3 perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses 9swt6)jdp j w($ 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 maneuvq(ph)mg4 e8w4 zvyu.x er 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 centrirp r* ;0rkf *h,o(+ 2tu,rmvpopd/ncipetal components of the net force exerted on the car (by the ground)i,* mr pok rn,u2rdrcp t/p;*v0 fo+(h 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 uniformly from the pit wn:p:qvjf72m area, going from res2pw7v q mj:fn:t 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 to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a dyk:xc(*)fwer x,sxq.g 6 h7whorizontal circle of radius 2.90 m . At a particular instant, ( cqkwx.g x6dhrf *x,ey7)ws: 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 grav0eopg6l0l- 8 hswr p2ca di*b0ity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s sub 82c glwdp 0e0i0arhl*-po 6srface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mag 61drt8/cm ovvnitude ofotd1/6 v8crmv 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 g0 cvmg0qk0lc(h f4 0 jz1.orseg6 vv+eravity on the Moon. The Moon's radius is 1.74moh 00 4c1(ksc0 gg+rvvv6jql0.ee fz $\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 has the same bj:r wu4ao8;q py gp(lw y:ty tv(.8-mmass. What is the wj vm8p;a4.gwbutt: -(yq8l pr (y o:yacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eart54945njor swoivkz +gh, but the same radius. What is g near s9o z4jnw5i4+g v k5orits surface?   

  Two objects attract each other gravitationally with a fodwt1o d7ab9s ,rce 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 o+lk y rmhp7l,8o)p qx9f gravity, at (a) 3200 m mppllyx)o7qk9+ h, 8r   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from t5s* u ex;adud9t1po7z2pmb 4qep;q+es n5rh2he Earth’s center to a point outside the Earth where thegravit4+euo 5 z;t;sd1hmpeb x*er92a2 q 7p5nsdpquational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star j8enxn lu- 3acu9ca7:has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on:nxcl uj89a -3ca7eun this monster.    $\times10^12$

  A typical white-dwarf star, which once was b 9ee-gm8fmp:emo::i an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surp8m: 9m og-e:ib :mfeeface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting inyvs 1uy.j:j8 o 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 thev8 uyyojjs.:1 acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located a j+-gw) dof5eekf4 l(st the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphl)dwfo eg(-5sk fe4+jere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets linehe;hw64n0 )kuya25at fmz(lb up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fonw;) aty0ae z 5k26lh fbh(4umur 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 Mars is 0.3bjqgrsrm(t: 6-g0pcu vyr; 0 +8 of what it is on Earth, and that Mars’ radimtq:v0gr-6 y r pjgu0s;c(+rbus is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knowntdwe6zx : a 4:g6 gk+bof0hfn* value for the period of the Earth and its distance from the Sun. [Nxt6f*: k bg:ofzdw +64 ga0ehnote: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sateg*6 pafy+q;lvmb )*i fllite moving in a stable circular orbit about the Earth at a height of 3600ay q*p lfm+fg6;*i )bv km.    $\times 10^3$

  The space shuttle releases a sa:jq3c6.pko )kk 5yibatellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occu:ic y3.)pbkkjoaqk 6 5rs?    $\times 10^3$

  At what rate must a cylindrical spacesf3k6pymsgb59 /pj2 og(f t m82w elj(phip 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 needef t2jyjlpkm9f5 gwg 26 m(/sboe3p p(8d for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit thekeq gv2/v,/mox f)+f(t :w awh Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the kwamevofq) /2,gxf+vw(ht: / surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite .ae7zcpqb0 h;x dew7s-/u ij3have to be launched from the top of Mt. Ew-c37 udx;h aj.ez bq7sepi/0 verest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command mod aa)ol.7()c ;h0nzk zimj sbx(ule continued to orbit thzb(7nm 0aazil. k(;c) h)j xose Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that 8j z,umj 04vbiorbit the planet. The inner ra vzmij0,j4bu8dius of 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 15xu * xfn3z)m/c.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, andfc/m 3un)z x*x (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fro lgl9ug*tvj9, m the center of the Earth's Moon in a space vehicle * 9lv,jggt9lu(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 st59r/2iqd.nih af0 xaz ars 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 them5dfz. hi9xqn02/i r aa. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg e f7ww -oqo8*dwoman in an elevator thatfw *dqo -8o7we moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling ofor9e qx ov 87u.vsnbltq*b5;/ an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minit79lx5oq ueqv/b brvo.*sn8; mum acceleration (magnitude and direction)? a =   

Show that if a satellite sz9xgx))sve ) 5 ghgujl6 9y:sorbits very near the surface of a planet with period T , the density (mass/volume) of the planet is she u9jvg)y lzgg )sx5:s9 x6)$\rho=m / V=3 \pi / G T^{2}$ .
(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 Moon0phz.g 13p4 -yyyk khj (27.4 d) to determine the period of an artificial satellite orbiting 4p -1yp03k y kyzhjgh.very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mehf 2e /k9;k-y7hlwpz jters across, orbits the Sun like the planets. Its period is 410 d. Whahe2khl pfw;9z7 y j/k-t is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distas g5 +:oje jp:pq80lvfnce 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 the3(-c6 uub(zqk glj 1my Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Keklc36yz -mbj u (1qu(gpler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centqcj/t fg+ f0*w(y 9zwier 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 for5bdzn(6roz* 3gi:8b)ner1v5k c sgke the four largest moons of Jupitern(o vr*35e5:z8 zckr1g i)gesb6 bdkn (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 permp* ly 62vln( 9 exlo9jcjz7b0iod and distance of the Moon. nvo0cxl z*e6jl 9b29pjm l7( y   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mo zw,2m,ubi vevo9me3/ons, using Kepler’s third law. Use thob m, iv2ewe/v3 ,mzu9e distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betwewc+ li j*x p:k 8gjnzcipg;5:jj.v4w+en Mars and Jupiter consists of many fragments (which some space scientists think came from a planet th5:*pjipv;8.c: 4++w jznc j kjigwlxgat once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the fo6 1vl prs6pr6hrm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is 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. Whh6l pv r6p1s6rat will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in ntu iv9 aq p78d,)kgcg/6* siuan arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a foi ,i q/gg7u*)duat89sn6ckv prce 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 surfo)jiep(zmpj+ )5km1vgk np) +) ww+ hgace will the acceleration of gravity be half what it is o m po+vp k)gj)w+pinzek1m jw() )+5hgn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal zjdut96 wfm/z67k cp1 mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg1 /76wzmtz9uj pck fd6, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acx/otzr cv*:zpm1h e*7c4)phr celeration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effec:p47xh1vo p*/mzc)rrce z *tht. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direc3jk13b7q*2cmdd0z ocg je/yp tly from the Earth to the Moon experience zero nety mjcz12p* d7j qc0ko3bg d3e/ force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is amxa3edzixahts*33+is 7 d9- 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the e-iist33h3xma azsd de*97+ axlevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circularqe x2t2qj m+9wo8yw/lu8mn8 l tube that will rotate about its center (like x+l8u8 2nq wo 2jtm q/lye89wma tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertg,ox b p sh5f6red6z1,ical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius0-hc 5i jl/xox r, the acceleration due to gravity at l0jo/i -xhxc 5its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is defli xdch o*4*coi*p,ig8 ected from the vertical by an anii*,ogcp 8 i*h*oxd 4cgle $\theta$ 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 coefficientx lics;uz;x+by y86f : of static friction is 0.30 (wet pavement), at what range of speeds+cxxfu:b;;8sz6 iy l y can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast z;gtyty*d*j2 that objects at the equator were ady*zj; t2gy*t pparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a coj(va vn3 l9ej1yy/8 wxnstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a consn-dge(g ka(2b r(/gog p3 )afrtant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out tr3p gbegfgg(d ()an( -ka2ro /o 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 Earth. T am-sxf7qpay( 4m8 :wy nqq9h-hus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of (4ay -wq-hqps: 7mq9f8anx mysuch 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 dl/e hl:zh n4:r4ia o,beduced the presence of an extremely massive ,eobhri:la / h zn4l:4core 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 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 hil5uxqmy9)g,nisi z f.;*j+a y sl 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 tq5g*i, 9fy+n). ;isaumsy xj zhe car go without losing contact with the road at A?

  The Navstar Global Positioning System (Go5 f(ey vpnb5)dg-l 5oPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of a 5lvnb5 oe)oy -(d5pgfpproximately 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 billion km0mwk)2bkpg4ie nh6q*ah l3b4lg k4t4d- cs n+, is meant to orbit the asteroid elk4hbn +qkpkn)3*t 4cldwha gb 0si42m 46g-Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space zbrx3owyv -had);:w0 shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the saao)hzy d-;:b0 w3vrwxtellite (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. (b)tdchvhfbe87a -8aq,k l 2p;a) What is its mean distance from the Sun? - vedbk2 )h,qlca7f ; a88tpbh  
(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 couldiw-*n2g 5k4 czvh.f ds actually "feel" yourself gravitationally attif.4-vn dc* 2ghzsk5wracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a distah *l0ppnc+1 mxnce of about 30,000 light-years from p l hmcn1xp0*+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 ark w6ie, ;bwau w-0rb.eq i87bte located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of th;ki0bub7wwt-68 ,q r. eebiawe square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 550c hyf rxirm /-,*5 :6uugslzh70 kg 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-long swee0 6g/3ns jgkykp second hay nkkjg/6gs3 0nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored qlmams 3 ,elq9o9,rd 8and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: Seeamdml ,q9,oq8 3ls9er Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desii ae :z94 cs5:skwoig8gned so that a car traveling95kg i:swo8cs ia:ze4 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 +q 6 nmat+ abnac/ w/7;qezn.ec,zt1ntrain, the Acela, utilizes 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 acceleration, is thn+ ;6n,nz/cn c aqzmtb 7a/awee+1.tqe 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.$\approx$    $\times 10^2$