Sometimes people say that 1(daismd bh v-x7 ty1eh3b 0-eyt6iv7water is removed from clothes in a spin dryer by centrifugal force throwing the watb0 6y71-xie h-b(3mhtsd 7yitv1d aev er outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a c w9b1 hlstlsstkos;1 -.te01sharp curve at a constant 60 km/h as w -9 e;1ttw kbts.1ssl1sholc0hen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hmf)ql w pr+yd-z::ce9illy road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on aq:+mecy:- w drp9flz ) level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hjzjxnf o4+6c7a3 fc9 rorse on a merry-go-round. Wh3xafzcfcoj 69j4 rn+7ich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled im,joe,- 58stma ut oo9n a vertical circle without the water spilling out, even at the top of the circle when the bucket is ooe8t5 auj, 9osmt,-m upside down. Explain.

How many “accelerators” do you have in your car? There arei8: -wan3yda a at least three controls in the car whiadnw3 8:i a-yach can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a bpqwf, och yui56p0sz/l8+o+small hill, 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 slf0u l pp c/zoywo5+6,8 biq+hsed 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 high skf-* e9j-k1irgomgu3 peed?

Why do airplanes bank when they turn? How would you compute the5-xgu hvv /xw; banking angle given its speed and rad5vwux x;g hv/-ius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shekcfdrnm5ha r --yc;.uk )q38b wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the umkyh-q .r c8kb -5fnc)d; 3arstring?

Does an apple exert a gravitatuaf/ i xm vp4r-ftv.*9ional force on the Earth? If so, how large a force? Conside4- fu.mp/ ifra9*vxtvr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubl-q5oh e.j 7x a1-leeode what it is, in what ways would the Moon’s orbit be differeeeoq.-d7la- j5xe1 ohnt?

Which pulls harder gravitationally, the Earth on th.8leh6e6. i -fihr zhe7 c+pvfe Moon, or the Moon on the Earhc-7ih.repf+ .fvh eezl6i68 th? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet2omhh51 (1yy(gqjtnbz rs9 8 i the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in g io5b ygnt1 rj(sh(mhy9281zqravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at t.qwe jaii cxgi*s38q qjr( ,+(he poles? What two effects are at wori.jw rq8+, 3*g (qaxiijcs (eqk? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half t ajz4l ;j7u7akibcm5*he force on the Moon due to the Sun. Why isn’t the 4zl57*jakma ju7i;b cMoon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger o8ijp c fsvnr. d2hx0 .ri3v7c1r smaller than the centrirr7xnhij 0vcv s2f.p1.83 cid petal acceleration of the Earth?

Would it require less speed to launch a satellite-jk07ja0c y+gbd. n 4l/fmduo (a) toward the east or (b) toward the west? Consider the Earth’s rotation di-0 +mkfnyodg7 c./bjljdu 0 4arection.

When will your apparent weigv0 uq0xc8(knb ht be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downwaru8nxv cb(k0 q0d, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the 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 adverseloo91q h wjf;vuz(2m3mm j v)t5y affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. j z;oj u92vmm5qwv(3 fmh )t1o5–32). 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 experiwsmqj8z a sr q57+2ba5ences “free fall” or “apparent weightlessness” between stepr857qmsa zb 2s+ajq w5s.

The Earth moves faster in its orbit around the Sun in January than in Ju*r1w2 purqr 8hly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.rp h*w 2rq1u8r]

The mass of Pluto was not known until it was discovered to n7vooyz ;9:-h p kcgue,j,cu1have a moon. Explain how this discovery enp,ok -u7e1y, on:u; 9hcgjzc vabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muptw al *dm b 5,c2w3lr5q-g.bmch larger than the Moon's. Yet the Moon's is mainly responsible for the tcpbtw5,a*d5 m-l l 2mgw b3qr.ides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed 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 j20skvp( g7ir 0rgz0e 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 tyvdsl246 3vkm7l*3gka+jkoh/h : we l he Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force3j+ls3k/ a4 le2g* v:hhkmwdy76 vlok 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 exe of ;9;av-bvy 6rhnoo1yp+l c,rted on a 2.0-kg discus as it rotates uniformlyo hf+la ;1opc9ynbv- ,v;ry o6 in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbin; aoua o.jpkw4rym8w4 *q /2lt 400 km 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 acce4 ;m 4nyk*wp2 lqa8wooa/ru.jleration at the Earth's surface. $\approx$    g

  What is the magnitude* 2dz khv-1inn of the acceleration of a speck of clay on the edge of a potter’s wheen2iznkd v* -h1l turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at )w uybczk38 4q4tgb7*s*ruvca uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed i *ub*43 )qrysk ucgb84vw t7czs 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 tq 26:kgxhyqo((gz 8wzurn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass ofhqkwz6: xqgg (2z(y o8 the car?   

  How large must the coefficient of static fri4 eihwo52 ,q1jguc:8jvoc9a ri )qc 4jction be between the tires and the road if a car is to roun r2io:cvgq59ecj4qc1 8uo ai,h)wjj 4d a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training7v*z cxp lb5(n81nmeu astronauts and jet fighter pilots is designed to rotate a trainee in a 58e n b7(zu1mv*p nlcxhorizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of vfd f a(hg871efy1dumi;)s 8hnariable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 ru;ffsfm h1a1i(nhe )7 y dg88dpm 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 d x8909isavo, /hs sgtwown at the top of awvoi,9 g ahss/08xt9s circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass jerrkw( ( sjb lml07+*950 kg (including the driver) crosses the rounded top owrjlm(0ebs7( r*jlk+f a 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 would a 15-m-diameter Ferris whe;xw9/rt z bshw+w)b7del need to make for 9h/s;xwd7wz rw t)bb+ the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vwso6;;s k rv2sertical circle of radius 1.10 m. At the lowest point of svk6s;2 ;w sorits motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axisd2f: 5la ahksl uc(a-- of rotation is to experiehfls-:alcaka d5(u 2-nce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrn xz/bb8 6/hawically walled "room." (See F/zbh 86b n/xawig. 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 frictis354-n0pryu hylzcc*;2jf c fonless air-hockey tabletop, and is held in this orbit by hccjly*2-z3f pnyc 0 ;4 r5fsua 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 m06c 0n icz9hnball which revolvn9 mni60zhc0ces 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 /hik ryh1sek8q3 i0rhx -x3+2acz oi8of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massesv9g 9gyq3: z4: ,wtljarc2wci $ 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 evy*0n9r l u5v8 oqn(0 pib-khm((q mkymasive 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 oo1nh* jw,ha 9 bz2 n/wrpa*w(fn the car (byz/ wwh j2*,pa*n9n 1whab f(ro the 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 accelerate6oi9 hta5gg17v5ld,vtwc a nr-( jnl0s uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of stati1 jg7irtvg l,two6 nc 5-a(95nd alhv0c 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 cir/ck-c)4 i,-bq ibmvqxcle of radius 2.90 m . At a particular instant, its acceleration is bv,bc x-q )/-mickiq41.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 ofc * fwrh:;-5yp7kytkg Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 13-r yw:gy*tpk7c;f 5hk 50 kg.   

  At the surface of a certain planet, the gravitational +ypmjzc,8gp 4m +br1af5 8wqpacceleration g has a magnitude of 12 f agy+b ppm85p,81m+j zr wcq4m/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 acceleratix sxcglz. 4. 0ew(-hlron due to gravity on the Moon. The Moon's radius is 1.74 4.lr 0gwc-lsx(zhx .e $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a*cppa5m 52dpb radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gra *2pbpmdc5 5pavity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but to v r -mpek .kfu a2z 8w)x(/5.,evbnw(wc,wgthe same radius. What is g near its su,co/f xv bnake vgte-r.(wmw8uk(5)w2pz,w. rface?   

  Two objects attract each other gravitati0. 8s yybwcrfp3k- hb;onally 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 grf1u ui3p i:q4kavity, at (a) 3200 m 1quf 43:kpiiu    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsi /k jl;/anxv4fmq/ qc8de the Earth where thegravitation8ql n/f v/;xjcamq4 /kal 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 /n* 2ptvz**3kp wntxkinto a sphere about 10 km in radius. Espnt*z* k3 2kt *nxpwv/timate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whisjs* .3 ba3*thoq sc t6b*tv.dc+v1yc; qcda: ch once was 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 oursva qc+3 c6sj *st1bc bhdvd3o t*yt. ;*.ca:q Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why vx+b zp(u 39yhastronauts feel weightless while orbiting in the space shuttle. Your friend+zpu (b9v3y xhs 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 surface in terms of g.   

  Four 9.5-kg spheres are located at the cor6wx9j7ck1o 1:we 7 l7vhdtip yners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerthvw97 iwjo7 t: 1d1yekxcl6p7ed on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of tzqb x x-w r/pj5y*,m3vhe planets line up on the same side of the Sun. Calculate the totazxr jp, /x5qb3-m*vyw l force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at 1tg, v6ewmrjly kwai6lv h,w h75+ m*5the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the ma76,r5mkeaylw1+5 wv t 6m,vlh*g wih jss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for /-q,p4xyvt 0sq dp b*wthe period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, E xp*0qb,v4qpy-ws /td xample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orab- zfy5n8wf x2w;gqwcv.36l h0sbb- bit about the Earth at a heighgc y5 .bal2q-z3sx8 -ffn;bh0wwwvb6 t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65 6mir: 3i-dek.l ot2voncl +u;0 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the re lt.oum;k n:oiri23d-+lce 6vlease occurs?    $\times 10^3$

  At what rate must a cylindcv7y1t2yll kc, l3ub:rical spaceship 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:2 , yvul 1l7ctlyb3ck needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ealu2yg+,v8 obrrth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above tvgy8 b2lu +ro,he 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 have to be launched +7n e imdzkc1,, 6tvtzfrom the top of Mt. Everest to be placed in a circular orbit around the nev6t 1dmcz+ 7tik,z, Earth?   

  During an Apollo lunw 1/ vbv 4pxy-2nwdu9tar landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go a4n/-wy2pt1 x9b vuw vdround the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The i,)rcz z,h98cqbwq m 5jnner radius of the rings8q b h5wmz)z q9,,rjcc 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 10aa3s b01 a.pgxoqpw/ 5.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (baw3 p.bq s0a1p/ 0aoxg) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg ass9fi4u+ fys j yb./o,stronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving a+/yiy49o, sbfss fu .jt 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 5asv tmh*t)+dof equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a pointv+dm)tha s*5 t midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevat44nu rex9knc;a3 jv1 kor that moves v1 ek3j;4nn r kcxu4a9
(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 suspe3k +f i ey*nxfj*x*q)q2m y nhjs3,;mfnded 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’ j2f ;mq *) nhfs y3i3qexn*my,+fxjk*s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planggcd;p94 0xgq qsr n8+et with period T , the density (maspgg +0 8;xcr9s qg4ndqs/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws andhjn d(r+3rndbpg5cz x6.(n6h the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near thdhz6.(r n3+hn cg(p65nxr j bde Earth’s surface.    s

  The asteroid Icarus, though onlb h(yi) 7ic ec yxs*ka+6/prauvup35:y a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Su*ruicb k/ap)6+shvpxcu:7a y5 y3 (ie n?    $\times 10^{11}$

  Neptune is an average distance of; kuko mzk;((q 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 roughl c9/e9en4 4 pw,8sh:u-fg/xadx:hm( hpphmdo y 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,g 9daeh dfp:48 //(ho:mc9phx- 4muwhpesxn s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galax7 rvbwmka 57; ln5rir6i4f8 4gcvx6ck y $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, per (wmuy/ur+)j0m4 e evbiod, and mean distance for the four largest moons of Jupitj+e/umbvm ure)( wy4 0er (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 perio 4-e vs:nc)p 0dojt8dca s8ja(l,l/std and distance of the Moon. j8)ac v-nleajt,p8 ( ls4sd scdt/0:o    $\times 10^{24}$

  Determine the mean distance fnux tsl gffo w/ e963s*v *a7vk5q2ii*rom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use i *23o7egnlwsf *9vs qaut*x/i6k v5fthe 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 between Mars and Jupiter consists of many fragmenwed2d :f* kblo.,jia0ts (which some sp kae ,:f2dl0w b*.ojidace scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form ofrf j14j8 n9bs xqa;1xi.dtm*g 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 qui9sxg 1ma48jf. q1dtr;ni*x j bckly 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 hanging vin b;9nb(nd*l oye (Fig. 5–41). If hisb9 *bnl;(od yn 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 s/kzqerwp1ug3ah7;q -w xrj17 urface will the acceleration of gravity be half what it is on the surface?wzxgp re w/1j7q r 7-q13uah;k    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and sj uz7jf ,z9qz:pin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masq,j:jz 7zu fz9ses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once p)6tahfbfkq4 ji. gt* bm)8+dc er day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction ofm 8i*k) h t4f bq6+gtfac.jdb) g is this?    $\times 10^{-1}$

  At what distance from the Ea-3ae- y8-.s xf ai 4ju4zlpuzirth will a spacecraft traveling directly from the Earth to the Moon experience zero nete48-a zx -ij3zs pfuayu-4i .l force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sca vsd6(6ioq)mhle in an elevator, it do6qvsmi6)h(says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thap(ub: k5ds)nfbk- e3xt will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the te un-k)bs5p fkxb (:d3ube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fiyqw+d+0c 5p 8facd9vyg. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acceleiov2(+nyn hh5q/h; o n d4.oyq(yyp.0 /hdkt qration due to gravity at its surface and the gra(0n dp qy2 ndo/hqk/h5h+oyy y4.h;q.not i(vvitational constant G.

A plumb bob (a mass m hanging lwb ,uy0vmxb+(60mlg on a string) is deflected from the vertical by an angl 0 ,w+ygmvbmu6bx(l 0le $\theta$ 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 ,f)6j5abnuom x2nbk .banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what ra2x)6.b nomf,bknj5au nge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotathp6z-)zc3az05js )i *o jgnswing so fast that objects at the equator were apparently weightless phczg * zsoaz0jwi)5n6 sj)-3?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apv+wll2:sky qn 5p9mh ,art of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve;5s rxm w.*gol of radius 235 m. A lamp suspends; .rg*lox5mwed from 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 massive /(v5 d.ewuiq uas the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet theqd5viu. uw e/( size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the ock3 svd h*ebyj h8(;8presence of an extremely massive 8eoh3 (d;sj k8by vc*hcore 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 e8kv+2qak,d9-mvpl8v7z z3m tv w w,d 6wda0u hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature dz9 avkv,d w+u,w8 qkv73-mpv02 6 zwl8 adtmeR. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (Gp):zypf34ej ;cwy- e gPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determic;g3p ye jp-w4zfe ):yne 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 :hbzea/w if(0-ze 6we.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . e(0iw bzh waeze:f6 /-Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in n-1hk(ch*7fj7g 1zw pgpaz- oaeed of repair. You are in a circular orbit of the same radiu 7(pk1wohac*1p-zzahg7j fg-s 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. ( 6v-o)ap ta v*i,z-y9-brkjd na) What is its mean distance from) -6ayjr-opa- vi tn z,9b*kvd 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 yokcwb4pj s ,m2uah .*-yp:(cxru could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumpc m-r b2(s:,xj* .ucyp 4awhkptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ocl-.qo xupud 9 b92ptv1*lx( zf the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center9douz9vcu2pl( -x1 ltbqpx* . $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on ea77ip ,m8q*yq euija-v)22)hai qx f;y.opsya ch side. Find the magnitude aj hp)fy7v) aoq-, qxuiyai 8a*y 2;e pi.s7q2mnd direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500f4f +ezq4yfk6klq y +3 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 thxi/f(d6h *(z2c vcuvh p8v+rc e tip of the 1.5-cm-long sweep second hand on your wri(i2z(v ch/fvcvx8p u* cr d+h6st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in7ye0+ae (e )ifztdp-tdil0 4n 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 ane)( t z 7nfad y0id4tl+0-eiepgle 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 th)qfdej2x 2wy jds2y)5 ht6 p.nuwe.4iat a car traveling at speed2)4s2uwi f6 yep.)e2q jx dwdh.tj5yn $ 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 nexu(kug a(c2 fsp9-:2y c ilv0agotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less 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 th92u-p 2 xc uigay (:ca0ksvfl(e 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.$\approx$    $\times 10^2$