Sometimes people say that water is removetn*wg :hvlhl+x0ou+sw;9 8ftlk,ph;4 v f t-ed from clothes in a spin dryer by centrifugal force;l,k+t+ ug-hw0ltnhfv 9so l4;f w hp* 8vx:te throwing the water outward. What is wrong with this statement?

Will the acceleration of a)r,h; 5 nt4c xnlf:rag car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explannxa)trr;, lf g:c 5h4in.

Suppose a car moves at constant speed alongqid v3 u(79j xl:,fag9zzhjg /g1nuw+ a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) :xz,(/3 zag7fqdh1 n jlj9+uug9w gi vat a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting j q0i -x3ik9edon a child riding a horse on a merry-go-round. Which of 3- jkedxq90i ithese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci bxy/lkc5ymuhg 4:4z6rcle without the water spilling out, even at the top of the circle whe4/ yy:zg c5hku6x 4lbmn the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leasceqolsa4c 0k:h d(y:a;si py9 n4gd12t three controls in the car which can be used to cause the car tshg 42(1;c yld9ne0ai:4kpoya c :sdqo accelerate. What are they? What accelerations do they produce?

A child on a sled comesfz.13 8 f8w,mn. yichwh( g(e- tngxcb flying 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 feels the normal force between his chest and the sled decrease as he goes over thy.n cht .8inm3hgw(1w(bzgef x-8 c,fe hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speedbbw5 q6(r.gu i?

Why do airplanes bank when they turn? How would you compute abjc:tkxmvb ((,4g5ethe banking angle given its speed and radius of t(vm4axg :bjbe (5t,ckhe turn?

A girl is whirling a ball on a string around her hqzqj-r)er 9f6q k7x7x ead in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side oe)z 6rf7kxr 9q-jq7xq f the yard. When should she let go of the string?

Does an apple exert a gravitational for)ar);,.ap wx peakky6ce on the Earth? If so, how large a force? Conswa.a6; )pk )kp,ea xryider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wpl0 (ogch/ f7lays would the Moon’s orbit be diffe0 ocpl hf(l7/grent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon onyjz 6 pl6)dj3p8jyz;n the Earth? Which accelerates more?86p znpl)z ;6 3jdyjjy

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tr-a 4lc2o(ht lhe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationahloc-(la 2t4 rl pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whafx6+ax mh x1eoxt6 oc1cl3:6xt two effects are at work? ftoaex+ m 66ccxo3h6 x1x1 xl:Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the fwqo6 ;.t l+ds; n5mjcaorce on the Moon due to the Sun. Why isn’ ;+wj5lcqnm;ad t o.s6t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit ar gig6sb:yz55sound the Sun larger or smaller than the centripetal acceleration of the Earth?65sy: sgbig5z

Would it require less speed to launch a satellite (a) toward the eastsp 28x;nygaj 9 or (b) toward the west? Consider the Eaa8x ys2g njp9;rth’s rotation direction.

When will your apparent weight be the my6mvz. .jcbuc qd**1greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c*.*c y1z.um jm dbqcv6) 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 adv9xwt2dqohkqf y9 *3 m;ersely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) ttyh9fd9 kqqmw*; o23xhe force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “k5cpstf bt5v4den 3l:p:sg+a4c2ou 0free fall” or “apparent weightlessness” between ste4apf0:g+d sl:4 pctso2 uknce35tv5b ps.

The Earth moves faster in its orbit arykhj2glhusf0 0:6 c. gound the Sun in January than in July. 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 k2gs :0ygu0ljh6 hf.crelative to the plane of its orbit.]

The mass of Pluto was not known until gexryd w.d;h9b5+ 0m6anl)ar qyg 4u.it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass.9y46xbr.d 0u lry+g; g.nh)dm aaqew5

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet thk; hhuk4jpcg 4m1) f0oe 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 cente go)uhkp14mck 0j ;f4hr 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 4scf8g7 w:clx1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleraty) 3m6voo/r-y7y4 py n)fwvwgion of the Earth in its orbit around the Sun, and the net force exerted on th/og yo nmr67y 4v)wfyw-3yp)ve 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 exerted on a 2.0-kg discus as it rotates unifh7y z.61ip(y yol2vqj ormly in a horizontal circle (a 2oz1v(p.y67y qhyiljt arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttr9mq( riz6zldc )/ tk4le is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space zi/kz6d)m( 9rlt c q4rshuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of ae5d nk, :gp:ek potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dia:,dke5 g enkp:meter is 32 cm?   

  A ball on the end of a string is revolv8.e0 .nwu nc20 hktpkyed at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig.u2w80knehk0tp. yn. c 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 r kwje,8w)rrrq9cee 0 a7l: w.aadius 77 m on a flat road if the coefficient of static fricti.re0a8,)ekwq7 : rw9 rwaelcj on 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 betwp z 3p (-9olrb,4zk jp4yzn1fueen the tires and the road if a car is to round a level curve of radius 85 m at a speedpf -zzpl9(kjy 4n4rb, 3upz1o of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed 152no ,brxmwum o,-zqhb : 7rdto rotate a trainee in a horizontal circle of radius 12.0 m . If the force feloru bmb-rdz5 ,7:, h2mxo nwq1t 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 1jn; oja7an3e )1.*yo.pkyuz mvr 3p da rotating turntable of variable speed. When the speed of the turntable is slowly increased, t;e1u) 7kda.n.zyn rp1oa3o myj 3j*pvhe coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mut frt-wbh 5amj-g9m ,nj6a(;fst a roller coaster be traveling when upside down at the top of a ,mtt -5rh(fjgaj- mf6b9nw ;acircle
(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)wcnskr4jy:q;s0s* 0n r,j3w rle7qn: crosses the rounded top of a hill (radius nqc ;s,3n4 rs0 ys*qj 7knr w::je0wlr=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 wheel9v8y;ou kti6c need to make for th;ikucot8y 96 ve passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kgk cimd-0 o4n4s is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope su0k-csi dn4 mo4pporting 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 t3 9jbds1 evbe 7sr8f9whe axis of rotation is to experieb9fjves7s13 9rbd w8e nce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival y eckj3* pytq9oybn91n(4)sl , people are rotated in a cylindrically walled "room."tyj(3p 9yo 9 yen)*4kqsb1nl c (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hocke26vuvp* 4 .xwzotayu3y tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown zo w6p24u 3*yu tavx.vin 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 this5*zju378dl,ea xxeig.fcl*p time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, fina .jlgf7e3z licx x8**p5,du ed 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 peuffedvh30)-kt sg-p , dp ;jo1rfectly 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 masse6lc9y ng mjyx5qaabj/ r/r+e ax50( (is $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertical45rem:-aipg tly 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 -4fir 4sk/l mucomponents of the net force exerted on the car (by the ground) in Er-4m ilkfus/4xample 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 pi gy/2p nukws:2t 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 u2yg k 2nwsp/:friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rawg:ufl1e.)eg hl *en t2r 5tm9dius 2.90 m . At a particular instant, its accele2g 51 we*hg9 mun.fel):elttr ration 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 spacecraft 12,mcd9l ijb ((b1800 km (2 Earth radii) above the Earc(ilb dm (1bj9th’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, thh *x5dpokm9iyl (gik er syu ,-.30m8ke gravitational acceleration g has a magnitude of 12 s5 ehuk3-kmyd*k. ipl(yxom 8i r,9g0 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 grrqecbav+ ilvp)9hk * x17r1*a avity on the Moon. The Moon's radius is 1.74 ixv7** c +rkbarpl11 eqahv9)$\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 yz .w ;1ydv9rp- qawa*)h z3bhthe same massprz3dhw a-9yb1y*ha qzwv;.) . What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timm r3x,u-a s/ asl90sdfes that of Earth, but the same radius. What is g near its surface?/0 s rsfm,su-a93lda x   

  Two objects attract each other gravitationally with n*dsn z0-,qn y)ifpr 6a 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 gravvtf2g,i:ab f 5ity, at (a) 3200 m atf:i,g52 vfb   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ear - sc3qvz//xkuup49 cq8vswk9th where thegravitational acceleration due txqs-s c w39p49v/ zqku /8kvuco the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the m*, i-s9chj0o 8tupjo4yl 8o gmass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity ou8h-*ty8icglops9 4j,oo m j0 n this monster.    $\times10^12$

  A typical white-dwarf star, which pfentq9(snwfy f(a7sd /(9*w 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 our Sun. What is the surface gravity on this stardfnt/sq*enfp7w( ay(9 9fw( s ?    $\times 10^7$

  You are explaining why astronauts fee0pf:bxy ro:5uv d3r3wl weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity vodp35: fb0 rxwu3ry: 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners ,6 yfh)2 a*ai def,xqcof a square of side 0.60 m. Calculate the magnitude and direction of the total gravita6dyef ic xq,h* a,2fa)tional force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planl) 41h0zolvdojr (z jckb 79l3ets line up on the same side 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 masses arehkl47co (jlzbzjrvl931) d0o $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 grk4x(xl p fgk;u;)so 7yavity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 kl 7gpsxk y(ko u;);x4fm, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value ,b-qmawf5 cv )for the period of the Earth and its distancw-qm 5ba)vfc ,e 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 stable cirgl;.y4tpu fc:q:cv 7ucular orbit about the Earg 7uy4v qlpt; uc.:f:cth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellit44ph9of;txo k(hs ; qzlkh v530p x*lye into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (4;hhkyz ol3hx po5vp *4kt0l9fs( x;qrelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spacev ;mwt-gijyo1g-kc5 7ship rotate if occupants are to experience simulated gravity of 0.60 g? Assume;kg--t71ijvg 5m ow cy the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orb 80vo 3mg3hgbuit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satelliteg0 83vg3o mubh?    s ~    min

  At what horizontal velocity would a satellite have to be launched fr t2u*3j vq fp;,:rmtvm:2ogyvom the top of Mt. Everest to be placed in a circular orbit around t3vo ,*trjm vg:t y2 2qmfp;:vuhe Earth?   

  During an Apollo lunar landing mission, the command moduleqr*5o * /p-rg))ufj)f o ue-jjfkbna, continued to orbit the Moon at an altitude gfjp f)eb-ouo,-a/rj jn*ku )f) *5qr of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed oms0v6hq7 z( gt, z)b (ohhpci:f chunks of ice that orbit the planet. The inner r6toph ighb0 ):scv (hq,(z7zmadius 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 kpal c+z:d80pdiameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weigl 0 acpz:k8p+dht (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km frk*q4gb+ fc8okom the center of the Earth's Moon in a space vehicle (a) moving qk 8+ ckfogb*4at 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 consisj)ijik1n is71l wrt20 ts of two stars of equal mass. They are observed to be separated by 360 millioniwtk nsjl1 1r 2ji)7i0 km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale0i yn-ty v)u hdo50d6g read for the weight of a 55-kg woman in an elevator thatd -n 5)0hug60vtyoidy 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 o7 dhe8bnqx;1m il vpd5o0bk/0k5s6 w qf an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direnkvhilx10qs q 68d/b705md;5 wkp eobction)? a =   

Show that if a satellite orbits very near the surface of a planet with period 4 vomgx-h22f82 owc/qnw nu e. T , the density (mass/volume) of the planet g2xo/q w2f28v-ohnn 4 umc.ew is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the per iv2s3t/8(/f +wbfj,s 9/pjlnscz btz iod of afj ,i/ p 82sfnbwz bs3tzjs v9+/c/(ltn artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few 2b 90x4iibdng hundred meters across, orbits the Sun like the planets. Its period isgdb02 i4ibxn9 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dista itxlqzc3,g-4 9q;4usj0qv b nnce 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. 9)m/de61 lz: .n ;z krn2 vtx ggbm+ohafw+sm(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 whenf:z2t.w9 v )mskmlb rh;n(m /6o+xn dazgg+e1 it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about thuj+d8d ao ;py9e center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for thet wh+lj2f 42 2peck7ql6ta a7x four largest moons of Jupiter (those discovered by Gx47ht2wkl27fq6e + l a2tc apjalileo 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 m)j1: dq8vwgb of the Moon. v :dqmj1)bwg8   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupy a:6wso 2t82qwwap9p iter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table:wq9w2psa w 628 otpya.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments p1zs1cekou s8 6fd.yr m;7nv9(which some space scientists think came from a planet that once 8n9scp1od7ey1k ; u.fvm s6rz 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 :l(3hy+qb-se: +wy )xl xdzrqform 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 di-: + qs+ rwh z:l3xxb)qyle(dystance 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 swingioz yp+xi, fa5(pu/:s-nc- z;csy1rs m+ hwl+rng in an arc from a hanging vine (Fig. 5–41). I+f;sily(mw5 sxu-+,sp1 :chyz -r/raz+opcnf his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what gd+*,7k rd gaqox 01wyf/n: zrit is on the 7g+x* : oq 0rdg,znray1dw/f ksurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in 6g8chw 4l58o-dm*pwyj kcr(ha mutual circle once every 2.5 s. If we assg*m4cw6w ph-c5 8rjyol hk(8d ume 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. h+frzxsa45 w 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 of wh+af5 .4rsz xg is this?    $\times 10^{-1}$

  At what distance from the:qm,byyh)gw mab0 n2 2;p 7rli Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with er2yiqgn:lbpahby ;m w m) 270,qual and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand oh twl9z e4h(t3a/29gd xsu6e bn a bathroom scale in an elevator, it says your mass is 82 kg. What x3u (dtlbh g9ew4h2s a/ez6t9is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stat 97af(*epwawp ion consists of a circular tube that will rotate about its cena pe*(7 w9pfwater (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 surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vernk2jmjo)*up0:g (xfb tical 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 pl 2qhxb/u5g*l vq- yd4janet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constant xj2 gh* qdu5-l/yv q4bG.

A plumb bob (a mass m hanging on a string) a03qra iz)lk1mt.bf z 5k5qw,is deflected from the vertical by an k1m. w3 b0q ki5,aztr laz5)qfangle $\theta$ 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 fd*l)rpxl2 et,qw-+jq or a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a ca+qe, - *j qr)tllwxdp2r safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects atx0w/yf5um 13otes; o o the equator were apparently weightwo13;omfe5 xu0 yt/soless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distabawe1g5bya ;czx9*s0 vk(u ,p nce 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 constant speed rounds a curve of radyq f+ r7fen+bilj: 0r5ius 235 m. A lamp suspended from the c +b yif0j:rn75efl+ rqeiling 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 Earth. Thus, it has been claimed w90 g/g*gq gsfc:pl(n 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 gp*gc gn( /gwqf l0:9s'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 d1l nhir0i6:(g vi6 iphc89 hmxeduced the presence of an extremely massive core in the dista1i8i6 6hpcxni9: l0ih vm r(ghnt 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 v.8vqcpx c -7s bql- jgdu2: fitb9g2( as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? q8iq (g j. x 7lfg-2bt29 vdusbvc-pc:(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) utilizes a group of 24 satellites o4 b :v55 cmk*w-yzyml/(v hqz; bb,be7+am gdwrbiting the Earth. Using “triangulation” an y :b,g -v(dbk/mz mlwh4bc; vay5*5qwmz7 be+d 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) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid n2h:jw/-gsdt Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abou: jw-nh/gts d2t 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 o,sih 1t)wc y26 bgf*espace shuttle pursuing a satellite in need of repair. You are i62 fw *gsc o),teiby1hn a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dis 8r, e4-aqsteb9+lo;dny cm/bk6 zt 0htance fro/hm-cys;b erq+d0noe,bz t lt69 48 akm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you u/a+a: ,t* uh )1wvkmpjbdti,could actually "feel" yourself gravitationally attracted to someone naw1tjit k/v,hp u*:a)+,u bdmear 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 d-vmw4kz , i9j8wd:c mfistance of am,cvdw4-w:m98 zfk j ibout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0. yipi+5+n ysydwr3 /)h- ;aheu50 m on each side. Find the magnitude and direction of the gravitational5yh+;w + pu/3)-nriays hdyie 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 orbits the Earth57rl;eouwz*kt4j 4lp2goy z + $ \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 experiencedo uzzzr/(9ar07w7yef ze ,t3h by the tip of the 1.5-cm-long sweep second hanf zty (7 o0u9rze7a3zzw r,e/hd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight a.(3yq lus7mh v-fi. kqround 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 i.(yu -.lv3fhm7ki qsqs the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is d1q ugz:gpdkwvj*p4 b)( 8x9/mcs 3kbqesigned so that a car traveling at spe1 g9p:k j xm*u3bsz(kcvdqgbp8/4w)qed $ 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 whenz*v83v;. di)qen l*op*g2s ag hk tdn. negotiating 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 traivdnz h.3ea*isg* p8 l;dnvtkg.q ) *2on 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.$\approx$    $\times 10^2$