Sometimes people say that water is removed from clothes in a spin d vozyxx 2a1w1zs;ba;1ryer by centrifugal force throwing the water outward. What is wrong w ;abozx21vw;s1 yx1 zaith this statement?

Will the acceleration of a car b (j(wv8co(dsjh47 jkre the same when the car travels around a sharp curve at a consta jos(j4c7d vr(8wjhk (nt 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 h035t, f.uw7myqba b ogilly 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, (caut5mbyq07gf. , obw3 ) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wh, jr ( qh9osjb ;7u;1qvwits6giq;9h; 61ubt qis(s,vw7 jgor jch of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the2ouqvhuz6i py4o+ 9 0tdt.d52pim n0b water spilling out, even at the top of the cir0tv nuu29.imqobd5h4 z2 0p6d+ tpoy icle when the bucket is upside down. Explain.

How many “accelerators” y/d cs4aq 04qkdo you have in your car? There are at least three controls in the car which can be used to cause the car yqk0dqcas/ 4 4to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hilly xk,ld,qkvcty5 onvek-- ;*:, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal for-e*nk5ko-ydt;kl: xqyvc , v,ce 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 mhhv n c/ok(:n;,0pyp b2yia, lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankin:,0ow9 dcg h c ka3kz -nc1vvo*-p-ykgg angle given its speed and radiukvyg9gao,h: onwcd z0 c3kc*v- -p 1k-s of the turn?

A girl is whirling a ball on a string around her hk2 2c67wi5ns0 wimndfead in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on 67k20c w 5nsiifnmw2dthe other side of the yard. When should she let go of the string?

Does an apple exert a gravitational forcj1k hqbf g175(ky 1eo( uvcor7e on the Earth? If so, how large a force? Consider5kvgehr(7k oby cu (jq17f1o1 an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would ther dvcr9u:s h,. Moon’s orbit be differen:, rhd svrcu.9t?

Which pulls harder gr/.m6 bjjc9n hwfjpjws/9 u;.kavitationally, the Earth on the Moon, or the Moon on the Earth? w9f.j wupks;9n 6bjhm/jjc /.Which accelerates more?

The Sun's gravitational pull on the Earth is mu7a1 d ujrx 5tmxxv*)vf /ix09ech larger than the Moon's. Yet the Moon's is mainly resx uj)x*ea/ 7 91irx mdv0xft5vponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the pol- dh06xe exz)*kxybic. oqz++es? What two effects are at work? Do k+-o+xxex)z zq 0b ie6.*hdycthey oppose each other?

The gravitational force on the Moon due to the Earth is only a8jepazs (:xm:bout half the force on the Moonp8::mj axz(es due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larg+ ,tih7af j8h+ urclzo7/l5m ger or smallmg t ,7+7+lac/ zjor8hhlf5uier than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (g6 u/i,+7qjs xc l h1zx+lyl;va) toward the east or (b) toward the west? Consider the Earth’s r+v z7j gxu+ls/,iyhl6 cl1;xqotation direction.

When will your apparen,a:uhymg0s(o ypi-/q +q dr+vja) v9yt weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In whi/vrd0yqm( u q s-),:vo+gjaphyi 9+aych 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 adversely affected by m m;f361* yw2ue swsbzweightlessness. 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 (as6mzmw;3y*f w 2u1bes ) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “ h uf47t.06 e3 fjvumd62zprtkapparent weightlessness” between stepspev.uk3r2 60tdum6fz 7 4 htjf.

The Earth moves faster in its orbit;)xt 8nuj;s)qqhnw0 u around 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 relative t)n0sjq;qu ;h)wn xtu8 o the plane of its orbit.]

The mass of Pluto was not known until it was discovered to havirbrg-t 6p qf.q.k5l7e a moon. Explain how this discovery enabled an estimate of P- k5rqf 6p.tblqg r7i.luto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon' +.yv m h2 ;xbx 60.f+k4cntt+scqyylss. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cocs+.m +vt yyk2nc0fqxl x+h 6yt.s4 b;nsider 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 travelingsfx2g rdbh(3ix/p 19 t 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 accelerationv l (eqd(fl* 7ucee.5 zg,zfpl+d ji5; of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume th7vd5f.p ge cd(elle;z,+ 5 f*zj(qiulat 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 os ny5:6d : *kybjdxear1krduu c;9o7 5f 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the *5crbue5n kuodxy;9 d7 rdaj:1k :y6sdiscus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's 4fev-r0*1ufz wlh ap qty ;u,1surface, 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 gravit utlhvfe0ay;r4p1 -,ufz1qw* ational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerati +romwht( ugpda9 vo g54:,wh+on of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameterow++4:g 9 d,rhpumgt aw(5v ho is 32 cm?   

  A ball on the end of a string is revolved at a unih f;dh,+t ao i*:.zltxform rate in a vertical circle ofxfo.,at t*i ;dh+ zl:h radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radi cm6,x5lhr6 tcr.yu,e e,7myw us 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 of the car? heer. y w,tc5 ymumcx67,,6rl  

  How large must the coefficient of static frictioh 7/q)s jd1mjj yrk/f-g. xjs7n be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ? 1jh r j.mj/gd7xsys)q jk7/-f   

  A device for training astronautx1/2 5dudq ffc y;hjh-s and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is1 dx j f-u5cqfh2hy;/d 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 va :s*e tliht5u(riable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rah *tes :5tuli(te of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be t/ u e rec--lj/i.ic3yvraveling when upside down at the top ve--erlciy/jui3. c/ of a 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 950 kg (including the gi ts6nevjy, qlg99j5 .)y :mbdriver) crosses the rounded top of a hill (ra gb,jy9)tgym.lei j5sqnv69:dius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to /- q;jfs th(nqmake for the passengers to feel “weightless” /htqjsf(;n-qat the topmost point?    rpm

  A bucket of mass 2.00 kg is whir(3wa;p7f m.3pexro 5dhi*fqn led in a vertical circle of radius 1.10 m. At thampf7d o(f p*3; hwn3r .e5xiqe lowest point of its 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 the1ko dd0 y30sarwbdn(/ axis of rotation is to experience an acce1downd3s b0yd k/a(0rleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pw -v,dfiq2b b)eople are rotated in a cylindrically walled "room." (See Fig. b-,f) qivw2bd 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 o.tax29hxumdaz(a.r.jq /yu : n a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling m9t2 qdrz.uh.aajyx .(:/ax u 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 t ug;ipx;p+qbu -s)6qf 0oat v2he weight of the ball which revolv gi +ap26tu s;)qpvx0 u;bofq-es on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a c:x:w bitk*/ ohar 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 o6k+qmv8ay jwj z7- :ic6z 8kyrsx1q)$ 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 vertically at 31 p (jm,k8;pcer0 $\mathrm{~m} / \mathrm{s}$ . 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 exez uty.f trt9of( t6y(6rted on the car (by the grounof(zuy rt(6t6ttf .y9 d) 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 area, going frop*+ , efuy9ocuf)q)kb m rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road )q* )pf9cb, oekfu +yuto provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At m ntdh6o6+8t 16jvhvl a particular instant, its acceleration is 1.05 j16 vnm6lh8+t hvd o6t$\mathrm{~m} / \mathrm{s}^{2}$ , 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-k,bz:yg luss d,ih; 0’s gravity on a spacecraft 12,800 km (2 Earth radii) ab ,s z-h;g:ksb0 ,liyudove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accusx c(m/kb-l5 oax,v 9eleration g has a magnitude of 1bls-5 ,9xuocvmx( a/k2 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 accelerati t4oou95bvp 9con due to gravity on the Moon. The Moon's radius is 1.749p4 b9oov5tuc $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiu3yz)e ooiu6 u 8df//ips 1.5 times that of Earth, but has the same mass. What is the acceleration du )oop ie u83dzy//fiu6e to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timeh3e r*mfljq *(s that of Earth, but the same radius. What is g near *(hf3*rlqme j its surface?   

  Two objects attract each other gravitationally with akuiif9ttje+3e /*ks( force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 v v8klue+n7ze ,/m+ z-fwu ,cpm+pun/wzeuv vf 8c,+e7mklz - ,    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’syk1he q/+kk f8 center to a point outside the Earth where thegravitational acceleration due to the Eark /+y8 f1kkheqth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a g ,hl rl)xklg s5:53kesphere about 10 km in rrs5xl) k:,53ge gllhkadius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but4tu wb /rotd9k5ks5(a is now in the last stage of its evolution, is the sizuaw/ (5kdt5tb 4sork 9e of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining wh8w/ dk( kj;r:) pmzwlfv(ov50t.v ur6m) yxc by astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them andcm/ot r5mv)yx8v)v( 6.u fp;dbkwl (w0k:zjr 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 corners of a square of side 0.(k mzi5. 6hmgt)o-vjqv am)6d60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere5z g6odq v(.m))akmj-6tm iv h by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pwkw5 1,ogx4 lo. a( 5ivn (lh-3stdpbwlanets line up on the same side of the Sun. Calculate the total forcep gt.5-l3oh(dov5 4lk(b1 wi, nwxw as 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 gravakdv45 xe1 /quity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ rauq/a dx5v4ke 1dius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass o o;+cwavgd6t9+f z j:nf the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawt6 d9o v a:wfg+;c+njzs, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit d7+w.v h9 ajmh)x9on q rl9a,-olyti) about the Earth at a height of 3600 km.olrhn j)l-d9q 7y9t )m,ow9+i xhvaa.    $\times 10^3$

  The space shuttle releases a satellite (fse+l+ok* wm6 +(yzg5kpen yinto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to E+ seny(emfpkokyg(zw*5l 6++ arth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if oc-yfl uh/-90 tz 7xmfemcupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diamet0l-/zx et-9 hufm7 fmyer 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 satel 8uoq6c,srds5 lite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the d8u,rs6q s oc5Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be lau7cii+:tbk.y4 6g q4 j(hxu j2*d wuynsnched from the top of Mt. Everest to be placed i*bd y.jisgti:64q7nu(c4 wyjk +xhu2n a circular orbit around the Earth?   

  During an Apollo lunar landing u m5o7:xl q p+qqvwkjz1dpkg982 60hsmission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go :0mv19qs kopdl g678qwq5uhj +2zxp karound the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Th/i90rnmha f:m e inner radius ofm /mr90if h:an 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 15.5 t)zd8 8hq(v/mr i0lwgcuct ( (s (see Fig. 5–9). What is the ratio of a person’s appalqhw 8c 0d8(grut(cziv)(t m/rent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight0v2iap,1- mlg8fjd hs of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a sm-10ajg2lpi,vfh s8d pace vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of g2zmovw il )/tiy1*zz67t .igtwo stars of equal mass. They are observed to be separ7o6liv tgywgz.z2 *zt1) mi/iated by 360 million 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 scale read for the weight of a 55-6 )ohs/i *h5 q2jkamfekg woman in an elevator thath)j eo26as f5h/qkim* 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 :h 7n2vvc/xev ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was tnv2chv/7v:e xhe elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of ivjl r91e qk-)a planet with period T , the densi l1- )r9qeijkvty (mass/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 and the perik. fp p, -uq;xsn5ux)iod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near t k np-uiq,p;.x5sx )fuhe Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metersw7 urv;vs/5zn across, orbits the Sun like the planets. Its period is 410 us7r5z/;wvnv d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average disell79 8 ltrzbec82ks7tance 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 mm h9bn)qe,i6the Sun roughly once every 76 years. It comes very close to,qnem6h 9i) mb the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the dskv(x wu3, y(wta9d n;n;4hwz+j9r jcenter 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 mas x/f blyow7ak(.snmug1):tk / s, period, and mean distance for the four largest moons of Jupiter (those disclau/7 f/kn:( x )swtmyk1bo g.overed 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 period and distance of the Mo3ybk 5eo6ay+mon. a36 b5+ye myok   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiterzrl;y) (pc 8zxeo8xnimu7;0vlhc* . h ’s moons, using Kepler’s third law. Use the dioc0l p)yurmv hhz*8l8x z7e n(.;cix;stance 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 bet9 h+vib *;uoopvo,v62sgn; +hzw hnx9 ween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sunh;v9 o2xuvb +6*swh9p+ nn hgo;i vzo, 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) gicvo 3fu ,gn9i(j*tz.. fxm an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (whereu. .ctv i3gj,9mig)z of(*x fn it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in3eq( 2-pdh1ljxqf dtjx7 rf03 an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kgxd frlhq2jx7jeqpdf33 t-1 0(, and the vine is 5.5 m long.   

  How far above the Eaqx gox8u tx003rth’s surface will the acceleration of gravity be half what itug0xxot0x8 3q is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circloa+tk3kr zv0o-jxwdsw( 56/ le once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 6kz0wj3 -a6sol5wdo r v(x tk+/0.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, btzwfn(4ndkx,z9: 2w*ldh3 s the apparent acceleration of gravity at the eqh ,4 (bnlwd3ndk9ztf *z2s w:xuator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a s1h 8a:3er so xqy4,oivpacecraft traveling directly from the Earth to the Moon experienca8 so3r41,ev hq :ixyoe zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,4eh1z k8/(yr(k.ji,qj k hmzw but when you stand on a bathroom scale in an elevator, it says yj,zjekz mq/( 8kryw1(hh. ki4our 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 that will ro1( vbxo 6s40opvg qp)state about its center (like a t4vgb so s)o(1p6xpqv0ubular 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 h(px:: mg yxe3/zlgeh : :jhu0a vertical 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 radius r, the a j1yli*iy-:w qt;*fxsjtx2 e-cceleration due to gravit-yy qwtxi; l -*ifets2 xj*1j:y at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from ;je pxly9j (zsd(d( k bs91rjpltn7m :k61lz;the vertical by an zl (xkr ;(pktj;(deydjjpblz :ns 11m69s7l9angle $\theta$ 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 ba did m6nlq(q5.gj 8h4cnked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), aq8(6n dq.jcd ghlim45t what range of speeds can a car safely handle the curve?

  How long would a day be if th ucwzydr tv.e 3id,875e Earth were rotating so fast that objects at the equator were apparently weigh58yd 3ewzvc,ti dr.7 utless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apav)1,rqy:f) yl- thcsbrt 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 roug i(-lbpj1a/ onds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle ob j/pagil-(o1f 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mas h3 fjgovq()lky -7h/ssive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few jyhsg/o 3lk)qv -f7h( 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 Teles6*. wf2 6l,dbjuxgasdcope deduced the presence of an extremely massive core in the distant gal.bx2a*glf us, wdd66jaxy 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 thes/je4l(;w kun 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? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (ceknu4j(sw ;l /) 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 satellit), mk/rbnu,dtes orbiting the Earth u,knrm)t /bd,. 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) 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 billio1g: ; ytfdioms s.9a9 )djqne5n km, is meant to orbit the asteroid Er 9ysi) 5j.9 gm1set;dof: ndaqos 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 shuttt aofxj2/b8 ;+xh,z-7pbv yxo0k. flole pursuing a satellite in need of repair. You are in a circular orbit of the same radiusb;f0jfk-t/b 7,ap yxhov2 lz8ooxx+. 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 distance fr o 26q eeb1:gw,x f0bz+u;qwm-2p/ snwchk6xmom the Sunh ; f cbw nq-wzwb:u/x6xqeek g+6 0mmo21p,s2?   
(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 could ac(6x0i8 d:lunkhzbo x+y9 .l natually "feel" yourself gravio(lxyxh:nd i .bz098k n+l6ua tationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center:2,y .w-ze1 ph7j l .9)lrieqvmf soaf of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000- l1 )fyz rq:fawevm72i.9 o,lhe.pjs 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 0.50 m on eac0pxs5ou1o 2ich side. Find the magnitude and direction of the gravitational forco 25p 0ox1siuce 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 550r6+p2s8vgxq 3pr*ab-0 qymho/ km(sd0 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 1jp0x( (j20unr;tdzcv grkh,* b j1-h b.5-cm-long sweep second hand on your wrist watthp,;bj grnz jhc0*-2j (0x (kr vub1dch?    $\times 10^{-4}$

  While fishing, you get bored and start to swinw+9x+cpy mdl rsr3mq 3/m gr,,g a sinker weight around in a circle bmlmgq,dy/s,+r39m r+ cwp rx 3elow 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: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that:*mep , xlug4 4u0 onesbl*+ct a car traveling a,ug e *oteb +n0xll* u4p:s4mct 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 a bjv ;+yzgxfzl w-atds81*71train, 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 the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an At-v7zfw; j1 *8lg xsda+b1yzacela 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.$\approx$    $\times 10^2$