Sometimes people say that water is removed from clothes in -39lkc hs6kiqhnw0 g 7a spin dryer by centrifuglhk6cks3 nih 0q-97gwal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the saovz+ l:3oc) nswl x:xd :j5.ylme when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curvexlwz y:)lo5dos:+lnx 3 :vc.j at the same speed? Explain.

Suppose a car moves at constant wn0u ):cgweljn/ ap44 cz6b o0speed along a hilly 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) og lb/nwj4 4cu0nwa zoc0)ep:6n a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on asv g ywk4:w4t6 merry-go-round. Which of these forces provides the centripetal acceleration of the: y4ws4wk t6gv child?

A bucket of water can be whirled ic*frll- -ya5l7 lorv1hp5u7p n a vertical circle without the water spilling out, even at the top of the ciroyp*lhcruf 1- 7-rp5allv7l 5cle when the bucket is upside down. Explain.

How many “accelerators” do youg7pdaal /r), b 8dol4l have in your car? There are at least three controls in the car which can be used to cause the car t8bp),lglda7o4 r /ldao accelerate. What are they? What accelerations do they produce?

A child on a sled comes flhu fql4/o,*e zh sut8/ying 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 chh4us t8q/, zl/ou*e fhest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when ge9(q5l/ tuyil+kd 1 )6cyhpq rounding a curve at high speed?

Why do airplanes bank when they turn? How would you computil2k4zn*qf* x u(5m pt epgl46e the banking angle given its speed and radunll* p z kq2ft6p(i44g mx*e5ius of the turn?

A girl is whirling a ballnu): f-ernfkhy jr v62p;xhn,aw:4 q* on a string around her head 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 sid wr,uyvr) :x; 4n:hn6qeffj n-k2a hp*e of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Eam9x43ydd l6jjd,o 9 nygtkv:/rth? If so, how large a force? Cd9y3 t,ydoj4d6k9/n:vmx g jlonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublebv;0st6oi q l6 what it is, in what ways would the Moon’s orbit be differes;oti6 ql06 bvnt?

Which pulls harder gravitational5h 32yzrjsma8ly, the Earth on the Moon, or the Moon on the Earth? Which accehsy3m8 2 zr5jalerates more?

The Sun's gravitational pull 3 zz u/ qurt0c(ibpwg- x75qbx(bh/:von the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diffe7 q0 u(/:(bx/pzb3gicw5rb hzvxu t-qrence in gravitational pull from one side of the Earth to the other.]

Will an object weigh more a7a (hds3ud qe3t the equator or at the poles? What two effects are at work? Do they oppose eacd hq3sd7a e3u(h other?

The gravitational force on the Moon due to the Earth is only about half the forgn (nvx2)yho3 r*rm mw(5 jxu.ce on thr* (wu)xhrnnmg vy m(.oj52x3e Moon 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 lah/k9b,(i dv kn/vjqeq+ h-en4,x w1oerger or smaller than the centripetah e1n whbk/+,noqve (i,jq-9vxe/d k4l acceleration of the Earth?

Would it require less speed to launch a satellite (a) towark2 e.zc+k+ pcvd the east or (b) toward the west? Consider the Earth’s kcp .2c+vkz e+rotation direction.

When will your apparent weighn;3j-rin w+/vnm vqz( t 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) move z3i+n-(/rv wnmnv q;js 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 periojv k9j*1/nawg ds in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with tnv1kw ja/j* 9ghe astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betwe)cq:c*ld i .awen steal .ci)w*qcd:ps.

The Earth moves faster in its orbit aro, 9-1rtyea u vigov7(yund the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. ruivv 79e yogyt (a-1,[Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discove c ,ryu)af2bkeg7;p)m red to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass;pkgearfcub72 , )y)m .

  The Sun's gravitational pull on the Earth is much larger than the zw2-)wk k gvkn cyv5-3Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenkn5)3 vkzv-2w w-gckyce 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 1rp*tl;ib w;g /980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its oe 51/sdvx*x zirbit around the Sun, andx/5e zdi*1svx the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is e mge:(m6y49opfo+kued,5m5hz67r ivh e7 ej e xerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate t9 jm5zh, vup5 :r+(o dmhe7 eg iom6y6fe4ke7ehe speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth5r/4c 1mrqkvi cf l1+m'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 accelerati/c1m v4mf i15rlkq +cron at the Earth's surface. $\approx$    g

  What is the magnitude of the accelpf54mg vwm0je9c xm 6)eration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolf0mm m )vpj 94wgxce56utions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate iu(zlj4vn b0d 8n a vertical circle of radius 72.0 cm 4(dujl0 nz bv8, 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 woo-, bgpvqg 5vm+/ot)ith which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient )o ,mv5ogg/+-qt obvp of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between s6/ro4dcpnk3w2x4 wb the tires and the road if a car is to round a level curve of radius wsb44/r 2d3w6 pxckon85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotatexkxqt lq x ;i6*6b89zk a trainee in a horizontal circle of radius 12.0 m . If the force felt by the traineel xq6 b*kx qzi6t;xk89 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 variable sp5/yqcvr m 9 xj.m(p vy2hy2t(leed. When the speed of the turntable is slowly increased, the coin remains fixed on the 92mr5 v(vhqx(jy/ p2mly y.ct 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 must a roller c* f;rzj f/vr:voaster be traveling when upside down at therzv;/*v fr: fj top 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 9/2vsql5fj/ xkye(k) jq6hr4pb l-o9g 50 kg (including the driver) crosses the rounded top 9e (/l gxk2rol6k yp)q4s q-jj/ vb5fhof 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 minuteo-z 1q)dyy wy+.ly gzsadl f+z7b9)3l would a 15-m-diameter Ferris wheel need to make for the pay +o)al+l3 bfy gq1 zs.79ywzzly)-ddssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirgz -x;9mjt8tu 06l s;5fnupmp led in a vertical circle of radius 1.10 m. At the lowest point;f 9ng muz5m;xptu- 8st6 0ljp 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 the axy,lh d-4g n skb9b20idc i:szcs -8z1uis of rotation is to experience g0ydns,i- b- s b4 :zdhi9 z21culskc8an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricallx6 c-eohn12i57uy t uhy walled "room." e12iyx hct5uuoh7 n6- (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-hoq(mhy7x0fp d.a :q-lu ckey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5- l-(uy.:ph0 7xaq m qfd
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 ignoringr8pdv q;3exnm4.fiaby 8;b)y2/poj, d5u dt l the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitudbedd8m8)r;, yybiq;o 5pv3j24p /n .lua xtdfe 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 car traveling q)rqr7 7lpp2u /) olko75 $\mathrm{~km} / \mathrm{h}$ , 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 masseqen 8ibcl;nu /851 vids $ 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 dir/s* j82(dn rlnt6alujy5(vx ving 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 tangentialv m;3se55d3yjdtt1 ld .bh 2dnpt(r1z and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when p;y vl(rtd d5e ttds33.2hz5b1mj 1dnits 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 th d2kh(i/ g07 esc6expkucnb ,8e pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no 20isdch( eg /ube, c7pnkx6k8slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m my 1a. e1-qwg5 dk8(3ksra pqk. At a particular instant, its acceleration is 8mp r5s akqg3d1ayq - ek.(1kw1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 Eartmft di72jrnydwi8r- +nys5; 2h’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its 8ydynjrin ; 5rf 2wd-t+ 2ism7mass is 1350 kg.   

  At the surface of a 1ai-k oogy6 z4certain planet, the gravitational acceleration g has a magnitude of yi 4ka-oog1z6 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius p*uli u r3zv;y*x9n0y lw6.hs8zg,a tis 1.74 wh;8gxy*usyi* tr. 9pnu0, 6l zv3 laz$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet 0+qy4jt 1-yuqtosr v7has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfaceyrt oqt70 y4jq 1v+s-u?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiw x8*k fvgp8,tus. What is g near itg v8pw*ft x8,ks surface?   

  Two objects attract eacluhdms*2 j.+tx fsh+*h other gravitationally 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 gravity, ath h)-xm09axmrxb w ;4mnnqox: q( 4u,m (a) 3200 m,4(h a0x uh: nnmobxx9mmq r;mw-4xq )    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wqab1 vzo g0l7-here thegravitational ac1 7gzo-aqv0l bceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into rnb4)t c (rll;49 gwp:nx zx;ma sphere about 10 km in radwm ;rcb( rxp4lzt4:nlgnx)9 ;ius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was drj 9ev) /pbm6an average star like our Sun but is now in the last stage of its evolution, i medj9r)/p bv6s the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronaat 35zchp2 fbve ,m53buts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weake2hev5b3 amc f ,5bz3ptr 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 corners of a square of sidds j-rc xmdet3z:f(,9e33rxv e 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thrsz e3t9v(m dfce3:3 ,djxx rr-ee.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of z/bar no10clevw8 (;rthe planets 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).bnrc al; 1(wr8 zvo0/e 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 acceleratio01dh/ :avwn zsn of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radiuv:0saw zn1h/ds is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val ay 8kn*6:zalaq- xrm0ue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 58y x6aa*0maqzn -kl:r–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable ck xix65wi hyx-6y0d4 bircular orbit about the Earth at a 6bx xhyiixw-d5y046k height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circu5y(bvkhwd32*k8 bu:jzks vw. lar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the relsd.zb:uv32(8 wjyvk* kb 5whk ease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants a: (lv q k:2j/y(juju g1pfvo6lre to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give6f qoj:j u1l(pu2(vlgk:y/ vj your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it t8 vizyf3) gd:iakes for a satellite 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 Eag yf)8d3: zivirth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellit8ssqkl 6e2al (e have to be launched from the top of Mt. e s2k( a6llsq8Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missi)d n14 2xqgjd3n5lgpuon, the command module continued to orbit the Moon at an altitude of about 100 km. How long di 4ld1np)d23g jux 5qngd it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Theclpb+k(;+ tqec 2jvf+ inner radius of the rings is 73,000e k++ +jcq;tlf2cv p(b $\mathrm{~km}$ , 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 1dk *3s/i,lv sni7 w5dt5.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the topl*dds n3sik, 5v 7/twi, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronatmqkot 5)o) zxtl+ qfvum)6fl *p 07o6ut 4200 km from the center of the Earth's Moon in a sq)t6*f op)0u7 f5ool km x6m)tvlqzt+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 two stars of equalyi+eah;xcp 2 pf,1m-n mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betw;a p1m- + c2nhiexp,yfeen 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 elevator thu,* m9 mp2qpukat ,pp 2umm*9k uqmoves
(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 w3,in /:x9x urz*cbn pof 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 direct,w3*c/n: 9bnz xir xpuion)? a =   

Show that if a satellite orbits very near the surface of a plan0l mettyigm.bt 04: n b( 5/sd6cv+odtet with period T , the density (mass/vbmittv/+dtedbm 0gc.n4y60lto(5 :s olume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period 5 p:zm c(cmvmf2e1kz( x 6px7nof the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfacez1nm7m6mppc xxkcz :((e 25fv.    s

  The asteroid Icarus, though only a few hundred mqaig n;( ng,:qeters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the ;ig:annq ,( qgSun?    $\times 10^{11}$

  Neptune is an averags/ . e9)rr/dkj(ylqlwe distance 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 76w6c o( f9fhbd7nl6/6 an7g sbt 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 distanc/fh 7(atodcwl6 9n 66gbb 7nsfe 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 ztxk 34o 8bs2u luzf1+hx m(y4center 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 the four largdeuf /w 6fxn )3hdi+6jhy l4mq 0k-j-iest moons of Jupiter (thos jliundk+jh xf4eh)d-iq3/yf mw06-6e 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 knownr z/ rh/xg2uq42i ig vmy6e/x9 period and distance of the Moon. z9g6e/24y/i2/ xg hxvuirqrm   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupite5sxlmw awyj 8(xl;n1(+fwc ;b r’s moons, using Kepler’s third law. Use the distance of Io and tmyc( 8l1 ( 5x lw;;fwwa+xjsbnhe 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 fragments (qt2n qyy10 ahjdk7a81 )jq)82n mcvoswhich some space scientists think came from a planet that once orbited the Sun but) )1n8a28ocy7am0thqs qnvjjq 2dyk1 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 uo kfm/0upz6b xf): m9of 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 th)bm9zm6ff/:x 0uk o upe same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc frox jb/;r*r4shges9 y /km 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 kg, and the vb;gss*/yh e rrj9/4 xkine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration fl97tqrhhhzb 4*d i+4of gravity be half what it is o7r4b ih9h4ql*fzhd + tn the surface?    $\times 10^6$

  On an ice rink, two skatersw)l,7 bzi-rgani,fr8lnk *c4 of equal mass grab hands and spin in a mutual circle oncerw8*f,g-illrb 4c n7knz ia), every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerat 43;juc2m/ks vflx xf1ion of gravity at the equf u j413mk/x2f; vclxsator 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 spacecraft travelin78w (m 424wngiylq)zuyqa;e wg directly from the Earth to tn42y euw 4qgi;()zw7l ya8m wqhe Moon experience zero net 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 scale in anny)ewt /t-1)iseyfm(m6 elr 2 elevator, it says your mass is 822teiyr(s6w fl ) )1m/ymtn- ee kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationdqvvu0ji3 alg**nf7 , ;jm. wk consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 a3jqwf*mdvjug*; 7 .lk,i0vnkm. 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 8bo l :z;o9be w1rd.jtvertical 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 thvp2:3 ioqbga1hp3 q,ge mass of a planet in terms of its radius r, the acceleration due to gravity:vaq2po hp3 ,1gqg 3ib at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on 0lbxz v2 ns)2t(6 uzbes9 ibkp5bqd;6a string) is deflected from the vertical by an angl 9bx26uei2nqzbpb l zs5 d6)0( ;ktvbse $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design scd1 r4bemm0t: :yy;brpeed of If the coefficient of static friction is 0.30 (wet pavement), at what ry: b1 e4ym0dtrr mc:;bange of speeds can a car safely handle the curve?

  How long would a day be if the Earth wer i ol9v;s4gb9j;h z7bwe rotating so fast that objects at the equagb47zo;slb v9w i;9h jtor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant kdcp fkmc+n30 cc+22idistance 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 constantqh8za .cy( jg9 speed rounds a curve of radius 235 m. A lamp suspended from ta.(gh9yj z c8qhe 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 a (16zaibgisnsad)nu 9 v3(pf3s massive 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 g 's. Calculate the number of g 's a person would experience at the equazv9iu6if pbs)( sd 3 agna3n1(tor 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 ded*ebndze8dc -/uced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to bze d/-b*en8c de 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill an d .k )pwp4gko*iml2)md valley shown in Fig. 5–45. Both the hill ando k* 4p 2ilw.)kmpmdg) valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Syup zlz z)hn3wl3+;( zh4 nxab7stem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the posinz( h+p z;4l h 37auwz3)bznlxtion 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 billion km, is malqw:yo9 4uq+q(qoq h 9l f;-beant to orbquq(:q +qf 4-w ooly9ahq;l9bit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need c;urnb)rvg( - of repair. You aregrrb)vnu(- ;c in 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 uyehyer 1q 9;;n 9oip)its mean distance from the Sun? e ;oe qyp y91iu9;hrn)  
(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 actually "feel" dui wng/l)sxqa 0fl2l(ud cm.5507r zyourself gravitationally a/cxdf g0 (swlur d0 m)uin72ql5la .5zttracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ok q:h 3rxeu58nyao7f 8f the Milky Way Galaxy (Fig. 5-46) at a distance of about 3qe7hu5 8nark3 8y :oxf0,000 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 locateyx 3lns3o 9ga5 4r+7b gqwryb*d at the corners of a square 0.50 m on each side. Find the magnitude and direction o n ax9qby4l r73oggr*ys3b5w+f 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 550i34z7utq fnl1gdb j8a.wlz :4 0 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cmipk+6l att29v-long sweep second hand on your wrist w26t a v9k+iltpatch?    $\times 10^{-4}$

  While fishing, you get boretmv(rc z0a3a iy* ry0,6l1 rttd and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig.yy 0vtz r6c1m*rlitt,(a r03a 5–10.]    $^{\circ}$

A circular curve of radius R in auq 0s5a/m9vht+dt ys,rs0dc6 / jcj; c new highway is designed so that a car traveling atcyatcs;u /r/0mv,c06 jdsh5 q js9+dt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tip5r+2qq*ld v7u v3cbwlt 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 aga7db vcpwr25 +l *3uvqqinst the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$