Sometimes people say th488eoru ql ot7at water is removed from clothes in a spin dryer by centrifugal force throwing the water outward7o rt8ql ueo84. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp cm 7,)z7sgi bxiurve at a cons,7is g7xzi bm)tant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road.4) trxfcn2soj6-h z f. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hilln4. js2hrz-f6tc)xfo?

Describe all the forces acting on a child riding a hord r:t6b88gs-lhrbv 7v se on a merry-go-round. Which of these forces provides the centripetal acceleration ovv8-bs6lr rd:8 tgbh 7f the child?

A bucket of water can be whirled in a vez 0tdn8 (. qhb2nn;duzrtical circle without the water spilling out, even at the top of the zu80zh ;nd.qt( bnd n2circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? The8i4u. b3h zumrhz*k7 mre are at least three controls in the car which can be used to cause the car to ac zhmh ki3mzuu* 7.rb48celerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest ofl:y3i kg*mn/v 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 the hill. kmvyl i:*n3 /gExplain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at 9b7hswr2j,q 81d hnpkhigh speed?

Why do airplanes bank when they turn? How would you compute the banko*mqhpz5a nxf9 w6/0 ving angle given its speed and radius ofn hq zow6xa95*vm/pf0 the turn?

A girl is whirling a ball on a su)p,2t/vitb2n , o.(ue( d 4twkfhrmetring around her head in a horizontal plane. She wants to let go at precisely the right time so that tt)wt(/m huboe,r4 (it2d f.nkeu p 2,vhe ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational forcedb , w77bqttsab+ ,g0f on the Earth? If so, how large a force? Considd f,07tbt+sqb7 wga b,er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doub:w:p0 4,k 5jvnit mif() gjdisnhsm65le what it is, in what ways would the Moon’s orbit bih i(p5j kdmtiwf jg5n:s6,4:mn 0v )se different?

Which pulls harder gravitationally, tv-d05m fwa o( x*o2l9sq o5kxnhe Earth on the Moon, or the Moon on the Earthvosda 5( lqfknwo-m*5 9ox0x2 ? Which accelerates more?

The Sun's gravitational pull on the Earth is md(; zogc278e2v tdn;obr-rwcuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational puled2 ocv;toc7r;gd2znwb -8(rl from one side of the Earth to the other.]

Will an object weigh more at the cthkjo 2xh 161equator or at the poles? What two effects are at work? Do they okxh 6jt2c 1oh1ppose each other?

The gravitational forj(gs 1 k j*9e2q-ivakdce on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pus q92aj*-iv(kkdjg e1lled away from the Earth?

Is the centripetal acceleration ofx h/l;hph8ys8 Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of8hl/h;psx8h y the Earth?

Would it require less speed to launch a satellite (a) toward thu07iy1-hj 4h el6b4/ufj sv wne east or (b) toward the west? Consider the Earth’s rotation diyv-b 1704 fnhwe4 jsu /6jihlurection.

When will your apparent weight be the greatest, as measured by a scale 1som ekh)4bf.in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at consek.mhbf1 o4)stant 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 *.3: fccqxnq douter space could be adversely 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 * ccf x:.dqq3nthis 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 qqf 5o w4c(m l6n*f,y: c1ayz1ix/zhbfall” or “apparent weightlessness” between ste1ia zl6/fwq5 ,cyqy4b o:1zh*nxcf(mps.

The Earth moves faster in it1vkw(ps47 zsjr wgps+a* nz03s orbit 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 to the akjsrzvpz*w0gp +w1s3 4n (s7plane of its orbit.]

The mass of Pluto was not known until it was discovered to +ylu u;4 kb4l2nfx0.tmcw c3tu ag/s.have a moon. Explain how+c kt.u wlu 3y .lbgmaxc24/;sun4tf0 this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mu ckat;ex,r5 ,uch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1t, ,xrcke5a u;.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 18w ) eodo,xk.c980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratio*lv*, o(ktonq n of the Earth in its orbit around the Sun, and the net force exerted on the Earth. Whqnto, vlo(k** at 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 exeru65agb 2.b px9 t9coejted 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 disocbe9x ut92gb.p5 a6 jcus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfac96fs,m u+ lsavfw;a d9e, and circles the Earth about once every 90 minutes. Find the centripetal accelerl vsw +ad9;ffams9,6u ation of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of abmw j9c w57*ny potter’s wheel turning at 45 rpm (revolutions per y*mn b 79wjwc5minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unih/+)puw )khhth t u39kform rate in a vertical circle of radius 72.0 cm , as hh3thuu w/9kh))t+ pkshown 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 +gxcbme.3u )e of radius 77 m on a flat road if the coefficient of static f +.cgumeb)3e xriction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficientxexm *- ml )*g7jfptf- ;msg,s of static friction be between the tires and the road if a car is to round a level curve of radm 7;xfmsgs-fgxpm* -*)eltj,ius 85 m at a speed of 95km/h ?   

  A device for training as,sehi t.3v 0ektronauts 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 vs. hk,e3 0teiher 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 6 k. + jv,,7.+pnxgqnwlaibe3w;uxa xa rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reac iw nunkx3,awa,.x7 b ;ex+g.j6pqv+lhed and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling 6 g(ps* 4-5s vf -hfk7povp:tvrcmv1kwhen upside down at the top tp7s5rg64-( cp:kv* p o-s1m kv fvvhfof 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 drv.wi7abuypq;b * .z6ziver) crosses the rounded top of a hill (radius =95; iv.b w*zp.7yqa6u bz$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris whe s1ncq de-vn08el need to make for the passengers to f1qev nc -8ds0neel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.eto6h s5x6 lmj e)mp),10 m. At the lowest point of its motion the tension 5mmeohjts))le ,66 xpin 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 9.032cwp7qb;w,097qkz rxxwygq;)ug mq 0 cm from the axis of rotation i wubgqwm x;7q q7qg0wkp2x9rcz;) 3 ,ys to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnbk dv-c 8s32eyboj;x7( q4ofaival, people are rotated in a cylindrically walled "room." (kec-2o(jys x4bdb 87fvo3; qaSee 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 friction8hawd(jx0 a( aless air-hockey tabletop, and is held in this orbit by a light8h0aawad x( j( cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not i a2 eztt-uu20ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitudeuua tte2i20z- 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 b 8vak.7p w:)widkvn2 perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses 1al+sy (qh et,5 lv.pw+gf1m hhub/v: $ 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 *mt- v+1-gv oqm pj0q0a)v5lbyay-zf by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted/c9ur/r 0 7wmxj, (rzchaosz - on the car (by the ground) in Example 5-7 hzzrrwo-ca/ mx/jr09u(c s,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 acceleratelwc7u l(9 .rbw0 ;hobhs uniformly from the pit area, going from rcwu0hrl h;. lb bo7w(9est to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particulazx q1 yo+do gxuo07*g;r insta0+u1o*zox gy7 qg;xodnt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth rac7kh5 (pum v6c(bdbm5dii) above tb dh c(vu56pcm57kbm(he Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationaeu9 i6l krx.g(yt 1psy+u/gw2l acceleration g has a magnit9glp /s.kru y6gey i 2x+(t1uwude of 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 ddw ch q;kn)fy4y05ubh9n ( /c0a2da ulue to gravity on the Moon. The Moon's radius is 1.74 cqh2n;uayc) k9/(4h0afd5ywubln0 d$\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 k +ye 93ea)5nitv0exbhas the same mass. What is the acce39 e 5tiba )+vxenyk0eleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of ph0dssmp td)p a.*i/(f(7vtu Earth, but the same radius. What is g near its hpdp (tsa*u0v .7(mp) tdf/issurface?   

  Two objects attract each other gravitationally with a force o ,r.z t5yifp/bij7i3f f 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 oflpw a2 +a2v+b0xukm0v gravity, at (a) 3200 m 2p+0a0mvwalkv2 xu+b    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centabh*s6m -7,yc( qg 0vdt9iis4fh ct y8er to a point outside the Earth where thegravitational acceleration due to the Eari6 tcvsiqhcs -db m84a,9*f 07(ythgyth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star h,at i(ghim a9:*-iptyas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate th: yi*pi mia( t9,-athge surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like -)eq er ;l rq13+bvvgdour Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sunb1er3)e+q -rlvq;dg v. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astrra7syhy;x* oq,d;j2w onauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought ;jwa x;* ory qy2s7,dhgravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located a- 4cypuekytto:: g *no3ae(;tt the corners of a square of side 0.60 m. Calculate the magnitude and direction oe:n:yytt3oa*ce- tp(; oku4g f the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most o 4u*8di yu1.-n l,wg2gjxaly zf the 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 li1 z u4x .ugyln l*8-gyi,aw2jdne (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 ofuk)3 ahu0p 9zs what it is on Eartha3zk) 90usu ph, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the are 5 qdea2o*jk.f: d-4n kk9jperiod of the Earth and its distance from the Sun. [Note: Compare you-oqeea 4d jjk25* .k9rkd:nafr answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cirn1. r 5wpxrg,4npd 9zicular orbit about the Earth at a height of 3600 ,p4x dwgni1n9zr.rp 5km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbi0 nl(/u5 f5yeva megle,2i w.gt 650 km above the Earth. How fast must the shuttle be moving (relative to Ear20emeg5 nf y5ug l.ai(w/e v,lth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arez3 ads)zxk38wjq-ea7 w34y lqm han(( to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Questx7q3zj8y3ws((n-w ama3qakh zle)d 4ion 21, Fig 5–32.)   

  Determine the time it takes for a satellite 0ceuvb3 :h1 midcfe+. 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 whiud beh+v3: ic0mc.fe1ch is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launchem(8* nv) ae2ddyxvc:bc r-e :kir.r9y d from the top of Mt. Everest to be plac-r n *.e8 iredbc)r2d::(akmvc y9vyxed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, tkmmdb h3x+1g4dp 1oy0 twk13qhe command module continued to orbit the Moon at an altitude of about 100 km. d 3g03 t kdq+x1p11w mmkyboh4How long did it take to go around the Moon once?    s

  The rings of Saturn arew8( 5xb9u wxxk3vtbv 2 composed of chunks of ice that orbit the planet. The innx t3vkb 9v5x(b 8xwu2wer radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5mu1a;nrp(s o1 ytc0i+–9). What is the ratio of a person’s appare(1y1 o0u+ cts riamnp;nt weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 vidp0y+u4ji9 a9rcy:u - om.s dotd4,x4k(sfkm from the center of the Earth's Moon in a space vehicle (a) moving adp 9du, o4csi(r4jk x+f m.ds: vayu4io09-ytt 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 std dl+w)2z9lni x vj qf-bg..z enyl1,)ars of equal mass. They are observed to be separated by 360 million km and take 5.7 Ea 2 9nind.dl- zegwvj).ll by,1)fxz+qrth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring sps ja/w,*a ml,cale read for the weight of a 55-kg woman in an elevator that movm/aa,l p*,sj wes
(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 of an elevatorak phigj :8g,(. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude andg8jh, agkp :i( direction)? a =   

Show that if a satellite orbits very near the surface of a planet witm po7nci +7iw8gxtn1a, hgv/ 1h period T , the density (mass/volume) of the p +ao/71nm 1gxn,ivwtipgh8 c7lanet 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 si;wh 3)vqyavwh9pt9aks-g.92 ha/y period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface.h.3aaphw g/v99hs y2s ) -ti;yqkavw9    s

  The asteroid Icarus, though only a few hundrede+uouich1/u 5h;t5sm meters across, orbits the Sun like the planets. Its peri5h5 th/omeuiu cu1s;+od is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distaetp,p pd1)h7fnce 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 yl i0xkj8 7kffj;kwc1ldw u..3ears. 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 distance3;ckdi.lkxf w.8w1ljfk0u j7 s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G na/me;whni3 f.w 2uh3alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 meanhihs;3ie-i ero-o50 w distance for the four largest moons of Jupiter (those discovs iiro-0ehweoh -i 5;3ered 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 knowkogxr: hfb59dd imz5v+ 7n, 0gn period and distance of the Moon. +ng95dm5dio:v7rg zx fk,h0 b   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kep1bm- jgswjy-9ler’s third lag-b-ws ym 9jj1w. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmentsts 8igm3ygdp*1nmo,4 (which some space scientists think came from a planet that8 m i*m4,1n3d tsggpyo once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale ded9 m 7,7m0keg.etslf lm4:naxscribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an appgs 097el,md xtnle7 4.amm:k farent 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 go(nz j b5 ccl9lpweu7wj+e6/:v rge by swinging in 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 lowe bc:j ncz6v7wel+lu/9w5(jpe st point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s sue9 b7tymahcslu45 8,orface will the acceleration of gravity be half what it is on the surfacebt9mey s4a8 co, u75lh?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab ham6 (ubps;/y- m0eww cmnds and spin in a mutual circle once every 2.5 puym0;w -e m(b6wsm/cs. 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 da+bbg2c 97ifw(0iv xx6kqnc o :y, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the ma +ioc2(v 06bb:qn f97kw xcxiggnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the E rd+;f4vqen x)arth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because thvf+n ;q drx4e)e 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 bathrookwll6;f ji(af v7: lj l90ut3tm scale in an elevator, it says your masst (la ;93ul:jkl0vjli6f ftw7 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 rotate about its +am2jgm3ekea.* qoa t;7 bl6d1;tsql center mg*sqlo2;1a 3+. 6l;beea 7ajdqmtkt (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 vertipqx6h,.4k yet:3jt w l1m+qejcal 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 radic;lh 5q.ku,gsus r, the acceleration due to gravity atg,qh5.c sukl; its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by4wrhtm oqh4w6h9eqe/b-i.2r s 3t t w+ an an9w 6w4h2-mr o+hqiw34r.t/ bettsehqgle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If t pql,;7l * o+(yxzyi q7sgrf/qhe coefficient of static friction y xi,*gzs/r(;ypo 7 ll+fqqq7is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Ey 79uf b0xue8oo rn8q3arth were rotating so fast that objects at the equaqnue3bxo87fur o089 ytor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintai; *l87gpvx7fm* n zjaan a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp su/t9eg.k fou2 qspended fro/ufgeot kq .29m the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massi-joqj a; g3:qsve 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 mog:3 sqa qj;j-ore than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduw mbf8;ycmdq45 ux; s(ced the presence of an extremely massive core in thm(y ;bfqmxw584ds u; ce distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill2 o6 s0uggcbxbc) 4ml; and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (xms 06)g;g ucc2l4bbo a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 smk1ncbn 3 78sqz2eg8ig2p6 esatellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites k8ne6 s3pcg2 n28se7b q gi1zmorbit 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 Asteroidmp-6nsr6u:vndx /(ls Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros a(rlpns sv6dn- xm/6u:t 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 shux-1 j8tx9awl p0s;jzks c52ekttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abox2kzj85plj1ktxwas s ;e 9c0-ve 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 .cgur r1,g 6 f11iv -lp)flul)qqu ,gya period of 3000 years. (a) What is its mean distance from the Sun? 1gglr)fuf-6q.l1 ,iryq cu1l)upv,g   
(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 ifb + n7(cnrk7lma6b c 1t4vaz,t you could actually "feel" yourself gravitationally attracted to b tm+bc46 7l7 (va,cnakrt1 znsomeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Ga.6:qw dkv ),)qw)epc(v 28nai vexijulaxy (Fig. 5-46) at a distance ofc vvi2diw: )6qe.) pvqk(j)nue8 xw,a about 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 0.50 m on each side. b4j/2h xbc7ode5 vw:sFind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoin:24 v5bwbxhjsd 7/oc et of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ortq 6y+a vf0*zgiot )8b rkuv w5bfi0s)+mvt)2 bits 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 b)6dm; h0e -j4yxcyh mp5zn+;c r:3gm h 2uowsby the tip of the 1.5-cm-long sweep second hand on youyuz3xmrd hno5y+h2 s;-m wcj;: 4) cgphm6b 0er wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swin. bn(m2o h(n r46 lu1 mj/biwk9pmnlk2g 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. Whno6b 4i l.khn(num2k1(jlp 2mb m/9wr at 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 a car trave-0q(jjg)(h 77ii w;qfc eqw fo;aua2jli )jqaiu je7f(qhg cw07(fw2;-;jioaq ng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed t,qihpsb7 xx8 5rain, 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 Acela train that rounds a curve with a radius of 620 m at qs8i ,bxxh5p7 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.$\approx$    $\times 10^2$