Sometimes people say that water is removed from clothes in a spik3se/,a yws;.a+ m6 to,fchy un dryer by centrifugal force throwing the water 6y. eso w+3am;kat su, /fyhc,outward. What is wrong with this statement?

Will the acceleration of a cjslyby1 d.mz* hn7)3x ar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at tyzdx ymb.l*h 1j)3 ns7he same speed? Explain.

Suppose a car moves at const f j.esuj65zrz.-d;xv ant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top ofj;sxdz- .6ru ej5zfv. a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forceku3 jca kg,9em,j4.q(kzea:r.k. z wzs acting on a child riding a horse on a merry-go-round. Which of these forces provides the cenz4ame 3 zuj9kg. aj,z.k.krec:q(w , ktripetal acceleration of the child?

A bucket of water can be wh: n gri) 864eat. y/kmk8svzi8b i.rgrirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down.k.)t .i:i8vai4ysmg6eg krn /8bz 8r r Explain.

How many “accelerators” do you have in your carh(: k:)xdpda y? There are at least three controls in the car which can be used to cause the car to accelerate. What arka:d)(yh px:d e they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, a d jdzzryf:,b*8ms0g4b l 3:)9pfdh lus 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 sr8lmb93*l: y bp):,hj4fuz0 zfdgdd as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high spee( oj w +,d6o pbk w5wuw/gz5jc:c,rc2wd?

Why do airplanes bank when they turn? How would you compute thckk591zb 5kty mh5(mp(pcjra6 aa -w h5)uv5qe banking angle given its speed and radius of the tu9a5(uzyvkw -( 56k5qrc mhpp)1mc5t5bhkj aa rn?

A girl is whirling a ball on a string around her head in a hr-molh (e. ,sdorizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she .rhm,os(edl- let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how la3wblcmg 66vurdn bot+1x9, h :rge a force? Consider an apct,+b6m nbrhw61lx9gv3 o du: ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double w +fp.iv4)cx+ odc8 zwuhat it is, in what ways would the Moon’s orbit bp 8iuowv f4.)xc+z+dce different?

Which pulls harder gravitationally, the Earth on the Moon, or the bl5 ggp (k.yz8Moon on the Earth? Wypkbgz l5(.8g hich accelerates more?

The Sun's gravitational pull on t mv dgn;bp(t,esv0a6t5 iud* 7he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in d ptm6ntuviva ds5*,;e(b0g7 gravitational pull from one side of the Earth to the other.]

Will an object weigh more at then+ wp)y fsbgh7;6pp) i: u0gvu equator or at the poles? What two effects are at work? Do they oppose each otherg) bup pv+6fy0p7siugh)n;w: ?

The gravitational force on the Moon due to thykosxt1y7c:lf 4yg)5v 1m ug4e Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moo1c 7vgy5f1lo 4ysytg4mux :)kn pulled away from the Earth?

Is the centripetal acceleration of Mars in its or5ipenb65 6asr bit around the Sun larger or sma5sa 6pnib5 6erller than the centripetal acceleration of the Earth?

Would it require less spe+w, n*k,avq0b obu3 shed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotati3vqb,asn,0 uw o*bh+k on direction.

When will your apparent weight be the greatest bhvuux6ptjq4e24j +fzk o7mep3f )44smz+w 0, as measured by a scale in a moving elevator: when the elevator uouwp)7mfh 6jbz0mep4k 2f +4q3xvs+jt ez4 4(a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely ahir4b5g4re -bffected by weightlessness. One way to simulate gravity is to shape the spacesr g-ihbbr 44e5hip like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) 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” :f.adff2.oj( v*xh4 a7we dhabetweenoxaj (vda .2:.faefh* wf d7h4 steps.

The Earth moves faste.spl /xf3)wcxr in its 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 p xs3cpx)/w .flroducing 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 discovered to hvnndj)qit;6)5 7td0 etphvg )ave a moon. Explain how this discovery enabled an estimatign dv56t0q) v;nt e))j7tdphe of Pluto’s mass.

  The Sun's gravitational pull on tnw1d,vq.96j(c* ev g:bjfs wghe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cov sj(c9jggwq.w,:nebv6d * 1f 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 travelingau v d26xj2 dp;ztl,+a1;l/s 1cugstp 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Eakok,bhmraf s/6:pk2t;m )u u) rth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on )krufk6h)b:t /a ko,p2mmus ;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 exerwtiy k* mrs638ted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate thwmksr i3t*y 68e speed of the discus.   

  Suppose the space shuttle is in orbit 400 km frj +1 y6x7nrpaudu-+m tom the Earth's surface, and circles the Earth about oncjp+u 1tamndx-yur 6 +7e every 90 minutes. Find the centripetal acceleration 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 )lnvd(yi1t:(g yi sm -of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diame:ym (-1tg)(ily s vidnter is 32 cm?   

  A ball on the end of a strit duqjj:21 poyp3+wd :g+t ox.ng is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its1.o:x+top 2t3qdgu+ pdy:jjw 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 cazg 4eebd6zpv e.6eyu8 b l(-,qj ix*+kr can round a turn of radius 77 m on a flat road if the coefficient of statize.*(jubg ey8k eebi-4+,qdxpz6 lv6c 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 frictiwg9x0b)2thf +ecicx 1on be between the tires and the road if a car is to round a level cu 90xef bg +cchx2)t1wirve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pmx aspa7qy w,g:y)*b:ilots is designed to rotate a trainee in a horizontal circle of radiu:ya my, :)ag*qb7xpsws 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable speg-l 8sp;yev 7xz mm-6ted. When the speed of the 7;6lmp-sem- zx8g tyv turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rolle .o9c9qq aomsom4) 5blr coaster be traveling when upside down at the top of a com)9bsoml 5qc. 9o4aqircle
(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 (ir jly1s-,h5m6 y8b u qg()-q( usprnzancluding the driver) crosses the rounded top of a hill (radius =zla -rq,8 n 5yy(u(g u jhs6m1b)-qsrp95$ \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 mc0xv lk696kycinute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost pointcvly6xc 69 kk0?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiupdwwpn:+6cqil. /e:c zppg58 s 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N/qgp i:5p6wn8le:dc+ .w p pcz.
(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 3o 9 b*0fqg wtyf)yp5acygh t:nu8k5 *rotate if a particle 9.00 cm from the axis of rotation is to experience an kc503gbf*yt9nawhuf )5g 8 yty*o:p qacceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are riz. )e vfa0wg +9odv/wotated in a cylindrically walled "room.. dzai9+)o gv w/vw0fe" (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 fr0 x0 ( eqjjdr20aenmmbw1*a c6ictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mas q0axb *edwj r0(e26nam1cm0js 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, +6m lcm.n .g2da9;g krohd2 hyby not ignoring the weight of the ball which revolves on a string 0.600 m long. In odg;h r a. 2ndkh69+2lmc gmy.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 car traveling lb2xihnosi7 ( e*c4kr0. pj6h 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 pij q xszggj/81k n+56)jjq3l $ 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 b; a74 jhbnug 8+d0rprry 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 8we1(;9tohwxh (rjac force exerted on the car (by the gh j1x(wcetar9o8 h(w; round) 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 5uzh:h4vb(*5b (mnw3/vg tm; o4modg o00 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, asmmbgum*hvb /4zhogn4 t:d ;5vw ((o3o suming 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 horizont/)*z qzrwd+ffal circle of radius 2.90 m . At a particular instaqz/w+*) dfzfr nt, 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 gra5 dlc)j 7biwe25ankd 2vity on a spacecraft 12,800 km (2 Earth radii) above5il e5kj2dn2wc)a b7d the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational2g87)sqnfg x2 k h 1bi:h)mkjanzvy7 : acceleration g has a magnitude of 1m7xqiz ns vgjyh1:) 7f g:kk28a)2nhb2 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 radiu 418wbjtfrqz/g1 4yvul. cbv 0lse2 c:s is 1.74yr8wbv 2jub:t 1l.4q 1sv4gzccef /l0 $\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 Earthfx, 6k o:z*o/cb7zsv x, but has the same mass. What is the acceleration due to gravity near its surfz:7 bf cxvx sk*o/z6o,ace?   

  A hypothetical planet has a mass 1.66 times ih3xyiw,v- ix3hf,xvje m+o+ h5p8/hthat of Earth, but the same radius. What is g near its surface/ix3h,8v xw+phhi5i,-hfxo+ej vym 3?   

  Two objects attract each other gravitationally with a44uim.yqo l*1z(wxj s; b 7yuw 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 swzh:k0hp78ni fggh-+w l7f0 j r4j 4zof gravity, at (a) 3200 mrl4s j:7hzjz p +8f4-0 iwhw0ghkfn7g    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthexbl()ga31 ch/6gc, tx s9jkb where thegravit6ab gxtk3, ec) /91x(ljhsbcgational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Su 0vbc:n 9e--j w4srsduwu4j ia*s/zk)d9go3q n packed into a sphere about 10 km in radius. d49 ujs /u340wwbejrna io c 9g):skds-*z-qv Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an ave0w mlc5/ zzfm pc.61herage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on w5c/0 mz.p6 mzfhlc1e this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting inx(qwnct9 cr6*/og5xu:ny5 l xrlr4( p the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of lql6 r5ot*ucr9cn5(nr4x xx g/(yw:p g.   

  Four 9.5-kg spheres are locateb- wq;gpz o- k2st/2axd at the corners of a square of side 0.60 m. Calculate the magnitudtxp sqb2-k ag;zw2-o/e and direction of 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 of the planets line up b4o-k)c jnaf z 3hhpoilv6;24 on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assumv ocjka h p2nb6hlf-o3;i4z 4)ing 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 accel-sg ye*7md:2vk r,ikl eration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400g:i2ym k,l 7rdsev *-k km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass ot( ev7ifgh ul 7+p-jy4f 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 laws, Examph+g(tvyu77ie l-f 4jple 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellit+h+e6 jhy* jyje moving in a stable circular orbit about the Earth a*y+jejj6 hh y+t a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 659 cjq:glih-vgqo/6 .tl lr:f.o pp,k40 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the releas-/9gglo p:jp:cl k4 .vf ,lqiq6oht.re occurs?    $\times 10^3$

  At what rate must a cyl(val) (ll1njr0f n2rw indrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolutioj )lr( n2n lvar(fwl10n. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a c (r)59a cxatfyircular “near-Earty5af )t(a xc9rh” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched frmc o 1(bp8t2:-r anmxtom the top of Mt. Everest to be placed in a circular orbit no amtt(81xpb-cmr:2 around the Earth?   

  During an Apollo lunar landing mission, the command ( fh-v74v sbrya0z9mp module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around t( bf as40vy-z 7mvhrp9he Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pla7nqv5tnba,0skfh0.rk 8c ,ldnet. The inner radius of the rings is 73,0f,b80nn hkv akrsl.c,50t 7 qd00 $\mathrm{~km}$ , 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 evxhk ;v 4y3j8q9vlmeo7 i3kw c-ery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight tyxhi3k-lvo k qw3 9;84c7 jmveo 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 km from t : ,ojuvcxz2 nr1 pse63k,1yjjhe center of the Earth's Moon in a 61zkr2:1j nv ,j3pcyoxj e,usspace 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 eq t s9bo w/ti : 6gy-j8vepcwa6ve05ha:ual mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a vv /:j96eot8g hwa -bpt50s wa:i ye6cpoint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scaleue32 d py9/s5gnwe6ma read for the weight of a 55-kg woman in an elevator that movye/6pmu 2ang95dews 3es
(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 suspend +ap.1gvq1c3 xy* jhzced from the ceiling of an elevator. The cord can withstand a tension of 220 N an1cqa1hpz*g+ x 3yjcv.d breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfa/su lr0 ra6bryl. ;is8ce of a planet with period T , the density (mas0;6sluysa /8.bli rrrs/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 pergd8hea6 .hgjxa+ t;c-iod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting veg;ta6 hach exd jg+.-8ry near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the S0jc7;hi p6woz un like the planets. Itsiwh 0poz 6;7cj period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 brm18 ,fowb(8/ j7i4 -etnlekwz9gej$\times 10^{9} \mathrm{~km}$ 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 :d2p0hi -qa702-bmtgeoig7hyh y cu; kdb( 1h years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.] 2;od phy7d7t:e-icah(g- 1bhb2qmkghui 0 y0    $\times 10^6$

  Our Sun rotates about the centki flj2hc+1r;xi f; q7er 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 masf zp kh cm3o)a /v70dtgjco+ 3ee 5eg);w3zkg6s, period, and mean distance for the four largest moons of Jupiter (thoh/zkac+g g033e67k e 5v) ;efwmjptc )ozod3gse discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known periodboqr 8kus5rxlx6 z3;at* (bd7 and distance of the Moon. qx ;*o3lu578tx bs bazkdr 6(r   $\times 10^{24}$

  Determine the mean distance;e guebb0:6 ol from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distanceelg;b60oe: bu 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 J.p co7i:q5lf7c v+aosupiter consists of many fragments (which some space scientists think came from a planecolpcq: +7 .57ofiav st that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describeua6.p3t12zk zh pe:cbgd 0bd+s an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). Thb 3k db:dtp.phz2 uc+1 60azgee 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 apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. pcb8kjd ;m7s:jea*k+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 ps7mjbj*+ ke; kdc:a8swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerationlu 69ka2m 60kjeq/fb y of gravity be half what it is on the surface? 02 /6e mb9jykkql6a fu   $\times 10^6$

  On an ice rink, two skag t/qbvbb3j 2 ee,6 64au,ekqjters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long ekbj/ 6,j3 eb,bgtvuq6aeq24and 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 acceleration o*c 9qy+0 6id6ytclll*pkc+w pf gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this lpc lkly p+q0w9dycti*c+ 66 *effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrt i8/ic vupd1.aft traveling directly from the Earth to the Moon experience zero net force because the pvtdi8iu.1 c/Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kft cith78;c74yil.imic(*x kg, but when you stand on a bathroom scale in an elevator, it says youric7. yfkt4*xc ; mh(iiic 8tl7 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 thaing9t55m7i fnsxw7 6m t will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube hain5 w s ti9576mmgxf7ns 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 aircra0t33cd 5qq oywft in a 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 acc6vk+is. 5g b-fhng*iceleration due to gravity at its surfacegnhi6fbvsk* -g.c+i5 and the gravitational constant G.

A plumb bob (a mass m hang,rsxajv.zft4 g4wan011 xo2 5:x xwuting on a string) is deflected from the vertical by an a0wvatx11sj 45 gw4uxxf,z:rt x2an .o ngle $\theta$ 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 I zbea,e3 (ti .1vgp/ime7p u1m1ioni/f the coefficient of static friction is 0.30 (wettz/iioem1 p( 1 v.inpeubie, /g13 am7 pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotare5uk:u .i4(avq e xl,ting so fast that objects at the equator were ap ,lei eaq xk(uru.v4:5parently weightless?    $\times 10^3$s

  Two equal-mass stars myx v1g 8+:qozmaintain 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 2qqt:ds /n63x/bv*o wd 1w zn,zjx+6sh35 m. A lamp suspended from the ceiling swings out to an angle of 1qwx*1w//t3h dn zs6z,x+j6osndbq:v 7.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timnw/r +kjbzl 7j7 1-nw u*ic*ryes as 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 survic 1+j7zb/rnj rwnkwl 7iu* *y-ve more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubb*7-xp gqhai )dle Space Telescope deduced the presence of an extremely massive core in the distan)q7ig hd *xa-pt 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 cons8)jdu 8df7o,a-mckeetu t 4n3tant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radiu )do 7mdec8-unt ek8t4aj,f3 us 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 System (GPS) uti3pk80b lz( l*i-kfy m,z*l boslizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimz i0b* - fmlll(38p,zo sbykk*eters. 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 Aster u45 :6km i(.s)ejqolv 8yr8ndfk+bf qoid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is:iyrfk+ n)uv d.l8m8q5 e(4qj s6fkob 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 injla7 0rpdyp3 3q,n-e j the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite d0rn-73jq y,pja lep3(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 its0t8e8 + sfk/edwwfh7m mean distance from the Sun? /dtwe0 f8e+7mks 8w hf  
(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 "feewb/ p6f hgb+i2*b/vh el" yourself gravitationally att2bbw6+ *fip /hh bvg/eracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at hzq46u i8c.9l-d4n cxc1+r.j jperhja distance of abou4prxrjq -hzielj 6c nj. .d9 1+uhc48ct 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 ofneuhd g*zogul+x(a( :;e.o9o a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpointue oa o.g (e9oz+d;hg l(n*ux: of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi y.y)m*u3nrkt+v w2m e l(fy(qts 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 ka7eky7 0gi.jk 6 ti)kof the 1.5-cm-long sweep second hand o aki)k eg 07.i7kj6tykn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a (t zd ji j6:h,*:c+x(dcypimlcircle 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 lin yt ji ccjd*( h:+xl,:dp6(zime makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is dg+kc b.q* 0lnx o,rvu :veie;9esigned so that a car traveling at speed rc0bo9iq.xe:un g kv;*ve,+l $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whe02wauk dq w*i e;1bb,x ej0zm(n 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,2 wb,1dwkq0*xbm j(ez;i e0au 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.$\approx$    $\times 10^2$