Sometimes people say that water is removed tflvy. db3.fywi5tk3s .6 i *bfrom clothes in a spin dryer by centrifugal force throwing the water outward. Whatitiy f5 b.wb.lkf3d6y *s3vt. is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sha*kmh/o.cpc/7b3vr l o rp curve at a constant 60 km/h as when it travels around a o7/vh*clm cb.kp/ r3o gentle curve at the same speed? Explain.

Suppose a car moves at constane ,be3) .y ax7(ioxbh yq7;jfqt speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (ba) q37x qyb; 7ieoyjf h,ebx(.) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry- o,/zefq ;ip/ego-round. Whi eq;,opie/z/ fch of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical f bo gk bcf2 d.83n+ro zrzi**i(coyi/ sao4/3circle without the water spilling out, even at the top of the rc8cg/ai nyzz*od+bifo o/sk. rf 4b ( i*3o23circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least th v4nxgp6xwq ;9ree controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they pro 4x6vp;qn gw9xduce?

A child on a sled comes flying over the crest of a 0uofvty-iu4g6)we,e 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. Explu6y ,e-g4efw 0tiu)ovain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hiyphcj 6i nh aznz62-kn0b37 a*o 2gr8jgh speed?

Why do airplanes bank 2lsdi 8v .noy7when they turn? How would you compute the banking angle given its speed and radiyn27.lo8 sv dius of the turn?

A girl is whirling a2zr9 m1(jsg vg ball on a string around her head in a horizontal plane. She wants to let go at preciser 9gsmzvg(2j1ly the right time so that the 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 force on 8 ci+(dyws6wjpk6s ,z the Earth? If so, how large a force? C 6 ydwzw (ic6ssj,8pk+onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, cef 3)+fm ,rsoin what ways would the Moon’s orbit bs m,ef o3fcr)+e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Eaham1wwrfizqw4 lgz - c 36+8)krth? Which accz + wlmzwr8q3)wfi6a4-k cg1 helerates more?

The Sun's gravitational pull on the Eal* c 5r k:nodus:(lh1hrth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Conside:l: so 5(1d*rcl hnuhkr the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the lk (s n be*mr8*hhn*6tc-iv-bequator or at the poles? What two effects are at work? Do theym l6t h8-chb*r-nie* b(kv*ns oppose each other?

The gravitational force on the Moon due to theq,a mc( 4+mwc7z 4nabm Earth is only about half the force on the Moon dbacmmnq4acw+ z4, 7m(ue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its u3u,9bo ujqk2orbit around the Sun larger or smaller than the centkubu9qj3 o,2 uripetal acceleration of the Earth?

Would it require less speed to launch v 756h1ykhy+h/o jkevy /vfb0a satellite (a) toward the east or (b) toward the west? Consi5 yvh kfo/ h/hbjyey0+v67k1vder the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a m(gn:26p *r1glycgoa- dkxkw7v0zww3oving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would yg7k0(a*vwo6 3zd2p1cyrgx:nk w - l gwour 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 spack6p fp+7e6 z) r9p.,wz aehpoce 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 this simulateo pz9e c+)f,h7krapw6ze. p 6ps 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” o9+x+z ijg+h7h m o9eaur “apparent weightlessness” between steps.agz+x+ umjh9he79+i o

The Earth moves faster in its or: w02v o(mdknybit 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 produ(dom kvy:20w ncing 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 w o n iv1u0y3.a(w8hkegas discovered to have a moon. Explain how this discovery enabl1k yia eg3 (no0wvh.8ued an estimate of Pluto’s mass.

  The Sun's gravitational k :4b(opkz0ggctmxg.77s a2cpull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsa o2bcsc 0txg7k:gkp z(m.47 gible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the 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 who w 1i1gu:9s 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 accfdny.1 .g*zdc eleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orb*gy z.d f1n.dcit 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 zkig+;fx-z: n vraf3y ;qt+g, 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal f;+ -3tqyk+z,i arnvx:gf;gz circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circ9co bhjc44youc 8e-b)v)) g-wfaxkk..ba /fz les the Earth about /y -obucx9abeo fk)z4cvkg.)hw-8.j)f ba4 c once 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 of clay on the edge of a rrlq *8 c/d+anh3avt0 potter’s whdv+ *a3ac rtqh8nrl0/ eel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ver*nz -.iv9qas ztical circle of aqi.n9 zvs*-z radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 105xqtn7w vio)kc,/,h6whhzr6rpn8t 7 -wjf+z2 0-kg car can round a turn of radius 77 m on a flat road if the coefficient o6zkf,qxh77nn8 w+ t,/ztrw2woj- 6hv)hir cpf 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 thl ui 77a,es *via/w.4ka; xuloe tires and the road if a car is to round aivu k;4ei l ,xua wsa.ao7/*l7 level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fig: 7bz)ewn1h3fje jdqg, 017:olsg cn whter pilots is designed to rotate a trainee in a horizontal circle of radius b ggo1e z07jq3:ew):c, l1wsjn7hd fn12.0 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 vaaaz ssog/x47)h p /(ikfcj) s;riable speed. When the speed of the 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 th(js/fss a7a k);xp4g/o i) zche coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at b5qjyvuabwn/ na)8))/c6 +fxfx p0bsthenfvjq ba)asb )5//) 8cfw0y6p+ xnubx 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 950 kg (including the driver) crj60b uiterip mtt-368p/*gq tosses the rounded top of aitb u*/3q 8tgp6pt0t-jrmie 6 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 minute would a 15-m-diameter Ferr)-ejlqpb)b) 8 bi t6qiis wheel need to make for the passengers )eqi- i plb6qt)bjb8)to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirledzrs plmn2 82r; in a vertical circle of radius 1.10 m. At the lowest point of its mn lr8z;2pr2smotion 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 centriflgu.a5;/ qep 6ik3oeu uge rotate if a particle 9.00 cm from the axis of rotation is to expe/. qlkgepiu3 e65u;aorience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are r s ww:x6ew.j2rotated in a cylindrically walled "room." (See Fig. 5-35.)es62: wrxw wj.
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 ci :dw1 aoe7xr-t c,ngdx 97tk:nrcle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass md,ax d1n-77r woe:k:t9ctnx g ) 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 notk-re8p 1sb lfj ;9p,,ihwe-zk ignoring the weight of the ball which revolves on a string 0.600 m ls-pif 9- jkh8,zwpreb1 e,;lkong. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is pe.n .heusn3a7i rfectly 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 masse-edd /zrzfw: :e:)vv gs $ 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 divingaun3lzbp.* x - 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 componen 3d my+6zewb83vir 3yl4hyn4uts of the net force exerted on the car (by the ground) in Examiy8mb63u+r d44ye3yl3 z wv nhple 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 gw391c7kkscc q: + cal500 accelerates uniformly from the pit area, going from ck9gcl w+c7qck:a 1s3rest 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 inld9 ov,uvr )m; a horizontal circle of radius 2.90 m . At a particular instant, its ac,vm9d) u rol;vceleration 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 gravir5/icxonr0bjqvr6z b,1k +tk (( f y3nty on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is,/nkr 51onky(3cqib f r z0(t6jbr +vx 1350 kg.   

  At the surface of a certain planet, the gravvk7,r qc2l .lckl y74kjo+m x)itational acceleration g has a magnitude of 12 m/sj7m7lky)4lkcqlcr 2,x k vo +.$^2$ 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 gra c;uo q*kk/.zyvity on the Moon. The Moon's radius is 1.7/* ;.cuy kqzko4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 :cr(6wtcp uen2:il,q:,ewslu a v 9(ptimes that of Earth, but has the same mass. What is the acceleration due to gravity n tr(p:w, uluecn:,qe 9ap l 6i:(wvsc2ear its surface?   

  A hypothetical planet has a mass rxx 8xp 3xn b:* t2jz87/ba5gjjf0miq 1.66 times that of Earth, but the same radius. What is7bt 3n*2jx8qamrxxx/ :5jpib 8 0jgfz g near its surface?   

  Two objects attract each other gravitationally with a force osyawmi6v ,)3x 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 ofamj*q toz *+5m gravity, at (a) 3200 m 5q *o+jtmz ma*   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ouj4l ktya389w stside the Earth where thegravitational acceleration due yw3j9t84 k salto 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 k4 cxq, p)6t iq5c7 pcw::abswsj2ko*our Sun packed into a sphere about 10 km in radius. Estimate toitx5wk:c,ssc64c:k 7qb*2wp)pa jq he surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which3dr/;c4jlm be vm:+a ou4gsd5 once was an average star like our Sun but is now in the last stage of its evolution, is the jea/4b d+ :url;cd 3vosg5 m4msize 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 astronauts feel weightless while jg*,v bn:jxsj;c.s)7 )-em8e aqrcqz orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating mse-) 87q sn,bx*eaq)z.jvg;j j :crcthe acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lof /hx oi)sxi3 -gpf8 -xyh13atcated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitao fhi-a3h )1/xg- fy p3s8tixxtional 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(dt+r q y*fkx, on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The mf rq*, (xk+ytdasses 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 t, 1tq-km+ncri+gby7j* w sv/x9 hns8of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the j8ygk+7n cht9ni+mxs/ t1qr v- ws*b,mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perizvz2h)t*n(6q o7 flds3rmkv4g x z3k/od of the Earth and its distance from the Sun. [Note: Compare your a)vzhm *4skr7otdlv263q3xkz nf g / z(nswer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cczveuz gm380g zu 5o.pdn0+ k8ircular orbit about the Earth at a height of 3600 km. g3mkz8zuvp 0.e o0+z 8 ugnc5d   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ewax0 qo).:.sjq nh*v xarth. How fast must the shuttle be moving (relative to Earth) when the release occurs? x vox h.qa0q:)sjn*.w    $\times 10^3$

  At what rate must a cylindriu0uo uz o z/xelp7obwgv +/;/-cal spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 buo/lep/zgo; z/7wu o +0u-xvm, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a sgbdyb* 0tar9lw q,67catellite to orbit the Earth in a circular “near-Earth” orbit.bq,y7 w9a lbgc 6*drt0 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 velw04rtc;67viayc 6uwq f- )hwtocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orb7qa6) c4tw tc-wyr;h 0 6vwufiit around the Earth?   

  During an Apollo lunar landing mission, the comms , 6- u43sroc -0z2jijbovhehand module continued to orbit the Moon at an altitude of about 100 km. How long didzjv 4 e2hho, isrc3o0-6sb-u j it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit ;(5 hp2xbset ymkx 8r1the planet. The inner radius of the ringk;p(s 2rx x5eytb18mhs 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 dt8ukto( x8jkza k 7+4kiameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent kka t7+okz 4 tu8x(jk8weight 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 km mib5:qei2f i k2b9 zih+ +y0xofrom the center of the Earth's Moo :hx5+q +2ibf2i z 9yomie0ibkn in a space 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 syste08gs hb+g1v6(zh a ztmm consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between t(+vhag t0bg z1 z8ms6hhem. 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 ld ifakpnj- 06 -4)vrethat mk04n)pid - rajf-e l6voves
(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 o*zayre f0 h+zqo/1r5 df an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Waz01h5q /+rd y*z roefhat was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelll.2-7gkve x xcite orbits very near the surface of a planet with period T , the density (mass/vol-lx. x c7e2vkgume) 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 of the a0utt; *gkaa (Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s satg (0ka;*tua urface.    s

  The asteroid Icarus, though only a r;z)ns 8wo4yohv2yf +by. 4tn few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance n 8+.4 2ho vyf);4yzsrtobw ynfrom the Sun?    $\times 10^{11}$

  Neptune is an average distance oe qq-z022: j )ro/-pqs0aisy0vh cninf 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. Ix.;-d2frf iz ta (x:vjt comes very close to the surface of the Sun on its closest approach (Fig. 5–39). (:j frdx;-zv2 tix. faEstimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G* *gqf9ej5cg2ilo;om +rzk u7 alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 disq7lum3 *o/5cdyb bd7u)7-rwe bh*yap tance for the four largest moons of Jupiter (those discd7-ul7cp5m w d/b**eyy3 ba)r7qohub overed by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of dnec8sl ;d x;*the Earth from the known period and distance of the Moon. d*; en8s;l dcx   $\times 10^{24}$

  Determine the mean distance ffmg2)ds81c b pv/ snf(rom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Comp s/m(fsf)c1 vgb2 npd8are 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 (wh5h sis5m ze5iic5 h7hn9pr., aich some space scientists think camcshi5,55izeah5h ns9m . ir7 pe from a planet 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 describes an artificial "plan7stb *to:vor;g k-l2x u 4o8znet" 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 apparent gravity of g as on Earth. Wha7k;oru x l b4 tvs:zgon8*to2-t will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc )ect9ov1h .bqfrom a hanging vine (Fig. 5–41). I9b. )hto eq1cvf his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of grgmq37- hfn j 3a5osja,avity be half what it i3sj h afnga,7-j qo53ms on the surface?    $\times 10^6$

  On an ice rink, two skaters of 7xp.hj1f- nwtabk1va18t5qk 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 and their individual masses are 60.0 kg, how hard are theyatfw tq pjha1v7-x 51.k1k8nb pulling on one another?    $\times 10^2$

  Because the Earth rotates once per damc* owq1q9gb qa;vi2 2y, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of giq9; qvg 2q*1b2omw ac is this?    $\times 10^{-1}$

  At what distance from the Earth will a spaczura+j 57sw q-4 in.fgecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppos7angjq4+z-u i.5 rwfsite forces?    $\times 10^8$

  You know your mass is 65 kg, but whmlz a/sk :6n8 *d-mbfjen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directs*-/ zmlmbdjfka 8:n6 ion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about mlv1 s1kih3q;its center (like a tubular bicycle tire) (Fig. 5–42). The circle lm3s1 iqvhk1; 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 vertical loop (Fig. 5u-fl02lzkt3 5yo q lm*–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 itz91p+sujvuj7 c+.ao )sy0 ixts radius r, the acceleration due to gra.s 9 )jiya +0upczxoj7svt1 u+vity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) 3 +t1jotzy/04 wqqlz ris deflected from the vertical by an angw ry 4lj tzo30+q/qt1zle $\theta$ 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 the coefue mu71d*t 5rdficient of static friction is 0.30u* u751dr emtd (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fastq( mv8; (edd wrsn1 1w89xvaff that objects at the equwrd8fq9nvv(dam xse(w1f 1 8; ator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanceejibo:grz 3(3 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 ra:zy.n3mc(dp 7ymjl swq 2d43wdius 235 m. A lamp suspended from theny2 m :j(pdd.3ysmcw w47qz3 l 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 massive asw6tv92so7)jqoqdb *ge 1w)tf 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 equatorjw qt1fwd)eq*t9 sbog7 2o)v6 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 deducef(y pqz6iv:dwql;32h m/ q t9ad the presence of an extremely massive corm6/ hl;q 9ywqa(tf2 zq3ipdv: e 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 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 rurk*p, o (krxn7vz j8vw;63 vthe hill and valley shown in Fig. 5–45. Both the hill and valley have a radiusjv68rr;n7rk *ovk z3(uwx p ,v 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) utilizes a groupayr f+o nk f (h)rxxhf9i8d)n;0u1wc5 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 centimet8ix9x +)5drhk f1hr; f)wnauco f0n(yers. 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 billiwf,oe)p ym4;r q(p yf)on km, is meant to orbit the asteroid Eros at a height ofepp(mofr))y4 fy , ;wq 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 spacbrm 8/ kpyml5bmj.5v oo eh+,:e shuttle pursuing a satellite in need of repair. You are in a circular orbit of t 5mv.ye5,o: m j+/lmbohrbkp8he 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 tky5xh (k q6tgek0p+e m(3rxeg-j f gh- :.0bfhas a period of 3000 years. (a) What is its mean distance from the Set0hexk gbt -peq65.fj-yk+g:m(0 hgr3 xkf(un?   
(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 vle 0ca1c8 ocodx 8.z6of3ez)3 ,jjm icould actually "feel" yourself gravitationally attracted to someone near you. Make reasonable .8v fl aecz1 ocj i6eo83 0dmz),3xcjoassumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky ygab kx)doy87etns.k+67z+e Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yea +yt.k b d+gzo)s8xeank ey677rs 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. F9ec :lv*x+j* qruiw e2s0s, xkind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass place :l*qe*sek 2 s,0jcw+xvuir 9xd at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the y :xqcm;t4g)lm6az-r 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-cm-l-t o xtc:0ruxhufn 0t0x1f3 .fong sweep second hand on your wrist watch?t:xho0tt ffxrunx3 01c 0.u-f    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a ei9 ay;w:6ae3syop :ivd4+qs circle below you on a 0.25-m piece of fishing line. The weight makes a complete coev 4;:s+d9s i3 yq:apeay6wiircle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is01m ;hwc)nvr6zrgy,u,4+qm ydra b s; designed so that a car traveli+bm;ur6 gwqvms,0 r, zyy;a) cr4nd h1ng 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 train, the Acela, utili. 9i4o1-sr gkb4phwzw zes 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 a speed of (approximately ). (a) Calculate the friction force needed on a train passenp9okwb-.4rwzhgi s41 ger 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.$\approx$    $\times 10^2$