Sometimes people say that water is removed from clothes in a spin dryer by centrch5gv,8i sft9 ifugal force throwing the g t5hf sc9i8v,water outward. What is wrong with this statement?

Will the acceleration of a car be the same when th: v st,6aznd3ge car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explai tz6:san,v d3gn.

Suppose a car moves at constanm iw3qs)1is 0b; l6rggt speed along a hilly road. Where does the car exert the greatest a10 il srbiw6;q3sgmg )nd 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 hill?

Describe all the forces acting nff.n*o kt.og 64uc m6on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accel6 nfuon*ogt6m f.c. 4keration of the child?

A bucket of water can be whirled in a vertical circle withouz r 5to4l4dz9se)o1dh t the water spilling out, even at the toood1sdtz)h e4z5r 9l4p of the circle when the bucket is upside down. Explain.

How many “acceleratorsusk w.fe- p. y2gz32gg” do you have in your car? There are at least three controls in the car which can be used tgp.gyek 2z f 2ugs-3w.o cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown ie. .cjvxvp7 3wn 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. Explain this decrease using Newton’s second la7v.3xcp.vw ejw.

Why do bicycle riders lean inward when roundjxu qfi :+9hmh+ b; nd::khr2fing a curve at high speed?

Why do airplanes bank when they tuzrk485 s/nfgfye(blibl//wx ( 4r.sorn? How would you compute the banking angle given its speed and radirwy(kx i/bgo fsbn4e5.8r(zs4fl l//us of the turn?

A girl is whirling a ball on a strin, /g*bsxu 9 0mv,yoovtg around her head in a horizontal plane. She wants to let go at precisely the right time st,, *u9v0vym/ b osgxoo 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 fopjzs(3.)e xvlt0vea )*dyad ( rce on the Earth? If so, how large a force? Consider anezv ()l x e(yda0j)d3*t.psa v apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublr(f7(. mt jghke what it is, in what ways would the Moon’s orbit be rhf7 .gmjkt((different?

Which pulls harder gravitationally, the Earth on the Moon, or ggl ,3.;m w. uevhhkjd(*7xcxthe Moon on the Earth? Which acch3,7.kxh cgxde.*vgm;j (lu welerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'wats+f8)l ( ox(k5zpiu ldi sgz: *(-ts. Yet th s5(diu (fzo(-t kwsi)*tz8 p :galxl+e 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.]

Will an object weigh mnz)pb8 ,4-us*xuvd m 1dks1wfore at the equator or at the poles? What two effects are at work? Do x kdzunsf u4p) 1v-d*8,wms1bthey oppose each other?

The gravitational force on the Moon due to the Earth is only about half the eag.3uu7 7)k6p88xta ,w7i/ tbicmve ku2 bqqforce on thxb6uivu/3g,7ai cb. aek)7p8m2e qwk7 8t qute Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of May/t2w*.qicdqxzmnh ( o(z-3xbx n.b- rs in its orbit around the Sun larger or smaller than the centripetal acceleration of the Ea.*i nwyx3btx-o.(c(d mq- z/ n hz2xqbrth?

Would it require less speed to launch w:6g 6bny9x-o 1nycawa satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotat: 1g ywyn-a wx6oc9n6bion direction.

When will your apparent weight be the greatest, as measured by a scale i+ 84ui r 2rxv6f)xepsuia)9ofn a moving elevator: when the elevf+e o9ar u xsui2f)8r4x6i)vpator (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 ipvqienxqz *w tkb )b-/3)g5+ in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the for k 3ngvtbqbp/xz *)w-5+q ii)ece we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “asmc32z x zw0m*pparent weightlessness” between *czsmzwx2 0m3steps.

The Earth moves faster in its orbit around the Sun in w80br;ulh .vkw-shw ( January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not-w0vh8wb hwulk. s (r; much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was d:8 cnbj;rhygs n2c+k8y * j axn:h1;bnot known until it was discovered to have a moon. Explain how this discovery enajk8n;:sj:1 bdc gbc anr 2*hyynhx;+8bled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth g976 0pk lmliris much 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 1.10 m from the center of a merry-go-round moves wit6mlgl k07pr9i h 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 1fi x k ks3kz- zxtbfz:036zo,+ls p5e tsmg;15980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 tx+f+7 p*zu:ql k -kzoicr-j )Earth in its orbit around the Sun, and the net force exerted +ok:7f)+pl xj iqkzzt*u-r-c on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as ik79ghj;,v1wn w,llaj88 av se t rotates uniformly in a horiz8s1lwj8vhj a7gk9l ,n av,;weontal 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 tv;e* ndyfm97al2qw2 the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Eart*792q;lmaf2 edn y vwth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck o/ng nr56a;yzqeg dhhrf+qm1v2q4f - / f clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’eh2-aq 5 +gfdnq;/ 1 fyrvhgmrzqn64 /s diameter is 32 cm?   

  A ball on the end of a string is revolved at a un;u+ aat7c-*dpwylr hz j9is.:iform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speewa;p*lcyz:iu9t-a7h +j .rsd d 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 cafp .okdd5(n *zr can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepe n5k.fzd(do *pndent of the mass of the car?   

  How large must the coefficient of statb/n9 dslu b*8hcmk7hw;+fm 3ric friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h3+cmn97rlb * dm /h;hb kfws8u ?   

  A device for training s5x; 5il axrcxq5/q7 sastronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 ;xa ssrqx7i/5qc5x 5ltimes 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 dagf 3 c23fj-1 xocf(uaxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remaina 3cjg-d(fffu 3 xoc12s 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 roller coaster be traveling wrxeeidfo 2g uf*m/i7jf 3 c3z8 )f.jp*hen upside down at the top 7)mi283jfdfjce r.3ifu * z/ fox *pegof 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 dril6h xbj/yd)h 9ver) crosses the rounded top of a hill (rxhd9ly6bh /)jadius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel n*yun6qwghb6) ; ra7ydeed to make for the passengers to feel “weightless” at the t ;r ydg6 wyqh*bna)7u6opmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius qnoos1ezfk4c 5r4, 4 v1.10 m. At the lowest point of its motion the 5ecs 41orfzk4vno q,4tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axijsvbfpyet kc3.mh6j 1xie8y74q1mxy r-)f+0s of rotation is to experience an accelerationjts-x3 i rmmb7e6c)+kvyhy 1xp1e. f q0y4j8f of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyliu648avn jb 1h5mbq1v3yq:q vp ndrically walled "room." (See Fig. 5-vyq mjb 165 q pbn:v8vh3ua4q135.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey,bv; 1xgco-yl ky.ce 0 b4a:ac tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centrabb0c aoyyv -.4 e:lcgxkc1;a,l 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 /j8 da 3d:j54 sntzwcynot ignoring the weight of the ball which revolves on a string 0.600 m long. In particulz/38a n:5d scjdwy4j tar, 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 l9tr m:ip*-o t75 $\mathrm{~km} / \mathrm{h}$ , 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 massed 5ww8:, x7h+h)vzyqru zd //dbux,sis $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 3z ,vh4o/z6o p0ck.ied10 $\mathrm{~m} / \mathrm{s}$ . 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 exertedimfaq m )vkfy7,z 810e on the car (by the ground) in Example 5-8 when its spemz) 8q01ymf ,k7efavied is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uni 8 )knajkr1-cf y1,chhformly from the pit area, going frokr-j,f 8n )khy1hcc a1m rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontm;(nd6hmw4nb 0metm w q:k4v n8z:1gk al circle of radius 2.90 m . At a particular instant, b(nnm4 1k n mewd tqm ;40hzw:mgv6:k8its 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 s l2mc7xjp/( xi(e e3riwx j4/dab6hzxy), b9gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.h2)l76wd4e3xijxi pme( yxz c/ra sx j/b,b(9   

  At the surface of a certain planet, cdv/i5kda -8chp09dg the gravitational acceleration g has a magni8cpci 9gk5h a ddd0-/vtude 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 due to gravity on the Moon. The Moon'sl)s8y0yisj*k cwcd8t)5 pi8 o radius is 1.74 oylci)s ) 8djw8*pyts8kc50i $\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, b kv,*jz 8fb4biut has the same mass. What is the acceleration due to gravity near its s4kfi8bv * zjb,urface?   

  A hypothetical planet has a mass 1./el9kskf(y 2hq, 9 ksq66 times that of Earth, but the same radius. What is q sh/ ye,lqk9k(f9s k2g near its surface?   

  Two objects attract each other gravitationally with a force of 2.60mlwrce92t4 x ctsj 05$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (6r . osu:6wm0.fl vtsaa) 3200 m6u6 .l:s0so m fv.tawr    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’;3v0 her3y6fj5 q0c rrdh* ljyd0ia 7ks center to a point outside the Earth where thegravitat ka hq5036 l0j 0fir ;yercj7y3d*vdrhional 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 z2wgem6- fqx/the mass of our Sun packed into a sphere about 10 km in radius. Estimate the suz-2/xge qfw m6rface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which onc v se3b;+n gb*)wpdiwmd g:cao)-y0;re was an average star like our Sun but is now in the last stage of its evolution, wia;m3g:+p*0;-)dw) rogbc n evysd bis the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting iny4q rz9zfs::0vt b)zgs u; o wz.;/umf the space shuttle. Your friends gsmqz.4u bz9 zrzuf /t:)vs yf:0wo;;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 g.   

  Four 9.5-kg spheres are located at the cornero*8el:ms*izp4cruzaba7v i(m/w9j ; s of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other three.v*z/z em(iu849iw m pj;7caar so*:lb   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up n oeum/u7d;9spikj ;-x j/pe6g:vzw.on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planetjpz .n/u u:s9 jwdx;ev-/g7 po6 mei;ks are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at tgk8m kys::* f bvjq*u w.z;7gyhe surface of Mars is 0.38 of what it isj7mky :q.ysb8gf ;*wgvz u*k: on Earth, 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 per(zkorv5 n.zv(xz23nup)- lfz iod of the Earth and its distance from the Sun. [Note: Compare your ak-zx( . )zun5p(2f nrovlz3zvnswer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sate;pgm,eu 4q q5fk+wprtj 8wt;cs4x 0g:llite moving in a stable circular orbit about the Earth at a heig0s u:p; x+ j4gwq4eg;r8mt5kwft,p qcht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above dtloz,op:1 uck6k ;6 jthe Earth. How fast must the shuttle be moving (relative to Eartho kpcdlo 6u6,t1z:j;k ) when the release occurs?    $\times 10^3$

  At what rate must a cylindr 7:bgwy crb pfu*e:ca0elxt) u;;uc .*ical spaceship rotate if occupants are to experience simulated gublcueg7;*acwcx u . )py ;t:*b:0 refravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular d :1ev qr7pn96cq rk5/tji q6mv4q*ion2 qe q5“nekr:*2vvdqc6n6j4im/e55t e1npqqr7 iqq oq 9ar-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would 6z(km bz035 hskvr)wfa satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit aroundh3)kk(w fvzr05sz m 6b the Earth?   

  During an Apollo lunar landing mission, the command module contin42 s+ kytn w f:4ameh6(ldg(a 3tnu1kwued to orbit the Moon at an altitude on4+6eyw 24nht31 mk (fdg :t(ukaswa lf about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of icef8k vypw,0px.m(v o6rj,ccm 4 that orbit the planet. The inner radius of the rings is 73,00m, c8vco(p vpjf.x0mr 6k4yw,0 $\mathrm{~km}$ , 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 mr9by7(bo 3zbs in diameter rotates once every 15.5 s (see Fig. 5–9). What 7y9r (bbbs 3ozis the ratio of a person’s apparent 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 ascy(fj zlwv57 1tronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant vc5f (vw1yjzl 7elocity,     ----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 stn 6kbxl6wye il7 t8g(6ars 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 th 7i y6g(kewtlbn6l86xem. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg d0nkqj :bs,2uut/ s;ewoman in an elevator that moves /uk,sjq2:e st0d;nub
(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 elevator. T8wo0z bo6j epe: r)r( (klvzku )d8yb6he cord can withstand a tension of 220 N and breaks as the elevatolv puk6z68:)k(oo (r eb jdw ybez80r)r accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with pe bw-,-yzxib7r i6kz-rriod T , xry z w--zibb6k,i7-r the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period )gb:rr. ww*o+fq7zc7/vu 67t snf dc. ah.hjd of the Moon (27.4 d) to determine the period of an a+ f j*a.d nc:qu.wt7zr7s.7)h dhfb o v/wcrg6rtificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hgx. l:ku*t xz-undred meters across, orbits the Sun like the planets. Its period is 410 d. Whatlu z-xtk gx:.* is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o0s1r/,z rqepaf 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. Ijcj50 x g9:sa7l fo/wgt 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 orb wxg5o f/ja9clj7s0g: it 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 a tg4(xu /xzq8 4x;vztcenter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mdlz e.dzsv 8m/ (7v1gyakn5 (kean distance for the four largest moons of Jupiter (those discoverevs dzgndlz5 (yvm./ (e781kkad 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 k3;t eiu3ybbc ;nown period and distance of the Moon. yiuc3e ;; tb3b   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s d2p m,uwolusi/y) :+l8x3f kpmoons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compa,ol+x2:/ psuifyw )38 mludpkre 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 yb5n yk2b3m+ yMars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroye3y5bm 2 byyk+nd).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band pim.o1oe+ j)vcompletely 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 vjio. +omep)1 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 hqee0lz,nvw*)w8(1yjxdmp x70 c* cecanging vine (Fig. 5–41).n,7x * ( cdz)qxe yle0mjv1pe cw0*cw8 If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half wh oqzfdizwth un*it+p4)i 8z/,up e2 1*at it is on the surfod4)u ,que1 zz8npp + /*fttiwi*2ih zace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin i/u+u gfqkay 0p:m g,*kn 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 they pulling on one anothap+y*:ku,uq kmgg f0/er?    $\times 10^2$

  Because the Earth rotates once per day, the /kwd 3 0(mu5l.tovtf mapparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magn5k t v mod3ul.mtw/0(fitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacea 5bb ris hjdfq22v()5.g8 bwucraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moosf b5 (58v u gadrjbw2q)2ibh.n pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scaleaodw 5gx79).+kbod(qy+fo ny in an elevator, it say. o7 d(a+5) ybgfynq+kowo9dxs your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotoagh cpbt+.lf0,t9h 8ate about its center (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 eq0ph8 +o g., b9thcfaltual 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.;,r mv(03qle hf) lcyc 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 rj5q cem)0vwco4:-kg a7yy1v planet in terms of its radius r, the acceleration due to gravity at its surfa:)1-ywovjc5eyrq4k gm70 cva ce and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is dxb(0r . 92ztanpovt a7eflected from the vertical by an angle9 (a2avrxobzt.ntp 70 $\theta$ 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 d*iur3*)rcv j6 msxo4lesign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?uj6v4l3xs)mro* cir*

  How long would a day be if the Earth wer)rzfxz 3.h2v+m fo36n fz-iuxe rotating so fast that objects at the equator were apparently weightleshi x.zx3mf )6-zf+zf3vn oru2 s?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart w-ca )sde eqt)4 1ix0* hym*hnof 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 rw7rn2w7ickemt:*em: ounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle k:t7we72:rimm*wc neof 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it h y igwv(*/c1q6d8ing 29vdsn agc4;hmas been claimed that a person would be crushed by the force of gravity on a plav ndhgi* 4 ggv689 wdc1ic(q/yn;sa2mnet 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 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 deduced the presence of8u+-pvet. j dr an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 78jprv.tu -e+d 80 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley sho k5xp cgnf 0q7a:c4jowm,lq77 -ttw3ewn in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest?ke q7t 7jg:x 3focw,qw40tn7m5clap- 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 satellites eohg.:(q ea2 ldl/:hpmh)eb5c,og/ j orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be deej)/2og :/,5lhe:ho(glqbaemhdc p .termined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is mewe+ol i423 ppyant to orbit the asteroid Eros at a heigh4 l3 e+oy2ippwt 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 inj9ma+- b3h* a)uvb4spda v9ek the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behin939s )4v bjpm*+eabvkh -a audd 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.h.a:cy d78 gwi n7ljx* (a) What is its mean distance from i :w7ljc8da7y* xhng .the Sun?   
(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 necn5( zbs(jy;f ed to be if you could actually "feel" yourself gravitationally a; nsjc y(zfb5(ttracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of1bzdxi8 uc6)g the Milky Way Galaxy (Fig. 5-46) at a distance ofzubg)x86cd1 i 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 locatw s cr+p 3 db.f,;xa6lnr;z-bmed at the corners of a square 0.50 m on each side. Find the mac bbr;lr3m;ns6x - dpaz w,f+.gnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg g:b 29yz edxibkyk2;a5imrv;uv8 i 7( orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration exr:a1i m9rmtjm: knfom7- -gn7perienced by the tip of the 1.5-cm-long sweep second hand on your wrist watch? jnk9- :mmfmr7 rintm7oag1 -:   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a1 *azivim4l51wz1 vvo circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.ia z1 zm54vvw1ivol1*50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travelvl fwf w2fw*4ft9et( .f2*tw 9f .evwt (l4ffwing 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 Acel4ht:o6:sb7snrqot x x 60da;da, 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. Considedxht7ba66onxo0dqs:t : ;4 rsr 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.$\approx$    $\times 10^2$