Sometimes people say that water is removed from clothesnwxq2g , ovw ti,a1rx(dw87u g,q:ba; in a spin dryer by centrifugal force throwing the water outward. What is wrong wgwwqxtvi8:wnrxb;g7da q( ,,au12, oith this statement?

Will the acceleration of a car be the same when the car travels around a shy)ce q *s6m85ks dhai2arp curve at a constant 60 km/h as when it travels around a gentle curve c2 h)k68*5syimeadqsat the same speed? Explain.

Suppose a car moves at constant speed along a vbhjjtsr6 +(uf2km w13 r5 58jppr bn,hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between2(buv rwfp+53j,j6pr1j sht n8 kbm5r two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on bo 3/mup32kmsy,skhzun1y-0 a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratb 3y m1hyu sp3nmk02/so-z ,ukion of the child?

A bucket of water can be whirled in a vertical circ ut)bri/ j(o.ga ;msx9ez(5rhle without the water spilling out, even at the top of the circle when the bucket is upside down. Explairo mzb /(geu9t5aisxr.h)j ;(n.

How many “accelerators” do you have ir4 bgy88 m3nyajd bvwfy,9b2yp(x 6t l9c b2;hn your car? There are at least three controls 26m4ylh 39;2vwbfxynbd8y,tgj b ayr (bp8c9 in the car which can be used to 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 in Fig) . ndqhjg gj/av* pv::4mi/di *gcc/g. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between g::4i gnic daj vjghv/./c* mqg)d/*phis chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hm/lv(qqe4 )zirfv h* 2igh speed?

Why do airplanes bank whed, js .u)h5qd0wgn6w hn they turn? How would you compute the banking angle given its speed and r g)dq. n,js560wu whdhadius of the turn?

A girl is whirling a ball on a string around here1(bzpvev3ji6 xf 8cgm*24 fd head in a horizontal plane. She wants to let go at precisely the right time so that tf exce 4 d3gf8* 1jbv6mp2vzi(he ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert jw *vlap opmn67..oy0.l bh 4o;hq;lba gravitational force on the Earth? If so, how large a force?4w;0 bmoh.o6q . 7loayhb*p.vjn ll;p Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s l7*ge3uf8 ltvorbit be d g*l7tv8 fuel3ifferent?

Which pulls harder gravitationally, tha5ytfktt rs k6+ jp,ty b+;y)7e Earth on the Moon, or the Moon on the Earth? Which accelerates 6j,y+tks;5 ak)fbyyt+tr7tp more?

The Sun's gravitational pull on the Earth is much larger than the Mqqf 8)98 hcght 9dadx6oon's. Yet the Moon's is mainly res6cfh8h) q d9 9qda8tgxponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more :47mis6,a b a3lv,se*wn rfwp 1dw4n m/z0 gwyat the equator or at the poles? What two effects are at work? dnsf 01w p3b67wwra/4*lea nv,sz 4:mw,y gm iDo they oppose each other?

The gravitational force on the Moon due to the Earth is only about hal 0atz7;yu)mzyf the force on the Moon due to the Sun. Why isn’t the Moon pulled away fr ayut)zzy0m7; om the Earth?

Is the centripetal acceleration of Mars in its orbit around jk8 +l,/ozgu pbi bn4-3igf)nthe Sun larger or smaller than the centr igg)kui z -o48,nbn ljb/fp3+ipetal acceleration of the Earth?

Would it require less speed to launchtir y-y n(7y,q c0jgy/ a satellite (a) toward the east or (b) towar cy0yny7r ,(qij/ty- gd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatu 2m/z:l3qy nhest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which cy : mnl2qzh/3uase 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 spa1:ju4a37 gjiu nvbws9j+rb 8 nce 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 force we feel on our feet, and (c) au gn :j+3u89abji4rn1wv 7j bsny other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlky ob8 p f+.0ijk+eh:vessness” between steps i h+eokj:vp8+0yk.f b.

The Earth moves faster in its orbit around the Sun in January than in Julc zadza,q-)bb(,0qoar, o q9csu /k 7ly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main 9),z0baa cdqo /cz(ba7 -ql,qrks uo, 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 r er 95s/d:pbwka8i-y to have a moon. Explain how this discovery enabled an estimate of Pluto’s 9 p b-ksaird: we/r58ymass.

  The Sun's gravitational pull on the Earth is much la)84e: d 7 1v5dl gi6hvhdxqxnvwt./r hrger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatnxrd qiv8)6t5lh4hv7x1.g/wh :ve dd ional 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 travelin24o5ap qcc1 mm1f:qwog 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 Earth in its orbi* 2ydf11s uq/opi (bkrajh3e8t around the Sun, and the net force exerted on the Earth. What exerts this fhf*qy8 e3r1/2o( sjk1ud paiborce 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 ; i-as8sc 61(j32z(xuad 2a jq kdpnada 2.0-kg discus as it rotates uniformly in aac(d jad i sqk22j-xap 3n8adu ;6zs1( horizontal 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, anm*028m3ggnxj7t vxyo d circles the Earth abot78 0ogyn x3 2gxmv*mjut 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 arjf.*h5op9gdc3psy ;preib4 b(0u o5 speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter f.r5uo g; pyhbr ob*s(i5ped0p j43 9cis 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circlpwv: y7x; gqyguo 5d7 nq sk:;iyz3 88fo0k.dae of radius 72.0 cm , as shown in Fig. 5-33. If its speed is pya7syv::k.3wo; 85zd; 7qno 8gdu i fkxgq y0 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 twu(l.j 8f yx6h0sgk/ car can round a turn of radius 77 m on fg0h6s8 w jyt .kl/(xua flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coe;:.ak l9cgdt k,hvf3 ifficient of static friction be between the tires and the road if a car is to round a level curve of i, ck9fl: 3;avd. gthkradius 85 m at a speed of 95km/h ?   

  A device for training astronauts:n ogumb0 (.8ew y5a/ czrwfe: 4yh/ys 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 times her own weight, hownsoz0 y/ yeh5ga4:.8mcw:(f/br e ywu 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 fz:mw1e+e mc68 4p kz*ed-f.zqlo+cg cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between 4.ep-om fe+we df c *zkzqc+z:816lgm the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upskutq43 1 6vmjp b.vcsmk.9s5vide down at the top of a cir4k5pt 6s sukqj.m 3 bv1m9vc.vcle
(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)h .wq32 -t azg2bgwv s f,+9;i2quyxnk crosses the rounded top of a hill 2 iwx ;gbqq,s +2.3wf2gnv-aykth z9u(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 min7n(,mor86ox9s*7 ktturp z deute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost (ox8z n rtekut*797 mod ,prs6point?    rpm

  A bucket of mass 2.00 kg is whirled in a*vc3.-xzl vzy3 oql8wzw xz36 vertical circle of radius 1.10 m. At the lowest point of its motion the tensiv.xzl3 z3xy 6 -zw38coz *wvlqon 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 kr84a/jpub 6n uk e(lo4ca5h( centrifuge rotate if a particle 9.00 cm from the axis of rotati8 ocnk 5k 6hl(a4 /ube(japr4uon is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindribu9- pdxrg5b1x b tqlc8d vn(f7i ;jq9r /*uy/cally walled "room./ ;tx5r8p7/9qrb9*byjqdduv n l ( -cbg1fuxi" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air95l2 )dh g0bxd +jbevgqn/l;v :j(tno-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) througxv (5jov q;n/d+ d tbl:le)b9gghjn20 h a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of thetxi2tyo;w k..be ute5 m+/jm- ball which revolves on a string 0.600 m long. o;tu b-j 2w./mx5t tk+e.meyiIn 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 pn/6(l 1 .ed6eed llz oq *er3josj)4dserfectly 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 masse7 whp r2.7.vzs5 vvfyzs $ 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 verticallyusf5h0w +//-vg eo dey 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 aniz02l9db 4jb co9s.za zha n86d centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when ib hji b60 nc9 9dz4ao8.2zzlsats speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going froua8j,)zdlpsh3b) w i56fb i n)7mz* mtm rest to 320km/h in a semicircular arc with a radius of 3bm 6itns,8i*5dmp bhwl) u)zjf7 za)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 hor:ih0o64g zm1j z7g ygcizontal circle of radius 2.90 m . At a particular instant, its acceleration is 7o:i zh01 ggjgmzy4 6c1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 chjy vd *c*;xj3j 7+nukm (2 Earth radii) above tnh vu3xd7c y *;+*jjcjhe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accele(u3qh,dblbd,o sbvv*s/*f 4 ellc z. 2ration g has a magnitu ,s3lv/ulb(oq b4hc vlbd.*e*d,s 2fzde 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 tom ch.-9bqy8y+) mtfjr gravity on the Moon. The Moon's radius is 1.74 .m)jyyc+ -qfhrbmt8 9 $\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 Ear8nn n)tbu9 /kyei.gbtx*y) : fth, but has the same mass. What is the acceleration due to gravity near *yn t.:t/bne)b ukxnfgy )89iits surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,s h,l7sd6v/h a but the same radius. What is g near its /vds l,ha7h6ssurface?   

  Two objects attract each wqdt 5,o 8n0tuhvqmn;v3* ; fcother gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleratioefk 30fsc;: hh3-4oa+db qrisb6eim )n of gravity, at (a) 3200 m h3e: a;h s0sd+iqoc-bmebr f3f6ki )4   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside j*uzv9l vcup0 bk.oftxz /3*lh: (ea9the Earth where thegravitational acaev* pzl t(b9kulh x*:vu.j 390zo f/cceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sp n/xu5 s9w2ymfhere about 10 km in radius. Esw/s2uyf9x5 n mtimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averagenrzfl*yjjz.5 (dwm 72m7eyg : 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. Whryzje7f n2m7dj m(*.5 :lw zygat is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightle+ 4;9ggt m hyikaoyl3e o5h.d(gf* 6zhss while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot63ag5efi.hgl hkg (;z *htm+yod4oy 9 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 corners of a square o-7qbovv90rtus k)6j j f side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by th-v 7q 90 stkjr6bvo)jue other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Szdm;h,30ezo,dc / lrkun. Calculate the total force on the Earth due to Venus, Jupitelhd/ o,c, md0ezk3z;rr, and Saturn, assuming 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 acceleration of gravity at the surface of Mars /-3euu kvowe; is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deter3 ke eow-uv/;umine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun u/e o*ql rgu4 o4jdzd,*sing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to t*/,rzeodd4g* lj4q ouhat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sy zyx qe2r+v8ow /xa18atellite moving in a stable circular orbit about the Earth at a height of 3x8r8y x2e av +oqyzw/1600 km.    $\times 10^3$

  The space shuttle releases a satellite ih;: ttn(z ld2into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the reltz2dl n(;hit :ease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshwkc.a8cy2hqqw , g-* rip rotate if occupants are to experience sicw82w ,*-r.ygcqaqk hmulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circuq; 8rbu-b8 nrole6aj;lar “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does youre6bro8l;ab-jr ;n8u q result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would 2ib19 xucw xkz5* tm)xa satellite have to be launched from the top of Mt. Evere* t x9)bcxku1m5ix zw2st to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cr y/)o / bim2j; 6u5wm 1cmnyv km-;4+kobqqpiontinued to orbit the Moon at an alti/k 2 i)qr; pyi4+cbm-1mo/q5 u j6ok;bmvn ymwtude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice th+s nhr,ohu e) 77xz(wd khm5 ;zdnvt+8at orbit the planet. The inner radius of the ri hw7uhtvr nozsek5,mn8)dx7 z; (+hd+ngs is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotat hgm++ b,0rze;ky alzr(g v+;qes once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at t;ehgzg, yazkr + r0(+ +q;lvbmhe bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the zv+kci p zx5 ,o54x0bvcenter of the Earth's Moon in a spa ,v4pkz0+5 ixbvo5cxz ce 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 equal mass.4 a f.wkn9l9ak They are observed to be separated by 360 million km and take 5.7 Ea kw9.9aalk4n frth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an el484qlrv i(s dg 4cnkd*evator that (g4k q*d84ilrvc dsn 4moves
(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 z 6hgyxp* )c3ran elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude *yhpz63gc) xrand direction)? a =   

Show that if a satellite orbits very near the surface of a planet wit4st01(0yeidn rb ca6hhvm (rd92k ;nhh period T , the density (mass/volume) of the planet is nke 4av h(i0rtm92( y61 dds0brhnch ; $\rho=m / V=3 \pi / G T^{2}$ .
(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 Moon (27.4 d) to determine the cub tmiu0 5 95sglr3 5n:tzp.xperiod of an artificial satellite orbiting very neam5u 95i0s ubnxp3 5lt.tc:rg zr the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, b m9,glbpgyiv7 dt.jah: 3 cebm6( d84orbits the Sun like the planets.bymg p tdj:9mib7 lga(v b34 8,.hd6ec Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average pkz0z9gbqqh )4 1dzl*w8n e5wdistance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once everymlrf1224e45m9s c ytfv g3llm 76 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 the1m2l sy9cl rmfm 4l45e3tv2fgre? [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 th8 fz4xohujot ym18b9q )yc,3 ge 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, anjibmj1 3 rl5-vdcdpho: h10*kz(mn p1d mean distance for the four largest moons of Jupitvlm:o* n3c111 j0zdbhdjmpik p r5-(her (those 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 period i 2r )hov8toe*jb(k9j and distance of the Moon. hj eo(o9jtrk)8ib*v2   $\times 10^{24}$

  Determine the mean distance from Jupiter foq1l sr.obrvd 1q -+m3zr each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table q-lzod3mv.+r b1qsr 15–3. 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 tiqz3p2m; za)Mars and Jupiter consists of many fragments (which some space scientists think c aqt)ipz;zm 23ame 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 sz :ccbrh q lmvdbd 509zkx0,(a(ub26 describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quicklyd5mubbxqzbc6vlzk0a, 20( rsh dc(:9 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 gorgec42y-8vvjzu d by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the uvyz84 -dv2jc 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 oc23v0t rk)(vytb +jd rf gravity be half what it is on the su+t y 2)t(br0j vcrd3vkrface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mulju9ik62i i7gw e6jlt5mr301b1 tlph tual circle once ever 7ljrlg5iwp6thil1u e2 3j9ktmi0b61 y 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotanb y1 wjjwqr,9wp/ -6 nfjqt55+xx/lqtes once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotatj/ /xjn6l-5pwx wfqqnq w,9tb1 ry+5je. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Eaveza6g9:b4 l nth9 jt7rth to the Moon experience zero net force because the Earth and t7b6zh j:v tla4n e99gMoon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you sf dr-1eq uq+9 2w 2:oqm/eos-oaoj zt9tand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the ace29/a ooe2d9 wzo-sqfqj1 trm u- +o:qceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate a okf(dcnnc*,4bout its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a didk,*c 4 nfno(cameter 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 ) f vicwi0(tx+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(3jk 5l0.cwa4j gcyx ,exw.r m of a planet in terms of its radius r, the acceleration due to gravity at its surface awk l4.g 5w.c0(x x erajyj,mc3nd the gravitational constant G.

A plumb bob (a mass m hanging on a string) is defleuxmhbvu6)-hha, g k(k. pb73icted from the vertical by an ang7uv.bi )xk (k h-p6bma3 hghu,le $\theta$ 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 ofjc8qcg0uhlbntdng.90jb/ 0+ d (b qs+ If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely9bnjnl h bjcb.g/ 0d8 tqs(gcq+d0u +0 handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the e:dc: g16 jbpllilq4a3quator were apparently acq14:pd3llj g 6: lbiweightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apj7 le2ft7rj w1art 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 y lvi abx+eg3 n6f36:xcurve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of+v :3i nl6fxag6 yb3xe 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mass 2hf*.y elcoq;(ga5lb j4 nd9give as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a fe ylnjfo hl4cgd;bq.a *5 2eg9(w 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 hrn 7y 8j7dn-yo9jt+ap+*efl Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, sopj7fld j89yaynh roe*7t+ n-+ 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 trave/1 /a mj ,hyz yth7am3xcg+f)srses the hill and valley shown 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? Lightest? Explain. (c) How fast can thg h3c+ysf1x,j ma7za/th/y)me car go without losing contact with the road at A?

  The Navstar Global Positioning System ( g4gno0)hg u:sy.)mih GPS) utilizes 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 centimeters. The satellite orbits are distributed evenlgumy4: shg oh0g)i.)ny 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) rtp( bsg 0dc5z( (ayfn)qat93, after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of afnra3a( p(5b0c s zg tt(y9dq)bout 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a2(dm xvw,wc6 g satellite in need of repair. You are in a circular orbit of the same radius as the satellw 26xw(g,v mdcite (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 eliqzk +;ad:a+. 30( ziozvxt) What is its mean distance from the0.qo; 3exd zzalti v:k+ +(zai 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 need to be if you could actuallyaoo: (-5f xd:b qh/gnu "feel" yourself gravitationally attracted to someone near you. da5-:gfub(xo:hn/o qMake reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxzmh5 do68 +wnxy (Fig. 5-46) at a distance of about 30,000 light-years from the cennwho m6x d8z5+ter $ \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 locatenp1 mk6a5ob7 yk4 ;usvd at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitat;5a7 smpv 6y1kun kbo4ional 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 o2 p3k1tf, jtk,glie3a7ld g u2rbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long e0o1-v-k sp9re uf r5to7eu09 )ebomk sweep second han0k)o ome- u91f- ovste0 ur7 9bekerp5d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arl4rk: m ceim81ound in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fi kmli4rce m8:1shing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so th0qt7v)cyqwasfe j( /rl*mx (9 at a car traveling( 9j *leq s/m)ta7r(qfy x0vwc 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, utilizes tilt of the cars when negotiatin7ocm9t6bdmme g 7bfdw7f 4q/9g 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) Calculatedg9t fd be7w7cqm/4b9m7fo6m 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.$\approx$    $\times 10^2$