Sometimes people say that water is removed from clothes in a spin drxoms:q *x8 q-tbxqn8- yer by centrifugal force throwing the water outward 8qt-xqmsx*q:- on8bx. What is wrong with this statement?

Will the acceleration of a car be4/ ngook-wv/fc5hkvj. m y-d: the same when the car travels around a sharp curve at a constant 60 km/h as when it travgdf-//yo .5:oh vwkknjvc-4 mels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where dbou:h+or3 wwx,/: lz hu o8x(does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch neux( dz+hl3wxo:/r8h ,ooub:war the bottom of a hill?

Describe all the forces acting on a child riding a horsesa *fyk+93*y( kt;tiw .5 bxs4 zzyyi *1hnzum on a merry-go-round. Which of these forces provides thetnu 5z.(t+b3syxh s*fy*y1zyi kk z4m*i 9wa; centripetal acceleration of the child?

A bucket of water can be whirledsz2 u-yt cky*- in a vertical circle without the water spilling -st uzcky2 -*yout, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There z( z( 6ahz8o k+haz3wprm sv0z78 zz5eare at least three controls in the car w(8k5voza+8wzmz 30 azz7 rhzze(hs6phich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying oj.ydvf t2ku-3 v,ssu9 ver the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), b v2 -ksuy 3v.j,s9dutfut 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 law.

Why do bicycle riders lean inward when rounding a curve at high speg0gnrtq7w -t3 v d0t9sed?

Why do airplanes bank when the ksa.k2 xwwgxqx s:e9f6;6cc 0y turn? How would you compute the banking angle given its sp: cx9qg.6x2sws;k6f ceka0xw eed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.hz igd8(z bi99 She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go9igh8 9(z bizd of the string?

Does an apple exert a gravitational force on the Earth? If so, h5km-x10x ji;bgjw c2z x2+bb sow large a force? Consider an a ;k5+- ixz0 x 2xbcw1sbjmb2jgpple
(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 or ;:2 juicd.qzyrc eh0m(c w:(fkau :*obit be ( d :fmuyrz:k2 hwu .coqe;cj(:0i ac*different?

Which pulls harder gravitationally,duq-nk ia*8n 9 b:fnx/ the Earth on the Moon, or the Moon on the Earth? fuqd-x8*k /ia9n:nb n Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's.pn na;f 1as9) rg:u(zk Yet the gan1(pn)u9z:fs ak;rMoon'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 more at the equator or at the poles? What two effects are a3ueu8e/rse3 qlu36 id t work? Do they oppo633 ldreue3u8eq i/suse each other?

The gravitational force on the 7xk)9 agn;qn wMoon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the nk)gqxw9;7an Earth?

Is the centripetal acc yg/ mn+no6qk3nnp5 q.eleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?n 3kq5 ngq+y/n.pon 6m

Would it require less speed to launch a satellite jyyho/wy7 3x iw/2-hvw(jrs* (a) toward the east or (b) toward the west? Consider the oy h/wrisw 7 j/j-3xv*2hw(yyEarth’s rotation direction.

When will your apparent weight be the greatestm0 /tsmc7(u ii, 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 case would your weight be the leasts0ctii 7(mmu/ ? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space coulqa2kcp ;7n1p4mu 9 ii qo4yzxk :u-ik0d be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that roti-;iu1 7znqao9:kmyki pp4q0u 42kc xates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experienc4u8 l1 lkcmnxsnkf40/es “free fall” or “apparent weightlessness” between steflk4n4cnl8/ 1smk0u xps.

The Earth moves faster in its o,) tnu(bzp+g;z)3pu hj ru 0c r3fecw1rbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Expl)n1 pz t3;+ru(3 hej)zpccurgbw f0u,ain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discsa(ng(lm0i -5 knafo:overed to have a moon. Explain how this discovery enabled an estimate f im a5((loa:g0n-snkof Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than theqv/zcodg8wl d -f 3g4/ Moon's. Yet the Moon's is mainly responsible for the tide oz-l/ f/3w8vc4qggdd s. 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 ( 6v,qrnynea11pzx9 l 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 acc dllpehbve9,pz q s-*kg9hrw-z(( m6;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 h;ps*,hd-wez ge 99kq(r(v6bplzm- lorbit 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 it rotates uniform:r ;fn xb3 /wrk-ch+jqly in a horizontal circle (at arm’s lengtfb/j:q3xk + n-;r rchwh) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Etvd nyr;480p yarth's surface, and circles0v4r;tp ny yd8 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 Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a pz7gm7xj gh h55gz.l:totter’s wheel turning at 45 ghm 57lh.jgzt:57 x gzrpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvva)mf ;yc2t)oap.jk/ y9 z1m ued at a uniform rate in a vertical circle of radius 72.0 cm , as shownp)a .t2my;9ok avzjym/cf1u) in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can rou xvze5+f/y.bi :who8 and a turn of radius 77 m on a flat road if the coefficient of static friction between tires and r8yv /ehwbi5z.f ao:x+ oad is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fwp :jpm8 fe3r1a.df8 oriction be between the tires and the road if a car is to round a level curve 8:f1orp3f 8dja pw. meof radius 85 m at a speed of 95km/h ?   

  A device for training astronosv2c.x , m+b3cs vkkzo8lm:l ) 9uai(auts 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 he v bs9)ll,s+3 8k:mkxa c2io cuom.(vzr 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 therb o wbdqj*88. *njw/m 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 betbnbw.q88jmjwr/ *d * oween the coin and the turntable?   

  At what minimum speed must som ua mcc,fv:wh*sc)yqe:0mf0 /1yk )n/4hxa roller coaster be traveling when upside down at the top of a circle y0 oe01n:/ca:* smcsmf q)m , cwhv /)u4khfxy
(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) crossesq u/ep38 wdgx* the rounded top of a hill (rad /p*3exu8dgw qius =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 needyb /3 , sgbs1pi)defsu.;nqd- to make for the passengers to feel “weightless” at the topmost point?1/;pdf - .uysd3eng)b bs,isq    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of cnv: 2-i)j-wk ybm d-q.kxc:xradius 1.10 m. At the lowest point of its motion the tension in thq-y.d-bcn2-k)jvw xxkm i:c: e 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 c,hz00ly; w o ;kr37ddje (bmlwm from the axis of r,h(dlz0 ;d;3 wl07kbemrojyw otation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotaty()ooe .5cly:o aup ll/z ;.qzed in a cylindrically walled "room." (See Figez z/ll:pycloo u o.y5( qa).;. 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 frict z+g+nm.xn2 f5ku bciy-9kq6pionless air-hockey tabletop, and is held in thinqgnyck+i +xu5 26k f9 p.-bzms orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ball 4g20 eq+p3b pn-crqgraba (x* j)fnd- which revol gp0pr+anrc 2q-34- qx a) fn(jgbdeb*ves on a string 0.600 m long. 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 perfectly banked for a capfd1h ( jpcd3 nsa8b21r traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses lot(ytwnv;pt /6n3 d h.s(0rl $ 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 k; 4 qt-fiu62tk ;f8lgtqubh2at 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 componepersa.97jo ;11n7wkks qa+:yhc k )oren4vj 4nts of the net force exerted on the car (by the ground) in Example 5-8 whcko e :7kj ;1kwns+jaroq4y )h974a1evp .srnen its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 a3as(p i-.pi.z- 6vson: .zovql663 apau zq neccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the rvu(:ezzsa3-z aoqvp6.n.6 ai .6n p-s qo3plioad to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2nq/b 5 6txmbbm 9(v3o d qv-+cdl*aj1i.90 m . At a particular instant, its acceleration islb5tn6mda3o(qvqbi/ 9+dbj -cm* x1v 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 kmui5lrzm q 58o9qr56y 6iy;hawt1 y 7ck (2 Earth radii) above the Earth’s surface if its mass is 1350 5okhm7q5r6iy r685; cqyu1y9l awitzkg.   

  At the surface of a certain planet, the gravitational acceleratio8 ooyt 1p,p(nyn g has a magnitude of 12 m/o p8p,oyny(t 1s$^2$ 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 *nv u3j4v*h-r 7vz96os iiovxon the Moon. The Moon's radius is 1.74 r4n9v*iosjh7o zvv 3 xi-6uv*$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 . (dnyi/wq *q9/ulu:2nrrxpltimes that of Earth, but has the same mass. What is the acceleration due to gravit2n:(n qi9/u q.*udpr/ xlwyl ry near its surface?   

  A hypothetical planet has a mass 1.66814 gx3tvw534 (p1sqjjlu8fnynt rmj times that of Earth, but the same radius. 3m81sjj wplx ttq5ur1 43(4y8fnj n vgWhat is g near its surface?   

  Two objects attract each other gravitationally with a forcrba bzwof5ti nfq-g.8 (kg 8,2e 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 accelerati))eru en:h a(oon of gravity, at (a) 3200 m ane oeuh)r):(   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth eq,s7saq1p4z* 3w2ucn*acab where thegravitational acceleration due tsqc1p *u7*3 bez, n2sa wac4qao the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the maan)u 0j:sh7 d qy *tx5lnjm7x6ss of our Sun packed into a sphere about 10 km iq*h tjdy7ux 0sam5l nx7nj6 ):n radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average s.d2yy6:m(gm9 ls0rz yqj0a z 8j mo(fbtar like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity y2qyjryzm( l d96 z00jmg:(ob s.mf8aon this star?    $\times 10^7$

  You are explaining why astronautsbzamy k61sg;t2yl5ucda24 +di.g0bd feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Conv4 kcm2lsg02db5+a ta z1y.dd6iy; gubince 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 of side 0.60 m. Caq9,r pzg :l;6uvn/xy pbtn0)j,kzo 1, jy4tkslculate the magnitude and direction of the total g)bl,nsjz , pp:tyk/g vk unrtx9j0 yq,14z; o6ravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plc81 ;/ot 9thpfa x3uwmanets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupittma31uc9p fw8x ;/h toer, 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 is 0.38 of what iet,+ic;jj ; :bn .yh5cdczu7i8 fo0w xt is on Earth,ccoif.j05yw;t + j ezdnbic:; 8xh,7u and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun u a pkc; *xsu/ m. ee6chhiy1i*6(tfj,hsing the known value for the period of the Earth and its distance from the Sun. [Note: Compare you*eaeh6*ujpi c;s.t( cihk6mxh, f/1yr answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular 1 e) zdn:c5rjiorbit about the Earth)dj51i rn c:ze at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbikzrp7dp lw5 mt(yz-96uq b0)e t 650 km above the Earth. How fast must the shu97)- pt0rkqpzmw z (de5bl6uyttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupaslx1lba) yj:e vs0i20nts are to experience simulated gravity of 0.60 g? Assume the spacess0iaeyb 1 :sv ljlx02)hip’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 i1z.1ovjxiu z+ n a circular “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 your result depvozj1x1u z+i. end on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satell+)hfg;g 3h(bz xlu3qczb8e (jite have to be launched from the top of Mt. Everest to be (+zhcl ex 3q ghu(8j)z f;g3bbplaced in a circular orbit around the Earth?   

  During an Apollo lunar landil /f9ytr 3cy/h3uzetvim3 :;m ng mission, the command module continued to orbit the Moon at an a/ iceft mmv3:9r yy;3/3tzulhltitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are cc(co570l)ha gowwk j 5omposed of chunks of ice that orbit the planet. The inner radius of the rin5wgwl)a70oko jh 5(ccgs is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). 0qg zuwj3uh+ (What is the ratio of a person’s apparent weight to her real weight (a) at w zg3(u0qj+u hthe top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fro:/c)q twab -vom the center of the Earth's Moon in a space vehicle (a) moving at constant veloc)t-vwcbq/:o a ity,     ----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 4qfe/i.1v8 dup s-ogg of equal mass. They are observed to be separated by 360 million kmpoq1gi .vfge 8u4 /ds- and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale rea; ,tji8h)(f.wq sd p1ef1svd kd for the weight of a 55-kg woman in an elevator that mhj;kdd11 pwf) t(sqief s ,v.8oves
(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 r y7j*a7b ns/t/xb9xla cord suspended from the ceiling of an elevator. The cord can withstand a tension of 2/9abx /xyj 7b tnl*sr720 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very q,fx4i/z f9b8x:hnb cdq za8, near the surface of a planet with period T , the density (mass/vol/za ,:xq b9bi8nhzc, xf f48qdume) 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 Moon (27.4 d) to d i ,brf;gw0nhthaa+1 *etermine the period of an artificial satellite orbiting very near the Earth’s sur, r;0ignaw +ha*bhft 1face.    s

  The asteroid Icarus, though only a v m0m 76tnt49ptv9 kxx70vbwz few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from 0 vkt9x6zmb4977vptxwmn v t0the Sun?    $\times 10^{11}$

  Neptune is an average distance odzvo4 6 q+n*fbbc. wg-f 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 r7,c w,o5wez: mincc5zcy+-xvoughly once every 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 f ,zcwix5v,c: eyco-5zwcn+7 mrom 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 ce0oh+l fe -j)b/h- qgqpi9rm3wnter 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, peffa.o kz( *w2: )oxmjvn01quariod, and mean distance for the four largest moons of Jupite. xvz*qjf1wa):of n (02k uaomr (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(dwwk:hr/,ch +xn0 gh Earth from the known period and distance of the Moon. :+hdch x0(ghw,nk w/r   $\times 10^{24}$

  Determine the mean distance 5 zn;1)u fwomct)gklu) 6yta/from Jupiter for each of Jupiter’s moons, using Kepler’s third unzyfcgm o6lk) );twu15)a/ t law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Juk;ul od5a8 cb0piter consists of many fragments (which some space scientists think camc 08l;o uadb5ke 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 tadxnmg tdkg,.2se .ag-*,l.lale 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 quickly enough to produce an apparent gravity of g as on ,.ex*g2d am-t ,k. ldlng.gsaEarth. 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 fro z p*d. sq fggdq6r0o.;pi:u6nm a hanging vine (Fig. 5–41). If his arf. ido;r dpn6sgpuqq 60zg*.: ms 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 what *n6o +6 ehh5,hfxdf:2 iohyxtoxj7j6it is on thexh, 6:jtnoyoo i6 xfd*576+2fxh hhej surface?    $\times 10^6$

  On an ice rink, two skaters ofx-* zqnz.mjvk1( s 1jq 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 qz.x kv-*(1q 1jjzmsn their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apik4tcvlk 4j0 wk chzd07 vpi6w+u: z6dm;a3)hparent acceleration of gravity at the equator is slightly less than it would be if the Ea )3wi+j0a6dc4 kzpc kt:0d;vzkvl h7wmi4h u 6rth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the -u9:ti4swt hiEarth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Eatth-w 9:i4s iurth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when youyg pj wabtn(z908ia io( ekt7q4mi705 stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the aae7k95(nz (o ig0qiy i04btmtwa78 pjcceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a i +ai+ ;zsl/rr8jyxuu-a kt/pgb)n0+circular tube that will rotate about itsrub0/+ a+-u irjsxt 8k);in lg pa+/zy 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 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. srqo*87ud+d6j6 +kimt,6n bq2eev3 di0xagk5–43).
(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 me)b ya/8 cxy1nass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational cy axc)1nyb8/e onstant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by a;vn bokuc*s 3l.j8 dl.n.l n*v; cuol b3.jk8sd angle $\theta$ 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 coefficient of s je+h8wtg8zyrkqz )pfz9979cb :uw( jtatic friction is 0.30 (wet pavement), at j q+j:(rzwg 99 p)y8ktuzfbcw z8e 97hwhat range of speeds can a car safely handle the curve?

  How long would a day be if th9fonqfklh7kl *mt / 78 *ihdmd)3t s(ae Earth were rotating so fast that objects at the equator were apparently weightless?h8t7tmi3/ kqsdol9 knl h*a) (*7 ffdm    $\times 10^3$s

  Two equal-mass stars maintain a constant 3/.,aur*zfetagw 1l6 +cbhf s distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant smv5 uss.gzrri b/:5u1peed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle o s/r.5b gvu:5z ums1irf 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 has been claimed*u hdr ;; ,rmadfp0/px that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more d;u*prmdf, /xa0;prh 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 7xo bml-l:rc3 presence of an extremely massio cl l-r3:mxb7ve 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 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 thek8rjz961p 4fha)6 dok u ygk8b 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 actinpkgk 961kjuz hyd8a) ob8r64f g 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) utiliobb2v2 benwf*k m5b*2 zes 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 evenly b w*2 b*bv2bk5n 2fmoearound 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 ( c**4r7y ,lnfq:ks abbNEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Erosy bbr,4 s7*fkl:naqc* 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 ir87futh 5rg 8t( pguspa8i) 7the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (4007 8ut8)pgr7i(i h8rf g5usp ta km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its meanx8vgn8zm uw.0 distance from the 0u.vn8xzgwm 8Sun?   
(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 wour2jiee0e3afu, 6l e3bld need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, li2eee if3r0b, lea36juke F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cen: :f-vy o mmrjsn5w.xr1e+mg )ter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 l-f5+x)r.m e s:y1:mvmjn gworight-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.aq0o+7kqqye92 0td fp50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the 7p2tdyqq0f0a+ o 9qek midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eart:(3vind ynrlai2v500sl xo c8 h $ \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 sweep secondbdpia4td,a1u*i. c7d hand ou bd4.* ipt1d,a ca7din your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight amc-b;v cs+w89eh* dsh round 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 thatv8 mse ;hd 9*bwsch+-c the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway k.by rd-sk17csz2h r-is designed so that a car traveling at17-r ch2srsy-kz. d bk 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 ek ,0nn -ukjf a6;2ievof the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passeng6;n ,kvjek ni u-2aef0ers, 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 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.$\approx$    $\times 10^2$