Sometimes people say that water is removed from clothes in a spin dryer b5 w; hiqaq2ei pg9k /7gnh,zxb(*ur2nja- ge(y centrifugal force throwing the water outward. What is wrong wit;,g95k*-gxiqiaw2g pe(7ehh qj2br / zn(una h this statement?

Will the acceleration of a car be the same when the car travels around a shauofbyo51 8a6f1rqn(kh; w 2zc*i9ztcrp curve at a constant 60 km/aq2c*1hz8 rf6oitc f; nk59 ub1 ozw(yh as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along aaf j,a.kfu49wiq a48n hilly road. Where does the car exert the greatest and least forces on a fij,4k8fa wn qa94u.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 af +p2h.hm75x3pr; bul eo pi/tcting on a child riding a horse on a merry-go-round. Which of these fto ep2+u7 .fph/m5 i;lhx3bprorces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillingzzr/e9z w+f0mi d98 :cpp.6d fl r0zzt;t3cpl out,pc.z03/zfdcpltiz f p9d:z;06tl+9w z mer8 r even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in yourd3sl2l5g *:h 9x3 3o gdbczzco car? There are at least three controls in the car which can be usedb3o9l5gcgzd3 h3zs :dlo* cx2 to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over wx5 o+myw-fx+,c* o0gvklj3y yc sci71 m9,npthe crest of a small hill, as shown in Fig. 5–31. His sled does not l+*-5lc g+7i0k yoxpmc,y1f cw n,9mwxvjo y3seave 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 law.

Why do bicycle riders lean inward when rou iwr)g63 ob7t5act2q58hfyup nding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the06n9 le5kwx7dl/ b ujkf/k vum+f)pk4 banking angle given its j/kxud)vlb m6k9 l/un7f + f04k5k wepspeed and radius of the turn?

A girl is whirling a ball on a string around herw3a(q exhxtmc2m,j,kenw 2:uo) s 0(b head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should shek( meoe(wxxch3sm) q,0 2uj2w,at: nb let go of the string?

Does an apple exert a gravitational force onlh8p-*zy rerp,l1zy f/i*:.rh j kdz7 the Earth? If so, how large a force? rd * z/f*jzr7z .-kerpli:y18hl ph,yConsider 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 od h9w4f;*)h ppmu5ft phq,0up rbit be difu;wphf*ht qd94 ),p0mpp5uhfferent?

Which pulls harder gravitationally, the Earth on the M5 mo6by;w(h3)mfm+2ncas8h y r4tl qpoon, or the Moon on the Earth? Which 8b 6cymhhra52 l 4pyts(wm)+oqmf;n 3accelerates more?

The Sun's gravitational pull on ty)8l m ;uqfy: d)yxu jk9xbwg, n(79mjhe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consid 7x yqgjw9n9mu,(ux))jd; bl y myk:f8er 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 a.mme4a(iea;;: n5at+ a:1eamxq r om ire at work? Do they opposani;(5ammmaae 4 :r:+tae;o1i .e xmqe each other?

The gravitational force on the Moon due to q,c,e2kt 4zoa the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eartho qae ck4,2t,z?

Is the centripetal acceleration of Mars in its orbit aroc 3gy(ro 97ex+kk*6npra+dkne 0phx ,.vil7 c und the Sun larger or smaller than tire7 kaxvkn39er+n,7pp6 gh ( d cc0o* ylkx+.he centripetal acceleration of the Earth?

Would it require less speed tf zld3nmehb 3:;xf.-ao launch a satellite (a) toward the east or (b) toward the west?nhfd em :alz3.3x-f ;b Consider the Earth’s rotation direction.

When will your apparent weight be the grea.l lwq 1)sidz0hss/*mtest, as measured by a scale in a moving elevator: when the elevator (a) acceshs)mz/id lqs1 l *0.wlerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space abv 3 4/slu:+i4pm dvop;mm i9could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrid4mmai: iv u4 lpmp;3bvo9s/ +cal shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apmk/,+.i77fp kss7sfhc/y ih q 9f;nocparent weightlessness” betweeymh q.i ,s7k;ic9ssc o/pn+7f/fh7fk n steps.

The Earth moves faster in its orbit around the Sun in Janu/ graf-rwrjy+75kkz3ary than in July. Is the Earth closer to the Sun in January, or in July? Explain.r/7 k3g5 -wjfr+kaz yr [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 dib9w)g-7 yq tajscovered to have a moon. Explain how this discovery enable-79q ybtag)wj d an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth i l/u0o lo;7( faize8dzs 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 ofl/a(odz7z8ei;0 louf 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.zcg 1hc:vk2s 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 it;a j0tconthy,jj- 4fkf( y)b1s orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit4k 1j,y;c)jo y0(b a jnf-thtf 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 ;u1kqlx,c. z;k.ns54s7jckegshm j1 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculcs1k 4l 5j1;.quh xcekng7 ;z.mskj,sate the speed of the discus.   

  Suppose the space shuttle is in or 2u*e3yz1kaas7zti jh4 52 *(lpndzl*1 vugrrbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its oe 7zjds5 *3v*gl*p12rhrn1kta ay2 u 4u zil(zrbit. 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 tha-u2 zrdrm, ;v9pfbi+e edge of a potter’s wheel turning at 45 rpm (revolutio 9z+ 2dvfri,abu;rm -pns per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a u6:2m vvzkfd7k7nt4 h kniform rate in a vertical circle of radius 72.0 cmdhk:7k4 n zv7fk2vmt6 , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of deh ,79fx* p3bwpaoa(radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the cdx7* eo aha93(fbwp ,par?   

  How large must the coefficient of static friction be between t(2g; vcne,br yhe tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ? cv,yr bg n2e(;  

  A device for training a*6t-fl4e ct3*exd,x27 f,bwcw s bmkastronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If w3t,d6*m7xb,cslwt-c *fkef 42x eb athe force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntablek4peg5yhtw ;2 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 k; p42hyg5wtethe coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed muslrj kw(bl o;l;zgrr5m)) jj+2t a roller coaster be traveling when upside down at the topl jlobr) +wjl2;mjr;rk)(g5z of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top( zawx7 v6mojw; 56tvx of aw wt 7xa65mv v;(6xjzo hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need tod fnbz syg:d nfws+dd11r1-79 make for the 17dg:+sd sd fbrydn-1n1z 9 fwpassengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cisff +h:zmkd 92rcle of radius 1.10 m. At the lowest point of its motion the tensik:sz+9m ff2dhon 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 cltjgtd.vx) bz0o(ql- ix2 h-*entrifuge rotate if a particle 9.00 cm from the axis of rotation is to experietio-*zdx) vqt-b.0 lj (xl2 hgnce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrmw in7yr;u77 /u5d2z yx* cisgically walled "room." iy 7z2ir7yxw;u cud/* n7gm5 s(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 ) m d 42qe7z 8nfvs;x*yej)qeek yd;1:f is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected y* efxve n;z ded2f 417qq my:;s)kje8to 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 o fpl806)q f)bn vjvx.af the ball which revolves on a string 0.600 m long. In pap f)nj f.8l) bv0aqv6xrticular, 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 th2cyk9dn, pot;4+hgx+ u;yp is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse l .dx(v:/vkmxs $ 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 verti h 14c0vp x-qiqabj.k9cally 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 aq .l)2wcc33pv)b-i,0y8:6k iyhbb g j iczvxond centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is ))qcgio 3vl c. p0w3-xj2y6kbzb,hic:b 8vy i 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelert)5h f bji(/1wb3 mii7c9llyoates 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 tal(79i lib51 ctjyfomw3 )i/hbngential 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 horizontal circle of rad9le4 ku(amd;7xpib 2qj-- kjo p/xwh. ius 2.90 m . At a particular instant, its acceleration i 2 p.akilbo 7qx;(m/ x-pk4hejw-u9j ds 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 .iye gsrz ; mkt))k,1zon a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfacee )skyiz.)mgz;,t1 kr if its mass is 1350 kg.   

  At the surface of a certain planet, the gjfhmnut+ta u:u ( -kx,zeyks8 -3 :cq:ravitational acceleration g has a magnitud+u3j n ymx a, 8eku:k- uchqf-t(zst::e 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's radiu1o b0 dohf,:phs is 1.74: ,bd0p1o fohh $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius uzr*n4k0ra z+ 1.5 times that of Earth, but has the same mass. What is the acceleration dru40kz nzr *a+ue to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, u;q f9b zqxhhm5.8l cyk.a2g4but the same radius. What is g near its sur y .b25zqa uc4qlkxmh;8h .g9fface?   

  Two objects attract each other gra.wg f *2cft9bzljj)fgij 7g8 *vitationally 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 acc, xbv0 y:qn o4lzf/x0z4e:x eueleration of gravity, at (a) 3200 m y:0, 4oeq:/ bl4 fxxve nxzzu0   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsit57s ,xa)s0, m+lqudtlz/+ evr9 ei f(uwkt +xde the Earth where the wquss+ +7/ 90r eavtdf zelul(x5t,i),ktmx+gravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packeb2tv *zg0 i+kume ;;yod into a sphere about 10 km in radius. Estimate the surface gram;yzbv;uog+ k2it 0*evity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average izx dz5g4w-x ;star like our Sun but is now in the last stage of its evolution, isxz 5; 4gizxdw- 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 orbixxnk8 1vxm e8-mq+/pnting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. x/1xq+ emmnv8px8k-n 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 of s q39 t.ptn*rpxes6 0nside 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted onr0np etxs.qt 96*ps3n one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of tyn ;*z3ak h9hqhe planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are h;n39hkqza y* $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 acceleratv7f:oqbqtx zq20p6g hp;t5df(m f ts4iy:/n 0ion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, detet n (pft;zs05 0 f ig4dqyq::h7tm fvb6p/ox2qrmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known lqn,.s rb8ur3value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5ub q,38nr.rls–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abow; wgfg/4wb :tut the Earth at a h4bw;t gf/:gw weight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 659d);k0d.yeb:dus6y y*0 foxu d gxv b/0 km above the Earth. How fast must the shuttle be ex b gsy :dxkb.) 69o*0/;uyuddyfdv0moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if *3oaoffe eal76ie(b97t h7 rcoccupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answ7(cef 9 bael7io*3fah7 te ro6er as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for aluyd8 m/6h-y:w r(vft satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above tvly fr u8(ty-d6 /wh:mhe 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 veloci2z/,r9d0ilwimh 86jm yqm- hyty would a satellite have to be launched from the top of Mt. hm/l6iz90jr-m,hw dym 2qi8yEverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, thehb.yub eh;v8cl)( 0pu command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go aropu.y;0ble8 b )h hvuc(und the Moon once?    s

  The rings of Saturn are composed of chunks of ice thatz-8ylew,rgx) ua 7x8 e orbit the planet. The inner radius of the rings is 7gr,yz weul xex -a8)783,000 $\mathrm{~km}$ , 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). Whagh2np: 1oah2 t 6q4cydyk5o 9kt is the ratio of a p yd yp2ohn5 1ca2qkt9kh4:g6oerson’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-k3z r0)s6rxo gvk ceu.0g astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movingrzevxgk36r00u o. c)s 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 co6yr7e -hv8qm vnsists of two stars of equal mass. They are observed to be separae rmv- h86qv7yted by 360 million km 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-31oo1km tcat read for the weight of a 55-kg woman in an elevator that mc3oa kt1-ot1m oves
(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 ceilingh +ujmw* 78eea-p1x ni of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceue w-+p7n 8amh1exij* leration (magnitude and direction)? a =   

Show that if a satellite orbits ve,5 go3 v;zn5se2e vxt gw-g3cery near the surface of a planet with period T , the dwc,5 eo-s 2e33ze;ggx5v v tgnensity (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 ofexn .. ljzu* :/zmjk7w the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfaceze jz.jl.nw7*/:mku x.    s

  The asteroid Icarus, though only a few hunvo1c y n(h)rp7dred meters across, orbits the Sun like the plao7chrny (vp )1nets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan5la;kfqn v*9m6 zs4xhig*v y6ce 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 roughdp-.3pmt zxz c f4.;khly 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 from the Sun. Is it still “in” the.f;kzz3 tpp4 d-.mhcx Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga4pt2hm0n xt ;mq1. ktkt7hp+alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moonscl8w;t8xr yqe 3d f(r( of Jupiter 8frx (q;8 e d(ylctw3r(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 4r74)dihahzs 7;q z/dtoy i0r Earth from the known period and distance of the Moon. 74dtrzoq/) s0r4diyhiz 7 ah;   $\times 10^{24}$

  Determine the mean dista ;fbo t9)pvv/gw0s 6wnnce from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tabgo90bwnswtv f/6;vp) le.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (4kkzvgywv * g4 t9*th0which some space scientg tgkw*4hz0t*yv4 k9vists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "plan ml*a3 noovp,1et" 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 prna1p3l *ov mo,oduce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vin8;kiy q6u fmad4*s 2wne (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, whk*y; ind2sumafq84w6 at 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 wig6p mb()jbh2 -nigb9kll the acceleration of gravity be half what it is on the surfb (bimgh)b2pkg9 6j n-ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and s 0tn)1e/r i;kkilgsg ,pin in a mutual circle once every 2.5 s. If we assume their arms are each 0 s);ile1gktk,0/gn ir.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 rotates once per day, i t(kwl* nlk*u22 cv.ethe apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate.2w(l ck*nvkeu2 lit* . 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 direct r cwr0 g)5ozhzy(i5u7ly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite crrig5h)z 0yz5( uwo7forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a baoq y()p1t8 stqthroom scale in an elevator, it says your mass is 82 kg. What is the acceleratio1st )8y qptoq(n of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station con(h/tu8 mk .qhpsists of a circular tube that will rotate about its center (like a(thhmk .pu8/q 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 loonj1a, gq /38sjv8dd fqp (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of 9cbl7slax u trzc/+,xjc ,g5;y (:uhrits radius r, the acceleration , :x;crbrhsx/5ugt+cu9 ( ,zjly l7cadue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanginge0/w r4gcy;k3 jyp:ru on a string) is deflected from the vertical by an a4 gucypr /k3r: y0;jewngle $\theta$ 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 coefficir zk6e54zxaz6eue.xa3e -o f-ent of static friction is 0.30 (wet pavement), at what range o-45fzoez3k ex -eu6 6 xeaa.rzf speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obje g+k2w,u1c/7mt:mon iir4lokz gf-q9 cts at the equatoiun-figoo+k:gr14zm k2m ql/twc , 97r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cons+f iztim/+l 6bk* 3*lng f c76ah kx8*yayt/wztant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of c94 l-kxix0r7 zse q4dradius 235 m. A lamp suspended from q47x4s cez r0i-dxk9l the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the E i(/() 9mkvmqazc- mnfarth. 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 surviv amqmc-9vmk(zf/i n)(e 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 S /,v qk8 mx; 0x/s*iinfv3nrggpace Telescope deduced the presence of 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 t8m,q*knig0 vvr;xs3/ nx/igf o 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 tr- *1v5bg7ul.)rcfzn kmohq9g i9 f t9eaverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of cut1 fvckf r)*e 9-9 g9m uhnoqibl7g.5zrvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellit dzv-pf( dl89 3fbbkq.es 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 around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altd l89qfb(-3k bpf.vzd itude 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 tr221x ohoq8xj pzld/)z aveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of a z)jodo2q/8hp 1zlx2x 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 )xl*r rpowukuq ,9 ./npursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km aun l/ pk)qwx,9 ruor.*bove 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) Whatwaxtnua(y*3gkv y4 02 is its mean distance fro*g3(n2a0x4 t yakwyvum 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 need to be if you could actually:ak t0rflbslj 6+*fi ,a(;rm g*bnyo* "feel" yourself gravitationally attracted to someone near you. Make r:;b 6t(rjorfiak+ bm0g a**,n*ysflleasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-y,n/6hm 7br hj46) at a distance of about 30,000 light-years frojbh,/6 h7yn mrm 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 t wn 89(ir glnmyo18a6ehe corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed arei9o18l8myn 6 ag(wnt the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eay1u*5m hzerl5 9himvpk 6) 9tbrth $ \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 experi-7d3q(irmxsm6i h r1i6z/ai tenced by the tip of the 1.5-cm-long sweep second hand on your wrd-aih3 s(i / xm im67rqr1zt6iist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a6m4lr g*whc2k circle below you on a 0.25-m pierh6c2gm kwl *4ce of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new high.aphrjf8)g6 3 :ka1dj uvc 2tpway is designed so that a car traveling a kh6 dj vg23ta: apfp.c)j8r1ut 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 b-qe 3wdsg;n .when negotiating curves. The angled-wqeg3bs ;. n of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train 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.$\approx$    $\times 10^2$