Sometimes people say that water is re0q5:/ tn)lg./cfwp3ityd: a8nm b2rtd8oy nmmoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this sd.dmy rn/: 0mp8baqno3 iftl /ty8)2tgn cw5:tatement?

Will the accelerationrv88 .y 4r1vh-c9x+x gwed etk of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travelsv89. yr veg1 +-xx kwh8rdct4e around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hillyd ms 3aw(ck23x 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 between two hills, (c) kac d3s(mwx32 on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wh5 wqrb;zvflb,(qi s+3ich of thwl,vqqbs (;5if zb3r+ ese forces provides the centripetal acceleration of the child?

A bucket of water can.xsxes x161jt+ e;h:a nxdh y( be whirled in a vertical circle without the water spilling out, even at the top of the circle when the buckets6tdx ;+ xh s:jay.(hxxn e1e1 is upside down. Explain.

How many “accelerators” do you have in your car? There are at leasxos-:e od5qm u,8s4 d+xnpbw:t three controls in the car which can be used to cause the car to accelerate 45pnm d8xoqw - xuobs:de,:+s. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of yw3 + xadry55(. 6y* poqppavua small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force bowdy xp+qr6 (*papvya3 .u5 5yetween 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 egc/0vb.fh g3rounding a curve at high speed?

Why do airplanes bank whekh1 0 9 lgci3mter(o.sxq e.1wn they turn? How would you compute the banking angle given sh13(mi1o0t.kl.rexegwq 9c its speed and radius of the turn?

A girl is whirling a ba9etrsf.6b 2y uz(( hidll on a string around her head in a horizontal plane. She wants to let go2dstfu ih.6 (b(9 eyrz at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a fogq omb:rllk.s1 *y1j , 5yzp+brce? Consider an appy: m1* r+51ly s k,bopgl.zjbqle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whe)g/lvs 91vltwy6p x8e8 hy; oat ways would the Moon’s orbit be difpv 6xswhy)egle 8v9y1lo; t /8ferent?

Which pulls harder gravitationally, the Eartkqo6:. b3-txo)1;2pvc5whgklsyv eg h on the Moon, or the Moon on the Earth? Whickhqv3g-2 o.) s6c t1vowxg; 5key:pblh accelerates more?

The Sun's gravitational puwxog0s6g2 /qrqn*s8 gll on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differencoggw2qgxs/6n8*0 s qr e 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 ed, cp0cs y+/lie sk8z5ffects are at worzyel c s+/p50csk,d8ik? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only ajjv;qwcnf 6vg:sg:t(u7ky , :bout half the force on the Moon due to the Sun. nyfj:;c w6vkg t:vg jsq:, (7uWhy isn’t the Moon pulled away from the Earth?

Is the centripetal accelertugj-onbfs vw96ahu6.0 *5yv ation of Mars in its orbit around the Sun larger or smaller t59 avfj ut6.gy *vhonw0b6-suhan the centripetal acceleration of the Earth?

Would it require less speed to launch a satel6 s0.(seezt aklite (a) toward the east or (b) toward the west? Consider the Earth’.kesea( 0 stz6s rotation direction.

When will your apparent weight be the greatest, as measured by a ubr4 ,scl h9p7 )rlnb4ifb3zzq l6.i1scale 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 least? When would it be the same as when you are on the ground?ip7s9l1rc6).lfq3,zlurn 4ib bz 4bh

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space coutq4j3 s 9eglb0a7 ..c*fkmijt ld 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 in9f3kmb tc40jiast*l7 g jq .e.side 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 “apparent weightlessness” betwe /*e.:fo*zj*xiofvjsbg x )4ye):.gijfxo*x/ e *jsoby fv*z4n steps.

The Earth moves faster in its orbit around the Sun in January than in c7s v dih;g6+rJuly. 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 factor is the tilt of the E gd+rhs ;cv76iarth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expl)*zgdymp:z23 p0t dt7px5z cvj5zqx.ain how this discovery enabled an estimate oxjpv0t gcqz2 *tzzxz ):dp5 py753.dmf Pluto’s mass.

  The Sun's gravitational pull on the Earth7x .sr5nhcte * is much larger than the Moon's. Yet the Moon's.the5nx *c7sr is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves 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 t6bp*6(mq* ej:bc3qqnr* p cs 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 acceleratisnmj, ui;vw 4oz;-x8 ton of the Earth in its orbit around the Sun, and the net4x8z-o n,t;i uj ;wmvs force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a,demd4fsq+k (6 7,mghxzlmo4 2.0-kg discus as it rotates uniformly ,7l d szmedf4+4mk(gx6m,hoq in a 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 kh:5cfntc.k2 j2* t;w g;u k(shfqm4p-at,xb 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 orbit. Express your answer in termstn- 4umf5b.(2ck*qckj2 :h;,hfx;pg ats kwt of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a v ;3f:oq* f5nf:c)a5zspkisfspeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’szvqf nf55:;o ci s3)spkf*:fa diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a o,fc-:i 6tjajvertical circle of radiusj:t f ja-,oic6 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed withw q yt;(in.js 7b)2hjh which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is.7bn sjjyhi)q (w;t2h this result independent of the mass of the car?   

  How large must the coefficient on d5 0uh91,fl+ i hdtdj3ldd)hf static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speedi ul djtlh1f+dhd0dd hn), 359 of 95km/h ?   

  A device for training astronauts and jet fight1cw69ka bt .ljer 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 79lbtck 6awj1. .85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable sp.sjjv.o)l rw/ g2j:rceed. When the speed of the turntable is slowly increased, the coin remains fixed on the tu /woj)vrg s..j2jrc:l rntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when e9qw,:iz 3xatxnivu* n 0. ql6.uhgr9upside down at the top hri 3ntn 0viqu wq9.ez.:6x,xu al* 9gof 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 kg5;jgflcg) pt ,y1bt f) (including the driver) crosses the rounded top of a hill (r,1cl j5;p )tfbtyg) gfadius =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 minums*6hph7t 4 zd7 i*bkxo17ops80 mtlste would a 15-m-diameter Ferris wheel need to make for the passengers osol 4m* d1 h 7it67t7s0p*m8skzph xbto feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1mhb+g)omid9)+h,ayr 0 olim 81h:e oe .10 m. At the lowest point of ithyo0)g lhdbh+ roie8 1:m a)9oe +mmi,s motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotav-w* xe8jo 5uwiz56g 6nrv;zote if a particle 9.00 cm from the axis of rotation is to experience an acceliz wvg*wu8r 5ez;voxn6 j6o5-eration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically w: c86z(-eko g l2 7nfv2e5ow uvjuo8gjalled "room." g2z25loe-gc v(vuwnk7j:jeu8 oo6f 8 (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 frictionlesnes7i o5f+m 8 ew)pjif ep*5u)s air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hol*78 )iwsonepeeup5jm) if+ f5e 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 , precis oi u:eiwz)sew1;yk0xax48k/a.4 re d ely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m yxsa.i4w/ k;are4 kex 01oez8i:dwu) 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 car traveling 7,/ccuvsy pjj) d; fg fhs z5oy8u0,d(65 $\mathrm{~km} / \mathrm{h}$ , 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 masses9c:lo s :rt(mq: 3lsjp $ 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 e 2s/r19shw crjvasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted onezlld. : )u,kx17u aws the car (by the s1ud7 .kz)aw:l x eu,lground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniform7g rthx 2ulj6b :93(cx tszn(wly 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 road to provide thnh(lj:u tstr67 x3 2b xzw(9cgis acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a parte8tks 7k 7m-ckicular instant, its acceleracm-tk s 7k7ek8tion is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecrana yf(:y l+7,ggz*fy *qq.zda ft 12,800 km (2 Earth radii) above the Earth’s surface if aq*yzn,(ygyqzgff.d l *7 :a+its mass is 1350 kg.   

  At the surface of a certyi)gqm1 3) bhcn-oav2;8qfgnain planet, the gravitational acceleration g has a magnitude of 12 mnaf;hgqi nq) ) gy b83-12vmco/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 Mao 4c8wqi/xo )oon's radius is 1.74c/i8oxwoa )4q $\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 Ewn 6jn5emjya 08-e7) f +kdjbuarth, but has the same mass. What is j fweknjbem y+d5j8n6-7u) a0 the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but+7p jtmf33txw the same radius. Whattxjw+37tf mp3 is g near its surface?   

  Two objects attract each othej5i2p33u/je x;piy hx r 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 accelera (qqd k+xdjl:u+n4(u)m mr/uk tion of gravity, at (a) 3200 m l+xj4) (dq/dku :qm(rmukn+ u    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whergx;mmtj7nj3k7p/ ejn7e)1 s*)u wpsr e thegravitationa;1 nnje esgu7)3 p/7pw7sxj*m rmtjk)l 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 the0rn7lji7 f 6e*a8t wdx mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gr*a7iwld 07x8 ert6fn javity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wasjvm 2jnz lq, 5ff-7ng 2ja1r/a an average 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. What is the surface gravity on this -g2ln j5vf qaa/nj ,mj1fz r72star?    $\times 10^7$

  You are explaining why astronauts feel weightlessm(h5m9beh1m r4;jujv 5q oiwans:3 (b while orbiting in the space shuttle. Your friends respond that they thought gravity was (nrbj9i u;h:1 ems4 qbowv5(3ahmj 5mjust a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the cjhbp3wn.nva3chp 2i f*.k9 k;jw v -i9orners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one spher;wpjh. n9a.kj3hi p 32-*vk 9 iwbncvfe by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plaid u)0mjve6m: xti:+ inets 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 ie:v m)i: dt+6x um0ijmasses 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 Mayayvx3m 3 6r-+y hxl s:q6dh;srs is 0.38 of what it is on Earth, and that Mars’ radius is 34h;xyy ysmq+6hl6dx3 a s3 :rv-00 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eas)xeisi;/1 g3j l rxh4rth and its distance from ts/x)r l x 1j;3ieghs4ihe Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circulbj(47+n4 vnzqp 33h h ywhb(nnar orbit about the E 34+ (wjbnnp q3nb74hyh(hnzvarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 kmycenj/ zti*8du -0a)mi uw+a + above the Earth. How fast must the+8+izauenw-mti/j c u*0 y a)d shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantv*nxs x,gr2ycx xsn 1 5m*cag*5gm amb).g8:ws are to experience simulated gravity of 0.60 g? Assume the spaceship’s diamete.cb)m a1a,mn cyx 2*:8r5gsm w gx*gg5x*xvnsr 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 i-98nl6 7jfmtc) e1rba*ayg c in 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 radiac)ycneigm t17*bj 689a lf-r us of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velpam l++ 3:tis8*unqis ocity would a satellite have to be launched from the top of Mt. Everest p +8 unt*:qa+sl i3smito be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mmogj6go3;cy; : f4bzh c*e*er ission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take:oyz;;* 4cf 3gebjherm g6*oc to go around the Moon once?    s

  The rings of Saturn are composehk)i 0w;3k -m h91a/ oxkmnoald of chunks of ice that orbit the planet. The inner r)x hilkkano/aw hmkm 1o;90 -3adius of the rings 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 (+qy )07pgfbdo 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 the botp) 70bq+ ogdfytom?
(a)    (b)   

  What is the apparent weight of a6:ucoc8c x3vl 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movinl 3u 8cc6ocvx:g 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 o9a)b js 3 r.)tyebd;wef equal mass. They are observed to be separated by 360 million k3w )b.ed)e9 tjya bsr;m 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 read for the weight of a 55-kg woman in an el9uk -h*wwn w(kevator that mow-nk(9 ku*hww ves
(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 m 9/sc;c/co ;nl/;bs ,bo6 lhplz-rgycord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum hglmc,bcn-l;zbrcs;/9 yo6//lspo ; acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of ae,vy8:u i3hj)mg2j xx planet with period T , the density (mass/volug ,3y xjexj)vh82i: mume) 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 (27r8 gdr.na - +z1kbic6a.4 d) to determine the period of an artificial satellite orbiting a86dbi gr.r-+c1za nkvery near the Earth’s surface.    s

  The asteroid Icarus, thougj5 qboyg)2/tq(zptu0 h only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distqqttu(p by/o5)2z g j0ance from the Sun?    $\times 10^{11}$

  Neptune is an average distanczqqjz -*xa;iw2 / en:me 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 everym z4uz , ;fa,iolvv-8x g7fp2p 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 4, uip mv-pv 87 ;ff2,agloxzzorbit 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 th19l(kov+ /wjrm d -7g8.ipp/zqdbem ie 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, p iht/7,dlds:k*s/hf +o (nktand mean distance for the four largest moons of Jupiter (those discovered by Galileihk,*kfthd st/ 7+ :slon/ pd(o 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 fg9mdob6xa 08 c0 wwzrlw5v5: from the known period and distance of the Moon. d5 o :af950 gbwvzmw8l6x0rwc    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kes ppr.-z./ 7ndgtc*kqple./c .g7-psd pzqk*rntr’s third 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 Jupiter consispz--dq uzopc :lt:vw+1l6 0z qts of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyvc-ul oqzw:d 1p60+-pzq t:zled).
(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 "pamwt ;3fkb9z-5-no y llanet" 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 9t3-o;l a n- bzy5kfmwan 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 bi)kwi)0.tn mu y swinging in an arc from a hanging vine (Fig. 5–41). If hi) ku)w0int.mis arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surr5na -f3jy r7:hr scoz4sqq- /face will the acceleration of gravity be half what it is on the surfacenr7sz5 f- -qcjryso: ar3h4q /?    $\times 10^6$

  On an ice rink, two skaters of equal mm7y3 - .9g.jki qejvcp qli2l,ass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they3,eiqjy 2q g ll7 j.pm-cv9k.i pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the ac;: w4dt 6lmtdpparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimatd;l m4t6cw td:e 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 th 8 9zb,hj,t-w+dvq qfwe Earth to the Moon experience zero net force because dq,9j,v t8w- + bzfhqwthe Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on ap56bcx, br .tb ihks 1z/z0:ks bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whichz.b0sp5kshztr :bck6 ,b/xi1 direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotath3 +f+zdk;vk ue about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revzk d huf;kv+3+olutions 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 (Fi-iapsl w(7:h,7 jdm++ d ntuamg. 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 e,xknifmw6g r:+y++j of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitat:fk+xjewy+r+ nim, g 6ional constant G.

A plumb bob (a mass m hanging on a string) is deflected from th: v2gnhte( -lxh ) hd/1wbxfwko;o;+he vertical by an anh1xgvw :b2h o thlh;e(-nf;ko +/d )xwgle $\theta$ 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 bank5yz86xf a0 keied for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handly5e k0z8ifa 6xe the curve?

  How long would a day be if the Earth were) x4amgyvaf 4mu9.rupi 1+ gw. rotating so fast that objects at the equator were uvygr)4mwx9upg f a m..1a+4iapparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart afgp*s)ai( m2d p1m+v 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 radius 235 m. A lamp5. 0f k 4f,6rlexoptdf suspended frf.l06f , kf54xdretopom 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 Earthxm 9nn)lwpti y6m*ndn n16 :g9. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the) l p9d1g6i6nn ytn9nm xnm:*w 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 thz48 izzhegc7-.-i ichpx c4x4 e Hubble Space 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 mxi 4 -zg-e4. 7ipixh84cz chczeasuring 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 tra +ev7.d z6me9 s+fpvzcverses 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 azcpvsefe7+9 m .d6 zv+t 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 sa.-nd99 i ekblktellites 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,n b k.l9di9e-k 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 Ru rzq w 39n*0f2ryx6izendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 kmx 9 60yfz*rnu23qi rwz . 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 a satellite in need of r8 trnj1n,yhh raj 2d,4epair. You are in a circular orbit of the same radius as the satellite (400yr1jdnn,t 8a42r,h hj 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 s o -ccr)p70iuhas a period of 3000 years. (a) What is its mean distance froo)c p-s0ic7 rum 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 ri k 8/(vqf/bjwould need to be if you could actually "feel" yourself gravita/bfi8rj (q /kvtionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of theqcsb 9x389afn Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centq9ac 8ns3fbx 9er $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on/ced1ukyl 5mnym7 2mh7 v 94hu each side. Find the magnitude and directiocu4emv 79/ yhdy2umhnk1 m5 l7n of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 550du ko1we 2w*+qh: ge;jl) hh*m0 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cmta,q *x4k(vy l 9/mpnc-long sweep second hand on your wri9l natq(m*c,4 p/vk xyst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circ: t49pe b.fr 9a3hngfv) nshg(le belowat4)(:rp.s h3gfnv hbfn ge99 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 fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designdl: ra0(cc y7wo m5rm)ed so that a car traveling ac5ry7madc:wo r) 0(lmt 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 when7 qsgyw+azi3 r pav*uo50/t5f negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortabi g057r3w/ qs y5fz*v+aota uple. 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.$\approx$    $\times 10^2$