Sometimes people say that water is removed from clothes in a spin dryer by cen7l v9xh/m/8uku k-q0hlc ph v1trk70cx p9u - q/u8hhkhv1/lvlmifugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp .6 3thkt-0.ka,jbsul*tzjdp *ybpk5curve at a constantpbst0hy.lk- *zk5j.k 6p*at,tj3b ud 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. )g g c9ome4)a5 bpmpz*p*)yca 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) on a level stretch near) * c4mac5pgaoe p9gbpz)*y) m the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rox+o*6pgg8y bb und. Which of these foxpy+g*b 68g obrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a ver 8t(+ cxiun)mhtical circle without the water spilling out, even at the top of the circle whex(t)8uhm nic+n the bucket is upside down. Explain.

How many “accelerators” do you have i j r2trr)l) qag/+5nken your car? There are at least three controlskjr/n 5grr q)t 2)lae+ in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smalu9xnz2r 2(ewwrh8pa,4 /ogc ll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not uz(p / rwx282lrw,c4o9gh ae nachieve “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 rounding a curve8vbj/:.zj)xo p rqi0z at high speed?

Why do airplanes bank when they turn? How would you compute th tl as4dzwg930 yho+ z:q m84;j3zfkhxe banking angle giveagm;z+ ojhd hfq03l :stw 84ykxzz439n its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. 2tu0mmmtb/x4aqo3q u7k vv9 l0a(z h* She wants to let go at precisely the right time so that the ball will hit a target on the oth3 z/ hat mv7mulmba0 2* quvk(qot04x9er side of the yard. When should she let go of the string?

Does an apple exert a gr 1 rs myt (;ldokq(f3wyap5:y5avitational force on the Earth? If so, how large a force? Consider an apple5:(smpk1f5aly yy;r w3(dtq o
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dou fpuhdgtfu s 0c;ny0;9-zn6b8ble what it is, in what ways would the Moon’s orbit be different?8cny df gbts0u0;z -nuh;96fp

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on3 7;bk vkf+kp hs1,muw the Earth?wufs, vhm kp37 1kk+b; Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the f76-bg7 l) a ,egb5wkmmxzk5dMoon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cons zd)f bb5m -67glk 5m,xw7agkeider 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 effe/9 (jcjpo s+m. spzii:cts are at work? Do they oppose i(/ . spsz+:opjjicm9each other?

The gravitational force on the Mo6j:5xms o/( mtq7fnkfi g q q1snot)tg.o4 0n/on due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away q7:/t(.)ox5qgnk 4mso 1jointf6/ m0gnfqstfrom the Earth?

Is the centripetal acceleration of Mars in its2xv a7um- -- kg:./tfyutyf eb orbit around the Sun larger or smaller than the centripetal acceleration of the Ea/ ftvmf.g-xuykbe2- t7: u-ya rth?

Would it require less speed to launch a satellite (a) toward the east or (b) tow7jobod fg*;te*54.z w 2y vpjrard the west? Consider pzo7b*e4of j;dy.2rg tj*v 5wthe Earth’s rotation direction.

When will your apparent weight be the greatestf,nqy*:te, fri w 7y4r*a6kbp , as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerar*,enby 7 wyf6iftq4 *akpr:,tes 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 sezmg) wsb0w*,ng jeo9.y .e7uc mq+w6pace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulat*ew y.mb,u0cjggwzme 6oq e n.7w9 )s+es 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 exper0jz lihvau*6*4b suuv g 7cfwi/*q0 0siences “free fall” or “apparent weightlessness” between swsuh ca07l0u sv*ziu *f0 q*gv/i6 j4bteps.

The Earth moves faster in ik2o n*ymy5mip(4*b tur5c fi45 bn.bmts orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seant4 br 4 y2bm5*y(.5op i 5u*bminfkcmsons — 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 -p;1pt. rhvw. k m.pmluntil it was discovered to have a moon. Explain how this discovery enabled an estimap-kht .l;rp. . wm1mvpte of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon,iy:ga wei *c1zi261j zyr o)l's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from tcoigwey* z1 2z, :1yi6ij )larhe 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 1980 skyxn;4lml5,/ h2efs $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eart6 9.1ovq4du/ jktdyux h in its orbit around the Sun, 9 u.vkudx/4djy6 1tqoand the net 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 exertew n4i *m+-lnved on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. wl*n ve+-4i mnCalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 4b6 jg*i )ulm 4qf+mhz400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle ij h i6)mbm4uq*glz 4f+n 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 3*o(. dzet oqispeck of clay on the edge of a potter’s wheel turningzqid o( o.*3et at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in ajmfiqa evya csr,.4ck* 96nh96i8jc4 vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is cjr hvm9ky668i9, nea*.c c ifa4q4js4.00 $\mathrm{~m} / \mathrm{s}$ 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 ofz4p2fd5ar nvp k6 bf9) radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is nvpp k5dff)r4b26za 9this result independent of the mass of the car?   

  How large must the coe*uap i,ldl/f *:m, *d ekxhuw)fficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed ofx,w p/dlm,l*k*f uadhi )*u:e 95km/h ?   

  A device for training astronauts and jet fighter pilots is 9n q)k w(+0wcfsggq*d,5lx qgdesigned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the tra5q )+ ,kc*gswln qgd(w0xg qf9inee 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 aqiq o7;xs0 )( bw5wgyturntable 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 betwew5 ws )7 b(ixq0yag;qoen the coin and the turntable?   

  At what minimum speed must a roller coaster be tju3 z.4m3pd0mcubh2vraveling when upside down at the top of a cmjcu 302 d.4hzv 3pubmircle
(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 fzvqhgden 4 02wgx0 +o4,nxq( of a hill (radius =95qxfx,4 q 0(vo0gn ndwe4gz2+ h$ \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:xs5 vj 9avde2qth. 2l need to make for the passengers to feel “2j.vtav9sx5l d:ehq2weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circr )mgvzy6 l xrfn *9-vkat32n8le of radius 1.10 m. At the lowest point - ty a2xz9k) 8g3v6f rlnnm*vrof its 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 centrixrm7j : 3h.jlwhw, tu3fuge rotate if a particle 9.00 cm from the axis of rotation is to expewx uljh3,:w j3mthr .7rience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walledxkpvdat5f0 7oe98w+ a "r7 tk85a90a v fdoxpw+eoom." (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 k2g)f5-iq vh/e ;vn fyrotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (masskg5 f evqih/y )vfn;-2 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 thir31pl 7tq p-ems time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnituml7q 13rtpep -de 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 mb0q cul/gp7 :e 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 masseskifo;,0/fx b/4vz6oweq j b5o $ 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 vertiuy)z0 7z l(+xp:tiufgcally 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 cen 2:u(z g lu8ocgzqg-m5tripetal components of the net force exerted on t(oum z:guz2g-58l gcq he car (by the ground) 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 uniformly fro9cg so(rlg o37iak*(3vura9rm 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 this acceleration with no slipping or s uc 39(i*v7 sgrrlrkaoo(3ga9kidding? $\approx$   

  A particle revolves in a hor-dv; vjyxr+w0 izontal circle of radius 2.90 m . At a particular instant,v ;-0w x+rdjyv its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earthp)p;:2h xtso hs6 pwf3’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its maxfp2t )3;oh :shpwp s6ss is 1350 kg.   

  At the surface of a certain planet, the gravitatim);zfy,e7nzo onal acceleration g has a magnity; z 7nme,ozf)ude 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 Moon5 (/d9d b8zgyt cng 9bqei*u.v's radius is 1.74 5.vyicug 9b(zq9 d getd*n8 b/$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has as3p2bzw6v9gzg xkl m 7ic rt1zoi-r, 6)oo+z8 radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity nzp vz69 osr2 ,z 68xbwg3tclr-+mg o)1iizko7ear its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samem0q.nq c(le 5r xxakv)xz6gk.ur7+ ti 7fb1:y radius. What is g56rxqftxzq +cm0v.ne7 k 7aky u )ri(:l x1b.g near its surface?   

  Two objects attract each other gravitationally with a fo0 s67jze: ltltrce 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 acceleration of grac3 b5xi32vosq vity, at (a) 3200 m5 xq3c 2ivs3ob    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s ceno6sr p 8tqcg+0ter to a point outside the Earth where thegravitational+c6orqs08tp g acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star haszi)o q2.bilwro*ke*9jmrvimw8 x mx+ (.z 0r/ five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfac 2x9x/io.eribwv0+* rmz8 (iwm)* zmorjl.kqe gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which onczvi.lcp+ux7yd/ ,. qce was an average star like our Sun but is now in the last std.7x+u.qiyvp/, clc zage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spmsvy 36kr r ;y-nx,(lcuz2y4wace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acz -mv(y3cyw;r rkunls246y, xceleration 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 squarm8tfz lt9o) sam3xr+,e of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thre+9z 3mft,xrstl oa8m )e.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up /lc7f g9us ri:vzv*e :.3 jqsao/x(pron 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 lszp l:.eq:f/j(vao rg v9x3is/*rc7 uine (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 su5v5x+2iof52vr;)lk x icuk dq rface of Mars is 0.38 of what it is on Earth, and that Mars’ ra2vr55fcvuk5 l qi;+d)ix2kxo dius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the;o-s c4m;8;2e oxrt7 von.ojtyt y:ob period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s.oy vcoy motb:8t2 4;ero;;7-jnt sxo laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelli f:av i2.f/ x3,m q3treby;emfpb.5xste moving in a stable circular orbit about the Earth at a height of 3600 km. 2tvix mps/ax.5 m3.:yf; 3bfb,qefre   $\times 10^3$

  The space shuttle releases a satellite into a mg *pgn6/:w jscj .,dpcircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) p j*/:nswmd j gc6p.g,when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expergu9zn v7.jbwy v 7k/2 :oy x6fl5rjmm5ience simulated gravity of 0.60 g? Assume the spaceship’s diameter is5u7.bywvonv/9x52m jm:z jk7 f gy6 lr 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in ar 6isw6v lobqz cvs+r+ql( 2-wk f8*s. circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is verki2 flq-. s+c6q+6v bwsosv wr(z*l 8ry small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from t*9z,rw fyeb* ehe top of Mt. Everest to be placed in a circular o**y,rz9fe w ebrbit around the Earth?   

  During an Apollo lunar landing mission, the command module c(v g/ *l ow: anf0q0+box;tkiiontinued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once/f oxt:lgv*0ikq;+a o w(bi0n ?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The ina2.;cjjx vi0e9id dh2h*3 ps mo8 3)swlw1jfnner radius of the rings is 7d 3.)*n j2afp hv9lwmi8 jcie0xs1wh2jd ;so33,000 $\mathrm{~km}$ , 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 15.5xn lvcw5 w0jbf6: 6nlqm1lt3 * s (see Fig. 5–9). What is the ratio of a person’s apparen0ll nj*wcfw3t6q6n5 bv: 1mxlt weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 7vzf3p(3amjiy+ c:p v*5-kg astronaut 4200 km from the center of the Earth's Moon in jmpp :+fvy( vi*a3 z3ca space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star systems,c f3yyb( 7 v6gv)by.ik/fme consists of two stars of equal mass. They are observ 7ym/k)vf,(fv gbyb i.ye6c s3ed to be separated 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 read for the ,on q:c cp+2xfweight of a 55-kg woman in an elevator that moc p+f2,o:q xcnves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevar.;k jd:5kxmftor. The cord can withstand a tension of 220 N and breakskdrx j m5;k.f: as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wi*xdtjwf k3 ah.,o hh,7th period T , tjo*.h7xfdh tawkh3, ,he density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon ew r82+u ow n:+rh/n/4hgja(ej kvw +t(27.4 d) to determine the period of an aru+ e hjvjn t/4aekw: g++hw8 r/wn2o(rtificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundrsdsg8/k) n0 zsed meters across, orbits the Sun like the planets. Its period is 410 d. What is itsnz g0)kd/s s8s mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.r40fa fmn4r8f5 $\times 10^{9} \mathrm{~km}$ 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 r) rz::se3 hl adjy78hloughly 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 Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third lawh: yzjs)lhe:8 r3l 7da is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the (avw):chfmbqz;l1 toahu:5 vxoi/// 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, per ks)j gbh*cs:1iod, and mean distance for the four largest moons of J)b:gssch 1k *jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and dist4 qk7.j vmx )noqo)6olance of the Moon. 4o o qv7nx.k )q6mo)lj   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mo szd .h8v1.tb):q nhmvons, using Kepler’s third law. Use the qd. 8b. m1tzshvv)n:hdistance 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 M(aj48z ylyqo6sv17s nars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the64s(a j1q8yonz7 slvy 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 artificiaqdxczh4.1i0ew bvopva1, joc( 4k-h1 l "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 asbiv 1 (1 w,c 0hpvka1d4o4.eqco-j xzh on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swing8t6rs6gubsl/vf ;j/q yc e3p0 ing in an arc from a hanging vine (Fig. 5–jl3g6rbv e 0s6tc u/8;/fspqy41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be q7m1kiwf 8 at;ss mov5y .5(xohalf what it is on the surxf ( 585;ksms17qow vt.ioyam face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mqoe /x i5k.ls p:*mpt,m-5qbhutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they p5:mpb * mote 5xkp.hqsl/-iq,ulling on one another?    $\times 10^2$

  Because the Earth rotates once 9)xpa3 nt2-0va. :zbqzns juc per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnit23 z.nnaa- zts c)q9j:vubx0pude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tru(mb zl9 w,syv2t 4awgp20ym9aveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite fory2mw9 sz 2m(va0 49lpwb ,guytces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scaleb5bx 5ya ecz mqf8ox39x* d(q( in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direcy (bcfmb 5 o(*zqd58q3a 9xexxtion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube t pdu*zqmh/(u, hat will rotate 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. Wha p/ *uuzdh(,qmt 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 verx 6+u wrpg)j/ytical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radiul jt1 ue1m-w7ps r, the acceleration due to gravity at its surface and the gravitationawmt1 pu17- ejll constant G.

A plumb bob (a mass m v ppqg*, l7t23ah cj*lhanging on a string) is deflected from the vertical by anltq*gp 7v23*hj lc ,ap 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 wkw9uagj 8mq as;l*2) for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at)lmu2w9akgw;8ja *sq what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fastkhv11gdzo4 qa) ( b/2sb i9frm that objects at the equator were apparently weightz a4 /b1ko9srvhmbq( f2)id g1less?    $\times 10^3$s

  Two equal-mass stars maintain a consta7kdan *jjfbt - -n q:opb.(d7fnt 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 constwj8 v inx/0ha/)y(nmc oi1r 6cu4 tu2p8j2h aeant speed rounds a curve of radius 235 m. A lamp suspended from tmuvjn0/12i )/(4jiu t8c hyaaxew8pn26hcor he 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 ml+ qvk dm3iyws j *qqzz/+z351assive as the Earth. Thus, it has been claimed that a person would be crushed by thes1zzq3j5zy3 +kdiv /wq+ l*m q 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 equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an zypv6(: +;zewrw1 ybeextremely 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 thewzw1z: pe6 b( y;vyr+e 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 the hill ando(d1d32i :oz;wl)es vsxz gq7 valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losin e;zszi7dql1 )dsovo:(2xg w3g contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a grofv;8 1yw,ks nbco-*1bxgzuw /up of 24 satellites orbiting the Eak*,v wyc;gbfxz -1 sb/w1o8nurth. 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 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 (g)h i9 po0c1fs1w9f,ou,tkw2ysyl/(aych q, NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros fy2 0l ys1w (,ysh,pwh)c9t /ooq91cakig, fuis 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 pursuirq nnx/ker*6j7h g,/,aqaej*ng a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Ear,q,r/en*h geqajr *7 /kan j6xth), 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 mean disiy6tz2et8bvcoc7 q;,n )2qvwtance from in bvt2 qey6cv,)qt8; c2ow7zthe 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 "feel" ybr*iy 4om n3;(zxxf 9kourself gravitationally attracted to someone near you. Make reasonam4r fiy3; x *xkn(zob9ble assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-4zq d/v crq84d:rzx9 -q6) at a distance of about 30,000 light-years froz c4zxrd8v 9qrq:/ dq-m 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 locate8 7jg:umauj2zv* - burd at the 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 at the midpoint of the bottom side of ua-7jmgu r* 2ub:j8vzthe square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thjkdq8 nwq 1;v,n1 nwgkl *9r3ye 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 /ncl6 h rs- yj1,ck+mrof the 1.5-cm-long sweep second hand on your wrist watc6c rrl,+m jy-sc1 h/knh?    $\times 10^{-4}$

  While fishing, you get bored and start tovtuwk s+ 4v.4ydx(5i r swing a sinker weight around in a circle below you on asvikd4v4w. 5ytu +(xr 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 dey2ws 9fxh atx2mv :,7gsigned so that a car traveling at spe2hx,2s gv 7mx:9aftwyed $ 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, utili(h -pvv/ c/by0h9u nbwvv ,bg5zes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal f9-g / nvb 0hpcyv5w(vhvub/b,orce. 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.$\approx$    $\times 10^2$