Sometimes people say thj(xhyv 40 f 3s9jn.xhf8 qbii(at water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this sta (js(fx q3hhj40bifxn9 i yv8.tement?

Will the acceleration of jy 0 jbsn5s+y/a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travel+5 nbsyj/yj0ss around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a a:-txxsiw8 cc/ p;,pk hilly road. Where does the car exert the greatest and least forces on the road: (a) at the ;:c /sp8i kawtcx x-p,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 acting on a child riding9s*xsevq jrb9bp4/k 9 a horse on a merry-go-round. Which of these forces provides the centripetal acceleration o4s9sprb/ ebj99v kq*xf the child?

A bucket of water can be whirled in a verv 6ieymj1 0en* x,yct.tical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explc.j *ivmey0ne,6y x1 tain.

How many “accelerators” do you have in your car? mj k:6 (*u/ gs(vzrdeoThere are at least three controls in the car which can be used to cause the car to acceleratm j((/ogvd*kz:r su6e e. What are they? What accelerations do they produce?

A child on a sled comes flying tdm7 d.g1 pcn6over the crest of a 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 between his chest and the sled decrease as he goes over the hill. En.dp c g1dmt76xplain this decrease using Newton’s second law.

Why do bicycle rider(yj7t z/ 0wwnls lean inward when rounding a curve at high speed?

Why do airplanes bank when th/ /qltw 26-hcsr1wkxeey turn? How would you compute the banking angle given its speed and radius of the trk1 qs2wl-6//he tw cxurn?

A girl is whirling a ball on a string around her head i0.aqd/u m; g 1sy.,7e 0x a2mlbvxvtyqn a horizontal plane. She wants to let go at precisely the right tqyav1v;d x,t0 07l .b.m sa2/mge uqyxime 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 fkpef,2(+dn y0u 3qxztorce? Considerd 0zkpefynx+u ,q 2(t3 an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass we0t5d)h+-l k 2sktkmhs re double what it is, in what ways would the Moon’s orbit be differen- kslkh 20+smttkdh5) t?

Which pulls harder gravitationally, the Earth on the6x sn8p vwu m;fg*9)jj Moon, or the Moon on the Earth? Which acce) p f jwmn89us*6jgx;vlerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet5ai2z kh k t+rqg,j*edgwe ,0+ the Moon's is mainly responsible for the tides. Explain. [Hint: Consider tgk+ i ed wgat+qk0rez5* j2,h,he difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at-ztybp/n ;m- n3hnoy2 the poles? What two effects are ao3- ;-y nnyh/np mbz2tt work? Do they oppose each other?

The gravitational force on f5g :jq11w6 rat2zifgv5 i7wgthe Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled g zv 517qi:jwagirf6f1 5tw2 gaway from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Suntyf2 m49 b(xeq larger or smab xyqme (t942fller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward tp+w izuq zrpm:l -3z01he east or (b) toward the west? Consider the Earth’s rotation zm0ipz3-zlru wp+ :q 1direction.

When will your apparent weight be the greatest, as measured by a scale in alsq *n ak cq. ;oqkw7ymi)f+(, moving elki; k y)mq qq*+owaf c,sl7(n.evator: 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?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long p 3).lzk c)qx *u jxmpx l(86 zyf68h7/mnrpupperiods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical sh x z.6* 8)x7lkqy)jn6f8mr3(uulp ppczpmxh /ell 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 “apparentoz7n972ryxqgy b/*w o+ksfuu, xe 0s) weightlessness” betweewk 2bs7 qoxxeo +z yy*r9usf7,)gn/0un steps.

The Earth moves faster in its orbit around the Sun in January than in Ju sb(x p0e0eo7 ;oc1afyly. 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 — tcoyso7fapb 01e xe;(0 he main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knoxf-sd +xzu(nvqn7 f ;3wn until it was discovered to have a moon. Explain how this discovery enabled an estixxnufz3n(;dv7qs -f+mate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger m 9danw5c)q/ wthan the Moon's. Yet the Moon's is mainly responsible for the tidesnw 5/c9am d)qw. 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 19cqyi3/:zc/bc + p,ydj80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleh un+/ ;yy:vqbration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. Wha/u: yhqn yv+;bt 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 exerte/oc ;ldx ara+8herav8;aed,+ d on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) ofl ;d8a aa8 ve+ ea,hrdxr+;co/ radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth'st1),wprw ;t+ld8 wwdo surface, and circles the Earth about prwww,t+d1o lw );8d tonce every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of cpj w j+*c9awaqn8jd+5lay on the edge of a potter’s wc waj98 ++adpjnqj*5 wheel turning 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 6 rdw8rrf*o 1qrate in a vertical circle of radrw8 6 drrfo*q1ius 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 with which a 1050-kg car can round a(uqw9 .7 k+g1dekz7l banp ;fs turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepens 1k dwaq;une+.zf(7kp9 gl7 bdent of the mass of the car?   

  How large must the coefficient of static friction be y +pnv 8m4a7i-l. l7su,no -glm;b fazbetween the tires and the road if a car is to round a level curve of radius 85 m at a speedim+ng ,87l7a n-;-pa.f bloumlv z4 sy of 95km/h ?   

  A device for training astronauts and jet fighfj *ya-jb(ct nb/wi onv77i4+ter pilots is designed to rotate a trainee in a horizontal circle of radius 12 ynbo+7b*j nwij-/ vi f7act(4.0 m . If the 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 turntable of variablewyx omug889 p5pc1(q0 ettw6qtu,ej3 speed. When the speed of the turntable iw80pt yt,qep et 35w 98 (j16muuoqxcgs slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaste83kw fm 8 tjach387fwg6h iob)r be traveling when upside down at the topw3 hw8fcgtaf bh8oki3 8mj )67 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 dwavb4 *37msi*k t*x7vruke p2river) crosses the rounded top of a hill (* v4uv 7erx23 kws*7mp*tkabiradius =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 jphmgj)w x:tgz a(0) ;per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poinpg; 0w) z m(t)gxj:hjat?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At thu0t7mw- m /a4) v)imbu efs36f,6a 1nucqowb ge lowest point of its motion the tension in the ropbmvcq6 uuf 0aso i37bwm ae w-4fg n6u/m)1),te 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 centrif,s8 i 1p+ r7kdrr6rgekuge rotate if a particle 9.00 cm from the axis of rotation r,gsd8+rkkp6 i7r1 re is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated )r c(98 -rbgkgkz *vf1kprmz (in a cylindrically walled "romkv8* r(bkggz)1-9ckf(pz rrom." (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 frp+w o0v ls;aue*y(u 3,es+xs yictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole aou0;3(yp ua vx,ysse+sel w*+s 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 we(- 4kbtnlc w i (uz3o3z6v5rcgight of the ball whicgl4i3kc-5(b( wur zvctnz36oh revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is pew3 3dys52,mjged drm4 rfectly 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 massemq4 *r +9 qi+cblj ;ypvlww1;os $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 3100z.w -,qa ypaxgb-wl, $\mathrm{~m} / \mathrm{s}$ . 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 componen;wx x;2 d5xsdkts of the net force exerted on the car (by t wdk52 ;sxdx;xhe 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 from4; vlfv)a hss6s0ac e* the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tfa0 c6v)has s4;v* lesangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a h+w pyxh a/3ou9orizontal circle of radius 2.90 m . At a particular instant, it/a+puw39 ho xys 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 o.c5rrsgy+8y n., c,v liyu6tqf Earth’s gravity on a spacecraft 12,800 km (2 Earth radii),vt6c,q. sl + 8 5inru.ycgyyr above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational auyg1bd(qs6- x b5e r3zcceleration g has a magniz3r 5by-eds6(uq1x bgtude 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 (l7qm( a7p(*bh vaq(d r-vkbegravity on the Moon. The Moon's radius is 1.74 m a v(*d (b(qbl7rahpe(k 7q-v$\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 Earth, but has the same n:0y08we hy kw3w6dhjmass. Whatw 6j3wd08yken 0hh: wy is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times thatqn(ev n)+lqas8p cyj :9y j)w5 of Earth, but the same radius. What n)8jye(slnyv+p )9c5w aqq :j is g near its surface?   

  Two objects attract each other gravita1nv1of hlq+5dmrr.-0l/t m jitionally 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 accelerati4 exb2gd(ii)dvhb8i ,on of gravity, at (a) 3200 mh(b4,exvgibd 28d ) ii    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eny3t0 1l(k rxoarth where thegravitational accele(nyk 01x rlto3ration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a s8 clg 6gfp+qj7phere about 10 km in radius. Estimate the surface gravity on this mo8gf+lpq j 76cgnster.    $\times10^12$

  A typical white-dwarf /uqoz ;gg *wg x-v)hx. +wen6sstar, which once was an average star like our Sun but is now in the l; wq-6)g exug xvw+/so zhn.g*ast stage 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 whilb-;( ktbnt; exe orbiting in the space 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 accelerat-;t;kxte( bbnion of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 mckj fm34 6yp l3vzeswpug*7 ym2rj+ *,. Calculate the magnitudw4+s*yp37mvjy zj,g* pumc fe3 r2k6le and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sun.4 (tcp/,diwd,h uqvh+ Calculate the total force on the Earth due to Venusiw,,hpd ud4hct/( q+v, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars (dfhfao 9c/685;r0zvg/iju:opfos c ig9 go5is 0.38 of what it is on Earth, and that Marsur5o 0ch;ogdz5f/8 gg(jo osi6fa v99c fi:p/’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Szw5zs4qze)2 tc4 rwc9un using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examplw ce4r524 szz qt)9zcwe 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abou0ov 2ef0bphd:t the Earth at a height of 3600 kmf: ep0dho02b v.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbik1/lmw)xkbx:,nn hg )-mx c; tt 650 km above the Earth. How fast must the shuttle beb)k1;:lxwk)xcx nm,m-/t gnh moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiencetr15f9v ldw5o simulated gravity of 0.60 g? Assume the spacesh 5rft9o dvl15wip’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a 9lpn5u ,j3 dwocircular “near-Earth” orbit. u 9l3pd j,on5wA “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from mjj - r*9ezh/s*h-qx k3z c/gqthe top of Mt. Everest to be pl/-/ qk xrj c3-hs9*jgzem zqh*aced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission,m9b4gvm db6z ) the command module continued to orbit the Moon at an altitude of about 100 km. How long did zm 4vg)bb69md it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The i7+*dvxfv1+l.pib9 y fce y*w)eljo6snner radius f y.* ly* i+7xjfov)cp+wde9es1blv6of 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 diamet. q f.wjfo26veeer7fzpj5j lq* 3njo)u)( jp+ er rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s app5 qreoe3.n6p+j. 2w*jl u(jjp voq)ez 7f)fjfarent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from theawk f;y,cy* / cnti5qp:as 7i1 center of the Earth's Moon in a space vehicle (a) moving at constant veloci7qwy:p;a/ k, tsa in*5y ficc1ty,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. Thes-mcgg7xvy-5ce)q;pp * bv 2 uy are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midqs2 g7e-vg ;c*ux -) yv5pbcmpway 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 elevatof.ofbksng z6 t+ q0*x3n c-g.wr that mo f36-n+to0kqcgw.gn s*f. bxzves
(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 suspv:ogc51 bv, ffended 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 acceleration (magnb5f,v1voc :gf itude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periodb a)ni4-cs1n f T , thebca1-n )i4 fns 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 oyro o.p c7d-ghpw :,-rf the Moon (27.4 d) to determine the period of an artifi:op 7yrg --o. r,dhcpwcial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik()2x;wwi cb wikhn:0x8g dm)i e the planets. Its period is 410 d. What is its mean dish)i(wxg ):bk;idin8mww02cx tance from the Sun?    $\times 10^{11}$

  Neptune is an average distafv dfh 3-u m:30g,kh8b: 4yotqk kg:fince 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 rs5 m;yvvk 7; ehg;njz(oughly once every 76 years. It comes very close to the surface of the Sun on its closest yznv;5ehj7mgvs;k(; 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 law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the x2ms+ dycj* 3kcenter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, perio93c3 uyh;mlyndas w+4d, and mean distance for the four largest moons of Jupiter (those discovered by Gsl;cuah m3 yd+9 y4wn3alileo 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 distance of the Me-irmfu f0e /phpn as+45tj.5oon. -nt/p5 0u +r5heie4fm asjf.p   $\times 10^{24}$

  Determine the mean distance from Jupiter for eacxufj cwb1v6px26:14u :x bpv fh 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 Table.u:46wfc21upp1vj v x f bb:6xx
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupoo vtc:u :1l twv6vp6vhi:-n3 r,;umeiter consists of many fragments (which some space scientists think came from a ;wcu :ovr:i-ovth :en3lm pt,6vu 61vplanet 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 "pla7:0l0y7mqfxnrh0/r8. qvlizcvq im)net" in the form of a band completely encircling a sun (Fig. 5-40). Thfmzx8n hi00l/q mv.r7l c)7q0qv ryi:e inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on 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 hanginbk*284 uqyf oawl7ro5g vine (Fig. 5–41). 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 lyf4r bwau8q725*koo, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whata1/.e: ow(f3 zosfqcl it is on th1 as (oz/fw:q 3.feolce surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in vogo ,4rhocf*wsr4 .82, hjmoa mutual circle on.w,g8vj*,hr o4mc4shf r oo2oce 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 pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day,qh ( w5fg-0r c)kkgg9i the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t ro-f gqw0gi(9h5 c)kgrktate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly 6e ) yrs-wa3zejfnm 90from the Earth to the Moon experi3 -zseyj )am6e09fnwrence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sg.z3 ;y g, go:om)kkgacale in an elevator, ,)3ogokm ggyak.; :zg it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statiog.c( oge l4cso s7)gr-n consists of a circular tube that 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. What must be togg) egcl c7.s-s (4rohe rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). y: 9 dal0b.z;lwclgn;
(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 radius37jo kpj5sb9-*xvhif r, the acceleration due to gravity at its surh x9fb5*7oskjipvj- 3 face and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is detl0bon6v po90 flected from the vertical by an angle6t0pvo0 9lbon $\theta$ 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 67xl 6ihem1uip/h wh83) m is banked for a design speed of If the coefficient of static f13h lphih8im)u /6xewriction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the E. ine2:h )knmld,k.nwarth were rotating so fast that objects at the equator were apparently weightln:wd2. en,k.nh l)ikm ess?    $\times 10^3$s

  Two equal-mass stars maintain a constant dism1r;g2j m.6cyzq qsk.tance 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 constamem,: e.gq6n u*n atdd;(gpi4nt speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an and pmie.e6*( ; m:gtua ,nd4gqngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive asmcb5 2qjmt+n9 the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equat+95qtj mnbmc 2or 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 ,;zge4k+ cxuzsx1 gv elb-7p w81sch(of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whicgscblxp18;1sw uzh eg(xv,k- e 4 +7zch no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown hj7z;/aq/ agc-nobj * 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 /qajg*bzc7/;an -o jhlargest? 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 satellirdag-xcv 8g5q l(p.2stes orbiting the Earth. Using “triangulation” and signals transmitted blax (2r5qc8 dvsp. g-gy 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 (NEAR), after traveling 2.1 bse 2g.fl1p ks2illion km, is meant to orbit the asteroid Eros at a height of about 15 km . 2gsf1.lkp2e s 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 pur2jmxe .rw y8s*suing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite *m2ewrx. jsy8 (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yearsmq2 zwv :y00xgreoebnk, .x2n2( ri)7btr;mw. (a) What is its mean distance from . r )ryw :en2k;7(txgn,bmb0zrqx 2o0v wie2mthe 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 would6kc gjhj mrfz82u i1(( need to be if you could actually "feel" yourself gravitationallyu m6rgz(k2hfj i(8 jc1 attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fexx+q * )rrne7ig. 5-46) at a distance of about 30,000 ) *nxeq+xr r7elight-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a ql1kacqx+sdpr73ytc c 6(..b: nlf c9square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fif6safk(. bqct pnry . q3cl+9ccdlx:71 th 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 5jb shca; 0 s3*2mmr1vn500 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-cm-long i d,xqj+i5*m*;e euaf sweep second hand on your wrist iee*+ dxm;fuq*,j i5awatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around inn .lwe0*w+z5 gd dgpkrt 16k8b a circle below you on a 0.25-m piece of fishing line. The weight makes a compd zdr10l wkb*8n5 p.ggek+ t6wlete 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 des9l4rgz fxh18 , ybu4woigned so that a car traveling atr yxzo ufb9 glh4w,481 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 whed 2j*fs- 4zexa s(dj5wz4kn.kn 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 comfortable. Cons2dzj a5e*4kn-k szdjsx .4(fwider 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.$\approx$    $\times 10^2$