Sometimes people say that watfs x 8jpb)(9b(;zhlnp er is removed from clothes in a spin dryer by centrifugal for(h)fl8pbzjp ( ;bs 9nxce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the s1qn2 8lqvxq8xmi6z -uame when the car travels around a sharp curve at a constant 60 km/h as when it trav - 1uqz8x inqmlq62vx8els around a gentle curve at the same speed? Explain.

Suppose a car moves at constani4t5mz)-xl -imy9 p+m qjsb*et speed along a hilly road. Where does the car exert the greatest and least forces on thm s*iy-q)jm9z-54eib lt +xmpe road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on9 i l9 a/t9k-r6i:qnwt07c nxn;nysvf a merry-go-round. Which of thxn60f9yqttv9is kcn-: w7/i nr anl9;ese forces provides the centripetal acceleration of the child?

A bucket of water can 6:v mjx81t zitbe whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upt8 6ztm v:xi1jside down. Explain.

How many “accelerators” do ywie48 oyu3m1-a fxf tsp;nm*0ou have in your car? There are at least three controls in the car whichou 8 fmm0a-tpsew3x in *;4fy1 can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyinguf/t hb / l; g7 :lf/z3fuj(prfb6ab(p over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “ u;(f rp ugb/fzlp3ff:a/lh t (j7/b6bair”), 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 cury wev fm5fq1m/+jm-t kyz9e;9ve at high speed?

Why do airplanes bank whenb8x+9o3 u nrek oy3cs7 they turn? How would you compute the banking angle given its speed and radius of the turn3sce oo+73bu n9yxr8k ?

A girl is whirling a sb*ago(+ ymnc2lb( k0ball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on them lc+*bb(a(o y gk2sn0 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, y6 b1wy2u:rjzhow large a force? Consi yu1bw:2 yj6zrder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woulp2cn m+*(pzx z-bbk 7ud the Moon’s orbit be differ-(p2xu znz+* bpbck 7ment?

Which pulls harder gravitationally5e9lx:ex89tjl gtb r9.1dl jx- jik2w, the Earth on the Moon, or the Moon on the Earth? Which accele 5-9tliw :krl8xx9 .2dbjx91letejj grates more?

The Sun's gravitational pull v*7n dwx 9 tcq)dkn/l)p-yg+ bon the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the obg9ndl/)tk)yc +p q*wdv7 - nxther.]

Will an object weigh more at the equator or at the poles?ha m6cdb ;zj/l-xcg0 - What two effects are at workjcah/b g ;-lc0z xm6-d? Do they oppose each other?

The gravitational force on the Moon due d412yo 5b0ek yl *n bxcqp(nf3to the Earth is only about half the force on the M n1 oc5ylpxek23q*4bdbf n( 0yoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mvjp 5 ko3bb+;mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the E ;b+mov 5pjbk3arth?

Would it require less speed to launch a satellite (a) toward the easi g-ju*c6ai/ kt or (b) toward the west? Consider the Earth’s a-6j*k guici/rotation direction.

When will your apparent weight be the greatest, as measured by a scaler6qd2 gf2p4 te u w(+hnvk1sv* in a moving elevator: when the elevator (a) accelerates downward, (b) accelera(vgn4 f2e1h +qkruwv6p2dts *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 space could be adversely a6haeqij iu , c6.0cq)offected 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 simulates gravity. Consider (a) 6e,0uc iochjaqq.i)6 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” x d 8)8hgcfhmk/(puq (between sg(hxkpuqcf/ ( 8)8 dhmteps.

The Earth moves faster in its orbit around the Sun in January than in July. w it i+eb3p+6uIs 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 Eart upi3i+be6+t wh’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have t ,m-xp+y)n ztpero01 a moon. Explain how this discovery enabled an estim n0p)oy ,z-te rpxt+1mate of Pluto’s mass.

  The Sun's gravitational h cbg)p4r -wwoji:g+(pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-roun:(bc w)- w4+ihgrgoj pd 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 x 60m hooqxnw 7kbk0/(ezshl8e5: :amp4koh0 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Sunj-cm2e3d ro) qr)dwh,ofxp8., and the net force exerted on the Earth. What exerts this force on the Earth? Asscp.8)q- xdo, m3jwodr2rhe) fume 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 2.0-kg discus a4 ztnqa m0b2)as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the b2qt)4mazan 0 discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and0+dvf ; rqc37m yg3)llzcewg2 circles the Earth about once every 90 minutes. Find the centripetal acceleration of theecy 37f2c+mlqr0vlg; gdzw )3 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 sp. 3bjpk:bjln vlf-zk(bie1 ,9 eck of clay on the edge of a pob3b k-jj pi:(z.e1 fv k9bln,ltter’s 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 w42n(q9u kddbsdr,0t a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If dkst24q(0 ,wdudn9rb 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 w:mz0nk x8dw+g ith 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 this result independent of the mxz +d 8mg0:knwass of the car?   

  How large must the coefficient of static friction be between the tiodr-l;0le/3 h1swu gjnkn78 eres and the road sw 3 n;rllekun7/81gd0h jo-e if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots3ptlh/8h3e o s is designed to rotate a trainee in a horizontal circle3 t /spl3h8oeh of radius 12.0 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 turntak5 u* q2l/yeoo (hfgd4os l8k9ble 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 coeffici dlq 5e yhu*/g 2os9okok(lf84ent of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be trp0 bto2smzl f65v n(*saveling when upside down at the top of a vbs s 6z*m50t2o(nplf 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 drivemsna;40l/p k21zqt qpr) crosses the rounded top of aq nka1tszmq0 lp/2;4p hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutionse byc9( ;y ap1zqw(ptn+.: afe per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the top apn(9cq ;wpta yee+ 1fy:.(bzmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a veg3lt(8ccd o 2qrtical circle of radius 1.10 m. At the lowest point of its motion the tensq cg82 oldct(3ion 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 rotate if a partini4 *x, lnen2icle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000 nni24 iln,x* e$\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a weqo2z+gd2e l 53mj/dcarnival, people are rotated in a cylindrically walled "room." (See og32lewzmj5/ d qd2e +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 frictionlenx9f3re c :bc2ss air-hockey table f rnxc:3e29bctop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of thexb kw kh )n.xj-q4q,g* ball which revolves on a string 0.600 m long. In particular, find the magnitbqn kj qw*gk .4,h-xx)ude 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 +/41vuk h aavnz-8hek75 $\mathrm{~km} / \mathrm{h}$ , 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 massesd7 r9mq9x 9 2brv*s zfw0x0tci $ 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 p 47 wm6w;vazp310 $\mathrm{~m} / \mathrm{s}$ . 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 dvyta3j;i6:ifc: g4r1u j,v kcentripetal components of the net force exerted on the car (by the ground) in Example 5-8 when itc ij 3t:dviu,:4jga f 6y;rvk1s 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 from5x v:xm7qj;fa ;;ftuw 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 uqa;:7tvm5; ff;w xxjwould the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius ujjhzn5 z(h4ndq wk1+l.:m6v2.90 m . At a particular instant,kq n jv4(1h.zu:6 wz+dnjhml 5 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 Earth’s gravity on a spacecraft 12,800 km (2 Earth rart9p10ewdi*+ y+)ornhf * cyndii) above the Earth’s surface if its mass is 0c+d*nyrw)+pyfe1*tr9n i oh1350 kg.   

  At the surface of a certain planet, the gr,,7my) *ze0n9lmsuxvw5 z 0edt uh7eb- 5 mqafavitational acceleration g has a magnitadebm) 5e,w7 z l mvx0nu0tm-u sh9ey,q7*z5f 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 Mo.j*z5 zm7;h uu6s*u y ak3pzmson. The Moon's radius is 1.7 5mmaks *ujh z*uy3s zp67zu;.4 $\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 E(b )qqway1cx (arth, but has the same mass. What is the acceleration due to gravityqxy( 1wq) (cab near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth;9c kuqq 9mzplmuo850, but the same radius. What is g near its supum9mqq05uo cz89 l;krface?   

  Two objects attract eazwmvjz9fmwa ,p4o: / 5ch other 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 o + *edk1b,yrkkcd8ix2 f g , the acceleration of gravity, at (a) 3200 m dbcik* ,e +yk xk2rd81   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frm)ja2r3 7 kvuiom the Earth’s center to a point outside the Earth where thegravitatj 3a)k u7r2imvional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five y6f tmu7 409uvv61vdj)xnt ketimes the mass of our Sun packed into a sphere about 10 km ) 6v4j1etfumd t k x76vv0nuy9in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average starozj20j0 emq,ckn t6n8(+dq lg like our Sun but is now in the last stage of its evoluti0ekdngmt oj q +28 ,z6(j0qnclon, 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 t.uw e tu(if a+dg6kr.1,xn3u 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 t3teaw g k1nfxui.d,(u.u +6rthe acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcn, jrznz;:ahz5jdfm)rs ;) f ;ulate the m;n))z mf5nj:,rhs za;dfz; r jagnitude 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 Sot :x 5 xlso8wzh.hr*z4yt,+ex 4pjo3 un. Calc:x4ot5p+szjx 4xwh yto,r3h8l .eo*zulate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 o ny 6wd)17t p-o2fuiuof gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determn ytip61- 2d 7wou)uofine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usideji*2z/ h;m5 d kozf8ng the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtaineed8z5f /;diokh *jmz2d using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving inmy;2ej)a w+ sb a stable circular orbit about the Eeja+2;b)y s mwarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km aboh-. -m qoa3cduyj-l 8uve the Earth. How fast muq3- jh- odc8-maulyu.st the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupaab2 d 0kfjsb hij:+h.7nts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as thebh27j :. +d0ihskjfba 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 circh/i,jhcsyu. 36kih ve ,kw 38bular “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 radius3kh,hch3wj ./8s v,bi iuyek6 of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity (v.goz(qh ))rem,2u vdeh+o e would a satellite have to be launched from the top of Mt. Everest to be placed in emvh.zo)(e +h),e(2 q u ovdrga circular orbit around the Earth?   

  During an Apollo lunar land-0(qli ri 3)tsbk2jgxg8 pim *ing mission, the command module continued to orbit the Moon at an altitude of about 100 km. Howri)2(l8tpkm ii *gb- j30 qsgx long did it take to go around the Moon once?    s

  The rings of Saturn are composed;qlpw hha7+;owd(.)fzp ev4k of chunks of ice that orbit the planet. The inner )kp.o(wwhaqe+dlfph;4; v7 zradius 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 i)cw9xve d9 r7in diameter rotates once every 15.5 s (see Fig. 5–9). What isivc99e) wrxd7 the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center zwzr (6epf mpx+/b2 +kof the Earth's Moon in a spacxmwpfz(kr2 zp+b/e6+ e 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 system consists of two stars of equal mas-oo5l;1 rnc8l6 m xqhxs. They are observed to be separated by 360 million km and take 5.7 Earth yearhlx rq6xno-8c 5;lo1ms to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read fog5wf *;nd7.ta2zkfo j m et1o7r the weight of a 55-kg woman in an elevator that moves nzo; ftgw o2t7*jem7a 5k1.fd
(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 cepl.noj((h7df7i pb+ qiling of an elevator. The cord can withstand j+p ql7fd7n (ob(i p.ha tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of mnr f45yxq(si cwte 8u,69a5 ba planet with period T , the densitrqta wm5 bf8nsc,ux (6y94 5iey (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 (27.4 d) to determine the perioobck)py5q12ckvn sqvv ;;8 5vf6xx6w d of an artificial satellite orbiting very near the Earth’s surf 5cvsw xc1 yv; kpqvfq;nxvk5b )286o6ace.    s

  The asteroid Icarus, though only a few hundred meters across, orbits th,yze ;fv5,wv2y vk 5rke Sun like the planets. Its period is 410 d. What is,r ;5 5vyvf 2kveky,wz its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average2-:dbnhaxp4dr(),u7g chv9 y ejy1 se distance 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 tk9bwo4fjjz/0f 9oq2a wchp9uf u*;d k/9 r.mw he Sun roughly 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? [Hw .o 9kk9jzwjq;f0dmuahrp9c 4 f/ f*ou b2w9/int: 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 tfm)e-45fl1 66v5d )i wicpoj 6blbpxbhe center 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, period, and mean distance for the four la0t sue fn0 wzi9j6a11ehxmo a y7av996rgest moons of Jupiter (thve1w 9e am tiya096s17nj h6xa9z0fuoose 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 kn 1)h4y257uuq allmanw own period and distance of the Moon. ml4u517 yua) awhnl2q   $\times 10^{24}$

  Determine the mean dist kuf0 o9foz*..cqov rlly) tc,8*zx 8tance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to , focxlk.y q.ooc8lf z tu9v)t80** rzthe 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 between1bjz ziwe6fht 3*t 2+ x5hdc.e Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was h6ew h be5 zd1c3.*itt+jf2zxdestroyed).
(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 "planet" in the form of a band ci40,*)hm xt 0.dzgiul. mwalaompletely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the ia 0tudzgx)4.h , ll*m.mi0 awperiod of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in ( qwlz jxmy.5i+ xwt.m*1pz1man arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the v.5q1zm+z(*my1wixxw ml.j tpine, 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 ecke 87ncrian 51et*/ rr6mo 4acceleration of gravity be half what it isonmrte 16ikc 5r/4*ne a7c8r e on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gryof4p1q4 d d:cj 1 ln0g8jfw wuu:o.v(ab 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 w 1:. uf(uyf dpgcojwq 8vo40:1dnl4jindividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatesldq oll)*d (m7 once per day, the apparent acceleration of gravity at the equatq7odm l(*d l)lor is slightly less than it would be if the Earth didn’t rotate. 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 fqefc g(b qd714rom the Earth to the Moon experience zero net force because the Earth and Moon pull with equaf7c4 qd(qbeg1l and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a baw3nz48.c6ydg oor ev +throom scale in an elevator, it says your mass is 82dr3vw+coyg.oz 64ne8 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists yz31pzo jdk l +l)-jg,2fkf*wof 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 the rotation speed (revolujz3 *jpk wkz-2f 1 )+yfd,llogtions 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 (Figb*f1ttg+isw s2w*ewlo - r )w9. 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 raddw+d aou4cud/t)4t1iius r, the acceleratio/ t)i u dddcaw1u+t4o4n due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fr,hux b.8sh 2ogom the vertical by an a82ohu.bx g, hsngle $\theta$ 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 hy)e9wdc g/ /qfor a design speed of If the coefficient of static friction is 0.30 (wet pach/d/ge)q wy9 vement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fafp z-l h)3v*xt(2ul3 :yekokz st that objects at the equator were apparently weightl :zozev3k(*lp- )hl23utyfxkess?    $\times 10^3$s

  Two equal-mass stars mainp451buge gr p6yjh4lx)+xxxt *8w j)a r1; vqvtain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp suso2t9t+2 wbmrhwqo 8 )w5b:vx.m wwae,pended from the ceilm wq wa2e5ov ,8 o)t9m2wtbbhw r.x:w+ing 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 Earth. Thus, it has been ca t(8r like3z8o b)tb-laimed 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)8kr(boe-3bt 8lt za i 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 them :veec b.9/nx/kq7d q 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 ebvq ked:/qx/7mcn 9.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 spe8pd(l o(a2ipmed as it traverses 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 at A, B, and C compare? (Which is largest? Smallespp(im (lo ad82t?) 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 System8* mdjv0gn -l:e4pn8 lk8ksf*fec) lq (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with fm8*lnev8j 8f:ge*nc4qldk p)sl0 fk -our 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), afterihgelu 1(gyrhp )c+ )3 traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Ero)yu lgc i3hh(e1p+)g rs 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 pur:jmg* bvqzv0rxv)r.o o p6 d9-suing a satellite in need of repair. Yoqm -:b9jzrdvx o.*r0pvg v o)6u are in a circular orbit of the same radius as the satellite (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 yearue1t*z5 rbx*qzcs 8g4s. (a) What is its mean distance from the Sunrz ub1sxqg8tec **4 z5?   
(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 ne8 ygjtr 8c65oced to be if you could actually "feel" yourself gravitationc56tcy88jg roally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cen6;y.rm d+ pwn g zrpte/q-*cv6ter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from t ypwz6.g;r +*6qen- tcvd/rmphe center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each si(bku p.q et:0sts5:ij.4gnw ade. Find the magnitud0p:unt.sj( ie bqg a4ws:k5t.e and direction 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 5 :h,lam/1)r ojm 3stjc-s)+ ft hnkkg*500 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 oy5dzk v -29ak 3*allref the 1.5-cm-long sweep second hand on youl 5kly*3 revda9k-2zar wrist watch?    $\times 10^{-4}$

  While fishing, you get bortlkp)a +dl/x6 + rs3timwa+:k ed and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weigh/p+trm+l6d k)lwk3xia:sa t+ t 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 radiu5k68fot dp.kbs R in a new highway is designed so that a car traveling at spee kop. f5t6kdb8d $ 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 o72/b: c0pya/zq topp(fw4r i ef 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 force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius o /(qf4 7wcpb pz0rtay/pe:i 2of 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.$\approx$    $\times 10^2$