Sometimes people say that water is removed from clothes in a h. +:um90vt+gigakdd spin dryer by centrifugal force throwing the water outward. What isgt+ih0a + 9 .dumkdvg: wrong with this statement?

Will the acceleration of ;pc b(jabu +r4a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentrub(jabp4+ ;c le curve at the same speed? Explain.

Suppose a car moves at constan n1+lctel lwzdi:0; +xt speed along a hilly road. Where does the car exert the great+iltl:0+dz1;ewc n lxest 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 the bottom of a hill?

Describe all the forces acting on a child rtv6j97mz h 0huvm4k; v/0ryz qiding a horse on a merry-go-round. Which of these forces provides the centripetal accelera4uyv0mkvzt;vr/7q6 0 mh9jzh tion of the child?

A bucket of water can be whirled in a vertical circle withoubes8er((75 )kahoojwf9ut3 jt the water spilling out, even at the top of the circle when the buckt( j)ahe8je (9u3w7r osofk5bet is upside down. Explain.

How many “accelerators” do you have in your car? Thj:azidttwb s(4v/ 9t s: .q)dgere are at least three controls in the car whic/4zt:w(.tgijtd9) avq: d sbsh 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 smalj)*iofev bvu;l3: l k 0:nju9ol 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 hillf;9n0) o*:j v:l bivkuleu jo3. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward k:vc*m883ropi us;qrwhen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compwad1ubxn 43 9jqm98( nxc1wsqute the banking angle given its speed and radius of the tu4cw8an1 wu dx39bjmq x(nq9s1 rn?

A girl is whirling a ball on a string around her head in a hbys.o23ho8r0 zh qu2 lorizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go oo h3.z qo22y ls8bh0urf the string?

Does an apple exert a gravitational force on the Earth? If so, howobw8 mug-p1,z0v mhgk;,+ d6xo ynyv pz-8lk* large a force? Consider an apply,zgkb8 dv8x*0- ywl mhvp,m6 ozpknu- 1 go;+e
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whvf npbh73f7a, at ways would the Moon’s orbit be diff f3b7h7anpf ,verent?

Which pulls harder gravitationally, the Earth on the Moon, or th bj, zp1afaxog++,2 nce Moon on the Earth? Which accelerates +gn 2,1o,j zbp cfx+aamore?

The Sun's gravitationad7:twdxmp+f n0p r81k l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for d: 1ndpxpwf +trk87m0 the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weighi( q d2(za,z0q7 s dcitlp)(syrcjv8- more at the equator or at the poles? What two effects are at q7st-2y jp(z 0,l8d i)dqriacczvs((work? Do they oppose each other?

The gravitational force on the Moon duecgk1172jthuead o 1+d to the Earth is only about half the force on the gjd271tek1cu ho1d+ aMoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Su13r7* aq eyka +/y2+d.plk ctnpoj+qfsn6c 5pn larger or smaller thappkn al*c y71t2d os q. e5ya+npqck63fj+r+/ n the centripetal acceleration of the Earth?

Would it require less speed to t tq1+p+xk:ugp( nj8t launch a satellite (a) toward the east or (b) toward the wet:+ng+kupp 8(j xq1ttst? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movcmk 70/w swgf3ing elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case wouldgf c swm037wk/ 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 spacemy cv- vnt5/ feb73oj5 could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical s-jnt/y e5o7cv5v m3fb hell 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 expmws* cv2sm9, leriences “free fall” or “apparent weightlessness” betwee,vmscs*l m9w 2n steps.

The Earth moves faster in its orbit around the Sun in January than in Ju dc c;04g,*w/f btt(ghcpjt3i ly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in ghdit/tc,4b0c c3j;*t fw gp (producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knownlwdj*iu v:;(a until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s massui*v(:a; jd wl.

  The Sun's gravitational pull on the Earth is much largeernry(bw(/ i5r 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 tb5((y/rriewn he 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 1980 a*ub: 3n;-e5e jvkgqs-hm o,k$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 z;9 owc4*z0 vi*q sogwthe Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radiuscosz*gv4z09woq ;i* w 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 as it rotates unib0joqh- +wjwklo/fe4 gjs lu.74+7 hq formly in a horizontal circle (at arm’s length) of radius 0.bkwh7w7.j/g +lsojuq f -e qhj+ol40490 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from w,r7fpha; rj: the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answerrawhp, ;fr: 7j in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the/q;7o20 f y )usajrduc acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diam7oafuy;s2/0 j r cd)queter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circl fa)wsn90o r(je of radius 72.0 cm , as shown in Fig. 5-33. If its sr (f0sa )nwjo9peed 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 roun(vb 8zua2p8-mshq km oq+iur,/s9:ky d 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 res:r iq9u +,(qsm8av-okbm syuk/pzh8 2 ult independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and th1t dipn/npy45e road if a car is to round a4pn/5dpni ty1 level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astron5t -jqbs3wfsjaap:0/auts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If sa: -3wbfjj0 p/saq5tthe 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 1 3/smpgpy1j qturntable 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/1msj p qgy31p friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling whe 4er vnulxfs/. l(r2j3n upside down at the top of a circlexl3 u2lrvn.s f4r/(ej
(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 r 3u7g2s3 armcato64psounded top of a hillt 2aoau 6c 4s3m7rpg3s (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions fbi8cu9 l2(kdper minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost9 (ld k28bufic point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of -nbwg jj//j5 cradius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket i/ jnw/cj5gb j-s 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 particle 9.00 cm from the axis 0hpyx1r ;4knlaiy 2:s of rotation is to exks ha pxi0y41;:n yr2lperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival(i8lqr 0a tk:l, people are rotated in a cylindrically walled "rr q8l a(i0:lktoom." (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 frictionless air-hockey ta3ndnoa bhwpo,g8,7 k +bletop, and is held in this orbit by a light cord connected to a dangling block (mass d,n,7boh+oak n8p3 g w 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 ign98f3e,3xf rtnpu .lpcrlg v. bz -(xe,oring the weight of the ball which revolves on a string 0.600 m long. Inzeu ft9.3x8.,g3l lvbrxc(-,p e nrpf particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked f*-to- 0wwuv r:m pfsi;or 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 masses p*+8n v4hhousqzd39m$ 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 manei+avx+rsy ,1 zuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and cent )z(xzd/ (fibjripetal components of the net force exerted on the dzbx( z/f(ij) 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 Indianay:p;kalgf25.e t v9 dgpolis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleratiol; 2:y av9g. kg5efdtpn. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal 9eyt :/q*kl6a d. whnpcircle of radius 2.90 m . At a particular instant, its acceleration w: n h.dt*/kal9qpy6eis 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 rad fuvuj ir4c. p.4a9nh9ii) above the Earth’s surface if its mass is 1350uc u a4jfrv.. pn499ih kg.   

  At the surface of a certain planet, the gravitational acceleration g p5ib2hh 0:zkw has a magnitude z:0iph2w5h bk 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 Moo2m29th / wa otqrd 3(oaz.sl9gn. The Moon's radius is 1.7ol/m9 h(.ro wag2 3sqz 9d2tat4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tiew7t/ rud 3oc)mes that of Earth, but has the same mass. What is the acceleration due to grtu/7o e)3wcd ravity near its surface?   

  A hypothetical planet has a ma,/kaisf1mxnq iq 0gcl*,n.8n s6ehq7ss 1.66 times that of Earth, but the same radius. What is / 0enss*6ih,8qaln,qckxmnf .71 g qig near its surface?   

  Two objects attract each other gravitationally with a foxfba6t3 rz(k4g /ahx)w nc4/p rce 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 gravity, at (a) 3200d3bfxjtfm a ,kr9 rr+6 u30)jb m 6fdrft )j,kx3j3u0ab rbm+r9    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth6fvxcb ja6ih0w:( tk) ’s center to a point outside the Earth where th )wbj:ia66v k xt(0cfhegravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of oey9n/ n 06nsygur Sun packed into a sphere about 10 km in radius. Estimaten g6/0ny sey9n the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, wh ,pl9g9.r2dwnyq/f1f(5) e ok ds ygibich once was an average star like our Sun but is now in the last stage of its eb 9wy rd9fynd )./ qof(1,sik2p5gglevolution, 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 t,.mcq qa qxz9-he 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 acceleration of gravity 250 km above the Earth’s qmcz x,q9.- qasurface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. ryz * ;y 5 *5j-e,jn:z:z dswdqdbunq2Calculate the magnitude and direction of the total gravitational force exerted on one : z qbn*r2qwn*zz j-yyj,u5sdd;d5:esphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on th: d9f moukp6g5qrylfky //l;, e same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, andlk;o/ y6, fp5ykf/9rudglmq: 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 4ic+ 3 ,on+ vibx7wbseof gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass x,vboi3i+scn 7+ 4e wbof Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periog4jj knyp20pjj:7b 0 od of the Earth and its distance from the Sun. [Noj0o 0 4p:j2g7k njpbyjte: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abouppy+16sp..jwz6tqh -( uq puyt the Earth at a heighh.zuyp- utyp p1jw.(q6sq+p 6t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite inr1uw9gw s7 .xjffm+.uto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (re sfjr7 fwu.u9 1wmg.+xlative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to s kd66)ehttsj05y+ -iha uq 6sexperience simulated gravity of 0.60 g?u hi656-ytk+6ts qj) ah0 dsse Assume the spaceship’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 orbia7h1cwww s +)y chm7o:t the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result w+ cm7wwo:)a 17yh schdepend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be0bd u) d)yxii/4jef/m g-u/ vf launched from the top of Mt. Everest to be placed in a cir4mv/ieyf0 i d df//-)uxbj)gucular orbit around the Earth?   

  During an Apollo lunar landij3 2wo.q *d0w3qq vkr3+qbzvqzd2rv; ng mission, the command module continued to orbit the Moon at an altq k2+3qrv *q2jd0w d.roq3z3 z;qvvwbitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice (bnl 92uc353fy2 eurrxlg1 zj that orbit the planet. The inner radius of the 2 9c31lyfne(z urxlru2gbj3 5 rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s qs9 +lf hj+r * qn5)aouml;x,bc owt4/(see Fig. 5–9). What is the rau9aqnq owb ,/fcs+m;l t)h5o4rx+j*l tio 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 weigh..tehc coj5 p+t of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity5.+tcjho.pe c ,     ----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. xs;;f a*cpv t-3j6usrThey are observed 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 each6s;v3txp -;s f uacj*r?    $\times 10^{29}$

  What will a spring scale read for the w fsd+i2ti (ek0eight of a 55-kg woman in an elevator that +0ktf i2( seidmoves
(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 a jzqohjvl63-*pc17xipte qjdw)uze62k3 *x7 n elevator. The cord can withstand a tensiq6p7k*zp-6jhdle3v*czt3 )xoq j1u wi72x e j on 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 a planetdhyq,194 vemdv-tv :k with period T , the density (mass/volume) of the plyt94m qv: v vk-hd1,deanet 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 determi squ40 u0./tusyow yvu; yd7u1ne the period ofu/047uduq.us yt0;y1 wvyo us an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thouov mil,2g-a91o: wcbqj3z e g*gh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun?2v l:ziwag*9cq1og 3e,mj ob-    $\times 10^{11}$

  Neptune is an average distance,bcxl -1cuyszt s ,wy+/k.k:dw4 b i s)qwo0e; of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly oncnzs) v7zyhvc8 :22s oje 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 ouz)vsns2yc7o :8 v 2zjht 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 xrgu (cl-g;7scenter 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 distancer 7 p60e*ptc3bstszp . for the four largest moons of Jupitep. 7sbpz s3t 6cpt0r*er (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 distance of th voi5/h 2w-yare Moon. ha vw 2yri5o-/   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’8/q2 d;dgueejs moons, using Kepler’s thir j eed/q8;g2dud law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter coln)1lqezod , z:sh u da4lav*9m8v2- ynsists of many fragments (which some spaus :v-o8l, 1aad*)ydv2ne zhzmql94l ce scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band coc.e 1p4k(mqt++cuh rlmpletely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always nklp h 4m+ct c1q(r+u.eoon). 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 an1(6h0wdvwhb-ac)yr .cg g8 ow arc from a hanging 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? Hisc) ra0w.(d bggy-18ho6wvhwc mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratio3 9j5 ratlg80dr3-ggw flnzz/n of gravity be half what it is on thjw /zg5rrga nz9dllg-f3830t e surface?    $\times 10^6$

  On an ice rink, two skafj5l81)k,t)yp z)rt h f+ o8dlcn4 ijeters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume8yto + e4npl r5,di)lzt1k8f)fj j h)c 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, thepb7 oo zz(r),epft*,q apparent acceleration of gravity at the equator is slightly less than it would bpfb(* ) zo pzto7eq,r,e 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 .qetlo r61 q(cEarth will a spacecraft traveling directly from the Earth to t qqcl1(6teo r.he Moon experience 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 hjvarf*1i0g /a bathroom scale in an elevator, it says your mass *ij /f0a1r hgvis 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of)c 7hhc izzz uh+af(2x,y9rd0 a circular tube that will rotate about its center (like a tubular bicy iy9xcdhcz2f ,(h7az)z+r h0ucle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fi 5eq:*p3 j8but pi60u sw/ubueg. 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 radimucf+ *n -;r3rlwba 1-xse(acus r, the acceleration due to gravity at its surface and the gravit;b3- aunc1+(mrxla -frscew*ational constant G.

A plumb bob (a mass m hanging on a striin25em5um2* uju+k9vw)/z uaaqs7 sk ng) is deflected from the vertical by an k25uj)uk/zmnq9am ua7sevw 2i 5u+s* 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 for a design speed of If thzask ) u0qx1j2e coefficient of static friction is 0.30 (wet pavement), at what qsj0k x2uaz) 1range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects a/ 0egqw 6wt igd4y7d+ tfdrub.f m-8/nt the equator were appaedqi+ m84gr-dy w0f/7nu/ .6tdwf tbgrently weightless?    $\times 10^3$s

  Two equal-mass starsl*h-bl kyod+ s ca6x/( maintain 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.z o3t.jk,vn h. A lamp suspended from the ceiling swings outhojvz t.n., 3k 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 ha4zm.. l2w 0zl uk4+wvs6w;v d*lafibjs been claimed that a person would be crushed by the force of gravity on a planet the si.wz4vl+;j 2ikw.04lu f mbv za sw6*dlze 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 Telesc c 702-af fendfh p7l39ahpal+ope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of+- l7p afpe7nh0fd2 lh9 f3aac 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 coniw wz, b6ua,d0stant speed 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? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go withou ,0iz6 auwbdw,t losing contact with the road at A?

  The Navstar Global Posith8 fh a kqn(*ma;zl3v(ioning System (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 four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nauav*m hn(f;h 3lzaq(8ktical 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 8 )+a ahbnnjk+q 2)cqk2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roug+k a2jbqn +c n8)qah)khly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellibg:k+8*l6jfyy ix vt+ te in need of repair. You are in a circular orbit of the same radius as the satellite (40y j*+bgxfki v+:t6ly80 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 years. (a) What is its mean b;j(i j8fk0mnu5naz , distance from the8mj b50 nfj,nk;za(ui 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 iyhd4i 70oi j5t cfts*1f you could actually "feel" yourself gravitationally attracteo ti*f 4jcd0s1iy th75d to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the ce0fki qpfrs-y 1hz7) s,nter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ligh1prh-fs)7zy qik f,s 0t-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 square,8xfkkre4/ tk 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 ofr 4ek8/fxk, kt the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 (g+6ok qvmor, 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 od2 /li9 afl9asf the 1.5-cm-long sweep second hand on / l2d9a9alsf iyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroun)fg 6(vi7m vbu8:cqbid in a circle below yo8:qbb7(i6)v i f vugmcu on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travel7s2h6bn* wuvk ya r1-ming at sp brny 7*kw6uamh s21v-eed $ 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 when n pvsd2m, bs1/wegotiating curves. The angle of tilt is a w1/s,sm 2dbpvdjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$