Sometimes people say that water is removed from clothes i a/pxh* /ioah:n a spin dryer by centrifugal force throh:/xi/ ao*phawing the water outward. What is wrong with this statement?

Will the acceleration of a car b(+0stm.u wl dbjd2b/i*iyee 7 e the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gbj/esl*(dui7 y0+m .2 dtebwi entle curve at the same speed? Explain.

Suppose a car moves at constant speed alongij( j+a+ .pbwx a hilly road. Where does the car exert the greatest and least forces on the road: (aa+.jpix(w+j b ) 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 force 7nat6fwhs)1n s acting on a child riding a horse on a merry-go-round. Which of these fots n wa)h6fn17rces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spiwk4 10vijz8c hlling out, even at the top of the circle whekw 81j v4hciz0n the bucket is upside down. Explain.

How many “accelerators” do you have in yo1q6 -6bwaeu xmno4-o4 lu lsi( 6rsyy-ur car? There are at least three controls in the car which can be used to cause the cl 66yq6msa i(4 eb1o-wny-u xsuo-r 4lar to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown dbuf*r * 1 xtkr(j;y 0kydstb t* 9a5)rbl.i4qin Fig. 5–31. His sled does not leave the ground (he does not achieve ty rtf jkrq0rd* b*btsyl4a )dik(;*ub1 9x5.“air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high s4d;ojwex)o / wk6xy uz/nl(t2 peed?

Why do airplanes bank when they tur)j exygy)3zj 6n? How would you compute the banking angle given its speed and )jex zy) yj3g6radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal tx(ymph0,.byv r1o +yplane. She wants to let go at precisely the right time so 1.( ryhboxmv py0+t,y 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 f 3,n-7j 3c6wr7b9udkbb5u,;pje a.bja qd mri orce on the Earth? If so, how large a force? Consider an appb 7n39,drac au3rib7wkdb j p6m,j;q-.je5bule
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’skr28(o5nsvrdjd*hm , orbit ,8v *jd(r2 orkh5smdn be different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon - )mmnivr6-pst 2cr* xon the Earth? Which accelerates mctxp6m--*2i)r vrmns ore?

The Sun's gravitational pull o8t4(liz3 k hzx9ja1k kn 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 3zx9zktl k (a8hijk 14the other.]

Will an object weigh more at the equat.2qof7 ha-f 62irbmj5 (tfgolj 9t 8yfor or at the poles? What two effects are at work? Do they oppojtfo2ftl6(7i8 o9rf 2 -hq .a m5bfjygse each other?

The gravitational force on the Moon due to the Earth is only about hacxdwah .2 6o8gol6gc8p6 ea+qlf the force on the Moon due to the Sun. Why isn’t the Moon pulled away from +62lae8 cpdw x8oh 6ag co6qg.the Earth?

Is the centripetal accele-2ls .zq cp4rjration of Mars in its orbit around the Sun larger or smaller than the centripetal accelerq2j -l.r4zspc ation of the Earth?

Would it require less speed to launch a u1d,v wsy8hty+(e. a usatellite (a) toward the east or (b) toward ue8ys,t. ay1h(wvu+d the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest+bqhwb1bj)(-z, :hr xfu ph2 n, as measured by a scale in a movi h+(nxb-1u f,:b hjqz )rpbhw2ng elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer sybc ;xwcz t9.9e.gbau:o:r .wpace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on o 9rw9yxc. .e obw.g::;bzucatur feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “fre (7fn iabd5s3.e,1 u d,btyaqbe fall” or “apparent weightlessness” between step.,53due,b disatnf( 71yaqbb s.

The Earth moves faster in its orbit around the Sun in January th +p(uyu0pq21lommdz (4uow.c *hrj 2ean in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing th2(2+*40rw ( opoeyzhlqm. juu 1mdcup e 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 known until it was discovered to have a moobzs*/3i x1abhn. Explain how this discovery enabled an estimate ofb3*h /z axs1bi Pluto’s mass.

  The Sun's gravitational pull on the Earth is m2t temjj1b0k *imh: 6wuch larger than the Moon's. Yet the Moon's is mainly resbtjmemt 2* w160hki:j ponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling g..rd.cpt2 ,moi9xy y 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 orbmo12ieki jy8*o i yl-8rx+ 4mqit around the Sun, and thm1 8mix-y8 irqooe42kyilj +*e net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on avaurd2 r4h8f4 2.0-kg discus as it rotates uniformly fdvr 2au8 r4h4in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eartn.4r q5n o-faeh's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your ans5non- qr4 efa.wer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acfmk zjo1ghxf*x+j d- n97i;( cckj5r6celeration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheeij 5zk*f d+fjc onxx7;6j( k 9r-cgm1hl’s diameter is 32 cm?   

  A ball on the end of a string is revolved atw2f sk3qj* 5o.jsdgt, a uniform rate in a vertical circlejs,o5gf2 k3 qdtw j.*s of radius 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 turn of4od e-4aea m7y radius 77 m on a flat road if the coefficient 44m-a 7eeyo adof static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frwe*e1knnt 3;jf als;e 18/yxv iction be between the tires and the road if a car is to round a level curve of radius ewj/ 18 vk1s ;eantyf x3;ne*l85 m at a speed of 95km/h ?   

  A device for training as/h ilhqw1 k:g(aoob 8*tronauts and jet fighter pilots is designed to rotate a trainee in a horizontal cir( i1hkw:bh 8*gqo alo/cle 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 aml/ qy(;1e p*y2oci ie rotating turntable of variable speed. When the spe;cimiy p2oeq1 *l(e /yed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelify24dv84e8ehafmye ):uz0 ajng when upside down at the top)z4e e0f2afmvh ja:e8u8yy4d 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 n+-m/ojyk) mzj7 ic9f driver) crosses the rounded top of a hill (radom97izn)ckm j / fy-j+ius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diamete-hed2 z;qgz b-2- hvxrr Ferris wheel need to make for the passengers to2-h -e z2x-bgrhqdzv; feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cdu/ pv;od3mz9:.s lak 82n kyxircle of radius 1.10 m. At the l lv: o /3ds.kpxnadm;kzu9y 82owest point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from thkrz,3om+c 6cp(k jy j;e axis of rotation is to experience an acceleration of +py3 or(,z;jm jkck6c 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a c ;e k+0w0ijk ed:3rl,-,jozl c0mkt nnarnival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.) zen w30,j0i+e-ol ;c,dl ntkj: 0kmrk
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 f1 g))z.gko((iqbmm imrictionless air-hockey tableki )iggqb(m1(m)o z m.top, 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.eitx*a7(fo1xyl+ s a9vnes1da a2 +x, by not ignoring the weight of the ball which revolves on a strien+1diea 9altf x2a17sva( *y.x+xsong 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 perfectly banked for a car traveling n8y g oky4m:3vms y02o9k5peo 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 oj:9c /jf+ dik$ 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 vepyjz qzvc6w. em*opby/+so7 y ;;-)djrtically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of tn7o8r x+xiod8d c-uqdr v2kk0l za++ 6he net force exerted on the car (by the ground) in Example 5-8 when its sxz6qndd0x+k88+ 2icrou7kro-alv+ d peed 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 from the pit a-bvf/(xn(. ehjyg/hxo1 mch+ rea, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be be+ f ybjxv/coxh hn-(1g/m.(he tween the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular b),tlkdq vf;) instant, its acceleration ikdv ,f)t )b;lqs 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 voq. *- srtq6b1zrc7wEarth radii) above the Earth’s surface if its mass qr s6trc7*1.vzbqw -o is 1350 kg.   

  At the surface of a certain plu1xy,zubf 1g,0uo 1doanet, the gravitational acceleration g has a magnitude of 12 m/oz u1 g,by1f0uux 1od,s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon1wsw:bn ,a9vo's radius is 1.74 wwovnb1 9s ,a:$\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 ma14j g6fss x8k5midp ;vss. What is tv;mdp fxs kg i4sj6851he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass6aw+q u2 o3473bdi wddr*e3vkl-pkpc 1.66 times that of Earth, but the same radius. What is g7 - 2*cw 6ak 3wp3uedp4vkr+dblio3q d near its surface?   

  Two objects attract each other gravitationally with a forck jgexk 0p9 nx86b7sv9.q:h roe 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 gl9oxkw) je/e;a y5 t7gravity, at (a) 3200 m ej;x/ g7l5)t awk o9ey   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E lxcm k4+.aix78mgs0 warth’s center to a point outside the Earth where thegravitational acceleration due to the Earth lmamxcxki.40s7w+8g is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thqv: +ds (/u jwyqmkuxzm,.77 re mass of our Sun packed into a sphere about 10 km in radius. Estima.w+:s,uvxmkmzqrd 7uq/ 7 (jyte the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like ou; gb wi-8cw86bm 6s mxhj;v+hur Sun but is nowwvjxi s68u;-6 +m gcwb h;mhb8 in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feelnva tq tj- 8cs3y6fvp6rc b719 weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was ju98q7bc-sj3tpnfyc6avtv 61 rst a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners ofnb4zj nz::0 cok*rcrmf -/w y2 a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exertern :y:zb zo/*cnr0kjw-2m f4cd on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yerm gq ou7 w1cv30z gw,:ewi39a8o.hh tars most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming arg 3m9wzeo.uhw ,c7g3 qi08hva1o:twll 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 1 z1i pya1w,8ypccyok 220:ezt, mjqqof gravity at the surface of Mars is 0.38 of what it is on Earth, and that a 1p2y:k81 qy2,w ope qj1tzzi0yc,mcMars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valfamk. sck8x uszlks15 o96v4. ue for the period of the Earth and its distance from the Sun.x cso48ma s5lv69 1zs ..fkukk [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of kq2miv y t*f 8p1cy023 mji;ul qdc.v.a satellite moving in a stable circular orbit about the Earth at a *23q80cd kv iytcpm v .j.qy2m1ufli;height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circ, www5k*wx(lr ular orbit 650 km above the Earth. How5r(wkxw*w,l w fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experieqbrpnsuk4*g22 xkcfn3h9 ( -o nce simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Figsk4 xpc r-n2 nhk2qbf(9u*o3 g 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cd.ug3eh0w 0 xpircular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to w pu.e0 3xdh0gthe 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 f98v4vh/02vxwh * rogut9gv.ue 7mn xgrom the top of Mt. Ev m 2nxog8v9v9v*hxug7t ru0wgh. /4 veerest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar land*:vfbaf q(g v/ing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Mooaqbv*:fg v(f/n once?    s

  The rings of Saturn are composed of qdv6fn7 1gnvgabqn05e t ( ls-w9o 7sjr,/wt6 chunks of ice that orbit the planet. The inner radius of the rings6b7n-tg j9g wqqs5(l1/nefr st, 7wodnv 06av 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 15.4pioy1sn b f:*)y2y rw5 s (see Fig. 5–9). What is the ratio of 2)b*wp1 fyisn4 oyy:ra 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 420ywo8cj/1d 2gya2nw --6dkgs :kb si7l0 km from the center of the Earth's Moon in a space vehicle (a) moving at constanbawg-ys:sokdicl d2n / wyj 2k87 g1-6t 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 mass. They arey8 blrdm1f 3kd .k7s8h observed to be separated by 360 million km and take 5.7 Earth yed3hk8.fmrys 87k dbl1ars to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale r3z,pwn bpxqdf8des-5 p 7qi.e+0 wfj7 ead for the weight of a 55-kg woman in an elevator that q5p7d jxes,d80 w.fq 7+ we3zn-ifbpp moves
(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 susp h- p,;k4z;fxw-jqmi(oijykr( ton/s (;gq-fended 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 atr m(z;g;wq /siyjon-p 4,- h k-ojf;ki((xqfcceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with phdn*8hu7ps h9a8ngr +7you/e d06vyj eriod T , the density (mass/volume) of the planet i+7du9 pu*8ndhn 8hgvajs0y /o7yr h6 es $\rho=m / V=3 \pi / G T^{2}$ .
(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 de/4(;. b gl*1wxly+t stqkfrgqtermine the period of an artificial satellite orbiting very near the Earth’s suklg ; 4bqq.x*/ flt(ywt+r1g srface.    s

  The asteroid Icarus, though only a few hundred met 2fi4.ztbsg- 6dus *b8axgo*yers across, orbits the Sun like the planets. Its period is 410 d. What is its mean disfi. ds4gayz8b6o* xtb g2- us*tance from the Sun?    $\times 10^{11}$

  Neptune is an average distance -dmh+cl on+ 0 ,ygv5gdof 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very cleobzp 3o.be08ose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: Thp3o o.zbe 0be8e mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy cu;4a b2 jl/iq $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 largesb1y)k+ jyka +lt moons of Jy+a+b1kyk jl )upiter (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 perign:/if4tgi 8caxgbw. y mo .myek*8.+od and distance of the Moon. nxiyib t.k/y ef.8:oac w.+4gg 8mmg*    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of8vtww;v 9-vbb Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. vv-w 9bv;tbw8Compare 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 consists eig83:bzw a r:1usx -nof many fragments (which some -:n:8zwgx1rei sub3a space 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 )ai plgzn03fg(-o h-wan artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an appo3(z w-nalh -fgp0)gi arent 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 m5gwm24cx)l skb18al by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of ) g8mcla4xl wmbs51k2exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hhd,6v9-peclzn p0 jp5alf what it is jezvln 5pp96h -cdp0,on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hpi*74a8ha.eikulet/6 dge ( uands and spin in a mutual circle once every 2.5 s. If we assume their armsi7/gi6eud(* auklte hp8ae4. 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 oncrzwnm0 y q:dsq.gbo k13 q;x/5e per day, the apparent acceleration of gravity at the eb.0 :5w/g d 1q;nz kqmsx3oyrqquator 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 spaceu7gluop((c u, craft traveling directly from the Earth to the Moon experience zero net 7l u( guo,ucp(force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass isosi ay;k5-*k-a01;ap ltutqv 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which5a;k-i-q sa 0 p;yut oa*lv1kt direction?     ----待选择----upwartddown 

  A projected space station consists of c0bst4,)nfbrr6 kjs2 2ed 2ib 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 (revolutions per day) if an effect equal to gravb0sbekn j 2tr2)d,2bcf6 sir4ity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his8xdf)egv ;vt, aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a plae au.e )*;a:.x+sndknpmt: wynet in terms of its radius r, the acceleration due to gravity at its surface and the gymt: n ea*n)u:ep.dw+kxs. a;ravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ,6ts+ofw5g dovertical by an swo+g56ftdo , 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 baney n3 j ,9rb 7m-kkcu(g8uhp*hked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds canu,g8h(h-pnj k9yb mceu*3k7r a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at9/mps c3o:+qexp5r- thpq l. z the equator were apparently weightless?m.5qh:qz- l/s pe+ rc9x3tppo    $\times 10^3$s

  Two equal-mass stars main(5rjga- sajwvj 3i,4 y1t4xyh tain 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(b-1ow2ah3k6y(k neqahy8hgkxf24k89 r tb y suspended from the ceiling sgnk2-y 93e 46tqh1ak(kyrx8oh hy82b k af(w bwings 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, idz40 yl-cu t:dt has been claimed that a person would bdlt0: yzu-4cd e 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 equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extreme k2n0 ) i5kx5fujf78 aj1skhj, irrhou75wx+sly 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 gas clouds o7 a8xh1xj5ik5 jwhj rf5+urk)2n f,0ossiuk7rbiting 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 traversy ; 3ul5 e8n8iq0*lwgq*slvr les the hill and valley shown in Fig. 5–45.l;ll0w ys8nr8giu* lqv 5*e q3 Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a groue tif8 )vo(h3sp 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 a if)8tsvo( eh3re 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 Rende(cq2y vj( +pii xw .sgi88o,tpqggs5b zz;4u :zvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rouv yu b:qj i(gs ic+54gq;28pgwxso,z(.it8zpghly 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 shutt,i)mgown 6l+lle pursuing a satellite in need of repair.6+woglm) lin, You 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 years. (a) What is its me,(( s0:v bh;agkyknydan distance fro0y ( dkvyag(:; bns,hkm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuallphnc1v l/qbg2l oal160m 0 wt 9h,;txiy "feel" yourself gravitationally attracted to someone near you. Make reasonab0ttp/g6cl92, 1h owmla;b hvq nl1 xi0le assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wayia2h33t9+nv8zv q ghq Galaxy (Fig. 5-46) at a distance of about 30,000 li n 8izhqthv 39g+a3v2qght-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 0.50 m on each sidwtgj0vj7m2 6ye. Find the magnitude and direction of the gravitational force on 6j7 gjmwt2y0v 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 550 t9;,) dwoox: yjcx(o.aze:tbf 3in7t0 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 exper h*b w0sn-w5 2qp* b2xicrqqq4; +bqseienced by the tip of the 1.5-cm-long sweep second ha + 4qwsqw; *bsi2*qecb2qp0nxqr5 h b-nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinke hn fm09w83x s4auv(ecr weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: 908wh3n ume a(xv4cfs See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tcra6x6o;n v hs+/a /aeraveling atavsr+ xe/ 6ch ;/naoa6 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 vq-5ga (jpwu 4train, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal 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 (appr(gpav 54j w-uqoximately ). (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.$\approx$    $\times 10^2$