Sometimes people say that water is removed from clothesya/a-w7zu6 e7dk t 6e 6+r6r z5jqhbgk in a spin dryer by centrifugal force throwing the water outward. What is wrong with this sta65zj6 7bwqz +rhee/dr kkt au66ga7-y tement?

Will the acceleration of a)bjka8b m nft2p-0h; m8ynx.w car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle cbth fk2;nw-px8n 8a0. )ymmj burve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the cvlld3b86 ksn 1ar exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between tlskb18n6d v3 lwo hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child rij(w tkn(uk2l ,ding a horse on a merry-go-round. Which of these forces provides the centripetal acceleru nk(j,tklw2 (ation of the child?

A bucket of water can be whirled in a vertical circle without the wsc9lk pio71 6j(g 3cutater spilling out, even at the top of the circle when the bucket is upside k(6l9 3s1gccjtoup i7 down. Explain.

How many “accelerators” do you have in your car? There are at least three coj3zw7m0)vzv uz 5a8(qu*s dvintrols in the car which can be used to caus wi0qmv)a*zs5 (jd8v7z uu3zve the car 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 shownt9w pui c0*0w,wdfj+b in Fig. 5–31. His sled does not leave the grount0wpif+9 cd0w ,u*bj wd (he does not achieve “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 r*umz :h5 tv(doounding a curve at high speed?

Why do airplanes bank when they turn? How would you compuw8/rm )k, :fem63e5xv o tqnjmte the banking angle given it6kr tmqxm8)mvoj5 n3 few,/:e s speed and radius of the turn?

A girl is whirling a ball on a stril4 8ps/v w d4*geqds,6eiui25 cnwrz3ng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a ta5i/e42 edd 3u6*vipssrl8ncqww ,gz 4rget on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forc42 2m4i jyynwan*ic5n9( eb ghe? Chy(mnib9g* 4n5a2 cwi4y2 nej onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit naa66v.zaub gla- ) + ;exwot0mv )+eabeub lmx+avvanegzw ; ote+6 .a-6a0))a different?

Which pulls harder gravitationally, the Earth on the Moon, or ccq7x 0d2 hc;4eegtwlf.5b+wthe Moon on the Earth? Which acceleratesc xc 07 +wete2.5c hbw;qdg4lf more?

The Sun's gravitational pull on thq1xh jeu2 lpx3.bp*9ue 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 othh u*1xpu2.jq 93pxlbe er.]

Will an object weigh more at the equator or at the poles? Wuj i9/0) n/7ixlrq lpqhat two effects are at workj)0x//rlup9q nil 7iq? Do they oppose each other?

The gravitational force on thegt2b2 4g1imk i Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the 12mgkg42b tiiEarth?

Is the centripetal acce*ec:gchnd 3 e4leration of Mars in its orbit around the Sun larger or smalccn:ge3 4* dehler than the centripetal acceleration of the Earth?

Would it require less speed to la oo55gtv;w bcfc, c:3pl*nuy9unch a satellite (a) toward the east or (b) toward the west? Consider thegtfonpb y3:;9 5wcl5o* ucv,c Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a mo7-n8 g3( (f -qdgl/qlauefpnhving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case3un(q/87g -al- gfph(lfq den 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 + / hwt9fbyx,ube 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). Explainbw txfu+y9,/h how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free hb8c;e up atjql;u3;:fall” or “apparent weightlessness” between stepq3u;a:hl ;t;bc8pj eus.

The Earth moves faster in its orbit arox tcmj1gz3 n.sdf 8)7xund the Sun in January than in July. Is the Earth closer to the Sun ix318stdgfc)m. nzxj7 n 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 Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it w)nua34i 5vlw 4kigh*a88 v st:ff7l ltas discovered to have a moon. Explain how this discovery enabled an es)a48t 4iunvl:sat w fhf v8 7kl*li5g3timate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moo 8r4tj);g6rx3ksu uwkn'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 ch)r3kwu6k 4srjx8 ;tugild 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 db,h5be xeybo3ncpq; p.10kqz ut3 6: ybtm;6$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 cwobxj6yq xvd0/24h0orbit around the Sun, and the net force exerted on the Earth. What exerts this force on thexx60whd vjb42c/0 oyq 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 excnvy71,.g hy xerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at a1ncx y7.y, vghrm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in blc ) r5hp/cigfg3l32 orbit 400 km from 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 answer in terms of g , the gravitationairg35lf2c c/ l)pbgh3 l acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge o, oepzq)1 ruy-f a potter’s wheel turning at 45 rpm (revolutions per minute)o p,-yeuzr1q) if the wheel’s diameter is 32 cm?   

  A ball on the end of a s8 qzl+pv) n 6) iee/(lj ogmz87zakfcaial7 ,1tring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 7 )i /7paencl akeq(fmvl18 zi+8zazo),g6l j$\mathrm{~m} / \mathrm{s}$ 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 sgnkzh;50olrp)5g f1 m peed with which a 1050-kg car can round a turn of radius 77 m on a flatz05p gmkfn)gh5;1or l road if the coefficient of 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 frictie.pfsd y zcu0mve00; *on be between the tires and the road if a car is fc00 0 my;upse* z.evdto round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desi 3yj9idq5/-p qga(gpzgned to rotate a trainee in a horizontal circle of qja- /5(pqzp i9dy 3ggradius 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 turntable of varianqt lvi *:i9bvm2s 0q il/)xj1ble 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 fricj0v*i 2q1in/ xv9 ls ml:)biqttion between the coin and the turntable?   

  At what minimum speed must a rollefj fm m+)f8 rde s1(:c4jky*gyr coaster be traveling when upside down at the top of a circ4j8m1df ysjrm (:ffgk +*)cyele
(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 i4dq p(mq9x)mjt3i: h950 kg (including the driver) crosses the rounded top of a h9x 3 )m:i pj(qhitqmd4ill (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 per minute woqiddcj1su 62 7uld a 15-m-diameter Ferris wheel need to make for the passengers to feel u1ijq7dd62cs “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of9gp8*b+a*li oe 8 sjr:/rjadgx si7(z radius 1.10 m. At the lowest point of its motion the tension in the rope sg xjz /prdaeoa :8 7ij*+sgb(rli*89supporting 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 sstpm w d 9e u0)tr*wvp2+/(asparticle 9.00 cm from the axis of pv w9*up 2+r/at( ss)t0mdwse rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a z.g l4* .o fzlt2fibbof193 slcylindrically walled "room."o 3 zf l9ilbf 4.t1lboz*.2sfg (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 frictionus(bbb6gb:a 7less air-hockey tabletop,ga6b:sbbb 7u( 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 yjbn g1;1b 7mwtime, by not ignoring the weight of the ball which revolves on a string 0.6m7bgbn 1y; j1w00 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 9y yy;h2ov) rpof 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses v6 x3cbgz1 f5q9jsih9$ 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.so:7uqsvtb 3p ,qc0koz 3v8b 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 compont/ ttdn;f ;j hh8l0srk3/u 5w +rzin6yents of the net force exerted on the car (by rtk ;h/ 0;8 ytl/nuirj+ h35nzstd6fwthe ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going ftt6ap 2)pymlm omo28auh s9, 2rom rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial accelerationposymoa,8 u262l9m)t 2mptah of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in apjpba5az +( :d horizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05a b5pzja:( pd+ $\mathrm{~m} / \mathrm{s}^{2}$ , 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 spa o -ilzrky*a /7xlnv)tu)a;y 2cecraft 12,800 km (2 Earth radii) above the Earth ) n)al2xo *;-artuiy/yz vlk7’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationa7cv;-phez k j3giqg yk +o0n+.l acceleration g has a magnitude of 1 k+j3.h zyk; 0ggi-oqcenvp+ 72 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 acceleratio+pw g o6)1d. vs-kktc;fkg qj2n due to gravity on the Moon. The Moon's radius is 1.7fswgkj 1 -;6v)d+k2 .pto ckqg4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has je:8( )ua.y0jqlw cbs a radius 1.5 times that of Earth, but has the same mass. What is l qjj a.):8cbuewys(0the acceleration due to gravity near its surface?   

  A hypothetical planet has a masr q* gpug7x4eys 8 ff)/0cc4douu3on 4s 1.66 times that of Earth, but the same radius. What is gxfr4c0yes3u8o g 44c/)do *f u7q gupn near its surface?   

  Two objects attract each other gravitationally with a force of 2.5v26s zl*o r7p3gw ;y9fny+fr vsqh.u5$ \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 oemizm1 kbaoj c(4.j;ox kh) ckf77+/cf g , the acceleration of gravity, at (a) 3200 mjk1m47 zo(+ i;/ckhoc7mjax)ekc bf .    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center th0g5d,o: x kpxxqe7 (xo a point outside the Earth where thegravitational acceleration dx7p 5, xhg0ekq(:xxo due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fc(sus: 6. atjkive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity :.(stk j6ac uson this monster.    $\times10^12$

  A typical white-dwarf star, which once wased hq:(v. kmj3gg/ kj: an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass3qvj/kg jk em:(.dgh : of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitia6xus;0clz: -+xjgp f,m* or mng in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g. jr xgmc6 s :mlfa0;z,ux -+o*p  

  Four 9.5-kg spheres are located at the corners of a square of side 0.neekulv :6)*ho)nvze mw q2- 160 m. Calculate the magnitude and direction of the total gravun-e6: wenl evv ohz *)qm12k)itational 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 5rr kkah3 g10i)fnug1 the Sun. Calculate the total force on the Earth due to Ve)n 1 uka0ig f1rr3hgk5nus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 o yznnq7 6 sj;hfy99a,vf what it is on Earth, and that Mars’ radius is 3400 km, determine the m n9zj,hfav7s6; n9 qyyass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period sqd6)*b3 1ahd) laiufof the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usii*a)s d )16u3hq lbfdang Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about gd(* :u9m)enwnz6;ihmbbv4 klur*a . the Earth at a hezd)i*emhb ;a(bg49:nwu6m.*k r l uv night of 3600 km.    $\times 10^3$

  The space shuttle releases v; q- .:mub 1h)t cp8bk6pq5ws2elxrba satellite into a circular orbit 650 km above the Eaq w bl.1rmhv2b;6pcp8)b:s tx eku5-qrth. How 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 ex)n +v-2naw6fh la)6j z f95x5ic yfgpxperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your j y a66 5)fg29xi-wvfap)fn+l hxz5ncanswer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to o +1-a*q lluhz *qbxns0rbit the Earth in a circular “near-E-anhl 0u 1xlq*q+b zs*arth” 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 depend on the mass of the satellite?    s ~    min

  At what horizontal veloci s* 12s*d8 *estbly( qpaltlp69jhd 6uty would a satellite have to be launched from the top of Mt.* 61qj *2dp 9lbslst* 6dps( ltehu8ya Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contielo1( )3 1f(oq a5ugnmez4z r1ifk;gmnued to orbit the Moon at an aln u)or(41g;aioz q zm1e l5k gfm1(fe3titude 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 that orbit the planet.cyp/-t/v+a8llw6 wtxa cdw- , The inner radius o-tx+a - ,wv a/w y/tdpll8cc6wf the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in di9dv ar*ry4ig 9ameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at thev9rr4 *yaid9g top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of blb)8wpvqtf867 ayfodzfl-+ tr, k3+the Earth's Moon in a space vehicle (a) moving at constafbf)d+6ylp8ka8,7t wl vb+tzfr 3q -o nt 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.8px.szx6z*t c They are observed to be separated by 360 million km and take 5.7 Ear. xtp*zc6s x8zth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight oo v6x.pcq*xf ;g/2pw9d0u vvof a 55-kg woman in an elevator thatgw*.u29vvxo pd c/ 6p;f0 xoqv 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 suspended from the ceiling of an elevator. ex1: )6n4pg bsa2hhm x z9j1rnThe cord can withstand 4 ab: 6x)s nmr19xnez1hhg2pja 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 j4k:apblr 3m;b ,.czlv7d z9g surface of a planet with period T , the density (massa.pjb3;4lzz9 : bgv7 l,cmrd k/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 thctpv57l, ce( oq.by2 o(8hlmhe Moon (27.4 d) to determine the period of an artificial sah hltmv (e2p75cob(,olq8cy.tellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though onaxa4 :+5 r00g twetlelly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distal0+tra:te504xg w la ence from the Sun?    $\times 10^{11}$

  Neptune is an average 5;yg wqhufht4q, /rc :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 the Sun roughly once)) qzb/m4yfhv every 76 years. It comes very close to the surfahzmf)b4yv q )/ce of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third 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 Galaxyv2is ; )nxju00obx nb: $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 foi9 kbg+.p/q rfr the four largest moons of 9.+i rqb/pgk fJupiter (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 periodn+ 1*9ibyr*g za7 dwnw and distance of the Moon. iyg*wn 9wzn+d*1a 7 rb   $\times 10^{24}$

  Determine the mean distance from Jupiter c,ckz*oo5um ,7u cdjc8 u*h+bfor 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 the values in m+, bu7cuh*, kc*c8odo5juczthe 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 consistw1rzr ea.s1 k9s of many fragments (which some space scientists think came from a planet that once orbited the Su e9r1zrw .ska1n 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 co y7lny*:i9cq8ayzy ; vmpletely 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 ti y y79:*8ayzcny lv;qhe band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from*ln d2f 98whu :ok2cek bxn.u7 a hanging vine (Fig. 5–41). If his arms are capable of exerting a force uw :n2kfnh kle2 dxc8.b97uo*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 half whfgnw2:;v+copwfsdne5 m9--x at it is on the sp-fe2x5g:ow9wf ncm+vd n ;s-urface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin id* md* x pci8fm.em31,vegvt: n a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on m*v*vmtg p,dc83 1.d:efiexm one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparenth e8g+vn b53x1+e*dzyl la9 by acceleration of gravity at the equator is slightly less than it would be if t*y + 1zhvd 8e9+l bbax3ygln5ehe Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from f se q;dawya784sl4e- the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earthlaywq;8 asfes4d -e47 and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale2ksvkn,)u ss * in an elevator, it says your mass is 82 kg. What is the acceler vsk,)*usnks2ation of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statiox)cye2.g c(lafag/1cko -u .;qoi ,sb n consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Eartgy,okuaic.sq12 ;cl( ofbec.g-)/x ah (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a en2jie 3x; ip/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 planet in terggz h i rck ag7z;94ave4r(:0ems of its radius r, the acceleration due to gravity at its surface and the gravitational cee:g(g9 70akhva4z gr;c r 4izonstant G.

A plumb bob (a mass m hanging oo;,cb8e;v m xjn a string) is deflected from the vertical by an angle jvb ;cem ;xo,8 $\theta$ 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 banky-ic1: p8dga /dqtow ,ed for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safdy-1wop qgc iad, /8t:ely handle the curve?

  How long would a day be if the Earth were rotating so 11m fr+dv8am9r la q8vfast that objects at the equator were apparently weightlefrvq18daa9r1v8 + lm mss?    $\times 10^3$s

  Two equal-mass stars maintain a constant qexdhwd c6/-e/1 kx ;ddistance 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 7iaezy-yd 8ee/887n tame+ b s235 m. A lamp suspende8ee 8ma +yd87 nyisteb-7 ez/ad from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth.)*: ;d 9d8wnb6uwhu tvypz7-ye8 hu fk Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person wodw;u8 h-d)u ytzpk7bny8*hve 9wf6u :uld 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 ed )+e a/k(nuwwp7+paHubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87,n+ee /ad upp )ka7+w(w so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley sh3gy873b*ql8 n0av)lv wcn qs jown 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 cas3lgbn jw cn vq* )3ql87yv8a0n the car go without losing contact with the road at A?

  The Navstar Global Positioning System 1+gy9vfofr( 8ivx*co (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangr(fx*cv9y+ go vi1f8oulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bqf h5b/zvtt+lm 69v 0iillion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is vm05/tv ihfq6lt+zb9roughly 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 sh 5*+f xtzuy8v- nbk r(8c 8tnpq6jj(yruttle pursuing a satellite in need of repair. You are in a circular orbincyb x- r((j 6k5qry 88u ttpfzv8j*n+t 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 perio7a /zoi(6ej nnd of 3000 years. (a) What is its mean distance froanjo/76ei ( znm 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 +e url .2lmq5lcould actually "feel" yourself gravitationally attracted to sl5+rq.l2lm ue omeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy ( hty c-,)73racifzz x1Fig. 5-46) at a distance ofchry1)ci7z, 3a- t xzf about 30,000 light-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 ar x,9ofbg0n t6umfmf99 e located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fi9uf 9xnf0 mmf,gb6o9tfth 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 5500 kg orbits the plvg j+,- ov h6p ),eb2nb6kznEarth $ \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 experienceig( z( 1ip+c:z8viti(s i ;nxxd by the tip of the 1.5-cm-long sweep second hand on your wrisx v8z;p is:i((1niizg+x( ctit watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing d8kxo of x/lz/wcuc +d-,1in6 a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle ec-xozu81,f 6nkodw+/x/ c d ilvery 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 zp7yk/nw4nc5 xx i24ea new highway is designed so that a car traveling at spepyx/7w k 4nn24zce5ix ed $ 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 traiedir m 88dflvh+i,t3. si wb30n, 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 frii ersdbd8,fvw.83 3 mlt0hi i+ction 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.$\approx$    $\times 10^2$