Sometimes people say that water is removed from clothes in a spin dryer by 0 afps x:n4a9vcentrifugal forcfsv90ax :a 4pne throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when)+butc(fc+)xc u p z c/0lw6yg the car travels around a sharp curve at a)bw0t uy+upc+ zcc(c/f6xl) g constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly w2,*iyft /f leu(9r m7 ztikqav9/h2iroad. Where does the car exert the greatest and least forces on the road: (9i a9mqt27i(y vwi*h//f,ztrku2 lef 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 forbn f*,3u67et vuj 9l7la ghw;gii4 ta-ces acting on a child riding a horse on a merry-go-round. Which of these fo, u;lgbe wht4a76ivng*j9 3-lfa7tiu rces provides the centripetal acceleration of the child?

A bucket of water can be whirled i30 zlertul; a6n a vertical circle without the water spilling out, even ue0talr z 63l;at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? a34 ln5mh)ndxehbq 6 2There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What 63hbx mn lq4)nhde5a2accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shoyl++ *pcgrh8zwn in Fig. 5–31. His sled does not leave the groug h*+8 rlc+pzynd (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 inware6 m5rkier66;hmro u8d when rounding a curve at high speed?

Why do airplanes bank when -(xv.gd4s)tn 9dc 5vdiy. lu+zh es+tthey turn? How would you compute the banking angle givsc(.i)d nzsvt5d-+4g hu v.t9x + ledyen its speed and radius of the turn?

A girl is whirling a ball on a strin chp4xaz7 7sd1g around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of thph 1szd4xa7 7ce string?

Does an apple exert a gravitational force on a3ado :l;8b pm3xj-l 7 ys+lktthe Earth? If so, how large a force? Consider l3lp 3a lo;kbatmj8 :d7+x-syan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wo e0g6cdr53 zyxuld the Moon’s orbit be differen ed3 z5yrcg6x0t?

Which pulls harder gravitationally, the Earth on the Moon, or the Mooe6ykqay00 mic(/ kv)bn on the Earthb60c) y0 ye/vi(akm kq? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yeu gj.y2f; hp0**l ziiat the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational *. *ui;a y2h0zpfgljipull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles4tf- gnnasu7 z+e d 1/i1sfov)? What two effects are at work? Do they oppose each oi4nd11)fasv-go7ufn +et zs/ ther?

The gravitational force on the Moon due4) ma-gsk ,( vtz*tljk to the Earth is only about half the force on the Moon due to the Sun. Why isn’t t kgt)m 4 ,zv-ja(lkst*he Moon pulled away from the Earth?

Is the centripetal acceleratiow i;-jhonb3r croy56r9,x7m v n of Mars in its orbit around the Sun larger or smaller than the centripetal acceleraiohoyjcb 59 w7x,;36rrr-n mvtion of the Earth?

Would it require less speed to launch a satellite (a) toward q6bx,an(3bzp2av1 (nt cp zy* the east or (b) towc(2xa,a1ztv(qbz* pb pn 6ny 3ard the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured 5/k q :xgorld k/ae9x;g d*n/sw4cew )by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, :grde/*/l4o;nxewdxck/5qg 9aws k ) (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 if1:5hlw jievbp 8x.f 5n outer space 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. 85il1jwfpbe :.vfx 5hConsider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betweeze xb03 tjs4oz4np1ktqiku e . /84n .(lmcyx;nm. .zuz4/3 ;kiyntxo(jntx48c pseeq 10lb k4 steps.

The Earth moves faster lu4; gbzp+ -rmin its orbit around the Sun in January than 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 the seasons — the main factor is the tilt of the Earth’s axis relative to the plane mblp;r+ 4uzg-of its orbit.]

The mass of Pluto was not known until it was discovered to have a mo0+p,a i,ubiczuunkmm r8 /6 h9on. Explain how this dismnrp, 8u/ icbkzuh60i,a m9u+covery enabled an estimate of Pluto’s mass.

  The Sun's gravitationabrk5jld m,ihxzpn b1p*z(7:f e, e)i1l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the ot*(m1)k,z7e51i rb xp bh,ifz jnldp :eher.]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 0 8xerssutdf *i3 j.sncl7+ 8r1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratio :i mw3.* bh9/cbj5t:kzlj evwn of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume thaeb:w iwm35/: 9lhjjtcv. *k bzt 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 oftrbh74gla dp+i4eu88 g . qvm)3y5xqo 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circlu m.x 3qyhiob)g4pt84 5 vgq7e l8+drae (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in oc8op3regw e0x5w4s .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 ofs3epoo40.egw 58r c xw g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of xo::k g;q7xrrthe 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 dia:krxr:q7x o;g meter is 32 cm?   

  A ball on the end of a stringt x6i)dl9 kvo*um3c.v is revolved at a uniform rate in a vertical circle of radius 72.0 cm , uc txmvv d.*)l369kioas 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 turxbi,.:gjxan ne8)f g+aym: q *n of radius 77 m on a flat road if the coefficient of static friction between tires and roadf)nmgi ::x8q+aagb ,y.jen x* is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tl:u6l5qfo23 4ttn lvae3 -hn tires and the road if a nt6h lnt 53tfuoll:e42 qav-3car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet figh:6z;*mp0 r zqhf 2ikpwyb)0he ter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is r0p;qb hyek: )pzf m6iwh2z*07.85 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 tudkok 6pkhz0 )90, 7/vtbscqhwrntable of variable speed. When the speed of the tkchvokbd6, z)/hs90q tkw7p 0 urntable 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 +*o5hua...zbaow o tu du*4qibe traveling when upside down at the top of a circh4o +*zot*ubu aiq..5. uwodale
(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 950oc/odz am x2j oh(/z-7 kg (including the driver) crosses the rounded top of d/o x7a /omzzh-oc2j (a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a trhg8 tc,8 h f6fdu*u-(er+bj15-m-diameter Ferris wheel need to make for th8 tbf(8,uu gh+re tcr*-6djfh e passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ver4- v*xs;:cb jj hnsz.vtical circle of radius 1.10 m. At the lowest point of its motion the tensivvz- . n;hcjs*bx4j: son 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 frsroq*2qi1t hsh*b*9q om the axis of rotation is to experience an accel*2ht1*rqq b*qsoh9is eration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated i/2 v xkmr owwb+(oo+skdhy(3+n a cylindrically walled "room."b/ v3hk2+w +ywrmo +od(xko(s (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 frictionlessf 6fhybxj qf1n-va jk,+wle-0gi (h/. air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass mb0 -jfn qefvyxf1hkwj- h6+l(g.,a/i ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the b,v-hkh fzpq3/b87 zwvall which revolves 3k 7h/wzqp,hv f8 z-vbon a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfect bv .vbh2xpt( 0;tjap*ly 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 ac5kh q+silf o nc.ad2t +71,d$ 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 ev9m ))/nw)pxwqff4 sf9 fw )hpbasive maneuver 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 centripetal c bexh 1es)h20h;gc jf*,. khuxwu5wi6omponents of the net force exerted on the cax.w f2);s15w6 bkhx0cjhueui* eh, hgr (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 Indianapolis 500 accelerates uniformly from the pit area, going fro; qma(tp3-xf 1wh3f ,a9pitch m rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tan hw3h-1f i(3pmx tpqa af9ct,;gential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circlti+u khp+st j5 )hst)wbkd8sq5blkh1 88xz 04e of radius 2.90 m . At a particular instant, its acceleration is5 ks x)sttz4+i8htk0k1up8hs+b wj bh8ldq) 5 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 Earthz)6fq oltpg jl .2z3a9’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface iz plof q ztl)g3a.692jf its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerationr3e bxuzg3j l9;bzg :, g has a magnitud j:9;bg3 bu3x ezlg,zre 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 Moon. The Moon's radius a, ,dpgdlgh4js c 581tis 1.74 ch,p t84g,1sdj5al gd$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet f+g.gnv:f.rh has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfacv.h ngfg.:f+re?   

  A hypothetical planet has a mass 1.66 times that of Earth, but tbupezp6c2e,.iml u p.b4l4;vhe same radius. What is g near6p2pb ;.,cm4 iuuv4bp l.lz ee its surface?   

  Two objects attract a4- 9)io; n5.ld2g bdvyivzi yeach other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of vyt06/ dc0;wzgp ,asq gravity, at (a) 3200 mt vaspzwq00 dcy; 6,g/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eartug:.kho 8 phj*a1dg z;h where thegravitational acceleration jgz ;kap*g h ho.du:18due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star zp)/q7t8 * roxb xn :epmsg .nlk341eyhas five times the mass of our Sun packed into a sphere about 10 km in radius.g4bp r)3ek8: et xolz71 psmq.ny nx/* Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avery7/qu,m0k5p me : srk (cqcy8eage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What7 m0my8uqeks5c,: q pk(ye/r c is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fel gt 51rjjo+x.5as /vgel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just + rjox1g5j a l.v/gts5a 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 o,yf l vz2il7o6f a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other three, 62ill 7fozvy.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on tn; , kiz6ahja+kqhqt x.md7m9j ,+n7 jhe same side of the Sun. Calculate the total force on the x,zjq,n9q jnm;.67ath7k k+had mj+i Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleratio:e euoeo,*g+bc8a8r zg/pq)z3qo s .s n of gravity at the surface of Mars is 0.38 of what it is )+oec/8 gzo3q *8,g:ezsbursoea.pq on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the p/ h4bh k*d (;0kf35k9ejh.doocirv dreriod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examp;dfhv j ho3di bred( ro*5hkc94/0kk.le 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orb *4c.b ilwdc5sit about the Earth at a height 45icdcl *.sb wof 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circtvlfi ft 47e9(l1p(uv ular orbit 650 km above the Earth. How fast must the shuttle be moving (relal1 l9fiu7(4vp(tevf t tive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshi-h9)bk fii0,0htrr6v dby. wcp rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, a00tih.- rdbf vhw6i k)r9c,yb nd 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 n4v+ op (nagjf:7gzser*c3 :m orbit 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 dfgr:s( jncg +vanm p3* e:oz74epend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from im:chuaei b l) 612d:5xo/bshthe top of Mt. )dohh6/l2em bi1bausic: 5 x: Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar l2 p1x px3i s22ruycm /;tcf1(z.qdcrnanding mission, the command module continued to orbit the Moou/zfic2mn;1p.(x cr2trcps12 x qyd 3n at an altitude 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 plaq+d lb1 ve*s- 8cusy d9caeh3.net. The inner radius of the rings -s1vqasl+dcd*bh8 ye e3u9.c 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 (see Fig. 5–9). Wha ed8me/ ):o7 8ydwnw)hyutws 0t is the ratio of a person’s apparent weight to her real weight (a) at the top, and y7 0ede8s )wy u /wnmdh:wo8)t(b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of the1.ifm5t6 1 n7fyzh bgz Earth's Moon in a space vehiclethzf6i71fzgy n.bm5 1 (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. Theywjx1iex 3(:vp are observed to be separated by 360 million km ae3p:(xj1x vi wnd take 5.7 Earth 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 of a 55-kg woman -s0idxeut0 z-u/ zx sx5f1 )gkin an elevator that move f -x5uxz1ik z/-dx)0us0s gtes
(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 fro -v8b-fhk l vzcar.b)4m a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? b rcvl4f.-zv8hb a -)ka =   

Show that if a satellite orbits very near the surface ou*ik4zy8p+:s)jo xja5v+j kif a planet with period T , the density (mass/volume) of the planeis pua+8+5j) jx :*zy4 vkjokit is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine o s2ux mh9heo1;ycbt7,:i5a vp6llb:the period of an artificial e7co,osmbb9t:l65lauihv 2 y;h: x 1psatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a fewe.w g (dahe7n* hundred meters across, orbits the Sun like tw ngee h*7(da.he planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagei4 xf(-: ujcskw- yy5j 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 every 76 yearniw/ft w*x*qo84ds o-5wijl8s. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance ofx4w iwls-t 8noo5 fj wiqd8/** 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 thec/pwj e/ - m .ni5akw(rk,xgufo/89pw center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance fgq9zqt3z h9eyty 2i. )or the four largest moons of Jupiter (thy .eitgz 2tqzqy)h939ose 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 Ea xl9)24c ,q8 saxvvhwthtf2e7rth from the known period and distance of the Moon. t hvxs 8eq9x)4hw2ftlc7v2a ,   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Ke4 xo1a,:0tvalas(f x5ag3lospler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values a,x la(1taol3afo x:540svgs 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 betc,romk* s9ut*yq e2q 7ween Mars and Jupiter consists of many fragments (which some space scientists t 7t29qy omsk ,e*ucqr*hink 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 bpul*/7un:zhs)xsq8 kand completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this /pslkx8u:7* h zs u)nqsun 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 vz p:kk*sv :latm:) zqic, l)3a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms a) z:*kzs )lcqmia,vv:pk: 3tlre capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surn(5;whpi.uquoa3e;gq ;;nz mface will the acceleration of gravity be half what it is oziona5.(g ;qp w u 3em;nq;u;hn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cir 6tq oed xvezd8wm79:95 +jzcoda50- :pb gpjzcle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg,pqaged:o+ c 8 9omd 0wpj 6bd-jz9x55t:v7zz e how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelk e2z; -lhm6zheration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the - zm6h2lhkze; magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spaai ldd3; q9vr j45ai4lcecraft traveling directly from the Earth to th dlj4a3iv;49ad q lir5e Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass i la6s8e hr:c0ks 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 which direction?e 8rl: cah60sk     ----待选择----upwartddown 

  A projected space station consn1s*;sr.o1)ombqdu d ists 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 ab;1qmd 1s).os*rounb dout 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 (Fig9*.vk,q+m d9ke zec hm. 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 of488mk n6xp)qqm 8eaaw a planet in terms of its radius r, the acceleration due to gravity at its surface and th 8 q 8)maeamxwqpn68k4e gravitational constant G.

A plumb bob (a mass g bz4;g n c3jf;3. e;2abg3vm/+uyou qt-qjwkm hanging on a string) is deflected from the vertical by an q/wu3ftgbz e3m.jn q yvc2ou43;jb ;+;akgg- 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 banke1z 2tx8(tz (hwcdxh.q d for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely h(zw8qt z .cdt(2x1 hxhandle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the . j;1b*rztq ests/c+xequator were apparts; zs+b rce*q.x t1j/ently weightless?    $\times 10^3$s

  Two equal-mass stars mainta2ohplr 6g0 3bsin 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. ,* vb.e *o7nyl4tdab-.fm4 c3v6lmzvl mn vn+ A lamp suspended from the ceiling swings out to ano 6t*b y n4.md allcf,mm+ b-zvel3v*4vnnv7. angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timexbji+a m/r.:c )tc* (d ,hwivfs as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: m.mfth/dwa)* +,b rxi:ijv(cc ass =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 ded3d ,i7fpkh+ ko ychb/*l1mh)f fv/0jb uced the presence of an extremely massive core in the dis/ f 73ifjp dy1*mc+h f/h ,kok)lbh0bvtant 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 orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown in wgo5k)b: ddc6 rju8ou, w-3 xcFig. 5–45. Bothwo wk 5rg 6c8o:ddxc,)-jb 3uu 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) util3(./o y 7nzn 5imzgwgsizes 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 altitud/n7g zg(oi53.y wm zsne 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 Rdfkpo).tv vo8r **o0dendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 4t)p8 .*dvo*k0v dofr o0 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 satellite in wp)d*2e(prnb- q.ky bneed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 k b)rpbnw.dq(2 * pky-em 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 p wn2g, (e5zyyxeriod of 3000 years. (a) What is its mean distance from the Sun?yz,(xgw n52 ye   
(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 jp wi( lkhp74h37s(xbactually "feel" yourself gravitationalxl3ph((7 bws hk4jip 7ly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way G5s eyq ov5;tpcdnc 72*alaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ced7 nsc5ec*;p5o2qyv tnter $ \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 locate,ja73a3 y9nwrmg cd5gd at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravi75rad ,33mja9 gcgyn wtational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitsi,u9j oeluc/)er6o l* 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 thp b9e,-5f l4u3i wiaxv0raep2 e tip of the 1.5-cm-long sweep second hand oex p3apifu l5 -ab42i09ew,vrn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a si6,l0. sdehzo inker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a comd 6 zo.0hisel,plete 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 trxg+cyk6 f f,p/aveling at f+kg,y6c f /xpspeed $ 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 n596-n nbrq.4dzjx,b f/ g 0vhsvz6 waoegotiating 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 p0 ofgj n6s/bwh- za 4dvz5x.6nbrvq,9 assengers 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.$\approx$    $\times 10^2$