Sometimes people say that water is removed from clothes in a spin dr qurub846 0alo.f(oj cyer by centrifugal f4oq jar80uulo (6fbc .orce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car t ope id556efda89ml3:c5 qnxuravels around a sharp curve at a constant 60 km/h as whenu6m8a9elp doq fd3i n555: ecx it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constauk /qf(sw8ad3nt speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) onqa/f u8(w d3ks a level stretch near the bottom of a hill?

Describe all the for0l kxulgou,6e qh,n/( d*)ib 4d ajrp-ces acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratioxh /6 lrn0d*q ,-lg4 jodupb ,ak)uie(n of the child?

A bucket of water can be whirled in a vertical circle without the water slvcij5;nn y .;pilling out, even at the top on; l;ni 5yj.cvf the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leb vbq(+o s95cpqzb g- b/v0sy2dq,e /aast three controls in the car which can be used to cause the car to accelerate. What are they? What acceleroy g /qd- q sp9eba,/+bbs0 (z5b2vvcqations do they produce?

A child on a sled comes flying over ta++k* ivs;gq1k x,.qq. sjzro he crest of a small hill, as shown in Fig. 5–31. His sled doe1.v k;k+sqqiz.s+ qo* r ,gajxs not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when r3- /jze v)tbqtounding a curve at high speed?

Why do airplanes bank wun m-6 w/,bnuzhen they turn? How would you compute the banking angle given its speed anub/zw-n m6, und radius of the turn?

A girl is whirling a ball on a string around her head in a hfn8 t8epr+h78ge l,ky6:beld sp 3el*orizontal plane. She wants to let go at precisely the right time 3f, 7ypk+6lg t*88:repn e elhe8bsd lso 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 force on the Earth? If so,ti/9 ;nx sg bf7o r2vt8x)pi)e+z3jjb(5 epy r how large a force? Consider an appl;+)jyp5n 97gr stx)(t/2xe if b3zrebpj i8voe
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, ina1mamu gsy+0f8,u1q eax5)hqf/h 4 um what ways would the Moon’s orbit be diff 0 mu,1 4yem1uh)ufm8qa+/h5gxaqa fserent?

Which pulls harder gravitationally, theba/, y*fy u)(zfbnbi9fk-g5 q Earth on the Moon, or the Moon on the Earth? Which ab* g)fu-f9(y/aq nif ,5b bzykccelerates more?

The Sun's gravitational pull on th r6tkoa 9e6i,mm02llh9sum eh: k+3fh7kmn2 le Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitakus6m9k m76a+hfhhek:0 r,93lm 2ilntel om2tional pull from one side of the Earth to the other.]

Will an object weigh more at ther ;k .t67e4-feb su0aczz3ug):ynpbzm kjx55 equator or at the poles? What two effects are atk45up fbu5 ; cg 0r.6 :jxzez73bey -akm)zstn work? Do they oppose each other?

The gravitational force on the Moon due to the*0is5dx0 bif kkdu :4k Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the*u4 f 5k0kxdibdi:s 0k Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger orbm,i i,f8g+p-c9 plw s smaller than the centripetal acceleration of the E+i8b,-pf splgicm 9,warth?

Would it require less speed3ia ;.j4ypi/7l8 ycfe fkh *ikdht;q6 to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s roq64.;k3aci7 8ih;hfjfkiy y dlp/*e ttation direction.

When will your apparent weight be the goi 9g7h*iw ny*reatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free 7*i9yw*hng io fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could uz7f xi3.ci/ tnyt3/l be adversely affected by weightlessness. One way to simulate graviti 3tfi/c/xy.7ln u 3zty 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 our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner exper wmt75z lras:3yh+sk(iences “free fall” or “apparent weightlessness” between s z5+w ryskt3m(hs: l7ateps.

The Earth moves faster in its orbit arounlj)zq)f nmq)t3 p8lv) t*;rwgh0* ypm d the Sun in January than in July. Is the Earth closer to tyr 8)0p ) tt qm); gmfh)wl**3plvjzqnhe 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 of its orbit.]

The mass of Pluto was not known until it was discovered to have a moob uvqimx/g77zaw35 dy02s q2 bn. Explain how7bb sqxy3 g2wai2zdq7vu50m/ this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pullv 5yg *;se0p5ym23en iphh m6v on the Earth is much larger than the Moon's. Yet the Mo52 hhynp6p mvv5ge*0 s3i me;yon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-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 travelin+r laeww;n0j 4:cp k65bdtso5g 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 acce4dnnkm i h8kmz (2coy-).vm5yleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Eart4.nvy(i5 2oy-z) kmd8nm kmhch? 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 fy *g o(6*/sbzy:cb(vtl fzzb5d d8p.210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circlel*z8go* /:.b ys( t(fb5bv dfzy zd6cp (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in or/qf9,ejsqj f5cv2 fx x9f3k *8wruo5q bit 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 gravitational accel sfx 3qq o 9ve5ru* 98w2jxc/qf,kjff5eration at the Earth's surface. $\approx$    g

  What is the magnitude x0g 9a;lxukkc-yoo ,( of the 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 diameter isk-,oy 0l(kgx; uoxc 9a 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circ t ,cmvj4,rx*zle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0,* zmvr4xt, cj0 $\mathrm{~m} / \mathrm{s}$ 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 csotqr. y .61wijsem/jy hv+;ol1+6 qhan round a turn of radius 77 m on a flat road if the coefficienh+1w.olr s ;qmye tojiyj6/.s6+ 1 hvqt 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 static4gwo1 .yv8z6zg i+ g47nil new friction be between the tires and the road if a car is to round a level curv4 o.6ni +eyzzlgw1g7 8ng4 viwe of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is vdxp(dq74k kzcv: z6gm ;b0q2designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the tradpk (6 ;vmv4qdk:b2zcgzq x70 inee 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 turntaph11)rf4.* qj l zhqrfble of variable speed. When the speed of the turntable is slowly increased, the coqqfh 1zj*)p hr 1r4f.lin 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 coad5;sb3c zjn 6tster be traveling when upside down at the top ;n5 d3c6bszjtof 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 9knol*dkt;lpt dv i829.v(u s :50 kg (including the driver) crosses the rounded top of a 82ls;9:ptnv ikdktv . lud o(*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 15-m-diametesw nqbq,+ p7n/va5/axr Ferris wheel need to make for the passengers to feel “weightless” at the topm +n7v a/,qswnp/5b axqost point?    rpm

  A bucket of mass 2.00c(dwd( m0obu3 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope dcw(du m 3b(o0supporting 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 fromncefl9s *x5 /o the axis of rota5/ lo*s9c xfnetion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a; ek(i ) vgf-hdhu+s.d cylindrically walled "room)dsd+ ghvkiu-.he f; (." (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 5/bbmbrjx+0 e30n kpu 9gh 3eqrotated in a circle on a frictionless air-hockey tabletop, gp0x3b5mebn j+0 3h ubq 9/ekrand is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight ofgc.wn5w*yl 0s pd3y7 n the ball which revolves on a string 0.600 m long. In particular, fiw 5w .0yn*gsyldn7pc3nd 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 radi+:)k 3 fhjjaypus of 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 massew-1 e0wuc pkqk.l .i 36sp6qiqs $ 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 v3k;qlsj m* d+dertically 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 7l.ba1 ac 9psethe net force exerted on the car (by the ground) in Example 5-8 when its speecla 9s.bp7e1a d is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniforml7a(n o v5v8ojn2rk,yp y from the pit area, going from rest to 320km/h in a semicircular arc with8p5 nao(v n2yvk ,jr7o 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 between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a him/lc.9df0 wvmw t-4 gorizontal circle of radius 2.90 m . At a particular instant, its acceleratio-c /g0wim4v t9lwmd.f n is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity hq* c)) lljr1gon a spacecraft 12,800 km (2 Earth radii) above the Eart)cr) gj*llqh 1h’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accoal4e0 ea 6 z;81ajfhveleration g has a magnitude of 12l0z;h6eoe a14v 8faj a 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 gravitie 4x7rmn7dy3y on the Moon. The Moon's radius is 1.7inm 3 4exdy77r4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tiffcnqn 77d6 :hmes that of Earth, but has the same mass. What is the acceleration due to gravity near c7:ff nd q67hnits surface?   

  A hypothetical planet has a mass 1.66 times that of Ea(jxsf z5cu *m+rth, but the same radius. What is g near izm5xcfs( * +juts surface?   

  Two objects attract each other4y3 l,6 d r)um4pximxk 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 vy6 :u3zt7)bh g qdosa2alue of g , the acceleration of gravity, at (a) 3200 m h )gqt ysuo67:b3zd2 a   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cente(b;kfwlh; my3mjzp 48 t.6aksr to a point outside the Earth where thegravitational accbp ;m(a .8lkt z4fwkmhs3jy6 ;eleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packqu z6 .lv1kc+puybv6*+i:oxmj7r e/ ced into a sphere about 10 km in radius. Estimate the surface gravity on this mons/6v .6:u qlzyvu x*c+jimbkrc 1o+7pe ter.    $\times10^12$

  A typical white-dwarf star, which once was an averaddg2pgg; .uzx uq39;ymd9)h vge 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. What is the surface gravity on this st;g3yuhg;gqd2dx9 pumv.9z)d ar?    $\times 10^7$

  You are explaining why astronauts feelo,-vy1,r,5*bdd-ckio c 6sjd5 l p9x esgi u.r weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calc6k,5.x r9sp- -ocudrsydove 5*cg il d,1ji b,ulating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at l5v66( hsea3vb ev+b ithe corners of a square of side 0.60 m. Calculate the magnitude i6 b5ebh63svv+a(vle and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the/ /bwulrpq0 x5 same side of the Sun. Calcb0x/ur /5lqpw ulate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mwvo7 .g9mzzx 2ars is 0.38 of what it is on Earth, an .wzxz97o vg2md that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Suvws(n- kg- r7mn using the known value for the period of the Earth and its distance from the Sun. [Note: Compare ym nv7-w sr(gk-our answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about4 p. xcgi(le9f the Earth at a height of 3600 kmi4c. xp eg(f9l.    $\times 10^3$

  The space shuttle releases g6zz0rzp 5hr (ave) e9a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relativzgep6 z0rra5h )z(v9ee to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylixqpg 0);k8/3j fblnltndrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spajk/bqx8)3 gt l f;nlp0ceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it p8sk9 b qb4 xswqs4wtlbp51,6 takes for a satellite to 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 ver4bsq5wp sk6 tpbb q9s18 x4l,wy small compared to the 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 t: crw +nz.g 1ovb.f:blaunched from the top of Mt. Everest to be placed in a c1 :b fv.nrwo:+g .czbtircular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbi pan *)*nzhet)7t xcno,jv7.dt the Moon at an altitude of about 100 km. Hc7 )t7dze,n* a*jv t)hpn.onxow long did it take to go around the Moon once?    s

  The rings of Saturn are composedv 1ciqm;tn r7u+w8ab 48eej2f7co p-b of chunks of ice that orbit the planet. The inner rajite8 p18b4a;v +277 o uefqwccbn-rmdius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fighh* ))iuzuokb;u).m h . 5–9). What is t uk)bmi)) u. ;zhh*huohe ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronauwud;k h0s6a9 ht 4200 km from the center of the a 90kwhd6h ;usEarth's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star sybvj2ijs0/* 4 hrjdv3lstem consists of two stars of equal mass. They are observed to be separated by 360 million km l0v j/isjbh3 r2*4djvand 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:z) k;thjw:v gfw0s6vk75oe zc -hyk, a 55-kg woman in an elevator thatw ) zf- 6e,v:gjk 7k:stvk0;y wohh5zc 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 fromiwn) /wzok m( le3s3w8 a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N anmw ni3we()o38 lswz k/d breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits x:1lxi;(0 prebzdh9end( 3hk; dp(wsvery near the surface of a planet with period T , the density (mass/volume) :(xzd; ;3d w h(1iepxbr pndkesh(09lof the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to dea32i si w6q+0 qae(22oq +h3ujxgorf itermine the period of an artificial satellite orbiting very near the Earth’s sogf6u22 +he(33qr0ixqao+ ij2q wsaiurface.    s

  The asteroid Icarus, though only a few hundred meters across, cgrzz/ggc:r cs +.sw;29zjs: 7bzu v6orbits the Sun like the planets. Its period is 41u;gzcz+6 /c:29sgjcwsvzzsg r 7. br:0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average ;:au8blv x srgofvot1y l+ f30u4si8+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 rxyqwc0re*l - *oughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distancr e0xc*w* yq-le 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 centersrv- s (on3ea+ 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, 8r4pyk hysc81;i.f kyand mean distance for the four largest moons of Jupiter (those discovered bc kps8. y 18iyhy4frk;y 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 x9r ;2wvptm wo)v5gc2the Earth from the known period and distance of the Moon. r2c2;w m)w5xv9vg pto   $\times 10^{24}$

  Determine the mean distance from Jupiter for eachqn +k5jb*-kbv of Jupiter’s moons, using Kepler’s third law. Use the distance okbb -kvq*5+ njf Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of c(be2:rt u3kx many fragments (which some (32ce:x brukt 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 an ari(9pr/; rsogv5hb;urtificial "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 ouur v; 5psrrbio 9hg(;/r own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swingi4n 9o2jjlqmk7 ng in an arc from a hanging vine (Fig. 5–41). If his arms are caom kjqn j42l79pable 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’otxb) n8al8(ce ty 0v00sa0zxs surface will the acceleration of gravity be half what it is on the000onxzeasty ) va8c 8btlx(0 surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circlelscmezqd7 sb crd;15, p)hz 9+ oncsc+7s cledh,mp5r1;db9 z qz )e 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 one another?    $\times 10^2$

  Because the Earth rotates once per daygskl :pu1ddb+* d)mu h*cx2 1pca 75ab, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effectd lu2:cgmk*p c)d +s11dpba xu*b75h a. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spmb3em38afg3gmcry 8nr,j t*n t 2n8k,acecraft traveling directly from the Earth to the Moon experience zero net force because t t nbmrk8c ,t 3m 382,3yngg*a8refnmjhe Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bub 33dmhate 3t(o)ea 3ct when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acce33d)at mecat (h3e3 boleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consv- ,n 5h4bv;waa z/imlz)(on+v kq)xaists of a circular tube that will rotate about its cent+)ko)v xa4ma/zv za ln-h5i,vqn bw; (er (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 Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft ic;a gid /d od8c5zl2x/n 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 planet in bqdsi 849divxw niw54p4ia e8 eml2i,1.srd:terms of its radius r, the acceleration da45m4s:8 wib nd48di,iewrd2pi s ix1 e9q .lvue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is -x-lfkh bdr.5deflected from the vertical by an al-.x b-rfd5hk ngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffici5+ji 98 ygselnent of static friction is e9yjl5i+gns 80.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast tq/ee8/t wf.yohat objects at the equator were apparentleq o8fe.w/ /yty weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apt+hqbwm.k::i-g3 75gyg x u mdart 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 speec4f i p+wpz97ad rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5 9+caf iwpzp47$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claim5 wj*th;k0jgxed that a person would be crushed by the force of j 5* hxtgkw;j0gravity 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 Spnppcopy+qh0y vzs-s so5 g si62/5w pw+ s83c,ace Telescope deduced the presence of an extremely massive core in the distant galaxy +s/p s,cw sp6w5p58i co+vzs0y-pn q 3sg2yhoM87, 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 vavj+8 9+fx2 wco- ujk mfodldd7+9 qx.xlley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which+qmcjofd2xlv kx9 89dw7x+ou-jf.+d 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) utw. 5wcc;fa 3cyi9u2(q 3epxecilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each s2;9 payc5 .eiwfeux (qc3c wc3atellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asterld:mjj31i1q,t b cduxd3k10f oid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid 1f: j3j1 10icktludqbx3 mdd,Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the spi8u7ia7w zne 8ace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km be7eun8izw8 7 aihind 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 per- 6okbqbs xdbbjy: 9,9iod of 3000 years. (a) What is its mean distance from the Sun j-sy9bk6b, o9:xb dbq?   
(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 i/gq cl0d e(2eto be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonablce0i2( / egdqle assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-kr lz8n*ilru ;yz41en+ zj;z2p an0e) 46) at a distance of about 30,000 ylzn2na0 ) eu*pr4z; lje18;z k+irznlight-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 mfytzqrr(zig.+ k:wp1*t9r - n on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass plt:9gk+i* r zqwzr(ry-np1 f. taced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orv66y nu6vk p*zbits 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 acceleratg6,l a9j:utx8 gvn:ltion experienced by the tip of the 1.5-cm-long sweep second han tt8x6l,9n: uag gjlv:d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weighti+l xfn(m5.vu; . cngc 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 verti mucl n 5(nv+ic.gxf;.cal? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trave. zrdi,8nywg.9 cx rp6ling x.9y nzgpd, cr ir68.wat 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 train, the Acela, utilizefqu7m7 udb;h2 s tilt of the cars when negotiating cur f;27udh bq7muves. 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 (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.$\approx$    $\times 10^2$