Sometimes people say that water ism34l i.n0ubvx removed from clothes in a spin dryer by centrifugal force throwinx4i.l30nb vu mg the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car traved6z z6ul di5qwx *u2c8ls around a sharp curve at a c26dqli 5uzu*d 8z6xwconstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along wwo)ou q5g3 f r t2zm3nghc.20a hilly road. Where does the car exert the greatest and least forces on the roadmzfw0gqh 3g25 3n) ot2o .wrcu: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merryf0t-. ;aj8k3u ry ioby2u jr5q-go-round. Which of these forces provides the centrip8 ab2 ukfj3tqjy0ir5 o.ru-;y etal acceleration of the child?

A bucket of water can be whirled in a 8h njbn; nib++oqr*q08k not 0vertical circle without the water spilling out, even at the top of the circle when+8+nnnbhob0r0ki q *q 8t ;njo the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leazvudx ao8*3 pz0109:v4u- pwsx todxx ok-bs+st three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do tt 8d 4 0saz9xv+:-bppx103-os vu d*uzowxkxohey produce?

A child on a sled comes flying over the crest of a small hill, as shown 3h5h*jka6y,kx ncc ;u in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between an6yucj5h k,;3h*x ckhis chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwy*d*jl: totx /ip ;t-pard when rounding a curve at high speed?

Why do airplanes bank when they turn? How fn-h2 w+z0h /fc3zmcuwould you compute the banking angle given its speed and+ -z wc3mh0czfu/ fn2h radius of the turn?

A girl is whirling a ball on a string around her head e,cw p14o+epoin a horizontal plane. She wants to let go at precisely the right time so that the e4, p 1+pecwooball 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 vg dk6)7+q plo 9edkz2)sf h.cEarth? If so, how large a force? Conodq7sk . +gkz6 d)h p)vl92fcesider 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 qyg;u9xp1b4vsy 7s qxnv.7 (aorbit bs yvg x1 vsqqpy(b9u.7 4xn7;ae different?

Which pulls harder gravitatioama6kl2h;+qfy(h y( gnally, the Earth on the Moon, or the Moon on the Earth? Which accelerates moygyk2ha ;ml+ qfh((a6re?

The Sun's gravitational pull on the Earth is much larger jtx 0iwoa 84t8/t 7ljsthan the Moon's. Yet the Moon's ii 7/t48tw jtaxl 80sojs mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at:jysusa;t 3fy(1,2-v cyk- gmux zwg+ the equator or at the poles? What two effects are at work? Do they oppose each z uuy-(gm:;k-x y,wsca 1sj2vytg f +3other?

The gravitational force on the Moon due to the Earth is only about half the fgib7 d,8eb q,,(+vylo fao t3force on the Moon t7vql gdy ooe,(af,f,i8b 3 +bdue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its owj 1 -i bjji23e kuch(k*5w9m-(ilg hwrbit around the Sun larger or smallergimjh 2w 9 w-klu3-j5 (*ije( hwbikc1 than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east xy6chzsw1:k4 or (b) toward the west? Consider the Earth’s rotation directi yk:1hw4z6 scxon.

When will your apparent weight be thd5e +o( 5qkmhjya /nk8e greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as wh8 +j admk/ey55(khoqn en you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods i.l95wyulk g6v)z rya25g x*b s ue3rf5db-vo 7n 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. Consider b 97yfs v6r)g-r53ebw zgv.u*2x l5y5 okdlua(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” be(tbv eb) ,(28ofa ept:q;y zaltween sa t(b)8e(pzly2 ;b :ef, ovqatteps.

The Earth moves faster in its orbit around tcwykqvli m/l*,. ..0j ywaas7dck 8c+he 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 they7.w k*+qcikvld ,w .jy/s80mc.laca plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explainc+uk.u3 qhrm 3f9pu8 hf2)ckk how this discovery enabl2 u8m9 . +rkfpk3ckufh3c)uhq ed an estimate of Pluto’s mass.

  The Sun's gravitational pull27dutww+ .kgs 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 o.wwt72gd+ k sune side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling oumk77kz rjiuv06 y k87h46xr 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth hb+ni9g4k q)t in its orbit around the Sun, and the net forc) i+h9tgnk4qbe exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on807co6 : -x otxgtotjr a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lenot6x87 xct 0-gto:r jogth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle ko.lbt.td a1 c1/fk 5his in 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 itft11bk/5do a.l.chkt s orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edj rx+.5h qiogsu;4mt f2)liv4ge of a po5f +jos4 u t)24hxim;r.lqvigtter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniforq4m( qilojldu 0 -l,08sm)r)o7f hxz nm rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-(ohfl,0uml8d) 4qi)o n x q lr7mjzs0-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of rad9mqylhv.ama2: 0 /0l ga.owts ius 77 m on a flat road if the coefficient of static friction bemy0 hqmag0as.t9o2.: l wav/ltween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between th) jhj exfa-zfw+( bgguiv (rw(ds6*-( e tires and the roadz(*f rieu(jf(hws-g+ 6gdb)j(-xwv a if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts an:yki+95q p iqnc * 7h6lv *dudksd5:rqd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . I5urp 7niy6vq* s qk:9kicd d:+*hd5q lf 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 theyho *x910ws0gu / uuem axis of a rotating turntable of variable speed/ 1uwhy*0 u9ogumx0s e. 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 friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down mpm7a h,gp43x at the top of a circ m m4h7,gxpp3ale
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (om2f.f)v;p 0*g akh mcincluding the driver) crosses the rounded top of a hillgho*0f2m.k );mv caf p (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-diameter Ferris wheelw:h(zyps 37nta xm0k; need to make for the passengers 3:x(wmnz 7a;ys 0kphtto feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At th pwl )88ly7,5qqs+xzani4pkwe l p ,l)az7 yp88sixn+q45wqlk wowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particledy5j w0n6 lw- 4gjmd-oxj *ff4 9.00 cm from the axis of rotation is to experfl-oj -d*0 wy4jx6n5 dwfm4 gjience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peo0qs85:3 y+acucotqpu l )6jgrple are rotated in a cylindrically walled "room." (See Fig. 5-y) qa6sc gl jcot5+03uu r8:qp35.)
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 frictionles13s(7o3zwbjbr .g02 e omulmss air-hockey tabletop, zeo3 72us10rosmb3gm.blj( wand 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 of the ball wq) .n6qpjoi2which revolves on a string 0.600 m long. In particularnwq2)p j qi.6o, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a y93/r/air nk gcar 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 9 lvqukvp)m:o z6neo8or0 4kjjo1n:/) hy5jl$ 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 verticah/1dxt p dj9:clly 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 the net force exerted on+uid xat;gfoi-3 j5u/ the car (by ;/f g+iodu x5 -atuij3the 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, 9g6a k1jrxn 0a;v*kregoing from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or gnka;kx j rr0e1 va9*6skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular 6f4 3n geq q0lpszn2,qinstant, its acceleration is 1.0eq2gqz,s 60n 3lnqfp45 $\mathrm{~m} / \mathrm{s}^{2}$ , 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’xr q7k140hbsr s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its m0 sqrxh br41k7ass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnknme.5j c9) xxitude of nmcej9k5x.x ) 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 t 6y+alugl 3za+yrh 6m7o gravity on the Moon. The Moon's radius is 1.74a7lg6l3uzryha m+y6+ $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a r,h :qk9 :clshqr2q; osadius 1.5 times that of Earth, but has the same mass. What is the acceleration due to l2 sh;:r qqqsck9ho:, gravity near its surface?   

  A hypothetical planet hss.o4qo. 9u plf .gw(pas a mass 1.66 times that of Earth, but the same radius. What is g near its surfaceol.pgu 4os.wspfq9(. ?   

  Two objects attract each other gravitationally with a force of9mu7 9vt4 osmcboya7oj hr94: 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 , th)gbn93ugfe7b dx/ bhe0r2l 7w e acceleration of gravity, at (a) 3200 mb9hefw/xn7 d elgg)r3b0bu72    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eq t4e r19;ay4l4eeyt narth where thegrav;tle4yer1qynae t494 itational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our 4 )lw chp*3k :g9h3ohybn2iy iSun packed into a sphere about 10 km in radius. Estimate the surfa*3hg34yk wopiy9icl :hnb2 ) hce gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an av0ra455 spp u klz*gsw5w -n7tzerage 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 gravtr wsk s5lapg0w 4n5zpu5z-7*ity on this star?    $\times 10^7$

  You are explaining why astronautsgbh;wufkbu 3/ci o(f,u a;6p / feel weightless while orbiting in the space shuttle. Your friends re buw/icf/;u3h6gub p,aok;(f spond 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.   

  Four 9.5-kg spheres are locate0e0i r 6o1*zharu ko1+brfwy +d at the corners of a square of side 0.60 m. Calculate the magnitude and direru r10ak1 +zr6yo0wh*fe +oibction 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 same uy zb( 1*kb8jpside of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fk*p8zb y (1bujour 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 surfv 1wa-5/wyybe5t wd*lx mi:kz .5nr 6sace of Mars is 0.38 of what it is on Earth,y5wbml15n/i- :6 k z*5 ax .wewydrtsv 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 period of the Earth 1 : 6-szbhnynrsa our,y*)pcb. e(u2p and its distance from the Sun. [Note: 6(o*,.urerby pczsnbsanhy- p2: )u 1Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a md.1e3-8f/mczs a0r kjl.jmd satellite moving in a stable circular orbit about the Earth at a height ofcdm -as 0/81 krzmjem3. df.jl 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km +fetyu 6bh. +eabove the Earth. How fast must the shuttle be moving (relative to Earth) when the release occure. +bthefu6y +s?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to,j,*rc2c atd/yi6l kwan+m hr1) ry;c experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your ans jc*y+ ,1lra ck,i62t)wdr; rna c/hmywer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in.n)od1m .fqx n a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth wm.) qfnno1 d.xhich 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 velocity would a satellite have to be launched :q y lc6k9g7pk4x:i jffrom the top of Mt. Everest to be placed in a circular orbit around the Eart pjixky964gcfkl7q ::h?   

  During an Apollo lunar landing mka3/gs8iqd jsqj6xz5*(gc6v ission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it takcgzv5( gsqsk 8dqji6j3/*ax 6e to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The ini oi(b-5ix xeam ,j2v; w01wsener radius of the rings 1exbia;5xi oesimjv(2w0,-w 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 Figo(; vbr 9roti(hsp4c ,. 5–9). What is the ratio of a personrrohbco(tpv(,; 9 4is’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the t6wkl,olz gidn(324ncenter of the Earth's Moon in a space vehicle (a) moving at con,ntl4(g ilo nzd36kw2stant 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 eq ee ,j4ba-*oconsists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth y ,qaj4ee -be*oears 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 in an o m8r3 /hace7et:sc;dv 2ad(n elevator that moves avto(ec r3d2;/7cm8en dash:
(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 suspende58*e zli 5vlufd 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 acceleratvi 5*fuel58zl ion (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pll:x 5. 7a jei+dis3nbzanet with period T , the density (mass/vnj7lsxi35. de+zbia:olume) 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 th b0 or*y2yzyoc 5rsx0:,-ns uye period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very :0 0*yuny,ysyoco2 brzs5rx -near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundredgwsg8w g*6r*) iq lf*.a,tej a meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun? r ww *sj*g.8gfai)tg6l qe,*a   $\times 10^{11}$

  Neptune is an average distan.lyi mlk5z *w)ce 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 year7;1sbi3g o5bgq:xzxr t)6jnj-cj id 8s. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estijxbg-q1bx )7itz jsr63cgjd5ni ; 8o:mate 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 aboutgey ma ,5n+:u(gpno (kc luw)8j+p9gfm/ue;j the 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 for 9qb5,s- c*pfgh o+nxhthe four largest moons of Jupiter (those discovered by Gali-5nh b+ ,fhsc9*qg poxleo 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 knf0l,d 1wl nns;own period and distance of the Moon. d nn l1s;fw0l,   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usin3 -l.w wr:9 m( lctq ifest-arc:k*yj)g Kepler’s third law. Use the distance of Io and the pe.la )t-lr cj3:ks-m(t *e wqcwf9y i:rriods 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 consistsy0w3h x9skgu : of many fragments (which some space scientists think came from a planet that once orbited the x9uy3k:shgw0 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 arjq)k.o6n c9gx tificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Ear kxcong).6q 9jth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging v-/4hr-7u1tl53 2 ugwzvc-tupuln tbin an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N ontuu 3 lt--l uu4hvzgtrc5-7w p/nvb21 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 acxx tqk5++ *xvjceleration of gravity be half what it is on the sxvtx +qx5jk+*urface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and: gm l,8nk/nqz spin in a mutual circle o nl/ :q,nmgz8knce 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 day, the apparent acceleration ofszimxth6ep -c67w wk5q7 :4 gr gravity at the equator is slightly less than it would be if thpm- 7rx6 :4wkeizcts wh5 g76qe Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wirlt z9nwn :pk8-kbix; u +c5w56biqa/ll a spacecraft traveling directly from the Earth kpt65ix+5bl k 8w i-qnc/ar;:bw9nuzto the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is hhm+qwt+ .nd5 -s*silmf3vd 465 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acci4ms 5hmvdf*q. -hw+l ns3 t+deleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station copz 5wk.yw)im(n*)t6 ci8x oflnsists 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 speem*5wpyno wl 8)(fx z6ck.t) iid (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 (Fig. 5c 2smcwfax: y(/ n5z .8nfs7ch–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 zv tssyn7 qwt3 v-,98k( p 5pvmqvsy:8terms of its radius r, the acceleration due to gravity at its surface and the gravitationvw 7v8-3pky,n (:p8s9m5sv zqyqtt vsal constant G.

A plumb bob (a mass m hanging onyt4jj+ s3h8 ox.upq.x a string) is deflected from the vertical by an angoy8u3.tps4 +x. jjxhq le $\theta$ 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 c yfz7azh1rsi+u6( (; )z tbfwyoefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle thu1zf )sybi rf(6 yzh ;7azw(t+e curve?

  How long would a day be if the Earth were rotating s o8 h6fuy)2xh/+ ciafmo fast that objects at the equator6 ofmfh+ /a)x8 uihy2c were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distho) 8f f6aoa*ec*etz7ance 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 7m7zj jje g;koiu7l mt3u s.--a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17 jts3-kg7z i.7u jm7jm;eou-l.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Eart2ax psy6e6j yng4la.6h. 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 planxyy.2e 6a npa6s4lj 6get. 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- wvjid 4k63zf Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by mej fd3 -zw4ki6vasuring 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 speed5qd e c*wmh;rt p70k7d as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of r tdk 7w0 d7cep*;q5mhcurvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a grou;)2dzl /bcya hp of 24 satellites orbiting the Earth. Using “triangulation” and signals trald;c)hyz2/ ab nsmitted 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 2fxj /vx;h: 6oe.1 billion km, is meant to orbit the asteo/efxx;v :hj6 roid 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 space shuttle pursuing ai r)vgd js z -ka/y6 s99v:i1x,jyi0nz 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 behind it. ak v,jv/:rz6sj dn 9 0 -iix19z)yyigs
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) o k(g2; vr1alwacp.g0What is its mean distance from the Sugpr2.k;gaocv a(l w10 n?   
(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 axl/ n(na/gs/l5rhkk / 7ux r6would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Maa5kn/n7h/gsrl6 / x(xa/r lu kke reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.(( co- tbpo kv3iuw-p7 5-46) at a distance of about 30,000 7p -vbt3p( w(i -okcoulight-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 z4to si(ji7niw; 1a5othe corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg 5( jznisoa4;1oii7 wt 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 Eartzz k9g(n apdi05-zac+h $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep seclw48v3 k0.ojkfng a9oond hand on your wrist j0 nwkg9a.o8o 3fvl4kwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circv9d /vc3. c y3,mbug 8q*8smmzfp + r8kld(jwqle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. W.lubc 3j y8f/dmr8q9kcqgm8wd3 s(*+vz ,pm v hat is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of rt:xd6yox p/ 8gadius R in a new highway is designed so that a car travelo6td yx8 /gx:ping at 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, utilizes tilt of the cars when ws;llvj/ ji;*negotiating curves. The angle of tilt iss ; /;ljwljvi* 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.$\approx$    $\times 10^2$