Sometimes people say that water is removed from clp6n r+lr.*m jjothes in a spin dryer by centrifugal force throwing the water .*pl+rnjr6j moutward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travecn6ru u45tao +;1 2txi-ybx ymls around a sharp curve at a constant 60 km/h as wh5t- xb6rx;mnuu4+ya o12yciten it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where b/xh35t6 rwbq does the car exert the greatest and least forces on thet 6hq5r3 bx/wb road: (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 -qhre7f fq75cacting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerqhqr- 5ce f77fation of the child?

A bucket of water can be whirled in a verticaub6 g54ng;6e .1oi u)fgccruq l circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explq u ibocg.e gu5;6 64g)fnu1crain.

How many “accelerators” do you have in your car? There are at least three con3p mith un2dy4- t;5xgtrols in the car which can be used to cause the car to accelerate. What are they? What accelerations do the ntgdx-;y tip2 54uhm3y produce?

A child on a sled comes flying over the crest of a small hill, as shownsy15kg;6lxesoc m 91b in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the xy ek59omlgss;611bc 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 roundix.) 7uagi)v).io ldoong a curve at high speed?

Why do airplanes bank when they turn? How zyw8v rb8sois l(-71pwould you compute the banking angle given its speed an8 iv8z (y-srspw17blo d radius of the turn?

A girl is whirling a ball on a string around her head in a horis6t r0tk b/uf;zontal 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 the kut/6b; r0stfstring?

Does an apple exert a gravitational force on the Eavt3 md:e*svf)wlv a *4rth? If so, how large a force? m4fs *v):v3wde*atlv Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wpwb ; n8tdvh-7ould the Moon’s orbit be different?p v;twnbhd 78-

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the k;gku1 moi8.r;mxj:hEarth? Which accelerates more?k;m:gk m;ourx 1ij8 h.

The Sun's gravitational pull on the Earth is much larger than the Moon's dlj9 uxxs5(3o. Yet the Moon's is mainly rxxd39 (lj5 suoesponsible 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 the equator or at the poles? What two+u,wq(;gir* kjh yr*i effects are at work? Do twjhq*+ki *(yru,r g i;hey oppose each other?

The gravitational force on the Moon due to the Eo75f d7kkp g+n0 (gojoarth is only about half the force on the Moon due to the Sun. Why isn’t thep gg7koj+o f(0 75kodn Moon pulled away from the Earth?

Is the centripetal accelerat ud f;n3+rzvi0d1j:e tion of Mars in its orbit around the Sun larger or smaller than the centripetal acceler n0e d+t:r3dvizj;uf1 ation of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b)t*gss-z,vh//):ke;xb cx xxq toward the west? Consider the Earth’s rot xck,v;x): bqtesx /-xgz/*hsation direction.

When will your apparent wei5 zajc0 1 .c3vwbyh*)+nklkzj ght be the 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 youz5*lncyzch. )a+3k 0v kbw 1jjr 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 be akxoo .te93i,wwqs z6- dversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like , iw zostxe9.o-kw3q6a 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 expe,jj +j0 u-spxhy (*gqi hb /)cqi8j:pariences “free fall” or “apparent weightlessness” betwee+( sacy:/ji* ,jqgxhuip0 q8jh-jp )bn steps.

The Earth moves faster in its orbit around the Sun in January than in Juldl( den-6mm6jy. Is the Earth closmd-lm (enj6d 6er 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 of its orbit.]

The mass of Pluto was not know fg 5buij*-ukhm t+i./n until it was discovered to have a moon. Explain how thisk5b+it/ujf -ui.g m *h discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's.qgsp;* k65jyd 5i1x5uewfg(m 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 xg iwuy(eq55p kj f*sd6m 1;5gother.]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 1g*pp 2)oro;w c)e/jyc 980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 a a2ru2l45neg qcceleration 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 that the Earth's orbit is a cuenr2g4a 25lqircle 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 21ohop*nn6 h (j( 3 .f,vlwoh6eg0 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speej h*gn (fo3nh 6.(polv, 6hweod of the discus.   

  Suppose the space shuttle is in j5.mjg1ak +z zorbit 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 anzg m1zja+5k .jswer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleraaa6 7zh61h koltion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per 6ao16h zlk ha7minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verti:o -m0.x2 bicpcc .vnt/6w vjjcal circle of radius 72.0 cm , a/: xp -.wt.m6v2ccbjvcj0oi ns shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of 0+fw)3bic psn vb 5-yxradius 77 m on a f)3v 0bwp s5f-cxi+bnylat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient oaoxo +zu 1c45xf static friction be between the tires and the road if a car is to round 1c+ xa4ouoz5x a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and s6+(oh qj:t3h aglbd9jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force f(as9:o6d 3htjlg + bqhelt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of(lxk7 /dm:y pc variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached7pxdm cy:/k( l and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rol 7 61t36)uzr0sgjvj ++smavwdetd1 c gler coaster be traveling when upside down at the top of a cjev61r)dg+ 1d3+z jtwm 70ucva t6ssgircle
(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 q9mjld+rm- k-mass 950 kg (including the driver) crosses the rounded top of a hill (radius m j dl9+-kr-qm=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 wheel nkfe.o 3kiyp+*gln, :t 6q74l-sjq j rreed to make for the passengers to feel “weightless” at the ll*r qq s,3 ij 7f+ 64.:okgryne-jptktopmost point?    rpm

  A bucket of mass 2.00 gawe lhr;;l-fz)lb6/zy r/ )lkg is whirled in a vertical circle of radius 1.10 m. At the lowest po6) w/; ar f-zblr/zlylg;)h leint 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 palpj76m*kxcu 2 nth,0i rticle 9.00 cm from the axis of rotation is to experience an acceleration j2 un6hp0il ,7m ckt*xof 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically f x,*w/ynjck 7b4j:sswalled "roomj cxysb:7nj /s*wfk4 ,." (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 4 y(1v6-mc sot )ofwzt) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fitz4w(t1c o6m-soy )fvg. 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 7pal ,-hc3 j.y/kqyxkignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find /jkqypc73a,xy .hkl - 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.e-cmbg.h2c8y) a,k6ni pb u q 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 masse9tdppr 6ss:/xek5 :i js $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310 c 6bw7ibd vhp(n+,ta q;,8 eah$\mathrm{~m} / \mathrm{s}$ . 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 exerte51*mliy kit7j d on the car (by the ground) in Example 5-8 whenl1my5j ii 7kt* 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 frote9v:dzr v9 7hm4i;vgm the pit area, going from rest to 320km/h in a semiz :9h9 gv4v7m;e rvtidcircular 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 skidding? $\approx$   

  A particle revolves in a horizontal circle of rvcg:jp)a- u)porbsyf4ds g h l 8.s7;:adius 2.90 m . At a particular instant, its acceler::sl )fgp47r ujdsa h;ybvgcsp-8 ).oation 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 grh8i4xr-vi;u/su,e:8 a fco70btu mucavity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if itse4i a-u,cmfh88c0t; uxr7osuui: vb / mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g harqtm /7.n-jy 8uffs ;ts a magnitude -f7rm8jq ;utfs/tyn. 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 2cau j7rj ,tx.ls 8i*pradius is 1.7xac7*pi 8,s uj 2tljr.4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical plane;fbg22z wdew*2sfan+t has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near itsnf ws;f22 bdezg+2w* a surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiusm mctezwgc l)o;(-g )+. What is g near iw)ml egm g(;)+ocz- ctts surface?   

  Two objects attract e6m hda75a 6+h/tbsv zqach 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 cz*mn:g2qld 3gxrw -8 value of g , the acceleration of gravity, at (a) 3200 mdq-*2rc m gz wlxn38g:    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s fl.w) ,bu 8nzncenter to a point outside the Earth where thegravitational acceleration due w8f ), nlb.nuzto the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fi -s l, ww9 ba08iwnw;3zh9mvcqve times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on th;-w,l3 cs 8bznm hawv9w90iqwis monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is n:px+ hw1 0yx tw0 phf1swhr+x:1gz 6dcow 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 thisw+ h+pd:zfr cy16hps1t00:xxg h wx w1 star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space sh c2v fpddgds7)+q766pfw(lv ovj*;pluttle. Your friends respond that they thought gravity wav6p+7w2 vp 7;*d6o vj d(lfgqlc spdf)s 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 located at the corners of a square of si7/at+ gbouvo5 de 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the ovog at7+/5u bother three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets li;)qs jz u ylj/1rn0h/.t1iz me+ dxih:ne up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5i.n// x)esu;t + zlirjhyd 0qj1h1z :m-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 acceleratk9dgbmgyk - 7;ion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass -gy7kkdmg b9 ;of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valu9q,6gp7 vnhf2wlyf o0 iw,a9ce for the period of the Earth and its distance from, 7if90ohg wq y pf,c9v6an2lw the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a s;luy p o0td0v7atellite moving in a stable circular orbit about the Earth at a height of 3o7;tl u yd0pv0600 km.    $\times 10^3$

  The space shuttle releases a satellite 4xh4bc fiv2rilb*q( 62 4kwdqinto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whe22ri( dqwflik hb qxbvc464*4n the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience7jrqo 0f+0us ap08to a simulated gravity of 0.60 g? Assuf07pr 00o + sutqaoaj8me the spaceship’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 takes for a satellite to orbit the Eartj0b1wg 3itx/z6a wrlt(s87 c o9n ddk4h 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 depend on the mass of the sateobc9 6dg0 z 3i1/at( 4rlnksww7tj8xd llite?    s ~    min

  At what horizontal velocity wou bfuqh) (c0+lajjazd)k78 8auld a satellite have to be launched from the top of Mt. Everest to be placed in a circular orb)8jza aub8k0+ h()l7fqadjucit around the Earth?   

  During an Apollo lunar landing mission, the command module co7zxc)un, m2r:lyu r3sntinued to orbit the Moon at an altitude of about 1 ylz:7,su)r3uncr m2x 00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of icez)t :,oiw+c fbe*9 hds that orbit the planet. The inner radius of the rings is 7o *ihcb)+tfws :de9, z3,000 $\mathrm{~km}$ , 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. 5b+8h q7rq7l cj6 ym*rr;5dmxq–9). What is the ratio of a perso*; rrc qjbxm85ml rh7d67yq+q n’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 gjt4ixz- *e1u75-kg astronaut 4200 km from the center of the Earth's Mijx4 g-*z1teu oon 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 system consists of two stars w;k 6b/8ox e(gpavr: vof equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yb;w/ ox(krpe: 8 vgv6aears 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 weigj;hebryy 88b 88wn 3qo jnr2;ne(,zoaht of a 55-kg woman in an elevator tha8 n jb n(2rzj;ro88qyey n,;hw3eoa b8t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended fromi y cqsm( hpc*8v:w09;6h qnmz 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 (mag*mh ( c m8:cz9y;wn0iqshpqv6nitude and direction)? a =   

Show that if a satellite orbits very nexw;wihxz)w a8v9 8 d1g 5suz1rar the surface of a planet with period T , the density (mass/volume)whxw1 gir );s9588awvz1xduz of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period ofncs (v t a:qnp/o mvyv8-h2c,6 the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Ea:oapy2 ,68cqt/v mn-s h vvn(crth’s surface.    s

  The asteroid Icarus, though only a few hundred eyqp *x1udv-(g5uim9 meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fro( q9 1*d5x-gmpuyuv iem the Sun?    $\times 10^{11}$

  Neptune is an average distancermvm 8j0c)x j2 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 years. It comes very clospizb7oqwt5yhi- 0*o/ 8 4 dyrue to the surface of the Sun on its closezoh/iq0 7 -yu* bwprd58y4iotst approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about ps rww.+ec 7(hthe 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 fo8. n6rj,aoze s4ez (xtr the four largest moons of Jupiter (those discover r, nz6ezoje(a.84stxed by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth fr)qgwrnc uin2)2og qq- y8ysz (p2zy. -om the known period and distance of the Moon. ci2q)(ygqy2gz-q2u s.8owrp znny -)    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moq1+7;- jb/ jzamjhid:uh- gjwons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3gq7jjj+jh:w -ihad/1 zm b ;u-. 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 Jupiteru-ld9 i 52qgko consists of many fragments (which some space sc9 l gi-kq5dou2ientists 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 arm wv+7u1py9oytificial "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 o1m9u+pw7 y vyis 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 swileir1lu18x84 8ihhc0nmx 6jq nging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of hi0rxlec4uj8 h8q h m 1i16nx8ils swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceler, 4u40weq mzhyh8zx/+f4wc xhation of gravity be half what it is onxf0w8, h yx /zcu+zme hq44w4h the surface?    $\times 10^6$

  On an ice rink, two skco ze4zn y3y9g-,1g gbaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 9bge ,zg4cyz -gn3 o1y60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatckvlr-rual8h:m2kqrea .: xd;nd /27es once per day, the apparent acceleration of gravity at the equator is slightly less thanl:reu8cn /r:k 2;l qmv 2a.axdk7h-dr it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direzde d(x:;f1 qgpcen(kol/*8 nctly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and op ;*e8pkoqzd:l(ngd1c ( f /exnposite forces?    $\times 10^8$

  You know your mass is 6p *8fc)wj gm0c3f8t cj5 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 f8m cjtc )g80*p3c jfwkg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo ,-.,g wgepgndisqd5 *ut 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 rotn ,.s i dqedg5*p-g,wgation 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 );:ry 5g/ 5a,jm t:exexy2anb luqnh. (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 terms of its radius wdtaa59)fm4v 82 fsgjr, the acceleration due to gravity at its surface and the gravitational consta s4t)w98fd5gfm a2j avnt G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by apz 9-n15m7qeu/lk b;oz6pq6 qqfe (yan a(b7 9-yqua eop1zkl pe n6z6fqqq; m/5ngle $\theta$ 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 bab09ecr pa b9)i2a0n+x ul8ggpc09t ocnked for a design speed of If the coefficient of static friction is 0.30 (wet )lp9i pa9+0r800 baxgoctb9ec 2 c ungpavement), 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 that oxm9dwh4wo6 s- :ys4i zof6r/ibjects at the equaty dzmis-6rif swo9x/h4:o 6w4 or were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart4x9jhd5i i eg2 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 c+0hm.kjofd 7uurve of radius 235 m. A lamp suspended from the ceiling swings out to j+ouh7d0k.m fan angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been d5 jhq u7)3yfsclaimed that a pers)5d7s h yfj3quon 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: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an ex1 6m9 4qsf41mixo4jfjcij7rttremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbitinms449 jq jr6c ixi 1m4ff7to1jg 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 shoo icmroo33(uv 0v4a1z rtf8 do:j-6aown in Fig. 5–45. Both the hill and valley have a1o03aurrf6 - oodj :3v8mc4v z(iotoa 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 Posi/j-5a,hkclz jjk8 j3+u 1gcm wtioning System (GPS) utilizes 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 continu 1a3jl umjwcj5 kz/j,+8ck h-gous 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 travedxeox3d- 6x 9*z5pzmi1v* tgm ling 2.1 billion km, is meant to*dxp1d e z*mz5mxiotv6gx- 93 orbit the asteroid 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 a ssq rpizm3r*:0 atellite in need of repair. You are in a circular orbit of the same radius as the satep0zr 3:mqs ri*llite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its meanm4 :ztecuqi.cnv hq- e pqkut)z (lrm)z.),7/ distance from t qrcezq u.4m7eunz,:)ml ) qt(z tvh./k-c)pihe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of 2c7o;y0gl-g9k rirmmh gy1+fG would need to be if you could actually "feel" yourself gravitationally attracted to someone near y o-rgr0h+9m1ic gky gfm;2yl7ou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. nfd,y:w5, bdm 5-46) at a distance of abnd ,bd,5fywm :out 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located ah3te4mr ,5 z vejx:+cp77nc kft the 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 mass placed at the midpoint of the bottom jk :457,7txecc h3m evfnzr p+side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 khw2s hph- 2c*zg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep shfsn8)o ieg gqe8y:.lj +ai8 .econd hand n8fghj ie8+ysgol )ia: .. q8eon your wrist watch?    $\times 10^{-4}$

  While fishing, you ga .a6x:grd w,h;80,8whg bi -gbhco vlet bored and start to swing a sinker weight around in a circle below you on a 0.25-m wvwabg:,r,ilx8b gh68 - hcog;ad0 h. piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trzelfne8(s-+/k9zrfl , r,s o waveling at ls - owfz9sle8 , krz,e+r/(nfspeed $ 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 Acelab -q2*qe/u yij, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerte* uqqey2 bij-/d 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.$\approx$    $\times 10^2$