Sometimes people say that water is removed from clothes in a spin dryer by cen g:fnw7jeicx9)5/ poitrifugal force throwing the water outward. What ie:7 ij5iwpcg) 9ox /fns wrong with this statement?

Will the acceleration of a car be the same wh;hgbve2ouqe mq ob3 cmrv . j7ak29.1*en the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expjm9 2.hbraoq; .v* c u37bmgq2eeokv1lain.

Suppose a car moves at constant speed along a hillyi88/ hmbws +uad; 0dti road. Where does the car exert the greatest and least forces on th/0hds md;8bwau8+t i ie 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 acting on a child riding a horse on a merry-go/bcf c(zsg g37-round. Which of these forces provides the cenc(s7 b/cfg 3gztripetal acceleration of the child?

A bucket of water can be whm2x9(uhww a s6dz 7i7mirled in a vertical circle without the water spilling out, even at the top of hmsxz7a92wd7i (6wu m the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There qjoh04nk*i sf9,b 1cq are at least three controls in tbk f*,q0n9hi1oc4qjshe car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comescvo )z ush4s-6.go lk8 2sx5ds flying over the crest of a small hill, as shown in Fig. 5–31. Hiscs4x-u)86so.kv2goz5 hl ds s sled does 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 rounding a curve at high speed?y e43nl72 ( al-3jxaakbcpolsb-o 0;j

Why do airplanes bank when they turn? How would you com8k ayyd wh -s: a5.0raisd4m,gpute the banking angle given its speed and radius oaia sgwy-sy.h05m 4a8 dd:rk ,f the turn?

A girl is whirling a ball on a string3 ipinxn25:/;r * k dvgvnr.rx1b6vg k around her head in a horizontal plane. She wants to let go at precisely the rigp5ik*v1 rxn/k :.6g birnd3nv;gx 2rvht time so 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, how large a for/onzphtgw ,y1lv sb1-r.g8 2bce? 2tho118,bg/l zv.wsg bny-rp Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it 3zk8b z,q6m zzis, in what ways would the Moon’s orbit be differeqbkzz mz63z8 ,nt?

Which pulls harder gravitationally, the Earth on the Moon, or th m gm(ino;zis)tmyz hjjb1-hj-84 +r :e Moon on the Earth? Which ac+b;rt: 1js(zzim h4ho-m)j ijy8gn- mcelerates more?

The Sun's gravitational pull on the Earth is much larger thau+ms af+sfw /h9i5ap:n the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth +a msf s i:puh9fwa/5+to the other.]

Will an object weigh more at the equator or at the poles? Whad.t0q0:xbbmm f v o6 e,-emp-mt two effects are at work? Do th6bdp 0vemm ,et:mfbox.- m0q -ey oppose each other?

The gravitational force on the Moon due to the Earth is only ab0n 0k9pk:vz6k ;zgmt sout half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Ea;t 0k sn9vzk:m0 kzpg6rth?

Is the centripetal acceleration oa06nnn l q zmr5.slv:/f Mars in its orbit around the Sun larger or smaller than the centripetal accelerns50m 6:lz/lar .nqvnation of the Earth?

Would it require less spea7(+f skga*n fed to launch a satellite (a) toward the east or (b) toward the west? Consids+ n 7(faafkg*er the Earth’s rotation direction.

When will your apparentlra2a u32 )ocx weight 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 consaro23 l caxu2)tant 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 be a 3c)v c3zex4ln:zl *yhdversely 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 simula3):yl3*vcz 4hn zcxletes gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apch d93jswms2n2 /mtr +parent weightlessness” between stepj/ dtm hc2s+r29snmw3s.

The Earth moves faster i5jkw+ 0)o abkeemu3m6 n its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seaso)kkb6u m5oe3w0 mja+ens — 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 moon. Explailvp49g73nxw:wv pyi 4n how this disc7lw9ig4:ppv xy3w n 4vovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th,2nekud fv948ywlzc *e Moon's is mainly responsible for the tides. Explain. [Hintu*eznfwd l92ck8v4,y: 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 traveling 1x /3ph jjtr6f8 sz+xbk+yhi-(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 acceleration of the Earth in its orbit around the aw ,oq dqa 4xjjem4-ak7i8x.3Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbitj 4.wqx d-xj8eqm,a4a i3 aok7 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 onrtg,d i834y cs a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of thi ,rg84yts3cd e discus.   

  Suppose the space shuttle is in )+ x:4macwvt blg1cabw4wu42 zpt b):orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational accl: twpc:wuztb4)1m2 ag+4 cxa b4vb)weleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of accfvo*7 a et0. potter’s whe ct .7evfo*ac0el 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 uniform rate in a verti/3cj*d5e xdt g.tqu -e0gp/qk cal circle of radius 72.0 cm , as shown in Fig. 5-33. / ug3dtq*/. tqjkd0xg5c-e epIf 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 whv2wdrd3 rv g:+x5p2s+dvia5w+be gw; ich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepe5;2wd revd3wdiprs: v++vbw+g52x ga ndent of the mass of the car?   

  How large must the coefficient of static friction b9:x 8xq+ 3n6bernay.juz. ptqe between the tires and the road if a car is to round a level curve of radius 85 m x. a+nx.: tez6uqrj8y 3p9nbq at a speed of 95km/h ?   

  A device for training astronautiy9 3oyd 3 r( p6/n*zinbpb6uus and jet fighter pilots is designed to rotate a trainee in a h yd6n/n* 6rbp iu(9zbup33yio orizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 67ey y: *n0mblvp+ozvcm from the axis of a rotating turntable of 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 reached and t blvn0*y z7 mpo6+:veyhe coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a ror 1qyguu2fr /7ller coaster be traveling when upside down at the top ouyq72fr1/r guf 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 950 kg (including the driver) crosses the rounded ix m;31/w,sik9:3sbtyacp y c top of :psk/bwsmiycyi , ;atx9 13c 3a 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-diameter Ferris wheel need to m.h9p)aby+n2 n5pkpoxd yus;4d4y4c lake for the passe)d4 by+d 9xpaoc;p4y 54yns2unhkpl.ngers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of r buy ra5h/;vvsafnz gtq+*06/adius 1.10 m. At the lowest point of its motion the tension in the rope supporazs +y*g fhvtnabu;r56q 0/v/ting 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 cent0rhoy:q 1kaa9++ aj-mb7cpourifuge rotate if a particle 9.00 cm from the axis of rotat:o c b1jaaomh-y9k0u+p+a qr7ion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivab6a+ u,qi:rnql, people are rotated in a cylindrically walled "room." ( +:anruiqb,6qSee 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 rotatevm4 x0nvoml dy3w-a:) d in a circle on a frictionless air-hockey tabletop, and is held in this orbiw0): 3nl ma4vodv x-myt 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 ,;i,tk 0bbdiq this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particuid 0qtbb, i,k;lar, 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 8y2ts:u7jy)xsycv enf vr44z ejkt ,pa:;,e*. 8 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses :pjhp buq d0j88oo,/c$ 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 ver) n+3 bmp21k;ll,iw widcqfo2tically 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 t(y32t2bunj db0ggdguj xchsh7 +01 v-he net force exerted on the car (by the db3 j +10jt ngv2bdsg0huhx7c2gy- (uground) 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);hnd 1cxey ,uy n5 stx263bogp6 :+tkkp-svq pit area, going 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 consc6ks+t bpnkdnxyp2 he ,;5x t)o3-:q6g1uys vtant 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 radius 2.90 m . At a particular inqi6-)s g ln6twpa2s f:stan2w6 :-g6aiqs) nltsfpt, its acceleration 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 53*yrskzo.dxqz 6mf, on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfaf.my,xd kr35z oq *sz6ce if its mass is 1350 kg.   

  At the surface of a cexh,el ck ugm,z:g(e*.cr46aq rtain planet, the gravitational acceleration g has a magnize*g mqhg 6c.:4u,a lr, c(xektude 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 xp xfzz zmls)yhf2.m 703 v**rj+r57ost)iy nthe Moon. The Moon's radius is 1.7*zrj)+ v0 37z sff x.5smrp *yi yz)htonm27xl4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but hasksjs9 o uaw1asj/knwa5 /n2/ . the same mass. What is the aau/2 9 a5okswa1/j.nsnwkj/scceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timesd ;xeanjdi/4l:d w /0s that of Earth, but the same radius. What is g near ;/:lwix4sd/ a0nde djits surface?   

  Two objects attract each other gravitationally with a force;;mdn 0e zmt,a of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration ofi;a8 esu1)are gravity, at (a) 3200 ma)es8i ;aru e1    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsidi4*,ipc6 ejf+t+ r9zu bop/ ude the Earth where thegravitational acceleration due to the Earth+d 6 i*r/czj9t ieuu 4fop+,bp is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of d2r3cnaff /- qour Sun packed into a sphere about 10 km in radius. Estimate the surf-q/23fa nf rcdace gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but /z(zj3w rjji 1is 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 gravjr(/j3 1i zzjwity on this star?    $\times 10^7$

  You are explaining why ast- gy3z 50lyrsyronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince th53 ygzs0r-yy lem 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 afer) ei9f2ai. qiz; *zre located at the corners of a square of side 0.60 m. Calculate tzff*9i ;iaz2 q)r iee.he magnitude 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 a( f ewxhj:;t6most of the planets line up on the same side of the Sun. Cw h(jt;x 6a:efalculate 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 accelerationtduyvuoecx,sy +n90ka(mj i w 1 92s)3 of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius )9m3ukx+jtvyd20 sawu oc( 9 ,syi1 neis 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of eb,3(rop2ni8 q gxp ,bthe Sun using the known value for the period of the Earth and its distance from the Sun. [Note3oi ,2bb pexg8p,(nrq : Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satc j 3hx8o:9e44pdjby wellite moving in a stable circular orbit about the Earth at a height of 3600 km.bpw3y4 d4 x cj9ehj8:o    $\times 10^3$

  The space shuttle releases a sate8b*)wwbh4zj6 pc8 l isllite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?8bzjw6wp )4c*b hsl8i    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are ts /,)4yogcufxvhcr .+e )ova fnqf s 2+co:x*,o experience simulated gravity of 0.60 ,vn:fh,g)qfav c.fo)xc+ y4 ur *c s+s ooxe/2g? Assume 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 orn aag)4f3e)i abit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of a3g ) afi4ea)nthe satellite?    s ~    min

  At what horizontal velocity would + (j2pb,dbwt t9.wy ry,f8pgda satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earthtb+8 2d b rpt(.w,dpy,gj9fy w?   

  During an Apollo lunar landing misgn*:fga5pj ;fsion, the command module continued to orbit the Moon at pa* :g;fgn5jf an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that or +3ckxtc5 m.pqbit the planet. The inner radius of the r5 .cp3+tcmxqkings 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 eve6dsf20 azb hc9t)oted iy/l;) ry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top a9t bszdf /ed6)yihlc)0 ;2ot, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200k,i;q*) u wzvi7**u fz/l eteo km from the center of the Earth's Moon in a sp*ik oe/fqw),l uv7iu; zt** zeace 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 of equa6t:esvtjr ej1i/8br;l mass. They are observed te j t8jvit1r/e6:;brso be separated by 360 million km and 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 weig 5 pb(i l3)f0 z..bzou2jaabboht of a 55-kg woman in an elevator that mpj.u5f.boa(ob 3 2 i0)zlba bzoves
(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 hang4;sjeheti*4d n wxqp g: g0z8.s from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directiox ep8 j*4;z: edw4sg0gi.qhn tn)? a =   

Show that if a satellite orbits very near the surface of a planet iehml+b0:op w*o,d7r 8. k qphwith period T , the density (mass/volume) of rw0 ko7 d+qib8:lom.hh e,*p pthe 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 trqjk j j/c+x7+he period of the Moon (27.4 d) to determine the period of an artificj/7xc+ kq+jrj ial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thoughu7 4 g4tzyvuh(t7xov4 zs 2j,q only a few hundred meters across, orbits the Sun like thez t74 vsoqj 4yu,(u txv2z47gh planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of -k/0jw:n2m 5u(gn s xxsg /t qwb/sop14.5 $\times 10^{9} \mathrm{~km}$ 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 verlzi rn0g*/-gy 3pvke8 y close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law isygv g0p8- /3l n*rkiez half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy eyu:.91xs:p leus )xi $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 tyb p ovqy6,xnb*m- :s sz,-34c fzrrq/he four largest moons of Jupiter (thszxr:m *cbsb q6, pqz4yv o ,--f/ynr3ose discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and dist-3ezj9dbod, h l 1.gknance of the Moon. .l g31h ,odjzb-9dk en   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of q*ot;slka o82Jupiter’s moons, using Kepler’s third law. Use the distance of Io and thq8;skto 2*l aoe 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 many fragments (which sj hvr16 coj,eqf c5-f1ome space scientists think came from a planet that once orbited the Sun but wforc-v 1jqje6h5c,f 1as destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" gnh+ hx8/ lw:uin the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noonlwxn+8 hhu: g/). 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 Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5–/ z xeksfe;u , agm*lyk,x(0+r41). If his arms are capable of exerting a fsag ux e0kl+/f,e, x;mkrz*(y orce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hald8(as 6qlbq- h84eh tcf what it is on the suea688b tqhlh4 dsqc(-rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands-upc; m:xt2 y:n5secy -6mhu j 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 e6t-u yucymn;::x mj5-2hc s pmasses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelera l/hpl4 f(u)csfvyx4o h;6o,gtion of gravity at the equator is slightly less than it would be ,o hyc o4g(uxf/l)lph 6;f 4svif 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 E(:el jb8(xw jdarth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? dx(:j jbe(w8 l   $\times 10^8$

  You know your mass is 65 kg, but wheus j;sb0p9e ;jn you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in;b9j espu0;js which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular kyg/.dr9ysrj+qpf* 5 tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The c5./rp9rgf *sj+qydky ircle 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 vb) oh3 e* rbzchhqt2a5y859zin 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 inmwo ;ay -m b1eyc: bi.f9m0-of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitationalaic;weom.fb -i9:ym10mn -y b constant G.

A plumb bob (a mass m hanging on a string) iu*1ssw r*) hh2myej)np19rz+ mv p-bks deflected from the vertical by a )s 1hsn wrk*b9z*-2re u+ 1pphvmjy)mn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of Ijt6h3d4pfz a: f the coefficient of static friction is 0.30 (wet pavement),346dap f:thzj at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth whjusry2vcuxpi 0vl;547 p+b (ere rotating so fast that objects at the equator were appars(cu;r7 v 5u +bivp20x4hjp lyently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of ewf : thr 5xrsz31;yblk) f8:l8.0 $\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 speedzjo4xktryvniq;et.;8vig* l d.7 ly2 2:sy+ h rounds a curve of radius 235 m. A lamp suspended from the ceikoe4 l ;y .2s8vi+hxtdy7zq r; lvinj ty*:2g.ling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as thy jh:z.h 9eo;mpra( i0e Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a fe h(j; hie.azop:9y r0mw 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 Hu+v3aatr d(mj4x, teg9 bble 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 measuring the speed of gas clouds orbiting the core to be 9dra e av,3tj4(xmt+ g 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 vb*wd qf1i:g e:alley shown in Fig. 5–45. Both the hill and valley have a radius of curvatur1wq:dgbe f:*ie 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 (G6swc(cpp8w9ln 5p ilfn +lf,, PS) 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 co,ipcp6+(p8l w5,9fn nflwlcsntinuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion kmt m1h2 pk/iekwsg(c,0, is meant to orbit the asteroid Eros a1 m2p,(tk/ws i ck0geht 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 spadf83/t) h ctczce shuttle pursuing a satellite in need of repair. You are in a c tcz8t hc)f/d3ircular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period ofk9hnclm:3qh(ndnk/mi4 y( o+ 3000 years. (a) What is its mean distance from 3(lhnh4dcy ( noim/ qnk:9k+m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of m kqjnq--k36d G would need to be if you could actually "feel" yourself gravitationally attracted to somek-qq-k3d6jn mone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center o(yk65k txytn*w8b rg4 juq ,(pf the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,005t tkk( yux(qjw86r4* bnygp,0 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 at the corners of a square 0.50 fj;, (b i :vvjrke-bh5mkzg -(m on each side. Find the magnitude and direction of the gravitational hk(:v z-j- frvmjg5(k ,;bbieforce on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg* s(bvoi,u,z/ps8(kz, k nhhq 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 sw69iwmr/kxhs c /2(utrov2d/s eep second hand tox2c/r d iu(w/kr 962ssmv/hon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start1eg)m1mb w;u y to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a compbw) ;y11 ummeglete 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 0k.bdd (-qpucrj:hw9: 0pvrj so that a car traveling at 0pbcv.dq:(d0-9r h k:pjw rjuspeed $ 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 ofysc jvw9 zkx6 ,w3v(y1 the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the ssy ,yvjw3c( 6z19v xkweat, 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.$\approx$    $\times 10^2$