Sometimes people say that water is removed from clothes in a spin dwjs 2ljsag7bq/3 )ol9t*bv4 kr nb .m)ryer by centrifugal force throwing the water outward. Wl3bb 9sjrv a )q42lwo smn). gb7tjk*/hat is wrong with this statement?

Will the acceleration of a cauil28afx l w.dok )cnh-2gxq5v 9 47ikr be the same when the car travels around a sharp curve at a constant 60 km/h lau4 .kn7oih dqx5l8)c22wfxi-9gkvas when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed al)d. n3dgfc:spwn (v7inaf4 w3ong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a lef)wand( g vwnn:f ds4i7c3.3pvel stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse +eh3 v/1idn vhon a merry-go-round. Which of these forces provides the centripetal acceleratv d/n+3ehh1vi ion of the child?

A bucket of water can be9 a60ajjspz( 2cumhnf wy6* xm0(wa6v whirled in a vertical circle without the water spilling out, even at the top of the circle whjh6 w(6x sua6f 0 *am9znc(mw2ajvp0yen the bucket is upside down. Explain.

How many “acceleratosuxa 9j1clf9 u 1 l6 pf5kx2fvxs5v+ 5l/e:imprs” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?1k: av u /x u5+j 2lps5li9f1xc5vxme6f sfl9p

A child on a sled comes flying over the crest of a spu 7h;w+r 8y7 bww*avf +rq:qdmall hill, as shown in Fig. 5–31. His 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 N:7abh f+rvr* qdu qw7 wp8;y+wewton’s second law.

Why do bicycle riders lean inward when rounding a curve at high sp i4-6ga, aabh: y+mddpeed?

Why do airplanes bank when they turn? How would you compute the ban0a 2jouzq6:9l 5uazkwking angle given its z65oka0zu9 u: lqaj2wspeed and radius of the turn?

A girl is whirling a ball on a string arou on0ir6;9 q0 ht4itstgnd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should shet64gq0ti irsn9h;o0t let go of the string?

Does an apple exert a gx) vdl2m te/; yb+p0vy e -ni;axovp+:mx(v2wravitational force on the Earth? If so, how large a force? Consideo(xvet)x yvm/i:a d m+xv 2pb2;+-y 0v lpnw;er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass werey(v( o)veo9d0mvx 9p er7nj .c double what it is, in what ways would the Moon’s orbit be differeve9ec9 .po7)xy0vmdon(j( rv nt?

Which pulls harder gravitationally, the Earth x*w-pde0x zu: on the Moon, or the Moon on the Earth? W exx0 wpu-z:d*hich accelerates more?

The Sun's gravitational pull on the Earth is much larger th3zyvqr ym *88kglrv d h(v+m*s7oo(( ian the Moon's. Yet the Moon's is v*ig8r3zsdyy*oqkmm 7oh+ ( v8l(r v(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 thej4 qv6q z fp2hecoj-:iskqi/9w*.+do equator or at the poles? What two effects are atqw ci 9pj sevqokd 6-*4zhi: o+./fqj2 work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only aboutyx*rgywfqt7i 6 1kn( - half the force on the Moon due to the Sun. k7rqy*(i16xgfy nt-w Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orws )c)d;wd 4fqbit around the Sun larger or smaller than the centripetal acce;c dq)w4wd sf)leration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or+7odop :82x -kt cjqkm (b) toward the west? Consider the Earth’s rotatmt:p-c kjo+ 2xq7dko 8ion direction.

When will your apparent weight be the greatest, as measured by a scale in j 1t-ad;b, sqla 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 when yod b 1-q;l,atsju are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer spac0a 4e1pu o2hsfe 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 (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can thinks0h2fep 4o au1 of.

Explain how a runner experiences “frj,sxk9oj b 9g+:: eeqnpyu-i:ee fall” or “apparent weightlessness” between sn :- xj:ej9ip: ,9yusqe+kogbteps.

The Earth moves faster in i8 waq1 v2k0ujrml8md)ts orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Eart8u mj0qdwkal 18)r m2vh’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was ddv8 ad(9wjz8q9+sdzbsv qj (n b-m;b,iscovered to have a moon. Explain how this discovery enabled an qdnb+8 vszd;a mv9z,w(jb(b8 q9js- destimate of Pluto’s mass.

  The Sun's gravitational pull onveh w/u6)y13q9a vexw the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]v)h93uxe/ wwveaq y61 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 travelin4jb6yci)p;7 gvi:znvg 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 in it+jchr* 93gp2)fi mdt ybx/;xs s orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? j *xh)29rdmbix/ t+g s;3fycpAssume 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 ex5ub0i5nu y,9yfb90e wb7 rsvjerted on a 2.0-kg discus as it rotates uniformly in a horizontal cirue0vyj 0bb5 rsbu95fw 9n,yi7 cle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, anfe yqwdzr7vm*nx-vuqe 1)71f:xu(7zd 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 gravitationu fvmxdeyz17(:- 1qxfwvz*7)u qe7nral acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accele 8ktc pth 1c:7swn.y4uration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cu1 :ty47sh pkc t8n.wcm?   

  A ball on the end ofr,d 4z0i 4gx)5dzdrvh a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as xr dvg0z d h4ir4)z5,dshown 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-+n km5l:g;d zvkg 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 ind5nv kmz:d ;lg+ependent of the mass of the car?   

  How large must the coefficient of static friction be between the tires0.d dzg75d5+tmyzqy52k deup and the road if a car is to round a level curve of radius 85 ut5 dm yy5qz7.kpz 2d+5d0gdem at a speed of 95km/h ?   

  A device for training astronauts and jet fighter piudjknr i/o9*kfhc 01,lots is designed to rotate a trainee in a horizontal circle of od/9fj1,uk0 irhknc* 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 nh5v 2/35pfearduzrg 0w*t .lcm 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 the coin slides off. What is the coefficient of static friction between the coin andzdvrf2l*n ar/weugt5hp3 . 5 0 the turntable?   

  At what minimum speed must a roller coaster be traveling wxr942)pmxrhi hen upside down at the top m 4ri)px9rxh2 of 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 roundedrp,wtb ( 2zkwprx1-mxs22uo+ top of a hill (radiuwsx 2 pzwomrb(p-ru2x,1k2+ ts =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)bes(1n9wm :w yb3 ndm to make for n wswey mbdmb3 :n)(91the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius nfxo*36zqk09 s nz+5f2qgyqa1.10 m. At the lowest point of its motion the tension in the rope supporting x2gn3qfsz*qyq+5fo 6 n kz09athe 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 ai fq p1v60rif ktf7v)9 centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an ar t v7qf01fvif9kp6i) cceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylina4m mlfbwh8iy2yv *n n 1+;w9udrically walled "room." (Swymu an1hiywv+b9 m4*8;l2f nee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tas7cr90ic .m)8,qm qyf k9yam fbletop, and is m f qy)fmy,8ciskarm97c 0.q9held 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 irn1.tr9me+as gnoring the weight of the ball which revolves on a string 0.600 m long. In prnats. e9 +1rmarticular, 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 df6g unl f/sa+()lbe- of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse1-t9ef x bnw4j )h6 yw8l5mdb*z 3uhdgs $ 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 di0*7 qavtj n3rnving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components ;aektos,+ls/u /1 chw bj6z(o of the net force exerted on the car (by the gssz+/1o aw;bjcet/lu , ho6 (kround) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going wy2oq1jt-,rsfrom rest to 320km/h in a semicircjswq y,t2or -1ular 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 horq g t*;oxwi*u+izontal circle of radius 2.90 m . At a particular instant, its aci*gwu ;+ xt*oqceleration 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 o (zvvr/9q zh5rf Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if it (9z5z r/vqrvhs mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratib3adg )/z+p kkvfz9 qts;;uy ,on g has a magnitudebpzu;ky d9ftv+k / ;,)qs zg3a 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 gravf r/l;(7 bfu:)d idw,ncytc/gity on the Moon. The Moon's radius is 1.74 :fitl7f/c/w,rnd ducy( ;gb) $\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 has the same l xbt7ud:6 o2bzj+:3 2ydgdygmasj7g3b t:do+gy2d:yzud2 bl6 xs. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 e w y1p,2y v3krq4fc9utimes that of Earth, but the same radius. Whfckq2e pyu 13v, 4yrw9at is g near its surface?   

  Two objects attract each other gravitationally with a force of )s.sxr s)0atvam-k:wgo b.3,vfpf2g 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity,gusf;i0yi)o-5. u)q gji *b gf at (a) 3200 m uo i)ysqfig-gf 0.5 ;jui*)bg    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to vu zu5 fpv(b(:co 1m8la point outside the Earth where thegravitational acceleration due to the Eau(8ol:vc(zf bpuv1 5m rth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed in/bzkfdm2u j3 f:8ml *nx5dv y-to a sphere about 10 km in radius. Estimat:dnv8xfb-d5k2zjf y m3 m* /ule the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an a n(.ba-h, hjua/ qvpn3i:x7li verage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has thebhv-ju(. : /na a,iqhn73iplx mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astw brl6 .)p7dkfronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acce )l 6pw.bf7kdrleration 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 side 0.60 m. Cmck)hv (fl u8(alculate the magnitude and direction of the total gravitational force exertev u c8fhmk)(l(d on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of ck4r5 s;12*pxkvf+p it0uov h the planets line up on the same side of the Sun. Calx1 v;so htck5+20fpi4pv urk *culate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity atmpbrdw0pu 3los7l0f. d3 m-3 g the surface of Mars is 0.38 of what it is on Earth, 0l lf3pdmw.su3m -ro0bp 73gdand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of ta5z+hav8l9f9o,twxbh c +) smhe Sun using the known value for the period of the Earth and its distance from the Sun. l), 5a++ ms89 zaohbxc9wvf th[Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the 83c4m5zsqife s )s mb2Ears2ime z b) qss35mc4f8th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satxc0mfsjk *k f,/+ch0kellite into a circular orbit 650 km above the Earth. How fast must the shuttle be movingx k k*cjm ck,0+f0/hfs (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are tl7ih;q s6v ;oao experience simu 7sa6qo; v;ilhlated gravity of 0.60 g? 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 ite(3a2 sj/behzm/e 8od1g t9xj7efuh 3 takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. hueexe jt 8/om(dz ag31jhf39esb /72A “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 satellite?    s ~    min

  At what horizontal velocity would a +m -atf,)xhirsatellite have to be launched from the top of Mt. Everest to be placed,hfxr mita- +) in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, th fbho )) .0dp8.ncp spiww3;exe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once? ps.bc30n;i.d))w8oeh xpfp w    s

  The rings of Saturn are compos4.qnj6o bbu 0led of chunks of ice that orbit the planet. The inner radius of the rings isnb04 6jl qoub. 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 (o7xmf uls9fw+e *;n.8xl :pi csee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top*: +mloic8xxl;we9fn.upf s 7 , and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from theod , ihits d8 +/,9zpya;yffo10szx -e center of the Earth's Moon in a space vehicle (a) movi os-0z9stii/8,fxd;e pyd fyz 1h,o+a ng 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 oz;t8hmfl y7 zl4aw+ g*f two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years ha*fz ;+zy7lt m4l8gwto 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 688fhiumdl. k2s unq+of a 55-kg woman in an elevator thaf8hmq . k+2dsu8u li6nt 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 from the ceiling of an elevi 87yfe 8z z5dtsgo).mator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minis)8eyiz7zd.mg t5 8fo mum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near theji5c5s,x tcu j,5 a1sl surface of a planet with period T , the density (mass/vola55sstj1x5j c,, licuume) 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 tp (.18gc0.pks jr0ou+ ioqen0u*rosthe period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfacr0gso (r0cuqk p8 1js. o*oe.p n+iut0e.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun 8lo )ht;y,) 5 fn8bk(zygwv8ap7ys lt0yjgx0like the planets. Its periodoyzt8 (p00 gyxj y,hgy8slbwv5 8l)kf 7;)ta n is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancb0, jokiy5 ;sy2 woly6.*lqdoe 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 comesw7vb*8 c*/q z;ync x dzd3w;gt very 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 ;n qc vz* cx3db *gdwyt;78/zwthird law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galov( 7g-eaf) ewo1 )wsfaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 di b lac, zqxg0z48s1uz8stance for the four largest moons of Jupiter (those discovered by zc0u 81lzqg 8 bx4,aszGalileo 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 distance of the *qd)3g/r gadf Moon. fd*g3/ rqd ga)   $\times 10^{24}$

  Determine the mean distance fromtv 2t k+qqw+ omko v.8l34+lro Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Cvmqo4ovr++l +k8oktlwt 32q.ompare 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 (whcp 2+i:syo p*b-d3+valmvlw,xa t+4x ich some sp+ -x vll mba+sy+2:*,toa4dxpwpi c3 vace scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes nq 5 nuw9g, k5ms(np)yan artificial "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(upk gwy nn9)q 5,m5ns 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 a8tq.(fm 7amslav9fs,0dxra 9 rc from a hanging vine (Fig. 5–41). If his arms are capable of exertingra0a9l,.mm7axds9f8s qt( f v a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the ac 66r5k + ,zq/tpyi lvrz;0yusjceleration of gravity be half what it is on the;ry ijz /s5kz+rlyt0 q,uv6p6 surface?    $\times 10^6$

  On an ice rink, two skaters of equal massbwrn8x y5 r2i9 grab hands and spin in a mutual circle once every 2.5 s. If we assuiwx 2rnry5b9 8me 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 ap6fqe wyr kk;-8parent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnituder6fy8;qk wk- e of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrzvhthcu ql4eh2 +t1tk.vz7765k, f imaft traveling directly from the Earth to the Moon experience zero net forcezz4ctivqk+ehf tk, 7h2lhm17u6. t5v because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale i*; b:fvl7qkg in an elevatoq7vi* :g k;bflr, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistsfi(z1 k0 z;qwr of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The cirzw ir0;k(1f zqcle 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 in a vertical loopd kbg;7r hjc/ svjj+0+ (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 terdru +m7 -fyxg*ms of its radius r, the acceleration due to gravity at u-yd7 +* gfxrmits surface and the gravitational constant G.

A plumb bob (a mass m hangty b 2.w8*,fhk9vb ayfing on a string) is deflected from the vertical by ab,tkwff2b.y9hv8* a yn 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 1g dd vc)*a 1*rqg+iobis banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curog )cagb+*d1id vr1q*ve?

  How long would a day be if the Earth 4 rlik v9m*a qh) zvi76)edhy1were rotating so fast that objects at the equatol6)v4zv79*khy em1qi harid )r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dist 7wdznwkk1*z;n(f rm/ance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a cc p1cp.vmzu26 p62( uiloi hsa -2e2 v;vjdk0turve of radius 235 m. A lamp suspended from the ceiling swings out to an amv2i60v2 k.ae 2po;dp(s 1u-cizphtjclu6v 2ngle 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 claimed sqwyf8o 4 +h2nthat a person would be crushed by the force of gravity on a planet the size ownfs24+ 8 qyhof 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 Telesed g* 2)t*7j.bjklysn py8v.dcope 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 th72 )dpv k*yjj*yl.ns .8tdebgis by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speefi3rp(6.lw+lu hosu +d as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R.rsl(.i oul6pw+ 3 u+hf (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 gro7ebl2c*k ojol k3c* 7eup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude*bo7 2lek* 7eoj3lk cc 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 bbn(27e 6c bs(nf5/guo 9aq iobillion km, is meant to orbit the asteroid Eros at a height of about 15 km . Er2a b95s b/qb uefo(7nnc6 (iogos 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 satellite in need of repac cygac1bi*pq d095m u xg xin*+i04a;ir. You are in a circular orbit of the same radiqy; x+0 *9c0 m1iia ad ngbicxcu54*gpus 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 hn , n)e.suyi g(n0exsftd5;cr3e5:ul as a period of 3000 years. (a) What is its mean distance from the:,enset y;d n nu(xl3 5u)crfi0s5ge. 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 G would need bpvzaw1y8kl7te ky-b; x2; w ;to be if you could actually "feel" yourself gravitationally attracted to someone pv-;b za1wkbx2y; ;t7k8eylw near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroun 5ovsr.j*(ppid the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 li(sp.p5* vrio jght-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 a .rdq ,-j2ezrwkee7s, t 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 side k-w7qe e,rrzd j s,.e2of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the u9jdrqz:ou ;nj7)m -u 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 sweeph*woer:n- *tqv0w 9z/bwk au4 second hand on your wrist watch?w ubkwwq 0vz*-t* r4e:9hn/ao    $\times 10^{-4}$

  While fishing, you get bored ands ipwp:mr g)(4 start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing rpwm )4spi: (gline. 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 s nt5reos4xu,z;la)8l*pl2ddesigned so that a car traveling at spl nu lo p2te lr)zx4ds8a5,*;seed $ 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, uek;ho r f7fmv-gju5(xc2 8 i/y2qn)xf 1tj)q ytilizes tilt of 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 seat, thus feeling more comfortable. Consider an Acela train that rounds a curve wi qj25th(;f2 rkj )1uf8 gx)x y f-niymqo7cev/th 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.$\approx$    $\times 10^2$