Sometimes people say that j cj8m 7wlq0.ofv52pj water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stat5.qvf jm2708cwpjjlo ement?

Will the acceleration of a car be the same when the car traz,l3e dpknl+ 9vels around a sharp cuezn9 p,+lk3d lrve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a -w.d+ww psxa6hilly 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 levewsx.+d6 paw-wl stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse (nal h */tsal 16rnuh/on a merry-go-round. Wh//h ua16alrlst( * hnnich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertic*t-*6xpznq bm al circle without the water spilling out, even at the top of the circle when the bucket is upside do-*bnqmtp x z*6wn. Explain.

How many “accelerators” do you have in your car? There are at least threec;q fq)5 /v w nbw9qbl1+wv9fv controls in the car which can be used to cause the car to accell/ wqnvfv9q 9)w5qc;b 1f+wvberate. What are they? What accelerations do they produce?

A child on a sled comapw6tva (l 1vj 4y uawq1y:q,9p 77pkhes flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels theyj: p v 4hu9w1a1vq6(pk 7t,lpq ayw7a 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 hinnr12p rum46sdvr8o6wu+ssi :yu4 2jgh speed?

Why do airplanes bane *oxy/c.m:h )dhr4j dk when they turn? How would you compute the banking angle given its speed and 4 .mreocxdy/ hj)*:dhradius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. nd 1z1z5ebc a4She wants to let go at precisely the right time so that the b1nez 4c5zd ba1all 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 Earnq k 3gl 96yerh,hh3ks*zp3d .4mgcy)th? If so, how large a force? Consider ange*knkpm)chy yz6qs3h34,.g3r hl 9d apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Mjd p-(vd vjg g:42f8zvoon’s orbit be different?jdj d p 4(f-8vvvzgg2:

Which pulls harder gravitationally, the Earth on the Moon, or the M92x+eji3t xc ,rs *knpoon on the Earth? Which accelerates xr2spk i93t,+jxenc * more?

The Sun's gravitational pull on the Earth i ha7i1qtdc(ww uld8f* *p2) pis 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 Eard1 2ai(icwdpp7q 8w*h*)t uf lth to the other.]

Will an object weigh more at +h3 5zmnl*ktgthe equator or at the poles? What two effects are at work? h* l+kg3ntmz5 Do they oppose each other?

The gravitational force on the lq.8nff9pvj;0pap s5Moon due to the Earth is only about half the force on the Moon due to the Sun. 5f098l vp jsqfppa;. nWhy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratep5pucg3 0dwa 8rv6,h))v4 j kre*dation of Mars in its orbit around the Sun larger or smaller dv5rka6w*)a4pvh gtdp , 08)cerue j3than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the etxso/dlxo0r4s8 f j/5ast or (b) toward the west? Consito4l f8r/5 ssxd/oxj0der the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale infibozl;6nc 9srvnj5 a+t9/t* a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?b* n9j+/ra5ovlt t96; sczifn

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long p9qxp rxe*qpn6 )ept*ykusrns7idv;6z c00 9 :eriods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of tsxpx9q7k u*pcv 6q y9r;pz6*nn0 :i re)sed0gravity you can think of.

Explain how a runner /lqo; z b jsrzj3+py8 o1x*0tt8truyad xd019experiences “free fall” or “apparent weightlessness” between so+9 trps8/ yj; dr081ulozby1ta0jx3z*xdt q teps.

The Earth moves faster in its orbit around the Sun 8)r9 zuo2u:g, aogwfy :gra4oin 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 sew:4ao fozyg,g 8:9 2gur )aourasons — 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 s,c 99mswvk7k9twwt bs /g)9kn until it was discovered to have a moon. Explain how this tsgc/9ssw9 tk9b vk 79,k)mww discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mf ss7 w8p09vmpoon'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.]A child sitting 1.10 m from the censv8pfp wm07s 9ter 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 1980p,zthlc *p/p:p7g o b7 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Su(29 tbae.px snn, and the net force exerted on the Earth. What exerts this fotxne9 aps. b2(rce on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniw-hh2-7g-q.lpa,ezxb4qad 4 n+ae ufformly in a horizontal circle (at arm’s lenghuqfb4ng-z a2a q4 a-7h+wd, e-xle.p th) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sunpe/4se25u z5y 8 nwzkrface, and circles the Earth abouten2y8 ne k5pz/4zuw5s once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accect8u( x:ly :p 104s ix*rdzssmleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revot8 ru0sl :(y s1mdszci:pxx4*lutions 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 vertical cir3cws2)j yl)z fcle of radius 72.0 cm , as shown in Fil)f czysw3) 2jg. 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 roundm6ues)9jp,+0a fs l,6eie i4y4l pevga3 t+ ga 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 resu+sl vg+4y,p9p jl0egii4a ue,e)m6at63sa fe lt independent of the mass of the car?   

  How large must the co jrwh 2 xzsowz3x:o13)efficient of static friction be between the tires and the road if a car isz3: zw3jwsh x2)oox r1 to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is des xvtoyd6f9d; iz +)2utauj5r 5igned to rotate a trainee in a horizontal circle of radi zdda fui)txyt9;5256+o u jvrus 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.;8hz u1ob wjm4(* yuklr**b ay0 cm 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 y8 uohb*j; wrzyua1(k*4blm *the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at deb6sz 7f1qx erh.9i*n j+.qjthe top of a ci* 97i. er nj+s6qezb1h jdfx.qrcle
(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 top ;dm0* eb6kb4 bal 1uu/t dphkso 8m:k,of a hill (radius = 481bb t*bhdm:pudae,/0k sl6u k;kom95$ \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 sdh/t wm9l u4w*1m+x-9tzkvc wheel need to make for the passengers vmhc+ws / 91t4m9zu-t*dxwlkto feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirle.6 4+:.ayachylucdvmm /un:v z98 j lrd in a vertical circle of radius 1.10 m. At the lowest point of its motion the tccryh6 :/mzda.v:l8j+ m4nuv a .yu9lension 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 centrl vph :q +uc42fhs9-fdifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 1f4dhh2fl-pc9+usv: q 15,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, .ae8rt-m2wk0 aso (iq e,pkn 9people are rotated in a cylindrically walled "room." (See Fig. ,re ptoaw2 a980 m(ski.nekq- 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 ) .7u(cs8s,nt cu1yt zx 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 (mas 1(.yc,stzu8 usn tc7xs m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the bgnr*ge,; gf6a/tqz+c+a 2d csall which revolves on a s*act+;+g qfz n,g62/ cade grstring 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling dhisbkpdhhs(:gys (jjcq9 v p):u19330j db- 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 massesy3jnbol4 bnlp7z*d- 7 $ 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 vert(*spi 2nspjr /ically 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 cent 85ekmnj kv0c4ripetal components of the net force exerted on the car (by the grok4v c05nmkj e8und) 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 khv ;:/t x1ummarea, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Detemu mx;th/k :v1rmine 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 radius mo l ma0dy,f7-qgp70w2.90 m . At a particular instant, its acceled,ma qy g-7 0w0o7fpmlration 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 on a spacecraft 12,800 km (2 Eartunl;c db - ;c6l12z :rax+ bnv0jgev-wh radii) above the Earth’ldcz-ejlx a:+bvnvrg1 c2b;0wn -6;us surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravisgm5 +bixb+1 l7pwsvd;*p/zg tational acceleration g has a magnitude of 12bwp lggm+sd*p;vxi5+s 17 b/z 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 M-rh 5pyhj7 vpp e64ai9s.ey 7b(if5zcoon's radius is 1.745 a9irh4e7 pvby5jf7c p 6zs.iey (hp- $\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, bu2ioz p1n,zz5(d mk:yct has the same mass. What is the accepcknz,(z51 ydi:2mo zleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of E+ rtno4kb-jq;nr k :)darth, but the same radius. What is g near its surfa;:qd4trokb jkn r+n)-ce?   

  Two objects attract each other gravitationally wi iom w;o3i,d)jy+z.n eth 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 effectirz37mc)*2,axky vwj 5ms g/jl ve value of g , the acceleration of gravity, at (a) 3200 m c ml k/,w z5mj 27)gxjs*3yavr   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where tg/blzz;7 uqj4 hegravita z4l;/7gbzqjutional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a qd sd2- 0j9mvssphere about 10 km90sjv msqd2 -d in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our i z dee 0rzfbf+k/ub* xwm75+k. ;oyf,Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is k dx,+ yf*fow 5 /.fm;bibzzuke+70erthe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spyc r;h.pl 3i:pace shuttle. Your friends respond that the. ; cphyp:3liry thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of :ym(kq zs s4 mtar(-caa ahqu-0.d3;ka square of side 0.60 m. Calculate the magnitude anzrm0.:qa3dq4y-kh tsc m-a ((k asu;a d direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the sa n+aql;fj*y/sbjk2j -me side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, a;bjkfs jan2/ - q+jy*lssuming 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 atm3wv)m;8+q dx req *et the surface of Mars is 0.38 of what it is on Earth, and that Mar+d3*)eqrw vm ; xmt8qes’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usioz/ a37g2sr .-s x zhijqgfz1t io6o)0ng the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.] tozg2.ash1q) f3jrz06i-g /ixz 7 oos   $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the E ms4r -kt/,yoab81ug k+e 1rlnarth atm, ro84u/ la- ky ns+krteg1b1 a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular or glahir44 zf(4 z1,tfebit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when theh4gt41 lf ,r4faezz i( release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if oc ,8 xqdo3w6hnctru 7a4cupants are to experience simulated gravity of 3 q7ct auhx4wo8 6,rdn0.60 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 it takes for a satellite to orbim) n sy,s8f2uh9t 9zyit 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 massfsz28y ,hytui9s9 )n m of the satellite?    s ~    min

  At what horizontal velocity wor29d qhh a.z)nw,u7 pvuld a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit )7hhq uz,pn9rw2adv. around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit thc t :)yjvrch-*e Moon at an altitude of about 100 km. How long did it take to goc:-v h*yj rc)t around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The q40swzo;p9h5 ioxhxqcd .0p5 inne5.hds xq;04hc5p9xozwqpo0i r radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every g+yx/iv6q8ecu5t ;pv15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her rypvi x/+ ;u6vqg8c5e teal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of twtaq2slni7a vqyh4 c6*,:)nu he Earth's Moon in a space vehicle (a) moving at constant veloca uhyw )v47:tqnq2l * sia,c6nity,     ----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 binar;nh)jl30qx p qc(//dh o1x aevy-star system consists of two stars of equal mass. They are observed to be separated by 360 mi/qhxvd0nj(;q ) 1lxecahp3o/ llion 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 5a43.em0h;avodor g q for the weight of a 55-kg woman in an elevator that moga3;va.5 4m0hqod reoves
(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 -bet80my p,,gzspy( b4eb g4sa cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accee 4b0zg yg4e s8b( m,pt,yp-bslerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period w ijq 5nj0*purv/3;juh -:fgz Thp:* u3jujf/ir0j - 5n;zgvqw , the density (mass/volume) 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 of the Moon (27.4 d) to determ93q ;s+s.mlkwojvz a;3zrfzr5 1aza) ine the period of an aas;k a)f 9 q51 vo.mzw +3zlzrzr3j;sartificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun tx,zd(1 )zsw wiupi( )like the planets. Its period is 410 d. What is its mean distanc(iid,uxz)wzwps t( ) 1e from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4gwu --2agq(7 )jn gney.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 7;3laf9b 4 tzxd+vizo v.tn,b s/;bl6f6 years. It comes 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 plv;6a ,bs93x4l z ti+b ovlbt/.nfdfz;anet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce f f nzq 6us27m(ux)k*fxt;yu6nter 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,4fd -qx03 uvax and mean distance for the four largest moons of Jupite-x43xa0u vqdfr (those 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 Ec2do8p;0m ese arth from the known period and distance of the Moon. 82osd c;e 0pem   $\times 10^{24}$

  Determine the mean distance from Jupiter for each*f 8,k4xmtbzn of Jupiter’s moons, using Keple8nm fbx*zt,k4 r’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (wh/ nn1 t .e:o *xdfs;9pei8pmmwich some space scientists think came from a planet that once orbited the Sun butip e:pwo1mne msx9 n*; .dft/8 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 artificial "planet" in the apr-t;u* 8rq 6 xtdc1yw(9)x7 w jijupform of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotat j-w8uq7x9r)xwtc 6jy; t*ppi ( dra1ues 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 frocpnm hchdl8i3k2 /t:.j/a ; zy,vg4mvm a hanging vine (Fig. 5–41). If his arms arj2ac38n4:v t lm ,dvi/g my.z phh/ck;e capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whh5.9pke7xvziv cc;7z3s m5 arat it i crxh5zkc3si7vpm7;e. a vz59s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in mje:vajdyjs bq-,i+y78k 02 or, crl6+-la fga mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.f :k8be0 +c-,mq, jya+yr g l 6ad2svoi7-jlrj0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rot:m c*5wmxj d/9f:ida+l.b yuts 6eyv6ates once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if t y:v ws ldf/md6jmb.t9 5x+iayec6:* uhe 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 directly from qzzw8a9ytb b5z* zv-+v pq1r )the Earth to the Moon experience zero net force because the Earth and Moon pull with equal +zvprq 9) z*-8qabtv b z5w1zyand opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elqq ,5k-ku-vks evator, it says your mass is 82 kg.uk s- kqv5k,q- 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 ro ;(w(ygwe ooo7tate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be;ygowo 7(ow (e felt?$\approx$    $\times 10^3$

  A jet pilot takes hisf. gbh ,xy64tf5nty /s aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of it-qkb( :xdt*f+qq ( 7;iewj thws radius r, the acceleration due to gravity at its surfacedxw jq(;+ibq(*: fqwt7t-hke and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve1 yyn. fc:eeonal*x);rtical by an.ey e;)cfax: *1lynon 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 ofqjv*u68tgn2 9lx d4e, xfus-n If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car s69* ufxsx vlngnt4q- 8 eu2dj,afely handle the curve?

  How long would a day be if the Earth werefk .h.u/5b+gf) wg- sz fh.lru rotating so fast that objects at the equator hffgs fb)u.+/z-hul .5gkwr. were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cons j v / q y5cxw..p:vajf5qrk:oz6yl4l)tant distance 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 curve of radius 235 m. A lamp j13f5h quusmrytt8/v 2xts 8+cn6:aj suspftsch2 :t+a u883j 6vnm 5s1yuj/xr tqended from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timesolzf- 1wjl)o, as massive as the 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 few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Usell)-zw 1fo,oj 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 thg-s fz)s so6;) btw4nre presence of an extremely massive core in the distant galfw nsb6s-;rzg)tos4 )axy 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 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 consn :om8hw.t: fftant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Efmfw nh :t.o8:xplain. (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 (G,/ewkjglh)9w cc/1 v93 nae tuPS) 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 aroundjh9w3a) v le e/twk/u,c9c1ng the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvf.gl u-:wo) t i9shea-ous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 9wuilt.-s: fgeaho) - 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 s)eo tusp:5h w 2ke0(ixpace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km be0w)o k pie uh:2(5xstehind 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 lgp-rnnz 90e2)alf(l years. (a) What is its mean distance from the Sun2fnrzl (a9-epl0 )l gn?   
(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 to be if you could actually "f*hch5f: khhz/ry 7) hfeel" yourself gravitationally attracted to someone near yofr/k57 cfhz:)yh h*hhu. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxyw0yvx)r . /die (Fig. 5-46) at a distance of about 30,00 w0vy e)xrdi./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 r1+8 c w8orf7 hg76trle)heti2t pq(z square 0.50 m on each side. Find the magnitude and direction of the gravitationa 1r6pchro g7l72tt )z irt e8e+h8fwq(l force 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 orbits the Earth3r0ib//iz ym+ d dpi.(e3gku l $ \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 oft/ slh3mz*)u :hir/ v- ,u lpfp8ea.qd the 1.5-cm-long sweep second hand onf lu/ie q z/sph)l tuh:vd ar3*-,.pm8 your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker 9axl*- z a: yglma5os8weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes wx 59l-mlas*a8g yo:zaith the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car traveli d/3un uvgu6*ing at sp id/3*u ug6vuneed $ 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 u/v1ta ewkea05yn86 2 ngx/y(wz q;iotrain, the Acela, utilizes 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 expean/ aiekwn68 (5xyv 1g tw;yze2uq/o0rience 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.$\approx$    $\times 10^2$