Sometimes people say that wah;e:u3pjb c; il/te;m ter is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this sta elc3 ujipb; mt:;/;ehtement?

Will the acceleration of a car be the same when the car travels around a mi iz7q/z0)hrsharp curve at a constant 60 km/h as when i z0z)7hirm/iqt travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does themq-emfl:)oo /ij lf4 1j.w c-/.phulw 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).loup ww o/-jm:f-/ hjicqfl1e4m.l) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse .aze ow5+sxfb 1 i+ge:lfd(v;on a merry-go-round. Which of these forces provides the centripetal accelerati ee lfg+swazd1vf.x+(;bo i5:on of the child?

A bucket of water can be whirled in a vertical circle without the water spil72dk xwyj63p4wh cdo) ling out, even at the top of the circle when the bucket is upsid73whcdp4 k oj 6w2y)dxe down. Explain.

How many “accelerators” do you have in your car? Thef ::/ cr96;e ipuovtrore are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleration/:pue;6 iof:r9v cor ts do they produce?

A child on a sled comes flying over the crest of a small hill, as sho3/ yu: ujan:ofwn 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: n/f o:juyau3 using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high 7yt2tg*cjf-i0jv3 w dspeed?

Why do airplanes bank when they .y:0ubpl vcx sk 3hzf 07-up9hturn? How would you compute the banking angle given its speed and radius b 0k7:v0y zc-psl ph3uxfu.h9of the turn?

A girl is whirling a ball on a string around her head in a horizon:j.v/avqu +b4atyc k2 tal plane. She wants to let go at: +ty/4b vv.ac2jkq ua precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forceq m*jjci: f,6r3f9f;w alcy/s ? Consider an a6j/9ri :s3,y; fqa f*wfcm ljcpple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double gi axwf x4,b*4sb5fgf r)e5a07qoq 3awhat it is, in what ways would the Moon’s orbit be di*foe xgib43)qag5fr 7s aw0bx4q a5f,fferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on t pyhmf7:x2*u( viabq .he Earth? Which ac (x2yhbm*a:p.fviu7 q celerates more?

The Sun's gravitational pull on the Earth is much larger th2;4rs58 ; zws mcttyakan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain45tc a;rs8m ;ywt sk2z. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects ar8-ipbted ef13 g-6tsre at work? Do they oppose each ottbpf6g -iste13r d e-8her?

The gravitational force on the Moon due to the Earth z wcy;n3whg+/is only about half the force on the Moon due nhygwc+3 w/;zto the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars a+e v;d)5 m3-daw gt+sobjeu0 nc iz2/in its orbit around the Sun larger or smaller than the centripetand o+5s/v+ai mdc ejzgt-;a 3b )02uwel acceleration of the Earth?

Would it require less speed to launch a f0 kldh4*2q0zpb/ nxtfc.m+a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dir2btfd/04*af+ h x q .pkmlncz0ection.

When will your apparent weight be the greatest, as me86kud1 vhhl8bc+87/guto .)om xbta f asured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates u+u/t.kcblbh 7atdg88)o8h6mu x fv1 opward, (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?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely af*yu2m u -(qznpv 5l;mmfected 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 think uz;ymvm5-2 mn*qpu l( of.

Explain how a runner experiences “free fall” or “apparent wei 0xqtzaf:gr*nl51;i c ghtlessness” between steps gx z1:c rq5n*tlf0a;i.

The Earth moves faster in its orbit around the Sun in January than in July. Ise(v-y4ixiqe tw1-; 2.wqnftb 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 1tn q4 ebxii-(qy-evw.f2;twof the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known und8r *m1em2 er0bj+ begtil it was discovered to have a moon. Explain how thi0e d2bm8ge*+ er1mrbj s discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'pw v3rhsymvj5/ -ru.(s. Yet the Moon's is mainly responsible for the tidesv yh-.j3rrm5/spv( uw. 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 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 1 -qi2ca k 1*4yhtufyt:59ti ay980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Ea*qj hews:c xtg3(q)p.vf ;;yt rth in its orbit around the Sun, and the net force exerted on the (v:c.;eg h)q;j* p3qstt yxf wEarth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exe1(u /qiyp n;ec2ag1crrted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s leeip(/ruc21;a yngc1qngth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ea; 2yaoj o:/ xi+uck3zrrth's surface, and circles the Earth about once every 90 minutes. Find the centripetal accelero :kuc3yx2o ji/az ;+ration 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 accedx,vxm /9t( hw9z:cvv leration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) iv(vvcxtw d9/hm9,: xz f the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform v5uj dvpng.o*x4y.e2 rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33on4v .y2 5.ev*xp djug. 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 roundvb(o tinoh-2/ 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 independent of the mass of the c/ nhotb2( v-oiar?   

  How large must the coefficient of static 9bx x03 wov4agqyg+*c friction be between the tires and the road if a car is to round a level cyaqw049gx + x3*vgboc urve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots4vhrpsv+e j1 r:-k dx0 is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times he0rj xes 4:v1phk r-vd+r own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable spe *iug7;5nsnyqlma,es zm*; 3ued. 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 betweennl;7ms*ung;zm es*qi ya, 3u5 the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when 571fd fnsz)ik upside down at the top of a cirzs 15fi)df nk7cle
(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 (inm osq2c4dbusowo; 63o5p9: +ql mhmahg2cm,:cluding the driver) crosses the rounded top of a hill (radius =95 ;cdmh2loo m sq2m+:woco a3 ,4pg5 mh6:9squb$ \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-fvjid-ue*. m*m-diameter Ferris wheel need to make for the passengers tf*je .dim- v*uo feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ofj+/t/vk. u( tognqg 3hnh-q0v radius 1.10 m. At the lowest point of its motion the tension 0 v/. +jqg/gv(-qt houkt3hnnin 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*68nmu nh gcc1lm- b(e7-ojax centrifuge rotate if a particle 9.00 cm from the axis of roo lexcc1n-n- m8m u6*(jbh7 gatation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricall7a.oe: w 2*+cv)4iiuo+vlal a hldv)uy walled "room." (Seea.d2ul o+l io h:v)+vec 4a*)aliwv7u 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-hockedx)q;jk fnwsttqzm/* :l8 6) dy tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ndkm:8;d*q /t q6)jl txfw z)s ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ball 89mfu7whf4cc g (gk4:.lruil which revolves on a string 0.600 m long. In :igf.8l(uw4f 4 kc h9lcmu7rgparticular, 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 fo2wdn) y:nai *er 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 y u2 4cbre1 hlcf2h3 c6.bohx5$ 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 divjoxki z1 ;+0+0cwacfetb 8q)p ing 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 of tornq0o*1b jm 2he net force exerted on the car (by the ground) in Example 5-8 when its sp *no12jr oqmb0eed 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 +rn0e z um+pbvh1/c7yarea, going from rest to 320km/h in a semicircular arc with a+ /h01nmucyr+p z vbe7 radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius7( ig+g+glgzrl-u(+ njh 6 pbs 2.90 m . At a particular instanthz +brggusgl ((+7 +p6gjil-n , 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 on a spacecraft 12,800 km (2 Earth: bbr6b a)t4u skfryqu.+b78b8l(tsk radii) above the Earth’s surface if its mass if t6:.skarb 7)r yubq4b(u8lbk8ts +bs 1350 kg.   

  At the surface of a cgl 3 q+lwy6nu xqw3qw -d4:iv7ertain planet, the gravitational acceleration g has a magnitud3uv3q:q7 xl +i gyw6nldw4q-we of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is yf*kokm -58hw 1.74fhky- wm5 o8*k $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1v jnkxe2o65vsc f +w/f3;t /nw.5 times that of Earth, but has the same mass. What is the acceleration2 vfvtnfocjw/w n +k;35xs/e 6 due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, kq79c k9e sdez;jo4 k(but the same radius. What is g near its (4kjoe z ;qc9e9ksk7dsurface?   

  Two objects attract each other gravitationally with a force of 2.2 a2y1trg5omvsm+1r b5$ \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, at (a) 33h3tlkq53c/i i ff;x t200 mqxl;it c5 hfk3t /f3i3    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s c ;iz6)1erdxh9 ueb)-dj-nel henter to a point outside the Earth where thegravitatrxee)j bulz i;-d -9neh)dh61ional 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 t:kakdw 22f hp,2nkw)k he mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity kkdkkw nf: p)h2w2,2a on this monster.    $\times10^12$

  A typical white-dwarf star, which once was anq;k a e(mfs9f;v t-gf0 average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Wa-e0qg9mtf;f vk(f ;shat is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts f6plx+jdj;2 *ufy7.pia-nhwz qp/,lz eel 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 acceleration of gravity 250 km aba xi2,l+hp;jz-fyq j/.lp*6pw u 7ndzove the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are l.y/0b u5pn zop)ilq g+gll l:+ocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of theq/l yo+g lz0pnb:.5g i)+ ulpl total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same sh*p0b)0*ykt v h),zggkla q4dide of the Sun. Calculate the total force on the Earth due to Venuslhq 4 b)g*z*a,dv p0y0)tkkgh, 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 gravlxomq no( * tl/6(rd4kity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine thqr(t4xd*m6lo/ o k(lne mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known v ivc ;ct6y+rrnvc/2a a/xy .wbwm.o, 6alue for the period of the Earth and its distancec/ a. wcbwiv2c6nvor/tr y6 xay.;m+, from the Sun. [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 sjlzrycoi-8 kjc. g(5;p 6pptiz1*1 f xtable circular orbit about the Earth at a heii lzxy5(1 p ;jc8o1c rzpf-.t*k6ijgpght of 3600 km.    $\times 10^3$

  The space shuttle releqynklh7* (v0bases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when th0q*yvhk ( bln7e release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to e0fkucyao; v3zxzr y.w387; kvh z,p1experience simulated gravity of 0.60 g? Assume the spaceship’vy0a 78c1.3rzpof,x; ;zvw3yz hue kks 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 satellii8jh, ;usmgvdnt ,m(qb* :j+ate to orbit the Earth in a circular “near-Earth” orbit. A “near-Eart(,*gm d8aj mh ;,nubt:qiv+sjh” 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 satellite have to be launched fr4t6c7an*1m/vf9 fsh4pk a ;mee e1tmxom the top of Mt. Everest to be placed in a circularmmfax 41tm49hs* ;e1/p7 e6ke cvanft orbit around the Earth?   

  During an Apollo lunar landing missioi*2xx7hpxpy qh x3l/o/lv9 hq q,o46 jn, the command module continued to orbit the Moon at qo xhq3yx,p7 /lxp/9ovq2hhi4ljx* 6 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 or3 kcb km-: ais 9zdsh(;n;qrl0bit the planet. The inner radius os:n-hi3l9rksm( dqk0cbz ;a;f 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 rotatescli+m ty49y(m once every 15.5 s (see Fig. 5–9). What is the ratio of cm4lt yiy(m+9a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of the 2+d1l jnc*gp 5o 2xihkEarth's Moon in a space veh+h125onj g kd picl*2xicle (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 equal mass. They a7b09qt )zbh rv-n4q.n vce8 i7xf m(cmre observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the(9qxc ri.8b nfc nvtv70m7z e-)q4bh m mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of q6 d* thkcx 9j;ro4d ausv(0mhv0 j4i5a 55-kg woman in an elevator that moves 6 sv*4h95hrjumk4ovd0 t0(jc a; qxi d
(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 cordj:sx jdj: .b4 9hszf/q suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. bs/sdz:j j:j94 .hxf qWhat was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near sv8puqdm25d0 ggw;z45zru h /the surface of a planet with period T , the densitz u2gu;0pwgs 8m/ 5qr4 dzv5hdy (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 n. jgw2dh;:w4 4id,bcnpjq-x +:mddo the period of the Moon (27.4 d) to determine the period of an artificial satellite orbitin 4 djnwj.;+-,g 2ddcowq m4hnd ibp:x:g very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundocomszizcy;c+4 9lr (r98v4tw* 3 sb) wznyh 5red meters across, orbits the Sun like the planets. Its period is 410 d. What is its 9 44m5*9ico rnhvyz+wrwoszc stzlcyb) 8( 3; mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dij(xn/k73kgk2 e b mh3a.h 7:oa)f udaestance 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 thepoyq 1ey f5xc1vc/q+ g(z*b /e Sun roughly once every 76 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 planet’s orbit is nearest when it is out there? [Hint: The mean distance /v1qexy(zq/*+coc15fpb ge y 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 cent7c k0k75;uloz kjxjev6 hk/8. bz pxu6er of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distah*0 0aou ne)vpd6) yelnce for the four largest moons of Jupiter (thu)dpny0a)v6l0 o e e*hose 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 tkv0eq2b( x7q from the known period and distance of the Moon. t20k7qebxv (q   $\times 10^{24}$

  Determine the mean distance from Jupitenujcz2,6ohbojr- w 3/w*j x a-r for each of Jupiter’s moons, using Kepler’s third law. Use the dis xwj/zo2c6u-h3jwr n,o-j*a btance 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 be a;3ng-t f)2) shktujftween Mars and Jupiter consists of many fragments (which some space scientists think came from a n2-3a; )fg)ustf tjkhplanet 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 describns 6gj-3+hpgz*qc fq93gz:rf es an 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 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 revolgn -3q+*z:fgch f 9jz6s 3rpqgution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vinnackt uqs zv. 1*te*3)j h 6hzk,84ilte (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point szht z .v)n,lk3ha6qk8itc*j4t1* eu 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 accelerarudl+:4/q-de qldzo 7 tion of gravity be half what it is on the surface?/do74le qr dl-u:qdz+    $\times 10^6$

  On an ice rink, two skaters of eqw7a92 x7rdp1 od+8p-fczavdf ual mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, h7v8 1ar7 +fdoppa-2x9 fwzcddow hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the av 7z4p4ryqo l4s, l/chbv(99h3w ktccpparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimathl3p/hwv4k,7 ylc 4 cq z(b v9r9o4cste the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dibi:yh; bzf -/xrectly from the Earth to the Moon experience zero net force because the Earth and Moon pu b:fxyzh/ -ib;ll with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but xavr: (k(-vjwu. xr5bcq k :z9when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the v(xkj.qv ukzar:bx(-w5 :9rc elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abouoz rnbi1: n38r(rms)pt 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 E bizr)r:8s3r on1 p(nmarth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 55gz4, pmchz o6–43).
(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 plyge8mm1 k7 ;onk9set /sh;rr+anet in terms of its radius r, the acceleration due to gravity at its surface and the gravita9yk/rm1o7shesm terk+ng 8; ;tional constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertp rj* u2fmx(p zo+i0ac+*xdn9ical by an ang+dja0x2p *zm9cxnrp *iu( f+ole $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of syjm ss 63qhx32tatic friction is 062 qxh jyss3m3.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at thettpp+iejb5 38 equator were appar pti+ p5jeb3t8ently weightless?    $\times 10^3$s

  Two equal-mass stars maiel 5;/ 2hbacayntain a constant 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 roun7 cp 9bxw bcz.en189jpq*at (uds a curve of radius 235 m. A lamp suspended from the ceiling swings out to ecap1*.p9w njub cxt(97bzq8an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the memd(6a i)me)+;oe yrEarth. 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 numbed m)a+;e (y6o)mimere r of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduce oren4e wm3.o;d the presence of an extremely mroe 4o n;.3wmeassive 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 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 spev)oon g.xh);dy,ik/x/g3ws li+ d,.j om9xd qed 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?) Explain. (b) Where would the driver feel heaviest xw/gq,kixsj, hidoxn9m3ygo)d o+/lv ; .)d .? 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 group of 24 satellites orrpwlraj+489jq y squnji7o(4 o,j u((biting 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 orbiujupson +8i9(,l qj 4q7 4w(r(yojarjt 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 trag8v/r l 4(kx ,vfxva4eveling 2.1 billion km, is meant to orbit the asteroe/4 vvvxka4l( xrf8g,id Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in n-qvizt)3 nrsflj)+z5 eed of repair. Ys5z)litfz+q) n3-vr j ou are in a circular 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 of 3000 years. (a) What is its mea3ic ; rpylgc5,3i(s)cdl c*k on distance from the lr;c s)3gi,cp d 3iol(cy5c*kSun?   
(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 actuale1k faa5h +7cfly "feel" yourself gravitationalch+ 1aek57f faly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of th *hb /aag5xm.he Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from hbax g5.mh/a*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 ayfpqy3 dc.:l2 y*z5s p square 0.50 m on each side. Find thy df2 3:.pyzcy*5ps lqe magnitude and direction of the gravitational 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 5500w5 n 1kx( xk3qkm)a+qu kg 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 byqhb(b,qtd+s. / a4afk the tip of the 1.5-cm-long sweep second hand on your wris.bt4 dfaq (kh+s,bq/at watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aro1p+.t bm*x 7ecxjvgy (und 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 with the vertical? [Hint:yc b(.tegjvp*x1+xm7 See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R +0( zkw0gb wss in a new highway is designed so that a car traveling aws 0bskz+(0g wt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes mp gowyus j*4a*o263k(0z vkptilt 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 sg4 kamjz2(p u w vpo03*6yo*kseat, 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.$\approx$    $\times 10^2$