Sometimes people say that water is removed from clothes in a spin:ohi)3f5 lof9z s6ej o dryer by centrifugal eh5 s6f:9l)3jooifz oforce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels;zg rxw qqudm+qyyb/c(r ,/3) around a sharp curve at a constant 60 km/h as when it travels around a gentle c+rz ;bdy)/q3urq ywmx g(/,cqurve at the same speed? Explain.

Suppose a car moves at constant speed along a :x:rf8v4fy y ghilly road. Where does the car exert the greatest and fv4y :grx8:yfleast forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces act+c :viacr1 bn,ing on a child riding a horse on a merry-go-round. Which of these forces pr+ibvn1ca, :crovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without tmpuwhb;t mzv,2;g4wv dtp9y(dm4+ p 6he water spilling out, even v+bm pyghtm42tm d;p6ww9 4dup (z,;vat the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three con *c v. vlj5jecu+mgoyjs -,0,ptrols in the car which can be used to cause the car to accelerate. What are they? What accelerations do they jy-,ejm.*guv5 0c lvjco ,+ps produce?

A child on a sled comes flying over the crest of awffc81xfm o+q w wfv/u9h;pguk8y, 58 small hill, as shown in Fig. 5–31. His sled does not leave the ground (hwv;8pf h ucm5xw 9 8y,g kq8ff/1+fwoue does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders8)tgeipbd. /di5 avg + lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the b 7kbb1.aqh8+wsb jh qa;1lz:j anking angle giw1b jaqahz7qbjb. 1 l:ks +h;8ven its speed and radius of the turn?

A girl is whirling a ball on a+rebtw+5o ep j w-2.tc string around her head in a horizontal plane. She wants to let go at precisely the right time so that theopjw-e+t etrb+c.w52 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 stcsyz1lh4* g*mmid 6qbfqy xf40n t b*f)*5. do, how large a force? Cohgd *q0ln)mf qm4fc*d .bi5*y*1by4t s6xzft nsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dougf m,+e;ape p(kxl 01 )u8zmjpble what it is, in what ways would the Moon’s orbit be di fz 8 1kuxe l)+,0jpa;em(ppmgfferent?

Which pulls harder gravitationally, the Ear7vupm cvwqh,-6xj.. rth on the Moon, or the Moon on the Earth? Which accelerates mour pvcv 6 .x7-,hqwm.jre?

The Sun's gravitational pull on the Earth is much largz p43do4hlt;5hndg9 aer than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from dz 5g oh9ld;3 4hntp4aone side of the Earth to the other.]

Will an object weighwkx87 f m08sdd more at the equator or at the poles? What two effects are at work? Do t0k d w7fm8sdx8hey oppose each other?

The gravitational force on the Moon due to the Earth is only about ha beh4n 3az /tyi fqlnw4co5jft54-;z;lf the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the E;lin4btec 34j a5 w4hyzf f;otz-n/q5 arth?

Is the centripetal acceleration of Mars in its orbi 39l vgni-xg/pkp+69o l7tpygrh5 -mwt around the Sun larger or smaller t hw9 t7lx or-m6gpl5/- kg9pngipy+3 vhan the centripetal acceleration of the Earth?

Would it require less0i5h cyx;-ahw u,jj:h speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directio i:ahjhwuhjc5;0, y- xn.

When will your appare(xo) tqi0j -;s 54tm0t msngrmnt weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same arx45to)jt ;qm(mt0 sni- g0s ms when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer sp1 r6wdm(,t ,.tb zdrflace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindricad6wt.1,r(blrz, m dtfl shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experie:z1aszhf7 xr/-o d bndca:-d) nces “free fall” or “apparent weightlessness” betweencdrb fana-z):hs :7dz1/ dxo- steps.

The Earth moves faster in its orbi,ayg4qvupz.b 6 0fcgo8 cm85pt 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 seau5c8 pvzom fg0c4 6a .p,8ybgqsons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Exp ;z5d-ta(qbimlain how this discovery enabled an estimate of Pluto’s mass.5-;bdm(ti zqa

  The Sun's gravitational pull on the Earth is much larger than the Moon'6 6omm,jwy;y /- ecxnks. Yet the Moon's is mainly responsible 6 n;jwkm6e/, -mxoycyfor 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 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 1lb +2alz ih)9p980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ow ) 9t:7mt7z w5l1ofuhik;4wwre 0 ivtf the Earth in its orbit around the Sun, and the net force o0e i mwf th;zr9uw517 w)4lt:t7ivwkexerted on the Earth. 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 exerted on a 2.0-kg discus as itzws.uz /1 epx //hrhx( rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the/zsuz( xp1 e//rh.h wx discus.   

  Suppose the space shuttle f*ix6x8n;dh p ea5rh8 is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripe8e8h *pxhnf 5 ;aidr6xtal 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 accelerat ltnlm) 0t(xm(z2c;ckion of a speck of clay on the edge of a potter’xk m2ttzc c)l0(n(m l;s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate iwxvv 0at fa*:.n a vertical circle of radius 72.0 cm , as shown in Fig. 5-330a.vf ta*:xwv. 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 1050a l4/mnaaw-pyg) odv( :9g1zf-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car? mv-p( :9ozgalafny /1) gwd4a   

  How large must the coeffic6 wafss/ xi:r9ient of static friction be between the tires and the road if a car is to round a level cssrx9 /6fwia:urve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a1ok7ls b.c ;t w3pda8;ut5e nj trainee in a horizontal circle of radius 12.0 m . If the force felt by the train3 tk87ejc1abwu sp .5ltndo;;ee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variablegc0 (ac iks0*r speed. When the speed of the turntable is slowly inc grc0ia( *k0screased, 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 and the turntable?   

  At what minimum speed must a roller coaster be traveling when upgbog 7(*suu 5srbf17wside down at the top of a circle7 7sr uo(sgg15bwub*f
(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 massglb4:n ) vl4qfq xj((s 950 kg (including the driver) crosses the rounded top of a:ls4bqxf4j (glq (nv) hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheexpu6(wm .n cb2l need to make for the passengers to feel “weightless” at the topmostn62wp(xub mc . point?    rpm

  A bucket of mass 2.0v. h zb.hnxw(q5t/ 4em3ns o*t0 kg is whirled in a vertical circle of radius 1.10 m. At the lowest3.w x.nt (qh ht/zm 4s5ve*nbo point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a cenp(li nneg yd8w 4m+nd ar5.73wtrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration wnmldd.y+p4n3g5wrnae 8( i 7of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people a tvsjv,i9h)mj3 ; rw0od9n r.sre rotated in a cylindrically walled "room 9;v.nj h0rr3tms) 9v,wi jods." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-htevo 38uythp5( olf30 ockey tabletop, and is held in this orbit( lv83h p5tuo f0e3oty 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 ignoring the weightn jz7u7n / ofyt0;lqyihf b,5: of the ball which revolves on a str7,jtfio;z yh f/7q05n lyb :nuing 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 tz(/rd-igwjw 9 raveling 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 ck 6yk ,trf4m+$ 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 matj4f)u c sqh x-0oxe *7clkw.5neuver by diving 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 componenvq 7mj3(7xaq6md(d sdts of the net force exerted on the car (by the ground) in Example 5-8 when its v s( dx q7a(mjm3qd67dspeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unif4ga (euezch2 9ormly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming 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 skiddin za2(gec e4u9hg? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . s oj.e+kt86iel1g 7g6j)zm vjAt a particular instant, its accel+ o)ig 6selet8jkg.zmjv 6j71eration 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 vwzj;45 u.xd xhrz06-kcf;l 0os*euwon a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its massj60ru450 df wo;kx wu-v*hz.z excls; is 1350 kg.   

  At the surface of a certain planet, the grasrf +ge8r 5wn+hmfsa2k u) :yhg8c/-pvitational acceleration g has a magnitude of 12 mkr +f)8 nc8a s5 sw2mhp:e-/gruf+ghy/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 1d w1n cp,wv:tsr30.xv.74c03d.:1w twn x vsrvp, $\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, botv v+a sdb ,cw*2dz*0ut has the same mass. What is the acceleration due to gravazv *dc2v* d+bso0, wtity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,y(-ze,lt g3bv but the same radius. What is g near tvlb( y 3-,egzits surface?   

  Two objects attract each other gravitationally with a force :yqpg 5vhh ,(mof 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 accelerationp,5 l1i2v+ w5o :f e4hf5n pinjvks6hu of gravity, at (a) 3200 mji1kns56ffvv2 wh+n :h ueo4 l 5i5p,p    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E my /xj)ss-xp1arth’s center to a point outside the Earth where thegravitational acceleration due t jp)-yms/xx s1o 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 Su poii8qhtt0 ;)n packed into a sphere about 10 km in radius. p iiottqh ;8)0Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which bz50rl /) wym7q 5gjjjonce was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but ha0qw7y lz 5)rj/jbmg5 js the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless why+2ucn6 uxyh 7xk,y e3ile orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that xuuh3e c,kyyn 7+xy26it 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 locatek/ y64da+eylq gx(c.) ,jqdmld at the corners of a square of side 0.60 m. Calculate the magnitude and direction of thegq ymx4j6q)/c+ dl e,ay(.k ld total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most o5 bxr ac.y:h(nn2vd/gf the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are 5n arbx .2:gdc(yvh /nin 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 at the surfz4 1gw1v5zbi face of Mars is 0.38 of what it is on Eartwf1ig4vb z5z1h, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using tz2,f3ns ij* ukhe known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usingzf*3 2ijn,s ku Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit :rllx. 7kw.yq9 7n ptxabout the Earth at a height of 3l9nrx .:7w.pq7y tlxk 600 km.    $\times 10^3$

  The space shuttle relvali125y araou nw.k- / ;p8tke 2i4oreases a satellite into a circular orbit 650 km above the Earth. How fast mustile .ky 5;-np/2u k1oiwa8t2r araov 4 the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are 1*6f wgc 7nbb ujw .y12deluw f(udp72to experience simulated 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 Ques1w71(duy2 fe pjlw6u*f7 u c.b wbng2dtion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Exei6gdt, +m; d /0i)fb xmqf.e38b imjarth in a circular “near-Earth” orbit. A “near-Earth” orbit is o/xm68 xtqge)m; ,i.m feb3idf +jidb0 ne 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 fromc pvklvz+n i69yw5y)7 the top of Mt. Everest v 9ilvnky c5)p w+y6z7to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t:lfqlhfwx0 + u1rk24 .t ie9mihe Moon at an alt iilme9 q1fu f:x4t+0hkrl.w2 itude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are .lm +flgpx:c 3hm0wh) cipe(. composed of chunks of ice that orbit the planet. The inner radius of th 3+lf xigp0ew( :pmm.hch. )lce 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 15.5 s (syoeji)ip ;.1 zee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at thee;.p jyoi)i1 z top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fromts 3x qhmbz86g jfx097 the center of the Earth's Moon in a space vehicle (aq8z3b9x0 xs6 mftg7jh) 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 u8v) prf gisah:*b(6lz ec37ystars of equal mass. They are 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 mass of each6 lis*zyb7:v) aegu8r(3ph fc?    $\times 10^{29}$

  What will a spring scale read for the we h/iia1/ 0*kwhgj1i*onkk nw 2vp2ga-ight of a 55-kg woman in an elevator that mov j1/ho-21pn /n a2 a*k0 iwvwk*kgiighes
(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 hjro/yo 5f1gf7olnoj)j i a,q1l3*p:ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the p)/ir3n :oofj1y 5goj*1ahj7l of,lqelevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near tq m ; n96me.ne/eka,gkhe surface of a planet with period T , the densitm ,ke9 qneg /;nm6eak.y (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 determin qa-y dt9-102l jzx k;joh+0blhazn e,e the period of an artificial satellite orbiting very near the ,e1hob-kj a dj209 qnzlha-y 0lt;zx+Earth’s surface.    s

  The asteroid Icarus, though only a few xi9a8 j /hjohn)9ikz/ hundred meters across, orbits the Sun like the plj ka h o8x9hzii/)jn/9anets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4* )20bj/c n)-xgdtg:dinuk b y.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close told(ib eyxv6j )p b,qmex(u5; 1 xs0zp*s3v.jo the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the 5(0svi6y(deo; ,je1bs .z xx3mbqup )* pjx lvSun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy :n/c qh/*t d/:v,gmus d6fkvjfdh)d;x h xc0.$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moonu,ox;df-:/tmk:m +z w/mwg* jubap q:s of Jupiter (those discovered by Galileo in 1w*b: mm:,xwg;ptjou/k:/m dzq-afu +609).
(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 th2ud9)jk7d hs.(onb vxd9 oi t(e Earth from the known period and distance of the Moon. jtxv)hi .o9dsnb72d9k( uo (d   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter( m8dehtqp 6 l)3r7shq’s moons, using Kepler’s third law. Use the distan 7)(tr shpm eh86dl3qqce 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 consistsb1h 3l q2ps6sl of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destrolp3lhs sb21q 6yed).
(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" i7 k +m4(xshsuy-j x yu:bgj7i8n 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 yub(-4xs g8 x+jhikm7sujy7 :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 swt:aat5wlgz q9jx+* cy 3fi sjz 3em-6.-mzoa1inging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and eqtl ajz3i.fa 9t mogjs16mx:za -5w+yc3-z*the vine is 5.5 m long.   

  How far above the Earth’s sqb y: +pzxiu3)urface will the acceleration of gravity be half what it is on the suuz+px:q by3) irface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutuag+6sbi-y f.i ul circle once every 2.5 s. If we assume their arms are each+ii-s .gfyb6u 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 j khhj6+rs r/,f:lg u4apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of gg+6:j,kh r shlru4fj/ is this?    $\times 10^{-1}$

  At what distance from the Earth will a spa /ygy-2)fb2 ngh sa,npcecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal y/a f 2),ghbnsp2-nygand opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an eleva * / 0wmdhjfea8hd.:ektor, it says your mass is 82med/ea dw*:.j hh80kf kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circu n ke 99gmiu;3j3v-fkwhl7tw ;lar tube that will rotate 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 ik39 nhgw3wjlmfu 7ev9 ;t ;k-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 aircraft1; nnn13od(growv .vw 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 its radius r, the25fxaakyj wh0(ati qfdq 0(:6 acceleration due to gravity at its surface and the gravitational constant 6a xh a2( a 0i:jyw5q(0fdqkftG.

A plumb bob (a mass m d8 y7/v ay6l;i cpufp bv5d2a8hanging on a string) is deflected from the vertical by an anyf6a ;2p8a/d7 dy 8iubl5cv vpgle $\theta$ 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 bm-* bosm9f b;design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safbfsbb-9;o m *mely handle the curve?

  How long would a day whaz9i4u )czz*z 70cmbe if the Earth were rotating so fast that objects at the equator were app9mwzchz zu4az ci*)70arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aparpsl2 r22tc; x1tfxdb5t 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 curves3 :;digz+ oj.ojyv ;r of radius 235 m. A lamp suspended from+iv: .osoj dgyr3;;j z 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 times as massive as the Eacgi cb35u-7 eerth. 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 equatoreugbe -7c35ic 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 4if b1xjx0b 1:arj/ui Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light es0i:ux 1br4 jj if1b/xacapes). 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 speed as ipsf6vq /,upv*y08es ct 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, yq pu v,/8fve p6s*0scand 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 j2gs8z1mqx)4rvi9s(u+ d ,lx kyvd7xlzy/8i (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Exid s1g9u2z(mlxlsz7yi/vqyk+d),x8 4rj 8 varth 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 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 2.1ous o77y21 2 qwa(; fme zq:eq)8ymmbm billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rm uyemo2e2q(qfo1 z)qwy7 :8;ambs7moughly 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 repaire -sm(swdf sxm-1e j)yy(io1w qom781. You are in a circular orbit of the same radius as the satellit(s8imxfm1 os-sw7oyeq e1 )(m-j 1dwye (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 30009qqf9rat e2 o*;afo,e years. (a) What is its mean distance from t ffqa9a;,rq*eoteo2 9he 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 to be if you could actual+mb3pnf.4yme ;m-r kq ly "feel" yourself gravitationally attract; q- yepm.r3b+f4mnkmed to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center nm0(utazeyb6a1 ae u( 1+6 nw*htefh( of the Milky Way Galaxy (Fig. 5-46) at a distance of abohfm1*(b6(yhut a(t+n1z euwn6a ea0eut 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are locq 6cv; jcixt5- :qov6iated at 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 of the squactiivq x 65 qj;v:c6-ore.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the hjco7 xuz(lcu2 2 kg,2Earth $ \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 accelerat nx0j09uzu/f rion experienced by the tip of the 1.5-cm-long sweep second hand on 09n zfr jxu0u/your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sihd(f.,pa(pb w nker weight around in a circle below you on a 0.25-m piece of f(wh( bad, .fppishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is deuv-r *o(c. hzlsigned so that a car travelingc-ou.v z*hr(l at 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 tilt of the cars when negotiath4-csviw h( k3 3a3m7o hrc3e qnr8d3bing 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 trainchc(r n 3shi-7 okwq43hdv3m3 ab8er3 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.$\approx$    $\times 10^2$