Sometimes people say that water is removed from clothes in a spin dryeq)y3 q2k9c(sx+r p polr by centrifugal force throwing the water outward. What is q 93yoslcq p(rp)kx 2+wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharpg87sib( zg9y2pyq; i qwz1.x d curve at a constant9s 218x yiw;.qyzd7q ( pgzbgi 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at m -w 0mp 2hf,kkjg (7z ;3pdqyh0*bsxtconstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretchdb 0m7 kfh3j(mpw; hzx,-t* yq 0k2pgs near the bottom of a hill?

Describe all the forces acting on a child ridinggn19ymz;iur3jmw5g t 3u23tp a horse on a merry-go-round. Which of these forces provides the centripurg;jn3 5p z 29tui3wty1 mg3metal acceleration of the child?

A bucket of water can be whirled in a vertical circle wite8t+24)r( k-2cnfztnu,h pkv d:momehout the water spilling out, even at the top of the circle when the bucket is upside down. Explai,r(phm )4okz- vt+ umtc2 2n:d efken8n.

How many “accelerators” do you have in your car? Ther:+jy1jgcs 6 qle are at least three controls in the cay+l1:q jc sjg6r which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill,7o5koqp zr murq.agalx62(9 mi99u ,r as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he apxzmmr9q, u l rao75(o2u g.9q6 irk9feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding kvc c ,lrhv(blof;8:*u +ifel.rl* g-a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banki7ereeykmqpp(s yc 5 -aq8t :bxg3)5i)ng angle given its speed and radius of the tu gcq5-(aixqry)k7mtb e3epe py58 )s :rn?

A girl is whirling a ball on a string aroun41 dwbsk8 d(/ olo:*o:ynawvxd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go o*ldo soo(kw: 8vax w4dy /1bn:f the string?

Does an apple exert a gravitational force on the Earth? If so, -cipoj6 dp9vhvs33(yhow large a force? Co3po( sy9vicjd- 3h 6pvnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wayo +yq;g2kxd51lr9 ne ds would the Moon’s orbit ben51 +ergykx2l ddoq 9; different?

Which pulls harder gravitationally, the Earth on the Moobga:7 x2(qzvwn, or the Moon on the Earth?bv( waq:z7gx2 Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yvmx4:lkhyq e4jjm5 k; r6(md2 et the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Eam;re5qjj2k mlk:x6y m(vh4d4 rth to the other.]

Will an object weigh more at the equator or at the poles? What two eff.7u kb3jm vds.s2oph*ects are at work? Do they oppose each other? m . o37ks.v*j2usdhbp

The gravitational force on the Moo .7i-jr,kox()qy hhf2lw, (tc c9lqru n due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulledtci.-(rxq2(j h ohwkyl 97 rcl)u,q, f away from the Earth?

Is the centripetal acceleration of Marsxq)5mmn b gk5( in its orbit around the Sun larger or smaller than the centripetal accele)mk5( x5bg nmqration of the Earth?

Would it require less speed to launch a satpbm7mri7b8.;: g o/(r lp 3 iijo+unnqellite (a) toward the east or (b) toward the west? Consider the Earth’s rotpnimgom3ljpbb+ rq u.8:7ro/i7 ; (ination direction.

When will your apparent weigur24k,-bkto6z p;w4m3p)e x+ hnrtr bht be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates4por46t);bt nk e +w-rupzbx2 r3k hm, 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?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectey) cl, ,2mddsnwq)nq8d 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 simuyqm8 ,2 scdql dn,))nwlates 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 expj*e5c sv ,md*reriences “free fall” or “apparent weightlessness” between st*5c*s , vjdmreeps.

The Earth moves faster in its orbit around the Sun in vwe;g6gemkn t5c(/wo z(nh (7 January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative t57tkwweoz 6cem((vng g(;h n/o the plane of its orbit.]

The mass of Pluto was not known until it was sxomi2u2 s()qdiscovered to have a moon. Explain how)oxu sm2(q 2si this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull .bk:wyq k3 a9jni2uf(on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gra29uk qy: jn3.i(bkwfavitational 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 1980 cr*4zm )/hdennu:g0 h8 ;b vop$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 offs n,*+ecx pm5 the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts,e *sxfn+5cmp 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 it rotates unifod0inlaix6 + i**b9r s*k+ kqatrmly in a horizontal circlis6ltiqa k*xr i+9*+0 kandb* e (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from thenj-ireyjjps 96;g,i 2 Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shu;esj9yg-j iji, r6p2nttle 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 acceleration of a speck of clayu11r jj 91anub on the edge of a potter’s whr91n1 u1bjua jeel 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 l -al),/qo:ubfp xpp6 uniform rate in a vertical circle of radius 72lx qp:bfu,o/ p6 pal-).0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can rh (e5z5- dbiukound 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 independenbedhk 5iu-z5 (t of the mass of the car?   

  How large must the coefficient of static frismaa*e9nr a2d )a7nin (to .o0ction be between the tires and the road if a car is to round a level curve of radia(7aamr2 e0o)dsintno n.9*a us 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designv :xvll.k+6y1. h ypfsed 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 her own weight, how fast is she rot slf.yylv.+hxp6 1v:kating?    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 speq15uabz g l6i;ed. 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 betw6g q5biu laz;1een the coin and the turntable?   

  At what minimum speed must a roller coaster be b/x+ u4f 1rqyv9/tswstraveling when upside down at the top of a circle +f 4rx/b9vs1qty uws/
(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 drd 3b-qe(fqjmv2-n t2f iver) crosses the rounded top of a hill (radius-tndqf vb2 je-2 3(qfm =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 et5(ehk m3kr)goa5.h 50rc lobr b29l minute would a 15-m-diameter Ferris wheel need to make for the passengers t c.r0e3r5rb 2kalb(k h l 5th5eom)g9oo feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Adp4.nz *i1m *eu,l gibt the lowest point of its motion the tension in the rope supportz*1mi. d, *lu pe4gibning 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 centrifuge rotate if a particle 9.00 cm from the a qn mjtlzj74b-5d) oq/xis of rotation is to experience an j obtj /7 )qd4l-5mqnzacceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot4 jieal.u,oh uerg9dj9/u t6sv4 pg77 ated in a cylindrically walled "room." (ep4dige/4.os 9uj7,ru97 t 6jh uaglvSee 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 ra4v(ry2t.lulr3 4 kvi otated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centrai4t 3u(rk . v24ayllrvl 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 o4b99xym x*h vxf the ball which revolves on a string *hbxyxx4v 99m0.600 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 travouecvd;-m6 +y( 3 pidfeling 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 massep:sbkshh(g )inl 0z00 s $ 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 maneuvel :0 n)mt+9efbydgi,-o a9kfer 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 componen 1d;a5)ph bfto6 ga4zqts of the net force exerted on the car (btga5p h6;4)d1azqo fb y the ground) 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 pi8h56cu1jt rwp gczad /t72 y*kic;e*o t 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 tangent7icc* e;g/ c8tdah526 u koyz*r1twp jial 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 cirjnk4j0by ; ksdl/-p e/cle of radius 2.90 m . At a particular instant, its acceleration is 1.05p; ksejdjkn/ 0y-lb /4 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 r - ,k/h4k3 0mbcnnn m56+4azovcmkmgb adii) above the Earth’s surface if km4no ah ,v65-0bkbkc3 +mgcmznm4 n/its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magvz t x8sj5l* -w)ymv4onituj8)v-5yo* zm4vxlswtde 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. Thellwbp-c1e.l7;qz4 c)z kxt4 v Moon's radius is 1.7 4tzp.keq17cv4w -;)zllc l bx4 $\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 tha7qsmq/x0p .svt of Earth, but has the same mass. What is the acceleration due to gravity near ivq7m/s0 q xp.sts surface?   

  A hypothetical planet has a mass 1.66 times that of Eartdps w z08hyz q8jy(awh 28z6:jh, but the same radius. What is g near i 88y6wh :8zzwqhzy( js02jpdats surface?   

  Two objects attract each other gravitationally witj f /z84lqowb1.zy 5uyh 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 effective value of g k;*sx +jun)(:syml7r ft:dln , the acceleration of gravity, at (a) 3200 m nf7 su*;mt: ():dljlr yxs+kn    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth qquueiaxu+ m24e(5f/h bm,,swhere thegravit (q h+q4um2usxa i fem/b,u5,eational 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 q vzpz 0mmyps-.u h4gd65 k.lw7o/. ulmass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity.suk .vwh0 pq 7l45z-ymu.o6 gzl pmd/ on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but bzkvv .8(tk.nkl 4 pohw+9m*nis now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the swh.nmk*k.o tp84nz(b vv9 l+ kurface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in theg*kh9j. / o:g-rkxal g 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 cal*jhgkg/o-.ak rl9x g:culating 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 a square of 7t b5uzxel(bi 8e 34saside 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other three.e ax3l butib5e(847sz   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on thz 2 d2og0*lqawe same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, anqwlo*2 0z2 gadd 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 gravix6- */ dwuwc mp.ghk9aty at the surface of Mars is 0.38 of what it is on Eawpgc 6*. uwhd/9x kma-rth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun u38pa6gi +twlzacr d)1 sing the known value for the period of the Earth and its distance from the Sac81alpd 3+)6i wzg rtun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the g0jvrk 7bo61iEarij 6go1bv 0rk7th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular rf/ 2y* g60j,aa hdskoorbit 650 km above the Earth. How fast must the shuttle beahr o*yd,2skg a 6jf0/ moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants a4u )8f/okrz(v6edvl s: i i90)dhsukzre to 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 revoivu0zlu h/ z9v:8ed)(riso4s)dkk 6flution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ear u(jiy,2p*yh xth 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 resulp2xy,uj* h(iy t depend on the mass of the satellite?    s ~    min

  At what horizontal velocitymlkfd :ik3w7.;d jz .t would a satellite have to be launched from the top of Mt. Ev.zid7jmk:. fd ;w tlk3erest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to n*am9hv5:9 xb czs.gi orbit the Moon at an altitude of about 100 km. How long did it take to go in5mzg.xahb* s9 9c v:around the Moon once?    s

  The rings of Saturn are composed of chunks of ice thabo vc g19 w h7rd)ps5(r)e0fw*q hspx*t orbit the planet. The inner radiw)1(pd** fsbe50swq7v go hrr9 pcx)h us 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 15.5 s (see Fig. 2fk ur fsr. :ae52h*gs5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom? kef:.s5 ahsf2 rru*g2
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cenmr(l+-nc4v .re.efg1t c*ax -h cpis3ter of the Earth's Moon in a space ve fm-nr-(3cic ae 1c.g.+r* 4tvsxlh ephicle (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 5vkbih.(bxf.*da d c; two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit aboutikxb( fb; *d.dha5.vc a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weil zh+-/:kyqej ght of a 55-kg woman in an elevator that m/kyez q+ljh:-oves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevaeoe-jih4gaii3 alsj(dra;/ l1+ +c 9ytor. The cord can withstand a tension of 220 N and 43jraehi+o9+/-( e djaclla ;i1is ygbreaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wix.ocn)c ,* txt.jbd7 45t0wmxlj4vz *y ;w onxth period T , the density (mass/volume) of the planet is vx0*bzt)c*xto47xd4xwc, jw. 5 ymjlt;no n. $\rho=m / V=3 \pi / G T^{2}$ .
(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) td,gkyc7brz; um4 mbz(+gwk/b2 n1ji+ o determine the period of an artificial satellite orbiting very near thedm+wckr 1b42n7(km+,/bzyiu bg ;gzj Earth’s surface.    s

  The asteroid Icarus,tkh rxci j8nh+ 6iu8nsm:7 1/v though only a few hundred meters across, orbits the Sun like the planets. Its period is/icht 1jvknn+ 67h:8 8xrm isu 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5ya awui az3b9:/xq+s* $\times 10^{9} \mathrm{~km}$ 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 th n4 w: 2c88.wo *+drumnlpvdno 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 distanmn .p 8+wr 42nuwh*:ncvodl8d ce 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 center of the Galaxy ,ws65m91b4,mdevapw6yxbk j5f6se k $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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* dx 0n(ev9*ptt dc-mw, and mean distance for the four largest moons o*-0m (ce d*t pdwntxv9f Jupiter (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 Ear*frwu34y57 j0s sv 4- vekatlxth from the known period and distance of the Moon. e tjy7skx5fr-4u03sa4v * vwl   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter8t mu5sv1qn qh4k.fcj, ;z g+l’s moons, using Kepler’s third law. Use theu.5jqk8,;qm+zc4tvl 1 hnfsg 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 Marj gfk9 u,)7kp)hxsk/ts and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbite ,u9kf)kxk) jgph7 /std the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form)+ ec y.xujik9)upw)d 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 disy))p)w.jkux9e +c iud tance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinginaghg*.k(dg w x)gx;8v/ re4pk g in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a forceg /x.k 8gwe xgrkp)vah4(gd;* 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 b1 /ka3d,x/w9oof1s 14zyaao0kjuak ae half what it is on the surfa1a3k9j oosk of 0 ayxau/,dk/1a41wz ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab ha * 2.xfdayoy2/-q nb8 b ,i,7epbxtrwands 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, how hard are they pulling on bn22p,e-fb wyx7i ab.*yr8 ad/xq, toone another?    $\times 10^2$

  Because the Earth rotates0g .xvq7 rd+ni2hg xc,hzl :j9 once per day, the apparent acceleration of gravity at the equator is slightly less than it would bgh:d.in0 ,qxrz+c jlhg2v x79e if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Earc1t78g yzlu(rth to the Moon experience zero net force because the Earu7g8tyz(r cl1th and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroefema(7 7nay((vu t80(kox gnom scale in an elevator, it says your mass is 82 kg. What is 7xmevegn7a( (a t ufy8(kn0 (othe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circularnhmrt.f s,r3d00 w6 kb tube that will rotate about its center (like a tubular bicycb f0 hkrwmdtns.,063rle 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 felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Figi th t8u70 0d,mnd ge.z1e-kdw. 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 rn 3l *zji3mnl3, the acceleram iznj* l33ln3tion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vere x)pn 3si0ndo7uh (t2tical by an poe(hnnix) d 7 s30ut2angle $\theta$ 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 spe) tzlum603kr dn4ws4lq -qg )eed of If the coefficient of static friction is 0.30 (wet pavement), at what r lqz gq lds4-)wnu3e0t46k )mrange of speeds can a car safely handle the curve?

  How long would a day be if the Earth 9if1be 63sm ccwere rotating so fast that objects at the equas3m c1cb efi69tor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cz / f)neylg0-rr v0/c;h 6prweonstant 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 lar lkxu*(x7 pyj .,+gbu o h8bn2c1s8vvmp suspended from the ceiling swings out to an angle ofv v.x yx,7hlor(u gksc +p2bbn8j*u1 8 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimegkxo y)jpo-5i9t:r1u rim1r +d that a person would be crushed by the for+prm: tuoj1r9i r k)yoi5g1- xce 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. 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 Telescet: sb 4qoxr5f cz)v;2z,yb5o ope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 75vs2f)xo4;zbreo5qb zy,: tc 80 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it travers 73f.o; 36kg dcqkyqsxes the hill and valley shown in Fig. 5–45. Bog7 33;qocfq.y kxsdk6th 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? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) u .d26+f )j5pz uaxeqaqo:bn)o tilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational qpbn5ooaxjf+2a.e)u z6q: d) “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 Rendezvof z,rc0;fz6 v gs;jsi9us (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rou6;csrz;fjzif,0v9 sg ghly 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 oefg.;6 vlhx.uui ,+mmjgl/w),v.i qff repair. You are in a circular orbit of the same radius as the samg,vf6 geu;il./m fi ljh wx),.v+uq. tellite (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 mean distacou)3qgjq o 0(nce fromqc o(j03u)q og the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G wou0-y+fjn iq )e )f*ayymld need to be if you could actually "feel" yourself gravitationally attracted to someone near y y *)0fn aej)qymfyi+-ou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mil.0 g42 kucsp4 i+ fipsf2q*dqsky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lid *04pq2fup .cq4igsfs+sk 2ight-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 th wc.kitx/3-(bx0bqq5 gg vp b+3u tf:we corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth tb3 + b/ 0ugqx:v-w tib(kg5.fqpwx3c1.0-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 k + 104a,tp;zu xlqwxjzg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long dg6b . 9;hif8q zmfuu9sweep second hand on youbif 9dq.hg mz6f8 u;u9r wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and stareuuw/g8v4sy*,dmfz7xv 4 kj ol/ - t:yt to swing a sinker weight 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. Wham uxed4gyftu//-oz4k ,s*vwv8y j :l 7t is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a ccdh q,dr, k7j- hx(6lu.k)vzmar travel6m )hj kv(c-dl7xkqruz,hd,. ing 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 e;ta + dwt hz(gw 6gk0) lgg1z+1;sxrwh0(nrpAcela, 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 e1ewlg06;w(h1nsrpt w zrx; hk )a0t+ g+zgdg(xperience 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.$\approx$    $\times 10^2$