Sometimes people say wsh3ds f p)l1/nq6lu5 that water is removed from clothes in a spin dryer by centrifugal force throwing the water ou)ll/5u dnsq1f3h wsp6tward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels arsv.euk24xu k,zh dw9 *ound a sharp curve at*xkew d zk, 2vh.4uus9 a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hi t ay:xssz.b;,lly 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 betwzt :.sabys, x;een two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces actin xv jy+r8 lfz/7lyg9xdv4x3sb0 d0y2tg on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration s7 /xy8l f0gydz 40l+23vtbdyrv9xxj of the child?

A bucket of water can be whirled in a vertical circle wiiis;mshy2a )y:e7hs+ thout the water spilling out, even at the top of the circle when the bucket is upsyhs:2+h7e iya msi;)side down. Explain.

How many “accelerators” do you yecclj)maes;a 4k8-/ have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prod;e-4la ca/ys)ce8 kjmuce?

A child on a sled comes flying over the crest of a small hill, as s j4ccm/m3 (7em.1igkg4 kmwfz hown in Fig. 5–31. His sled does not leave 4j/zgi7 c3mm.(mckfemwk 14 g the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundiiyw,bzk k 5p1+ng a curve at high speed?

Why do airplanes bank when they turn? How would you com cb98i*q)l/-h r )lp3bbqbxmopute the banking angle given its speed and radm)3lh obb/r)b -i lp8qc x*q9bius of the turn?

A girl is whirling a bt hndsq/cmq)8 t 4g15eall on a string around her head in a horizontal plane. She wants to let go at precisely the right ti5 enc/sq4 8ttq d1mgh)me 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 fo:f2ai,4s) an(+ nxo7 kxznsic h-y(vwrce on the Earth? If so, how large a force-niyns as:k2aoh(c),4i(z7 +x wxfv n ? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it iscqw/l )v2; l0mc5onk/oq fx8x, in what ways would the Moon’s orbit be8 0qcklm25oxf o)n lxcw/q/;v different?

Which pulls harder gravitationally, the Earth on th 7b (e)ua-1kvvo5q( 0lkzz lybe Moon, or the Moon on the Earth? Which acceloq vzyz1vkluae-)bk0 5l7 ( b(erates more?

The Sun's gravitational pull on the Earth iior1rzu9 b0 uu05bq y4s much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of tbur15rqz 0o0bu ui4y9 he Earth to the other.]

Will an object weigh more at the equator or at the poles? What t:1a 8koh-miyw wo effects are at work? Do they oppose e81-o:wymk h iaach other?

The gravitational forcy/)fiiug+sv0 8e2j q6/p1+ pbhuvv /b0uqjsoe on the Moon due to the Earth is only about half the force on thevpu+jbp)o+ /guu/v sy62ih0 fve0 q/s81 bqji Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its : ,1u:2p u5 jqwwgnk7wdj5wxvorbit around the Sun larger or smaller than the cen ,vuuk5q :xdwpj751w g:w n2jwtripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward thek k41ll.dxnf a0i we o2,wc;j.c+ pr )k.+qxbm east or (b) toward jw.xkm)l l;+ ,benarp4k0qkw.+ . d cio2fcx 1the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scalel. (0likso c 28d9;bvplscyu, 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 as when y 9 (l. c,;lbss yv0lp2ckuo8diou 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 aff xoy-j*(zzabei.8g tpshwl-d m l n8:+y6 -mg1ected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the insi( : e-b-mgzn smyxpl1 y*6.w8z-h+i8djatolgde 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 experiences “free fall” or “apparen qvhvx1)ma1+4* jxpzm-jz mo2t weightlessness” between ste +v x*)-h1vzjm14oz jmqpxam 2ps.

The Earth moves faster in its orbit around the Sun in January xc04u xdvqd38nax,z fw 6((xi 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 to the plane of its o8 f0(3q x,a u(6x4dcwv xxndizrbit.]

The mass of Pluto was not known until it was discovered to b q(w;1z v.hi8yznl.vhave a moon. Explain how t q1wv;.z8.nzyi( blhvhis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull d uth6) br 5bwd ,z1c(rlelh4p f*00tion 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 graviufhh* ttr ( i4dz,0w0 cr1bldp ble65)tational 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 198(v,li w25tycv 0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thmm a 0kjf;98bbj +z-kce Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that thebkz+-b;8fmj9a jk 0cm 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 2106iq xwm, / e+ lau1+.6tbankjz N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circnjx zb6qta.ki1,wa/+ + 6lemule (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eartho6kw;2k 4l0wg4bv ul p's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Elvul ;60b p2w4 okwgk4arth's surface. $\approx$    g

  What is the magnitude of the accelerj v cn)qh(w*u4ation of a speck of clay on the edge of a potter’s wheel tjwu4) chv(*nq urning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revow 15mct;oi*hzlved at a uniform rate in a vertical circle of ra;hwtco5i*z m1 dius 72.0 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 round a xsbf6*pq.ia i3p 4 5iwturn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this re i3xq*i4w6s5 pf biap.sult independent of the mass of the car?   

  How large must the coefficient of static friction be (bg6 buwz ;(2 ljadarf9g+6ocbetween the tires and the road if a car is to round a level curve of radius 85 m at a speed of(c+9g roblj;az6 b fw6 (2uagd 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed tbbu. jzkh+ 1zt v4j:oy089upro rotate a trainee in a horizontal circle of 9 :ztbjko+4 yjhp .ub r8z0uv1radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of var s,xzpn:uaiqoe2k/-2iable speed. When the speed of the turntable is slouixseqn2/po2: -, akzwly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down aj17s37d4uqb m ,thh8 3kzrcn5qfa wi 2t the top of asj3rk 3iu tc78z4nmd2b1fa7,qw 5hq h circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 m3,xg(tvf z qav*e 50bkg (including the driver) crosses the rounded top of a hillfa m v5*vzt0xqeb 3g,( (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 wou9lx2uc7zu ur0x1b)+ubq 4lir ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlu2q0b ul14 xlu+b)rc9i 7u xrzess” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirledrrcc en63s49ck rr, wt z/-s(h in a vertical circle of radius 1.10 m. At the lowest point of its motion the tents9csrcr /6ec 3,nrhz(-wrk4sion 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 centrifuge rotate if a par rbz19bttqmlc*ma 192ticle 9.00 cm from the axis of rot z29q alt1c19r*mbmbtation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a ca uz7sp/ c(3y jlka+)dxrnival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.) 3s+jazkup7) d ycx/(l
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 airc:noos -,f2ty -hockey tabletop, and is held in this orbit by a light cord conne:s nycoo2t, f-cted 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 ignorind(rvz/gvcb208, 0wrlpii 2g hg the weight of the ball d(i0/,gz v ih2rv0 82grbpwlcwhich revolves on a string 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 perfect1 :j*gdtng y0c/(h xzwly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse4x0:5 hxc gkkl6b7kzj 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 maneuver by diving vertically atzz-0dfwc*pea8 :e j c* 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 a /uyusbkx4 + ohxty64)nd centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed yyu4+tk )6s/h xoub4xis 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 aeb a )kcf75tc)rea, 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 coeffib) e5 k)actc7fcient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular f f41os xu;+poc9;cgpinstant, its accelersp;fx;co94pcgf+1 u o ation 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 onyld: ty/ o5 o:a2y:x t6n4onyd a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfa oa2 65dx:yytdyo4n/l:oy:tnce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerao6m,ieff6wb,zlvm5 2 k *bcx5tion g has a magnitudew 2x*b55b kcm6 mo,lze6f,ifv 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 toc fgd:((krqio9 ,s 4fg gravity on the Moon. The Moon's radius is 1.74q 4, kifg:9(sf cro(dg $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a r / gpym ic-w/8ix,l5.rj80lmp zkuc+ kadius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface xk, .58llpikzcyw / gpc +r/8i0mjm-u?   

  A hypothetical planet ha rb3w3;9g kpmus a mass 1.66 times that of Earth, but the same radius. Wbu ;9r wkg3m3phat is g near its surface?   

  Two objects attract each other 8s,4i3vxfdq9u0ko a:rp(fp 7l pn /li gravitationally with 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 , the acceleration cwe.ki 6d )jaq;6h mv8of gravity, at (a) 3200 mcq; jed6 vma8k6 iwh.)    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eartd;x;fk,sum w,pkc;i(d .+phvh where thegravitational accel h(uxip v;;k p.,dwf+;cs,d kmeration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fi1bs1gp*e. sn x4)mfrnve times the mass of our Sun packed into a sphere abxb.p m4srs*g nef1n1)out 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, w(h su yxn08 9dnt5/ss aqfpn21hich once was an 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. What is the surface gravity 1tdyn 9nas(ns x0 qh/ 8sup5f2on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space sh8bvs9 pa1 wex+uttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them98 bvxpwa1 e+s and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corn zt/*bw+vohx)le xoy)e 8 :9tpers of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphereo)p yox8 ht/lb+t*) 9vze:x ew by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on thv/n rof /w6a *n*jr9rde same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (ja vrdo*rn9rf n/6*/ wFig. 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 surface otdo*f7 m/ hn5tf Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine 5f*ht7 otnm/ dthe mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perm dce1/,lpiqi es,+w7n(q8z eiod of the Earth and its distance from the Sun. [Note: Compare your 7el,d ew,mc8ieqnpi q/+(zs 1 answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stab)t m z2(yefnb8le circular orbit about the E2 fm) te(bzn8yarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbil-+bfm 1k u s2.y,epbtt 650 km above the Earth. How fast must the by-.s febulpk2+m, t1 shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrizzm2ykx3av 3,cal spaceship rotate if occupants are to experience simulated gravity of 0.60 g v3mzz3ka,2x y? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circul9wb7gw0aadnm7 5u x(z ar “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is g d0795axaww7z(b unmvery small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocit 8nbwtm h9wp-bn s8w;n(.n 5 rkh1pnudsc)-i(y would a satellite have to be launched from the top ofch nnhkw;8(idmsb8n-s - ( .pwp1wbtnu5n r9) Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the combc 5u 1sshz:5umand module continued to orbit the Moon at an altitude of about 100 km. Hozuubcs5: h1s 5w long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks ,)-:wk, va -undpm bktcx7fmqxn( 50fof ice that orbit the planet. The inner radius of the rings is 73,00,(mwbk :-nf-x0,dmuc) qpx k n f5at7v0 $\mathrm{~km}$ , 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 ever u9hi(fa/:g5j 1nveggy 15.5 s (see Fig. 5–9). What ivh9je/a:ggu5fn (1ig s the ratio of a 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 cnk d.7tf hr2(tenter of the Earth's Moon in a space vehicle (a) moving at constant velocity,f t rh2.nk7(td     ----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 da ;bh9oza/t-6ea) nc system consists of two stars 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 betwee6;/coeazt9d-)n hb aan them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg4 z+rtzf(g3g9t xlf1z woman in an elevator that movez x+fg9lz(1t 4trfg 3zs
(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 fr+d g elhq e)qe+6q-du8om a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directid +du)q8q eeeg-+qh6l on)? a =   

Show that if a satellite orbits very near the surface of a planet with perio16z:zdejjmuy v -gae776 dj y;d T , the density (mass/volume) of the planet is -6y6 71g:du zv7azjejdy;ej m $\rho=m / V=3 \pi / G T^{2}$ .
(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 *9v xx ,ct ygc 7fq75ifu:iyb9the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surf,cftx5fi:cyb 7x * 7gvuq99 yiace.    s

  The asteroid Icarus, though only a few hundred meters across, orbits th ufpj h;,8 t mymv8c*(qk;wp4ce Sun like the planets. Itst;wcmvc,q(4y mp; *8uh pkfj8 period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distag5 wrr4kuug5,(uaqjpz gw8 o3 ;g/: abnce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 yehco(f1tqa6o 8/ m09oj l2aays ars. 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 s in Kepler’s third law is half the sum of the neareo2 q0oj(8m ac/lft691 hyo asast and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the erq2)djnxgl;,f o.: 64kjc ac center 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 distance for the four largest mooo jq3nkq 6;rxsrx9p::ns of Jupiter (those discovered by Galileo in 1jprs6k93 x:o q;nr x:q609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the knownw.3 hka/awzn3 . wi:uz period and distance of the Moon. w3:u.iwnah/ka. z z 3w   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mo*r9(rc uve7 vv3 7q lc9bfweg*ons, using Kepler’s third law. Use the distance of Io and thl9 * 73vcb vgeef7q* w(crruv9e 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 betweeni uzv( *8rwb6sm j9(f34cfml 1jjp.t9cxrh/m Mars and Jupiter consists of many fragments (which some space scientists think came from a plan(tum9h r 8c1p3jb4i/ *fm rmjf.x6(vj9zcslwet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the forr gmv98ooand v8 4ny/6m of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that4v98 vynm og6da/rno 8 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 revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a ha * qwoxrf)0rg7nging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum sp7froxr) * q0wgeed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be c5x :fh,.oij 3qya jrl::v(tzhalf what it i:c,y 5 z vxrlt.h:foqj:a(j 3is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal du,p9d k+jn 45zng0*x zt-qcj mass grab hands and spin in a mutual circle once every 2.5 * kdn0n9tjdzc p-u4j5 ,gx+qzs. 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 one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratitzw04u12g,f nq xzxgtr :pk4r553rax on of gravity at thn przaxxr:5q4t, 2g01gk3x4 5wz rtufe equator is slightly less than it would be 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 f+8pq7avm kr0 2jbft:gk.* u -xmgh ;asrom the Earth to the Moon experience zero net force because the Ear p28x rb:;vhajmt .+gmk7k0-sgf* au qth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elevat 0ev(l1o7clhoor, it says your mass is 82 kg. What(1h7olcol e 0v is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists ofhua 9y)sx9jn gj/5 ed0tu8k,b a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter o5jay nxe8 gd,b 9jh9sku0/)tuf 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 dbt9ifs78- vvb(htl 4 aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accel5llo5.)zkb (pbmhph r) 1e ,cweration due to gravity at its surh5pe 51 )clrmlhk,b)b( pzo.w face and the gravitational constant G.

A plumb bob (a mass m hanging on a s l(8wz6i uvbw5tring) is deflected from the vertical by an wu6wvil5(z b8angle $\theta$ 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 )aaee :d6is/7(wddlgfor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of sdd egwa /e:7da()il6speeds can a car safely handle the curve?

  How long would a day be if lvl;cfvz8o25 the Earth were rotating so fast that objects at the equator were apparently weightcvzov2 8 5;llfless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dktqwc: 6tj.) v -t-zkfistance 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 ro* q/ci 44 l(uop2/xwkd bgtg 6nw)5nksunds a curve of radius 235 m. A lamp suspendedc4wu/x(5so*g4ln62kdpign)q/ k wbt from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been cl/2 dxnzvw/xh1 e*tq ( 7dw:caoaimed that a person woxw/ 1h(odd2vaqc7nw :tzxe * /uld be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. 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 kzn2h, (m,;ib)qs)jm+ my tvqSpace 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 escapes). They did this by measuring the speed of gas clouds orbiting the corj n;))m m(,,yz smitbk2hqv+q e 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 it 9j7cuw 4o+ r q-i0giritraverses 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 7 rwri uj-i 4+iqogc09compare? (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) utilizj- 0 v iqcvca1y i6977zl9gfxyes 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 centimaxiy- 79v7zc6 fi01 gc9yjvqleters. 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 2.1 bil mccc 6- hd*4eqb0l n;be*ygl1lion km, is meant to orbit the asteroid0c4bhl 6b- *l;mgydenqec*c 1 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 spc /* djeg;by ,95.gifkmol 5vpace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth),9*.glvc5y e;, kg5b mfodip/j 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) What0gwl 58o 8v6pmxt1tos is its mean distance from the60spx8wt 8m51tvo o lg 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 a) 1p ouh4:y mq(eja*n)ymfd* need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumpmaqn4 d 1*muo*h fy):a)pj(e ytions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center rb 338-sw.a1ai v,cmffnwyun8xub9m -a)3f dof the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lim8f x --i.vcm)3aafbuw s3,1any8u9ndr 3bfwght-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners 0uue*huc;k c5of a square 0.50 m on each side. Find the magh *;cke0uc u5unitude 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 5500 kg y7ih .l) lxx2qpst -7torbits 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 sq9r9 avf*w lj;cn kd91weep second hand on your9*1jr9flcnwdk a v;q9 wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swkt wch a-jff.*46y: vhing 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. What is the angle that the fishing line makes w:a f*vj c.-hw4fht6ykith the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwjwaxth, vnbu 30grw0m u/b680 80x tspay is designed so that a car traveling at spvjb08 w,/u t6xmbh 80wa x3rn00su gpteed $ 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*v1xm djo cx nff2, 9n*xcak66 tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve witm,fa6d *v 2 jx1ck*nn 9xoxcf6h 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.$\approx$    $\times 10^2$