Sometimes people say that wat3 ( todva2+sc0qvy4lber is removed from clothes in a spin dryer by centrifugal force throwing the water outward.o0ly2sc d4q 3vb( vt+a What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a s ,1w+uf of3huuharp curve at a constant 60 km/h as wuh+u1 fwu3,fo hen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a s:m c8eegc+ 0vx/w9ol,ih, ivhilly road. Where does the car exert the greatest anol/h ,8:esxv 9i,e cvc 0mgiw+d least 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 acting on a chy 3ijs ue 1 t)p*irigsr3l20u4ild riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratt 3yijp )l32i geus*u104 isrrion of the child?

A bucket of water can beant632xuvk ,l whirled in a vertical circle without the water spilling out, even at the top of the circle when the but l,2x36aun kvcket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cyy+cf1v ::2p(ypk1f 2wd mxlx ontrols in the car wh 1:2pmcw vfyxdyx1:+fk2 pl(y ich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying o0 f*5f 1o5u3eanxzi *8 bmjdhqver the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decreasehi 1fb*58qoujad3 ef*x0 5zmn as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hi w7i0tct 7k3) azt1ocxgh speed?

Why do airplanes bank when the8i:m*p b7d- oy lnii1fy turn? How would you compute the banking angle given its speed and radius of7y1i:*m 8dnlfb opii- the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shejq;1w0 h3lm im wants to let go at precisely the right time so that the l i hwmm;q0j13ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitatio n(lf*hi/e am6-;04 faensgim nal force on the Earth? If so, how large a force? Conside*;siea/ m6h(fa4 m -g ilnf0ner an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Mmsan-hv, xm(fj(:re 4oon’s orbit be eh m r4,nsj(v:(ma x-fdifferent?

Which pulls harder gravitationally, t* er+e,dej0;3f;emiw h ew/ kbhe Earth on the Moon, or the Moon on the Earth? Which acceleebdiw*m+jeke;w,3he/ 0f er ;rates more?

The Sun's gravitational pull on the Earth iw6-(8 hb bqdwes much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravi(b w-edwq6 h8btational pull from one side of the Earth to the other.]

Will an object weigh more at the equator o e9t3+pbgv bt8r at the poles? What two effects are at work? Do they oppose ea vbtbpg+8t9 e3ch other?

The gravitational force on the Moon due to )khlgiqp,+ 3ythe Earth is only about half the force on the Moon due to 3+ ,gy )lhpiqkthe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around t5hmrcn+,/khnj 1(qz ih-eh9hhe Sun larger or smaller than the centripetal acceleration ofi1(n, m+hz-h /c59hj nherhk q the Earth?

Would it require less speed to launch a u f o3q7j(mxh3satellite (a) toward the east or (b) toward the west(x3u3qm jh7f o? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in1 tmh;aby:g.nmf t-2y a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at cm h ty-y m:;21.gbtfanonstant 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 x1 x1spzka19 8bas :pwadversely affected by weightlessness. One way to simulate gravity is to shaxs1sxzpkp:a1 91w8 bape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessne8ugm1 wls68g9r.fnzjgt 3:i oss” between16z8nmroi 8t g.gfu:9j glws3 steps.

The Earth moves faster 5e x* cv9l,mwt8ymz7e in its orbit 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 seasons — the main factor is the tilt of the Earth’s aez 5c97tm*,8v ym wlexxis relative to the plane of its orbit.]

The mass of Pluto was not known u2fa7gv(d3 hkqlgzy/hi8 4 vo/ntil it was discovered to have a moon. Explain how this discovery enable(zhlv k 7a4/ fhqgov /gd283iyd an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thth;rb 6hijd6ha43p5kbq /5vcvj2w u5an the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earthp;hbt6 /wk45iv5 6rb c2qjahvd 35j uh 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 198mso:yu *)fv5u jwl:3k0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 outh8(ss l w;9sf the Earth in its orbit around the Sun, and the net force exerted onslswu(; t9 8hs 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 it rotates unifor swtz jn.r*;ef*xd/j+ mly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculatnj.s/ +* tedzxjw;*r fe the speed of the discus.   

  Suppose the space shuttle is in orbit 400 de p*vo5ob* y2ev s )sgnqpv4ejj*93* km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle )ejo vy*b*sjp 9 pe2qos3vg5*n v4ed*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 ths9m:ese pt+d(bjg +0o e acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diamet ds:(0 pe bgm+ojt9s+eer is 32 cm?   

  A ball on the end of a string is revolved at a unklh ,l.)t*hu uiform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. Iuh*).,tllh uk f 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 rounv56jw7up snvc/ :i.bod a turn of radius 77 m on a flat road if the coefficient of :/cbs7nivw5o jv6u.p static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static f- nj).db xpqpx(4(obbriction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed 4o-)ppbbd(.b qj( x xnof 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotae/po3 izl n4(ate a trainee ii aze/4 3nol(pn 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 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 r,n l f/*bcn2( vu(j. byelfn)iotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin nl e /fb2)(lvnc fi,jb*y(.unslides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling whec q:t6euo*ths5sd /w/n upside down at the top o6sq * h/ew: suct/t5odf a 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 kg (including the diwszz,ts /; sj (f*st6river) crosses the rounded top of a hill (radius =95z,zf/ sit;6jsswt (*s $ \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-objbi m 3-j1m)m-diameter Ferris wheel need to make for the passengers to feel “weightless” at tmj31j-i )bobm he topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m.bmnqi7/ery;jz :;o 2ktco n0kkc3q54)) nb rp At the lowest point of its motion the tension in the ro)tycq/ 7 4ni2c0)ez;kj o: b5 rrbq;mnkkpon3pe 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 par9)lv s7r5sbax ticle 9.00 cm from the axis of rotation is to experssxr 759)lvbaience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyl 4xyyqc9/gwt -qp e;tw l+)l9vindrically walled "ro-l/t 9+gtx4cpywe l 9)vqqw;yom." (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 o29iueripbnzjp: *) 9 mn a frictionless air-hockey tabletor2)be pz:9 ium j9*inpp, and is held in this orbit 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 , e0 j8aqpjx0n8precisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particux a q88ejnp00jlar, 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 gr k 7ox;mhp54) g2pmgperfectly 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 massesv -eyxvno)we 42pxn84 $ 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 a76a:xwpao sq(kzzw t x.t;j+)t 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 tangentiap ; pbft*d3ngvnq vv:-n/so3:l and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its * n q:pft vnv;-3sv3pb:dong /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*.re /5 ybarvn uniformly 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 constantra5yn v e/.rb* tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . l)l 7 *yuhzgh4y ktan .5e)s*cAt a particular instant, its acceleration is 1.ce zh)4 l)k7. *guls hy*yt5na05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 spac :/tgh ul(u/ :tlpvr518 hweeyj;fuv8ecraft 12,800 km (2 Earth radii) a :u(uutw/8pfv8t:y1h ;/hjler e5gvlbove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a bosr6nbvxbw3m ju)-af7-0) j magnitude of 12 m/sr xujw0bmfb) bsn6jv 7)ao3--$^2$ 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 t k11nm2uo 747rekxv wphe Moon. The Moon's radius is 1.7uw1krmn1 x4p 772evo k4 $\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, but has 8y;-d)k nowkibwe3l30en r1 xomv :u6the same mass. What 6vdoreik 38ew0mw)yxlbu1 n 3:k-on;is the acceleration due to gravity near its surface?   

  A hypothetical planet has aafvu +5jmno)2 mass 1.66 times that of Earth, but the same radius. What is g near its surfmjn v2 )ufoa+5ace?   

  Two objects attract each othe o,*z*.3s 6h8fl s2cws 68o deizsstpkr 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 gi cz o(rg z90i52jdwleby)um2 03c0ik , the acceleration of gravity, at (a) 3200 m wzdu2ei crb3ko)y0 0l2j m5 iz9cgi(0    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Ea6j dv3t .jpp5 ;ugjm:jrth’s center to a point outside the Earth where thegravitational acceleration due to the Eagd j; .upt63j5vj: pmjrth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sp fncpp253f.ol- ipx/ z/sxmj (here about 10 km in radius. Estimate the surface gravity on this m f z(/pml.5if/p pn3x-2jocsxonster.    $\times10^12$

  A typical white-dwarf star, which once was an avo)ug eok:gf9cu 4h5c5r xb2b+erage star like our Sun but is now ib9)uxo25ck gc4:h o e+grf5ubn the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting i xfiy yj/ e zmy6m9dn0528jaf3n the space shuttle. Your friends respond that they thouy m6j5d39ny jex08y/z ia2mffght gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0:y(1pvzh f5sx c 699u i, u,m2x5twxwjyled5o.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere b2o m tc55x5x,wijfyyl,h: p1wzv(e 9d9uxu s6y the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of m/t8e(zeb;bgthe planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jet;e( mgz/8b bupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mt(s8) 7 hnscf9gr cgk*ars is 0.38 of what it is on Earth, and that Mars’ rag(*r7 ctsh98 kcs) fngdius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usip ccp 2l+ w6cx,kqg fpdph.f9yx /9h:.ng the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s .p9 y f pgd9,wx+ fplc/p kc.xhc6h2:qlaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a st(vybz:tn 5(aie9aj ;zm6hm/rable circular orbit about the Earthn(m tav9h(bie:y5;6zr ja z/m at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satz7 w8.ldsq butom awm9:. 7es8ellite into a circular orbit 650 km above the Earth. Hoozmwtw. s 8mqlad7.9s: 8eb 7uw fast must 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 to experiem,- w63kz;oj ifbckr ;nce simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the;f -z;jk6mkc3,r b wio time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for as,i kc ,vafu0, )x3gcu ,(iq)aslde w0 satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one ax)kq0,iucau0 ) lcg w (dfe ,sia,,sv3t 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 velociomt obg j,p i)xv61jw dq80+3oty would a satellite have to be launched from the top ofd ijtjo+3w o6q g mb8pv1,xo)0 Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing 8t0r) s1gikp vmission, the command module continued to orbit the Mo1is8)gkvr0 tp on at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn ias3f yt0e h8+are composed of chunks of ice that orbit the planet. The inner radius of the rings is 73, yitasf he380+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 dia whfitr*9 ,w/vmeter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottrvi 9hw/*fw,tom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the )1t0j bla-pqicenter of the Earth's Mp)lqi 10jtab-oon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. T+ r.*)7ytgpwe qzht 8fhey are observed to f rtg*.zyet8w p7+q)hbe separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read fnyi *h.5,xog:: e rvflor the weight of a 55-kg woman in an elevator that mriv.ygx, h:5 f *nol:eoves
(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 hangskb)0hqg1,)z wzc da 4r from a cord suspended from the ceiling of an elevator. The cord cadz q4,crwg 0bz1h k)a)n withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbitsiz jiyz*:ji/ a eo;l08 very near the surface of a planet with period T , the denj:l/e*8iy iziz0 ;ao jsity (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 peren+z216qwqr s b*be +-srox+kiod of the Moon (27.4 d) to determine the period of an artificial s16ee+bxqsb wz+n sro+*k2q-ratellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thoughgi3)2k)kcpq u z/ nm;v tgb-4m)bem+o only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What opm- z gkcebk/utmm 3)bq;in2+g ))4v is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance 6 zatj9k-x,t2z:yiku 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 years. It comes vejs *ig qf p:p-fwv*:6sry 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 nearest and farthest distance from the p p* qis6fwvg*-j:s:fSun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy ec.q 4;0xdu8toawc, p (x6pkb $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 fou,q,bwtu4p l 5dr largest moons of Jupiter (those discovered by Galileo in 1609). p,,tlwb5 4qdu
(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 known period and distance of the Moz4j t4nfzz( x7eg jvv2)-hq2pon. fzj)q44xn(vzz722p h vjet-g    $\times 10^{24}$

  Determine the mean distancee zqn 5vxlb(5+ from Jupiter for each of Jupiter’s moons, using Kepler’s third law. +l 5ebv5nx q(zUse the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which sopi u p1u2f7 to15e5ipsme space scientistsioipp u215p5 ut sfe71 think came from a planet 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 6lru w7e / v(qt2te(oathe 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 temper/vtelow7 qua6 t(2re( ate), 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 cros-qku jdqb4:)g blao-wxo, a;9s a gorge by swinging 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, wh- go la)j-qwd4abx ou9, ;kq:bat 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 grav ,jgd*cut3qo4 ity be half what it is on the surface?jc3dto*u,g q 4    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circls-q1 4a4r oixle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, oq14rx - l4isahow hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of d52w f3ykxd o.7z cna7gravity at the equator is slightly less than it would be if the Earth didn’t rotatedo c yn5w7xadk3f7z2.. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earlhs6yolkt5k( z7-;x4of0 k xlth will a spacecraft traveling directly from the Earth to the Moonl57 koxz0f( y;tlhl-kk46oxs experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass isl loxaew*qew82*oq0sf +*e- w 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelera oowf *x0ls- w+*lq*eea2w8eq tion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circpmy52wed 1bysij6 25n ular tube that will rotate about its centeri5 5bew 21y2dsnmy6pj (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vhg8 p.*osgaa 5ertical 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 ted 91edwf-e6b m( hc2qgrms of its radius r, the acceleration due to gravity at (2-d1 qgmfedcw6eh b9its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strdcwjj 7 .gguk xdowl1+zd49/(ing) is deflected from the vertical by an ang c9w1jx (+l4z7ukgjoddw d/g.le $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the co)mmf,ux dnnzr)mi3+ qj s7o** efficient of static friction d3)7 msjim,ofr+n)q*n xuz*m is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be ixl oh:iiv5s0 7f the Earth were rotating so fast that objects at the equator were apparently weoii:7 xs50hvlightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartg;u:vo/t c klw 4n8k2- ru*wuh 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 roun6hjvxzu*99d .x1 ftqy ds a curve of radius 235 m. A lamp suspended from the jx9uv6f* .9yhxt1dqz 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 tsefw + a0 q)0cd:u+il9kic b,as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity owd0i 0i kaeclutq+)b+9 cs,:f n 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 Telescope deduced the presence gx-08f*rlt qj t;rg*yof 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 t gqftrtjxl*r80; g-y*o 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 traverses the hill and valley shop8 ui9+wdd1vb*d rnj tit40e 8wn in Fig. 5–45. Both the hill and valley have d*8v nep t01ijud48trdw9+b i 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 Poszbvxj j 0* 3clgu)94m;s/ :fp:cjrli oitioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellite vi jx )c*u:l43slzgofm;p:c0r9/ bjjs, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites 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 Rendezvoup89hzp2mb g 8g+ 2ynu+n ff2pus (NEAR), after traveling 2.1 billion km, is me9+g pf u8 p+2yu8z hmpgb22fnnant to orbit the asteroid 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 th rked:l31du)89tk ne ; ls;cnye space shuttle pursuing a satellite in need of repair. You are in a circull8dt ck k;;)nnlre9 d:u 31seyar orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dist*7 fp 93ivwanqance from the Su p*9wqniav7f 3n?   
(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 acf,ky ;.u h7xki2ks1pwwv) g ,ctually "feel" yourself gravitationally attracted to someone near you. Make rvk,2f1k,uw) y . wich;xk7pg seasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the rgs)w 7*xwfq.5qx8 3x x5 rgpdMilky Way Galaxy (Fig. 5-46) at a distance of abou*5wp gxs8x7 r)w.dx q qgfxr53t 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 located abe iy17 rhq s-qf2-8en,m, p0 poalar8t 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 midpointq ri qpln2oree-,1 psyhf0a,8 amb7 -8 of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eart :iy7,x)qqdbdh $ \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.(k lvldk7d7 ryhref9 36 bk+n05-cm-long sweep second hand9ny r7d6 v 0d(+hbr kelflk73k on your wrist watch?    $\times 10^{-4}$

  While fishing, you get b25m8trym51niy o;nsbored and start to swing a sinker weight around in a circle below you on a 0.25-m piey inr 2moy58tm5sb1;nce of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed s*tyc)h t;hrn)yq p** zo that a car traveling at;cphyn t)*z)h*y *rqt 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 tra aj4.-.sogn*6juw+ qjfjgrzy t 1u)y1in, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train f*tj-ujy6.j)o+ wz ggsj1 41yrnau.q 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.$\approx$    $\times 10^2$