Sometimes people say thvfaohz(i3f 1,at water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statfovhf( ,3aiz1 ement?

Will the acceleration of a car be the same when the car travels around m flavx;35ge koh3 ac.(;mcm.a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Exmf. ve hg ;mlm(o ka3a5c;3x.cplain.

Suppose a car moves at constant speed along a hilly road(m 10a1a u c;hbkwb7b7ivik ,q. 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) a,kmb 0b(u7bkw1 q7iv;1c aihon a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-gr(rej; tr-nk6 qlp4y /o-round. Which of these fre6p y-ql/r rt 4;(njkorces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ;mrkz;*-sma2md( z.mylhtw :circle without the water spilling out, eve s;m k;wy.-a ztlm* 2hdz(rmm:n at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car?8fluqbynt +1g , 0ju*vu.d6k 7k/a rhb There are at least three controls in the car which can be used to cause the ca6df htbqbv8+/g 7l,u uyjkr 1.ua0*nkr to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as showc)d ;nlom)x sbh((k i6n in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels skoln)m d(x6) ;b ih(cthe 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 le pt) id-q;k86/ta dux5 cvuj4ban inward when rounding a curve at high speed?

Why do airplanes bank whefp( 7i5:*j fdevp h;kxn they turn? How would you compute the banking angle given its speed and radius of thf i*px7hd( ; epfv:5jke turn?

A girl is whirling a ball on a stridzhy,lt m0(oco 0 1.i6hr*gvz ng around her head in a horizontal plane. She wants to let go at precisely t, 0.r1yhvzh(m go*zcil6d o 0the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a8at wj wdv)-lh.e+1xs gravitational force on the Earth? If so, how large a force? Consider an.x8)ajs thdw-1 vwe+l apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dof9fe n(uc.ux0l n ux.j-2+j4rav ict:uble what it is, in what ways would the Moon’s orbit be differenjjvai:t .x42 f( l0rfx .un c+c9neu-ut?

Which pulls harder gravitationally, the Earth on tfwa) ,hy+rs 33eant3 the Moon, or the Moon on the Earth? Which ac,yae3nr)attw+3h s3 fcelerates more?

The Sun's gravitational pull on the Earta+wj;y uye+ -eh is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Exejueyy+a-;+ w plain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or ata30zmuys0qh ov *(lx2+ yl7gh the poles? What two effects are at so02hyx3qhz7 lu(lm *a0+gyvwork? Do they oppose each other?

The gravitational force np y; -esnob9a*ck7v, 1n:ynwon the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t oa cpn -*9;skynv71b,:ney nwthe Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or sm(3kn,i: *a u)e:zlqi mwjud x:aller than the centripetal acceleratiod3 :i::uen(ua*x jkq,)lmiz w n of the Earth?

Would it require less speed to launch a satellite (,z*sqqo+0cok a) toward the east or (b) towaro* qksoz+,qc0 d the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a s;nb 9t7 x9aw4trgkzj.s.b c;z( ic aboj.f/k1cale in a moving elevator: when the elevator (a) act9 at;1n9b7bcb/r. kkfwa4j.so.zi; j (z cgxcelerates 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 you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend le-h9c w-,mxsmong periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity yo-m, c9xw h-emsu can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” b 2x* peaya3s8hn :25okjo1 nxwetween 1e8:kxoa jyp25nn 3o*w hxs2asteps.

The Earth moves faster in its orbit around the Sun in January t e+i(me7q t:xxg(+flt o2qj5rhan 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 p+2 jfxt5rtqie(em l+7 x:( qgolane of its orbit.]

The mass of Pluto was not known until it was discoveredffx;5x z)e r,f to have a moon. Explain how this discovery enabled an estima;fe xxf r5,fz)te of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet f+jf u,px-.9rf,ps 0zc /m cbythe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from on+,ysm9 fbfx0cruz jppf.- /,c e 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 travelingjm 7e9+rolh.m wn2n4rau( h0u 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratkzl8a9-b tj ;k5qh(jz :wwx)xion of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Eartk)axb8h-w;jxjklt :(q wz5z 9h? 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 rotmcc6zz0d-tumjm zyp )iu 524)ates uniformly in a horizontal circle (at arm’s length) of ruzmc)t cp- 0yz6uz)4 imj5m2d adius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 kr.itk*:/sb0b8i4 w) aj whl ivm from the Earth'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 rsh0ibtw:ik*j 8v .)lw i/ b4aterms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the eidw9(2ag.soi-; 0l8z8l hvtkkqe bb 7dge of a potter’s wheel turning at 45 rpm (revolutions per minute) if thedeli9 tbl. kv;0zg-a(8k b wh87i2qso wheel’s diameter is 32 cm?   

  A ball on the end of a string is revd3b5cd3 m(kn6: f n c7q+ouy wf:ag+spolved at a uniform rate in a vertical circle of radius 72.0 cm ,3+k3un d f s :m5a7qd6bwgc np:+c(oyf 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- 2iy-63lvu:) 4 a3rv+ gtbm(pl1+kzm vbgesavkg car can round a turn of radius 77 m on a flat road if the coefficieiv :+p ylbm(mz+a)e-r vg l1ua6vt 332bvs4kgnt of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficien v;tm2r,.jf o6uc)e xtt of static friction be between the tires and the road if a.) f,rvc; et umojx62t car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training as w ym ;o5;m.gspmpkk(1j:id, qtronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rd:qm 1s.y mmg,k ;(5kp;wi jopotating?    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 bf(f4 w uvbw*8xcsk6zp4 o(k8 axis of a rotating 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 slides off. What is the coefficient of static friction bepf f((6 wxw *o4zkc8 u8vbk4bstween the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling q q1oge7e5w-c when upside down at the top of a ciree-5c1og w 7qqcle
(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 esp/;wwcsk *0qgm 72ymass 950 kg (including the driver) crosses the rounded top of a hi 7we*mg;s0wsp2/ qcyk ll (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 min)z6mq -p )eqvly+ yo2uute would a 15-m-diameter Ferris wheel need to make forzeq2 u)l+y o-)mpvyq6 the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ra(ezdjmgncc 54ht5 * -edius 1.10 m. At the lowest hc jez(55-gd4*en ctmpoint of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrif e5zgepm(y5/ fuge rotate if a particle 9.00 cm from the axis of f(/5z 5megp eyrotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carni0d4w- sa-c2 judj ht0ival, people are rotated in a cylindrically walled "room4 dit-uh0ja20c-wsd j ." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless ai qdb5tu ;skc a4/:rrw:f+foz6 r-hockey tabletop, and is held in this orbit by a light cord connected to a dangl 6bfao qwf+t4r5s d :/ukc:zr;ing 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 , l/pzs4p *z us7.u9r gmprecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m pp 7 umu*.r 9sz/4zgsllong. 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 perfectly86qibmsp *n7i be0a5)m*r+: rvgt fhl 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 masseszq9+7 ctuvx .duv* ea73n y*tf $ 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 at+7d mm cf :w3g78tuimx 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 centrip m/ukq 5o;aa,petal components of the net force exerted on the car (by the ground) in Example 5-8 ao;5m /ukap q, 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 unifor.k v7had-v8v 6gms(qdmly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleratdvq svgh( kad m87v6.-ion. 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 ofnpch8w p6k 5n6 radius 2.90 m . At a particular instant, its8kh56 wcpnnp6 acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Ea) wbn-aystlx;f28 6dyd td1 3bo45tmurth radii) above the t3d8 a4 m-ltns b)1ydwbfu ox6 5t;d2yEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g haspqq*lxq +g+ ,g a magnitud qxg,q+q+pgl*e of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radiuslye+s2i il*s7 *uy. st;r7el y is 1.7yuty;s+li*iyl2es .* 7r s el74 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius yi3ma u* p;wps 3s,hr uc0i0g ;)p4pdc1.5 times that of Earth, but has the same mass. What is the acceleration due to gcp)y* p3;,hu r um0piwsag p3ds c0;i4ravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the afnm:at1h+ /rsame radius. What is g near its surface? mra/f: na +1th  

  Two objects attract each other gravitationallyf2ebt +1dus6q 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 of gr5 y pza/i:cth 8ss9w(ravity, at (a) 3200 m (/h9:ysp az5ct8wirs    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tax;5 uewwn;8 4i(pvflfg yj:*o a point outside the Earth where thegravitationu4*;fl fvpw;ea 58ixygnj: (w al 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 mass of our Sun packed a1j/2upe2 0t0 hoj3w(anzibw into a sphere about 10 km in radius. Estima w ajtboh/a w0j0eupz3 1i(2n2te the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an av r8/wl xyx)c1werage 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. What1x w/r x8y)lwc is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space shh 0)96(uuwifykx: haufv0eq5 omp)x2 uttle:i 0(6 x9qwkomhuuayp)5exvf )h uf02. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squareowf,*7,g t)jz f7 /-tkgei qve of side 0.60 m. Calculate the magnitude and directijk)fgz vt,-tg 7e*/,oqe 7wfion of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets dk b 20p g4zq6fn1bs6gline up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fibgq2 zgp64fk ds b016ng. 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 Marsz;v/;c ;5ksg r*dnju x is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, dgs; xczk/; *u;rn5jvd etermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known v1j*ni(*u1qg fjskzc4:n 2 aqk alue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, uijna4 sq(qk: zn 1f*g2jk *1cExample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a sta j: zvy:i-0vfxlz(a;pble circular orbit about the Earth at a ly:v(av 0x i p;fj:z-zheight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into*7.zdul. r:di 34 qcm3vpygc m a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the re3qvm l.3d7m .cip*rc4 zy:dgu lease occurs?    $\times 10^3$

  At what rate must a cylin0:7cwxumg .j mdrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answe70c :w xmm.jgur as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for xgob *7ovqf7( a satellite to orbit the Earth 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 result depe (7o g*bqx7ofvnd on the mass of the satellite?    s ~    min

  At what horizontal velocity would a jms:t0 u3had6 satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the s:m36d0uhtja Earth?   

  During an Apollo lunar landing mission, the command module continued15pa/i)g+mnhh pa8 .*xxy vl i to orbit the Moon a)ag8vaixmpxy hl.n 5+/1*h pit an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are coa yabh44dm.2fcyvp .5 s;yc+bmposed of chunks of ice that orbit the planet. The inner radius of the rings is d .c ps2yb5h4cam+yf bv;ay4. 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 diametehdh8.h8aa *6gy u1flesjnb. :r rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her re :fj hedgsh l6bu.h8*1n .ya8aal 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 t*f ejl,1x6jrn/rjm) ,wne*fytlr 1b v.7:blf he center of the Earth's Moon in a space vehicle (a) moving ay l 6j w/:7ee*mlvr )l,fnxjr,jf.1tnr1 bb*ft 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 kt )l+: 5ebklcmass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the masstb c):5llk+ke of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wwc(y ljxvxq gr568r 24k(5khs oman in an elevator that move8ksx56w( g(hx c yj5rq l4rv2ks
(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 s925m+r*nq 6x aab zysuuspended from the ceiling of an elevator. The cord can wiaay b5xn 2*9mu6+ zrqsthstand 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 orbits very neaqw3st va u1,.xlszx -/r the surface of a planet with period T , the density (m1sq.svz w/ utaxx ,l3-ass/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 anjwos2vx;v4, b/e hy5 id the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earv se;/y2h b5wijxv,4 oth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits thfrxf a* s ea+d+dmce)2f-35khe Sun like the planets.fe2ara5k++fhx)smf*ed 3d c - Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanu/h 7ci+c, o7)+k phz 2oux(r ao0eesnce 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 very close kqo b gi;m 8+* gzsw;vgz:ngvhw4k),, 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 p,b,:zv mzq;* 8)+gk wkg4hvi ;ogg swnlanet’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 Sun.]    $\times 10^6$

  Our Sun rotates about the0( i /sa-/kodisbnn. l 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, periodq h 9yvgla.z2/ 4(wswl, and mean distance for the four largest moons oz.a 4 hw(lgyq 9lswv2/f 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 Earthjzt +- 0r5* nqcovhmukmwg(59 from the known period and distance of the Moon. *km-j5gv 0 (5h 9mqunzocw +rt   $\times 10^{24}$

  Determine the mean distance from Jupiter for each o ,voqyuzfijti tr46z, 6yvg ,.+ -jsx*f Jupiter’s moons, using Kepli xjoq,6fyt. t zzuy4,jv6 srg-,v+i*er’s third law. Use 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 Jup 5svm6 maa2k:ce*t g*fy;rw1 kiter consists of many fragments (which some space scientists think cam ;1 *vf25*6 aty:rm kkageswmce 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 artificia;bp; g)r- n6m1n:ndr3shk c dcl "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's y)dkmc3-pcn;:s;dgrb nn hr 61ear, in Earth days?   

  Tarzan plans to cross99 **sxr**l +utt;mtu c dbn( jthqu(d 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, what is the maxi csnhtrb*t xujq(**t+(u9t ldm9*ud; mum 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 be half : hil8wxugt:;what it is on the surface? iw x8lht:; :ug   $\times 10^6$

  On an ice rink, two skaters of equal m:d.u a5;8one h,7oe6al bzukoass grab hands and spin in a mutual circle once evlo.nuob;:dh56 z eaeo8,auk7ery 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 one another?    $\times 10^2$

  Because the Earth rotates l: c)pziz8 m s6g06wtfonce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Est : z8pm6fi)0sgzt lw6cimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directvmkd:p:m-)wi+m67 .mxzhuib ly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite fdmbmm+ vpw:xuh7)z i 6:.- imkorces?    $\times 10^8$

  You know your mass is 65 kg, but when yo549yx96bi0u+*+o)u pm fiqy kl qxstdu stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration offkxtp l yiqsbim9y56u+ q )od*9u4+ x0 the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistsm*zli(2m)qal(4 zwzv of 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 of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of thqm(mw(azzv)zl2 * i l4e Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft olu 1l 8id8nr *4v )uv7zf,lgqin 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 radiu76i6 v4aoc hnv8 9i3x ucm+yru eun:d3s r, the acceleration due to gravity at its surface and the gravitational constant n6 3ar4e+ucuxcm dni:37v yi69 hv8ouG.

A plumb bob (a mass m hanging on a string) is deflec4bc/iknri fxa;c*2csl :7 sq5 ted from the vertical by an angle b;faliq/c ki r4scs5c7:2*xn $\theta$ 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 cxc,;fhkkdk 7 3oefficient of static friction is 0.30 (wet pavement), kkdxkc,f ; h73at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the e 1squimk2h d5)quator were aq k2s)duh5i 1mpparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant d;rqgr *ndl c* ck(erb2. h*vl3istance 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 lamp sxqv-.1 9lkl*ja(w p oauspended from the ceiling swingsqx l-( a.o*avw1ljpk9 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 h+ e0/fc bd*bj0hnocwdh:p9lc w.5 wt1as been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a pe/5c.e b wptnbh: j*lf09cdc hw+10wdorson 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 Syolojaic4 1vqn:z .h758e, ujpace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could bla,7 hc.5v:o8zijqejnu y1o4e a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the h w9w.u4d3c zyknlayzfb0:rhiak(4 + .ill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) .0w:3zb9yc ky+dku ni4rlza4fawh .(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) utilizes a(ztqt 7+9kn. pu.iln;b u -vkm 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 “fixes.” The satellites or.b9uz7.-ul iv mqntkp(t kn;+bit 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), aftertvd /6 giv ryi9i9l+i; traveling 2.1 billion km, is meant toirv;vly9i /ti dig9+ 6 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 the space shuttle pursuid1y yuiwgz efp *-f*x2 6/0ljk+y2ts j1 (rpegng a satellite in need of repair. You are in a circular orbit of y2 1d+ fe* *-prwpl0 /uj6kyx(gyiezj 21sfg tthe 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 distance fm9 xbh/.7mrwg p-lqp; o0qgs. bqx,0q roqo r,mw 07.pgbxmq0lbpq- gx/h9s.q;m 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 would need to be if you could actually "feer:f,b9c(-3cl)rg1lewo 5 sn/nv w bxf l" yourself gravitationally attracted to someone near you. Makwbf 93):,ef/rnl wcrx5bg-n l v1oc (se reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gal4 x+bx3umggq /z 3wjv:axy (Fig. 5-46) at a distance of about 30,000 light-ye :q3/gvx3mgz+ 4wbxuj ars 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 zem vq +2/ws5x)pa:qnxpb(k7 located at the corners of a square 0.50 m on each side. Find the map5pas2 q (mq xb/7e+vx)k z:wngnitude 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 orbitu:qejix:zw ,tsh:t6+t nw3 eoa: o g4,s 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 x-i-kek4w6usby the tip of the 1.5-cm-long sweep second hand on yo-ksukw x-ie 64ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around iiz( 5qpae vivp-ey s8p+l8;m jg: 40xgn a circle below you on a 0.25-m piece of fishing line. The wy+ m0epgev avzg ;4x 8jl :5iq8p(-piseight 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 desi(- u waep51girgned so that a car traveling at spe5 -w1i(gaer uped $ 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, tx 9izlnr2de/n lu7g3/s 3h/aahe 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 acrsxanula 2 /ge9l7/h 3zd/i3 nceleration, 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 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.$\approx$    $\times 10^2$