Sometimes people say that watero ey2:z/tbafp1j1 llgw6+ x5s is removed from clothes in a spin dryer by centrifug5z+ 1 jlwfxo1s:pb6y2ta/g e lal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same whenpf,nza: gn3j- the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at tap:nfnjg3- z, he same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wh ot+d/ 9ewp)*aqw) jwtere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom p )w*j/eq9t+t wwao)d of a hill?

Describe all the forces acting on a child riding a -o t+;gdl;sdi v l.t/lhorse on a merry-go-round. Which of these forces provides the centripetal acceleration tvli ;l tgsd;/d l+-o.of the child?

A bucket of water can be whirled in a vertical circle without theo,,-gd9mwzky0;x uwdeq h8w - water spilling out, even at the top of the circle when the bucket is up,,hqoz--89 wmu0; kdew ygxwd side down. Explain.

How many “accelerators” do you have in your car? There are atk mg;/n6pmq 9 ar1l4xqzizc8a,tw;8 g least three controls in the car which can be used to cause the car to accelerate. What /kx6prnz48qmg1qw ;i9altgc, a z8;m are they? What accelerations do they produce?

A child on a sled comes flying over the cresucf ;y0c h*t+w.p0lid 6vd 9kkt 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 forcet0h9 p;6lv+dk0 d uw*iyfc.ck 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 ri wz8 u q1kn*d g12dr5j,ra1qxounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle kmti u,f0qntc271 ou)given its speed and radius of the tut7c1 ,0if)qt2uknuomrn?

A girl is whirling a ball on ai0fqp rjardv-0en6he/ 6 9 .ft string around her head in a horizontal plane. She wants to let g.vq66e a-r fd pi/0nf 9jrhet0o at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the ys 47cc7la ,iovq/r2g;0bqig Earth? If so, how large a force ib /gr7;qcca4syqi vg70,ol2? Consider 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 Moon’s orbit 7 bfxk*h pm1j3pz p1m.yrz 0;ubeb zmx uy r0p.1f h;zk7m31ppj* different?

Which pulls harder guvr8h i ujew)*+w j/rl2usz) n/6m/qjravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates mor)r iv8/rjnu+le2j/jms/ *uhq w)6uzw e?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th4 8x7x +1fy saqw: pnqnjr5b-gue2e -ee Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Eaq1gu4w+ee n jr:f-e58pxn 2sq ya -x7brth to the other.]

Will an object weigh more at tf :usphab8; ayrcji3d28 *aa) he equator or at the poles? What two effects are at work? Do they oppose each oth8)dy;:a aaiph8*ua 3 jfbc2rser?

The gravitational force on the Moon due to the Earth is only about hup. kv w2xju +b*cpcpgs7l .+;alf the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eartu cwp*g. ;7vp+bx2up +k .sljch?

Is the centripetal acceleration of Mars in itsvp)82jwuey7 s orbit around the Sun larger or smallerup w8yv e7j)2s than the centripetal acceleration of the Earth?

Would it require less speed to lna.w nzq:vuk+ xju +4.aunch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation diu qk+n nxz:a4.ju vw.+rection.

When will your apparent weight be the greatest, a -cdk;+82 7cx. zkkgstyrwxd. s measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same +-r.k2cg.yc 7sz8xt; kddk xw as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectedfg. yf ln3o9c, by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walkinglg f,noc9f y3. 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 “app-8m/ i hj4 f)gv6sfmwtarent weightlessness” between /tw -sm86fmg 4hj)if vsteps.

The Earth moves fasterb 2rz p.1z0hnvhlnn 12 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 v2hplz b. 1z20nnrh1nin producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known un9+(uucvhyrum/kk)t ) til it was discovered to have a moon. Explain how this discovery enabled an estimm u/c(+h)u ktry )9ukvate of Pluto’s mass.

  The Sun's gravitational pull on t g5(kxc )vagk*he Earth is 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 the Earth to the other.]A child sitting 1.10xkkc *ga5 v)(g 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 qshok(3qj49/aueph /u-5yh pou d8o 7 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 qm2p;,mowg3 b acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on themwgm qp3;,b2o 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 ox./6xrd7d hbsa;brah5yi -(wx 5: q lon a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculal.-rdi 5 5bqrd(b7xyw :ho6as /xhax ;te the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eartjw4+j yp5zn xqj 297 oj,q+bichl/:l th's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in itspjnq9cwjt52 x h ol:+iz4 lj b+/qy,j7 orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of tqj +6.y9tlvevz , - yn*l3vtyclay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameterttvelvy+36l . z*jyqv9,- ynt is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical raq- iq/wib0 /9zh5qp circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is bz/ r/qqhwaqp0ii5 9- 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 t0t0qp6h3: hlo , weepfurn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of 36hl ,p0 othqeew:0f pthe car?   

  How large must the coefficient of static friction be between the l4m,ej6ct:39b u5m.bdgp8iosk on 8ctires and the road if a car is to round a level curve of radius 85 m at abu.l jm p3 e8doo98:6b gsnmc5k,ic4 t speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rl4 bjdy7+/b2fk,iuc h otate a trainee in a horizontal circle of radius 12.0 m . If the k ib j+,fc2l4u7h/bdy 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 turntablev+qfj/h(x. a(wx5 ugl of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntah.g q/fa ulxx+(wj5(vble 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 aj zffafb;ph9884,pk jt thebzpfjk h p49f ,f;88ja top of 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 driver) crosses the rounded top -k-k st23c,ho nhof5moff25tcksh - - o,knmh3o a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter 4fthzr dbh g vf9p+2064fu;gkFerris wheel need to make for the passengers tf fz06d rb;h p4h g94tfvgu+2ko feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertica.r,gasxw+ ) kql circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportinq. sag) xrw+k,g the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm froco/:dq(4snws qez-y8 m the axis of rotation is to experience an acceleration of 115,0z : e8o-ywscqs4 q/nd(00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, mt,(htn* ny(irs.s-mpeople are rotated in a cylindrically walled "room." (See Fii.y-(h*tn,s n mmtrs (g. 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 * uv4pfts41-smaqdx3 9ncz.o ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orb4.pfcqt31a9s- vsmzdoxun *4it by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring th h81evyj: ;ffre weight of the ball which revolves on a strirv ehf8jf:; 1yng 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 o*b g icpanz3,rn p1a*tjs-;)) g9ph*k hgm7oyf 88 m is perfectly 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 masse,gna2 : 2ee/o/j-d aohc-ubios $ 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 divj+kna -m 9p)6 -ed2s buf4 sjvwk-v0zhing vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exertkdqoa-l5 b2:ted on the car (by the ground) iqbo adk-:l25 tn Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pits : ,kxvi:b,tt5da:z c area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road ix ,adbvtcz5, k::t:sto provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular i 46afywo4 x xhcf;8wn9nstant, its accelera4ywfw6cxx; 9 haf8 o4ntion 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 Earth rgt( c:jqvgv4c.h(q e5adii) above the Earth’s surfacevq tc5:v4(ghqce. j g( if its mass is 1350 kg.   

  At the surface of a cert:0am,5qnaby ijd x:p(ain planet, the gravitational acceleration g has a magnitude of 12 m/sij:y p5x0qbnam a,d :($^2$ 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 8wqs4o- f3cxi /bsc4ldue to gravity on the Moon. The Moon's radius is 1.7s8/ ibcf3oq w-lxc4 s44 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has *qh+lyg85vuu;qez u6ign5x +a radius 1.5 times that of Earth, but has the same mass. What is the guu*uxh;z+ vg5l+56e q8q nyiacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eargn7-ha 8 is58xvyyc (pcp6 x0y 4ig)hqth, but the same radius. What is g near its05 hv h ypi8xns4yg7-()xc8ycqpi a6g surface?   

  Two objects attract each other gravitationally witflue(mc9) 3wk5*lzm0z7u7ka; q an ldh 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 effect i2keir-)8 b:sf og4ocive value of g , the acceleration of gravity, at (a) 3200 mkf8:boi2goi )c s4er-    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outs25i7 0uswba ) ndvsu;wide the Earth where thegravitational acceleration due ;sa05uib s dw72v)un wto the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times *6nb7 wv-itgo( p7rsay(a q-h the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravihvty67asp( nqi *-og rb7(-wa ty on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average st rxlw979sca1,q w r( pfwzho mr0;0y1kar like our Sun but is now in the last stage of its evolution, is the size of our r ,0wkyca(owr91z9lmqps ;x fw 01hr7Moon 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 in 8vrfnjvz7:7qcv/gv 6the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceler8c7gnv:f/6q rj7z vvv ation 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 0.60 m. Calog 5;zcrerohw -s ;,4hculate the magnitude and direction of the total gravitational force exerted on one sphere byzscor, rew;54h-gh ; o the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred ye nk*lmxp.9(/r9 pu v0oqd/amxars most of the planets line up on the same side of the Sun. Ca/mup99xr*mkdov x0/paq .(nl lculate the total force on the Earth due to Venus, Jupiter, 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 gra/:0b4c/mlznd os kln 2vity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determin:l /msblc nnk240zd o/e the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for ./3wg vnn0aix the period of the Earth nw a.n0 /vgx3iand its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed oer;usje8-)8 uksrw ko1, h/j hf a satellite moving in a stable circular orbit about the Earth at a 8u-hj/ r eeshro,kju)w;ks1 8height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circula9stwz:t d (3kx pjowa8 d8iz2:r orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occ:9d 8 io dxja:p8 (z2wtkt3szwurs?    $\times 10^3$

  At what rate must a cydgx n1+n,z: /k( s,i nj:fze:lvi;g vblindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s ,lv(zzk/:j+fnn ,vg :;dibngix1s :e 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 cir 6t99chlj9h zb:eb6 hvcular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surfv:l9jc zbthh 696b9ehace of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite vu25k e,hjejr(p; 9l vhave to be launched from the top of Mt. Everes (ev9h,vu ;5jrepkj2 lt to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contm /yn(r/i0r.jbv.vf 6sa7lwpinued to orbit the Moon ar (bj fpl.7avsmy vin0r/w6./ t an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Thyp 5 dq4/dx;o t(fdnu-e inner(t;dn5 /u ypdoxfdq4- radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once ev5no3/rchq3g7bm0ne 9.jp x s7 m fyh7yery 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, ro bx/07hmejm g n.cq nsfy735p7 93hyand (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from to7-dqg*0 f rgk+-wmvxhe center of the Earth's Moon+xg0k7fv wr g q-d-om* 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. They are 4d((75 jbuc r0rasquvobserved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of qr d47brsu5u(j0 v(ca each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevg)izjw o;mqvra-s).ynj 08dt kk +) e(ator thatitdo)). jgqy kvn z0-s8+);mwrae ( kj moves
(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 fromlzoat wby) t(w0 ktk8q:2 9lc* 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’s9boaql(w2tk)y 0*t 8tkl: wcz minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface 5 h98j:csr k0ydqodq,of a planet with period T , the density (mass/volume) ofdk0o d5r:q yq,j98sc h the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to(dun7f+ y.d fg4x+f1jm dlm9i determine the period of an artificial satellite orbiting very near the Earth’s surfdff9n.4gm+ 1uxfm j( li+dyd7ace.    s

  The asteroid Icarus, though only ao.n 6i: cnd0wt few hundred meters across, orbits the Sun like the planets. Its perio:n dno60t .cwid is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of -c..wwi ryqbi;h x*6i4.5 $\times 10^{9} \mathrm{~km}$ 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.;ia 5 +yapw)+4ooc gax fd*h-v 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 w +ic5;xg*aoo y+pdf a-4v)hais 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 the cxc)uzlg7.r j b9ti90h enter 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 mass5qty-t0wi0 j- yxm+oc , period, and mean distance for the four largest moons of Jupiter (those discove+ t 0qjow-x yy-imtc50red 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 Earth from the known per) addxb4i- od*hma(m)iod and distance of the Moon. i4m ddd)ax*-m( o)b ah   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moo;ydi/ 7 9hcn6guyu3 scns, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Com uh 9yusndy/ i;c67cg3pare 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 fpnfo:( x8pm, pm3s)jie 27 y 7trq+oiwragments (which some space scientists think came from a planet that once orbited the Sun but was destot8op+ ,7pxjn7mf 3 ime:r piw)(syq2royed).
(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 ani4o 4nsu3vsk2j ; m:6 ia1aqan artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it 4aq aa1ovni i ;4n62mu 3k:jssis 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 year, in Earth days?   

  Tarzan plans to cross a gorge by swinginlqzc 8l oh4 c;:d7chcz1 d0d*gg in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass4cdldgc*1o:0cc8hdq h l;7zz is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gnyx f i2hqkd+k,096w aravity be half what i+q nfkk d,60ihwyx9 2at is on the surface?    $\times 10^6$

  On an ice rink, two skaters ,w6s 1jjhhl,4*tdpnq of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling tj wdpq,4sl*hnhj 16 ,on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravityg0j 0n.kknvuo49w/b o at n.wo/n ouk j0gb9 k4v0the 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 traveli +i0;q z5wkwozng directly from the Earth to the Moon experience zero net force because the Earth and Moon pull wit kz+q z0o5ww;ih equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you standos :1+umso .j*h c1fjg on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elj *fg1msu1o+h:.oscj evator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wx+e-q bxb8d ddx765-bgkzh;yaoala*n/ eb 6, ill rotate about its center (like a tubular bicycle tire) (Fig. 5–47 ,dz/*xb5 6de + gk8baqbon 6 xldbehx;a--ay2). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–46ddlpv(cq c) 3a8 hld+/wqyj-3).
(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 op:(: tc. yvlodd*4pfo f a planet in terms of its radius r, the acceleration due to gravity at its4y ol*o:tv cd.pfd(:p surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectejuvbh5+6lf*pc a2kn/rh3 ,mh 2wydk/d from the vertical by an k/m6 h2/h5fh v3+lkby* c2duj n wr,paangle $\theta$ 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 b astoh )dxv20.g8dafszri,6 ( anked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at d vixsfzo0sa)gdr2,ta8.( h 6what range of speeds can a car safely handle the curve?

  How long would a day be b8p*itesw *)j if the Earth were rotating so fast that objects at the equator were apparently weightbp t*i*esw8)jless?    $\times 10^3$s

  Two equal-mass stars maintain a co m,iumi*u :0-tsqzmg7nstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at kkd.5zkc0z wia (54lbgmx 6s9a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling slz (9 i.5a4kks 60xw 5mckdbgzwings 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. Thumy5-cqy --f uu*wm7p5q- bza gp-uf*r s, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a p*7q q p-my-yp-ufwfgb-*u5ru5- cmzaerson 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 Spaui 9o4(kw adm2ce Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be (49ma wdouik 2a 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 hill*ji- (lb do.,0zhs:7 yu6tomk3zdlsp 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 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 witi-k70 s, *dpbtluszool 3:h.(m6zd yjh the road at A?

  The Navstar Global Positioning System (GPS) utilize2gbe45h 9am m2hc7i rx2m 90msgyvca.i/r.a ns a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellitecg2smh2xamg.en 59ar 9y .amic7ih 02vrbm4 / s, 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 Rendezvous (NEAR)ow p vf.q:-7gnx vi, 0dljcj;9, after traveling 2.1 billion km, is me jv xjcw-,vio7df0.qpgl:;9n ant 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 the space shuttle pursuing a sagqhk*(q9z6jfaui-3iq5knxz xbu 7 /u s,ky51 tellite in need of repair. You are in a circular orbit of the same radius as the sauf bkn3,9i( azk5 uy17 - g6kq5xjqhux zi*/sqtellite (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 distancyjw gj 02 *mxuj6b)t5le from th5g026xt) jj wuym*jble 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 wou8uyq,w3+fmcartz5c3 ld need to be if you could actually "feel" yourself gravitationally attrz+ufaqt3,m8 3yc w r5cacted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the(6 :sucow xyqum s.5 qk.t//yj Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 uj oy.5xkw m6/cqy(t.s us:/qlight-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 of atlxtyiou6 3tyd 23- 7h square 0.50 m on each side. Find the m outi-yyt36l t3dh27xagnitude 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 5509-gd.gdf7d5x6j olo i 0 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of tha.fe ;ers81nv e 1.5-cm-long sweep second hand on your wri;1. en fsa8ervst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ni95 x1xfll0hrc td;zb*9yv. around in a circle below you on a 0.25-m piece of fishing line. Tz9dr blxnfx1 ;ti0vh . 5*9lcyhe 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 wzlbdw oeq (at dp3-9(afmv u;s+t*29radius R in a new highway is designed so that a car travelt3;w +qlsafmt-(uzo( da92 9* e wdvbping at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whe2pqvfob9g *5 s:ge,zjn negotiating curves. The angle of tilt is g: zvjp5b 29qe,sgf*o 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 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.$\approx$    $\times 10^2$