Sometimes people say that water is removed from clothes in a spin dryer by c3pw x9l*p/doww v9l7 t4wle3mentrifugal force throwtd leo9l wv3p*43wx/ m7pww 9ling the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the cam:ej0 f5w uv* vf05tpdr travels around a sharp curv0dvvf:we 0jpu55 *tmfe at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed aloi v;3enq8uxa5 ng a hilly road. Where does the car exert the greatest and least forces on the ro3 e8ai;vux q5nad: (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 child riding a horse on a merry-go-round*lpqysa9 j32xvnyl; 3: npnb :. Which of these forces provides the centripetal acceleration of th 3qn2anxpl9:pnyy*bs 3; jvl:e child?

A bucket of water can be whirled in a vertical circle witho 4mfjz ;h0f6iz1xx 8svut the water spilling out, even at the top of the circle when the buckzx4xms v iz6018fh;jf et is upside down. Explain.

How many “accelerators” do you have in i8o ise+oi8: iqj7,veyour car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations doj+ieio8esq i7i :,v 8o they produce?

A child on a sled comes flying over the crest of a small hiw bzn2tqc ,,e1u (gho2ll, as shown in Fig. 5–31. His sled does not leave the ground (he does not achubz2 h,cq 1o(, gew2tnieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at h -ke);ph-e8gqu kuk:gf g(f2high speed?

Why do airplanes bank when they turn? How would you compute the banking angle y)eqzb d 8 w 8w0si3ag7ttz61 xrsxq25given its speed and radius of the turnrq1a7y 8t8weiz) 6 g0xswd zt2sq53bx?

A girl is whirling a ball on a string ar. chrr/w,8xj eound her head in a horizontal plane. She wants to let go at precisely the right time so that the ball c .ejwh8/rrx ,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 Earth? If somznr/9;n hq w;i1dnd 3, how large a force? 9w1n;q3h/nid; znrd m Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what e1k/3-q opwq igvg;*fit is, in what ways would the Moon’s orbit beigq1v oek3g fqw-/p ;* different?

Which pulls harder gravitationally, the q0c okp-/vnk+ y66f +x slsq8q0v- grhEarth on the Moon, or the Moon on the Earth? Whvkpgsh6 rcq0 q-q v8fkoy-xl+s/n 60+ich accelerates more?

The Sun's gravitational pull on the Earth is much larger than tah+ 7anv l3m ap(ia/o5he Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side o hp7(avim /aa+l3an5 of the Earth to the other.]

Will an object weigh more aa.+i1 d3oizcat the equator or at the poles? What two effects are a3d. ai+z1 caoit work? Do they oppose each other?

The gravitational force on the Mo1tbcz( 2dhezw ap0z(,on due to the Earth is only about half the force on the Moon due to the Sun. Whyapw (zb,et2d01(zzc h isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun wxu h; .cm67b8g-dx wdlarger or smaller than the centripetal accelerath8 cxb wmud6dgwx- ;.7ion of the Earth?

Would it require less speed to launch a satellite (a) toward the e/m(yjold g++c ast or (b) toward the west? Consider the Earth’s rotaty/lm(c++o jg dion direction.

When will your apparent weight be thd;*u m wozks0;e greatest, as 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 leask; s*;u m0wzdot? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely ar r61vz ii2l/effected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, w6z21vi ier/lr ith 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 weightlesp:qmkr tw368w sness” between3rw 8qtmkw :p6 steps.

The Earth moves faster in its orbit around the Sujf,sl81pm2t a6t oc-b n 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 tc fp-,t 6jms812bla oproducing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto wavkel02 wont d20e( /ia25kv8sg i6cb rs not known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Plad 6lec2ko8vgen5(v022iiktw /bs0r uto’s mass.

  The Sun's gravitational pull on the Earble)+16xn/ h0gz 9x nf 4wujzqth 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 s xl)n bf4nzhg j9wz/6+01 qeuxitting 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 travelinglrq(ij.h/g ax /uf3 5n 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 acceleration of the Earth in its orbit around the ud uldlb6 zb i9d8e+9p3 6xle9Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circl69d+9lldi 963upb l ue8zedbxe 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-k/qp 3pn db:52h *lrpveg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. C pl:bqpdh 352r/*pvn ealculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earthce.qbob02s+ .0ye dqy's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth'.e+oy dqy2 q .0besb0cs surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of l q5zk f)+e 5t2ijhd 8m 6v0w ;k(elht-7npybka potter’s wheel turning at 45 rpm (revolutions per minute) if-j ti5 75kdk2pk 0zletn he8+q6;l)yfb(hvmw the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vr);cfz xejd s;(90jp zertical circle of radius 72.0 cm ,j0 cxdzzr( 9j eps);;f as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn ofnb p8bh 8c-d-o radius 77 m on a flat road if the coefficient of static friction between tires and r8hpnod8 -b cb-oad is 0.80? Is this result independent of the mass of the car?   

  How large must the coefvt) tk2:n24wa x / ol1wgyjpo :k5ghn3ficient of static friction be between the tires and the road if a cag1j53gtyko4:twh )x2k non :w/pva2l r is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astron;1:onjc w:)oh x5 ioxqauts and jet fighter pilots is designed to rotate a trac);woio x j5h:1 xq:oninee 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 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 rot hl,2//ld;i2aomfp.m7 q fy8 p79prt6 obuajoating turntable of variable speed. When f f/ r;9lj.pto ho qpa/opaudbm22iy, 87l6m7the 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 between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at th jbjyw*r8bz0; e top j8yb0z*j;bwr 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) croz.8d *r f g2ta) a;yc(n,qrg4ery6ijbsses the rounded top of a hill (radius =95z q(8 a4gric a) r2frb*;gt,ed6.nyyj$ \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 perubk+ 6 8hcyzs3fp8,ja minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poaz fj3s ykh, c6p+8ub8int?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle opjl e:5sz1o9 pf radius 1.10 m. At the lowest point of its motion the tension in the re j51:osz9l ppope 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) mus)pytrweef (zph y9)fse 6k6f)1* x.c jt a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelery) e fw.zfk6rehcf6j)(p yptxe*s)1 9ation of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cagnt q4,h- , fppj71zyf .qcy/prnival, people are rotated in a cylindrically walled "room." (Sqhgfn/-c, 1tpjp4z p 7,yfq. yee 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 frictionl0(ybpsm e: )guess air-hockey tabletop, and is held in this orbit by a light cord connecteuge0 :bpsy) (md 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 thwyi2 m6 hdi136v /dgnbe3-k zais time, by not ignoring the weight of the ball which remad-i1zy v3 6hk/b32edwi 6 gnvolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfeieruey5tl 7p(a9fz r-u8 t*: jctly 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 masseszh1,5oti :- umc.ozbu $ 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 myn0bhi0nee8/(7 ;)mdxu m fl taneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted ono, )wnva,akys g5(l au j,s-3n the car (by the ground) in Exampleyo,u(3wna ask,lnjva, -s g)5 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 Indianapolz fjw l.)rnk7xp+p1*4os5o x xis 500 accelerates 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 constant tangential acceleration. If the curve were flat, what pxp *4k.f)rozn 51owj sxx7+lwould 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 . At a partic1 3adv1 ah01yvv aco:hular instant11a v0 dva1av: yho3hc, its 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 gro/-hbe+/du c havity on a spacecraft 12,800 km (2 Earth radii) above the Earh-eo/ /b+uc dhth’s surface if its mass is 1350 kg.   

  At the surface of a certain planeqta01y4yp+.6/ ( baongfprc kt, the gravitational acceleration g has a magnitude of 12 cn/kpy41 ay g+of6 (.p rbtqa0m/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 radius is 1.v)8bm+pq . j9cm1ug ag74+. abq8 1gm cmpguj)9v $\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 the sam flmg)d l(yfi8+4 bo2ee mass. Wy8oeb l( mgi+dl24)ffhat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ev(k; zr rq.;dnguum2 6arth, but the same radius. Whatqk(d;;.rvz nru2 gmu 6 is g near its surface?   

  Two objects attract each other gravitationally wl7s/cnq 79wjxith 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 acc5:xezv j; nhln; t:n:zeleration of gravity, at (a) 3200 mzhn :5n jtl:v n;ze;x:    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a a w8ixw tg, :()0*;ndekrrl wnpoint outside the Earth where ther( ) g x;8 dn:0wwrntel*awk,igravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fiwl+ 5bm3qbkkcd;ozy :z +/fy8ve times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster8bdb zf/wk:5oyl y+q ;ck3+ mz.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is :7 j3p yga 6kbkh mf)w(eb92sfnow in the last stage of its evolution, is t hkg) k(wyjefb:f7p s6m9a 32bhe 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 orbiti vq3dyjz :8+/i,xgdb-d5m fmsn q9va 0ng in the space shuttle. Your friends respond that they thought gravity was just a lot weaker9dgqz vsmd3qx+vadmnbi 0 -:,5j/ f8y 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 0.64)be./r dd -wd8e 0wb 3ddagrwvy)u)c 0 m. Calculate the magnitude and direction of the total /wd.yrvw )adcw8 )b-ede d) ur34bdg0gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yea*z m m3n8,lnsars most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fou,s3 mzlna*mn 8r 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 acceleratio w*4;yqrw3/caz xyx ,kn of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass z4ar/3;xw *kw y yc,qxof Mars.    $\times 10^{23}$

  Determine the mass of the Sun usinger wzhp*w7+r9 the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtwz 7e9hwp+r* rained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving inmb 7o3 s tes-hj2z m)ba91lg4w a stable circular orbit about the Earth at a height lwt e947)zmg s b23ab1soh-mjof 3600 km.    $\times 10^3$

  The space shuttle releae4 b3qb0839aks0 bwkn scrxy7 ses a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurxbnyr78w3b as0q s k39ceb0k 4s?    $\times 10^3$

  At what rate must a cylindrical spacz+3clob9j(- f /sbb sdeship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter ijlcbsb(o- +b df/3 9szs 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 shrapa j*w37790cx ix/ zolkh. atellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit 7xpwox/0k *. hh zr73ja9cial 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 depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a sat.k2bu h hc2fsh 9i6ge0ellite have to be launched from the top of Mt. Everest 9h2bfec2h guhis6 0k.to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit th p(qijp/kjg:v8b ( pk: 7m6wjge Moon at an altitude of about 10mpkp6gjw7jq(g b( p 8 :/ikj:v0 km. How long did it take to go around the Moon once?    s

  The rings of Saturn ach4pp i:it()d i6w1bare composed of chunks of ice that orbit the planet. The inner radius of the rings is 76 b)1:4pc(wpt iaihi d3,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. h+0y chm+ov 8l5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the topol8+hymv+ h 0c, and (b) at the bottom?
(a)    (b)   

  What is the apparent wei74ok9ua 9yv07h9 nflveck2t4m xvxv 5ght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constauvvtaxofvmy k79 vc 2n 7kl 445990ehxnt 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 consist8 h (zyz9 j6nbv3vto9rs of two stars of equal mass. They are obsehyv 3nr(bt9vzjo 9z86rved 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 each?    $\times 10^{29}$

  What will a spring scaleej.vleke r: v (o-nb2;(ic7uy nww77h read for the weight of a 55-kg woman in an elevator that( -y b7 veo(wrnjue;.chn72iv:lk e7w 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 from a cord suspended from th7w)dya*l w/ ore ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevato)wy*o 7/l rdwar’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planc-x) h xv6xt/ 7sfl ivuf*3(uyet with period T , the density (mass/vo3(s7)yl u *6v f xxvcf-uhix/tlume) 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 period of the Moon (27.4 dt+tfn ts a0+*gn899(q) sepc/lpvervli8(wn ) to determine the period of an artificial satellite orbitines tlp8(9snf r cvnpg vnq +it/)t8le09a+ w*(g very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mgl7 qo/;z6mmis ylpt-(d6r;mpw(j(z eters across, orbits the Sun like the planets. lzmoq li/ (g-yrm7 zms6p (jdtpw;;(6Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dvbbxs2 z 4yrt7a ,dwo 7:vg06iv5e x;yistance 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 rou9 (3i8 f7r9t snz-opn en5behvghly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distaz9s35eoie(vnbnn8 th -rf7 9pnce s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center ol0;/ya rvq rsba-c+;a f the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mephp8)cv 2g b-ejo4*boan distance for the four largest moons of Jupiteh4 )pp*c ovo-2ejbb 8gr (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 or 6,yi h1,skldf the Earth from the known period and distance of the Moon. i1lysh,d,r6 k   $\times 10^{24}$

  Determine the mean distance from Jupiter dv.4 g-c8/dmtiw; bevfor each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the;bcv4 et/ddw gv.m8-i 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 aeci; 5oge :a.odk8; s 4ncg1z-zrn 6cfragments (which some space scientists think came from a planet that once orbited thegc4c18 aie;6g z ok 5:-on d;car.snze Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a banvcyd vofj(- -y 5pg*:od 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 revolutifpg5j (vy*y o--d:vo con, this planet's year, in Earth days?   

  Tarzan plans to cross a g(u9xgug /:mb0bj 0mb borge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable u/j 0mb9bmb(ug:0x bgof 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 mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravi;gqo 2io z,rg2ty be half what it is o, rzg2 ;ooigq2n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsee v kvv.83 m-a(0e:yfos0ns/ oyqz8w 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 pullin.-kmy0azss8 y0 (wenvoqvev/ 8:3 eofg on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravityi4zyua-x,84a*h q ohx at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the mag h qi4z ax,48uah*-yxonitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly;q (h7f v-s -if3yhhuaieask92ph1g ) from the Earth ti kiy-79 f)u3g- 1p;qh2efhhvhs(asa o the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an e8s/,ys8p 8zmhvl u7y qlevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which /s7qyuy88hpsl,v 8 zmdirection?     ----待选择----upwartddown 

  A projected space station consiszl 9x*:bo9f j:r.l rdhts 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 the :fhlzo9j .9r*b: xdl rEarth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verte5wfep;0qt ygf ;7u,oical 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 thermp(;)p slvu4 mass of a planet in terms of its radius r, the acceleration m r ;l(u4p)spvdue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical z qx t:ya-jmj*f.;x/5z lcatlcx2,a (by an ax q*clamly xj:-xz 25. /t zft;,ajac(ngle $\theta$ 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 63+ d 6izeo0cz 9avmegof If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle6+ozc6g0zv 3e9iea dm the curve?

  How long would a day be if the Earth were rotating so fast that objects at the enm j4+lmm c0*squator were appamjnl* 4m 0mc+srently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di5;wsu(/zsv0perik0 d 7 cx-exstance 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 (gk,k ojfmb-2s53j hb a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of h bgskj-5(o2km3,jfb17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it hadege vulpbzjn ), ;rk6n1t 0ix5p4s ;zj9 (mv)s 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 persjtplxk1)mv, bj 0 negrz)5(usz9vne6 p;i4;d on 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 *0c0 6q8l/ 8qe-xce cunbmnkxTelescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense thatc0e8kc 6q/l8cm*xx-n bu qen0 it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 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 thqths jh0*t+ :raverses the hill and valley shown in shqhh0:ttj+*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 with the road at A?

  The Navstar Global Positioning System (GPS) utilize 3n7ze*qi+yra(. htzes a group of 24 satellites orbiting the Earth. Using “hqan.z+ ie73yt z*er(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 orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after :t( azo ktfh1vjfy4 .7traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is y:v1fohta k(7z.jft4 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 satellite in need of rht(9qrqo ( .iyepair. You are in a circular (q(rhtqy 9o. iorbit 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. 4- y* owofx.pjcbt:2b (a) What is its mean distance from thec oyo2wx f.b*b4 -t:jp 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 7au9u b d, yavs779yxz k4nq)rG would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, li)7zd, yb9u7k qausv9x n7a4yrke F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) no7 h7th5 p56;ca togeat a distance of about 30,000 lcaon7thp75o 5t6 h ;geight-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 z9mi3 7milm6 ga square 0.50 m on each side. Find the magnitude and direction of zim7m6li9m 3 gthe 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 orbits the g,;fwe 3c+yiq0y 0immEarth $ \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 thn ruwd;y98tfu.8zha 0sd 6q vue,f ,x1+gg5 nme 1.5-cm-long sweep second hand on your wrist um n wf6aed;dgxr,+n. 1z0tfu8q9g y,8h5 uvswatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a zn c.( 4 n2yi:qkzgmbn8ak(4usinker weight around in a circle below you on a 0.25-m piece of fishing line. The weq4(k y.g u4acnn:knb (8izzm2ight 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 dezi5iwh u gcr (84p-p,wsigned so that a car traveling,w5i-ug8wzr p hc (pi4 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 tray4ui ikc)h5-b5g 1g68qde r afin, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main fug bgk6df5-1r8cqe5) y4aihiorce 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.$\approx$    $\times 10^2$