Sometimes people say that water is removed fy8 er5z269+ j1rzseg- g mgzstrom clothes in a spin dryer by centrifugal force throwinjz15g8g+m rzes2z9r eyg6- st g the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when 2+bhf/y/f3c2 )ym orlalwj 4dthe car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at thcaowjl hb/3)2yr 2myf+dl4 /fe same speed? Explain.

Suppose a car moves at constant speed along a h8ye -uv b s-ff)j.eo(qilly road. Where does the car exert the greatest and least forces on the road:-).s-eb8vofqf(y jeu (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 onx +pbr +p4g3nlo6ef5 n a merry-go-round. Which of these forces provides thenl6+gepxbr+fp n3o 45 centripetal acceleration of the child?

A bucket of water can be whirlxpm;+xnl 9 d/iply x52w -slr-ed in a vertical circle without the water spilling out, even at+5dpmx-l2r9wnsx yx-;pi l/ l the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leas2a;33) fsgiwdizlik c,1nkp dh1fk6/ t three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they proid1 /1nk6az3d gic);3 ,ihfspw2l fkkduce?

A child on a sled comes o6tx zw+8j hm;flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decreasewt+z j8x;mo h6 using Newton’s second law.

Why do bicycle riders lean inwar v7bv )c*q5bllmz1 +u(w s3d1l9thxoq d when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankiv hqfhq9t.wutrr 0r0vp 7j+.5ng angle given its speed and radius of the tur rq.7 twh50qvj9rhfp+ 0 .tuvrn?

A girl is whirling a ball on a strfumd(6w/e l h/ing around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on th mwe(du/h 6l/fe other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? Igveso ix rx*rq5-10k3 wc 2+avf so, how large a force? Consider an apple gvc3rxq- e xk15rs 0o2ivaw+*
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moont/kl8uxr7;i s4kh, l5s wv ym8’s orbit bhl/x,vm5ut lk 7w;y8s i rs48ke different?

Which pulls harder gravitationally, the Earth on the Moon, foek(p *n w*w)11l9c9yqvd t uor the Moon on the Earth? Which accelerates mfqpv1 9eltw *w(d)*k1u o nyc9ore?

The Sun's gravitational pull on the Ear0b.j 7yxlh67mg.;ecuo fx1( wg,yyi dth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diff .,y7lugxeoj0yi; yw c7 6.b(d1 mghfxerence in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles?/;hy49si0mdc z5uc:;q5 c nlhhiuql; What two effects are at work? Do they oppose each ot4uqmh;5 clchn9/izyih dl ;s0;qc u5:her?

The gravitational force on db-sw*:1qx 3zvst wq; the Moon due to the Earth is only about half the force on the Moon due to thbx1sws:tvd;w *-q z3qe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accymcc /lw9;0 nm:phck0w:qy6ueleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration l0qw:km chcyu :w 9n0yp ;/c6mof the Earth?

Would it require less speed to launch a satellite (a) to- i6gl- usuejkp4pb bw5g*i +e4o8p8yward the east or (b) toward the westk s6p-lb8*pg+i- e8gp 4bwyj5o4iuue ? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as1 xw 1g pcub.ip,b.i/h measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, p1 /ih .,.p 1gcbuwbix(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 long periods in outer space could be adverse 2+qk:mdx,(bbqy97owvq ;u slly affected by weightlessness. One way to sq,y9;qsq uk7+2oxl d: b mwb(vimulate 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 you can think of.

Explain how a runner experiences “free fall” or “apparent weifj,tali vto:(r)9h ) zghtlessness” between steps(t)vo)f t,l:jhz 9ari.

The Earth moves faster in its orbi71y7 qpj c7dn.bo jq;o83 -ziee g6bhit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing 1di7b8bqgenyq-6 ec7 7 p3oijohj;. zthe 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 know9ru cz +o2x+oqn until it was discovered to have a moon. Explain how th+uqxc+oz 2o r9is discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ea zk*izcot4y23b*e v 7erth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenc*4k e 32e7*ytbic vzzoe in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19b,2 xqt-aqryzl 6;m80 tskno 780 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Ere7ux)4+)l 6 zajt2z 7of unmgarth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assun)er7u 7otjf6 uz) la +4gmx2zme 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 uanm);cat- r9 as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discuu;cn9 t-r )amas.   

  Suppose the space shuttle is in ot8w nbfdy ,8a6rbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of th,nt a68 fy8bwde space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a sp3dgm b ib k/wpx.3q -k+v8f(nheck of clay on the edge of a potter’s wheel turning at 45 rpm (revolib 3nq fxg.kd+(k-8b3w v hpm/utions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string vs8);j,o n *- gekp/vyjsyz4zis revolved at a uniform rate in a vertical circle of radius 72.0 cm ,jg; j*y/sy4zn -8s , zpveov)k 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 with5mxwl(lj 4tt/i /x l,s which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this relwxxl5lm tt/,/s4 j( isult independent of the mass of the car?   

  How large must the coefficien. 0a quj uvcq1yy,-mk2zd7x) bt of static friction be between the tires and the road if a ca-dq) qkj bu0yax2.1c,vyu m z7r is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts andnx2iek+sk six/f a4,; 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,2e/an,x+kiif s sx 4k; how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable 6 dy.8do tp f-maq k xngjdn/+s/y.2j;0ewj2kof variable speed. When the speed of the turntable is slowly incrydx ;62j d.ky/w2 kf j08os/ g +qdj.tnmaepn-eased, 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 m ukt2 sovcl.+pmq6m9 7ust a roller coaster be traveling when upside down at the top of apc t6lq.o+29s u vmm7k 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 dr(-g7e7j :aacxhxfs)xiver) crosses the rounded top of a hill (radius =x)7aaej7:-gxf(c hx s 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 Ferrig tc35yi// ae m6 9bf3rkba(rdmya14ls wheel need to make for the passengers to feel “weightleimr3 bdma/c4lygt/35 ( 6f9e1arky abss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticaiz 70smgpoh5 kg 1/d/nl circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bdops7i50 n/ kgz m/1ghucket 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 rotagy5g9jr e x2x1j,0d 7lcmg9v ete if a particle 9.00 cm from the axis of rotation is to expe g75xm1,jerc0jv9g gle y29dxrience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carn11afv; )lyse4j ik5 viival, people are rotated in a cylindrically walled "room." (See Fig. 5;)i1vl4afjs vye 1ki 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 rota8e y2 h4fuscy9ted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cuhy9c4s2 yfe8 entral 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 the weight of ty,y jc,v )x47irasts2he ball which revolves on a string 0.600 m long. In particular, find the magnitude of riy4 t asyxv,)s,27j c$\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 perfectly bm9xc u8sfqm 6(c0dhu:m. jh nwqiq8* 8anked 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 massey.9o.3s ynfkm s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by didx eh*oubd4dzo 17 zsx2g23 , fa08filving 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 centripe.:urita 2lxy5tal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 1tx:y .5 2ulair5$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from thvvu -sk):dw5lac zq;pv ,e) w- ev0z(n2i oru0e pit area, going from rest to 32w c lv z-,-5:0;2 u(snqvv)e k)uopza 0irevwd0km/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 to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rad fq lo: n;i1k*ae4+tc pj/r0nrius 2.90 m . At a particular instant, itaf 1lrc/0 n :iqknt *ro4jp;+es 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 12,8tiw9 hz z9epyd*4i,1s 00 km (2 Earth radii) above the91shp9izd* wti4ye , z Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain plani1-er ivmz v.:et, the gravitational acceleration g has a magnitude of 12 m/v1v: .iremz -is$^2$ 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 iv*m2n . / ui5guaq8uidue to gravity on the Moon. The Moon's radius is 1.74 /v528. uin*muiuagiq $\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 hfv17;j0d efxy ef;/ll1ozs .pr z)f2was the same mass. What is thfde) 1z v1xfo/y0.wfl e2pl;zjrs7f;e acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but r m;u2jvun; m-5u v;xxjl-e g/the same radius. What igj;xue l5-2vur;n /x;mvm- jus g near its surface?   

  Two objects attract each oe+x) d2id1 ,o3vk+f jz*lof xqther gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value o /+chsrzo.n,tf g , the acceleration of gravity, at (a) 3200 m t+n/hr z.s oc,   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ecdl vd(r*e5evoo:w;u xt*; (e arth where thegravitational acceleration due to the Eartxo;t5r(:d(o *ecvwve* l;ud eh is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of oul h*ql2:: zeiz5zj q7nr Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monst*z:qh : 7ejzl2q znl5ier.    $\times10^12$

  A typical white-dwarf star, which once was an average star like )wnyoisgy sy-8d7n4c j6t)dqwca+5 1 our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on th-ny gwj 5dy)s+ts4c w )na86y1qio 7cdis star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiw u-ydx*-s+z lting in the 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 swu +*- -lzxydby 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 atjht e8h : aombf+s9wn0b4l0. square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sph +nj t8ambbl 0h4t0:hfow.s9eere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets linag94c zwd8.gue up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planz 48.c9guwad gets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of whaty9mrol.he4f+2qj 3s v it is on Earth, and that Mars’ radius is 3400 km, detejo+9mvh3q l4.sey 2f rrmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sq::fc fu tge(7pw) he9un using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtainew9 :hfcg qu7pe():fted using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about (e)e n goc4-/opw gs)1vcn6b pthe Ea)e4o g)b(p6sp cg/cn-ve nwo 1rth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 yt1g j(li1m) bkm above the Earth. How fast must mbi 1(1yjg)lt the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occk7oa/wr am93.hq f0cg1rx1a cupants are to experience sigrc ac q./30fxr1akha9mw7 o1mulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular ;0 sx. u*in*owf8o uh/mkftg/“near-Earth” orbit. A “near-Earth” orbit is one at a height above the suw u;/i0fsg*ou.k h/no *mtf8xrface 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 have tlci9+0(f w 8zq+z/x iqh3byhio be launched from the top of Mt. Everest to be placed in a circular orbit around t8+0hzicib qxylw9+/ h 3 zif(qhe Earth?   

  During an Apollo lunar landing mission, the command module continued to1 j a* nsyzv)dq7zwm ,aza rd6c2w47r, orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onc4ma1wr ,dcz77*adnysr qvzzwj),62ae?    s

  The rings of Saturn are composed of chunks o cg5h r(0nslwc(rl ,1jo7 k.gaf ice that orbit the planet. The inner radirlg ash,jln0cgckr7 (o5 . w1(us 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 everl7)8je9zuxgjyz l / h+wm )e mnf:;2zfy 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real w)jy8 /f+m e:u g ;9z)hfwlzl je7xzmn2eight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-k 5 rx)r9cdgcrq( ml9 (4zueez1g astronaut 4200 km from the center of the Earth's Moon in a spqe9r4xde1r 5 9uml(c z(rgcz)ace 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 are3szrj3: uux.a observed to be separated by ux 3zsa .ru3:j360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-rs;:(/xc vplqouj)8y kg woman in an elevator that movsuy j :;)rx(8oqcp /lves
(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 the ceiling of an el1* y*nn674c4x ghdsykkj* bdqevator. The cord can withstand a tenchj n b* 76*dgsydny4 4qkkx1*sion of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellites jenw+ g/z- :elr(q)r orbits very near the surface of a planet with period T , the derjq/+-e :l)r n gwz(esnsity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to de)k 9y5f 4xqln eobe0c6p+m9wl0 lk5aetermine the period of an artificial satellite orbiting very near the Eartho lelb5e+ 5)xa4mly6f9pe90 kn0kc qw’s surface.    s

  The asteroid Icarus, though only a few h 86ifthc-b: laxr8i0qundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance frcqi:l8bt 6r 0x-8ah fiom the Sun?    $\times 10^{11}$

  Neptune is an average distancl+50un9pcap(/ k owofe 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 yean ;e3ygweu;fo5r)dp ,rs. It comes very close to the surface of the Sun o); nop3u;e5gryfed w,n its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center8t5hjxjv:h-s g8* piy amb0i) of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons 3xoryen/ (rua /a5f9 g0y+nrnlc+r1h of Jupiter (those discovered by Gali/rn erug ny5h(r+ra / ya+xnfco103l9leo 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 period and distance of the Moon. od)ibxv. *dk* .*xdk v)ibd*o   $\times 10^{24}$

  Determine the mean distance from Jupiter for each*wasrnacc ew3,8 ;dl+ 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 valuerl+;caasnd*8c3,we w s 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 consi91.nscq;d i2psldw)l sts of many fragments (which some space scientists think came from a planet t1p qis29)l;lsd.d wcnhat once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a lr f:7 dh8hi*fem;2/a u36lzxz6 sk(4ntgwkr 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 willdzlinfe6lt/fh;876k*3u wzag:m( sr2 4 h rxk be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a ha-o+fh sw-ca* nnging 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 tws*-hn- c+ofa he 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 accelerp;*dl,t* 9ehg +h+a di(mxz oqation of gravity be half what it is oz hap t9dx;gem+lq,i+* h (o*dn the surface?    $\times 10^6$

  On an ice rink, two skaters o/972m)ijxvet ron5(.vsd cqs f 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.)7ec mnt d5x/ ovisrj9 2v(sq hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparrk3 y(st+ 0ty9w.txvgent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate txgt ykwy9 0+3s tv.r(the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft d 08)-m4im okmhn*h vntraveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equakmh)m8v d*omn-h i4n0l and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bamnz 8( iu:;inl,3kmomqxv60 bthroom scale in an elevator, it xubn;8 ivqi(n,3lmz: mom0k6 says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thatdq f1lv4daiea e96 +a- will rotate about its center (like a tubular bicycle tire) (Fi f14iaed v+9aald-6q eg. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertirtpu x+34 2* ib+uyl2 my l7vvd:(jvnical 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 z)htyd;to k.8 its radius r, the acceleration due to gravity at its surface and tyk;d8 h ot)zt.he gravitational constant G.

A plumb bob (a mass m * v6ch ;llynt:hanging on a string) is deflected from the vertical by an angle nc6l: lv*y;h t $\theta$ 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 nen:n-*5 vobpep ;ds,coefficient of static friction isve;e-,*nnp bo5d s:np 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Ear,c1ad-h 9syf+so2tg qth were rotating so fast that objects at the equator were apparen syo9 ,s2-ct 1fqgha+dtly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a .wty/;vh.occytbp -r3q8:47tz g48led y rqo constant 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 a constant speed rounds a curve of raeb5+ o0ugo+l ddius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.u+0bood5 e+gl5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massivke:z,z+oms b 8jln5k.e as the Earth. Thus, 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 m+zksj.5l ,zon:8emb kore than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Tecllm f9dkh: gcs)2c/, lescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light esc:,hcsgfk9)/l cld c m2apes). 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 const ,n7:nhhz okq5ant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Whic: ,k7hznh5onq h 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 hzxb5acww. 6: (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few 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 ]:. ah 6wcwz5xb. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, iy5c:7 r*lilr us meant to orbit the asteroid Eros at a height of aboutiur*rlc75 :ly 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 satellite in netj.k7kn adq-;ed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km bekqt-d. n7 kj;ahind 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 dist2iz6cgg ,zvt ub 5r2u3, r7jkhance from the Sun3z76 jz, kch2 tur5,r2gbuvig ?   
(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 af55zlevkiri4 -qc(* d+ : udtjctually "feel" yourself gravitationally attracted to someone near you. Make reasonable k*+l r(q5e jud:vzt cdfi4-5i assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around r.3 6+aqf*wr yp ec)4jedp1 me8vtpn 9the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from thpdwfpvmc6q4398r ja+ *ee yptn )1. ree 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 at9z umy wum656q the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bmwm9uz5u6q6 yottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the E9(le-bax pg(sarth $ \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 experieq sce2ho9u6aag1-x dr1zrs-+nced by the tip of the 1.5-cm-long sweep second hand on your wrist-rau1zae q g do9r6+21s-hcxs watch?    $\times 10^{-4}$

  While fishing, you get bored3 h(bws5 q+ut/mzy mxvy97re9ujdrcp/;5 .fw and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that twuzfe tr9/b7uq/ csm+ vy 35jyd ;95m(hrpx.whe fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R ieiy /ilq+q(b* n a new highway is designed so that a car travelingqe +iiq/yl (b* 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 whp4:vr fn0 sv)zen negotiating curves. The angle of tilt is adj:fzs 4 0pvr)vnusted 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.$\approx$    $\times 10^2$