Sometimes people say that water is removed from clothes in a sgx;41u+1decya iy dt4 pin dryer by centrifugal force throwing theedx d+tca1y1u4;g iy4 water outward. What is wrong with this statement?

Will the acceleration of a car be the sam n ,fcs/bm+-voe when the car travels around a sharp curve at a constant 60 km/h as when it trave+/,f v- onscmbls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whjpmj v7q*+x4tg5 ;cekere does the car exert the greatest and least forces on the road: (a) atkxqvtg 4+j;c *j epm57 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 merrh/ymtqp:n: btxe;)r -g( x07 au6 zavzy-go-round. Which of these forces provides the centripetal acceleration of tttme/06y(anh g:p) 7:zv- rbaqux x; zhe child?

A bucket of water can be whirled in a vertical circle without the wlued):omtg *l+sz5 h*+i7cl3zuc)ng ater spilling out, even at thegz:e host 5z 37*l+u+nd* cc)g)umlli top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have i t f+b4hu:z9t3zg,qktee-f- gnujtv/3y p v1.n your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What a3e49tjzf3: p+t z/1f q-vn ukt.vu b-,ggt eyhccelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. gq*fa30(irzs5–31. His sleg*i0qa3z (srfd 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 decrease using Newton’s second law.

Why do bicycle riders lean inward when roundinw p s17.6nm zzl)-xqieg0 cdq+g a curve at high speed?

Why do airplanes bank when they turn? How would you compute the q4f zq)bi.y/vozx0-c banking angle gi)z-0 v b.qqo/zfc 4yixven its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal p3tdoim7serfk7nx:g 25c .hu6qfk 3j ;lane. She wants to let go at preciselxr7mf eqfhnd k;76u3 sc 5ok32:t.gij y 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 Eart+n+ kxmb. eamr,ohr22yxth6w** r z+hh? If so, how large a force? Co*oae2,n b rr6*twm +x zm.k+ryh2h+xhnsider 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*) 0i3q9quj k 35u 9wnwkt vcs3sz:nkc be diffe)wv qs si3wck9ucj*uknq5 n933zk: t0rent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on t:no93etjf 7aemaebv4u./ n8the Earth? Which accelerates more bn8 e f/o.j7at34eae9u:vtmn?

The Sun's gravitationw) q 0m.9xzct+(;cmkt; 5sqd* vehork al pull on the 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 pull0mwrtx)q5(mk .;sh+ c kt9 qodez;cv* from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are5).a +yelqq jy:3-wxhc l;e rh at work? Do the5q c3e :a;xhylwj eqy+-).hlry oppose each other?

The gravitational force on the Moon due to the Earth is only about half the foraamg m0 *ox58nzgc5 1ru *xxd)--r qszce zz5rdxx 5 ag-0x-gu1n8 m)cos*mra*qon the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Marsqf:y:0/ bc pkb32 epit in its orbit around the Sun larger or smaller than the centripetal acceleration of the : 3bf kp0y i/c2tbep:qEarth?

Would it require less simf,g0 t/ ps0)ku v9wib1;gmg peed to launch a satellite (a) toward the east or (b) toward the west? Consider them iv0p gk)/sfmgigt0bu; 91w , Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movi6k3q) pwhnsu q8z6xfi)(ad+d v n 7sm,ng elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In u3n,wv 6m)nzaq hxk sp(d)sd7fi6+ q 8which 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 periwlfr(92jil2*3ngi9 x w ek4u zods in outer space could be adversely affected by weightlessness. One way to simulate gravity i x3 i(k4l9z wf w2nigl92j*reus 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 weightlessfkdci .3a:7jz*sujhuoq+utd k n597 :ness” between o3: 9a.+7n7dd5qu*ujf u tiks:ck zh jsteps.

The Earth moves faster in itsn; u/yb8 pgvh8 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 n8;h gybv/un p8ot much of a factor in 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 until it was discoveria5n6gj /zp +lb8 5srvtz)8c ced to have a moon. Explain how this discovery enabled an estimate of Pluto’5pja/8is + )tgrc z6 vzb8ln5cs mass.

  The Sun's gravitational puc tp-znx+(-/c, gheh ull on the 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.-t,exczu / h+ pg-h(nc]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 1980 mc .i1 mavur)2$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 t5a4ft wc,4 pc1j 6gheyhe Sun, and the net force exerted on the Earth. What exerts thf wpc5c,h 1644jegyta is force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N ib d7a9ufssdy-3t +x5r s exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate thysd +b x3dufr5at-7s 9e speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cir 8dcl9f)jutsr -*w), fy pt )(a7oxwahcles the Earth about once every 90 minutes. Find the centripetal acceleration o(jo,pyux 8 r9s7- h ff)tcatlwdwa*)) f the 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 speck of cl2ggdvoz +ol*w ul5 7d,ay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?g,lgu d2+o*d zlw57vo   

  A ball on the end of a string is revolved at a uniform x3yhax,* hj 3 f/p9sxcrate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 3/y,xh9pxc3 *sfjahx $\mathrm{~m} / \mathrm{s}$ 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 of radiu ;bkkv;v l6qp1m)p9gz4qe 0wzs 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 the z1vgqlk z4;v9)m0 e pwb;pkq6car?   

  How large must the coefficient of static friction be between the tilu5yt7 s5a/*sv fc11ji)vd j tres and the road if a car is to round a level curve of radius 85 m at a speed ofs i*l1vudjc 7av5j)tft sy/ 51 95km/h ?   

  A device for training astronauts and jet fig.ft3 k3m,dc wzhter pilots is designed to rotate a trainee k3fwz dtmc,.3in 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 rotating turntablew6*o7fk9bojv1w) ni z of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and tjio*7bn) 9 o kfw6wz1vhe coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rollerz i 48o+3y myjm9xvrj f.zix;18vqcd1 coaster be traveling when upside down at the top of a circl4xi.91;+mz fjmxo y81yvc8jrq i 3dv ze
(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 (includingkgm 0 umzjt /cj,c;-p)b7:i(bj/ f mb rn-gpp( the driver) crosses the rounded top ofu-mj pc:m-bn;pcp,)i rbbz7f 0gk gt(j/ mj/( 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 Ferris wheel need t fy,; zb;nk1b0 5bc9:hebczl to make for the passengers to feel “weightless” at thet0be l,k;y91zzfbc:;c5nb hb topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of r4 cuk*.q0.z fww )1u6fwcinqd adius 1.10 m. At the lowest point of its motion the d.nw6zi40fcwuk*.1 )qfqu wctension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the apo7 l- ck3xec.xis of rotation is k c.3xce o7lp-to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cok8gle3md7 hda(, 74xtsa( ixarnival, people are rotated in a cylindrically walled "rot74g8 oh m,sdaxia(3de(kl 7xom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rot*4 ;:tfirjoa zated in a circle on a frictionless air-hockey tabletop, and :i zr o;*ja4ftis held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weigcc0u keom/f2yr + tv8v lzkf(v5 :h9-oht of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of vr9 ch v2 -f/ zokvef8ut5y0ck+ol:m ( $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 per 23)3)r3hwbv fu1xqbg u sxdq2fectly 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 masses lk z)8 ls3 6ywkcdpuq/n/1 7: nxan:tv$ 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 mane5enx3)2k;adiuqn x)g3g pwd9uver 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 c:kwb )klitcebb6h;5/entripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is wk)bi h6/lkt b5;e c:b 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniql7r3k/otomr. .w-uyformly 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 would the coefficient of statiy..m7w /l3ruortqok- c 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 owyf1 7sp 9hmz:ask-iz- :xn4tf radius 2.90 m . At a particular instant, its acmwz khaftzp1s7n49 :sxy-i :-celeration 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 Eart ( )*v-q uigzlh:vf)awh radii) above the Earth’s surface if :l u( *vzv gq)wfh-a)iits mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has aehd(oo. )o7b( hr dnz3 magnituroe nh3.(d(hdb7 o)zode of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Mo .-(n;h2pe6c6dh fl)dtt 3v vkgct.nyon's radius is 1.7dc yethvvt n-. np)l ft3c6(g;k6h. 2d4 $\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 :zq/ n0x8 mmyyidfu);that of Earth, but has the same mass. What is the acc)ym0 um n;xi :yf8q/dzeleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius4jr br y o/)wt9+lv6qa. What is g near ita qr/4b+lrvty 9o)w6 js surface?   

  Two objects attract each other gravi4bq7(akrc vlpg0 8ia mmsl54,tationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accel3cae43 rvu gl8eration of gravity, at (a) 3200 m cae8gl3u34rv    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cqzq1g ig4/ xq9enter to a point outside the Earth where thegravitational acceleratigxi z9/qq4gq1 on due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a s)8oi0f2* yh a j6x(sbddxi at.phere about 10 km in radius. Estaat6h xo ys* ji8(xdd)bi2.0 fimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncefe4e:q*fi 89c6ku;wfjz+i/sxxs /g k was an average star like our Sun but is now in tf8ju9fxe x:/icksq/;4wzi 6fs +* gkehe last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlib9b qt((u+c 2r mpx +3ul+ztgess while orbiting in the space shuttle. Your friendpq + ttb g(xiu3+ 9cumr(bzl2+s respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a nc/ 6f v 2bvjak402pdmsquare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by 2pk2mvf6vjn/ 4b ca0 dthe other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the ezd6aky62i5v.diaviopz u/pu+106c Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The cpva / p5 e0ud a+ido1266 .k6iziyvzumasses 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/30 yigmms5l p of Mars is 0.38 of what it i03impmly/5gs s on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using th.j khtz2* 9dame known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Ke9jk.t h *a2mzdpler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movinm/d1a p3lt.l 4- xwaxrg in a stable circular orbit about the Earth at a height /-1.a3l w4pmxtxdal r of 3600 km.    $\times 10^3$

  The space shuttle releases a swu eahja; h x(*+ymka.57z vd4atellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth ha 4+dje7;zv*xuah k a.w5my() when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants 4otdywuam un 0 zkg2t;6g:2z /are to experience simulated gravity of 0.60 g? Assume the spaceship’s diagt ad2ou6 g2tnm/z;ku z0:y 4wmeter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it tb(u+8z u/q:2q5 zk otvd ohtm2akes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very smhq25kq d2ob (+t zmuuzv/to8 :all compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wo0p x1ac 2 c3vm)rmj7ckrsr ,4culd a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbitacc3241c,r0p v)j m7cr x mkrs around the Earth?   

  During an Apollo lunar landing mission, tvoi+lwxafu-i48sow6 o + 74dshe command module continued to orbit the Moon at an altitude of about 100 km. How long did it ta 74idowas s +4wl6+8-vifuxooke to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbuwld7w4 kf;v kpw );l,8iz qr(it the planet. The innew7)wpqri dlf kk;8vu,z l4(;wr 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 diamyrcqh 8mh.;9t * (*mt3p msvmxi9uv5ep,f0vm eter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a)vtuv8xe.mp r c3,m m9i**q0vpm 9 ts(hfmyh;5 at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 kmb w18 i,2.r*y;w 0avtbqe8 uu.cjsniv from the center of the Earth's Moon in a space vehicle (a) moving at constant velociv..qu 1eww jv8 ab82*brs,0c;uynitity,     ----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 binaryi,jlquws/gqz. o3r .3 -star system consists of two stars of equal mass. They are observed to be separated by 360 ,jz3rl3.u qws /.g oiqmillion 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-kg484ners w(g kb woman in an elevator thatksg 44n(b8 erw 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 f7 tdwc2wq+r(drom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnituqd7wr+ c2d( wtde and direction)? a =   

Show that if a satellite orbit5kxmw4w ir6 7ldt71o6; ln+m 02mp2rxfyyoz vs very near the surface of a planet with period T , the density (mass/volume) of t 76myorri kx+w lmoy4 lf7dv2pw;60 21nm5txz he 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 perio 1w .ra 2s5ae/c(gfwtxd of the Moon (27.4 d) to determine the period of an artificial satellite orbis5 g f2wwcaxer/1t( a.ting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrosssog/8)3: awul1opsvakh.b vs 9 b; c.x, orbits the Sun like the planets. Its periodb: ascp8;.wglovs3bax9 s1. ) h/ uokv is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average disjhd/md)-e x, ftance 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 roug3z0 f t)apkgxu4ia(i4hly 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 distance s in Kepler’s third law is half the sum of the nearest and farthest disti0)fg44zkx( apau 3it ance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cente1; 7f e; ntj/sf4rkumpr 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 fou0c n+yxluwncdn 0-se,5 8bmc.r largest moons of Jupiter (those dim -.cbcynl cxn,08d+n ue5sw 0scovered 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 period and distance of the Moon.8 bhofyj0f ifh4t2w (ije 4.f3 t ff3h o(e yi84fjbih2fwj40.   $\times 10^{24}$

  Determine the mean distance from Jupiter for :8ay; rtvyd 0beach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given y:ra 0v;dyt b8in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars ant 7 bzwf g:w:uc2w,3qqd Jupiter consists of many fragments (which some space scientists think came from a planet that once 7wqfwqw2u gbtz:3,: corbited 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 azvgus x.i;mzdm,s9w2:*c zd6 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 rzms zxw9c;2du mg,v 6.id*sz:otates 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 swizw kgmfh+p/wd8 , 6nw03+lmcuf u6ys)nging in an arc from a hanging vine (Fig. 5–41). I+k ws/3 wwum,60 czmh g)8+ndlfyu6 pff 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 mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the a+wi1 1iv p:q 7*ikieew02osobcceleration of gravity be half what i10e:ko sewb7*iq1+iivoi2 wp t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass ct)hw- o-v7vl5 jp0divo 5-mygrab 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 on onevlv iw)-mj hc70-ot5d5y-pv o another?    $\times 10^2$

  Because the Earth rotates once per day, the appr/ u0 )lk24ixt gw8k nn8qilp0c4gwk+arent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of np00 g 4wki+xunk8q)kgl 4w8 rt/i2lc this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Efs0c 6bt/si. farth will a spacecraft traveling directly from the Earth to the Moon experience zero netbi ffst6s0/.c 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 inkd4+yqf -job) an elevator, it says your mass is 82 kg. What is the accelera ) 4dyb+fj-koqtion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station cw;(jh s ash;8tupz8l( cje:b) oj22aj+ k (chhonsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by th):;ct(c wz e(oshk bh8+p(l8u2jjhsjaj2; h ae 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. 5–43). 7p 98axc0w ludd3dl7 y
(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 td,+h;0 qqkxt terms of its radius r, the acceleration due to gravity at its surface +;q h0kttxqd, and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from tkq0:lc-2extm l2xy jm9f 5mu0he vertical by an anm:x0t22l- 5jmq 9e ckly mfxu0gle $\theta$ 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 bxe+r2tb;u6 zog 5zzaj8n/cn- l) yc9 of If the coefficient of static frictionbny+j 8 5 9-agzt;2nl )ocz ub/zcr6ex is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were roz:m; k:e ,qa*+gek skbtating so fast that objects at the equator were apparently weightlessb:sqkkae; , mek:+z g*?    $\times 10^3$s

  Two equal-mass stars maintba,k h8ljykj9 jj3d83.bj 5sdv 5f9xs ain a 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 radius 235 m. A lamd*l7sd 4w(cb vp suspended from the ceiling swings out toc*(vdwd b 7ls4 an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed ttwv:ke*7. a wthat ktea*.wvt :w7a 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 person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence .;xfl y( fow0tu(4x 4z:royww of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They diz o(wry o( y;x:f4 x4tlufw0w.d 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 up6igns26 9cf 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? (Which is larg fc6gnusp9i2 6est? 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 Position9q6w0h) g dkxning System (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 org wx06kn)qhd9bits 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 traveling : m32 pmaddpw,2.1 billion km, is meant to orbit the asteroid mdm, d aw3pp:2Eros 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 satellite in need of repan)m duz/ fl;1uiiu ,f*s5 0gjmir. You are in a circular orbit of the same radius as the satellite (400 km above the Eartsmm/1zlndgu;u0 ,u jif5f *)ih), 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 30kwr1vmr;;5g2wt*w d:6gt p oy00 years. (a) What is its mean distance from thr ;dwwg6ktt:g 5 p;vomw*2 r1ye Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" yo wgv9/ lh3)o,r v172jmyyjdru ip6b+ yurself gravitationally attracted to someone near you. Make reasonable arul2jg3v pd /h,yj6 v)o9 7b1+wimyyrssumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a di /n4dp3 .hp. 3lgjyp xsy*gd9lstance of*.3sg d p49gydyx3pj/l.lh pn about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners ,mny h31qi(dtof 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 midpoinq3d,( t mh1yint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits th g-lp:+zgospu+ l7ym+ e 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 the 1.5-cm-long swr/5s p -3ldg x(kp)cuif i692wmv3ucveep second hand on your wrist x g)w5uvuk(3f2pis3 / lv p6cmc- idr9watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight a--d m*ytpxmjbaw2l1hhzd: 6-w,aw n 0 round in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 hw-dmw*1-batl0d a6p-z:y,jnx 2h wms. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiu/j0gszqm3 jj3 s R in a new highway is designed so that a car travelinqs3 0g3zjjm/j g 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 tilt3yi eas: ky vi)3;-msw of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (e);yysa: -vmw3ii3 sk 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.$\approx$    $\times 10^2$