Sometimes people say that w1(qrlr za wrfq 78 u9r w31yl-qsbj+8later is removed from clothes in a spin dryer by centrifugal force throwing the water our7j 1lqq9u3lbf (zsr 8w8yrwr+q1l-a tward. What is wrong with this statement?

Will the acceleration of a car be the samu*1go;ahyi9j:nyef* go tp+1e when the car travels around a sharp curve at a constant 60 kfiegt upo1 *j*aynyo +; :g91hm/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at co3a *pol;61qqz eedt h6nstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between;o 316p eda*zqthlq e6 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-rounvet;9,qx8u ks d. Which of these forces provides the cekx8e , 9vsq;tuntripetal acceleration of the child?

A bucket of water can be whirled in a vertical circm:a p9s(7czd wkms jd1k64li .le without the water spilling out, even at the top oflkmssa pk6mz49jwcd( 7 d. 1:i the circle when the bucket is upside down. Explain.

How many “accelerators- tfadkro4 1f:y4a8ma” do you have in 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 accelerations do they proa-4yarod: 14kffm at8duce?

A child on a sled comes ra ok7c y+2h5k0ndt10k chsps .l94of 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 he59c+1 cst0kop4oas7h0hflkd . y rn2k goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwardl4mrqbz al1.j u; y3k8c .se0n when rounding a curve at high speed?

Why do airplanes bank when they turnc4zx;o jj .n(bfw:h7n ? How would you compute the banking angle given itsw4jj hbn;f:nx7z( c o. speed and radius of the turn?

A girl is whirling a ball on a string au6 k--aotwj7i round her head in a horizontal plane. She wants to let go -w -iuaj6kto 7at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earthr(siyibt8xe:2 aj; :x ? If so, how large a force? Consbjrsax:iy28;te :ix( ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways 0)hhmk;3lh 5qqtt .6q;n tgosco9 t/w would the Moon’s orbit be diff9kc;/.l ho3q ) gt6tqto;mths5wq n0herent?

Which pulls harder gravitationally, the Earth on the M.0,x slw sfdzh i:wea -ba((l6oon, or the Moon on the Earth? zh6wdl s,.e l fbw0xsa -(a(:iWhich accelerates more?

The Sun's gravitational pukq6ciijthvt )04dh 9.ll 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 gravitatvj ) tihc04.9idq6 thkional pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects areb3psqnp/roojw* m*4ry7w15(ot fy v- at work? Do they op3f w1- o nypo74 qytvrm**jps/5rbw(o pose each other?

The gravitational force on the Moon due to the Eartwtl.kr6,1tb th is only about half the force on the 1.ttr l6k, tbwMoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger*sx nwlvzm4:sc*7xl , yxw(x8 or smaller than thes (4xwxnmx8wz: *v c* xl7y,ls centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward8lyizdy s1r4. the east or (b) toward the west? Consider the Eartz8l1.sir y4 dyh’s rotation direction.

When will your apparent weight be theh/th:n4f :xewm 0ouxx 9g+l g/ 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 sgl:gu+o x x/ 9fh0wmeht:nx4/ peed? 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 adversely affected bnu,.,p; 6w8iqmdcfhy y weightlessness. One way to simulate gravity i,m;i q cnuf.,h86yd pws 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 bmt uz- xew*;o/m, fm5experiences “free fall” or “apparent weightlessness” between stfx-o bz,e/*wm5tm um ;eps.

The Earth moves faster in its orbit around the Sx;q2 qxwx9+c1v0 .zl wps:ct 1uf /djjun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not muchwp1/x+;x2j 1d0lc wscxj zq .t9u:fqv 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 discovered to haveb17r zc dzw/0h a moon. Explain how this discovery eb 7hwz dcr01z/nabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eas u w:m8h,s2smrth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed ss2m:,m h w8suof 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 c)9kha*-cky 1u/1lj u jh)gvi$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 d3 )wf0z0 va/laxd6lg5uhe* lzqdvd 2u8-6nm its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Eax -z 02lzu6dwla*me3 8d)qd/ad6vvflh ng0 5urth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-k tdnc a4:dlz5/t 1shb. 7lsrn:g discus as it rotates uniformly in a horizld1nlt7zrd4 s. a:nctb /:s5 hontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from zau07k+ll yh3e5yi k3the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in itk37y u5 3ihla +z0keyls 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 clay on the edgqyiaxgfq1hcxnt4-1 * 8w xi6 0e of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diame 18yi0axn6w f4gqxht-1i x* cqter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate i*u f5 dpuz.5jbn a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If itsbu.j d5ufz*p5 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 .hvfava5em rnh 31q4)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 result independent of t h.eva54fq13vnr hm a)he mass of the car?   

  How large must the coefficient of static friction be between the tires, llz7 x(b*fle8fcg/p jqhr35 and the road if a car is to round a level curve of radius 85 m at a speed of 95lf hrz5plq*7/3,xc ljgbf8 (e km/h ?   

  A device for training astronauts and jet -fu)5yy gtgn 1 hkpg 5eb,9*kifighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?gg ) *5b-tfupn 915he,yigkyk    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 rotat kza- rzn 9q,unai/)n5- bvga,ing turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the ck/,-,abvr5azinq n )azu-g 9 noefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dq*ce3 8bq xp ,7 yhvlntc+(u6sown at the top ohe n vqbp76*stlyx c8, 3q+c(uf a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded t ic9/bl61 uyrmop of cbruym9li16 /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-dixqx:cl -9 lz/rameter Ferris wheel need to make for the passengers to fee:l/9 q-x zrxcll “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirlt vlbl.zam85 .kuf2 xza th9bdi,k7,.ed in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2tak.zt vlxb,79hml.. a5b,fui28zk d 5.0 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 axis /q wh x- 97o(nykvzn;uof rotation is to experience an acceleratio (97nq wk;x-nz/huy ovn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are0llt( )rnwb7 87 xnxrf rotated in a cylindrically walled "room." (See Fig. 7l(0x)l wb8 tr fnxr7n5-35.)
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 fcs2iag-: lavlxw .y13rictionless air-hockey tabletop, and is held in this orbit by a light3l 1lw 2-xy:.vgaasi c 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 weight ofdi ity8cj zx+-t(6jm1 the ball which revolves on a string 0.600mx+6jytcz-j(8 t1dii 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 perfectly bankedqfo8g, 8u*yq x 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 massen. e +grro e6/nfj1rc5s $ 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 manefz/;i7 zq e u**t hv(quwxc5f7uver 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 centripvn1 u2,bb .v ump8dor8;x+vmm etal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed v, +d8 1omupmb.2v;x8uvbnrm is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unifoqnby;w(o iq1.vj4u1 mrmly 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 . ujy4;inwv1q( o1qbmthe 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 ogn*jl y06,89 bvnyem lf radius 2.90 m . At a particular instant, its ace b 0*vlj9n,ylnym8g6celeration 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’zrcxyhr.( 2).5rfqk0pdd fn ,s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 k d rc xry(5),dq2fp f.hzn0r.kg.   

  At the surface of a certain planet, the g7p9+nk7 /3yufapct jw* nscq+ravitational acceleration g has a magnitude of 123+ua tp7kns/+*cjq p9cwfy n7 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 accelerz.d40hhdvc9xh / mag*h6sxxx9x79 rh ation due to gravity on the Moon. The Moon's radius is 1.74 xxh .a/xc6mh9dh0rsg9dzx x h v47*9h$\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, borg241 njs4zr ut has the same mass. What is the acceleratio4z 1rnrj s4og2n due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but t wklunl; pr-;8he same radius. What ilwk- n8 u;plr;s g near its surface?   

  Two objects attract each other gravi ( e asok4slvzf(f1-a7tationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) )zvcaux.vpm4 2.eot 4 3200 m a.2x em cvvo.zt) 4u4p   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centeb5ntd(*ybput9g2w/my 2 a p/ rr to a point outside the Earth where thegravitational acd9bbmuap2 5yt( wy t/pr /n2*gceleration 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 aiq/ xtj.x 5r(q sphere about 10 km in radius. Estimate the surface gravity on .5x/jt(r i qxqthis monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like o dd,,m5p .n0r gfonqr)ur Sun but is now in the last dgr.f0 nn,r qp),o5dmstage 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 weig j7evl9zsv.j0 htless while orbiting in the space shuttle. Your friends respond that they thought gravity was jusjj.0vles9z7 vt 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 square of side 0.60 w3/9r4t9 azn h jhn.jw7d4ito m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the ott ojjd.wnz nh49h3w ra4/ t97iher three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetsy 5di*+q/we lh line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four py5lw+/h ie*dqlanets 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 0.3s6kbzfbht-ch ;2lb; 38 of what it is on Earth, and that Mars’ radius is 3400 km, determine thez- ;fblt3k2h sb ch;6b mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the permn2-(4l,v is w*wozuwxk 4sx g.y/c6qiod of the Earth and its distance from the Sun. [,g 2sqiyw4k* n/.mwz46( uoclxwvsx-Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cil 9z2m5.d:rx(j)3hmc vz gzgn rcular orbit about the Earth at a height of zz v(g )jx5.hcm 9dm: lzg3r2n3600 km.    $\times 10^3$

  The space shuttle releases a satellitefc l*d0olal ;elffy9nd)9-109z zxws into a circular orbit 650 km above the Earth. How fast mf9)dl 9f9dwxle0z-*c0slo 1nl fya;zust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to .(tkz 2x uo3;gg0yevwexperience simulated gravity of 0.yk0ug2x;ew(ozg. v 3t60 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 sat1) 619iwvqq rqm zl.fiellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does yov 16irl9 fizwq1q).mq ur result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be laun 8ijot o w,akxl;t8).tched from the top of Mt. Everest to be pljk8 l,woo 8tx)iat t;.aced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command moduls ur xej9nppp 24j d ce+x6;q+4jxb0)de continued to orbit the Moon at an altitude of about 100 km. How longuxpeqj2 4p dnbj4j;cp+x0dsr6x 9) e+ did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet oic2 )yqnfe0g4tba3; . The inner radius of the rings is 73,0en0;)iobc qy g24fa3t 00 $\mathrm{~km}$ , 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 diamejpf ;cp/ms*h3 ter rotates once every 15.5 s (see Fig. 5–9). What/*fh c pp3sm;j is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a a3 lf gzou-);e75-kg astronaut 4200 km from the center of the Earth'e ;o)-3azflg us Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of twmvjl8 t4y,tl*o stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betwe8 mvtyt*l,l j4en them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator the(w1 y7*5w:rx)pjiwo0 duv lbat moves ol*p5ujb0rww)y(7 dxivw :1 e
(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 suspende )wv5g y3nkj;ije:4xjxgn 7d:d from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and dirn )j;7 nd yj:i4jx:xgk g3vew5ection)? a =   

Show that if a satellite orbits very near the surface ntctb* )qq--j of a planet with period T , the density (mass/volu*b )jt --ncqqtme) 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 determine the peri g3d u(q3-mxrbod of an artificial satellite orbiting rxm-u g3bqd(3 very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hun:ovs9njytg p53.c mp+dred meters across, orbits the Sun like the planets. Its g5 jymo:3 .ppt+9nv scperiod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dlb3l *q l(2kjsistance 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 7 nna:1d1f 0etovi9ml 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 fan 7m 1nei0at9fv o1:ldrthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the x 1jsp nv;x/57hs:rzl3n)uku 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 j1yrx,pphri 5v .a9 d1of Jupjrp,rd .95py1hai xv1iter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth )+9qk qoj i2x)b wid(ifrom the known period and distance of the Moon. o kiqi)bd+(9q)jixw2    $\times 10^{24}$

  Determine the mean distance from Jul l m:dtc5ze21piter for each of Jupiter’s moons, using Kepler’s third lz c lmle21:dt5aw. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which t6 ax cki:3q.g ueydjb/ms05(o62lya some space scientu e ld6oky.a5 qx( ij/2sm0b36cayt :gists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band c+/bt(cgs t 7n)cyq-n(jqzoo+ ompletely 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 n(b+-o o+gyntcqj(/t7cz q)sEarth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge bl((fim 1j r d8cpa5ssmn 8g,n*y swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what if1gsr l,adn( *n5msmp8ij 8c(s 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 at6fwf;i4fj;os2x,bqk;sg-r0 wk8 p gcceleration of gravity be half what it is on theq 0fpfk sx;2, 6wtigr-bj;;fwks 4g8o surface?    $\times 10^6$

  On an ice rink, two skaters of equal m40injj m 89)q;snz7:z ,jfwsukr zg+m ass grab hands and spin in a mutual circle once every 2.5 s. If we assume their a kw9su8z7n smrn:jjig ;z+m4z,0 j)fqrms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day do*gkitb9 zl22 (dgd-, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this g2- gz *ilod29 dd(tbkeffect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eadogq htc8gm20 r ):pa4re ;8x;co*l jirth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Mirc;* :h g84 )xem08aljtdcoro p;g2q oon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on z,sk 05 )eogdua bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of thekzgod) ,es05u elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statio*.euahf sj -9on consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42)9e. s*ujh-of a. The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (c )v7ww( oaq+pFig. 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 3d3qjc njfgv)4;d7 uwits radius r, the acceleration due to gravij)gq37 4jvc w3ddnuf;ty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strin c 2ia(8+ bjkzqiy*k*h+3 e(xpwwr+vyg) is deflected from the vertical by ay ecxy*(bi*viwz3(+ j rqk2p+h+w k8an angle $\theta$ 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(2(k m,4 kjy/,pzv:gaswycv r If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle th4,zk,2my vp: jywvkca/((grs e curve?

  How long would a day be if the Earth were rotating so fast sd9lp l/rxr(b-pgf x 9r94l/zthat objects at the equator were4 /l/pgzrs x9 (ll9rpd- rxbf9 apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a myq5sp9rwoq.gdv :ob*4uje1g.+f)n 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 co:zvxdc0 f6kc88g7ar- ic j -ourve of radius 235 m. A lamp suspended c 6-raoxgkv idc fz-808j: o7cfrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Enit-9pf q;rh-l l:n*tohyk +1arth. 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 more than a few g t- *9fl yntprkhil 1h+ ;nq-o:'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 of a(i+a6 ygpx n1b.zohv/n extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the spoy 1/n+vbg.z6h x ai(peed 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 travera /.gileqh:7yses 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 yl./qhig7:ae largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a m0c:chigv, rbx 3m:4rc m2uu92 shk-bgroup 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 navickhvumm:r 3c 94c-g2s0xbhm,u r i2: bgational “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 2.1 billion km, isj,)87 lolvxdj+ c.hxc meant to orbit the asteroid Eros at a height of abov78h ,c +).jcxljxd lout 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 lst4xffx.cx;-u n 2k(q4/s rpc5xay2 in need of repair. You are in n-srcx24f5f2 y xp/x x 4(ktsuc;qa.la circular orbit 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. (a) What is its mean distance frj id;oj . w5klfg q.b49vk(65u;vyghfw5sag4 om theubjfi5jd w5hlq4 9(vgyk o4. ;vsg gf ka.;6w5 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 coulzrfbn. e,igt )l.sy)f-k 9p* ccj6e)hd actually "feel" yourself gravitationally attracted to someone near you. Make r,kfcsb flty z.g e )9ep*n.-hij 6c)r)easonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy m5) w5 v7-uejyu9vrrr(Fig. 5-46) at a distance of about 30,000 wv57jm- )yurr5e9 vur 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 of au w0yt +wql7medq69:b 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 bottom 97du:lw 0+mqq eb6wytside of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbid) ;le ejb/4 s pczvigiuw 7n/yy q3;t96te0a,ts the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1:sjc g8.r 8vzh l zykdqby5:-+.5-cm-long sweep second hand on your wrist wy-h+ 885dzj szl qbvc y:gr:k.atch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a c/h gtewkn-g-d ,9kf *yircle bekk9- ngy,g df e*/-twhlow 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 the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so tc 1k9; .vygkz1 xsbi:5 nulzz;hat a car traveling z ug9c.z1n1;b sk5:ikylv ;z xat 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, utilt9z06 a zpo,dqizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling morq6a9d 0o pz,tze 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.$\approx$    $\times 10^2$