Sometimes people say that water is removed from clothesjk dtoke2q46c hpf*81ss a9n. in a spin dryer by centrifugal f2 6dak 1pefj8*sh s 9.qnok4tcorce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car ty));w a,q xgq zao9b1jravels around a sharp curve at a constant 60 km/h as when ita,zg xq)9way)q j;1bo travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly rovpe9 ft9q26i lad. Where does the car exert the greatest and t 92pfi9q6elv least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. mqswenj n nthj2l6n/q q.4k4 :51lc 065udcrxWhich of these q.s/tcw 4x nn41lhnnlq0j6 5rujd :5cmeqk26 forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertic 4 p; lxw;kkjz:u km184y1soktal circle without the water spillingk 1kl4m :;;jktwoxs4y8u zkp1 out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do pftfa6 1ywk lj 7)k, ofw0a3w9you 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 produ wfapt1 k,69k lj 3)waow0y7ffce?

A child on a sled comes flying over t90co(7 g4e9dno e aeqrhe crest of a small hill, as shown in Fig. 5–31. His sled d 7er( o9e0e9cngo 4dqaoes 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 rounding a qq:vv *mvl70t;awzy0 curve at high speed?

Why do airplanes bank when they turn? How would you compute the d +sxz3o w9:fm7 5f;ly-xhchog.l hf .banking angle given its speed3hxd:y ffm;9shhoz+c 7.fwgol.l-5x and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shq1 b;+zjtm24 sy4lryq3jymw* e wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. Whelq24 yt*m; zrq+mwbj1 yys43 jn should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how ln;n +bvh 6q/al v lw+r(l:1vfh *ebfc,arge a force? Considwllf: v/ qbnn+6crl1 v+ hae;* (fb,hver 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 Mor akawga +bcda.1+n cbd8d 421on’s orbit baca dka w+ 841ra d2cg.+b1bdne different?

Which pulls harder gravitationally xj . az /y2y ez+kmvvszs-4,fck0(io1, the Earth on the Moon, or the Moon on the Earth? Which accelerates m.ik+m-v ,yvac1xs k(0fjoy2 z4z/zseore?

The Sun's gravitational pull *3q6kdn:sl xf-2r uapq l44guon 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 gravitadgrq6nl puful:a*23s-4 qkx4 tional pull from one side of the Earth to the other.]

Will an object weigh more at the vwm0efxsan24 lb pau6 4(b*4ya(moa+equator or at the poles? What two effects are at work? Do they oppose eachsu v (b wa0f6xblo*(4np2amya +m44ae other?

The gravitational force on the Moon due to the Earth is only about half tqa* bqs c*y: )8bes9puhe force on the Moon due t by89 caqus)qe* *p:bso the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratiodz2kth-t 1ha0o i p,6nn of Mars in its orbit around the Sun larger or smaller hk0tz p6od nhia,-2 t1than the centripetal acceleration of the Earth?

Would it require less speed to launch a cqa7 *r 6qsaq+s;3nfm zvvn.,satellite (a) toward the east or (b) towann qcr v.*zq,3f;qs+a6as m7vrd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the gris y9 xzt8,)/h9fipxs zo8fr* eatest, 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 speedhr,9 xifs/yz8t*o8xfz 9)isp ? 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 perifsroa 4 r q:):ef*aez(ods in outer space could be adversely affected by weightlessness. One way to simulate 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 thr rafe4 z :aqe:*o)f(sis 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 weightlessness” betrhk;6mwbf-szq5,js af+ - h7 jween ste h;jaqfbj fw s-+,h657mkr-z sps.

The Earth moves faster i9:oh6i av5d7uhtr 1izg5lo u :m.z4ygn its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factou lt9im .hr: uh54:oydo6z71ag gvzi5r 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 have ho*f:cj6( b b z8itcqs.he*kfi7c9y *a moon. Explain how this discovery enablec7ih:*.9fye6 o hib*(bsj8ztcfqc k*d an estimate of Pluto’s mass.

  The Sun's gravitational pull on txco rw)+io1j4he 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 sidw jio)or4 1c+xe 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 travelingcm2zc v jd*u-; 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of thpm4ia1li ; j1 * bj;4pnaz0tawe Earth in its orbit around the Sun, and the net force exerted ;*a0ptja1l m w1bzpji;4 ia4non the Earth. What exerts this 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 3sibgho z51 ao,9s3c kaq )yf1N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length)g91ab) oh5fc3i 3,sq1sy ao zk of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ea) ms hg7fp*u y:wh5*fzrth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shutty7u* zh5w)p*msf: g fhle 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 accelerat7 b7xk3seyrfzfw)0 4 eion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’skf0sx7y)e 4e7wrzf b3 diameter is 32 cm?   

  A ball on the end of a strin2 3gm rw7a05rdsya( xzg is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig5sr 0a7xgyz32dmra( w. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can rol:qg3xvev)2 *mbi8n 7al l ac6und 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 i 8al*amq6 cnx vg)lb 3v72l:eresult independent of the mass of the car?   

  How large must the coefhu )h)p1+aj hbwq4+ lyficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a ha+l 4h y+j)b1u)w qhpspeed of 95km/h ?   

  A device for training astronauts and jet fm7x(fk(gm52 lts e/ wvighter 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 isfvtemx5gw (2m( /sl7k 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 ow k b7fty2oo39xbz,n6 f 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 3xb2bto9 k6,7 w nzyofis the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at6f iwfw (t5zm2 the top o(f2 wi6t 5mfzwf 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 dri470ymyg c-7nt6qf fzlver) crosses the rounded top of a hill (radiu-my64q 7fny0cz7lgft 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 Ferris wheel need to m: oka j4.mw)axake for the passengxa.:k mj )w4aoers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.rli-ok.(br 0 w10 m. At the lowest point of its motion the tension in the rope suppbl(k w r0-io.rorting 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 parti(ch3x)(jlr g1c ibsi d ia5.w3bnn2o0cle 9.00 cm from the axis of rotation is to experience a.b)b jign3 dswc5lc3 h(i2ixrno0 (1 an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wams ph)pbvama 07z340 u3:iu 7kkwyd7blz(a 1plled "room." (ad7wb l)3iva7 3bkuz:smmk4 zhap10y p0u p(7 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 rotated in a cir2kk,n ao*w 029zqz65tobh cyn cle on a frictionless air-hockey tablk5 c nq 2,ny*o0wkab h6tz92ozetop, and is 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 , precisy9l4ftl l*u 9e8lnw4lely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particularl8luw e*994fy tll n4l, 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 banked for a cardwup+;; -y0 cmzok sk+ traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masse+s57o,ql .ywplz 1w-a 1vmsxxs $ 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 maneue4zm 2z udco8;ver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exer 4e5y9mn1op zwted on the car (by the ground) in Example 5-8 when its1nyp m49 w5zoe speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 a 2;; k n4xjqz tkdiyc+w)c(nk1ccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would th;dj1zc x )2k4(wqn+kiktncy ; e coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 pl7t12m f9k0 rl(j zdcm . At a particular instant, its acce z7lkmlc( p19tdf2rj0leration 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 Earvn4wou(v )34pgab g* eth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 (o)g4eun av3w p* g4vbkg.   

  At the surface of a certain planet, the gravitational accelerati;.fmh7 ;qta l,yna-mson g has a magnitude of 12 mn.y ;7 ;t-fl sq,haamm/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 4 j/9 zdywd0x6xq0hbkMoon. The Moon's radius is 1.79x 6wj qdxhy4 z0k/b0d4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timqe rxudhmzmki+ 682b( da/zi 64xdls70 (s8zfes that of Earth, but has the same mass. What isiz rqs8 a(ddz8ue b/kz76s 6mf0h(2m xxdi4l+ the acceleration due to gravity near its surface?   

  A hypothetical planet has a mzy: ob juv,+1 )-evy+ xfxtc9vacg20bass 1.66 times that of Earth, but the same radius. What is g nea vbj9ga1vv ,z) +-tb:xyocfx+ e0ycu2r its surface?   

  Two objects attract ea:vsuc)b 2aes 4nv;+ rich other 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 of g , the accelerati)1nl ,7 3)zh f,krk 3dxhxvz)/ mhxahcon of gravity, at (a) 3200 m/x3 m7 )z,,xhz hr 1vckfk) 3)nhadxhl    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside t*6dxicui bj .-he Earth where thegravitational acceleration due i6ux c b.di*j-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 o)abx9t-.6bin 7 lewx0pawp p 2l84b3lfy ivg: f our Sun packed into a sphere about 10 km in radius. Estimate the surface gra3w)nx .bpbtia0pw6pfal xel8-yb9i 4v2 g7 :l vity on this monster.    $\times10^12$

  A typical white-dwarf bv kads8o .xf9msm8) 0star, which once was an average star like 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 thesm fb d09k)xo8.mvas8 surface gravity on this star?    $\times 10^7$

  You are explaining why astro,p-0(u4kelq )ets3i6 ubeuoinauts feel weightless while orbiting 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 by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of,isoq3ueb4eue) k- t6 (u0pi l g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 k605b(zc 9kte9btt yn m. Calculate the magnitude and directiontcy k bt5b6nzke(9 90t of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side ofv kd wokye* ie4op glbp602t/ g3;;nr4 the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assum po2nelwig rpg4*e y/kt0d4b; kvo;36ing all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravi/ ug xz4eva t 4dqp9z*qr-99xkty at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the9e x9z g-*qu 4a4/x9tkvrqd zp mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun uz daa/ 9)hjs/ gfws-+msing the known value for the period of the Earth and its distance from the Sun. [Note:dm/ajhas9+-wgz fs/) Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in /qh n c5je4z/g(x e gr+yluk60k4x h9ba stable circular orbit about the Eare/+h9xh0 kez64yc nbujgqxkg 5(l4/ rth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above bqew-*b2o k7uq x2ho3the Earth. How fast must the shuttle be moving (rw2bqq3h u*7-2x boeokelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expej dopbn3 qd fon0hj. iia69;91rience simulated 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 Questio91ob no jhf.3a;i dq069pj ndin 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ea.3yd jgm 4 gealwk,2ip1en(k )rth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above jgp,ykd)gnkee2l1.( wam34ithe surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitertehy *rz6: jtt57rg, have to be launched from the top of Mt. Everest to be placed in a circular orbit arounh tz*76 jrrtrg5y ,te:d the Earth?   

  During an Apollo lunar landing mission, the command module ccryew.7(s x/tn++(wf tj t8ht2n6pi pontinued to orbit the Moon at an altitude of about 100 km. How long did it take to hxnr6t pstyfi(j p+t(wcw/72ne +.8t go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice0, *t4ilc wg1 dxxfiy, that orbit the planet. The inner radius c ,x,dlg0ii*yw xf4 1tof 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 onbbed-*j qpk4 .ce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the tb p.e *-qkjdb4op, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of ai ez/(x-wujs: 7 sv,ji)gyi,i 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant veloui, ye / jgvs(z)i,wsj:xii7-city,     ----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 consisdw lno:t73 n0a8p1h zsts of two stars of equal mass. They are observed to be separatedz0d71t on 8:hs napw3l by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read usgd)*1g b qv-for the weight of a 55-kg woman in an elevator that1gvb*gs- )udq moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator.df9 ai7 dx9wfvcu7ef0a2r3qj35y p9c The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directioxc 53uc aa9djvyfp 90d2f7rqi397e fwn)? a =   

Show that if a satellite orbits very near the surface of a planepq1runm4u 6v99 a yh6st with period T , the densu6s n v6a ry1qmp99uh4ity (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 Morq4( 7q 1fh tb6kasoc3on (27.4 d) to determine the period of an artificiq 63(1akoh7f bqcrs4 tal satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, tho h+gxu 4bpdxg*gy61x-ugh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its meax-1*x bd6+y g xhgugp4n distance from the Sun?    $\times 10^{11}$

  Neptune is an average disti:fpz7e) uh)bance 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 8z jxc/ ,a8eztl2n2kx76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate/eanl,2cz82kt xz jx8 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 center of the Galaxy h5)pvc r*51h p7ws3czciv*wj $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 fouo8/u*t qojf1oj*balf; j, yzt5oyf3 1r largest moons of Jupiter (those discovered by Galileabojqt**y1 u, fzo oft/j;y15of j38lo 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 periyg/am6l)xr 5 xod and distance of the Moon. mx/5l6r gxay)    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using wf0o g5ju5v0aKepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to th ao0wv5jfu0g5 e 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 (w3nwsz0euz f- (c.fy/y hich some space scientists think came from a planet that once orbited the Sun but was destroyedyf.u /f- z3szewy0nc().
(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 b:uj9n/o 9;l dmd yijs,4 a,qoartificial "planet" in the form of a 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 ejuobn,d:l9y;m o9 j/ds, 4qia xactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinzos dc)5dv w ey7oxtfo -*v2r)4d,bz,ging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is-t foerc vd*)4,7 yzdo)bo,dsw5 vzx2 80 kg, and the vine is 5.5 m long.   

  How far above the Earth5ar3m awe687/loddrq sp.fj*a9n6zv slt/ k3 ’s surface will the acceleration of gravity be half what it is on the sulaf*7nd z3o8s a6re/ 9qad 5 wkmv .6/lps3rtjrface?    $\times 10^6$

  On an ice rink, two r7n4rna+ a8b jskaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 6 nrban+j78a4 r0.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparuk gad )i zlaop0k9*f7v8u8a/ent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effea89o*fug p/uaik a)0d lk vz87ct. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spaci;7nwyumgudsg9/lkie 94 .8r3 (j uegecraft traveling directly from the Earth to the Moon experience zero net force because the Earthi.ki89 eg 7grg/j(u9l;y4 wum us3edn and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroo kd(n+,o)mmwt.v o aueq0s -/im scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elem-)/,dueo a mv+qks o(.n wt0ivator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube pir. qh rx0; ba1-4zojf;sv) y7me.9 cum:yqhthat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is q1y )u:ziry4omx;qeh 7-b 0fvmrs 9h.aj pc;. to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verticqn. 0lf(qe( ncal 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 its r/eu/yy;.-q 8cj cy mgpadius r, the acceleration due to gravity at its surface ./eyqm/-gj;8 pyy u cc and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected 8o5c q(ot(cp tz9xq(kecx .,mfrom the vertical by an angltote .9(zpqc kx ((oc8mx,5qce $\theta$ 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 th1kuxgrp6 eo7z+ 1j z-oe coefficient of static frictiog zj6op rz 17-u+1exokn 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 rotating so fast 2. +jsb3sltmzhak5euc ,a )k5 that objects at the equator were apparently weightl2j3 +scu )5,tkazb.l5 eshmkaess?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart uk:tn1 k rl46qof 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 rouy9n ffl:+21mh0ihh1 tbbw(p hnds a curve of radius 235 m. A lamp suspended from the ceiling swings out b2b10+hyp1mh:t f wi9 hhln( fto 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 9d4mb um+tz b7claimed that a dz mmu+b749tb 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 of an extreuz e4 caovpg*z+60m0 tmely massive core in the0+gv6u0aeoz*z 4m ptc distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constanyx9pba 3;yo 4 du+wip4t 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? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road by+9pdio43a wpy u;4xat A?

  The Navstar Global Pos7 wag6q5 zdop-dz c/y9rcn;z:itioning 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 orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Detn/o dqp7 6dc cz9g:yr -;wa5zzermine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvouk- zdf*lq7ea jhi,e+8s (NEAR), after traveling 2.1 billion km, is meant to od kh+ zq 8jeilae-*7f,rbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of re9v o.qy ucr(t5+qp6y fpair. You are in a circular orbit of the same radius as the (+c yrp9fqo6.tq v5yusatellite (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 yearsj)fhh ri u** b..;iknv/rcw/h)i btq3. (a) What is its mean distance from wi k *q.ru) /)ifbbvt3 rh ;hc*/hi.jnthe 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 3nrk/l3aad 6k would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reaso6rk/3lad3 knanable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at-9*ncas8dix,, t uq:crigpaq 8u; e:z a distance of about 30,000 lightn8q,uda-8 i;eri tg:*cx pu9c, zq:as-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 aredv*gc a:/vl y5h - yvb8f/fu0zpp+b:v located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on bb lpv :dyv:+a/5g-z0 /8fy hvfcp*uva fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kss/ x4p2 gswr(l6 amz-th7la)zj5 )c5smv*ykg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of t7*vkpf-) ggn the 1.5-cm-long sweep second han)7fgnp k*vg-td on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to sw*uqze3o y65 izjl1rrel /: v;sing 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. Wha l v*ojz:6/rzqlsi5y;e 3reu 1t 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 d bu(wfro503xzesigned so that a car traveling at spf(b50o x3uzwr eed $ 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 carsxfat1 6/: yna+w xhgm*1 vyoc* when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide thex6g 1o**w y/:+x1m avnafytch 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.$\approx$    $\times 10^2$