Sometimes people say8/fvtjkajml)76: q (d aj m9by that water is removed from clothes in a spin dryer by centrifugal m( lmkft j6a/ )vy j97j8abqd:force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the cj i.: nsx qss ki/dd3ra6)z2v-ar travels around a sharp curve at a constant 60 km/h as when its6/ a) ids2kvj .qx-n3s:zird travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doeptdw1h ;0a:3c.gmky kt8cr f+ s the car exert the greatest and 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 b ;wc t0 gh.pf8d3amy t:+1kkrcottom of a hill?

Describe all the forces acting on a ch gqkhe6+sbp; /7cov* bild riding a horse on a merry-go-round. Which of these forces provides the centripetal accelec hbb pv+g7s ;*q/ko6eration of the child?

A bucket of water can be whirled in a vertical circle without tu,6 : b z00sbpnpmuzs)he water spilling out, even at the top of the circle when the u0b6u 0 )s:s,pznzmbpbucket is upside down. Explain.

How many “accelerators” dbm0. 0hkev)+mdfyxi rw+27r wo you have in your car? There are at least three controls in the car whichv mbr2+r.w7 d yih)fwk +e0m0x can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over trbk3d 4x w,2n0/qcsmtkp- j -mhe 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 m stxk, dw/4qjp-m23-brk 0cnand the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward wop1fae mry+zq;ki 20e,wyz(mz/. 1 cshen rounding a curve at high speed?

Why do airplanes bank when then4 +qi.3h3tvk t5 cu+itwt4 kzy turn? How would you compute the banking angle given its speedzn i +ht c.vk3kq3tt54iw4ut+ and radius of the turn?

A girl is whirling a ball on a string aroxd6: i e6h1 oy08iub.pk n)yrlund her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on borl0n 1 phikdxiy6.8 )euy:6the other side of the yard. When should she let go of the string?

Does an apple exert a gravitaqa(uxqn-f5p2eanl hhn*a+2 4 tional force on the Earth? If so, how large a force? x 2 4alhf -*(ua n+2qahn5qnpeConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouizr s4t4no dm 2yi9;2pld the Moon’s orbit be diffezor 4mp9iy2stn2d i ;4rent?

Which pulls harder gsmf lib:)d-b.so .* d1e4 cilbv*is3t ravitationally, the Earth on the Moon, or the Moon on the Earth? Which acceli.l 3o4 is)*vc:bbiblsed.ftd * s1 -merates more?

The Sun's gravitational pull on th1vjd f -njh /;paqh0a+jd4my 8: pzk;ce Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Ca;vdzk8c; d0: jjhn -hm1pj+pyf/ 4aq onsider the difference in gravitational 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 are acwh(y ix*),h ot iyoh* h(c,x w)work? Do they oppose each other?

The gravitational force on the Moon due t :0xkhxt)c3ono 81u1hh a,+ pbdmue-d o the Earth is only about half the force on the Moonec3t-p1,1bd:h)knxdma8u0h +ou ox h 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 Sde3eu.zdaff8v ,zgi-zhj 5tok 3 .x*(un larger or smaller g.dvojxk3faeh u3-. 5dzt*iez, f(z8 than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) towyd3qu* h0pf6y ard the u*pyd3yqf6 0h west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as ge rw7vm*/uph 9;ahb+ measured by a scale in a moving elevator: when the elevator (a) accelerates downwarv; h*a mwprbug9h+e/7d, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in ouah 62cc8f ;on5 bkc,abter 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 walkingo8a5cbh nbcc k;f ,26a 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 weightlessnessk evgi elz8o +oc:z-+1.w, ibz” between g: ie1ko+c l-zi .ov b,8ez+wzsteps.

The Earth moves faster in its e1 a1uyeoo) mhcuo- 025eu5xrorbit around the Sun in January than in July. Is the Earth clcmu 1 y1 )ea2exou5 r5ooeh0-uoser to the Sun in January, or in July? Explain. [Note: This is not 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 disc yr,dva8;pzl ,rlwy -a),g 2duovered to have a moon. Explain hv,wdllapu-y 2 8dr r; ,),gyzaow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pul0 ohk ir bq,/:;rzh9cwl 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.]A child sitting 1.10 m from the cen9q /wkh; oz:rchb0r i,ter 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 rfyssgfm0/.pz-9sc0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 bb . tpgllmdl16v +64hits orbit around the Sun, and the net forb1m6 l dl4ptv g.+b6lhce exerted on 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 2+ux8jd 7emajt-4l ddm 2s 64goe xaw2+10 N is 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 the 8+d6delxas jo2x m e 2jtua7m-4 w+dg4speed of the discus.   

  Suppose the space shuttle is in orbit 400 k xccn.3 ,i8o.)gsh n0 2d7bq:x*zrk 8xzsq ignm from the Earth's surface, and circles the Earth about once every 90 minutes. Find xzg*s7d)cix,k 38i:nq nxsrq.z o gc .nb028hthe centripetal acceleration of 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 clay on the edge ;8tp3kv e;sy zdiu5)s of a potter’s wheel y ks8izdu)t pev3;s5;turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is :t k)er8pl40(q3ktb vvbn* 6 s e-ejcsrevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown ib3 -nveke t4l:rc psj*b6(k)e 0qv 8stn Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can roza5plj2 m;c1 ound 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 the mass of mo cal2jz;p 51the car?   

  How large must the coefficie 4;p+f:d7gv oov9 ipy+13q +gbgxgxkcnt of static friction be between the tires and the road if a car is to round a level curve oo34pvi fgy1d:7 g+po +9qg;x+kv xgcbf radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a v7: +f.z:x i.hmq -xin*yxjfagra,k: trainee in a horizontal circle of radius 12.0 m . If the force felt by the fq* y.r i:mx: .ja+7xx fvkzhna -i,g: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 r7 ;*6fkgj,caazm6/l2wa vgis*pda4the axis of a rotating 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 a7jras/gl dav zfg 6a*pki4,2mw; c*6 is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at t4)itmgu, nj2n+2 zd tche top of a circle tcn, gm4u2) ij+dt2zn
(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 top joy ia1 e3(8p/d8bpoe.3f6dl ar c/f xof 813ob .o pey/j e8dl/ rf(dxaicpf63aa 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 F iq 6tn 2cj;oa3826uz 4kke:uuuv5xs zerris wheel need to make for the passengers to feuq:xnkcs35zj 2 ;uu4ai t26 k8e6uvzoel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ve1;cr n6p7gwakljuh iw5y 8 f3.rtical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 5rl7 68;1 wk.wa3nugyfh ipcjN.
(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 centrifuguc +nooecywx ,j+(l /8e rotate if a particle 9.00 cm from the axis of rotation is to expeclnw,uyo ++8 c(o e/xjrience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivaym cjf) +es/-gl, people are rotated in a cylindrically walled "room." (See Fig. 5-35.)m-+g c)e fjys/
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 frictionles(+m8den vp +eitjv:z,s air-hockey tabletop, and is heldvmd +n(v8e :zt pi+j,e 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 ty8 /q58v7lu mb0vimd1l w;1).mdqr geohwc 8ahis time, by not ignoring the weight of the ball which revolves on a string 0.60q1gh)0bwmwvrl 8vd lei5 u8;8 c7o1 m.qdm/ya0 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 perfecjl27 ( wzea+g v7k(ghftly 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 masseemh (*+a9lclr s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at tyh g-7 *as1gl 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 thzbx4h b(r:em3e net force exerted on the car (by the ground) in Example 5-8 when its b3rh (e4: mbzxspeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area (a 6kt psc6ida4 u 9qh)lj,a:kl8ur)a, 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.():ds6,ha9 4lq rp6cauula) ij8takk If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radiuf +4jre ;u6)tv8hl7 y pofvsrav3j) d(s 2.90 m . At a particular instale 3af o(vrvrfjp 74ut;) vy6h)+ds j8nt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a sh+e :bv;b i2napacecraft 12,800 km (2 Earth radii) above t2;bnbiea h:v +he Earth’s surface if its mass is 1350 kg.   

  At the surface of a cee+ mw6re1cbnvziz 7 14rtain planet, the gravitational acceleration g has a magnitude of 12 m/s4bei+ vzwec6zn7 1 r1m$^2$ 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 grj9)tf injjqakp5g 6jp .3 d:.8eiukf )r zu*/havity on the Moon. The Moon's radius is 1.7459h8 /zapq) .ftu*3) iefjjgpj i k.ujr6nk:d $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiuse9ffu6iest- , 1.5 times that of Earth, but has the same mass. What is the accelef6 i-,sf9e uetration due to gravity near its surface?   

  A hypothetical planet has a mass 1.6mwnv-2lmpi *g y/ixt5;jp (9k6 times that of Earth, but the same radius. What is ytk(nlxm-vimjg*wpi5;9 2 p/g near its surface?   

  Two objects attract eachqq .ess5rym ( c..dvk6 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 accelera(fv9jk2v7 lha6j5 clhc lwl1d3 cgl*: tion of gravity, at (a) 3200 m a cc jd*2lk69hf:1 57lw3llvvgc hlj(   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ouv- 4bqnd6yu13vve7j bgltmq,u(t/ w+tside the Earth where thegravitational acceleratiu gyb1d vt, jw7nbqu l +t-34mvv/q(e6on 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 5 *j gvsasw )+ di ersljb*k-gln02/d,Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thi+lrd- *0jgs * i2wj5n /e)sb sklvgda,s monster.    $\times10^12$

  A typical white-dwarf star, which once was an averag htk9of:hzu9l6 om*l, l1qgfk;c+)u oe star like our Sun but is now in c:ok mok+qf9f1, ll* t6h )g9uuhoz;lthe 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 weightless whrzs)x6 v4vnw0 ile 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’xv0 wrz)v46n ss surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. gy)mn7 knk 0/p3bfp /eCalculate the magnitude and direction of tp/mg)e3/nfn0 pybkk7 he total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most ad1xw; ).m ig prwtc**of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, x1 wr*wpm c;)i. dgt*aassuming 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 gravity at the surface of Mars is 0.38 of wh :oc plu-+t0djat it is on Earth,to+lj: 0cpu d- and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the grv0ah8 4m9mvrcu4k* known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–rvhmg8 a u*m40rk4v9 c16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable ciri +brb2)t9o-hkn3bb jcular orbit about the Earth at a hebb- t39bj2iro+ h)nbk ight of 3600 km.    $\times 10^3$

  The space shuttle relea s*s zjg, q(d5i*n,mr)pzd x8uses a satellite into a circular orbit 650 km above the Earth. How fast must the ,s8u*xm,g (dzszid j rn5p)*qshuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship ry +vam5 ihp4q2otate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your45q avp+ y2ihm answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orb yp9-i(w0c zug.lrf4 *cbb (ycit the Earth in a circular “near-Earth” orbit. A “near-Earthgypcl9 ( zc(4crbbif *wuy.0-” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellif- dlcj5 (aa: 9vf5jbkte have to be launched from the top of Mt. Everest to be placed in a cidj lav-fc kjf5b9 a5(:rcular orbit around the Earth?   

  During an Apollo lunar landing migeyi/9 pk2s nj-4tw gj-7f )xzssion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moi27t4gskwnfpzg- 9 ejyxj- /)on once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pl5 1sn4h0tjxkvppw ;n) anet. The inner jvxwh5 1p4pntk0;sn) 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 diameter rotates once every 15.5 s (ssz -+ij0zzvl,ee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, is+ zzj-0vlz, and (b) at the bottom?
(a)    (b)   

  What is the apparent weigq ;kf 9tzg / l,7a/c(nsf6ssxiht of a 75-kg astronaut 4200 km from the center of the Eaf(xs sa nt6qi9,g7/fsk ;z/clrth's 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 two stars of equal mass. They / pd.c4,xpm8 mv* i vltumn56aare observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is t ,.t avpn85ivpm l *x/64dcmmuhe mass of each?    $\times 10^{29}$

  What will a spring scale read for the*dmbjma2h l.jei ag0j,e;61lzk53i t weight of a 55-kg woman in an elevator that movl,h1zljatji53 g;e. 6kab *iemj0 d2mes
(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 elx /,l2gdkh64qq 4 wy( q3dbojyevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’ gd4 q/2db 4qq, 63(xolhjyywks minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wdtjmo9tec gr69 52o ;fith period T , the density (mass/volume) ofj5 oogm; er c29dttf69 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 anc +fg.y sdhut0b0 g uzugi a5sf:h92:/d the period of the Moon (27.4 d) to determine the period of an artificial satellite orbitici t2gd+sgbuufy: 5 a :0z f0hshg9./ung very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,3u0 c tvio0x ksv)i(y( orbits the Sun like the planets. Its period is 410 d. What is its me isi(0 x()ku ov3vtcy0an distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of mz by)y-m ph0h0 :v9if 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 y4mzep- h 4la/vears. It comes very close to theza-v 44mhep/l 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 distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of t02nuzj1t9m,(pse)gkqcp rv 5 he 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 m*g,c tisaf*:04un6lkual) r-vyv e7aass, period, and mean distance for the four largest moons of Jupiter (thosevevulgfr)-a,t y0 *asa:76ulcn k * 4i 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 from the known periodhnx( tjuxf:fj 38o 8s; and distance of the Moon. ujthjf 88 :n(xo;xsf3   $\times 10^{24}$

  Determine the mean distance from Jupiterm6slyr g(o;3+/ 6k)z x a kf2qrq;xfxw for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given ixq)okxy azw6k;r x(q63/g s; rffl+m2n 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 p(p 2;pengey8*l-b b mand Jupiter consists of many fragments (which some s*8(bl;2peg p- npbeym pace scientists 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 bandr9uw ,x6; eaqn completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce a;9qnx w,ar 6uen 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 swinging in an arc from a hanging ba 92 -(jsy nsy(y+slu.v1jz fvine (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 swiny (9.su- baf vyl j12+y(nszsjg? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will t(+gismz )d5xxhe acceleration of gravity be half what it is on the su5i(m zxg+xd s)rface?    $\times 10^6$

  On an ice rink, two skaters of eqdfibe: .y;dsq:.j+3mb zjzzyuk w;6:ual mass grab hands and spin in a mutual circle once every 2.5 s. If we assf;d q+ sz z6i wkd b.:jb.:y:zmjy;u3eume their arms 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 ol otsqan;.a 00nce per day, the apparent acceleration of gravity at the equator is0nl at; a0qo.s slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a s1j 3, p +acjh(,dqsbvbmzz:,n pacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equa (bd nvsmc,ajb ,q+,pz:z1jh3l and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bati2 8 a* vl/hxojm.g:hbhroom scale in an elevator, it says your mass is 82 /jgv2h:*mxa oi hl8 b.kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate f12fxr7k:vyc about its center (lik:2xc kr71 fyvfe 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 to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his+c7a 5nbgxyi5: )wg gw/dq wg8 aircraft in a vertical 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 rad0(4ez +j rvd a,5ldqf xgigx(:ius r, the acceleration due to gravity at its surface zf:rav,(dl(4jdxg qxg ei0 +5 and the gravitational constant G.

A plumb bob (a mass m hanging on a str/-y dlwm yov/.ing) is deflected from the vertical by an angle -dy /./vy woml$\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the cnd 9i/ (z,u)s)nj-diqom0 cbe oefficient of static friction is 0.30 (wet paveme ) sujm/()o0diiz bqe9-c,dnnnt), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fasicks.l:dt4 7-; 4mlzg hwra3bz+.:y, wkiiylt that objects at the equators3cm ;zl 4iid,bwz+hl .7w.-ilyya :k :trgk4 were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constad0-m (8ev vx/rc9mg /*pevqcgnt 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 confk na3 -fblaw+9-x 4uwstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angl3xw9+unl a-wafb-k4 fe of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth.a: t*m)i(p sexpjxl40 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 s(tex4a)j pl*0ixp :m 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 deduc uurzjjek8x;:/(o d- ced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (fr/k;(ruzx d:j8j u- oecom which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed asup/uz44s + 8kfvod *lqx9, pjm 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?) Explainof48j94dx*p pvl+ sqzuu ,/mk . (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 group of 24 wl-8h- pwaic 2satellites 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 ewc2wh-8l iap -venly 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 (NEARyv +yaku (+(i /8fej*fy h,pib), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of iyyf/ka+h y+f,e(*v8upb( j i 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 oapkd/89xto )au3 j8x0 w shv3u2n6gqp f repair. You are in a circu3u dj60vwak8n98x qptsu x 2ga)o/hp3lar 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 ofgq c+jvru7 /0b 3000 years. (a) What is its mean distance from the Su 0cj7g vuqr/+bn?   
(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 7 h/migzna k;,ofuzn,6-aml; would need to be if you could actually "feel" yourself gravitationally attracted ui;mf-z,alk ; o ann76,z g/hmto someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fd4a g 5l ll nc+wdf)rc.-owf;5ig. 5-46) at a distance of about 30,000 light-years from the cl+;-5w c5odfd)lg a rlcn.4fwenter $ \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 a square 0.50 tvsm7/xnd+ k4 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 side 4 s +/xm7tkdvnof the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits f3/-ot0zoj. wir4oc s/8pq m7xday.kthe 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 sweep seco *(hqt;x*d beor*s jk(zohk-+ nd hand on your wri*d j*-(e skt rhbx+ooqhzk(;* st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around esc* h;76 cvkf7ut0 ulin a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Figl70f 6ck7cus*t; euhv. 5–10.]    $^{\circ}$

A circular curve of radius R in4 ddkafqjn8ap ;7d 2m. a new highway is designed so that a car traveling. kjm8np4a7d2da f;q d at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the c 9rp h/:muig1bars 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 (/uh:mgibrp 19 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.$\approx$    $\times 10^2$