Sometimes people say that water is removed from clothes in a spin dryerx0g i,r8 dxzj 7lta d-v4g9w*y by centrifugal force throwing the water outward.,4*r ivtd lawyd0zxxj9 7-g g8 What is wrong with this statement?

Will the acceleration of a car / db2ehe/ (fz q1qf7j-8iaqx +upq5scbe the same when the car travels around a sharp curve at a constant 60 km/h as when it travels arouq1a e +qchujf7zxqbie/ fqd2s8 -p5(/nd a gentle curve at the same speed? Explain.

Suppose a car moves at c +fativ -hh+gh:o:n1tonstant 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 two hills, (c) on a level stretch near the bo1- :n :o+vgfthhha+itttom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-ro060rb7hc g31idx ia-1wbzyd yund. Which of these forc1yxdhb0w i3yg 7 c6-0rzid 1baes provides the centripetal acceleration of the child?

A bucket of water can beeddnw+ v.8s hkh*i6 m:t1xs m. whirled in a vertical circle without the water spilling out, even at ms hek h.dtn.mdws8:i+6 vx*1 the top of the circle when the bucket is upside down. Explain.

How many “accelerator w:nqmls/q*r;7 h85n;o02aiymd sr v es” do you have in your car? There are at least three controls in the car s*oe mrql 08a2 s:75ni/rmqy;dnvh; wwhich 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 the ck1-jm1cfj*3 jp rjzs:rest 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 b fjjjzp- rkm*c1s13j:etween his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle rider0h ntbl,+p w8nfxxi q,.o hk+(s lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How w+m,s1z( *e2 v4cuk t,i +kvjtov 5yivrould you compute the banking angle given its spvvutr4ksi,o+z, kyc(i*t+m vj 5v 21eeed and radius of the turn?

A girl is whirling a ball on a string around her head in a horie(k,s: 4k qm4v hk (r34a9w*qdq nvphozontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When shouvp:qa 9hkv3(nwk44e(kr 4*, sqmqohd ld she let go of the string?

Does an apple exert a gravitational forc0) j 7*1z krqdvjdmdj6e on the Earth? If so, how large a force? Consider an a)dd jz06vjmjr 7*d1kq pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thj/bo3e5yj3vs8c lts 7e Moon’s orbit be e/ssctb7yol3v5j8 3j different?

Which pulls harder gravitationally, the Earth on the Moob)ne3z c 9b .ug4-7aub5wqc lkeb9h-dn, or the Moon on the Earth? Which accelerkuwb)gec.e3 9c-hqnb l-bu9 b4d5a 7zates more?

The Sun's gravitational pull on the Earth.w e9qut p fp-6)yca,c,ftm)b is much larger than the Moon's. Yet the Moon's is)qpm wue pa)tby,c,ft 9 f.-6c mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the ero- e xufwvd 971t:l4xfo bf*7quator or at the poles? What two effects are at work? Do they oppose each o1ef rf w*xfub7 o-lo xvd9t4:7ther?

The gravitational force on the Moon duuw/er jrr30jcd. c9d)e to the Earth is only about half the force on the Moon due to the Sun. Why ij0ducrc9j .)r / r3dewsn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun la7pq zj 6 a(z5c kt4/ah8temb*t er,rt5rger or smaller than the ptrcz8rbt( 5/4zkae 6tma7t hq j5*e,centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east oxnr1 :x0/):3ve c,-i rx1 vpgkpam35sm lveww r (b) towa3xs /m m5ke ivxw 1 gal1c:vp0n,ep-r: wrv3)xrd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in5l-hk1- ptqchf*n.ik a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least?n* 1 c-hki5tkqhp-fl. 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 n yrdtoi*zm opd7r80b k2p*,1be 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 this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity yk7dro ztbdp , rmo p81i02y*n*ou can think of.

Explain how a runner experiences “free fall” or “apparent weightle9x 7bir,qb -pbssness” between steq-br7pbb ix,9ps.

The Earth moves faster in its orbit around the Sun in January than in July. Is t95hm g+osfm1t he Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in promo 19g5t f+mhsducing 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 iuex.jojy h o87mf- ;2qt was discovered to have a moon. Explain how this discovery 8 2y .;hjefuo7j oxmq-enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is m9tqcsji u11;(cbdq t* uch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Exp1q 9 icqcsjttudb1(*;lain. [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 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 y w,(gvu j-lh.$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 m,tsra *i d+cw k60;*;bz 8vok sx(lpsits orbit around the Sun, and the net force exerted on the Earth. What exertsbori*s; w ;mpxs0ad(lkz+t, c8v6ks * 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 a v5d1:blno(h 210 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 theavbd (1 h:on5l speed of the discus.   

  Suppose the space shuttle is inh97sjp3q 5)ai nvuqu ) orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Finvu) jqqaspn5h)i 9 3u7d the 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 clnanzoww i-hx- ( )uc29ay on the edge of a potter’s whew u2nanxc- - )(h9izwoel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertgv(x0i )kv1-a1oiyw1,b9z 5;pask ol qa dd5aical circle of radius 72.0 cm , as 1s-xw5qvdkl yg1 , po0o() 1 vi 9k;zba5idaaashown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a tu-i,nm+ djr )qjc (hu6q-yvw:qrn of radius 77 m on a flat road if the coefficient of stat-:hcq)+j- nvy r qmq 6u,i(wjdic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static 7bvihy ccz8yfxxqx4 h.(3 o*4s qx1e +friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed c xxe(qxycfi7o vqxhs*8y441+. zh3b of 95km/h ?   

  A device for training astronauts and jet u7md u j,02(t2eq5c7iwm mj pcfighter 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 c(jjtpcu medm70 2q 75wu,2m irotating?    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 tqph.grp v6z f.ze2p79 he 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 is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntabpv .ze 6.f2hpq9pg7 zrle?   

  At what minimum speed must a roller coaster be traveling when upside ka qw uye6 h2+(,d5o)kbxqqr( down at the top ofq+(daxkhrq ()k e,w5uyb 2o 6q 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 th- d3bf(,lcrr 1unk 0kme rounded top of a hill (radius =u m(rd, -l bkcf30nrk195$ \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 maw2 32 ifw- n 00 wtork,qy)n*pejiry-ike for the passengers to fee3w rry,ei fw-ktw - n*2ijpq0in02)oyl “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled -p+7kbc d:u8 aj9uk8wwoqz:w in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting k ba8coj-pk 7+8uww:qu:9 d zwthe 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 oa4 -7kzw- 00 ptmpmbp fd6;nzcentrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of b-t6 ;k0op7zpw4da fpnmz0m- 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatm6phrm l(5 xszbd 1q))ed in a cylindrically walled "room." (See Fig. 5-35(pdh6)5x1)bmqrz sml.)
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 frictik:ka6 *crq in1om5j/ oonless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fijk1:c* r6mq o/nkioa5g. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of thcjm 6 lj)4bmpa.rmu 7*i 40erl)aw4oje ball which revolves on a 7 4iajlc) b mpm4ea0rrj4. o*l6muj)wstring 0.600 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 id qw7nk)7;hbr s perfectly 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 masse 2)0dyy8vo tp7u3 mxkhs $ 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 evas8 /:j:bcurukg ive maneuver 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 ofk ,2ft,ya h(vu2pr-b q f*bq+o the net force exerted on the car pfvta, q kb,(urby-*fqo+22 h(by the ground) in Example 5-8 when its speed 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 fxh,b+dl7wd ) ,ls umlx+/5ehr rom the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of statillbduh, smx,h dle /x75 r++w)c friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radiushz r* ;,(wfs2if;yzfi 2.90 m . At a particular instant, its acceleration is 1.05rhi( z,sz*2wfi f ;fy; $\mathrm{~m} / \mathrm{s}^{2}$ , 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 bo9oxcbi1 57qEarth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfaceb qo79io5 cb1x if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational ab0* nuzz k+ue *4wmn,nd.su: wcceleration g has a magnitude nuu.n*u*m4w s+kznwbz:de,0 of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius iuub6j+zc c91d s 1.7b 1 zdcjuc+69u4 $\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 th(y,( p wsafo:cat of Earth, but has the same mass. What is the acc,c :wfypos(( aeleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66k1os8+mefz l8 times that of Earth, but the same radius. What is g near its surface? z+8lkmeo f1s8   

  Two objects attract each other gravitp5:vhdivzs5 ;:tufm nsa ufe o*;2n98ationally 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 v9ldzy. hp).fnwwl;o(p,uak9 alue of g , the acceleration of gravity, at (a) 3200 m l(w .p ufa )hn9w.zpd ;oly,9k   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside theihw0gt1 *e 2ux Earth where thegravitational acceleration due to the Eeg*i0twh2x u 1arth 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 pak)7n9ngaq3+z x kv 80lb t+ (gm+scuq c-qiks)cked into a sphere about 10 km in )s)z( tqv qm-+l k+c 3 +8sukqk nb970caxngigradius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an aveiq q9- kfbfeo47l 1wk6rage star like our Sun but is now in the last stage of its evolution, is the size of our Mqk4bi97 6el w- kqfof1oon 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 while3pa)s 8fogenasr3l b02-r. ri orbiting in the space shuttle. Your friends respond that the saesrg fn)ib0323p-a.rl8 roy thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square-rkm7w1uh * v9t*jlg4h n fhdz(-(iwg of side 0.60 m. Calcula gwd-hzfm h(*j*i 9nu4tghw(l vrk7-1 te the magnitude and direction 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 pl0y)/zr (fjwi oanets line up on the same side of the Sun. Calculate the total force on theyirjo/ )fz(w0 Earth due to Venus, Jupiter, and Saturn, assuming 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 Maro0 g6vyubbkgfuh ps (.*,d;z,3d+otz s is 0.38 of what it is on Earth, and that Mars’ radius i v dtgyp;k3 bzf*hz6o,d.b,(sugu o+0s 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usi(e nbkb: x:gvrdi *2j. .8behtng the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to thathr2k*b xiv:g: (jb8e.nd b.te obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about thytbr4a-5ri wl8eg:vtv, q;j8 j6.y rk e Earth at a height of 360rq.etytyj8iv5v4 :-j; r blwgk a8, r60 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 kme8fehl4ebm4 n -ha7o5 above the Earth. How fast must 5n4hflemeh a 8-74ebo 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 expeo9tafc1h 7 ai-rience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time neededh9c- i7a 1afot for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite 24s6meol t sr.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 oflt6s4o erm. s2 the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be le+osf 4h j0f wgo x2.e+l*l*laaunched from the top of Mt. Everest to be placed in a circular orbit around the+gsa2e+follj o*xf 0hwle*4. Earth?   

  During an Apollo lunar landing mission, the command m 3cbkd;6i+ u sywe-gu/ sq:pt:c-su 8qodule continued to orbit the Moon at an altituw p- 63:uid+ sceuqs/yq;g8tk:bu-s cde of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks oqpc8z(.agmgqx( )s5c f ice that orbit the planet. The inner radius of the rings is 73,000cgc.g (qm)psz(8xq5 a $\mathrm{~km}$ , 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 tyvx x(85 2gsbdiameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at thetx b(2vxs5 g8y top, and (b) at the bottom?
(a)    (b)   

  What is the apparent am1:t:l-jcbw7rkj1+m6l ott weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving alkja1 w-7:bom+ mtjtl1: 6c trt 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 consistbg;9vs+pp.:i 6 wtr-z admlo ;s of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth tswz+g-;b.rmppv 9da ; 6ilo:years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weights: us+jixt(2lvvoo63f2jx i 8l84ha k jo3g4c of a 55-kg woman in an elevator that2:l4 6xtj j ox8vs8 iaco 3h4svg(ko 3ul+i2jf 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. T f* l (su)z5i6:dzznekhe cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (mazz i*:z65un dk(e)sfl gnitude and direction)? a =   

Show that if a satellite orbits very near the susgz7v3,,8oclqxngrlv2k8 s * cvu4 1 rrface of a planet with period T , the density (mass/volume) of 32rkvc v8,gl*l,q8usn z7cs1or4 g xvthe 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 tzg6wix v 2j f(e8m;ph*he Moon (27.4 d) to determine the period of an artificial satellite8v;*6wepzi2x hm f gj( orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters ac8of1v7v/qy2aqhe y( il*s t1r v7rlm8ross, orbits the Sun like the planets. Its/ *oyhv8e 7fqyimav1svq (r81tl r7 2l period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagej5+yq h3o6 oho distance 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 roug3n dibh86d/ ak jzd)y-hly once every 76 years. It comes very close to the surface of the Siyb6 ddhd8 3aj/kn z-)un 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 abouw +kojg)q ,k7jglsm,i iz2:0pga.4 rrt the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four yeeab. 6c9x)/+eyuhvh:pz v5 largest moons of Jupiter (those/6uvhe.eyp ehcy)+9vb x za: 5 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 period and distance of qy:wtds:mk .bqs 6- 0xthe Moon. 0xys- qk ws.t6::dm qb   $\times 10^{24}$

  Determine the mean distance fromp tzqd 3 34 cf:u;a3lzow4de*e Jupiter for each of Jupiter’s moons, using Kepler’s third law.ow3e*34aql3 fu ;tdzecp:z4 d 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 som. 9kvx+ nsd u8jt9g7bbujst*:4yshi- e space scientists think came from a planet that once orbited the j yjsg*:nhdsxsvtb .uut 74k+8b-i9 9 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 artificzmy; cd*x bwdg .3cbo1c2tk r5h9*d4r ial "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 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 c* *mb4bwrzdc 5 y.2dtd3rh9g1oc xk; g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a) f;wz,*lyrwkds t6*f gorge by 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 is the maximum spe*tf;wsf 6 ,*dwz lk)ryed 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 acceleration of gravity bela3o+u 5kv4.kxgny1x half what it is on the surovu 1xkn5lk xag 3.+4yface?    $\times 10^6$

  On an ice rink, two skaters of equal mass3oocs9 ,h;r up,h ,eys grab hands and spin in a mutual circle once,,o spru9eh y ,;o3csh every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates onmot8e z5/vr m 09a.fqxce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth diremt8qz vmaf.05o/9 xdn’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 spacecraft /g 28wq ndcp*yu0.8 vy2 qjhlttraveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite for8t 2n0y2cqlwq j.y/pud v8gh*ces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroomwc9v pyfk0 rf:6h,wl3 scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, a:3,0lr yfwf 9kcwv6hpnd in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular(zphx*bq*kjt61 r8a/ f1 angj tube that will rotate about its center (like a tubular bicycle tire) gq fzxj81(kj**atr /h6 pa1nb(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 aircraft in a vertical loop (Fig. 5–.3r mf+ssbdij94vk f(i 7m-(hsya r1m43).
(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 ..u kq3di:tew/pj gc)+sm)l s*z jv 3qits radius r, the acceleration due to gravity at itg/cdzs j3q*u3m )q.w.+vp e:s) kjilts surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vert9-, yo+f iha4 hdf,mquical by an angle ,9m a+- y hf4uqidho,f$\theta$ 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 fi: )/2c,iq 6f:sdi se*wdprtlor a design speed of If the coefficient of static friction is 0.30 (wet pis rp i:2w/)e*6ftqi,sddcl :avement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth wee r2mknh+ fb7y t831ipre rotating so fast that objects at the equator were apparently weightless132ynk7phebm 8fr it +?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of4cbt xommcitx.3 u)tq)lh 9-4 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve ofpmdk 5)0c mflql0cv f)ji-otk:( 7 m0w radius 235 m. A lamp suspended from qj : k)cl5c(ompfk0m)fdt-iv0 70 lw mthe 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 Earth. Thus, it has been claimxzq rlscl9)d56d jc. 3ed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't sj d36dl.q)5r9c zl cxsurvive 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 Te t5pky 4e+)lhrhj 0hx5lescope deduced the presence of an extremely massive core in the distant gala rhhjl0+55t p) hxyke4xy 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 constant speed as it traverses t2 z lg7i4n(8ixw;r + lksbauh*he 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 g4w 8h n k2a(b sz*xirli+u7l;without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellalerdtv i 7 ,xh2i*)q5ites orbiting the Earth. Using “triangulation” and signals transmitted by these h)dt li q 7ae*ixv2,r5satellites, 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) 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 biatk*vx b)qj*+* seqa;llion km, is meant to orbktqxa e)* s+j;qbva**it 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 neraq a 2osa(z60z jl5x*ed of repair. You are in a circzrxjzoa0a(56qls * a 2ular 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) Wcfx*srfv .,;9 /l k jygepqk3vm 9+r5u-5bldi hat is its mean distance from the vr./brl9; 5f5lvyqp* m ,9c s duk3eif+jgxk- Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" y3k7+c hars,bn,ki m7wlp 3c2yourself gravitationally attracted to someoneks37 ,3c ,y 7w h2lpmrbiank+c 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 (Fig. 5-46) at a db3g9ih /d( 2 usqhjv:gistance of about 30,000 light-years from sbq:2ij/9d (3vhgg u hthe 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 a square 0.50 m on each side. m 8ng9tg4 +okc7upwiar ).7y)mr, lucFind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottomr rcu 7g, c8aymmlw)4u.opn+ gikt)97 side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbiwc94 0fi9z refts 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 ex4tstvi95ijr h (4 ltdr +8egwv1+zt+vperienced by the tip of the 1.5-cm-long sweep second hand r4gdt +t l+5i(eshr4vivtwj1v8 z+9ton your wrist watch?    $\times 10^{-4}$

  While fishing, you gac* +/f0a n:cpx -ggh9fc.oht rjd n).6ib7fa et bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with t.r c :jp9na)bth 0h d6nag/c7-xcof.ff g+a *ihe vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a/4)8.l-ud bkv fbeoykn,w1i x car traveling at k8v f ex,udw y) 1bbio/-n.4lkspeed $ 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 Ajr9(re8z 6j0 ri t v)la0zyhy0cela, utilizes 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 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 ofy0rzr9v(y r0e8)0zlh6jji t a 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.$\approx$    $\times 10^2$