Sometimes people say that watertgyj,(7i+ - +eeetxr( mocfi2 is removed from clothes in a spin dryer by centrotc((ee 7jget-+,i+ fxym2r iifugal force throwing the water outward. What is wrong with this statement?

Will the acceleration om8pz;, fdnfpsmo/v*pmz -96 cf a car be the same when the car travels around a sharp curve at a - 8fpmcmpp6zf v,/ nd9o;mz*sconstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a f k1f pe)*k;lyhilly road. Where does the car exert the greatestkpfk)f; l *y1e 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 bottom of a hill?

Describe all the forces acting on a child riding a h.rzn .:.decrl orse on a merry-go-round. Which of these force c:rz.rlne. d.s provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the waterh /g iymvq2io)+ot p.6 spilling out, even at the top of the circle 2oim6 g h+v.qy) ip/otwhen the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leagq5, twp+sx2hs8:zm7yp :h vqh nt(m 4st three controls in the car which can be used to cause the car to accelerate. What are they? Wzt 7qq(mhpg,st4+x: hs:2nhyvp8wm5hat accelerations do they produce?

A child on a sled comes flying over the crest of a sma(ic/f;b9: d;wikkzh;jew x4 h ll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hiewxi4 ;b9d ic(hw:z;/kkh;jf ll. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding au es9-evlu3 0xew)tm ,6c9 nwt curve at high speed?

Why do airplanes bank 6j ytghx s(ucsu4y7f6 a9 88fqwhen they turn? How would you compute the banking angle given its speed and radius of the turcsyjf97 fug 8q syh 6aut68x4(n?

A girl is whirling a ball on a 93z8xhy6 pzuq8e hi xbv;ub)0string around her head in a horizontal plane. She wanti9z3b8zp ;uvhu6)8e 0yqhxx bs to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If;h5kwv+yjl)r 5x3pkg so, how large a force? Consider an app r ;ykhwk5gpjvl) +53xle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways r;wm *wlf4 zomn94w*crt9257cmdmls would the Moon’s orbit lczm9n ; fcld*44 29o5m *t7rsrm mwwwbe different?

Which pulls harder gravitationally, the Earth on the Moon,mvitsf ix (b-80xs: *trtcx- . or the Moon on the Earth? Whic (xti8 vrs-t* f.btxim0sc :-xh accelerates more?

The Sun's gravitational pull on the Earth is much largerv 4 33oc9g uzczxynz(8 than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider to9 uvnz (y 43zxg83cczhe difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the polp cqi5nz0.h*ng-i) ec es? What two effects are at wor n5.0ch*cie nz)ip-gqk? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the forc7 n8 k3t*z zh8jw:9bj. mnbqlxt 8wl4rt9ck;x e on the Moon due to the Sun. Why itmrjbxl hk wl8kcnb.*z n 783: w4xq 89ttz9;jsn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orw*tyt.6f /h5j o7gq5nyow)h lbit around the Sun larger or smaller than the centripetal act5h56/lh)oo.qw t gf*wj y7ny celeration of the Earth?

Would it require less speed to launch a k9 f6 xbid-v,bihz( +ksatellite (a) toward the east or (b) toward the west? Consider the Ea,b z -9+hkvb(ixf6 idkrth’s rotation direction.

When will your apparent weight be the greatest, as measured gvfl-,xvl 5rtvm3ktw7( 1/seby 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 speed? In which case would your weight be the least? When wo /vwre lvm 53gl,kt7x tv-1(sfuld it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lon bjsv,m( w9tz3g periods 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 this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (3zjb mt9v(sw,c) any other aspects of gravity you can think of.

Explain how a runner expeq-5o x -hrmko5riences “free fall” or “apparent weightlessness” between ste r q5xok5om--hps.

The Earth moves faster in its orbit around the Sun in qq,2 947lpiqwu2j/r 7to jdum 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 factor is the tilt of the Earth’s aqr ilm/97q 2qw,tju4 pjod72u xis relative to the plane of its orbit.]

The mass of Pluto was not known uch6.nse:acnf /p v7o-,p0 pof4c 8lg xntil it was discovered to have a moon. Explain how this discovery enabled an estimate o o8p4 ./ oc,e0vapnplhc 7sng6-fcfx:f Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thac+8jqbrmke(,v fj1a wqv //k1n the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed ofj qmqk+// rabj1v,k( ec8fvw1 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 mip4jz,-x)sen-cu4 jg 2mj-x1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 theuns3s++g .hyr Earth in its orbit around the Sun, and the net force +un+g3rysh s. 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 210 N is exerted on a 2.0-kg discus as it rotates9r aqxy moi:7x*z7 lt1xuy ;4d uniformly in a horizontal circle (at arm’s length) of radiu 971lr umaxx*qdo7i ty z4x;y:s 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in o 0l5-e7 wkeoa kh8tt.2rbvd*krbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutetwdvl*2het5r 8 k o-.7k0bkeas. Find 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 )t5yf /3( bhglmahw2db h))z fthe acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if th3m)a f td5zgy)/h)b2fb(lh hwe wheel’s diameter is 32 cm?   

  A ball on the end of a string isafvgutv1t kaw(t +*21 p1a zk*.lg6gg revolved at a uniform rate in a vertical circle oftaakz*l+21tg u*f.a1gv6g kp1t(wvg radius 72.0 cm , as shown 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 cupm:)( wbb flvuv59 fqv+4 d9uan round a turn of radius 77 m on a flat road if the coefficient of statiu4m qvpb u9+:)fb95f l(vd wvuc 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 friction be between t) nuf. k8.c0de2bf kbxhe tires and the road if a car is to round a level curve of radius 85 m at a speed ok 0b8bfcuefx.k )n2d .f 95km/h ?   

  A device for training astwl6twvn: wn d.y3 v.q5ronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of rad3w.w.qyw ndt5:6 nl vvius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable ofr,)2kn2 h qgyf 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 slide) ghyf rq2kn,2s 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 yiw8, 2kj.hg r) iq.otthe top of a ci.i)2g ktroi qw8y h,j.rcle
(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) crossea,je;o*cms k 6r,pfa +qc s-y4;fvgb3s the rounded top of a hill*,- 3ckgj4qrf;6 vm,po;sa + ac ysbef (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris ;-tdfylnm(l p8w5lu n: -.3 vj rsquujm-x0-twheel need to make for the pas -53n-pm q mtr- v(lw;ulx0fu -s8ytl. j:djunsengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 f(0 utwmh.zna-(w v:ex3, ahw m. At the lowest point of its motion the tension in the rope supporting the bucf:-, m wtnaehwz(a. hu(30xv wket 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 rod*jvomwmd 97 /7l t(1jr +(slvs9ob lotate if a particle 9.00 cm from the axis of rotation is to exjl o*or1m/ld+ dw(9vvts7j 7 (mso9lbperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniva-wn9v,-ly 1vc ih s6on3mb6 zql, people are rotated in a cylindrically walled "room." (See Fig. 5,hv-svn6 6 3w9zc1- omyqinlb-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on +l pi9: fy:bhyseq;0i0o;tgva frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass ii hl 90 o;eyy0:;vp:qbtf+gs m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ba51*fy72 ;a vfy ;:xrleevh wxull which revolves on a string 0.600 m long. In particular, find the magnitude:*;lhvxxe7wf ; feru 1ayv5 y2 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 car travh3 nrkajxo 7b,m z.tyxq58 ;c,eling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses 81: cz*b:glrnaei/ hv $ 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 a(n3a -9k5:ae5ynfx0o v emre 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 tangentcz uc/a,ktk k8u.7d qw7 zn) yet().ybial and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its tz kb wcu, 7kqkn)8ay.cz(et/)d .7 yuspeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unr.(i oh) 6sqedtu0183mr oz fc8pgq(-5mfbfniformly from the pit area, going from rest to p(hqdq5t 0s cr)8morfu.gb31 zmoe f6fni-( 8 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 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 m . At a particular iqgw zi;d;p2g-nstant, its accelq2gdip; w-z;geration 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 gravi ybohfeotx r7/u4x10: ty on a spacecraft 12,800 km (2 Earth radii) above the Earth’s sury:hx1 xrt o704ebuof/ face if its mass is 1350 kg.   

  At the surface of a certain planet, the gravita21g mtm15,h ppf)m rrmtional acceleration g has a magnitude o1f)r 5mg t1hpmmmr2,p f 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 Mob (w 1 1aikcvcisdob89:ykv:) on's radius is 1.74 v:yc 81iwosi dk) 1bkv b:c9(a$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.55xb 0+ .uh jk*cg.wlem times that of Earth, but has the same mass. What is the l*bw km 0+ g..uxejc5hacceleration due to gravity near its surface?   

  A hypothetical planet 2x a*9kwzkq2erva (6n has a mass 1.66 times that of Earth, but the same radius. What i2znaqre k6k(av9wx2*s g near its surface?   

  Two objects attract each other gravit r(;t.( fuka t: t ar:om:*fcrewcziwsj5/c9:ationally 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 d.-er d+4 z 6li*nkm)g6ou ffi, the acceleration of gravity, at (a) 3200 mu)iddz*geo- k+if n6 rfm64l .    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’sjt.x-0gimg t8b)w l1x center to a point outside the Earth where thegravitational acceleration due to the Earttl 0x. gmw8gjbi)1-xt h is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sunw6b/ 9gk /kihl packed into a sphere about 10 km i gkkl 9/b/6hwin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarp03v9 ywm6 ioal-dqac07ms )yf star, which once was an average star like our Sun but is now in the last stage of its evolu9vc0q0mw-6m )3 7ap y slydioation, 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 while orbiting in the j(o(v0bff1/ un5hu7o 9 jm5sslklc- w 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 calculatinu(lw/ 1vk7l c0uofjmh(5-fnsj9 5o sbg the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.601,qe.c5u;qxdl3g f f8w*8h.umyu p vh m. Calculate the magnitude and direction of the total gravitatiqv.w*,f mucufl8yq gp 1e u. 35dh8;hxonal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yearofpw7vg-d9atk i y81 ;s most 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, assuming all four planets are in a line (Fiypv79; td8- 1wkifg oag. 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 0ht *w1i hi-/ng uq2l3h,.s qpz.38 of what it is on Earth, and that Mars’ rpq,*21ht-lhuzsi h3.w in/g qadius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the euhorivi(*+ 7v8g g9p period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtaiouhpg* 9vri7v8( ei g+ned using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sacvjhyv 45 w:.aw iq are,n818atellite moving in a stable circular orbit about the Earth at a height of 3600 kmearawv8 1,y8aj5c 4iqwhnv:..    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Eaggc si3w7br;exb n:my:0 0h j:rth. How fast i:0:c e0rhgys b7gx bnw;:jm3must 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 e;,t7il eyk ftcu e87/nxperience simulated gravity of 0.60 g? Assume the spac e/;t,nlef77t yuk8 iceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it (+yh9nkrrt, uy6f d k0takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the n06dkk(+ry h9fu ty, rEarth 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 gg1s 7aw5msn1 would a satellite have to be launched from the top of Mt. Everestsa17wng m15 sg to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module conti 9vf k3fn0.tdm r/dve(awi l:*whk*):cj* pjbnued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once0 i* rwv)jhdt:9e*cbk mpjw( vn/a.k :ld3f f*?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The5sth/u ym4p p;4: tqzo inner radius of tt:oum4y/ ; phzs4 p5tqhe 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 3y (cq* k g8.t *d7.e5kncx 7rgxlsonaonce 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 top, and (b) at the bottom? r n7q*( g*.o3snd 5.kxgltcyke87axc
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fromic k+ddi7fl +2 the center of the Earth's Moon in a space vehicle (a) moving at constant 7+ 2iflcd ikd+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-st6- outz ; vqlqy1oq)3goddm.7ar system consists of two stars of equal mass. They are observed to be3 )yodo7qm.q6tldo 1v;zu -gq separated 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 for the weight of a 55-kg woman ly+ y3 ju4cdc-t m)h5fa:0hhwin an elevator that moves 0h c jhm-3d4tc yfyh)aul+ 5:w
(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 f 8ch2bk8ejun7rom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as u8bcn278e hkjthe elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a sateli+dz vvft;5 8qlite orbits very near the surface of a planet with period T , the density (mass/volume) of the planettd;q85 vv+fi z 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 thet: pxko34e 47vmnjsy : Moon (27.4 d) to determine the period of an artificixem k73 4 oj4pvsy:t:nal satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thougzvqk0)1 /sa9*s:vnel8enf n2si ( i ldh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from thes8ike2fs)nqs0*d :ea19v/vi z (nll n Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 5vistqwkgy/*hq ;6v(gr at 05$\times 10^{9} \mathrm{~km}$ 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 years. It comes very cpft4iw:5kazvd - 5 lm+lose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest disl:i df z -av5t4pmk+w5tance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of theri:8n qp 8rgk2 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 mea,cahhx024m yg n distance for the four largest moons of Jupite0g4x,m yah2hc r (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the knownv r,6u c.vq3dfc* 9(bdok*9cgeqj w1f period and distance of the Moon. 9,dg(crd.w6 vvufefc b13o 9 q* kqcj*   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’srrrx1 02:qnbh moons, using Kepler’s third law. Use the distance of Io and the periods givenrqh brr2n01 x: 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 Mbtrz4xuv- 5 wxz(,* ci+awgf2ars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the S(zga,xt -i +bw5*vfxrw z 24ucun 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 "plan w z*rlns8fkvy7+7n 4oet" 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 rin sn8ok*4vyfrwz+7nl7 g 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 swinging in a ich+khr65 6zkn 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 rh ki+6hkz65cspeed 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 graml m f16hj pxo5ikmzoo:/2o,5vity be half what it is on the surface? o x56p/hmozj 21 ok5,iom: mfl   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mujbe vkqsob-az * ;0+h7tual circle o+ako *h v7;zbe s0bqj-nce 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 o nhx;);3 o7bae.xk :ngc +,xqhvk:ty wnce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. W+nx;hx:ceo3:qtx hwyvkb7gn, ;k ). ahat fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrav gcfy)h92 dzhsy6 //pft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppositczyfyv96pdhh/) g s/2e forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an h3wr wfb4d2/kjik4 x,elevator, it says your mass is 82 kg. What is the acceleration of hjdbk4ww2/fi43,krx the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboum wlz(9to3 g)z 7t)wyo8c;cuwt its center (like a tubular bicycle tire) (Fig. 5–42).(t3yz;cw t9um7 l)8zwogo )wc 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 vert l 0ltew81 flm/zktq35fn)1uf ical 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 radius r, the accel j5ub1didj- /aeration due to gravity at its surface /dj -i aj5u1dband the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vefdp--i 06l hportical by ai0--fl hp d6opn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked f3of 3mkflynty )+9jslmy)e 18or a design speed of If the coefficient of static friction is 0.30 (wet pavement), at wha1lknf mtyemlo 9j3s f))y3 y8+t range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fasem;z :pdv6qnu)xru a +*1 h g9qzyds:-t that objects at the equator were apparently weiz9mg*6 x-u :a)ry+q:;qh dpeuv ns1zd ghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartm.hy aha3lxph 5( (qn 7kbd6a20m mng; of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 23yn ci-hpsa g+sl1*,4gat 58c a5 m. A lamp suspended from the ceiling -yt1ha c8g+* plac,ns45sga iswings 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 Eartbv8xt-n ms/p:a d vao6 d-ug+1h. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiteraoavgm+n:bd- 8 s uv/t1 p-dx6 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 d oq hj jg1aj8:;e:8 pw6a6nmkdeduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no lightn61 g:;jem:pj8 kw6qodjh8a a 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 the hill and e 9zq5tce t9b-zu.or7valley 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 9oe7btre9.t-5zz u qccontact with the road at A?

  The Navstar Global Positiona(+ 7 ffc6tfzm-sj m y0mg3m)ding System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satelliz)mf mfs-agtd67 j3mc+ f0ym(tes, 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 (NEA nd t:)fng)-wvpl; gs0u su*ongnp;.(R), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros on(;gt v ;n:l u)sfn wp ug*gn.)d0s-pis 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 shut(czl(4xu tr7l9xy 8 mdtle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the sm 87czxldt( ylx(9ru 4atellite (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) Whud2 f-z8 o5guzat is its mean distance fro ufdz5g8zu2o -m the 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 "f+x* o9xf(kzmmk0 j 0nkeel" yourself gravitationally attracted to someone near you. Make reasonzmx*mj(fox nk9k+ k00able assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of* g(5ev4 7m9vxjo jvvx the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light *4vgxv5x7v(jj 9ovme-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m onk2o.w h3wxnl8 4m i5zb 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 si3 5.8ib lz4w xm2whnkode of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kwiyr 7h2ra yk7s/l *p+g 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 5gm5 ;9ez-b h*lq,qerys)jz dtip of the 1.5-cm-long sweep second hand on your h5sr ez-z5) bmqel* yg d;,j9qwrist watch?    $\times 10^{-4}$

  While fishing, you get bored ad*(u 4a pxn86po -i bjec-2upelb+c i3nd 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. Wix6b8c*-ul p e i(bau+o2ndp-43je pc hat 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 highwa2-ydh m6-.8k,fue ixeyf uk 0ly is designed so that a car travelin i-0u6xmkeyf, eyhk8fu.- 2dlg 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 t;5ddk o(bq;nk he 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 radiu; 5bd(dknqk o;s 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.$\approx$    $\times 10^2$