Sometimes people say that water is removed from clothes in a spin dryer beu(x-/cps6)juwih4 /da z ;zjy centrifugal force throwing the water outward. What is wroixw/jjc 4p6ahzu(z -;) /duesng with this statement?

Will the acceleration of a car be the same when the car travels arw ;acx nrz-1r,ound a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sanr, zr;x- c1wpeed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does thf;x)nqp:pj -y e car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hi j)pqn:f ;-pyxlls, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding z/m/s2dnb92 xrmw ays2 rv j+1a horse on a merry-go-round. Which of these forces provides the centripetal acceler/2 ds 9amrwzs2m nb2jxy 1r+/vation of the child?

A bucket of water can be whirled in a vertical circle without the water spi h6f,h3 ewc4jvlling out, even at the top of the circ3h 6 wh,ecj4fvle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There aqzxzqwr+ 8:g 1-7z,mv0 hdogq re at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerghq8oz 0w g:dq m+v z-,1qzx7rations do they produce?

A child on a sled comes flying over the crest of a small hilj3axo )dd5 3*:ykdd:dsx s2rx1p2gqbl, as shown in Fig. 5–31. His sled does not le :qjdasdo 3dd2x52dx3p g:k rbx1y*s)ave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high ssxpg sjx*pqc1a10uue+jq07 3peed?

Why do airplanes bank when they turn? How would you compute the bankin67t;kzt dn(u qg angle given its speed and ranzd(t7qk 6t;u dius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. 3r6bje7kf b wb; g9rdlv*; r6wShe wants to let go at precisely the right t *rb7kw;fge6 wr;63jbbdlrv 9ime 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 giy1*n c4j/ib5lvwi f+g k,7ynxoj: : oravitational force on the Earth? If so, how large a force?xn f5yijwo+cv*7 l:i :,/kn1bjgyo4 i Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s ofyp(hlb- uk7 9rbit be diffekyfhp-l ( b7u9rent?

Which pulls harder gravitationally, the Earth on the Moo,e+61 ahoz bpmn, or the Moon on the Earth? Whic,h1mapob 6e +zh accelerates more?

The Sun's gravitational pull on theyea4t., 1 t 63k 82njynpaiuwi Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider 1w2t .a8iie,nak3uy tn 6p 4jythe 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:k8z 72 qyc2a7zdxaee ? What two effects are at work? Do they oppose each otx7z z7cadkq 8ay2ee2:her?

The gravitational force on the Moon duesw+0zgt*gchlzx 6.8s 3u0oy / +js rzq to the Earth is only about half the force on the Moon due t scuzj *zh q/xly0+ s6+gr8gszow3t.0 o the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger o nv ob,6 9;kvs: eept5wfsc5+fr smaller than the centripetal accelerati: 5f;c +v6ebeswkov9sfp,t 5 non of the Earth?

Would it require less 4nhxjd,tl 5( 6mru*xc speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direct5l*6hx ,nmt4 ux(dcjrion.

When will your apparent weight be the greatest, as m tpt+ 4m02f9y* iuzrh,mup j(beasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at consta,t9p *zutm(rhip+4jm ufy2 0 bnt 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 outer space could be adversely affectedqe,1 48cf zrot 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 you can think of.8zreq oct 4f1,

Explain how a runner experiences “free fall” or “apparent weightlessness” bet bg0gm vfy)0r+ween stegg+ 0)mfyb0v rps.

The Earth moves faste/ypeb6ewgd 4z6zq8 4 ir in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — theb/z 46ei6 8 ywp4dqzeg 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 w)/xul chqvoza a4uy- :01rj:zas discovered to have a moon. Explain ho:a1-ayjzxc/ hzur q 4)u :l0vow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth i1-ibj. ndfb+j9j2q xjdjw8 o:s much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Conbjnj d+2.djfq wi:1b- 89xjjosider 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 j1mg*yv -npbm go5;) l 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripeqhipr-)z orj .*;i6:pd:sjw ftal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force -r6p sjpr )izo;wjh.di*::fqon 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 exczq fi v03y9+vqh/y0xerted 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 speed of the discvi /fv zx9c y+yqq3h00us.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sur :k )rx59o1jkib rpm6+gw dn5eface, and circles the Earth about once every 90 minutes. Findbjr56ew xd+m 5o)p :kri1k9 gn 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 clay on the edge vi/5 ebb w./heof a potter’s wheel turning at 45 h e/bw/5vib.e 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 vertical cirb9ups 5 4tnmm:cle of pt45 bumsnm:9radius 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 ufp exj6 e,+mu+kkz b69g2f *:fjlx k0can round a turn of radius 77 m on a flat road if the coefficie,k 296kb lef0eufzp:jju+ f x*k6gx m+nt of static 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 thezg+exm*kb rkt0jrb9a jb;5) / tires and the road if m+*/je5r;jbk a )gbxt9r0kbz a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rmbm-2lb vujz -d(e+4 l6 ihh(bu,e2s xotate a trainee in a horizontal circle of rad+ld,h vbe( u4ubj-(z -eh2x6i mmbs l2ius 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 cf *e3ptjkztpw3 9,v(km from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntj3k 9pv(e tw3*p,kz ftable 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 turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at then- e78d3cjsxotl0o,y top of -, ec3t7 l0 xdyosjo8na 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 (includin.n(chq na soqfk28;. zp8e7zr;raqh*g the driver) crosses the rounded top of a hill (radius 8 2 *.;q. o;es8z7phqzrar(hfnaqnkc =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)v)ej 2 yw+we2tuk -agerris wheel need to make for the passengers tvaeygt)k)wu 22e + j-wo feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg ip5ztbss( a-6ywh92 a9e/ n rwt8)on als whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tensio986p yo/2t5( wnn r9wsa)la b-tzeshan in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a c( mj laajo)/lbdx1)i8entrifuge rotate if a particle 9.00 cm from the axis of rotation is to expadx/a8 iol)m()l 1bj jerience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peop,y,5q2pgx)b -d7e smiz5*p ; lp cmitule are rotated in a cylindrically walled "room." (See Fip2 -q i p5,mu*cs),yzximdg;b5tp7l eg. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a fri(hgx 1de 5f+5r pwp3cwctionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blo3c+ r p1pwf(e5dgw 5xhck (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weighwcm cht 5 m5;mmvu8--5ipp xa*t of the ball which revolves on a string 0.600 m long. In particular, find the m iupmcp-c5*h; am5- 8mwtvmx5agnitude 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 bankeulaz7jy brbl0ih,. qyy v,d2c /,i;7p d 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 masses 4m)x: jp6yrucul5wd3fqq3k2y em2 3 g $ 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 a;aha 0lmn w 4lg2g,ha;t 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the nyrh66uo pgt5 3et force exerted on the car (by the ground) in Example 5-8 when its speed isyruo3hg66 t 5p 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates a cg/)lquhn4 qg6/e. (k vyi4vuniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with4 hay qlvkeigv(6q/. g4n u/c) no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.909y /ao3s*2 kxc0yds vt m . At a particular instant, its acceleration is 1.05 /9d 20yscxyo*tk 3as v$\mathrm{~m} / \mathrm{s}^{2}$ , 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 spacecraft 12,800 km qq dv60sww++akjrainio7+-6 (2 Earth radii) aqo6+6dniiasw v70 -++ jqkrwabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain p z6ub+su/c;qf75vc o vlanet, the gravitational acceleration g has a magnitude o;u5c7/of+uvq vs 6bc zf 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 is 9 / w(qtplg3dmf7fni) 1.77 9wn(3)q gfdl im/fpt4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same d8xz:v2 f9kxoz. y6) mrgwg(t mass. What xd6xoz( 2t:r8 wvfm gyz.)g9 kis the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sahh: xb/f i-7(n7+osggg pm;rkme radius. What is g near it7xpghosr7(g;hf/mn :+ gbik- s surface?   

  Two objects attract each other gravitationally with a forcux6 fh5+yv0xt2r7wote of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, ap1yukg,e z(mc .od8h5m9i x y5t (a) 3200 mcdy huyeo158m x(gm,5z 9 .kpi    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside thely m)m , khxs5badn*v1b,-ft9 Earth where thegravitational acceleration due to the Ea,vfd*n, 9-l a k)xmsytbh m51brth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five w.p-b.q3 kjf2 csp 1kztimes the mass of our Sun packed into a sphere about 10 km in radius3k wjbp -qskf p2zc.1.. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is*yh 3 r8 g3(jznc6:iyz9dsu8b(hrlc y now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface grahb(*jgs cc33rd6y: yy r zz8u(89lihn vity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the yj5/r )g,urf zspace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of r ,j)guyz5rf/g.   

  Four 9.5-kg spheres are located at thet8 wf ,1;iqpnmrbs7c4;l0h kp corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational ff,th0 cplqkrm ni ;81psbw7;4orce exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lingtn 0ho97g-,l 6rzcpse 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 (Fig. 5-38). The masses artpnrg g 6co, hl79z-s0e $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 accele.h3 ps( 07zneaapp p7x8 gr,ofration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine thx pf3p0n.sh78 g(appa z oe7r,e mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sunq.qey ( jky1 r aq+vfzshr4br-z*5) b0 using the known value for the period of the Earth and its a)q4jr k eq10z*brrs -zyq+(b.f vyh5distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in agfublya i7 .45c3m3z 3hun(t o stable circular orbit about the Earlo3 g(h 75. umftzc3inbyu4a3 th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a cg:tkj.(qz h2vms mr,s qk 13+kircular orbit 650 km above the Earth. How fast must the shuttle be moving (t(zkqsmjq ,kr31 :k2 . hmgv+srelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotavk5a l dm:kesia14j w ,o8+f)ite if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Figlavf)a45kd m ei+ ,ojwsi:1 k8 5–32.)   

  Determine the time it takes for a satellit-b ,wr k)p8+g5 ovdg3l jx,odze to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the s3 wr-gdb5)kx,8od zvpl,jgo +urface 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 satellite have to be launched froa z/n+m, apjgykrb4s 3y 7;xh5jm()x vm the top of Mt. Everest7/jkm;yy vxz m3jrxa+b5 ns) h a,4(pg to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, c9sf5xok8ip* d-e.lj h3 8rx kthe command module continued to orbit the Moon at an alc5rsk jlp9xeik8 38hf*d.-o xtitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The inedl6 o1r 537qnk+m;)bibp bl cner radius of the rings is 73,00+qc bdnlpr15 )e63ok b m7lib;0 $\mathrm{~km}$ , 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 (see0dtce lkq( .ipcktjf8 ux6b833vy ,; t Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) 8 k;djkicvl(qpxc 0e,t3.6t y83bu ftat the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the jzha3815el y6q ,oeiy center of the Earth's Moon in a space vehicle (a) moving at consq3 iho68yejal,5e yz 1tant 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 system8msjkzjt t5ra:9hf r*u z4y 5; consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is4szjj*5 trk5 yztrh m9a8:uf ; the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator usk53fxf 7p4dj5f gk4pt/ i v7thak7g j5v7if s4 fpkf/xp ut345dt 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 suup -bf) ,(+yaj s: ru7rp3renlspended from the ceiling of an elevator. The cord can withs+)( lrf,yp:ub 7p 3nrujse -artand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the sur/m.s*m)omrr0fsd7u k4 djdb+ face of a planet with period T , the d +du) d7ork rsjs4b.0 mmf*dm/ensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to det. ndsbj4h.1os7-ua ou ermine the period of dn. s1-au b.47hs uoojan artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a fe0shxch,)-gdw 8 wgdw .w hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is wxwghc,h w 0s8ddg-.)its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4 a/h4b g*n1w 3obnpuw..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 Sunndse,z67x pza23o* 5dr f0h svg psf,0 roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint2sz,o x,gh da5pnz0efs0dr*63 7fpvs : 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 os;m zfc89o:/f m4 x5.qovbji df 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 distga(xn z/ocmp )tvp -2e/ l0:gtance for the four largest moons of Jupiter (thosnp2tmg0pae/g)t (oz/ : -lvxce 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 the Moon. 2;9ginu q - so :aey6t q+,q1ar7zhijj iq;r9jj: -iuq+zatsygq6o12h ,ne7 a   $\times 10^{24}$

  Determine the mean distance from Jupit,/t fx n2oqn5nz.z0k ker for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. ,o knfx zn.z0 tkqn25/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 fragmei8c, wyq/3yss m8 fg5pnts (which some space scientists think came from a planet that owqipc f3y g/5y ,s8m8snce 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 for. 0r9aox9 )hby7izl dmm 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 iom)r 09dx b.l9zy7ahEarth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fcxk axs+s zah;**8op:ig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the max*zao+x s s;*p8xk ca:himum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Eaqodh-1y4oqdsd0v +i) rth’s surface will the acceleration of gravity be half what d od1v-yoqiq4 h)0sd +it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands xr v5slk/z+le+n (h1q-0mm i tand spin in a mutual circle h xil t0ln/zm++(m- eqs1v5kronce 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 once per day, the apparent acceleration of gg fi60k 9g9gjoravity at the equator is slightly less than igif9gj096 kog t 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 Ea/14h r2 ldrmri yk.su0rth will a spacecraft traveling directly from the Earth to the Moon exp rdk2u.s ri10 lm/h4yrerience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stm4f( 62aiskx+8mcr b /5qx wzoand on a bathroom scale in an elevator, it says your mass is 82 kg. What 8kf/(oiscrw2 zq4 +x 56m baxmis the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will ro;7ew9mt1;4gd zb grxb tate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must zx1 49;wegr g;tmb7bdbe 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;n 3xbsc 9u.s4 z6niig (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 accelpe fykz0r6+lufm * j-5eration due to gravity at its surface and the gravitational constant G.*jkf6z f-+plm yu5er0

A plumb bob (a mass m hanging7nzba pba wstmbd6:4+ k.j;i( on a string) is deflected from the vertical by a :kb4sz7; manbw+t a j.p(6idbn 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 c5o7rgqmlsn1lp-p8f z(s)b:m is banked for a design speed of If the coefficient of static fr1 bpfcr)(:ngoll8m z- q5sps7iction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were 7t w8lzj( s+j ;y5d0q5ornd exrotating so fast that objects at the equator were appa 0+7;85jn( d5qoj lwdyser tzxrently weightless?    $\times 10^3$s

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

  A train traveling at a constant speed rounds a curve of radius erydsm2n ,u xuc6+ 9;ukd g5vz6(zd w- 8ph7qi235 m. A lamp suspended f7 rw uz289ip 6+cd5yh;qnegx u,uzd-d( vks6 mrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 time); v3u.xrebqgfhk9 +vs as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the n)r.vfkqgh;x3v b e +u9umber 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 Hubb9p: uita8ki;hhb* 3m:pqpi: ts) hr 0ble Space Telescope deduced the presence of an extremely massive corei 3uphmpta s8:9h b;it):* phrqi:0bk in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the 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 th ourp-,)napfgwapplk h4q0:* m )93v xe hill and valley shown in Fig. 5–45. Both the hill and vppok, u)9a)-l xqarp : fg4*v03hnwm palley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positio,c7i,;odvmm k ning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles ikcd,m7,o;v m [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, isx:bn glo gmd/e3 :u-uqc+s1;k meant to orbit the asteroid Eros at a height dm-uu son l +e ;3kx:gq/cg1:bof 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 puk op1,e.wmnc 3rsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behi wepo3.1 km,ncnd it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its / ee-wgow5nlzu 9.0domean distance fro/5ol0 ee.g -9onuww zdm 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 actuap;mgq:u; . mpglly "feel" yourself gravitationally attracted to someone near you. Make reasonable m;q:;gp .pugm assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxyami)n6eg3n6lpnuw fo-ow 2/0z9 j bp* (Fig. 5-46) at a distance of about 30,000 light-years from the3aw0o* io -b96 lp/un e62n gmfw)zpjn 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 ea6 nz8q+x+9c2pbcjemi ch side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the m e6j m+8 9qbp2czn+cxiidpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits tnt43+b dtp/og he 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 experience19n**syddl kjd w d/im)oi.a8 d by the tip of the 1.5-cm-long sweep second handi*ldmo.s8nk9diwj)1* dy/ da on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to sw:-e2g hnv3vt fzk s0u0ing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight0-20uv sgknv3h:etz f makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a,vuj6 dd,t4icbo7 op j1 ptc/6kind16nr7wo1 car traveling at so d ,ict 7676o4jp,t1di6 r 1kdvojcn1bu/npwpeed $ 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 thlp1 e- tcz1cr f7p/*hye 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 of mass 75 kg if the track is not banked and the train does not tip hz1cy* 1fcp-l7/retlt. $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$