Sometimes people say that water is removed from clote7vsl;w r +ex( rx60g zjy:.yihes in a spin dryer by centrifugal force throwing the water outward. What is wrong with 0 iyrvej ;:e.xl( g6zwr7xs+y this statement?

Will the acceleration of a car-lfa kco wi cjtx6k;+nm0/(c.kf j64j be the same when the car travels around a sharp curve at a constantc4ak c+ l 6jowntk(jmj 0f6fkx/i-;c. 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed al6oapbqq kz3m w,:9d 0tffy.t.ong a hilly road. Where does the car exert the greatest and l.tfo,pwdmk 0 fzqt 9y.q6 a3b:east forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. c pm6ps(cr 4r5a;vp)x Which of these forces provid()x va5rp;rpc6m pc4 ses the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spill.0g f90tt/j8 t upeepting out, evejueep.tt /9 gpt8f0t0n at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have iozsx*ysritu 4l .*qo.m;2 c a2n your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations dur* *o4s az;sm2iclxtoy. 2q .o they produce?

A child on a sled comes flying over the crest of a small hill( upuy; p/vf,.f*tysa v(e hy:, 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 hill. Explain this decrease using Newton’s sea sy(uf t:*vh (,pp.ve;y fuy/cond law.

Why do bicycle riders lean inward when rounding a curve at high speed?bp z*7;d .4 ,50qcvmiwlr d2ka;lpnd t

Why do airplanes bank when they turn? n xhg5:2b1mh0/dr fg7uk1m rcHow would you compute the banking angle given its speed and radius of the turn?g:hmh 5f1mr02/kdb1ugx rn7 c

A girl is whirling a ball on a str mlh8:/dty(gr 73ercs ing around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the 3 gtlhycm8 /:s7(rder yard. When should she let go of the string?

Does an apple exert a gravitatioa)1z c7e yhxk7nal force on the Earth? If so, how large a force? Consider anxe7a 1c7)hyk z apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double tq.,ck 9bz(,wtw em z -6xegyg,6)gmvwhat it is, in what ways would the Moon’s orbit be differen-,q egtzmw,yvz.gx g ()emwbt kc6 96,t?

Which pulls harder gravixdfws t0yp z91z,)ky .tationally, the Earth on the Moon, or the Moon on the Earth? Which aw1 y0 zx.9pzftky)s,dccelerates more?

The Sun's gravitational pull on the Earth is much larger *w1elzw76k9d) v y; j5ulzpph than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in graw9djz) zy*kp ;l v5pwl617ue hvitational pull from one side of the Earth to the other.]

Will an object weigh more at 4 c/5eyy5lpz ethe equator or at the poles? What two effects are at l /yece54pzy 5work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is onf h)sl 5 xqe*xrh*b)+tly about half the force on the Moon due to the Sun. Why isnxbqseh5)l x*)hf*r t+’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around tv pqbwiqo-;2kw2l1,;p - efejmww-h ju7 l4z.he Sun larger or sm;zkbu;lpqqjo 1 hm w-7wiel-f2.p-j,w2 ew4valler than the centripetal acceleration of the Earth?

Would it require less speed to laun)5gbdmt.;ux +/y+f ca plms) sch a satellite (a) toward the east or (b) toward thfg +xu+by)s dpmal .5s/t)m;c e west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movi,ljpi 2zm9x, ang elevator: when the elevator (a) accelp9i2m zax,,l jerates 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 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 cog)5me5ur.c,6a/g8)4w) dj h iuur uwosrf6z muld 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, (u s546)arm 5 di wr/j),huuu6czefgo8 wgm).r b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall”dz g5*nahck/o sv*s 6t4v1m,p or “apparent weightlessness” between steps.5v o6g n,tk1hsa*v p4mcs zd/*

The Earth moves faster w qmq+ kw0(n 5jb:qe2bijuah 2/,wx n38v 8fcfin 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(2xnbifjwbwf:uhq /q285,c3 vam +ke n qjw08 is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was zo, .gu) jyofrl.drl4z n m63*discovered to have a moon. Explain how this discovery enabled an es . g.yz6)jlnorlfzu34 r, odm*timate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than thg3o9r)efaga 0n o/s/be Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side oe)grfb oag3n 9as0/o /f 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 19) rzsrrb2b 1;z80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ism+o/*q9sz 8a 2aobsrn its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a 9 qrsa zabo* 8/o+s2smcircle 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 rotaccmvp*.2ec8 htes uniformly in a horizontal circle (at arm’s length) of radius 0.90 pm*8 vhcce. 2cm. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fmqgr/rfdrn lb1 qx(uh --2(e2izh8n 8rom the Earth's surface, and circles the Earth aboutrf rq(h(z r8qm2eb/lxn8hund ig2- 1- once every 90 minutes. 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 the acceleration of a speck of clay on hb i5 f7jn5j :cnp7jj,fjf/0t the edge of a potter’s wheel turning atjn5fcfb i/0h:j7f7 j 5jtn,pj 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolve a/eygu,t(- euz 5vfpoeb,a76d at a uniform rate in a vertical circle of radius 7bfezu7 (6evt gau5,/a,-pye o2.0 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 cl26t5qink e5fw :tx ,oar can round a turn of radius 77 m on a flat road if the coefficient of static friction betweenflti55x t 6wnk:2q ,eo tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of statich4 nf1tixm0tg7e; w v; friction be between the tires and the road if a car is to rount0i; xfew; nvmg 714htd a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and wi6*u 1r7u3ih o6hvjc jet fighter pilots is designed to rotate a traineejicoh 3wi6 h*vu7u61r 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 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 of variable sk 6ztgyb *t:9kpeed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is rgy k6:k* b9ttzeached 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 tr ok*chsy:4/bi:,sj ,mooss. iaveling when upside down at the top of a cirsk.,,4y: c:isojoio h bss*/m cle
(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 m s*(vt,xi tz,hhi,/ whass 950 kg (including the driver) crosses the rounded top of a hill h, stx,htiz/w,h( *v i(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 wheel need tonh8uf5lk qh+ 0 make for the passengers to feel “weightless” at the topmost point? 5 +hul8 kqnfh0   rpm

  A bucket of mass 2.00 kg is whir9psy if:q0kq 4led in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the q 4fky0i9p qs: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 centrifuge rotate if a particle 9.00 cm from8 a+cnxj4m- 3;g;r xz7bx w15w pqhe l,qn4zip the axis of rotation is to experience an acceleration of i z+h-a,l7ngwwx q m ;543rp xc18qb zxnjp4e;115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically d9ld;r * gpsyz(us9 5swalled "room." (See Fig. 5-35.)lsr(d 9u*;s 9dszg py5
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 frictionless air-hockey -f ,(h1zf fh7-xh*tml0fyxth tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throughhl hm(h- fzx-t7f1xf *fth,y0 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 nos0f8 1nz0e:lbbjyo7e4 l y( pnt ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find th( el8zjs7:pbny0 n014elfo ybe magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfeczr*li sg8zt;8x o/3 yhtly 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 massejh636/nru91yfjz6p:a j gv zxeo xt/.s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically 1y 4:7azxd qx6sfz0, qmo8pbjat 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 4 oi)89 21yofh kz* 3*qly)o lqrjuxofnet force exerted on the car (by toryoqi) zlu*3o1f fj*x k2 oqh8l9) y4he 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 uniforpri 9d9, k6q pidnjjyw8fs6a4,nc, s8tz 8ci2mly 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 2a9jqwiy ik dscj8z f,n 4p686p9sd,ircn,t8to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a ,1h+ec6ada7yu 4 xrwz d5fw1ihorizontal circle of radius 2.90 m . At a particular instant,z7i+ 1 ,wwf1cr5ayhu dx e4ad6 its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Ea+o,8.yjgyq:d qu8 vxo rth radii) above the Earvj+,q o.u:y8qd gx8oyth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration ghla ht ,yvo)wv meelu*e- d*41 ;8ll8t has a magnitude of 12 -8wld*4)h,hv u aelt e oev8;yl1 ltm*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 icjekp (520g:yno k8)h wcf-ix s 1.74 fxy2ec: cg5wh8k )i(p-kjo n0$\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 s)pgti1vtl iq eea7 9 ;e3gr0k2ame mass. What7)epe1iqil3v ratk 9g20 ;eg t is the acceleration due to gravity near its surface?   

  A hypothetical planet has a w jqwa/j; -p/qmass 1.66 times that of Earth, but the same radius. Wj-q/;a w/pwqjhat is g near its surface?   

  Two objects attract each other gr) c3xum4 xqnm3x;miowb): 1mtavitationally 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 , 9zl6bieq z5sv4c n::rthe acceleration of gravity, at (a) 3200 m i4n rzl9b65 zecq:v:s   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to7v xav9ti4g cp p.yl 3)m4lfw/::grc m a point outside the Earth where thegravitational accelerati) gai4g m:lv.97m4rc cyl3ftw x /pv:pon due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mas1pi5 pwka gdd 74+99wret a-chs of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity o5 igw+d1 c7hr-pa4p dkwa9 9etn this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avera9/adh: x5fk sy5q a*rzf2ed w6ge star like our Sun but is now in the last stage of its 56 wa/d*ya59z 2k:qhs exdrffevolution, 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;ijk6x b/ l ltv+r ;,fvt+moo4 while orbiting in the space shuttle. Your friends respond that thei4;b+ /,l jt6;v+xrmtol fvok y 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 corne:o+l ovx: sy z+k+ka1grs of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othek:y ++ :av1xl+o kszogr three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line u 2e+srwx)ycd (thb8d7jdp / v2p 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 are 2ej)h7byx(ctr+ d 8v ds2pw/d $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 skn f my9r1t i1b s +m5kwg)40yq:mjjd*urface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determi1gmtyj9syf ) i*kr1q:w d bm+mk 45nj0ne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earthw*doxc f1 2*f g-nkkw7 and its distance from the Sun. [knkcd2fgwf7x 1o -* *wNote: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stablxj ut;-ud;j6ee circular orbit about the Earth at a height of 3600 km u;x jtj-;eud6.    $\times 10^3$

  The space shuttle releases a satellite into a circular*t (s.0gx 9dkipyn5o+q8uva g orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release g qgs5+dt98ko0 av(up* xi.nyoccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate i;clu/ay509kuj c4ef d f 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 Questi4jk5 c0duey/ 9calu ;fon 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth isw8ytnl5y-ipa11 fg , n a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which i g5n,1s18 typafilw-ys 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 laukyt0+pg70zkip:r* f znched from the top of Mt. Everest to :70*fyrgzp k z+ it0pkbe placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module 7o9q d r2*m z7i3bm .azl,koimcontinued to orbit the Moon at an altitude of about 100 km. How z rd*zbio2,o9k m7 i.m3aq lm7long did it take to go around the Moon once?    s

  The rings of Saturn are composed 1jd*c 8v x(qtnof chunks of ice that orbit the planet. The inner radius of the rings is 7d8x q nt*v1jc(3,000 $\mathrm{~km}$ , 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 swcau9.-zy2jwvnj ct. nu) 6ydx6w. *in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent wei6w w wv9-tyj su.)ua62nzxj. .yc*dncght to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centerw8f8 o7xbhgh3 of the Earth's Moon in a space vehicle fx7hw3o8gh b8(a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stamq,nj2c yb6 0xrs of equal mass. They are obser,6jycm 02n xqbved to be 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 sc37zlb5t(llii 8zf * k, 3pemmw3i,jhdale read for the weight of a 55-kg woman in an elevator that m5ml w3ptejb8 3l7ilif( k3z,zh m, i*doves
(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 fr+esaq 9teb ;2yom a cord suspended from the ceiling of an elevator. The cord cane+9 ;yqtbe 2sa withstand 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 orbeqqxla6/jup o/:(gn 8f(wi *r y)ws2 jits very near the surface of a planet with period T , the density (mass/volume) of lei r/fj)*xwg2:qq6/yo8apw j( snu (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 determine the periny5atu :zi;.fod of an arti.; y5ifna ut:zficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the h-vv6 (ilmy2f*j a4io wm0w z)Sun like the planets. Its period is 410 d. Wha4(6ym* - vmih jlfzv 0io)wa2wt is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average 52agmy,so-zqwh 3t (idistance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every gc di yq04/hj5h1jh m176 years. It comes very close to the surf 0/hq ch1j 5hyjdm1g4iace of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of rzhfhxp3o*p197z6xv 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, p2 b7uaqb/.nwzc;vx 8oeriod, and mean distance for the four largest moons of Jupiter (7bcxa v/q n. 2w8uo;zbthose 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 Mov*v7)g-72)mf6 oyfk rm jea vvon. kvf 77me*rog-v)va j2y f6 )vm   $\times 10^{24}$

  Determine the mean distance from Jupiteaa5ue sl4ril; 4 0)dkyeu9lp 2r for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3;a)el5ka ylur9e40 lp udi4s2. 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 (whii( -3ybq,hwb os m22ccch some space scie ysb2hccm 2-owqi ,b3(ntists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "plan(aq 2jwi;v er-et" 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 vwe- qj(ri a2;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 g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge 98ycm g4t,3npoiw3f jby swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N o cw yof,gn4m983jit3pn the vine, what is the maximum 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 Earth’s surface wvlyx 1/r;;x mzill the acceleration of gravity be half what it is on the surfzlx1rm;/v; yx ace?    $\times 10^6$

  On an ice rink, two ska-bxtzf/bdcb v /6v-tcr nm *8-ters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anotb-6 r tcmv/- f-/*tcnbz bxv8dher?    $\times 10^2$

  Because the Earth rotates once per day, thut8yus). b e/ 7y8xwtne apparent acceleration of gravity at the equator is slightly/.ubwnse8 ttu8 )7yyx less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly qlwg 7:u1vmh7x -3m htfrom the Earth to the Moon experience zero net for-7hluwvmtgh3 7m:1qxce because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an eleva0b0sxivpa/m /7hfa pm1r; u*gtor, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direct0f *1gx0ahp b;7a /vi umrsm/pion?     ----待选择----upwartddown 

  A projected space station.tfnpcydold, e:7 l** consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the l**d,n 7dte f :yo.pcltube 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 f(bosj+/p*gr o l q0m,a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radioo0kr* t 9.oms0tv wu5us r, the acceleration due to gravity at its surface and the gravitational constanv00o rwtooskm.t5* 9u t G.

A plumb bob (a mass m hanging on a string) is dtx 4o5 ad-ug.+s7wifteflected from the vertical by an angl.gwai+4od- xf75ttu se $\theta$ 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 bankedvl . x+vx/k+yz for a design speed of If the coefficient of statl+ .xx/ zvvyk+ic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects al8i:l:f:s alz t the equator were apparently weightlesi z a8:l::lflss?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance q; yjjv6+.gvmapart 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 speedyc :z:yswvq1cm94w7d rounds a curve of radius 235 m. A lamp suspended7d 9wwzq 1mcy:sv :4yc from 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 ti0hfsb .z/ a*mymes as massive as the Earth. Thus, it has been claimed that a persoy*sb0 af. zmh/n would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Spa,ue41n5 +k4 mqiler cdce Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dm,4 i1q deuec4lnrk5 +ense 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 the hil t *u.wxm8+u7wf-rlduc9 0-ownfkk y*l 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 cmu-ukfw.u- t +yc9l0 kxrdwwf n*87o*ar go without losing contact with the road at A?

  The Navstar Global Positioning Syx7ku7xeh s;1 il/4nroq g/x .dstem (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 eu .xdo7q4x/i rh7xnlg 1sk/; 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 travelim593mt2df m frng 2.1 billion km, is meant to orbit the asteroid Eros at a height tf3mf295 mm rdof 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 i+w6zhps zkzcx0/ q/+m n need of repair. You are in a circular orbit of the same radius as the satellite (400 km abovkch m/p+ x6/+sw zqzz0e 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) What is its mean dist 2bih 9ma(wim9ance from the b(ii9mmwh2a9 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 ggksq. t4uv09zv ngyf 6 ,2ww,need to be if you could actually "feel" yourself gravitationallywkgf 0 vg,zsy q.vg4tu926wn, attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mzw 0th8naecij2vds.)c3 k()tilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from tdh .ai cj0vs(zw8)knte2ct)3he 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. F4 ft0g5.ezr no./y vx vikhl/-ind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at thef0gn 5ikl.ox vr -yh/ z4.etv/ midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits 2tglv9j33wdr,m qmn )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 tirf n /rufxm+/ n*y)zr6jyia;5p of the 1.5-cm-long sweep second hand on your ynuir6y/f*r5zxa jf)m ;n/r+ wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in t9hxl42inrfvp sz hey/rc: 3 aq4-9.jdt e7c2a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–1tr99q/43 2p aec. 2lrifzvtdn:jehy7xc4h-s 0.]    $^{\circ}$

A circular curve of radiuspk1+rz ucd/ pu3t :7uy R in a new highway is designed so that a car traveling at speed p/3yukuu7t:p 1z+ dcr$ 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, utilize1f/ jr k h, ng5/6ky):h lg/7sxiaxhnes 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 talhsfh rx x7nh1)6 / g:5/iy gkkn,/jehe 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.$\approx$    $\times 10^2$