Sometimes people say that water is removed from clothes in g:2y o9ok *eima spin dryer by centrifugal force throwing the water outward. What is wrong with this29imeyo* k:og statement?

Will the acceleration of a car be the same when the car travels5pf*r 2;n t 0t2od0bx y8oybak around a sharp cupa r;obo0nkxd 05y 2tf2ty*b8rve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed s x7pg6sl7xy8e;v q1iefp r *1along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stre1vsiq;7yg pex8l p*xfs6 e71 rtch near the bottom of a hill?

Describe all the forces acting on a chive9exye 0ah +1ld riding a horse on a merry-go-round. Which of these forces provides the centripv+ a9 1eh0eexyetal acceleration of the child?

A bucket of water can be whctr50+ / dlmxwirled in a vertical circle without the water spilling out, even at the t 5rldtc0 w/x+mop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in youri5 -wmz.d:n yp ft7wpfbc 11o1 car? There are at least three controls in the car which can be used to causezt 5fio 1 n.my1fpw1c:wd-7p b the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smalmi/ i,wvty)am:ccc; +l hill, as shown in Fig. 5–31. His sleaw,i)yc:c c t/ivm ;m+d 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 second law.

Why do bicycle riders lean inward when rounding y66 ybwp2 1rme8caky2 a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bans02j,wxpwa6m iti2 +cking angle given its speed and radius of ws m,6c0 2iw 2ti+xjapthe turn?

A girl is whirling a ball on a string .p;7iw/sbk76u)f do aeo:sffaround 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 to w)6:ib;fa .sd uf/o77s pfekhe yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, howwjw4.l cjg.s.dg9 y3y large a force? Consider yg j3s..l d4.9gwwc jyan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would uh vn s4) oii.b :v+1r7yd3rkethe Moon’s orbit be differe )v :i+yrdbr 7.41iens 3oukvhnt?

Which pulls harder gravitationally, the Earth on the Moon, or thvjyes7* :wu,8y h4 xvgmr 56wte Moon on the Earth? Which acceler5w: se4uh*7yvw6jxyr8m,tv gates more?

The Sun's gravitational pull on th2 -v7uew.srsnyyd* *n e Earth is much larger than the Moon's. Yet th u7-d**nwrv2s.ys yn ee 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.]

Will an object weigh more at the equator or at the poles? What two effects;q)7e 6 m pa08gzordpty4m l gd+luo;4 are at work? Do they 6tmglp dpg40+ d;8;euam4r 7)oz l yqooppose each other?

The gravitational force lyb 6h5 vh/94w (wob4; rpgnvoon the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the;r46o4wwv5vln b ghpyh /ob9 ( Moon pulled away from the Earth?

Is the centripetal acceleration of Mars.ux9z, z i8:3q/yem x:dacpth in its orbit around the Sun larger or smalapc/ xz8eu q:3hm xzidy.: t9,ler than the centripetal acceleration of the Earth?

Would it require less speed to launcdd e; mv2 up,0kq:st vips2,)oxgz6i+h a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directio u2i2v,sodezqgi+ pmpx;,6:s )0 vdtkn.

When will your apparent wr 11/d- p(bmo)ajq h7b jgys h;/2wnteeight be the greatest, as measured by a scale in a moving elevatog;d1 7) /1(-esjm ab / nwphybjhqtr2or: 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 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 periodsql pc*/ue.3a i 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 wa.il * pu/qcae3lking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlecjt ) 4t8w/x9udz3t0.zw xygnssness” between t3t wd9yz8w n/zj4.xc0g )uxt steps.

The Earth moves faster in its orbit around the Sun in January than in Ju.mo;dxx;n0) g l8nj;jzm 6una ly. 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 axis relative;) ngxmj n;oujl8m; zx06ad n. to the plane of its orbit.]

The mass of Pluto was not known until it was discoveredbnm,2 krccr/px3z7 c/7ws;ly to have a moon. Explain how this discovery enabled lkp 7cz,rb c/r/m; 7s2wyxcn3 an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much u/o. fy:c2ovz larger than the Moon's. Yet the Moon's is mainly respoz yuof .o/:c2vnsible 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 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 2qa l822 cf em)xbq3lq 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 centripetal acceleray;55 t9ya8rv wzep m8)sy:tyn uh+ ja 9sd0ki)tion of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts ht y5ysad) 9j9+8u rzvpnis wm)a;508etyky: 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 exertegy9rig;mwlx:r y b-l4l+dw/5 d on a 2.0-kg discus as it rotates uniformly in a horizontal circle (g 4rlb/y9xy d rgww +l-ml;:5iat arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 qkw3z/e) ybp1 km from the Earth's surface, and circles the Earth about once every 90 ) y/bqk1zp3ewminutes. 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 the edge ofxcun)ildk; .9e(p7 p .d scaes0c9ns 5 a potter’s wheel turning at 45 rksa le . 7nepc9c.sicd(s 9 d)nx;0p5upm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniforq ;byhoyq s319m rate in a vertical circle of radiuhqs3byy1; 9oq s 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-kjszq4n.qa- 2wg.e8 d ag car can round a turn of radius 77 m on a flat road if the coefficient of static frictionq..e8 2naj4-qs z awdg 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+mziwha v; fcm1d+-f/ ex5e +m the tires and the road if a car is to round a level curve of radius 85 m at a zmeffc;mia++md/wev1 xh5 +- speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed dyr, o ;o(9pmgto rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trai9 mgpyod r,(;onee 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 cmqxyj( dvjt58j+otck /cgq65/ from the axis of a rotating turntable of variable speed. When the speej5o/qxqtd /cg yj5(v8+ c6jtkd of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling w-ordh :57,gk,ck;whmt/0nc cyx,rw phen upside down at the top of a hodr:nk krx,c/75mw;cpw y- ,,gtch0circle
(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 thxbcjg+- iz4sy :(44kw(k ftuhe driver) crosses the rounded top of a hill (radius =9kt+xi-w: f4zs(4 jcbguh4( ky5$ \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-dia- fipon544w v rs4,udkmeter Ferris wheel need to make for the passengers to feeldv5kun-pw4if 4o,s r4 “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle -hdfqz5be l. 4gdzvanh; +;7nof radius 1.10 m. At the lowest point of its mot4de- zdn nq;blv5z+ha;7fh g. ion the tension 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 centrifuge rotate if a par 4; 3qcwd,e rek :oh ;6r/kuulirwc40qticle 9.00 cm from the axis of rotation is to e6e k rdcq0crkh ruu44l;; e w,:iq/3owxperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa:p;q12sk75 e wjt3 2cczuuf0egq tzyu qux 13(lled "room." (See Figq73tuz1e:uz(s cty;u2q kcefj51 gx2wu30qp. 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 frictionless air-hockel fk6ixw1 o7h7y tabletop, axfk6w1 i lho77nd is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this timdfbf89 5wi h8ze, by not ignoring the weight of the ball which revolves bi8zff 89h d5won a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius ofzd mdm0j 9 ,aqg dp0z2*r0n*fe 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse1iv pgg7(n-n os $ 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 vertxtx3s7n 1 jz8eically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal compone3/e2+e ip ptzxnts of the net force exerted on the car (by the ground) in Exa 3i+pezpte2x/ mple 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 Indiana2an1k txcp2v :polis 500 accelerates uniformly 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 withk tx1v 2cp2:na no slipping or skidding? $\approx$   

  A particle revolves in a hori z6w gl-teeir:17jq/ szontal circle of radius 2.90 m . At a particular instant, its ac:qei 1w 6rj zt/g-s7leceleration 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 gau j i)svh3k,i82znq9 ravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass hv,8ju32 )ianz9kq siis 1350 kg.   

  At the surface of a certain plaqqw5t9ms eg*;5ur /v7w jsr q1net, the gravitational acceleration g has a magnitude of 12 m/j*57 q;vgq 1rts 9w swm/requ5s$^2$ 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 radiu tw oryf:1*h)us is 1.7wtfohr)y u 1:*4 $\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, bcfl t s s-t7zdocdme(,p6 yj2f0z66r2 ut has the same mass. What is the acceleration due to gravity near it6oty6sefpc d6m ,dt rlc-f20zjzs7 (2 s surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same ra,p6 w +ar k7tzfn7c, nq:mt,ypdius. What is g near its surfnrpm,na z7ty :k6q,t+ pw7,fcace?   

  Two objects attract each other gravitationa1,ph is(jfb (;n d)(fztn,h.tbctb e+lly 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 valu0a,0a1rew.iku 8un rde of g , the acceleration of gravity, at (a) 3200 mira r0d0uu8.w 1ke, na    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsi23upt2p.,-xybdwq/e k 6 jx jll*nsw 3de the Earth where thegravitational acceleration due to ttj3upqwp3e. k,l62 wsyj*xx b/n d-l2he Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ou(rf pf2ljo71br Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thi2oflf (1r p7jbs monster.    $\times10^12$

  A typical white-dwarf star, which ony-sah/j )4o7zsu)xcq lc0.ufl i6h k8ce was an average star like our Sun but is 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 gravity on this 7-y6uz.l0lcca k4x/ uhfo i) j s8sh)qstar?    $\times 10^7$

  You are explaining why astronsc zj9kqd/n j0;b*k f4auts feel weightless while orbiting in the space shuttle. Your friends kk*d4ns0bf9zj q jc/;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 g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.6h1xk*zlb: 7tgp a) bh(0 m. Calculate the magnitude and direction of the total gravitational force exerted on one spb1p hxa):ht bzl(kg*7here by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line u3;s9nui l44a-oyix+azhlp -w p 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 (Figa -i p3o; +zusn i-4x9ylhwal4. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of whz pvo8/2tyot f f:9;ud0qwg:kat it is on Earth, and that Mars’ radius is 3400 km, determit 8 fwq2/9o0kvoydu zfpg :t;:ne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun/w/ jgq9o x*e/ayw8 msgzn 2. nlt,2ra using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to t*way/, o qtwma x8 jrgngnzs9 22.el//hat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the E)n:k ul y. rgh1;(tqexz5fcwnz w2(i4 arth awgk(1e y2: in( 4 rnlzzxhutwc) .q5;ft a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km n*wbfaej731xy;u k8r :zr9cogxrb59+ z2 h muabove the Earth. How fast m :nkbwxuyzr+b3cor x5m19 afr*7ejhz;89u g 2ust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occup1mw.sj2jv zhf (o-z s:wu71vc0kmn; kants 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, Fig 5–cj;m n(1ms 7z2 zw 1-jwokv.s:0kvuhf32.)   

  Determine the time it takes for a satellite to orbit the Earth in ib 3o:/ dayn4 3)ocsnca circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite? ocbno) 4/:sy a3ncdi 3   s ~    min

  At what horizontal velocit10 nb23z4w(nxoeg 8uoa1q qrly would a satellite have to be launched from the top of Mt. Everest to bg0e 1on 8xw 1(4r z3no2qaluqbe placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missj y31 k qu(s-etbr4dh3ion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to -h3dkuty13 rs4qbje(go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The inig/sq1/9l f. l m*pwnvne nq*.pl9 vfgl/m/sw1ir radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once mv:8 8gmk,hr6kgy1bx i ,+i oaevery 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 bottommg y8xa+vb, km86 :ri1k,ihgo ?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 420bc)1k*kfg9.5vwti4 ) oj(h d )pyg hqo0 km from the center of the Earth's Moon h 1) )hgqfp)b5k9w*do.4vk(oitgjcy in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system con n jz e:2hkqdyn4m20s5sists of two stars of equal mass. They are observed to be separated by 360 mi:zsn q4jh keym0 2d2n5llion 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 -41pthf4+b eel+y p)za 7k5en;ghd jg the weight of a 55-kg woman in an elevator that moveshgn+a;p + lfhzkd4b e -pjg4ety7e)51
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceil/fxm j84*ni6joq te l y2x*kf9d9o 5cging of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and djqo 4im8od5jf ec6 g9x2*x f/y9nl*tkirection)? a =   

Show that if a satellite orbits very near the surface hrro)n tpb 9t/a6.+94hzlhpmof a planet with period T , the density (mass/volume) .o69/lm+rh ph 4btt rh)p a9znof 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 deter0pxzrm1itf iy90 5d1vmine the period of an artificial satellite orbiting very near the Eartv50mdip z0r119xyif th’s surface.    s

  The asteroid Icarus, though only a few hundred metersk0 2nwg4/uydeoo *un2 across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fromn uy0og k *un22o/4edw the Sun?    $\times 10^{11}$

  Neptune is an average dv5gv2 b h z(vut8x:gb(istance 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 76 years. It comes very closeder0h9 (wnk l+ to the surface of tkd+rl09e n(w hhe 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 centp.js /wzws: 1-mh3 rooer of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and z2x5d8kwdbm 1 mean distance for the four largest moons of Jupiter2x5m dz1 kb8dw (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 known pt87 iip3 (swgu(wh* fteriod and distance of the Moon. (3 sf87i *htwti(gu wp   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Ju+jz 3p;n f+ n;j6yksxopiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valufnk;zj6++xp 3n; js yoes 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 Jupi-xb2/flffyud+ kdw71ter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was f /2+bxul1yk wf7- ddfdestroyed).
(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 ta 3;iv ktqst+.xle describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhai.v +tkq3s ;xtbitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge vy4qif wk:*(nb/w xs0by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the nw (iy/xw4q:0kfsvb* 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 will 3sgt* ;fw4v .bsc,omx12d/i*cge o jot8lcx*the acceleration of gravity be half what it is on the surface?1o4v*sbigj*fxcxl83t *c2 c s, w/.g ot demo;    $\times 10^6$

  On an ice rink, two skaters of eqgog x).s+ps/sa+bfizq 3/8 odual mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms ar+d+if/ b 8o qgzos)3 sga/pxs.e 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 d3,of dt0jw ek6ay, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude odjw 0 t,e36fokf this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wix m6w6no+8 ui(oc ymf+vp-p4 ell a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces+mio p eufvm nw+-yxp6o8(4c6?    $\times 10^8$

  You know your mass iwuqo;fo1rw8ul++5t mox /7ygof )np 1 s 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelem r;yuu1/8of q5o)t gl pf+o+wo 17wxnration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consixvhrriw1o:23esl y4 -sts of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The c14 yw2i:o3 r-helxsvr ircle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical wp ks. s(nd0(tuuzxxcxd-5mq .5v6k+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 th4 uq/chc48 sque mass of a planet in terms of its radius r, the acceleration due to gravity at u qsuc4c8q/h4 its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical bymc)/y;oljslf 6na)bft :0d, p an s,;fm:y )bd/ o)t j pnl6lf0acangle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of s8d; *gfki+bm7v5f t 4nfzg x3wtatic friction is 0.30 (wet pavement), at what range v +x4z87tnwifff;* dg35gmkb of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so)4jx -f+ dvif8fjt44nyqsy 8b fast that objects at the equator were apvqfjy-)ns bd84i+jxf4 8 yf4tparently weightless?    $\times 10^3$s

  Two equal-mass stars maintasqsfz.(k zb95up fy. +in a 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 2p4d+ cad;bbxbti(. : e35 m. A lamp suspended d.adb;bi:x(bect p4+ 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 times as massivnvbi+kg,gu +m 1xdp +idi0f:3e 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 Jupit pi,b vid++3g ding+0u:mf k1xer 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 thekat 7 hgtoh+ezsa13 5. Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it o5z.he+ s3t7hgt k1 aacould 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 sp1dsj ht)):u8nm+ xq5vsw:gf, n8n w vgeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is larges tq mvng :5)1ndwjhsx)8:un ,svw+8g ft? 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 Positqvk -bsy63th9o+4f jue v/fr;ioning 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 e 43 j;thvb k+u/v6-y9fsrfoqof six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 b0 ifbqo/gsl0./:lrfgvvft;.,)t w we illion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly ivvq) ;b.0g.t:wt wef/r/s0o l,lg ff40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of rezh-u)g yc2 sota-pey6+h4l 5bpair. You are in-uy4t ol6gh)e5z cab yh+p2-s a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mea 5u* 4w)a5ru -8vmwvu vv-jrjzn distance from the)jra-* u8wr jvv zmvwu 5-u45v 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 " dqeq7btagtk;3um-m er+r6,1 feel" yourself gravitationally attracted to someone near you. Make reaso eqa67mk3gm-d +,qe 1rurt;tb nable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46)l kfls ki )vetrr9;k1;wv;,v5 at a distance of a;;r t9l rk slk ,iw;51f)vkvvebout 30,000 light-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 on each side. xy-i zxg(.u: fn8gf dt;- y19vlnyu 3nFind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square. n31 gy f-zduxv; :.yt( gyxun 8-i9fln   $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ebytk*:fzf3 ylv:gc b+ ,3rg: barth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep 0x5eqgkev*8 m second kxeem*g q805v hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swnp3z2u)/pd:nra7kl qing a sinker weight around in a circl2 n7pr)u3dlqp/k :azne 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. 5–10.]    $^{\circ}$

A circular curve of rvp)r5( j i7y mueiau7/adius R in a new highway is designed so that a car traveling at spyv i)/5 eujpu7(m7a ireed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whaae ;o.d8 m6jnen negotiating curves. The angle of tilt is adjusted so that the m aa e;no86djm.ain 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 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.$\approx$    $\times 10^2$