Sometimes people say that water is removed from clothes in a spin dryes.c1nix2 vg5jt o:t* zr by centrifugal force throwing1jnci s.*g5:x z 2tvto the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels aroukji) xigx ) ze3gd 0csj0,tg:4nd a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.gic)gg jtsxzd):ejk40i03,x

Suppose a car moves a6kdjrf38mh9 hiuwt 0 n3bg48m t constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) od ihm8g0 fj34kw9u8mbtn 63hrn a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a mel57 v;hk(xa nzrry-go-round. Which of these forces provides the centripet5vx n;az(hk7l al acceleration of the child?

A bucket of water can be 8qsfi;p(g 2j/kb d p2uwhirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain./8 2kdqs2gpi; b(jpuf

How many “accelerators” ;l -+e0obu 9-qzv)rl c v7oyaydo you have in your car? There are at least three controls in the9eq)b r l;lvz7 yc+av-oo0-yu car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest sj2oivdxsop / p(6v /k. n(o u5th1uo7f5pe7 lof a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and th t2vu(v/p5.i oo5oek(d71p sj/usfpn6x lho 7 e 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 curvejyfu3okg c 8t 34c:,z tv)4lss at high speed?

Why do airplanes bank when they r+hqdtv2-bo ezu +.t6 c*(lwy turn? How would you compute the banking angle givet+vh6w ye uo ql.(t*2rb zd-+cn its speed and radius of the turn?

A girl is whirling a ball on a stri*7fgieiv ij-7voawr 5 4p+k o+ng around her head in a horizontal plane. She wantvg7p 5kwv jo-i *4o arf+e7i+is to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a f h( ;v o3s8rs2ui .esr2.sbfztorce? ;s hs2 3.z 2r8fsi(seurvo.btConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wppy + rf5e-c ()meo5j8b zy:fnould the Moon’s orbit )5yyb+pme-cf (8e r5nzofp:j be different?

Which pulls harder gravitationally, the Eac bxb cy(v0*g ci uzttw7:13k-rth on the Moon, or the Moon on the Eartbvu-y t7wzccb:c1t k g*ix 0(3h? Which accelerates more?

The Sun's gravitational pull on the Earth is muco:*/ )yo9wsk :qcn*;ujk r+ goipiq9t h larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Conu)jc:9yo piq kqg+k*o9 o ;is* ntrw:/sider 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 t4t6 zyua 7tvpjc+ ga9-wo effects are at work? Do they opposet7j aapg+zc4tv 96yu- each other?

The gravitational force on t/q s qm1 zlxz,6lc+ci2he Moon due to the Earth is only about half the force on the Mc ,26qzis1+cl q/mzlx oon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largep+9,dxpu +9sqv2ksak r or smaller than the cena2x+qkk+spd ,9pu sv9tripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towj xl/*qkv1l7/6mv y rward the east or (b) toward th/x7 r*6vv jmlqkw/l 1ye west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by1; /s2bct.hbk7sxi q ny05jis a scale in a moving elevator: when the70bcx s 15hi/nts ij b2;ks.qy 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 periods in outer space could be adversely vsztbosn:9 -c233hi z affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shizovt h zbs9-s3 c:n32ell 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.

Explain how a runner experiences “free fall” or “apparent tye5 yq4:evj-weightlessness” between sy-j : vet5q4yeteps.

The Earth moves faster in its orbit around the S/p 8 f;t0svhwrun 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 fh;wt/r 8sp0fvactor 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 wa vp 7k8(dsm h/c/oj+jts not known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Plutosjpjkm7vd(t o hc//+ 8’s mass.

  The Sun's gravitationa -*ap2 ,xri.0zcyjndyo x5uj7l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m0 yj xc 5.y,rp uj-onxa72z*di 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 198 6p /gyka4 mr2i.gsq;l0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetalvrjm6sjq m7qn / fww -yi2qgz22; sk;; acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What ; 2 rvjsg s-;7wni62w qzk;qqm2jyf/mexerts 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 ecga;2 .mgp*njze20eh xerted 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 discus.c e0e. mg;22nazghj*p   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfac7fkt.c6 k 77kqf (nk ve)s)e5dfems; we, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the () m e7;)ds efetwqvff7kkkcs7 5.k6ngravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck tt(q g70k w li ghzlo7yc52.r1of clay on the edge of a potter’s wheel turning at tyh.wlo(ltkr g1q72 z75c0 gi 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate ionv8iilea ssc9 -y0,. n a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speedyi o90 s-sa,8inlev.c 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 c1hlni +;c+hf*zi r7fyar can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indep7hfic* +lrhi1+ ;zfynendent of the mass of the car?   

  How large must the coefficient of static friction be between the tm gnw8lb67x-q7zo 6x46iryixires and the road if a car is to round a level curx nxl7g q-m7yi46x rbizw686ove of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter .px (:lf.gxo9 -yybikpilots is designed to rotate a trainee in a horizontal circle of radius 12y gkl.bpo.-xx i:9(yf.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 vg(/pk fx61bglbqo* k. (u u0ueariable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and tq(b1o.g exb*6kl0 pu(ufukg /he turntable?   

  At what minimum speed must a roller coaster be traveling whec 9 p(-i)xbmgen upside down at the top of a cir9(epmicx) g-bcle
(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 (in. 23 8r22:hsh:bal jkgjhlqcbcluding the driver) crosses the rounded top of a hill (rh .ab3gl 2q:28hjl2bh crsk:j adius =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-diametebs 0uzn- 6e,)kl zoll(z2s*cxr Ferris wheel need to make for the passengers to feel “weightlessz l62)k*zsx0 (,ebznu l o-scl” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At tq */tdlsx-.6tde)+ m1v 9lmrb vfnijk9x s28 nhe lowest point of its motion the tension in the rope supporting the buslidd1x2qkr *9vb 8 9nel)v mf- m.snttj/x6+cket 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 ;qxeiaq6y /g-u( u2rrqcfvt6 s- :z*i a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accei6x6-rv-rgqs efy tqz2 acuu*qi;/ (:leration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rleft2cf6u 3d9 otated in a cylindrically walled "room." (See ue3t9cf6ld2f Fig. 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-h9 *e0hiabw )rcockey tabletop, and is held in this orbit by a lighti0ebha*)r w 9c 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 time, by not ignoring the weight of ty3hivuqmanm5a:a 10 6 he ball which revolves on a string 0.600 m lo auam 60vhmqn15y i3:ang. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfh jv: 5+fvp*d/z7yrp*y4ypd wectly 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 masses )uu q-7apanj6$ 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 a7xsjez 13 y:wyt 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 net wo1i wgk,q 8s;hcqn fiy(/;6b force exerted on the car (by the ground) in Example 5-8 when its speo1kbsw,cfg /in( q6i; 8h;y wqed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit arny6sihaz/ xs* z+ )e)jea, going from rest to 320km/h in a semicircular arc with a radius of 220 m+szx hiesyza)/*)nj 6. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circl/n dg i;9t afadll*+au 70/ybie of radius 2.90 m . At a particular instant, itsd* aa70;+gay inf/dt 9ul/ibl 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 gra*o)+wq dv8)p b *eybo6edgqd0 vity on a spacecraft 12,800 km (2 Earth radii) ab68vywqqp*+)*0b)db od edoge ove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the graotfo rw4.h4bb;8v qy/ vitational acceleration g has a magnitudvfq/;t4b h8ob .r wy4oe of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radimpps tc9i 7zt u4 9v3,,ag/smfus is 1.7avicf/mt 7t ,u,spp4m9g z9s34 $\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 Earvz1pv :0d,jmwwdn 2*m3v zjv3th, but has the same mass. Whadwv3m3 ,v2jz0 pjd: vm1zv n*wt is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but0 zk06x*azpqp:ur c -d the same radius. W0z*:x0- krdazp6u pcq hat is g near its surface?   

  Two objects attract each other gravitationally with a 3; ow0 ewha e5fegksedv23+9bforce 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 aj3q4ey fyp9q 72; tqm*g.t m5-aesad pcceleration of gravity, at (a) 3200 m q7yt953 ;pda*e.sm4t peja- my2gq fq    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from thp5o -g6nsg ki6e Earth’s center to a point outside the Earth where thegravitational accekopsi gn 566-gleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star sk/52ysoy l- nu0jq p/has five times the mass of our Sun packed into a sphere about 10 km in radius. Est//pks-ylsj25u0nqo yimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncnbewwpi* )).q ymex: sxt)p-d 8r1 8hle was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but dy*x eh) ex)rp-.s8n ww)m qi1t:8pbl has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in tokh+)4 .hyyrp :l tp l0w:if3whe space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yo:3wyltfo pl +4ph)rh w0ik.y:urself 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 0.60 mu7h )m2hrkeomdq+or ;u) q 0v(. Calculate the magnitude and direction(2ueq) um;+k7hd0orq) rmo v h of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostw/l ahf5 7epatom/c( 2 of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (oc5mlat /2ha7p (/w feFig. 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 what itjm obsifh 3ih6n: 3-k/(xyp7b is on Earth, and that Mars’ radius is 3400 km, determine the mass o3hxh- f m:/kbs o37bipyj 6in(f Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known9o:vktc)vs l 4qxay r(of1m s8u u.1gwkb(f6: value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, gcfy4osbvv( 6()9 8m. o1: a t 1su:ulxkqkwrfExample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbitvqh0md) 1hu6 50y0nllp+ jcft about the Earth t10u m5lp6j+l hh)00fndyc vq at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular ox4*fff;l a kc4a5ob m8 qr*m9nrbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release oq5 9 4for4f mxcflab *n*a8m;kccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantsvb x)sj 20zs2ur g+*c5 wgmkk4 are to experience simulated gravity of 0.60 g? Assume t)z*cks40sxugrk2jg 52+v mb whe spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satecw4u: lg bm0wfd02c7j llite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height abowucc2 7ld04 bg :0mjfwve 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?    s ~    min

  At what horizontal velocity would a satellite have to be laun tua nix;+w ,fc9u-jzvl*- :ihched from the top of Mt. Everest to be placed i;wj9xu i*cv:a- +hlzfn-u , tin a circular orbit around the Earth?   

  During an Apollo lunar landing mission, b swf;fo)6 jw 8i4e,uvthe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go ar s w fvfj4iu8;6o,bew)ound the Moon once?    s

  The rings of Saturn are composed of chunks of ice 1j(kiwdx /-,4qs6vi gbfq g wk or5+9ethat orbit the planet. The inner radius e kigq9bwq1(j4d+ 5 osx6/rfvgk,-i w 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 evmqv(o41* kkafrovu a3)k)i z(: p s9ekery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real wei ( :f(iookr1m*kkap) eavu3kzv) 4q s9ght (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 center k1gh 908wcm;,0wtzj7gj8d rlud m -nlof the Earth's Moon in a space vehicle (a) mov w c t8zg9-um8 gr,n0jwjd dmk1hll;70ing 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 stars b-7g n:b7vay6t( bvr yof equal mass. They are observed to be separated by 360 million km and take 5.7 Eart6r- vay7 nbbg b(y:tv7h years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-o, h182 jvuom5;ejdhgrl kv)3kg woman in an elevator that moves 8kvruo j,2;h3 jdm) lg1h5oev
(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 sllut:p.k + uc-p(xp*iuspended from the ceiling of an elevator. The cokplp ( l+pcx*.i uut-:rd can 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 orbits very near the surface of a planet with p)1aeq:l ms( ayeriod T , the densita:saq)e ym (1ly (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 determine the perfc. iv,b:pd3m+j u ns-iod of an artificial satellite orbiting very near the Earth’s surfac. :ifc,+ -vpdn3sumbj e.    s

  The asteroid Icarus, though onlalf91wvv/wp,l895lmeams2 63 oxxqqy a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is it5,9sx v 298mw a aoe lmvq1f6lq/wlpx3s mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distahd +*((vzmirk.;cgbc l*md 5pnce 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 Sy 5 juu5 ok(u.(qm:k2 4dohe,k ii0ad24ta bndun 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? [Hint: The mean distance s in Kepler’s third law is half the sua5ad (50ntuk ,h :o u2kjm424.ebd ikiud(yoqm of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center 0 6pfm0u ,ukjl 8-2nakcjg;agl: kl,tof 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,,-nd.qr* w r29hq9fvn ,ere7pnqyk y4 and mean distance for the four largest moons o yehn- p 2d4,9rwqv, q.ek79r*nfqnryf Jupiter (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 knuehy6 4s0enep-ry 0 mexz7l/ 9own period and distance of the Moon. 7ym p zxl9h4ruse-/eee60 yn0   $\times 10^{24}$

  Determine the mean distance from Jupiter for3cbj,ufin/x:)w / xtk each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valuef x /ijxnwku)/ :bt,c3s 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 6 *xpgf pas62nr,yso: consists of many fragments (which some space scientists think cn 6psor apxf,:g6s2y *ame 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 "planet" in the form of a band (ufa5m kwub35p:p91e nekt w:completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this plan35wnb::ektepm1a k f95 pw(u uet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5– f74xfqsp46e g41).p446x qgffs7e If his arms are capable of exerting a force of 1400 N on 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 will the acceleration of gr9 qoz1d o)5x6lpxtr7v avity be half what i759xq1d6tl xrvoz o)p t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spv-rxq: j1v,ha ,o-iwe in 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, hexa v: h 1v-,o,qwjir-ow hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra/5 hme+iedler55gtetd y:r, .vity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction ee5t5ddlei 5/myht, +gre.:rof g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spa3y5+iy ok e)jvcecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and + yiv3yj5eko)Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yifg yt6fsz;4p 64;tb iibp- xm .2nvt0mf-4j pou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is .6ipi4pmb ;n;v06tpibzxf2t4 m4yftfsj - -gthe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular 9wjab,o,f i2t0 a w3pjtube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a dia,wi30 fja paj9w bo,t2meter 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 lozq 7g6sk:f 4jaop (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 t+eeni/z76)i m k ftr*terms of its radius r, the acceleration due to gravity at itfk+ez t n6t*r7mie i/)s surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectem*3cc:b ne2/vwb(n lwd from the vertical by anev:n lbwbc2 mn*w/3 (c angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m i ixmep0(s:0 avs banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a c0i 0sex:(avm par safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects :ulu kdvc /8) umf)a2kat the equator were apparentl:klkf)v/udu ) 2mc8u ay weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distan aybzoc.6u xk viflt16y)h+)rc8 3k+ oce 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 cur1eexi:v2-, ziu9rn fe ve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.9ex:1ef-z,ui 2vr ein5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times am7af,6jmgc .h vckd 35s 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 gm c.md h35j7acvkg6,f 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extr c-exrw. u zdsy95q5y/emely massive core in the distant galaxxwuzs.rdy 9ey/-cq 55y 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 h 5:6se eg*-lyfh0u*n i2ohhqspeed 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, hg6:y- 0*oihslu q* 2n5hfeheB, 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 Positioning System (GPS) utilizes a grouwgf,asa b8 o.+p 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 ea8.b +fwa gaso,ch 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 travelingoh ,s i( cn i:ybup9w9s/e.(km 2.1 billion km, is meant to orbit the asteroid Eros at a height of abo mi/ecb( uy p s(:wn9.khi,s9out 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 s2p 4ecbc .xg5eatellite in need of repair. You are in a circular orbit of the e2e . 45bgcpxcsame 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 mean disvnyg 2jt eth: 1r3aq*ld8)h; -f( hi 4puof8cvtance fro8 2; fhhyrtu1 hn-e qjt 4*v8:(dpv)icfg3alom 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 dda2z.l/*f rr/ yhv9e could actually "feel" yourself gravitationally attracted to someone near you. Make dz2./dyhvf/9rr ela*reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mup-knhro 3l:3ilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-h- 3 k3:lnroupyears 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 li+: h7lw,ehkq ld.q; square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side ofe,k q.:hl+l i lw;7dhq the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitswpbat)i11axwxwhrue ,1e: +.5mv f 5j 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 th i hrqov1/y;/k0sia p(e tip of the 1.5-cm-long sweep second hand on y q/kaiipy vo1s (/r;h0our wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to d3f74 jhjildn:83k yih8j4 eeswing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0njfl3d :4jheiy3di 7 ek4h88j.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 soq ;scll 5n.f4q that a car travelsc; lnqfl45.qing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela. u- 1ik ,/rgln(rspxf, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that r.1p(rufsx n ,r-g/ilk ounds 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.$\approx$    $\times 10^2$