Sometimes people say that water is removed from clothes in a spib).7rkq+2 pmbw rz p x5 -4iulma/ qbdlas1;3rn dryer by centrifugal force throwing the water outwra x+zqrbm3m bk ipd7rs-u.bp )l4/q2w1 5l; aard. What is wrong with this statement?

Will the acceleration of a car be the same when thf*30c5 z/ustzywt7te bedr ( *e car travels around a sharp curve at a constant 60 km/h as when it travelz3b0t7 wfzt ce**u5 s(dyre/t s around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does th)t/cz te 8o9 /tlb,glksf 75mhe car exert the greatest and least forces on the road: (a) at the top of a h) c,ht9zs/ 5b/7toe8kt mflg lill, (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 childp f85zfcu) :az riding a horse on a merry-go-round. Which of these forces provides the centripetal accelera8u:c 5fz fzpa)tion of the child?

A bucket of water can be whirled in a vertical circlrska4 :lk gq;5e without the water spilling out, even at the top of the circle when slk;a q5r 4gk:the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least thar08y y0gzb847epd6 ry lw)uu ree controls4lb u8 r)8geay00dz wupy ry67 in the 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 of a small hill, as shownqp*an/njss rl 8094l o,raqnvqz 4+f1 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 go4f/jlqs+ 9ql*ar n4rnz pq o,sanv180es over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundit vfjaj- dlm1g0/n c(;ng a curve at high speed?

Why do airplanes bank whekd x.6e tqao,5n they turn? How would you compute the banking angle given its speed and radiu65qetadxk ,o.s of the turn?

A girl is whirling a ball on a string arouniy+d94g 8wc9fm2xpx 9)sjdlt d her head in a horizontal plane. She wants to let go at precisely t)pd49 8dygc2j9 f+x lm iw9tsxhe 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 Earthjz,t bchbkk7y sgf;5yj,7d6 ,x2 cdj *? If so, how large a force? Consider an apple *k7 ,6;xc,ky2fyz,jc5 bdt dj7hbgsj
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doub*z,bds5x,g dd le what it is, in what ways would the Moon’s orbit be differendgxs*d,b d 5z,t?

Which pulls harder gravitationally, the Earth on thef: va*tlr*r cqreba 2u,)37qb Moon, or the Moon on the Eartauq* q*t,ra7b vbrr 2 3)l:cfeh? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger ; i6bh-qvf:i zki,1 glrwby,6f8 j2dothan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the dif21i,wjydrh iqlb gb6f6i, :vf kz;-8 oference 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 effe74ng *xd,hytcw g:*zscts are at work? dt*xzsg47h*: ,cg ynw Do they oppose each other?

The gravitational force /q6knxu:q hgo npa78u):h 2rmon the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why mr: kuq:ouann82)7/gph6qhxisn’t the Moon pulled away from the Earth?

Is the centripetal acceleratijnsw w9)r nx7n6o3bj7on of Mars in its orbit around the Sun larger or smaller than the centripetal accele6n93wj jnn )x7b 7sorwration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) tol ;zr94r *,ej c*d6ppyog a+pxward the west? Consider the Earth’s rotatiocpezxr9l 6 *y dp4;+rjpao* g,n direction.

When will your apparent weight be the greatest, as p -4hy. l;ym2zj/vdml measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as /; lh.24yp d-l yvjzmmwhen 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 affect(o7gl7s o c yuhrv7r0j;n+6:ygu4kpt ed by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other asp+vpo7 7ychlugnt76 yj;krg r (os4: u0ects of gravity you can think of.

Explain how a runner experiencev; q n25o-d hp-ot5xdqs “free fall” or “apparent weightlessness” between -5d ;onqq vp-o5hdt2xsteps.

The Earth moves faster in its orbit around the Sun in January than in2rn; efhyzmfeq1qe: mi8 db4evg3 4;r1k2v 0c July. Is the Earth closer to the Sun izn8 q4c gff3r10hvem e2 ebr1k4;e:v ;qid2myn 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 to the plane of its orbit.]

The mass of Pluto was not known until it waa/lm5zq 1d8- sum/5knmdrv j(s discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s 5r d/ m5zadvsmu8m (lknjq1/-mass.

  The Sun's gravitational pull on the Earth is mumn cur72t 4ndtkj53(dch 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.]d 74 5ur(mt2j n3cdnktA 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 ohwf86 hwhozryw** 4 (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 acceleration of the Earth3 -m3tdb*b 0(b )*gg .;mchfck zhnt 2t3mltlv in its orbit around the Sun, and the net force exerted on the Earth. What k0bl2tt* ;mc33(3cbmfvbtdhh tmz *g n.-g)lexerts 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 N0r2f;v 3 cp por2lwbt6obp 1,p is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lenb2tvo,w;p o6rbp1l03r ppfc 2gth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is t0zy:svrfdd:ip48 9k m4f 9yrin orbit 400 km from the Earth's surface, 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 r::s8t0 9 iyfm4rdydv4fz9 pk g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a sp ha/f 1eb.r1/ (gymjuueck of clay on the edge of a potter’s wheel tumj1ahre(/f u1.gbuy/ rning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolve2s oz mt0 b/ wq5epak0ejtluvl6x/;,0d at a uniform rate in a vertical circle of5u pev;mlwt 2/6ebl0/oq jkatx,zs 00 radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kgf0np*l0pl+) dz-n orh0ic 0dsw;v8 l l car can round a turn of radius 77 m oph )0 lwf lc*z0r;n+ddl0lsnv-oi 0p8n a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betwet-5 ,1y derv2oqayiq 7en the tires and the road if a car isr q 72-ayet5,qiov 1dy to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training 0x+ svo2i /389nb tpq.zgp xmds 2n/idastronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of rax+gp.2nn03p otqs/8i/ddb i mx92svzdius 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 axisz3u(qnz( 3-n 3knl ; 3rhjwmmq of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between theqwrhnl 33-z jz (q33(k mmunn; coin and the turntable?   

  At what minimum speed must a roller coas :quybh ca-f)7(w fd)fter be traveling when upside down at the top w-):qh(du )afybf7cf of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the do3kx1a/; :jtszlq dmy 3ym:7rriver) crosses the rounded top of a hill (radilxz3k7r/tq 3ym;j odysm:a1 :us =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 whe 3 n7d.r/k9t.h+ )hgqyexedb)q2 lzdkel need to make for the passengers to feel .eg3d9 / rzhk)dy7qxtbq)hdenl + k.2“weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled +n ,6k4-zhzt*vfh qxpin a vertical circle of radius 1.10 m. At the lowest+ vhktnh4 -6 zzxq,*pf point of its motion 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 parx.axad2ws. /5q+jrkvd s )jo;ticle 9.00 cm from the axis of rotad .r+jkqa.)2v;/ xws sxaj5dotion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cbj))p qs :hr;larnival, people are rotated in a cylindrically walled "room." (See)h)rsq:j; blp 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 ai4gmikcj kyl2iiw480( r-hockey tabletop, and is hel 8 4lmikwiyc42i( g0jkd 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 , prpl ,u u0e02+zkixu,)ozfqad ( ecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In pazo a(q, pu2,di+ 0lxk0)u efzurticular, 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 perfectly banked for a car travelr/0cc,hed : p ajhg3u3i( it3aing 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 masse8 *tzq 0ssw)k-t6 ojtpx3 7dubs $ 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 eva-fz wm10uio , :p)0kktgxj53i0 gcwd nsive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of thvmmg bs*:3kz2*;kjat 8o x .d ib;ss0ve net force exerted on the car (by the ground) iv3mas2x0vd; :sk kzo*stm .b i;8*bjgn 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 Indianapozm( .q( z9v z2a-fsuvylis 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 itfu sz-zqmvz(2 9y(a.v 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 hor, h.fw 6v0g3jar.ap z.w5pa jyizontal circle of radius 2.90 m . At a particular instant, its ac3agjav ,y6.hrpj. 5. awwp0zfceleration 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 Earth rb p2o-svzk/x1hl7 ;mc adii) abovekhp17sb;-x omv/2l zc the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain 8*4g*yter u xlz6 ):nczbqtd 8planet, the gravitational acceleration g has a magnitude ob* u c8gne*z6z8xdlt q4 y):trf 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 Mokept*ses ) : wd;97kz. vbagt*on. The Moon's radius is 1.7 wpbtta7 s.vk: )9* *gedks;ze4 $\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, buten h 5y)lanm7+ has the same mass. What is the acceleration due to gravnm7l)e5yhn a+ ity near its surface?   

  A hypothetical planet has a mass 1.66 times s+n xcw ,v+,ygthat of Earth, but the same radius. What is g n,+,v+w cnsx ygear its surface?   

  Two objects attract each other gravitationa0(qmwrhy n/ e/ s*ri/ally 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 , the acceleration of gravity, at (a)0 -d.m1kvd.fc n;gwd/ : b.tj4r oyr2lenqh7 l 3200 mv r nl7/w2oj4d1dc0e:qb gr hkt.fm-ldy.n. ;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth r gu00.+bxshh2uogt ):, xjpd where thegravitational acceg20hupx .sh) gu, r0xd+ot :bjleration 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 mass of our Sun packed into a sphere a(ub6,sywaw+ ej od)w+8huym) bout 10 km in radius. E+m) )j,dw(8oaswy+hwueub6ystimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwar9 +.swsva6x0y ictvtabr. f* v(;mg-pf star, which once 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 pfvv..v * w-tbi 9tgra+a;sm6x( cs0your Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fee.h6k*3c 0jmu/cm z p nnm)kgy;l weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acmzj ugh ;cm3nnk p)k ./6m*cy0celeration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lok6mka8 na bw/-cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravimn68 k ab/-awktational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side osqlqd u5ql 4 h 140i)dq6r0bpnf the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Satuqr)4hdqsn1 d6l05q 4p iuq0blrn, assuming all four planets are in a line (Fig. 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 acceleraz3 gwiq rz06m+tion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine t0w rzq+z 6img3he mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the c5pvuo/a21 3 6d5zv)dmyedemEarth and/p1 2ezdd6)d5meyvv 3cuo 5a m its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the Eed axc:(e+d,barth ateed,bxd:a c+ ( a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circularpdd 2j;dx+gp6 7nz2rw4 l i czb/,eq)e orbit 650 km above the Earth. How fast mus/ dcw; nrle6d)zdp 4gb2e2,+ij zx qp7t the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiencmo tabla n4a-4o2a(8he simulated gravity of 0.60 g? Assume the spaceship’s diameter i(abn8aah4l42 om t- aos 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 satellite to orbit the Earth in a 0 u2r)98as9r x fugve h2awxt7circular “near-Earth” orbit. A “near-Earth” orbit is on9rxa0hv 7rg2au ) 2fswuxt8 e9e 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?    s ~    min

  At what horizontal velocity would a satellite have to be lafxfe 7d+r f96cunched from the top of Mt. Everest to be placed in6ecf d7fx+9fr a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module ccbti 5fv-9hkztf 6*+i 0 kyfn4ontinued to orbit the Moon at an altitude of abkfzfi k9tcbnih *4yv6 -5t +0fout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are cya8s01c v/hwte,yk arw 071 adfa00jb omposed of chunks of ice that orbit the planet. The innrva,j a 0y0c87 w0es1aahdtb01yfk / wer 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 rzr-, wl7,a3xw xx-tjonce every 15.5 s (see Fig. 5–9). What is txxw a 3z7l,tr,x- -rjwhe ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparentm nm q;6noz/r, weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle/mn 6,nmoq zr; (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 t7fy:;8;hng c ufuu v-ywo stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the m-h:;8vgyuy;ufc n7u fass of each?    $\times 10^{29}$

  What will a spring sj6:*4/0 esnwtnkqq mv,*h sklcale read for the weight of a 55-kg woman in an elevator that 6*kl* tk 4/:e hw,sv0sqmnqjnmoves
(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 coq4rlx/g jenc,.a s69erd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelerat,egqa/ e49lrnxs6.j cion (magnitude and direction)? a =   

Show that if a satel;2q8)ve8hgkiz g .i. f dsfg+ylite orbits very near the surface of a planet with period T , the density (mass/volud8q;gz. +8f.sk2vhfyigi) geme) 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 det4c4 3wxvcm2izermine the period of an artificial satellite orbiting very near the Ea43 xc42vcmw zirth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acr9l3(htig*-aq1 3 z ow, ym7adzui5ur eoss, orbits the Sun like the plt mz5, *o g a(3ez937lrdahyu1iqu i-wanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.p3ak wt3z)9 +3a sod 2dg0mtmg5 $\times 10^{9} \mathrm{~km}$ 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 everhzqjuy h3/9*:xse nlqb w(t 84y 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 near4ybtjhn* el9uq(/xhw38 zqs: est 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 the G na.m +-v.v: bzb-vkejalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four lpebq ii8xux h 5)1,tp2fz5 q4-tk2bqaargest moons of Jupiter (those disch) fat2,bx2 q i1 8z5-qpexq45kt ipbuovered 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 ,p;nh8,2fyew bv vtc (the Earth from the known period and distance of the Moon. ,h2bf pt (yevv,c; 8wn   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,-;a; 9h lnhrlx using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to h a-nhlr;l;9x 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 mtujm v,f3 av 53ltz12rany fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyet1v3zr,um l32tvf j5ad).
(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 arti9 ,q93 y3)wuj bdypyucficial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is j39duy bcw, up 3)qy9yalways 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 by swinging in an arc ym26o8mfis eo- 2fy)ffrom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can toler2 y f86)fo fei2ymmos-ate 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 gravity be h -mj4.vt.m hbo4my7dmalf what i..4 bt vmjo 47mydm-mht is on the surface?    $\times 10^6$

  On an ice rink, two skatersy) b5: -fhkaku of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms aukhf 5- :k)yabre each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerat*xfk cpd waz f66;.0rxion of gravity at the6;w.dxf0ckxarzfp 6 * equator is slightly 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 4s7a0siyiq9 e70 cri)pugjn3 the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull wit)07aspug4ey i qnic 3 j90sr7ih equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sc)e j1vfx (gqp*ale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator,)j(1xqevg p f* and in which direction?     ----待选择----upwartddown 

  A projected space stat lscct8egn,0 3ion consists of a circular tube that will rotate about its center (like a tubull,0sg 8en3tccar bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hiye 3ojtjr(q ) oru76i ,0pc+qss aircraft in 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 alh8s4s6wpiun11 7yr* lx8 vkk planet in terms of its radius r, the acceleration due to gravity at its surfac8vsysrl6x71l 8 uk wphn41*ike and the gravitational constant G.

A plumb bob (a mass m hanging on q3w hwomfq7rskbbl*9w58 f99a string) is deflected from the vertical by anq3*9 qw bwh5r sbow7m 89f9kfl angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design 1 11l0l dmxn8-d-i jtkc9m+l lx4db clwl7v2m speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of spj1-dl 921t -w4llmnll xvb1 +7ci80dmmclk xdeeds can a car safely handle the curve?

  How long would a day be if the Earth ws uc +5/dg*lkxere rotating so fast that objects at the equator were apparentlys/5l dk +gx*uc weightless?    $\times 10^3$s

  Two equal-mass stars maintain qp 5huby ,,kj8a 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 sa0:t6 s kvmn24gick u 1bli9*ppeed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to i2psbu1:9tvma4* n i cgk0lk6an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times j9 p48 mpkkwop48 +lg7b lgm-cas massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planekb 48jmk-+pcw9l4g m l7gppo8t 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 Hu2v wa9b:he6f2m0b hkf bble Space Telescope deduced the presence of an extremely massive core in the :2h9wv2f0bhkm bf 6 eadistant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valfl 7gg;l)0ysp wm xa7i7ou:.:x tj9ou ley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forcewmx.l:7yx 0 7i sp:gaou gtf7o ;l9ju)s acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Posidb5 + q 9hv*mf7.hf, v8uejf,ev1x ejotioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of ah+ 8fv1 evjbfd j7eex 9u5 ,vmh.,fo*qpproximately 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 travel ti.se;)fg sv 74(ks1 yodk:p(w 5fkuxing 2.1 billion km, is meant to orbit the asteroid Eros at a height of s y k 5 4f(.oikd v71:fksg(xe;)utspwabout 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 in neh-sk rco-6lqqw38 sw 7ed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. hq 6sw3kq rs8woc--7 l
(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 distance 0:3 ddrq9frh xq :i3x bsrv,t4from the Sunqr0d,s q4tx3v:xi r:b3r dhf9?   
(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 jmyyc27x8eo* actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like oec2jy 7yx *8m F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a f fslu-zr)36n rq3 4kndistance of about 30,000 light-years -r3n4k )u3sr f6lqnzf 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 corner 32plt,kgyzy1 s of a 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 of th t ypkzg1yl3,2e square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg n a ++16v;n 4n x,yyxrzvtr5fes14irh orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the (y/cdm- vxa(u n,,8xkk zu5lj1.5-cm-long sweep second hand on your wrist kad(uj/, xcmkun(v y8 l-z,x5 watch?    $\times 10^{-4}$

  While fishing, you get bo9 0hojp5lfme. go3w 5ored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle evle0.j w9m5f pg3oooh5ery 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tratwwbvy;:nx- 9t*avsf-3 ( hrdveling at speeda--(tv 9tysxdwrf bh 3n* vw;: $ 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 car fkw ne7/ upq,f6m,8nvs 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 at7qnuvk 6,mfnp,f e8w/ 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.$\approx$    $\times 10^2$