Sometimes people say that waterx;t la75z5z,9b to 6th6+ir7d ryoul b is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this sta6+tl 7 5ahi9 ,lzb bz7uox;6to5 rrydttement?

Will the acceleration of a car be the same when the car travels aroundw(0z4j/f ts wd a sharp curve at tf/wz(s4w d j0a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alongx(ca 2;lk/e.t1gh u3 ajl6ftmx2, pb:nvvk:c 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 stretch near the bottom of a hill?f2tnhk:,: x;3 /gejlmvvkx t l12auc6p a.bc(

Describe all the forces acting on a child rir . .m mvv 8hecn+:ruqr68cm.bding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of . mcv8 :v hu+r..mr6m 8qencbrthe child?

A bucket of water can be whirled ine6* kl ml)zce+ a vertical circle without the water spilling out, even at the top of the circle when zl*ml) eek+ c6the bucket is upside down. Explain.

How many “accelerators” do you have in your car:xi0) q lz;v ibmocj76? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do tv6); b:xz 7im 0lqiocjhey produce?

A child on a sled comes flying over the crestkq2)5 vgp 5d5i bvmy-u of 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 norm g mu5i d2)bvq5-v5pykal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a-r5irx 3 tp wksdx v2;(61ocv fq+mt1l curve at high speed?

Why do airplanes bank when they turn? How wou+ 59f tz17g4jyq,bl ciu uajt*ld you compute the banking angle given its speea ylf7qzu*u1b t54c ,itgj+ j9d and radius of the turn?

A girl is whirling a ball on a string around he1ihzr4 0-o agfr head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the stringzh 4orag0-f1i?

Does an apple exert a gravitational9 2e.-l/t5e fw.kjq8uvya xn f force on the Earth? If so, how large a force? Consiqyj9ke28n .5xe /vlaf w-fut. der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were douqof(u1kz3 6wbm 0aax(ble what it is, in what ways would the Moon’s orbit be differentk mwza0fo axu( (q631b?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thv) ch)gqo e-;za s;-que Earth? Which acceleratesqqg euh );z)s-v; o-ca more?

The Sun's gravitational pull on the Earth is much larger than the Moon/7pvqbsz tr4q;h1fq4v z.05ks 3e vrq's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one hsvz 1pr 4sf7 /qvrq3q k5v;4 .qztb0eside of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wh7vo09 yjvh3/vls ul4 jat two effects are at work? lh 0lvs v9vo4u j3/y7jDo they oppose each other?

The gravitational force oniawbs/+c 3zbb +f3 o-i the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t s bc 3w3i+-ib+f/a ozbthe Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit 2ocv+ bdba 7(earound the Sun larger or smaller than the centripetal acceleration of the Evc7boad+be2 ( arth?

Would it require less speed to launch a satellite (a) vg*yx w nb9.qqmr;2nyo9e0x*qju: y.toward the east or (b) toward the west? Consider the Earth’s rotatiojwq 0 b;9meo*9ynx vu.n. y*r2qyg:xqn direction.

When will your apparent weight be the 4vfo4l6r( d+z :wlh(enlu. bogreatest, as 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? Wh4zobw:hr edl6nof+l ((.u 4vlen 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 ad bpps:qnpu,y e2 q,wu+9 9o*rhversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the iuspuq 9+2pbn*w py,r:h,e9 qonside 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 weightlessness” b09h0ye/x6 olapr ia : dm5hhl)etween)idlroym /h:h 05x e60phl9 aa steps.

The Earth moves faster in its orbit around the Sun in January than in July. Is te-ge9q( j8k uihh91 fshe 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 to the plane of its1 i-sjkg h9h8e(ef9 qu orbit.]

The mass of Pluto was not known until it was discovered to have apwvsv8avx r( 40f;q.sq qq98 e moon. Explain how this discovery enabled an estimate ofsqepvv 4 ar8fvq0s 9.8qqw (x; Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largeri08 i67ew towcl.p h:h 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 m fr.o:pw wl06 i7hhe8ict om 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 m rfpc,;fz 4wq (y,d :3:vrtza1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centriocl6mo ehrf:qb:0xzt)x 3. + kpetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts rqco): zmlt.be+: 6xoh0 3 xkfthis 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 exerted on a 2.0-p, 0r3gye; 1duuq1 wrekg discus as it rotates uniformly in a horizontal circle (at arm’s length) ofrpeg1,ed uq31 uy0; wr radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from0 l , careqykf.7t7hr8 the Earth's surface, and circles the Earth about once every 90 minutes. Find hkty 0.falrce7r 8 q7,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 cl0w i9jyw o ld3vfj76rs-73bmday on the edge of a potter’s wheel turning at 703sdm 9vf6d-wwol b37 ijrjy45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revoz ,8p7;ub9 v ebd7 ppe-dbpyl;lved at a uniform rate in a vertical circle of radius 72.0 d8;,9v7pe y lp ub- p7;ebzbpdcm , 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 1ztb xk3h)e4fa + l8jrzcfx,+( 050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.8 fl4,j8 ez3rxatkcxzfh+(+ )b 0? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betwe1ch9t n0vbdl+,( ff ygen the tires and the road if a car is to round a level curve of radius 85 m at a speed of n cf0+,tyldf1 9bgv h(95km/h ?   

  A device for training astronauts and jet fighter pilots is design 2brgn2e niq0.ed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 tn 2b e.2grnq0iimes 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 rotata1qh,/ ds)u/g6c+intm)kpl ting turntable of variable speed. When the speed of the turntabl/a6p )hugtm /d1sict) nl ,k+qe 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 hd.pig4jo 6yj1yes(0 a roller coaster be traveling when upside down at the topioy4ysp0 .jh(gde j61 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 (includi(mt 3u0 +k p/ycawz)hing the driver) crosses the rounded top of a hill(u/iy+zp a)m 03wkthc (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Fer((o+ sgie+ka sris wheel need to make for the passengers to feel “weightless” at the topmost poik (s g(+ioe+asnt?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiu3b.;5g5cuqvj ru:nj ms 1.10 m. At the lowest point of its motion the jb.jc vr;3gn:uqu 55m 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 i : v-kmj.jhq2:s s7pkgf a particle 9.00 cm from the axis of rotation is to experie:s2s.hj7j :pkgmkq -vnce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival,m:8uwr w bt8,p0p-t9rlr: opa people are rotated in a cylindrically walled "room." (Seer9tr-8o ,ut8r0 pa pwbp::wml 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 q*q m9lh+su8f in a circle on a frictionless air-hockey tabletop, and is held i8h*+m qs uq9fln 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 timep x,,19cg svaa, by not ignoring the weight of the ball which revolves on a string 0.6,1s 9a,vp cxag00 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 of 88 m is perl9v ;n.7ysugwcay-++y r ;zjefectly 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 j ;nmj,b uk(ny3 .mrm3$ 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 dim(+i : shfv60o:u x6tg.1mzgpl qzpc 7ving 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 the net force exerted obqn0hzgb;erj. .7sdl8a/1yq j v0 d7ln the car (by the ground) in Example 5-8 when its speed ql 7bsj jz0 07. l1d8h;y.ner gbaq/dvis 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniforml-8k em(ag rgn-, zvl*oy 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 werez mae,*o g g8lvnk-r(- 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 circleta(-qcu ee;qdi( w530m.duu6+jr kcn of radius 2.90 m . At a particular instant, its acceleram0euuk 3-((qtd;qw.i 5cr6cda +e jun tion 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 spacec82np,hu jjeq((nz czs rai 0.,raft 12,800 km (2 Earth radii) above the Earth’s surface if its mass jn cazr0 zje(8n hsqp(,.u,2i is 1350 kg.   

  At the surface of a certain.rrzy/o;f ms68f:yth planet, the gravitational acceleration g has a magnitude of fh. 6o;rf8rty/s z:ym12 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 acceler;b;eiy *+ s6zpm x:yvv l46pzration due to gravity on the Moon. The Moon's radius is 1.76yvzy bl+xe*r64ms; vz:; ppi4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has th.vmg(v4:j b )5eyprun68c8t p7gq rwpgalo 3,e same mass. Whavy vew :qgp 7, m65ubcj8pg8(torr)n 3g.l4pat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of E -osqi+p/)qcsi f 3pi;arth, but the same radius. What is iq-ppc; is3/o)q fsi+g near its surface?   

  Two objects attract each other gravitationally with o .y ,)bee )y9ajtsaf: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 accel -u0yfhw vzgp4us x*w*a*dvqka0y0:.eration of gravity, at (a) 3200 m k0z0-y avvgwwy 4s. :a*xudfu **0h qp   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance lm.ig4qcdjzr1 (9 (jlb4p lz7 from the Earth’s center to a point outside the Earth where thegravitational accj9bd rj47z(l4plqzm(l ci1g. eleration 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 sphertyoz3*fy-ay07-ej pn 2x2lib e about 10 km in radius. Estimate the surface f-nyj ylo-2y02a7*3tip eb xzgravity on this monster.    $\times10^12$

  A typical white-dwarf star, whrz. wlu/zx c yji0514xich once was an average star like our Sun but is now in the lastc4 zyu05i z. r1ljxwx/ stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orb gm z *ti/tn6. 6k6vgx(gvtcy-iting in the space shuttle. Your friends respond that they thought gravity wag t6it6*k-n gvvt. c( yxgmz6/s 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 aremdhvphw+6:y+ bmve xbp ,i3* ; located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othy hm; +p:vvw xdp,bbihem+63*er three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetj9 r5.n usti. moi k9)oebd5hj+6v8ogs line up on the same side of the Sun. Calculate the total jjv8)r dni.9h sib+o5toou 95emg6 .k force on the Earth due to Venus, Jupiter, and Saturn, 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 acceleration of gravity kh ,yaofre0v73522 ,lrdjrt sat the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 yo2elr5 k,,0h vrfsadj2 t3r7km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sw gzm ;3mu/2tl:9ov jlgk -ev/un using the known value for the period of the Earth and its distance from the Su3:z;g mjle2vw/ o l-mvgt 9/kun. [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 circ0b c8;/1cwidgzq qc0l5pvam5 ular orbit about the Earth at a height of 36005v1cgpc0bd clz5am /;8q q0iw km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the ux7yiz)nyh ,mtt -e91Earth. Hoz-1t7t uymyxh9n, )i ew fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship r2 7l+o 1x-l cqkts)xkxa 95sv+p:pvk rotate if occupants are to experience simulated gxx-k+2lo s)5 r91q7xap:vktpcvk +lsravity 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 5–32.)   

  Determine the time it takes fwo6fr:+/ fud4td5ib ror a satellite to orbit the Earth in a 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 f6:dd+r otrw4u bi/5f 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 la)lkdq-elo(7zrs 4k7pegm m) *unched from the top of e-4z 7g)k)kqdl7mrslm(e*po Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the comm *-7ac1 7gcmhbztcrjk -yw-7nand module continued to orbit the Moon at an altitude of about 100 km. How l-cryw1 jnt 7ghcmkcz -7ab- 7*ong did it take to go around the Moon once?    s

  The rings of Saturn are composed of *dijs 8jx +yzs24 d5unchunks of ice that orbit the planet. The inner radiuss+nj85xzju 4id ds*y2 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 every 15.5 s (see Figow ;jf9dgsj3 r4r 4iz1idf rsk1* a-z1. 5–9). What is the ragz* ariisk - z41f;fsojd3w119dr4rjtio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight ofya44fby, iyy3y;+c r n a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving y nfbyy+yr4,ic 4;a3y 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 oy vzkhlm)/t .*l)c7qg.b 0rzm f equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit abo.g.)r *ztm/l7lzy qhmbkv)0cut 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 7*rv8eyhrw 6 vd.9hvh55-kg woman in an elevator that move*8hdvrhvy6e. wr9vh 7s
(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 )gw27 h)hx)waoh wma8suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator 72x mwg 8h) ))hwaahwoaccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the se //sg8rll4fwurface of a planet with period T , the density (mass /e8 gllsw/r4f/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 36ouuw ls1,1v nq ars;07g5ujw(lc t70f agjl(27.4 d) to determine the period of an artificial satellite ru01salfg1j5c,nlw6 ;u7( 3gw0t7a qovus jlorbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acros1ce( /xpu8 -nxh ;tzhks, orbits the Sun like the planets. Its period is 410 d. W(8th;xx 1zc/en- kuphhat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average24:tix-fy af7r5peknc3d : cz distance 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 roug,u1suc1cjh pdu.4kqz g,57b thly 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 fromp cjqhku1 ., 7u 51t4u,gcbsdz the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of uf/rr5y4+ p(skd oqp 4the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distanceew2v(.o) y ryt for the four largest moons of Jupiter (those discovered by Galileo in 1609)(tyo).yrvew 2 .
(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 Eqdyg e t(l9. dv3l3*obarth from the known period and distance of the Moon. gtyo .3 l*(3ldbdqe9v   $\times 10^{24}$

  Determine the mean distance from Ju oyqq/0wo2p8.ex7 w o *m)ccynpiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periwc8n)cy7e.2 omow0oxq/ qp y*ods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists o7 )9ipu s/o0v0mzce;x sj kbv3f many fragments (which some space scientists think came from a p0zseibuo9 ;7x) / sp03vvcjm klanet 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 m0.+8n6 pi kd7patvpmthe form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like o a pnd i7mp.+mt6vk08pur 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 from a hanging vine (Fed 88;:a,zn)a losrx mig. 5–41). 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 psom, nlea;xa r8z :8)doint 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 gravitygw5x- yr;evbjs2y .b 16he hpoc0fs01x ,aj ,g be half what it is on th;xb 0pf h,s gc2-be,1ejjoy shw5y01 gx.r6ave surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cy,fp:t9 (q 2( suufoetircle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anoth(poft9s, uy(uet 2 qf:er?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratio81+ b-wgb: agzgjw6dn n of gravity at the equat1jg:wbn d w+gg-za6b8 or 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 the Earth will a spacecraft traveling directly fw5l -x7coc/a t * w8m-jlr9zlorom the Earth to the Moon experience zero net force becaus/mc r8x7- aolcoj tl*9l-5 wzwe the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bat: 50u c-qya-dm.r m nr*9; zscu0le0tz 0pziuxhroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, andu.d ;sair pc00xc-*0ly u:et numz0rz mq59- z in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will ro8/w 3kznhs t4etate about its center (like a/84en 3z shktw tubular 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 his aircuu rx+4x5hm i duysd2-7e 3pm5raft 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 a planet in terms of its radius r, tb jx(x c97;gx2iep(d rhe acceleration due to gravity at its surface x(j 2rixge(b c; d79xpand the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecte-;hcmiesuqy7 x o+d m*; i enmc;c62rwllx4(*d from the vertical by an an2; - u 6;seeoli7*yqrmxc4+mi* cnm;wd x( lhcgle $\theta$ 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 k+biy z-7 r/ea yng)4rcoefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle i 47egy+a)rr- kbn/yzthe curve?

  How long would a day be if the Earth were roz expfvq*)l d6)grguh(h2m 9x3 :vu7itating so fast that objects at the equator were apparently weightless? (e qfg) *v6 z3)2hplh:u9igmu xd r7vx   $\times 10^3$s

  Two equal-mass stars maintain a constant distance apar3vbeb +h0 h+uft 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 235 hor2rmym v cf d*3ecs2*2sf9*m. A lamp suspended from the ceisyrcmos2*fmd* 2*92 e 3chv rfling 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 massive as the Earth. Thus, it has been claimed 9gxczneyh3 4p*e6 ru) that a person would be crushed by the force of gravity on ernu4g39x y cp h)z6*ea planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope dylg0 3bj+e 0pleduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a bl+jll3p 0ybg0e ack 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 traverses1z:sv.ul: gn cpsb:ydgn556pd v4e .u 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 largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. ( p5 u. dsbn5 1d6yv:sv. :pgnzcg:ue4lc) How fast can the car go without losing contact with the road at A?

  The Navstar Global Pgk1 futuv 0+j2ositioning 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 canj k 21gu0tufv+ be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rende1 t86pwq6gzoev 5v0/ky*t66 pcwav u xzvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abt tpkv/85 xc*y 6oq6 evg6z6p1wa0vwuout 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 need of rep gfih1.rp1wt9n*o* kk air. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind .i91 nrktf*wgo1kp h* 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 meanxm9vsd3y08 ,odlt6j4 c+ yjii distance from the Su 0tilvom,dj sd8i+xjy639yc 4n?   
(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 ohuw9ey-zixvtfac46e6 iy .,1f G would need to be if you could actually "feel" yourself gravitationally attracted to someone near i 9yze eviy t 6wa-x1h4.6u,fcyou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the n/0 ptc jfqc-5center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,05fq jpt0cc n-/00 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 y /yyd avf8d8 gng+0)s9v9h wt/x/dja located at the corners of a square 0.50 m on each side. Find the magnitud/9wgdg8)axjavn+/ 8 0vs9ddhyt/ fyye and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth .lkn y,3 nd*xf$ \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 a w o/*gr7ej)/(gafzn.5-cm-long sweep second hand on your wrist watch?g/rfa*e7 w) nz/o a(jg    $\times 10^{-4}$

  While fishing, you get bored and sb3ath* )suk*fv2ci)f4nehs 2tart to swing a sinker weight around in a circle below y kau2hes4c2)3sv b**f tfn )ihou 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 radius R in a new highway is designed so that a car travec8y8xvk*zr/ +6rm4t gxo h (dfling ax86crmz 4+h8f kyrv(d*to gx/t 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,i /, jgh9-sr2w a.rne, yq+pkk utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so th2hqgarkjr- .+/,k e9i,yswn pat the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not 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.$\approx$    $\times 10^2$