Sometimes people say that water is removed 6m4qgft*u t sta1k-w; from clothes in a spin dryer by centrifug utw-qt*gka;16sfm 4 tal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels ar( m4su-dl+u vsvks 2lr3nm+ p0ound a sharp curve at a constant 60 km/h as when it travels around a gentle curve at th+u-lmkpm +s 32us4r (snd0vvle same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wkb86( 1tv sr5l 0je4ypbth6 hvhere does the car exert the greatestth(jrb14 0kv y56tvl6 e8s pbh 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?

Describe all the forces acting on a child riding a horp90 aj: *hljlsse on a merry-go-round. Which of these forces provides thejsjl p09hl*:a centripetal acceleration of the child?

A bucket of water can j9w,1mkvt- wf:qr/ 32 vmor)m v)h sdlbe whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside dkmm t/wf)m91v2:qwhovr s v ,-3jldr)own. Explain.

How many “accelerators” do you have in )jh erl 1zg ;:jgqgygj b5 yvn(py)uavz/.-6 *your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are thg yjjq-)vu.6bay)*;v1: /rpj g (e hg5znlgyzey? What accelerations do they produce?

A child on a sled comes flying over t0 251jvui kpnnlt79xp. syzik)9zm *the crest 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 normal force between his chest and the sled dptz nji)lzm1sxntk9v2* 5k 7uyi9p0 .ecrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riderbp 5fqwh(:v0e s lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking anglubomxj6 d )z)6a,72qh2d,okxhm; l yfe given its speed and radius of the tud7,d,2jo);ybmmhx6lx2f h o6 ak qz) urn?

A girl is whirling a ball on a string around her head in a horizontal pla9yjc q8 y fvx;./gda2une. She wants to let af;u2j8yqd c.yv x9g/ 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 E182q i6*mt ichca vyb(arth? If so, how large a force?8i 6cihcb mq(*2vay1 t Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass 5k:6z h jli;ffwere double what it is, in what ways would the Moon’s orbit be differenti5kl6j ;zhf:f ?

Which pulls harder gravitationally, the Earth on thj.7t*olz7 x uze Moon, or the Moon on the Earth? Which accelerate7zz.utxo *jl7s more?

The Sun's gravitational pull o x g0dwq 4)sk)6t8 bpjubwtzov/ug;2:n the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Co u8dtv:ks)b);tqwwgb pj/ux z4go 602nsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh patj-/ bx5 h9s tja.-pmore at the equator or at the poles? What two effects are at work? Do they opa-.xtpjsbh 5t9- j/a ppose each other?

The gravitational force on the Moon due to the Earth is only about halxbxxfdr2.x+x, 66d; m 0 qlwdt7,jhdwf the force on the M6l x r0 2txwdqxdxf ;h,djdb.wm7+,x6oon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accelg 25;e4y+u)6iavxn cn zn/w -ovhl4hceration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of5cvxg6c4h 4n i y)/e zu +a-hwv2olnn; the Earth?

Would it require less speed to launch a satellite m, ihs1;*on +we)qjfa (a) toward the east or (b) toward thein wqfoj;hm+esa )*1, west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest,6.ckhkcuqn ndk-i54gync- 70opp)j 5 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?.oq5d) 6hkj-5c- ipyn 0k4ckp7c gnun 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 long2u /j(a/cixbf periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotac(fxb// jau2i tes, 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 exp9+ztof3nz81r13sk ujz t;c tieriences “free fall” or “apparent weightlessness” between step3zutf+kijtzn9so 18r z3 1;cts.

The Earth moves faster in its orbit around the Sun in Januaryo8 sttzc x-,2i b8l 3pijot93nyks,)x than in July. Is the Earth closers8b cx 9x2t k3j tzip8yo-o l,)n,st3i 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 its orbit.]

The mass of Pluto was not known untio9 0 zjn68hb kcnw/domh) ;(ke; d(qazl it was discovered to have a moon. Explain how this (o)dhjzzdn0ck m6 /b;a9w(qekn;h8 o discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'.6bc,gyuf4kr qxv7 6fs. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of theb6xk7f6. 4 qfy gvu,cr Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19 mlwjrr 5-v3/q80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 t imvv m9w(u(g,ao09jux md.h01aiu/jhe Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that th j(wu.o 0,u 9mih/ux0gaid (vmj ma9v1e 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.yur05o .hgz:n* ud 9ia0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the.5gdhanry0z:u u 9o*i discus.   

  Suppose the space shuttle cs b.bs bg2e;qx1tu,r+i77vnis in 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,7 .bs +tcgsru; bven 2iq17xb of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the e;xdt 0smz5y 2a3dv6nudge of a potter’s wheel turning at u3x06tdany5v mdzs2; 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 in a vertical circleut- 3zxp kd: z33/pkaj of radius 72.0 cm , as shown in Fig. 5-33. Ip3-ujk3pzxda tk3z /: f its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg carusyv17i7kap8t j y.wqo*5h6h can round a turn of radius 77 m on a flat road if the 8v5yu q1h7ha6t7.*py wkj osi 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 between the tires and the r3e2 xt o;kx3tm7 mbvc)oad if a car is to round a level curve of radius ctt3km) xb 72 3oem;xv85 m at a speed of 95km/h ?   

  A device for trainingl6pg54ocp9 ,qgdyd( (-xf q lm astronauts and jet fighter pilots is designed 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 times her own weight, howdq, loyfl( pg( -d mc45pqg6x9 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 fa-ezs t05rsf+ rom the axis 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 be- fras0s +tz5etween the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling wql+i e0jtm*+4pln 5w5khj) vr hen upside down at the top of a m+e5) 0tw5ijq+lpnl 4j*vrkh 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 driver) crosses the rounde3bo)p ncv 8uk( s*xvixqk6:h2d top of a hill (radv8(hvp:3n sb qix 6k xk)o*c2uius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel w6 1q, qut,dnfuli4d7need to make for the passengers to feel “weightless” at the topmost point?f, q1 lntu7u6dq4i dw,    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. fxm6xas- n*7j/huq0axaw 35 c n9xpk+At the lowest point of its motion the n0xck* amuaxfhxp59 as j 6w3 n7x-q+/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 cen;w9. ue5c;fdjt*mohgh9q-m o : bzot+ trifuge rotate if a particle 9.00 cm from the axis of rotation is to experietqbg-o *h;:oz99d j+mh5cetm ;fu.wo nce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylin2hxyi8def /( ogyh*+ adrically walled "room." (See Fig. h+xg iyah* 8yfoe/2d(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-hockey tga1knj+m( l mb,gh4o1 abletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through4m+ghjbkmolg(11 a,n 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 o ab.n2nx05wow5f sq6 nuoky) 3f the ball whics) 0ny b6uok5.nfx 32waon5qw h revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelis1pfpf 4qq.-gzc*b9kb e;us +oe9m 4c ng 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 masseshi du1b6 oh;h2x g,c9:o3w-f mlw+yli $ 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 ve6u 5gb+cd7naa rtically 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 tgty +46wfv.gd he net force exerted on the car (by the groung6f vtyg+w .d4d) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from thyw01k n *lu0x *mb-wo5asul/qe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Dete*sau x0 y 1 qul-b5lw0m*owk/nrmine 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 circle of radius 2.90 m . At a pa2,to zr7v kvxu9y h:+s.l +f1d)ilhkqsr 3q2krticular instant, its accelerati2sykt1ukq: i x )rlfhz2h,lo rk3.vq79+s+vdon 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’h 6 q )gbb3iwpo.g x6e*mqp5z;s gravity on a spacecraft 12,800 km (2 Earth radii)zgbq; *gi6 3moe x6pb)pq .h5w above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a cerl;4wosk ..glrtain planet, the gravitational acceleration g has a magnitl osl.4.wrg;k ude 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 dug/wi: 2)mpzpye to gravity on the Moon. The Moon's radius is 1.72:iy / wzgmpp)4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has tq+5nw;rhg3. pbk 57cc7 bkniwhe same mass. What is the acceleration due toh;757cb5k.b+wckn r nwigp q3 gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius.u k(4nu)1iqby What is g near its surkqi uun b)4(y1face?   

  Two objects attract each other g9a jcg*:u2eq rravitationally 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 jdpoq-,,;+fwrt a+ itu p*fj;of g , the acceleration of gravity, at (a) 3200 m; ,+-,td f;jpjoauq +r*fitpw    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from then, yr5qab xz9wp0/fp7s0oh *e Earth’s center to a point outside the Earth where thegravitational acceleration due tyxs b9az p0o/werhf n,5p *07qo the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star h 9pz9yk2f; gaxas five times the mass of our Sun packed into a sphere about 10 km in rad2xg p;f99yazkius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was anr*/zyc pw+*m-d beg0w average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is ww/**eb z d+ym c-r0pgthe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spatz /hry;/d )snbxw8ts 33tzt8+n ku (pce 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 calcula+z/pzyn3ttwsunx )8hs;dk/83tr( tbting the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locg /h7 ypci6hfbak(. 3lated at the corners of a square of side 0.60 m. Calculate the magnitude and directionf ba36ghcy/ h7i p.k(l 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 most of the planets line up on the same side of the Sun.1io vxzuh1+s6 Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are ih16ovz 1usi+x n 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 at theb+pm+s m z *.*aywa0 vx1pfs.l surface of Mars is 0.38 of what it is o+pwslzbxm 0m*p1* .f+aa. y vsn Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the peri a2;2oadht 8xh *qnu5kod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, E h*q28 2 uthanxoda;k5xample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satec 8tdthc5o5) hllite moving in a stable circular orbit about the Earth at a height of 3600 ko t)5h dccht85m.    $\times 10^3$

  The space shuttle releases a satellite in q5/xff)h e,v5o+uqd vap)*alto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative t,v )eqfaqf vl) +u55/hx*o pado Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spac nyq/e k5itchq06n+w/eship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the0 /nyhqek+i c6t5nwq/ time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time ilz7)l;r4h58ovm 6 krgy sc, wtt takes for 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 the radius of the Earth. Does your result depe6rlw)vsrkh7 z,5;om 8gc 4tylnd on the mass of the satellite?    s ~    min

  At what horizontal velocity wouldefob qn+0arntgn5 . *py:n; :m a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earthpmn tn:0b;qa .nn*egf5y:r+o ?   

  During an Apollo lunar landing mission, the command module con5ny; z3a)-zjdzrbg5i tinued to orbit the Moon at an altitude of about 100 km. How long did it taka 3zd5rzng5jbiy- ;z) e to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ic5/lmpt 5 i,gx 1*vjrooe that orbit the planet. The inner radius o pxg/o*jo51ir v ,lmt5f 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 rotatga/qhh6(ua8sr0 js+-fs8l gx es once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real we-l8h+ qa(axg/6j h s8sfgsru0ight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from thia6t2- 6ih)sd/aa t7 h woitp 3* dax1p5ctj5ne center of the Earth's Moon in a space vehicle (a) moving at cs 67*a2ian5 tadpxto) iwp-a 36/i h51jt dthconstant 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 syp4i ,/5 : fkee .ai*zf3om9l8ydpsluzstem consists of two 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 mass of each? * umoi 8pd5ayk.s9f3piez l:z/4e fl,   $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg w7lj ) :w+-xbtcf mbxzl/ks)dvg: *8njoman in an elevator that movesj8:t-):bdxjgsz7b ) v*kll f/ nw +cmx
(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 fromqtk--, o ;wlpw/chy9 w a cord suspended from the ceiling of an elevator. The cord can withstand a tension of ,ww/- 9q lhpk- ;otycw220 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 rr)z;7 e6rnp*z1x cvy surface of a planet with period T , the density (mass/volume) of the planet is v z*re7r p;cz 61y)nxr $\rho=m / V=3 \pi / G T^{2}$ .
(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 thecny1)wofdm o5vy -(, i Moon (27.4 d) to determine the period of an artific5)1f,y c-dmwn( ovoyiial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, n 7/n)yqhbykq73y0coorbits the Sun like the planets. Its period is 410 d. Wh/ by7)h 3qyn7ky0nc oqat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of p-+ckjk8 s 99skwh-dw 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once everyabw(h6s:w ,u v 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 sum of the nearest and farthest distance from the Sun.] vs:ww(hu6 b,a    $\times 10^6$

  Our Sun rotates about the center *v s71 59(pnrxdclssj of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, an oak(hv;k io88ma8y: kd mean distance for the four largest moons of Jupiter (th8(i;o: o8 yakk8a vmhkose 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 th 5suin1v9vzz2g7 p:yfslo+d bdlo9*tfh 4d 9/e known period and distance of the Moon. vt obp:l1 vf5d zz+soi7fdhudgn4 s2l/9y9 9*   $\times 10^{24}$

  Determine the mean distance fro ) ji5zp7oqwznz6s2 :d2u+flom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io anuwnz2 7zs fi+2d:lp 5ozo)qj 6d the periods 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 of many fragments (whic 8nx *4 fz)hcqr0g;lazh some space scienticlq 0 *8)nz4 rg;xfazhsts think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale descr4o )5dxr)(uty d ,vsk7y ,wlzao-g0i eibes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun 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 r i o7gy4e5ywoz,akrsdv,t) )x(-ld0u otates 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 by7 4vopo+ycal0 9f0lty swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the 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 locfvyal79y 4po+ l00otng.   

  How far above the Earth’s surfac0 ec.fbf)it- o: tejdx/9xsg)e will the acceleration of gravity be half what it is on the .t0-cotsji ff9dxbxg:e)/ e )surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inzlnf)h*g2z*( jw;n hoo (( dpj a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one ano wnfgpnoh* j*zzo(dh)(2l (;jther?    $\times 10^2$

  Because the Earth rotates once pelphuz879w;; atn u2dhr day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotpazu h7 28hl d;;ntuw9ate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wiluu -n:h2kxs -b2;qy zcl a spacecraft traveling directly from the Earth to the Moon exkz2;x-h-2yu :sqb nc uperience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroow,( 2buw iffep wlr1v 9z+:e5+l4o rcam scale in an elevator, it say4fbrv5:erc1(zwfie+ 2+, 9u o alw lpws your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular umhpnz ,ol *(nv iz(-9tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotatinm-(hu* vnpzl,( 9 ozion 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 verticalt0 q0oay bej50 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 termig .k*7h5m;k7btc zp :zo ;oxgs of its radius r, the acceleration due to gravity at its surface and the gravitationa.i;okhg*xo;z 7 gt k:mpzc5b7l constant G.

A plumb bob (a mass m hanging on a string) is deflected from raz1e;abe:75w; e rdzthe vertical by anzze15ew;a r7 bre; da: 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 speed of If the coeffici)* ng*l wgwp,hlh zl.,ent of static friction is 0.30 (wet pavement), at what range of ,,ww.ghl*lh)gn l pz* speeds can a car safely handle the curve?

  How long would a day be if the Earth wer j .c2foj /27lfxcawn,e rotating so fast that objects at the equator were apparently weign7 wjcj,2ol2. xf/cfa htless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.06 g2qw;ng mm i1gof4z2 $\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 qf-4dw +avps3gmd/ x 1rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an apmw1d g4 /sx+vafd-q 3ngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive onq(42blx t p*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 g 's. Calculq4b ( nxopl*2tate 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 deduc7 ,pta hy:f5h(4guruh ed the presence of an extremely massive core in7 uhap r4hfhtuy:g( ,5 the distant 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+:namtv43m7v +eoc0 f tr p la*;un(cz 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 heafmvmcvr:ltn 4za(7 p3n+ca0euo;* t+ viest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioningbq lb6 c5h1s8d 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 centimet qsbd568hl1cbers. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.. plq,rtu 9 4 9vcw.n;atme(vp1 billion km, is meant to orbit the asteroid E(9qv .c9vtpl;etn. mw4 aup,rros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuiv 0d+1mlpo4qi d b;y)ing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 qipy0v d omd1l) b+;4ikm 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 dis) amxywc, , fthb.m.s;t*1m ustance from s,wttbmm ,) amh.*cux. f1 s;ythe 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 tohar)6glvy(2 ww9h(a m be if you could actually "feel" yourself gravitata(rw(hm2)a 6lwvy g9 hionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fi).tjg px8n13qyb esm*g. 5-46) at a distance of about 30,000 light-years from the pgy* 3.t nxbqe)81mjscenter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on eacil lyeb*0 4)pctzh :u-ran-c) h side. Find the magnitude and direction of the gravitational force on a fifth 4h ailncyb)cr 0z -:t)eu-*l p1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5fphk / s9-xyv,500 kg 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 1.5-cm-long sweep secfzifpl 418k9rond hand on your wrist z lf8fi41 9krpwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around :sn0 zk-xssvz2hpq,i) a l( +qin a circle below you on a 0.25-m piece of fishing line. The wpq:zz(a-n shkvi,+)lq 0x2 sseight 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 ta uiy7vp:rv0x+ 7+ cvjraveling av7vprjyx+v0 ui:7+c 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, uti1/wtd8x5q rqe *kon8x(7yvau lizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a raou7ekw a/8 5(qr dyt*n xvq81xdius 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.$\approx$    $\times 10^2$