Sometimes people say that water is removed from clothes in a jfi 1bx:ej2i)gwb .9lspin dryer by centrifugal force bifxij:w91lb . 2j )gethrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the carnv; yr(rk x1m 0wt)l.j travels around a sharp curve at a c)x.0 r1ktwjn(r ;mlyvonstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wheps4,mkm5 6 *,trq kzrqre does the car exert the greatest and least forces on the road: (a) at the top o,p4 5tk*m6qsqr,rzkm f 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 horse on a merry-go-round. W*a2f hpezrz srhvl ;74./cx r,hich of these forces provides the centri arvl;*zrx27/ez s4rhhp.fc,petal acceleration of the child?

A bucket of water can ck obxy r*7((tz)y7e ,or r)fms g*/hebe whirled in a vertical circle without the water spilling out, even at the top of the circlecfo7)rs,( zxeym o yt bhg)r( k/7re** when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at r 9dpafnc6l;-h jgqrroad)dj32lo+ b b+(16kleast three controls in the car whic1an(kd6ohc qdgf+a- +lrpj 3br;92 oj 6bl)rdh 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 shown 3wal r s3 d7nxat0 e.zfx-t*s-hj;f 5gin Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his ch 7 t * a.ts0fxasef3 -w-;rhxd3gln5jzest 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/ac2c u6:a1mtie5h fa curve at high speed?

Why do airplanes bank when they turn? How would ymhz 8uo6gvzf eb7 9wa6n*a.3 zou compute the banking angle given its speed and radius.3fn79ve6bhm wza6g uo8 z*za of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.y e om,ggng, qah*k j6e98iw+f ;,hxx8 She wants to leyej8k, gxxgen98;ifho , *hmqw g,6a +t 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 gravi9cw++kpv8brp f l -rysy4y v/3tational force on the Earth? If so, how large a force? Consider b8 vprfk 9/wyp+-c3y+vylsr 4an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s ocw pme (3a04rbaxnj wg(c50/irbit be ga/wecnxcj 5(pam br043i w(0different?

Which pulls harder gravitationally, the Earth on the Moon, or tlfn j e6tj5a8duow ..e69n;oahe Moon on the Earth? Whi.6lea8uoat fw;jj659o end n.ch accelerates more?

The Sun's gravitational pull on the Earth is much larger tuddd64xs6 ty)ju(*)t nxoo ( rhan the Moon's. Yet the Moon's is mainly responsible for the) u6o (d4to(x*d 6tsydjrnxu) tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles6ed;n-z vpam7 clhs bs (y y(c8sp;03f? What two effects are at work? Do they mnsvacc(s6h b8yypefz0 73pl(;;d-s oppose each other?

The gravitational force on the Moon due to the Earth 2a7dhk5pbmztij,2vf3y.bo1cz 8w u. is only about half the force on the Moon due to the Sun. Why isn’t the Mo1 5mpkcuhozjztby 8.32.w2bv7ad, i fon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun 96azt ad f2r.slarger or smaller than the centripetal accat sfdr2.a96zeleration of the Earth?

Would it require less speed to launch a sad,7q. i:v,d ncnv9zv3 mm6k8 *jbakhj tellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dh:m 9vk,v3.d cj jd,m*nbva76 8z niqkirection.

When will your apparent w3f jhwx,opsmbr f :9;jc b-v,3eight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, ,:3vrb9p-hb j m fjsc3f ,wxo;(c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could b mez*;e9vez, ye adversely 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 inside surface (Fig. 5–32). Explain how this simuly*ze vme9z;e ,ates 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 “frai3a: qy*x6r4 i1jyawee fall” or “apparent weightlessness” between steps.r 3*iyx61i4 aqawy:j a

The Earth moves faster in its orbit around the Sun in January tux9:3qcc- kk3 c2 mz7,ezpg eqhan in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Ear3q,7 :- kp3 qkze2z mcc9xcuegth’s axis relative to the plane of its orbit.]

The mass of Pluto was no +ks38xhxa 0ost known until it was discovered to have a moon. Explain how this discovery exh3k0 8osa+s xnabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is ug-ni7 mz 5az5much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sit7z 55gu-in zamting 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 h8 u9oha(wyoqa29- aj 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 Earth in its orbisnr lp.ge7bev(u5t 9ql / ok*6t around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circl9/(eeltg6svq75pr ul *no b.ke 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-kg discus as it rotates uni,7.9hcu 5sw5bpe onwn formly in a horizontal circle (at arm’s length) o nwpsbou ne., 79w5h5cf radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fromvo1ypk9,qb:gv+58 jdtw hh*a the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Ex9*yvq1ho+8g dpvk :w 5jh b,atpress your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edgec b5ww +ro5fbh 9/epg2gq*j k4 of a potter’s wheel turning at 45 rpm (revolutions per minute) i9ohr eq bbw+ kf4*p2/cgjg55wf the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniforzlmb3q+ .1q5h l(x4 c *qlczvlm rate in a vertical circle of radius 72.0 cm ,l * v435.xl 1m bqcz+lhlqqzc( 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 speebg 31xz8cijm+d with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient o1j3zgb ic8+m xf 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 vxud104y*wq( (5r onvnc+,lejs a3lc rovj aql 3nxlcd,snu5ew4r0y(* 1+o( cv ad if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts a5gh;a-,xg8yei4;r 3o lkmx sznd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the traine ai5;;gkx34 lmo 8re,shg-y zxe on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of ab39.c0jfgco ,, qrlxrt a;q k7on02nu rotating turntable of variable speed. Whent. 9fok q2 ,qrlg a;un0,3ncbx0j7orc the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside++v ) vo4xu5nkcq o5s xmbb).z down at the onc vzkxmx) 5.5q4+busv bo)+top 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 drig05chb n6 tjs*ver) crosses the rounded top of a h50hgtnjs 6c* bill (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 Ferris ww3lb5q5gx1r dheel need to make for the passengers to feel “weightless” 5q3xl5b1wdrg at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circlf9y n8ke0 (yq q7 y5eob8n5thhvln 0q8e of radius 1.10 m. At the lowest point of its motion the tension in the ro(nhoyf5eky q8bv5nt8 qhy98e ln00q7pe 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 particle /4-ri+ xjgnldc ec+5 y9.00 cm from the axis of rotation is to -5ljrn+dyg+ exc4i c/experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivalgmc(q0gyz1l8b-pfk;k 0tf+ e dt 65 jp, people are rotated in a cylindrically walled "rootpezt- 8flyk c1jfp0k d(g05+bg6;mqm." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey toomq*z46 8j prabletop, and is held in this orbit by a light cord connec4o86r zpqo jm*ted to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the *rq*2:.uzkyah;kun lweight of the ball which revolves on a string 0n ul:z.2uq rk h;ky*a*.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 6tq4su4 dkxo+ 9v5yy vmspd6f;ajxe 5hm/ u02perfectly 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 mvwszg bbky0 a6usj7:9k9 m-9f 8qn /n$ 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 maz 6ex9w( bis;mneuver 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 the net1u( 7k lvb/efs bnmplzx ;x/6;td;b1fyuji-+ force exerted on the car (by the ground) in Example 5-8 e61lybfxzmxb/k/lv;1dus 7(ui p+;fbj t ;-n 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 twmj1k b1w3aak/:pk+9s u; wedhe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skiddi /;b1j:9k s pwwkae 1uadkm+w3ng? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a ifr7 j 6bpmt;f+o7ylgo 81m z,particular instant, itsi+z1fmolm 6ofp;b j78,t7 g ry acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2g/ k 6yu sps onbqdg98(-ch;4s1 idxpml7t1 v. Earth radii) above the Earth’s surface if its mass is 135st8i/b1 g17pvsqs kp6m9 gud .hdl ; cyo(-x4n0 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnlx ,v c3hopm11itude oflpc13hm,xv1 o 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's rw1i*fwtuz7 8rw sjyn; e3j.93a bkob9 adius is 1.7fk wwwa t13 unb3yb987*.9j i jozr;es4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius b eh4zt1whad6cz5 ;utyo /v-71.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?5zb7huty6 w-o14de; /t zahcv   

  A hypothetical planet has a mass (.h9pivanau(9th 8xf1.66 times that of Earth, but the same radius. What is g9i9hfux nhpv . 8(at(a near its surface?   

  Two objects attract each other gravitationally with a force of l99v u9szax d+u)) shu 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 valuv4vpm cuq0z5 2ka4v,ne of g , the acceleration of gravity, at (a) 3200 ma04qn 4p m5 2vzvk,uvc    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where s)sw zmz5j*0 ycp+u/ztj*syzs0z+ p)cm/u z 5whegravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times twk+278plc6t5qt : w jbomdj ;ahe mass of our Sun packed into a sphere about 10 kmk btmqc5 jj :2a;+w7o6wtldp8 in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wascq8n:w2pp mq+p4-* dx kik. vv an average star like our Sun but is now in nq -vimk8d vkqc *x. 4pp:2w+pthe last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting .4 yc:d so+os+tx1 lqx1 rdke(in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and your+1tyx4(:sxs c oedqordl +1 k.self 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 amvy-c d-)ht e5, rvep 9psh/p2re 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 h-e/- ervp2)5d h9yv psmct,pby 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.4:mq 7d kq;ac5 ffa:nz9ze, iw Calculate the total force on i e9;qcd:: az7z qmf f,5w4knathe 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 at the surface ofmvd 2(g4cuhi l gt6.+kej:)ob1ecr - t Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determint:g 62 . )-mudlj1gc(heerctbkv o +4ie the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the know9 ukup8lnd y-oxdm3:1n value for the period of the Earth and itsu:1kyuoxpld9 8 3m-nd distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed ofq7q*)a5x p+b negmq 6 fuyu60u a satellite moving in a stable circular orbit about the Earth at a height nugqa0u6y*6e+m xu5f q)7pbq of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into ac nx3,zf 1ibn4 circular orbit 650 km above the Earti x3znnf1c 4b,h. How fast must 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 experiencu 0l/fqkf ;dnil vw. :5evyng20qu:v( e simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time ;.v fd:v2in g fw0n(l yvqkle:/quu05needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit t/ f zasi9*l8zps m9 3zrluu+2khe 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 yo2lprmkz ifsuza3* zus/+99 l8 ur result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to weo*cc jrv)w i 35l1,kbe launched from the top of Mt. Everest to be placed in a circular orbit around the E5j,k* w3clce1 vowri)arth?   

  During an Apollo lunar landing mission, the command module continued to orb ;7gy-s 6mtvpbit the Moon at an altitude of about 100 km. How logmyvs-t6 b 7;png did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunbmq4 nh ).7m z+2q/d *i:zjzdkt7huviks of ice that orbit the planet. The inner radius of the rings is 73,q+dmk/ .bj)q tuz v4*zd7nzi h hm7:2i000 $\mathrm{~km}$ , 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 onc0wq5zr ad7:meo d9by) e every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight t:ra0q5ymw o9) ddez b7o her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 b/w*eesc4f9e u cr: d7km from the center of the Earth's Moon in e:cw e*4e9su7d fcb/ ra space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stawd ygo- hx5+ubfh6ta3, 46lux rs of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbi + w5d3xf6-tob6, auhyh4xg ult about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman ink*cf2p+gsy (m an elevator that mov(2g p*ck fm+syes
(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 pb9b8e2c, zlx suspended from the ceiling of an elevator. The ce2, zxblp8b9cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of qvnm - 4lw5.luik)8soa planet with period T , the density 8k lvim -ulwon.4)5sq(mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period vmkqkm7*hc 1 31e d5orof an artificial satellite orbiting vd*vmq7k31ch 51 mor keery near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits t5d ia-/d vclf)he Sun like tf /-acl5iddv)he planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis k47z 7 ysdlhvi0mr+t/tance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It oct5y 5 *vu5fvcomes very close to the surface of the Sy5v5cf*uto5v un on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of t vg-2gq dle;* h,h,c0yrzlvv(c *b(lghe 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, perio x5kpo)r(ya 5j;/dutpkwfc +-d, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in fx)rp ty(aod-+k/ujcw5;k5 p1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon. 6u4q19u nsm/pzft (y rnt/fzp (691s qr4 umuy   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usin22 (s wf-/taa rpqhrv7g Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the qwhp (72tf/ -s2rvaraTable.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Matoup(zvsaqr* z ztr*4n 511g)vk, uf;rs and Jupiter consists of many fragments (which some space scientists think came from 1tqn,zo4zksu*(gu; a zv15vpr )r* t fa planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "plane-hq y5r8l096uo3/ eok 8 soibmknefp9t" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface k-9o3kf/9ebu6i r85hopy ns0qo8 lm e (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging ikht bu h:kbti8t cgi +63w,w72n an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force o 3g b 6w7c2 b+ithk8:kutwth,if 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration ox;f u-w 70g w5cf(xxwvf gravity be half what it is on thv5-cxx(f0w x;ww f7 uge surface?    $\times 10^6$

  On an ice rink, two skaters of equuud.5u e4d /g9ohdp3bal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling 9oupd5d.u3u/ed bg4hon one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravitx, cnjajc,6pyu2i5 6oy at tc6y x ,n52 iujcp,aoj6he 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 the Earth will a spacecraft v msm8t.++bsbtraveling directly from the Eartb .+msvtb sm8+h to the Moon experience 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 bathroom scale in an a8- nxctk27z7wh 2ltaelevator, it says your mass is 82 kg. What is the acceleration ow8lt h k27a2ctnz 7-xaf the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statioy) c50/dpwv ytn consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig vt/ywpdc 5)y0. 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 aircraft in a vertical loop (Fig. 5–4l8i9 ziaagbv* 5sk/-*oybm z03).
(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 5b ej4-.mnqwdd p0zfdf/ 189h a6bonp a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitation4a dppf .5b61md 0/8 f9ojezd-qbnw hnal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticas(u)*sj9mv/tall qb +l by an an+ 9(*a butqjl)msl/svgle $\theta$ 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 b p6bh;jlra1-e ,w /azf*ubmg1anked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at whap/*e-awb 6z lgm,fj1r ab1hu;t range of speeds can a car safely handle the curve?

  How long would a day be ifg d 86qa)qahxe1 p1w 8xsmi-bxu88)la the Earth were rotating so fast that objects at the equator wer 1aemq 68)a 8xldg) 8bx81qpxawishu-e apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintaj.m/ e,7:ngi mcukk /r 7c;cytin a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed ry5 thw;y/k1j counds a curve of radius 235 m. A lamp suspended from the cykj;/hy t1 w5ceiling 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 kjc 9;lsboi+4 Earth. Thus, it has been claimed that a person would c+;jlbi9 4oksbe crushed by the force of gravity on a 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 deduced the presencl;bqie (k2hbjy y2 3 n4uc3*fne of an extremely massi*3ejb innb u;yl322 (chk4yf qve core in 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 5dgb7x c s)ub2traverses 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. (c) How fabd 5 cbu27)xsgst can the car go without losing contact with the road at A?

  The Navstar Global Positioning s qwd/egra gd93z*2 be46 gkp8System (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 acqewagdge83skd/4*2 gpz 69b rcuracy 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 Rendezvous (NEAR), afterrms4 g2gvod7 be2/ tm7 traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros472r27egom/btsm vgd 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 repail 6 t2y6cfdin1r. You are in a circular orbit ocyin2f1 66dtlf the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its meaj p1r0bjfni4 2-hz zvz):fn :kn distance from the Sun:iz)f4n-jz jhp2kb 1 v nfzr:0?   
(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 wouldshws4 -llf/add: hb+4 need to be if you could actually "feel" your+:hlh-4wlfbd a 4s/dsself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around tvq3;bm2:wme(kb059pxe hnd vhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lighk ew (9xeh 5:qmm2bn0d3b vvp;t-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 lo q-wrbh:c; 0emvgan 3cx3r 9v)cated at the corners 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 the squv 0h- ramxncv)9e3cq ;rb:3gware.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earthf16g 1dn5if hm $ \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 thep z kh-1.qpz+hqlk3(b tip of the 1.5-cm-long sweep second h1hzq+ ( pkpkl.q-b3 zhand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bdgoh76 rww+qu yyj0rji ov r03*xn 8+:ored and start to swing a sinker weight around in a circle below you on a 0.25-m py* 7o38ijrrx dw j+0+nyg0hw vuqo:r 6iece 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 sovkqza 84dm 8d: that a car traveling at spee kvddz aq4:m88d $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when n2ok/kzud tj7gat/ w,5 egotiating 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. Cons g/5w k2 7otjt,/zuadkider 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.$\approx$    $\times 10^2$