Sometimes people say that water is removed from clotheskal+a54143 cj zq*bpi7uh)ek4 a 5nehk vzf y5 in a spin dryer by centrifugal force throwing the water outward. What is wrong with 4+h1nev5zh*aiza5yqkl )fjpuek ak c 44 75b3 this statement?

Will the acceleration of a car be the same when the car travels around a 5wxdel- pr:/ jsharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.5 l w-d/p:jerx

Suppose a car moves at constant speed along a hilly road. Where does the car/q 8ew /+f:px cgge2idwhj iwaa8,g6/ exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, 8/ 6+ wd/aa/e2qeixpwjighfw:g8,c g(c) on a level stretch near the bottom of a hill?

Describe all the forces acting on atv ztu72.(mpf8bst v / child riding a horse on a merry-go-round. Which of these forces providvtft.7v( zu 28/bpmstes the centripetal acceleration of the child?

A bucket of water can be whirled in a verticai+llzb 720g;tb p8 zael circle without the water spilling out, even at thez 2lb0la;t7b +e8p zgi top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you havesuv2:r brtoy8 -eo.j/ in your car? There are at least three controls in the car which can be used t. v- yruboto je/28s:ro cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes w 0ua ev)*4ka4jvhz*6.jgrxnflying over the crest of a small hill, as shown in Fig. 5–31. His sled does not uwx*vh jv440 z.*6 erjgaan)kleave the ground (he does not achieve “air”), but he feels the normal 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 curve;mvs57a,t -jtosy/see+ 4b cd at high speed?

Why do airplanes bank when they turn? How would you compute the bankmabq+fdxmr3j9 h -4n:ing angle given its speed and radius of thrf+ 4:bmn- 9jh3q xmdae turn?

A girl is whirling a ball on a string around her head in a horizo5 z* 7f evylwhpw0.k4tntal 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. When5kp. wz047 yhvflwet* should she let go of the string?

Does an apple exert a gravitational force on th7t* yvf15wjp63bd k. rr;jvcfe Earth? If so, how large a force? Consider an apple.y6 t 5fbrr7v3jpd kvw fc1;*j
(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 orl: q1 ligina25bit b51: i lqingla2e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E) 18fsdkx;r q,mzenrt j2t1,8x ult 9nf2pj :qarth;njfx tdu8qxrz1st:) n29k,p1qfjtm ,8 2elr? Which accelerates more?

The Sun's gravitational pull on the Earth is 7/tx,o8jgt.i+gzjog ;.dp mw much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational px.ojm/+t ,;z d g gioj.8gpw7tull from one side of the Earth to the other.]

Will an object weigh monl xqz, 9;;pf2argyl0re at the equator or at the poles? What two effects are at work? Do they q90;pxlnya ;rg zl2,foppose each other?

The gravitational force on the Moon due ta*l m( :whx8uwb d-)ozo the Earth is only about half the force on the Moon due to the Sun. Why isn’t tmww)l a* -8z hux:bod(he Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around th-z )h w4a gj /9hxl- kfxf/bbsvn8;+due Sun larger or smaller than the centripetal acceleration of t -djx+v;wku98/)z n-/bl 4fhxa gfbsh he Earth?

Would it require less speed to launch a satellite (x .v 8vc svq3.7 e 1nzt-s1cqgcud+h4ba) toward the east or (b) toward the west? Consider tc.nq -gzc +e vqvb81v.1ht 7s4x3dusche Earth’s rotation direction.

When will your apparent weight be the greatest, as er6 jr dj.73tcg0ep-dmeasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) ar 0pdej67r .ctj3e-dg ccelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adverse3; qw v+tna(0+jgcj cbly 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 simulatevcj ntg cjw+;3(+0aq bs 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 weightlessnetunrv4bi6 s,1 8a 2lofss” between stepol6fu s 8nrt1 2,vbi4as.

The Earth moves faster in its orbit around the Sun in January thanb.ej: e3qhu1 n in July. Is the Earth cljqub :3ene1h .oser 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 until it was discoverkt,x s/mw ,zm2t *9fnoed to have a moon. Explain how this discovery enabled an estimate of xmf*9,n o/smz,wtk2t Pluto’s mass.

  The Sun's gravitational pull on thez+ rs9ja3r2: 37lkjvzl au5yx Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A cl3jlkasv 52j:9xa +37y rzzu rhild 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 whdx1sr 6nrf7s:2auh7 m:2 ir z/z .gi1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbit ar-,0yp .n 7qtkge sx/3lanko:53 ojlbyound the Sun, and the net force exerten,kbo k0ajlqyp3e7y3t5 n/s lox-.g : d on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 7 iia7b v3t *:bt im4 8k2v0 (1-jhgqtksosqegN is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of(k 7vt1qieqmvhtj3 *sat8- i0igb gk :7 2s4bo the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and5 *fch+h;h8 f+gx s4qdbqu)t *d7dmdq circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answefmq*d4 8;q*ch d+7fht gq dubdh )x5+sr in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a 1o;x8::bq /i6xaq (ksrgbo - 5etlezgspeck of clay on the edge of a potter’s whee (kx 1e/o6a; gxq:tqlg-sze:i58orbb l turning at 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 verticalesjj qsujw5b;f4 x8 vq*5b5x7,lz d5o circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.7,jxqw8bx eqzd;55 o5 jvfl 5u*jsb4 s00 $\mathrm{~m} / \mathrm{s}$ 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 84:izjr hhmf 97dilc+3 gp26i5ejanz+xvnk8car can round a turn of radius 77 m on a flat road if the coefficient of statck4 9xd8 z7l36+ : mjirvjfgh+ ihniaz58npe2ic 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 fric7a,:n(myl5:sd d ,)txl npps; hgz -uktion be between the tires and the road if a car is to round a level curve of radius spa)ysn, ,kt ;gdlmu5xh:-(ln zd7p :85 m at a speed of 95km/h ?   

  A device for training astronautgi6 yw) k piwzrf,0.q0s and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felyz 6 .0f)w,gkqi 0iwrpt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cio3vn3ly1 yb *m from 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 frictl* n3vyybi1 3oion between the coin and the turntable?   

  At what minimum speed must a rollrcj+q)vmq/x 33*bjzobi9kf6 er coaster be traveling when upside down at the top of a circoi+q)6q3 jvkbb3 /mxfz9 jrc* le
(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 d ( mgexlg6c3d3river) crosses the rounded top of mglgc 33x ed(6a hill (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 15-36a bk4 yuve,3ig5jns m-diameter Ferris wheel need to make for the pv536uienays4gk, jb 3assengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is wppm;ojvv n--yc9t 0o771gbc rhirled in a vertical circle of radius 1.10 m. At the lowest poi;7-ty cvbcoo1gvm 0rp 7j n-p9nt of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from- vb+4( z:cv kg5ysbsm the axis of rotation is to experience bgy5s(cmks : +4vzb -van acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pehaqcn-x1a4 s qh4(o0k,blr m5 ople are rotated in a cylindrically walled "room." (See Fig. 5-35.a4n,hlcq4r10o sq a -k (5bhmx)
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 frictiofp 2e hmrha-04 5a*vkenless air-hockey tabletop, and is held in this orbit by e ahe2-*v4krpa05 hmfa 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 , pduo,p7/7q s ukrecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In partic, s7pq kud7/ouular, 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 2d2hd-trke,1qkl5dmcg0k1x j7vr+ g 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 masseg*12aemcxw( b +v)khptmb42ys $ 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 v:3)qioev3xr 2rijq(b ertically 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 compon2dy6q9 n05 kh bqzvf 6uu-x)moents of the net force exerted on the car (by k2-9 yo dfh0xuu5zqq 6n 6mbv)the ground) 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(elufh/c*88dz :sy jk 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 were flat, what would the coefficient of yu:8cdjsl ( 8zkef/h* 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 mvhqa5(s,vr/ particular instant, its acceleavhrs,(v m q5/ration 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 : 7 *egkx:psczyjiv(2Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) py e2 zgk(v:s7 j:*cixabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hane n+8 q3 l63dneyk; pog,ci0uz;9jdgs a magnitude of 12 e;gc;ul9 6iednk3y3jn, z+pdgq0 on8m/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 accelerati7gvlj y*o+p;t 2lg , .3xchru2twf0cc on due to gravity on the Moon. The Moon's radius is 1.74 0w*2.l37 gt g2fjt;ycc,lxh u cv ro+p$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 t3 7;-fmenxwnhq9csk+ imes that of Earth, but has the same mass. What is the acceleration due to gravity near its surface sqw9xmk+f- e;nch 7n3?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the saf )rlr:u 01mgzw/eid (p3q +zome radius. What is g niw zm+3fup0 rel/grq o:)zd1(ear its surface?   

  Two objects attract each other gravitationally with a qaeq.)zur) :3g u2 9x+ tnvu7ywolze 6force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravpy*pfl q25gisq 1-(pr ity, at (a) 3200 m 1fppgryp qsq*i52 -l(    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wherecasbjbw a8 )0+ thegravitational acce8cbs0)awja+ bleration 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 ouj ;xe:ntfzy* 4r Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thit e;n*y 4:fjzxs monster.    $\times10^12$

  A typical white-dwarf star, which once was an c3tuemj8q76 :kfz uv;vlf sl9i7t,:naverage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has::jntf6z v7,elq9; 8m 7c i3fsuktvlu the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weigh)sfr 4glee:y/tless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the accelelgys4/)e:fr eration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are loca5w7/tdjzcl 21 a d6, d5vxb2mqxx ggv.ted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerte5l6xqgd agbdx x7, w21j.5dvm v2tcz/d on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most jx8-zu qvgu) /of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four plane8v-q u /ugxj)zts 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 gravi ij 4 (4xsjxf 5l+sgbeey1-1ghty at the surface of Mars is 0.38 of what it is on Earth, and tx be14g4ejifjsy( ghs- x 1+5lhat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun u8ql6;r ih 2 gdd.g3f duc.xz1dsing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained udd13 8 6g . cxgurzqd;2fidhl.sing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orb/ sx*7x/f5 qr i qoex+n9lsdcb-d w:(zit about the Earthbwq5 dox:(d s+le7-*xn f 9xszir /cq/ at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitiu fxpmlw (88n63uv 32zi otf0e into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release ont 2iofz fupv3 xm0i(8ul83w6 ccurs?    $\times 10^3$

  At what rate must a cylindrica vkxpizi1n1f4gdkdge5 l18; .l spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 8n1de x. ifi 1dk1gpgvk l5;4zm, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time iz1b0 +lrbg1bkt takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is oz1g brb k0l+b1ne at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wp7lddrie itn( y c0 2w50owa;5ould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earte5072a0lw5r;iydodip nct (wh?   

  During an Apollo lunar landing mission, the comman8v cd4ib tn0x. e2cco,d module continued to orbit the Moon at an altitude of about 1cx2en 8d4ct cob ,v.i000 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The in ,xhikp68g6 g,ti -9ao 2hr roh.7htvm0jk:oqner radius of the rings is h6 qt8o :p , -ij9haooiktg.hkvrg7, rx06h2 m73,000 $\mathrm{~km}$ , 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 Fig. 5–9 vei1+ q4ei5tby,ys 4p he:e0s). What is the ratio of a person’s apparent weh4e etvy4sp sye:+ei5 ,q0bi1ight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight 3:+0 wun 8uy kd kt4h0pzyq+zcof a 75-kg astronaut 4200 km from the center of the Earth's Moon in a spa84+ znh+tyw0pck dz3 k0uyq :uce 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-1e1+2mk4hat 1 jru w(5;xg u9gx bboqystar system 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 ogjb1q45ybokx u xm+ t1(9 21rugw;ehaf each?    $\times 10^{29}$

  What will a spring scale read for the weil5z n+ 7kgcrn9 7hqsr+ght of a 55-kg woman in an elevator that moves+ k9rnchsq7g5rn+ l 7z
(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 suspended from the ceiling of an elevato*nq8k5 hn..vfvrw( w .2ry1 ffe9edzor. The cord can withstand oev.dfvw1 .fh.8 5 nz*(qkryw2er9nf 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 thdk- enq)hah 0:e surface of a planet with period T , the density (mass/kn adehq) h:-0volume) 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 detpiw -7sp7qswz yk4 4j)ermine the period of an artificial satellite orbiting very near the 4q-i ww4p jspy)ks 7z7Earth’s surface.    s

  The asteroid Icarus, though only a few 9dl1z(7 h n)+slosf duhundred meters across, orbits the Sun like the planets. Its p9ld sd z1u7 (oh)+lsnferiod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o)5 uvog bh a4(lp/5latf 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 px+emdbgv2,i * f5u.blffg7; the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it stilb fixp7f fu*l+ ,gge5;b d2m.vl “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 c gpi9p n ipq.y,tpr+i13b- 7muenter 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, pgd m-(:da3 hnr85tn3b6tiu xheriod, and mean distance for the four largest moons of Jupiter (those nu6-dd (33g5ir :t8amb x hthndiscovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distanc37.rbn-z 4vy)sns r+h egj2 qse of the Moon. gv3y4. 7)qe-+zbss rr j2snhn   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter 5cnf6 hrkbc,syz( :d+’s moons, using Kepler’s third law. Use the distance of Io and the periods giv( f, b+crcd5y :khzn6sen 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 beu1a 6. g rbclh)mwu8ti,d05o dtween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed).6w)itg58o0l u. hm u, dacb1dr
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of nf*n;5eg f cn h03y n;l6cvgcr5dpk01a band completelyc5ffn ;0c kn 3 5gv0nyd1*eghrnlp;c6 encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine kmov uqe4 6xfn2: + a.3rxnju7(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 tolerat: 6fa +xu3mj24 qovkur7nnx.ee at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whaiy q f08x+qsj dr:oog k2b;*e9t it is o ore+ykfq92bj qx:0od8i;s*g n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab huenrb5v 4sk/b,hm0p8y1 ; cqs ands 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 on one/bhqeusyp5 s, 01m;v4r8nbk c another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleragu/ ke9 v1cxl*tion of gravity at the 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 thiv1k g*/ uelxc9s?    $\times 10^{-1}$

  At what distance froms4* qwn/du5k f the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moonskn/4u* qfwd 5 pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on askxr,b b w 5hi,;8d3v jv6z3eq bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the el5 8i,jq,vb 3d wk3xz;6er vbhsevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate al0t(dy 3um; rd 61sq:qbs8n 1up uy+xm,s3g jnbout 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 rotation speed (revoluqd yjm8 6uqpxln30t3 1nr, sgyss; u1(mb: +dutions 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 7u++4.jjaibwr-imjr 3s; n zzloop (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 q w87q9)8;akd pvnuy z3mlbu 2the mass of a planet in terms of its radius r, the acceleration due to gravity at its su8; m9q7bpuznlad)2k3w8 qv uyrface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is de5rz.a4unz7p m q* uekbt8 -e)dflected from the vertical by an ez b .nrk8aeu q-*5 um)z7t4dpangle $\theta$ 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 tss 7+0nha5zd If the coefficient of static frictio a5htdss 7+n0zn is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that sz(y 9 ueu0-lu1ik,a)nvao6v zwlx+ 0objects at the equator were apparently weightless z0s kva1w0 l9u6 vxu) +ale,yu(-izno?    $\times 10^3$s

  Two equal-mass stars mcmtds9ik+u2l;,s g1oaintain 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 rounds a curve of radius 235 m. Ayo+wqdcv0a3*: lgbv lk5 ./r3rfh6 vx lamp suspended frqllbdf*ghk v+.rcw:3 5 rv/a0v6oxy 3 om the ceiling 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 bee 6ws87hhz wu+5pe;dlz n claimed that a person would be crushed by the force of gravity on a planet5u;e7 6wl+ dpzh szwh8 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,qj qb0yl.hj 0 the presence of an extremely massive 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 spl,qqyhb0 . 0jjeed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the .o i vapyouosc3;d5 jztz; .::hill and valley shown in Fig. 5–45as:vc;pzu:ooz3 ot.id5jy .; . 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 fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utek i74q( fika:::wzpdilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational :fd7: e4(ik :w izpaqk“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), aftervb yvl:zmhv1:iz,(, b7v g mk94h+inl traveling 2.1 billion km, is meant tol7vvh+, mikv,v9:b: hn(z1glzym4i b orbit the asteroid Eros 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 pursuing a satellite in need of rv)e q-e, qktum(aev--epair. You are in a circular orbit of the same radius as the satellite (400 km ae()ve-uetmv k, -- qaqbove 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 mxh1(,ezuh dg02v, oxgean distance frohxh,1dvz ,gox2u(0g em the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the valuep+k)gcefh z3 : nk1.*zj)lpj 1kxdc* s of G would need to be if you could actually "feel" yourself gravitationally attractec3g*s1phje) j zn 1p)lxz*f +.:kckdkd to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of thhwqzkdq r *4d :ut5ri06,y w)b; u0vnfe Milky Way Galaxy (Fig. 5-46) at a distance 0;k whw5bu*rq4 r fi z 6)vddu:y,tn0qof about 30,000 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 located at the corners of a square 0.50 m on each u018cmywu0af: okg.k side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sid0uk af:ywg8m 1o.0cku e of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 55t0xz g1:qi- ng00 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-love(8c /)bgpkzc v i8-4vc 4s3ps: hwcang sweep second hand on your wrist wat c4eapvkc(:s8cpc 8/g )b-wvh3z 4vsich?    $\times 10^{-4}$

  While fishing, you get bored and start to swin wcq 5/ypmb1l6g a sinker weight around in a circle below you on a 0.25-m b156wy pcm ql/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 7ldvh 0hxn ejc5n++hrcp1reahb0o 0c o:y -99in a new highway is designed so that a car traveling at shnn+ rp9 9h0bc10-h5oyh:rel xc c jv+e7do 0apeed $ 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 ti x oenswoca/*(ek1a2 7lt of the cars when negotiating curves. The angle of tilt is adjusted so that the main feao wcs(/721*noxaekorce 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.$\approx$    $\times 10^2$