Sometimes people say that water iso npm-n a1i2m j)s61jq removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stat jp121 )-n snqo6immajement?

Will the acceleration of a caslkdf6;d/rovtcgwy, ( :* o 8ww)xc.sr be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expla/*o,8vr ;xsgws(wk6 dl )fytd.cocw :in.

Suppose a car moves at constant speev.jgyg3 y7x xoo g;f/ pji((/ed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip .yfyp(/o v;ij7 3xe(ogjx/ggbetween two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces2ypudh:m2mig10 g i l7af*y/ 45d;4vjndsm la acting on a child riding a horse on a merry-go-round. Which of these forces provides tg5l vmd ujimm7lgya412*:d;h0n s/2 f py4 adihe centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cir xa-v+y,3ibt97pmh 0;hf atee cle without the water spilling out, even at the top of the circle when the buckehx -a vhe 7ef9,typit;m0 +3abt is upside down. Explain.

How many “accelerators” do you have in your car? There argv5qg ;:w 0wzh/vs 5cze at least three controls in the car which can be used to cause v sgw qhvg0:;w5z5z/ cthe car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyin1erk347u kvv)f vo)gjwbmm.)p a 2l :gg over 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 theggku1).m2)bpv )4v a7:vewjfrkl 3o m 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 l b91ybbvd7voq58l(r j q.z3hd ean inward when rounding a curve at high speed?

Why do airplanes bank when the 6oy5i jt-ja;pciy (i+y turn? How would you compute the banking angle given its speed and radius of th(ip;- j5yitc o j6+iyae turn?

A girl is whirling a ball on a string around her head in a horizontal ph ihp mi87fcwu)z1 21nlane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let gohmiu8h 17czw2n i) 1fp of the string?

Does an apple exert a gravitatio916iqmuhzsd w.:ml2 orhl63 tnal force on the Earth? If so, how large a force? Cons6hmt1i2l :rzms3.ou h ldw69qider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, vhz30 +sm-zvdos36 z8jehel *in what ways would the Moon’s orbit b vj6+0e3zo- s8z*mhzvl 3s dhee different?

Which pulls harder gravitationally, the Earth on the Moon, or thm(7h:zc z snl gd:sz/1e Moon on the Earth? Which accelerates/s: :g n7zzd1hlcm(sz more?

The Sun's gravitational pull ouw 0izh(2p d *nu7zn0yn the Earth is much larger than the Moon's. Yet thehn27u ( uyz0zi0*p ndw 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.]

Will an object weigh more at the equator ehuj;hh. qb4 m19e0yoor at the poles? What two effects are at ojeyh10eb; 4 9mhh.q uwork? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the f9,0jea j14s pdlnor)porce on the Moon due to thesp9e410n rdj)aploj , Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars h 55cwxc7j mxf*-rwp 1in its orbit around the Sun larger or smaller than t*h prfxc1-cw 5xj5m7w he centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a)ygav mvu /gyk -tzjqv97)( yg6j ,/j,j toward the east or (b) toward the west? Consider the Earth’sgvyv/ ) jj(-qyvjujg gk/ay t6z,97m , rotation direction.

When will your apparent ssd*w2i8/lx t/m,xj ay2 b/w/vq b)brso5k u3weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are onsq/uvr2 2 wwidsmljabos5 b/xyx/bt,3)*k/ 8 the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectpbr-:.od q:o xed by weightl:pod rqb.x-o :essness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appa5u+.+bzwv spx 6b0sw)s o :r 61zowlidrent weightlessness” between stwp :d+w6+0oz1u)sx zbsr i.5sbwl vo6eps.

The Earth moves faster in its id 9 uvou)yva81: vro9orbit around the Sun in January than 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 thuav) 1ou9y8 9dvoriv: e 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 discovered to have a moon. a0j-dl mml18 )bv/qtxExplain how this discovery enabled an emjvt0ldq lxa m-)/1 b8stimate of Pluto’s mass.

  The Sun's gravitational pull on the Ead+kn3tq g ygs k;8/zy+rth 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 oth8z3 kg+kq/;y +ygtndser.]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 travelingwj2y) fkyi+7czdzno(0oq*3 37 o 7jbywvtz* p 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 centripetamhf+yr:ky+6c uvw1 6nom3 ,jml acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the ,yfr6m1u:vmjo+nhc k 63+wym 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 2xbwuas7mls6 c4v- jsuo qqx3h 70(u34if:3 kp10 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0 klu f4s3 x:(a 7-6iwj0psuq3xh vc3s4mboq7u.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit (pk:je94,yu y uzfm:d400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acu: ek(umy,zjf p:9 4dyceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the eyoc ap69xm)o5g08(ux v9fp omdge of a potter’s wheel turning at 45 rpm (revolutions per minutxoy(p g86ucmmf0vxp9 )5 9o oae) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertichwf2p 0pny,g ,al circle of radius 72.0 cm , asfp 0pw,hng2y, shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a tur9- uakx 6 p**m j,k+dzfxzuj1pn of radius 77 m on a flat rxfx pp* kkumj*zad- zj,9+u16 oad if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient 7.hlye w n2tw.of static friction be between the tires and the road if a car is to round a level lt.7ewwh 2ny .curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fightr v, 9o8ldm5drer 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, how fast is sheo5r rm9,dlv 8d rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a ro+m r:iyqp4s1ainz 9de9; *rqitating 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 reache9*qpmzai 4; n1y9s:rqiir+ded 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 upsideu sra 3)w0yeax(z63w8dzcb ) f down at the top of 3asrcu ( 6)w3z8xawy0f)ezbd 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 driver) crosses thcsa,jsa0m4ru2lq q d 7(b7x t*e rounded top of a hi csxu7s j7,a t4mq2r0*bd(a qlll (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 wheel neenwl,57s2 wh c1ptlh,fd to make for the passengers to feel “weighn,tll 7wcp1s2 5h ,wfhtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a 9fm6c upl3mfm+ bx( b6vertical circle of radius 1.10 m. At the lowest point of its motion the tenscb 6lmfmmf 9+ pxub(63ion 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 9w8:z g84zz ,yoc tw79sjrw0gf .00 cm from the axis of rotation is to experience an accelerat: cw 8,o79jzg04tsgzwfwry8 zion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, p p9 kh:pa;y()ey0t :h,n x9ibh2qt rwpeople are rotated in a cylindrically walled "room." (See Fig.y9kh hi9p a;r0py bn2tp :ewqxth:(,) 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 rotat k 5ab.6p; vchq0x;iynvuc)8 r(qu.eied in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connectede p bhva;xq80i6 un5v.;r.k(ycic)qu 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 , preciselu5kneubo 5o5iyh r:/0 y this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particul 5uku b:io hne0r/y5o5ar, 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 perfec (zugb ov2+u9q*bfsm4tly 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 c1s 7fa5u mbowrq931n $ 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 verti4zi4vt)kqh: vx z(rq2cally 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 tangentialip ,ia(8 ;q;mft izsl 59dm/ni and centripetal components of the net force exerted on the car (by the gro;l5/ f9p i8,mm i;ds zn(qitiaund) 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 Indianapo bl*(:;2qlpvva y b tvr812j)eyfw:rulis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car whev p:qybt*2 vbj w81 a):v;yl2eru(frln 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 mp2afix s.vz .) . At a particular inst zs vxpfi2.).aant, its 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 12,8 *n-(4,rxr0zsubrzi 5poe ,t c00 km (2 Earth radii) irrz pztn4sx,oe u0rc*( -5,b above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationapvlwdkyk 2 k /+;bvk4(l acceleration g has a magnitu/4(vbl;kpy v2w dk+kk de 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 due to gravity on the Moon. The Moon's radius is 1.7n/z xg6uugi /cm40n. p4x n04gi.m/czpg/u un 6 $\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 sv:k+9+ej oe5bgd i 74gqms6 ghas the same mass. What is the accelego:9ikvd5 4sb 6 +meqj+7ggse ration due to gravity near its surface?   

  A hypothetical planet has ;(gn14ba irgya mass 1.66 times that of Earth, but the same radius. What is g near its1a( ggr 4i;bny surface?   

  Two objects attract each other gravitationally with a forcej*r2yvj ,ekn ucsf-x5 0rxm4a(kv+n 6 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 acceleratio3tjzavr0z+au6a4: 4 kw * zbhdn of gravity, at (a) 3200 m abwduj3za 4zak:4*0r tz+h6v   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eartdi9 xf0a1rnr:dw*i 1 sh where thegravitational acceleration due to thw: f91x*nrd 0ai1ds ire Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pack1lestin12r1xsxogw 7s;8m t9 ed into a sphere about 10 km in radius. Estimate the surface gravity2l 1o9 1 1me8sgxtsstw;rx i7n on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an aveb3j ofi*ae-1y rage star like our Sun but is now in the last stage of its evolution, iie13j abf*y-os 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 fezpwyk-*;gs;t+ 2b bflel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was juswbpftyklsb;g +;-*z2 t a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a ozgrnmmd 2b;*x ky7vp5ho)v /,c cw/) square of side 0.60 m. Calcuc/ yc;h5*m2mb)gk 7o ),dw nvzoxv/rplate the magnitude and direction 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 so:n rphk/. *dyide of the Sun. Calculate the total force on d/. r:*hkn yopthe 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 uw -tsc/3je l7of Mars is 0.38 of what it is on Earth, and that3etwcl j7 -/us Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for 2l8ng-n7+d:wfk;gh v8v fvmh the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtaivgdn vw; km -l+h:28fv8fhng7ned using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular;ai 6kf -6lf2gci ppq o:kc41a orbit about the Earth at a height of 360coa 1ka4 fqipg f2k6:lp ;ic6-0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circu3t m8wcf7dsnr +69 prxlar orbit 650 km above the Earth. How fast must the shuttle be moving (relatirsnrwf6t7 m 8+39dxcpve to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship roted ekr *.ms./eate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diamete..ee*r m/ke dsr is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the j;;sy2jzlbs+n9k yad3 c6rj 1sug7-hEarth 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 depend on the mass of the sajjbs79 uajys1 -y2rkd3;nzg l+sh; 6c tellite?    s ~    min

  At what horizontal velocityb kz6zcd b,dh;;hx hp.4h 9c:z+n0q h:z j-rbr would a satellite have to be launched from the top of Mt.;9n hc:bqd cph4hrx.j -hz+hzz; 0d6rkb :bz, Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing miik2+r)o8to z2d 5v zgqssion, the command module continued to orbit the Moon rt52vkz d2zgi)q o8o +at an altitude of about 100 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. Thehj (fb1*hwzv a1,vg5v inner radius of the rings is 73,000vz1vabfg1h,( 5v*hwj $\mathrm{~km}$ , 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 esa. )di*9b1 9ve bbbervery 15.5 s (see Fig. 5–9). What is the ratio of a person’s iebv 1bb9r9as. * )ebdapparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg asw ni u,2o* tc6n/ivo e5nod,t7tronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) 7n5i*6,e2wo /,ud nicvnottomoving 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 consistj7am gag3 ;lp5s 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 bajl; p 7m5gg3aetween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator tb 0)x6k2+*8nn 2xvnb(n wucu,sv dedy hat modnv 6 xsdc wb+u,28u yevb) n0nnx2(*kves
(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 cp3n,z0 lg: lxhord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnituplg,l0 zx3 h:nde and direction)? a =   

Show that if a satellite orbits very near tk nnb :iad0)gxcl0a;.he surface of a planet with period T , the density a0ng0cdalb)in;:xk .(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 per9nuo*uhw+ j, riod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surjnu+*whu ro9, face.    s

  The asteroid Icarus, though only a few 6 u7bp u-,*kk;e4fptfx1wp zf hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from ;w1xp ffp u u-*,6fetbkz74kpthe Sun?    $\times 10^{11}$

  Neptune is an average diry3zc 1w8flm)b g)gh;g:qy -kstance 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 orbitc3 pnuk zx n/*z83je*ms the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estp*n j8mn/3 uzxkz3c*eimate 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 the n+ b8;asmu rl6lv7m qgs /qa3-4zv(kwGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and meanyv )0vudq f5h5 ;cral, distance for the four largest moons of Jupiter (those discovered )q5ld ah fru;y5, cvv0by 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 ant(:0c6 zloi1jxd9f+ le bqr.sd distance of the Moon. 0 c(i6jzl. q:fe+9lb 1 orxtds   $\times 10^{24}$

  Determine the mean distance from tm0zwl:4;l- s6lw fep Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in t m4swl ;60lw-ez:ft plhe 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 (whichy iq/,wwz1r) h some space qhiw) y/r,1 zwscientists 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 describes an artificial "planet" in the form of a band c k,)dir( w).a6flb wzjompletely encircling a sun (Fig. 5-40)6aw(i zjr)k dwlf,)b. . 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 vbvdasr 809y /arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 90a/8 vysbdvrN 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 acci3 8e1dqhpiw* 0i4 ltheleration of gravity be half what it is on the surfac h0t ie3qp 1iw8i*l4hde?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spi oeh 7fm )2dp bje82w2ggun*.hn in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses adwb8u*p.n mg 2h2ejo7fg )h2e re 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity at f8vlu9nah /c02mbtir4m vj3e6: dh.nthe equator is slightly less than it wora n9n 0 3cvm2t 86fjvui.dhb:helm/4uld 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 j+(* hn -ke 9f.fxnum;4zslsya spacecraft traveling directly from the Earth to x k flney*-(.m usj4+n;s9fzhthe 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 whv8+oe g7tc2vnw*br*uz 3b.te en you stand on a bathroom scale in an elevator, it says your mass is 8o+nv *3e8 7c et2v.gbw t*burz2 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular;w(w2he u*ewswov6 9h5p2rca tube 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 wv9ru2 w2*whhe6 sac(p;ewo5km. 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. 5j y:aln9n be-2–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of ir x(ij3 ccxi8db;w7q +ts radius r, the acceleration due to gravity at its surface and the gravitational consta3i7c + (rjqb8;iwxcd xnt G.

A plumb bob (a mass m ymom2v c,n i/8hanging on a string) is deflected from the vertical by an angl8vnoymm/ 2ic ,e $\theta$ 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 cdm3 f 9yx/u8nm is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely hanc m9x3/n8duy fdle the curve?

  How long would a day be if the Earth were rotating so fast that objecy8.slr0r 3 7db -sr8q o wr+pr5j3ie)tv o.tfhts at the equator were apparentlyorsr5lrr8 dy-i stv.w0pt .38obj hr+ fe) 73q weightless?    $\times 10^3$s

  Two equal-mass stars maintain nhgm;hntj) )6a 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 9ksks7qodk s yx)wm34*mg2, hradius 235 m. A lamp suspended from the ceiling swings out to an an2qso,*k47hwg39 m ) smykksxdgle 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 halhm 3 5z,s7rgxf 1q/iys 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. Calculate the number of g 's /f,gsyql 35z mhi1r x7a 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 presence of (wngmy,9 vz n9h hf-f)an extremely massive core in the distant galaxy M87, so dense that it could be a black hol9fh n(z-vn,h9 fw m)gye (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill 1d1( k:jlztw/p ozkb9and 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 wou/kljb9dwo zpk :(1t1z ld 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 Systemp c3+6pxh+s mugf;bt / (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of apprfc+hmg3bt 6+pux ;/spoximately 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 sw)htbs4a xn ;h 9u7s)traveling 2.1 billion km, is meant to orbit the asteroid Eros at wu t9bxn; h)7sass4)ha 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 sp hnxy,*/g:9rb 7ngzx oace shuttle pursuing a satellite in need of repair. You are in a circular orbit oy*n 7o,gxg9:rb nx/ hzf 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 mean -7tmqez2mytkwe(2ju q fhc o)aj;8cq/;*s; e distance frt ejt jq )2y e(w7fe* maco8/mc-;s qh;zuq;2kom 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 value of G would need to be if you d,(q lw.t5ofz at;r6ycould actually "feel" yourself gravitationally attracted to someone near you. Make reasyl w,toqz(;5t6. rfa donable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around t2q syt0r+-6rozgpv;sbj 6 .sm he center of the Milky Way Galaxy (Fig. 5-46) at a distay mt j ;-r6sgsv p0zo6qb+.s2rnce of 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 side.ewj ud.mt .w,jvsj.)aa( utvune77;. Find thjduv. us jt)7 7wjun.at.vw m,a;.( eee magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi-rlv8 e/6uo dlf9gvk*ts 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.k2h h7q:cy/q-mfo k r55-cm-long sweep second hand oqh7q :f om5kc-/2ykhrn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swy9qcxq3jh,4xgcp/ 4fyk -+vi on k4/ging a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that th4y fj+4 q -/kxq,4k vcp9xyg ig3hnco/e fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway ca x e0.i/mg*6cw7tnmis designed so that a car travelin7/w.m0c g*xa6ticn emg 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, utilizes tilt of the cars when negotiatin r9of;lo *o/ 0gwowig6nm hn,:g curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accelerat nr9w,w/gf0 mooo6;inl:og * hion, 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.$\approx$    $\times 10^2$