Sometimes people say that water is removed onmhm5f+4 dx. xo24b( w0bfxkfrom clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stat4 +ob52kfo0nx 4xb.fd(mmwx h ement?

Will the acceleration of a car be the samev;y34nql,gl o when the car travels around a sharp curve at a consta ;l,qv4 3onyglnt 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. Where doe:y 7,bdok x,ay xzsjfxw+.6 e8s the car exert the greatest and least forces on the e7 .wozkyx 6x,d 8yf:+ajbx ,sroad: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces actingl 8 hna5y*x5/l7he mrj on a child riding a horse on a merry-go-round. Which of these forces provides the centria57nyeh*5 jxlhl/r m 8petal acceleration of the child?

A bucket of water can be whirled in a vertical circle withou h+g-/gtt 9raiak-m ;dt the water spilling out, even at the top of the circmkg-haia r-t +d/9tg;le when the bucket is upside down. Explain.

How many “accelerators”1vmfm 2y q)se 2lb/bc2 do you have in your car? There are at least three controls in the car whvlqfm s2 1) e2bbm/2ycich 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 hil r4jv1ex a1n:pk m y(gus2tnm69n)gb7l, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal fk ntymr24m 1 69s1 (jgxavpbu7):g nenorce 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 cu uflz+0xefay(/t0 t (grve at high speed?

Why do airplanes bank when they ** 3fmib i64nxw3xakqturn? How would you compute the banking angle gi 34kx 6ni*f*aixm3bwqven its speed and radius of the turn?

A girl is whirling a ball on a string z(dkc97z:p(lfz b/laph td . ;noab 43around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of bd(l7z;hl:4c 3ppd tznf akz( .ao/9b the yard. When should she let go of the string?

Does an apple exert a gravitational forcewcz(o 1-hj) gb on the Earth? If so, how large a force? Consider ajo- )cwg(b h1zn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would toa.xg1m6kb+ vrz -ad :pl ;n+zhe Moon’s orbit be dzzrmn pobl6;a+ :a kxgv1d.+-ifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the lctyvf3 k myrsf-d*30:1v2qs:wl z6s Earth? Which accelerfvk1 :qr:yzflmvt6lsyc s3*sd w32 0-ates more?

The Sun's gravitational pull on the Earth is much largerdc9sdb 11psmc :-cr/ h than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the hd sc9r1/c:c1dp mb-sother.]

Will an object weigh more at the equator or at the poles? What two effec9v:;af;g j a)p8x ,+tdg 3pit6uvjjfcts are at wor9 g8pv+u,gta;fd cp3f):v6tj; ajjixk? Do they oppose each other?

The gravitational force on the Moon due to the .cluet02x8 qz Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from theq tzx e820ulc. Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger o vod1r,hpm*b 2yf*33waw q1ms (o0hlvr smaller than thvw1h(pm 1v,hlo3rsd0 m fwa2b3 yqo**e centripetal acceleration of the Earth?

Would it require less speed to lareazawr:.3 .cub;0 vh kyl9k3unch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dire.rlaukbh390 e r:yk;.3w acvzction.

When will your apparetxisg* a 4eg;8li 41/s( dcisnnt weight be the greatest, as measured by a scale in a movine; 4ig1nl ig s8ctas/xd(4is*g 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 on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long perio/l.ikh2km 37v;lpe8 tuuh k hb-jypv32 )f/qdds in outer space could be 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 insid. /jd8eku3m2h pi)3k-hf;t lbp7vqul/hvk2ye surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessna4h +h7(py; sbwh.o, duhq6jg6xw;rw ess” between (xq.7ahw ,rbwwy;h;+ s6hou6jdp4gh steps.

The Earth moves faster in its orbit around the gerbejiqwxib 72,,o l +p 3w.x6s tw1(Sun in January than in July. Is the Earth closer to the Sun in January, or in Ju,ibwg+s7ortwei3( ql1pxx ,2 .jb 6ewly? 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 discover 7 jx0crukg(/;apdpkbrui, 9 4ed to have a moon. Explain how this discovr/dbci (p4 u;u90a ,k7rxgjk pery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mue)r ) 0dxun5buch 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 sitting 1.10 m from the center of a merry-go-round moves wit) 5ubde xu0)rnh 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 19807saonncx y ,w 0tu g;hq29md;, $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accetc eszy)ee3 :4leration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force4 etezys: 3ec) on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg z:r 1ff8etrf1c idvd x.5+i. hdiscus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. tvd1r.dz hife+f . :c85ifrx1Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fro8zexsvdszldm+(xe 970 ,7z wfm the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal 7ewe70s (mdvdf, lzz8+sxz9x acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the eftlw;: 5vvvdmpg2 1q.dge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dv .2tvqv:lwp5mg1df;iameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in;e0y5 u k;e8. nj9rd(nwsyvbf a vertical circle o nr nvky;u5.08f(wj9 ybd e;esf radius 72.0 cm , 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 spt0 r0d7bqv4kdqsc( .feed with which a 1050-kg car can round a turn of radius 77 m on a flat road ifc7v0d0rdb 4qsktfq .( 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 of static frictiod3 j()rfy4xtfk497zipm fme 8n be between the tires and the road if a car is to round a level curve of radif(p j8eyrtd f34 )ki4 mfmz7x9us 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilot ,6lnrv3/xv;djz l:mj-m:ykws is designed to rotate a trainee in a horizontal circle of radius n:m z,dk;/yjj6r vlw3 :-mlvx12.0 m . If the force felt 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 cm from the axis of a rotating turntable ozkmm28e/0l k(xr8 jttx y:ve+f variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between t+xktx el2kemtv mzr(/ :8yj80 he coin and the turntable?   

  At what minimum speed must a roller coaster be dqk2((kfqte- traveling when upside down at the top of a cit-2q ef(k(kdq rcle
(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 t5onwx; v m 2*xsy bw5plv1)wi2he driver) crosses the rounded top of a hill (radius =ww1;l52nx yixpsv vb o )5*w2m95$ \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 wo wqyhjsrtwv. +wag-(j+sa/3( uld a 15-m-diameter Ferris wheel need to make for thes(qa.vj/+wr-s3+gwjtay h (w passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 3nw4.qo*s zvk 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N3ko.qsv*z4 nw.
(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 the s25 zt5chua) qaxis of rotation is to sz) 5auch2t 5qexperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people arxim3 ot2 *yh-tpig6 9w*dg 6lg(dm2v le rotated in a cylindrically walled "room." (See Fld g*623y6mvi tw2pgx l9tg oh*mi-(dig. 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 c kdi;hn.+::wez8 ykhtc( oq:) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a :c;:t h:iqho y(cenw.+kzd8k light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of th/dmo +*4al qkm 4v*wvse ball which revolves on a string 0.600 m long. In particular, find the magnitude od*mo a/+m*4 sw4vlq kvf $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelingp::d /,gfuyoqd exloc* zt+14 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 massejlfrwod7 z9jkql:ui 7 )n85 a8s $ 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 verticj8lqd0u.*kmjs gif 0: ally at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force ek e/i)fu80p0a qnf/ v9usb 48r q dflj1i7gx(yxerted on the car (by the giakq7 i8 04ybd1 / u re8fq9lff0/xuv)p(sjnground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit ar32v .y00cu6lsmpea mr ea, 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 c3mv.0esla0rm6u2p y 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 kace 2z6-c.s vr psg5-m . At a particular instant, its acspak v-25-sgc c .er6zceleration 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 (2 E+ qkej. r: pfd/ooy5+uarth radii) above the Earth’s surface if its m 5/:o+f.y+qejdoukr pass is 1350 kg.   

  At the surface of a certarc9 *nt hu3ipo; w *+vb4kc/qvin planet, the gravitational acceleration g has a magnitude of 12 9i3n/upt 4q *r *hovbc+vwkc;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*-eb9 qpizw uu n5zg30 radius is 1.74b- zuwpnuqi03* e gz59 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5rl-b (x1 wad:0xx2awa times that of Earth, but has the same mass. What is the acceleration due to b:1a( xx-dra la20wwxgravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but th:jfyeu( e 7y3tpjs)sl iqc(s+jw7i( 8e same radius. What is g near its le(ciifj : 7s8(p 3jysy+e7w)qs(utj surface?   

  Two objects attract each other gravitationally with a force of ,04sx 3 yzqiohr vnq)sm3c +w* 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 acceltso ;a ,0ak 56bbmmxnvc:-i(o3z r v:keration of gravity, at (a) 3200 mvx b:m3kk a bc,z;-m aoi(0o:r56nsvt    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eartckzt; e*28mjcz5ei)u h’s center to a point outside the Earth where thegravitational acceleration28ke*t5i)e ccjuzmz; due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed *uz*yzk 6n8+e/01 ov8 o5a yrqrva lxlinto a sphere about 10 km in radius. Estimate the surface gravia*v q1 rx*e 8 +ln/v rl6y5o8zozaku0yty on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likey3x;5fr w/7c5wbdqnh; 42xk gm; fl cz our Sun but is now in the last stage of its evolution, is the size of our Moon but has the wc; /5ng 4c3rylx2fk5mxzq ;hdbf;w7mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauys3qz dj0rm+ikoxf std 35r , ee:28*zts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them as0 ij32rzr,e *8zq x :myo+fe5tsdk3 dnd 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 2jg6:nprb-ml a square of side 0.60 m. Calculatepj26nglbr m:- 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 cf+ yawi,r 1e(b( vau0the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-+(a vb i1f,yr(uae0w c38). 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 of Mars is 0.38 of wh1 5//41nqp wmquwvvxyat it is on Earth, and that Mars’ radius i4mw5 v xnu1/p/1wqqvys 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the plq:8an:s c 9wceriod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5 :n8:q 9aslwcc–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cirtwq51m3e0) 0;eqd , ;ibwq1 zzkhjprpcular orbit about the Earth at a height 3 ;phj5z pqbm1q r1;ekq0i)e,tw0zwdof 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above tr56q cd-j.l yrhe Earth. How fast must the shuttle be moving (rel 5rlcq-djy6. rative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical sf ,iirpnui7 h.7ni.p7paceship rotate if occupants are to experience simulated gra 7prui .7nihi,7fp in.vity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a co +rv45to *b/nqd /nphircular “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 Eart//poqh+nv*n5bo4r dth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from40,cn;* tilbt p9r4 xthpj:cc the top of Mt. Everest to be placed in a circular orbit around the Eart txp ,*:0i br9t4jhnlct4c;cp h?   

  During an Apollo lunar landing mission, the command module congq+ty-yo2n s-5 ku)hqtinued to orbit the Moon at an altitude of about 100 km. H o5sutg+qy2q-h)n -yk ow 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. T 4:/,n me:mmpfkhwnok h)c73 zkfwi.6he inner radiw4h z)mc 6n.w pkfkohm:i e ,k7n3/:mfus of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Wpbl v*iv v9+lzwr;d )75hz4phhat is the ratio of a person’s apparen dlzhbpil*w p574+vr)h9v ;zv t 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 astronautmc x s2n y./i9bde4o)z 4200 km from the center of the Earth's Moon in a .cb92nzy/ x mo)sied4space 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 stars of equal mass. T433gbp ln87aevr62m 3qvg fjavtvte 2 r.k6:yhey are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of eab r4gteek2 vv8n3 l.vjg: f6p2ar33y mvqta67ch?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in a9fbk puu7n5m; n elevator thauu p; 9fb7mkn5t moves
(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 suspe8nug *x1 t8ybonded 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 x*o1gut88b ny (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period s-j8*qspn4s sm/ymk( T , the density (mass/volume) of tysm*psmqksn-8(s /4 j he 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 deterl s t(v/0;unlamine the period of an artificial satellite orbiva 0 ns;l/l(tuting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acgsrjl*hb7u3c3 e*f 9dross, orbits the Sun like the planets. Its period is 410 d. What is its ml9*e hgc37b* sr3fdju ean distance from the Sun?    $\times 10^{11}$

  Neptune is an average di ap 6x806;j5pb u:dh pzhe9qc0mzaub8stance 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 ev/r gkg(*s5jblmea(0v ery 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of (*lbamk rvg/ e5gjs( 0the nearest and farthest distance from the Sun.]    $\times 10^6$

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

  Table 5–3 gives the mass, period, and mean distance for the four largdsykmdv8 fw :hf3egxj.50 1b8est moons of Jupiter (those discovered by Galileo m8 8fw fedg5yds.1k:0j bv3h xin 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 a 2dhxyd. p f7t/;dl/aipmn;0Earth from the known period and distance of the Moon. /a d/;7nid;fx2ay. t m0ppd hl   $\times 10^{24}$

  Determine the mean di:9cyw icjw5 -istance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table cji wi-w5:9cy5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter ccycbzk3, l q,j.0n 6thonsists of many fragments (which some space scientists think came from a planet that once orbited the Su6chj,,zlc 0k3 qtbyn.n 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 af/yx5769cr d/cu;e 6hhj8 h deu qr3bfrtificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, thaejd c/hq 3/;ec7ur6dh8 69 fxfy5uhrb t 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 (Fcettex.ls9e .8em.a:yb e 3. lig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass i: ebm. x 3s8e.le9ealtyet.. cs 80 kg, and the vine is 5.5 m long.   

  How far above the Eartz:-tx l /cah qet1z y1n;vd22sh’s surface will the acceleration of gravity be half what it isc212 qy x zztdv:h;es-na/1lt on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spinmrwype(r. qsn3g /9 k+ 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 areek/9r wyg .q+ms3(r pn they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelepku1pi 8l)n3 hration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate h 3i pn)8kp1luthe magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a sh*8fl3du* t jhpacecraft traveling directly from the Earth to the Moon experience zero net forltj3d h*fh8* uce 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 )m:yqp s6 no y5fpj-*dbathroom scale in an elevator, jm6spf)5poy *y- nd:qit says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station c7,f2ai/hhm sdk7 fkf-onsists of a circular 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 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 hiad k -7sfhff,2k7/mg) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lojn cq 7s2(-cs y2ll8w7o0clao kq2(bf op (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the masqiruv, )*p/5t/hb - oblrctpg4 4ds0is of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravita*l,4-di tturcriq5p bhpb)0v g/ s4/otional constant G.

A plumb bob (a mass *pj9b 7h/q:labscu l9m hanging on a string) is deflected from the vertical by an a9b * bpq/l:7sjl9ua hcngle $\theta$ 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 banked18oqg 9;zozkh for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car soo91 zhqkz8g ;afely handle the curve?

  How long would a day be if the Earth were rotating so fast5o f 0,thdual+ that objects at the equator were l0h+d5ta u,of apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dmfr0ni x.am11up * c1listance 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. Abeekut 3ov+67 w8rj-eza(yd- lamp suspendd btv ru-zee3+y8ejkwa-7o 6(ed from 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 bg)6i9qvfzb.6 sfje .zeen claimed that a person would be crushed by the force of gravity on a planet the size )s9b qgfzvfej6z..6 iof 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 presence of an e(53eiuj 3ufb4zz. itlxtremely massive core in the distant galaxy M84jeu lb3 z3 u.f(it5iz7, 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 as8 )1xfzw6rxvli c 07cf it traverses 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 t01 r) wfx76 cczf8lvixhe 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) utilizes a gq rxq.3j3 7hucijwp1f+ ygz;4afe7 8aroup 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 distx.e7zhgi uq q31rpf 48cw 7+3afj a;yjributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 b se agcm41th.bkaj0.i; w 0)vtillion km, is meant to orbit the asteroid Eros at a height w sbthv.;j1a4 m0.e)kictg a0of 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 r:y.9.qtlfcrx p 2h3 nzepair. You are in a circular orbit of the same radius as the sate yc.p:h r9qtnxfl 23.zllite (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 p-,bo ;b.kyzxis its mean distance from tx. -oky,; pbzbhe 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 nen -a-z3lbg rd9ul6.abed to be if you could actually "feel" yourself gravitationally attracted to sul3 -nz6.b baal -9rdgomeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the M2kk5-itur q w4ilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years f5kk2i t- qu4wrrom 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 cornerf/h c)rq -fc9sm3byi +s of a square 0.50 m on each side. Fy 9 crfhi+fqmb3)/ s-cind 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 square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth jkhuvk*b67(h $ \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 accelerati*vjf wsen/qi(m0lm(95x d0mkon experienced by the tip of the 1.5-cm-long sweep second hand on your wrisi0(e9mmv0 dm (lq 5wfjkn /*xst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a (yreo0 dknc9,v4 ot+qcircle 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 the fishindoqe+t,nc09r4kv(y o g line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thn1qs6ync: 9lyz h d*g+at a car traveling ash +nzlnc16g*qyd :9yt 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 t*ltdj+ n qx )q4vzq;4ahb9hv.rain, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). lx;jhn9)q . d bvtv+hq4*4zqa (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.$\approx$    $\times 10^2$