Sometimes people say that water is removed vnxh;0wdzx :w 39: svlfrom clothes in a spin dryer by centrifugal force throwing the water outward. What i9vs:zn3;wlh:x d vx0w s wrong with this statement?

Will the acceleration of a cwv+:(pu-if.g2 hi ppyar be the same when the car travels around a sharp cuywp(p 2 g.v- iiuh+fp:rve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constuhfv(5k2 s3 iz 2;njztant speed 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) uzt2h35z(f;vks jin2 at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridin ssq 4jsy1y+/afclq+3g a horse on a merry-go-round. Which of thesayjfq1+ sc+3ss/ ylq4 e forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertix*dt qdol/ 7/jcal circle without the water spilling out d* qjo7/l/dxt, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you haky)4dwbgk+t8a 0f4u.d40 etxy ak pd, ve in your car? There are at least three controlx)ft e.4d84kw kptya ad,0yukdb+04gs in the car which 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 crest1jke7(jx* wf (c3 qs mx4 +lv;phgdpo; of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease asq cpe;fxl4vgd ;khjp* 7mxo+1(( w3sj he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at : j2 sel / 5mpai8qv2hvit2i1dhigh speed?

Why do airplanes bank when they turn? How would you compute rw z)phuyxyf8m:h25,np axd 8q- k4h 3the banking angle given its speqhfh )2d8a58mz,r3 w4xh yk:-yxp pnued and radius of the turn?

A girl is whirling a ball on a string aro/zlfjv8n 4u x 4jizl6*und 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 the yaju v z4*j8l/z64fi xlnrd. When should she let go of the string?

Does an apple exert a gravitational force on the E s7o:9t)ok53 nq amshtarth? If so, how large a force? Consider ano73 sq h )ks95attonm: apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the l;qpp2 5aoswtcd r7.xm9( 3buMoon’s orbit be differ7 u ;2x(o5mpbqdlr3t9swp.c aent?

Which pulls harder gravitationally, the Earth on the Moon, or the Mooncsr6+e of0l a9 on the Earth? Which accelera6f90oe +sc rlates more?

The Sun's gravitatioh sd1 o9qu7v b/8 tlb6zh5e2xmnal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explsx9h ld1hq7mb2e zt8/u6vob5ain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wharlrapqyq 1clb297z7. t two effects are at work? Do th 79 qypcrbrllz.aq127ey oppose each other?

The gravitational force on the+ 3dob0f.kzh9d8blvtrqxt a)- ( q1w n Moon due to the Earth is only about half the forcv- +b3(xk)nbzqw tf8ra dhd0ql 19o t.e on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration v4 a7snyy0miyf4 h()qof Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eartq4y yi4ah7fnv) m0 y(sh?

Would it require less speed 0jchqk( c(ed 5/ pse-wto launch a satellite (a) toward the east or (b) toward the wes(0wd/qjcc(e- spe kh5t? Consider the Earth’s rotation direction.

When will your apparhg8+plhi 8x .bent weight 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 le8bix+.p hl8h gast? 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 longu e2byk9z5j*ugk;-f i periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Figyge f;-2 5uzj*kkiu9 b. 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 weightlessness”;7v xsjo2jke fd +q57h between stepe jvo2 ;s 7fdq7+khjx5s.

The Earth moves faster in its orbit around the 6-yd)j0p qd+ zvn) lkpSun in January than in July. Is the Earth closer to the Sun in January, or in July? Expla+ kpz)q-l )6djpnv0 dyin. [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 discovered to have a moon.sy v ri;blzt2 v*qv 1e4z*f*5q Explain how this discovery enabled an estimateei4 * sv lzrz;*q*t51bqf 2vyv of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th: c(xyww0lj(be Moon's is mainly responsible for the :xj 0wb yc((wltides. 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 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 198d-l*dsvtnteq. t6d174f8g , ppeh z1 n0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 around the xm )p8xge xk,x(9nm(oSun, and the net forc 8m nx kpmxox(,9)g(exe exerted 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 N is exerted on a 2.0-kg discus as it rotates uniforml 6- ctg lgtp/pt5o -lm( k1:t2p1skmx0;qyplhykgchxq ttpl p21pl:mt t 6s1g 0m;(/y5l-o-k p in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km f+hn*mh3f jx *3--yrl*j:ia ml1g pd : zicsu.orom the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the spac3oym:n*dx1jum:gj * ic.h+-lrs*ifhalz3p- e 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 spedozg 6(pv :88e3fyzoy89 9auaum zv2x ck of clay on the edge of a poaoe96y98ogz uvyz( 2daz 8mx3f :vu8p tter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revo1;cvrh8oel9-8j hf*p vmh bh9lved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4*fev 9bhlv;h rhm8h1 9c 8j-po.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 spo.tvsuwhv+a au0 t-wk o60t- x, fe19need with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tatuvkoaf9--s.n+ 6w 0wt1othve ,ux0ires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficmcyxy tpm:l80 z-a:/ zient of static friction be between the tires and the road if a car is to round a level curvx a 8z yy/m-z0c:mt:lpe of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desiz * j;3.mjrxgcgned 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 frx;. j*m3cz jgast 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 of variablhmj oa/snv+ fv1;:j 2ze speed. When the ;z jvv/f1 mn2joas+ h:speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must avfk.uo8hoz0+ , i(wbd roller coaster be traveling when upside down at the top of a circlek+(ood 8fz 0ihw.,u bv
(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 vcj xz4r7uqqb0- 0/s0vcz(n akg (including the driver) crosses the rounded top of a hill v0aru-0czc s /q(nxv0q zb47j (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 /k7sy exguvh1v;3o,cFerris wheel need to make for the passengers to fevsc3hy/u;7 1kgveo,x el “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticp d-u2)x d5*as6ve 6ewpft(ph al circle of radius 1.10 m. At the lowest point of its mot5ud2t6 6esepv)a hp *w p-d(xfion 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) must8wz5u u 89gpojlkb6m/ a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelerati96u jomblgz/8p k85wu on of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotax ;. gt 0ihdmj9r36ngcted in a cylindrically walled "room.;m6x90 grji3 dgtc.hn " (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless /s uv22d9m yzjair-hockey tabletop, and is held in tsyumz /29j v2dhis orbit by a 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 j.03sn 2foaz;2r 7g sl-ldv0gnfrnt2not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mn 7d0lgs rfz2 3f 2gj;nnavr0s2to -.lagnitude 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 perfectlyjn p 4002lhwoq 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 masse i(cfap p;;85c,se pgss $ 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 manepz l-*wd ik7-s 29bbcva7g j m8j-1evpuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net forvq1/7p4tbc /mz 3e5z wt fhq j/,g8uns k1qq5gce exerted on the u7,/ k85/z n z m1vhtwj es gqq134tb/fqgqpc5car (by 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 from the pit am, fxdtc,qc+ +vk923gafv7myrea, 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 thex,gv y ,3f mc2camqtdv7f+9+ k 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 i n ))4:wl:1gty ( n j016ggwj r3dgjpnkur2omln a horizontal circle of radius 2.90 m . At a particular instantr)kjgdpn0 :ln(16goyg4wj ur:w3t j l) gn2m1, 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 grxhu3 *oa+,e 7daez;*hztp r1gavity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1e3;u+r xdz tza*ge7o1pha*h, 350 kg.   

  At the surface of a certain planeuj+*pw;zh+ i7 fu)vlh t, the gravitational acceleration g has a magnitude of 12 m/suj pw;lv+)fih*7h+uz$^2$ 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. Th-cx0q/6p:u kvb fc z9rnvcf83e Moon's radius is 1.74 :pq6cvcxuf r/zc8 0 kv -bn39f$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 ti-j+d6,d f cg3osu ;, nayzfk4pmes that of Earth, but has the same mass. What is the acceleration due to gravity nan su;dc,d-+ozk3fy g ,fj4p6ear its surface?   

  A hypothetical planet has a mass 1.66 times thah57.:ia :1con0f0cta nny a qet of Earth, but the same radius. What is g neaench:n5o0a.y aq1ifat0nc :7r its surface?   

  Two objects attract each otherj;k5gl. f 7hpho 9a*gh gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g fys-k9d,2:mzq 25xe-qjgjcx , the acceleration of gravity, at (a) 3200 m 5-k cfeq -d z, sm29j2yqxg:jx   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ouu6 m9m zkts3 v;vh*r+ceq: dr4tside the Earth where thegravitational acceleration due to the Earth is 3 msv rq:6v+ k49r*;hmduc tze$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has 5w7lhl t l )4qxi-odi9ru1d5vfive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate tw )1udlh7t5roiqdv l9lx-i4 5 he surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, w n4bw y29.arhqhich once was an average star like our Sun but is now in the last stage of its erwy.h qa9b4n 2volution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astro e+9oz,0nlsk 7uun zq*nauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lon*kz,l 0su+uno qe z97t 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 locat8au:wmktfv / 6ed at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravi ka/:wvm6 f8tutational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the 5sads)d* ow+2j5b6fc dcyiy 3planets 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 planets are in a line (Fig. 5-38). The massj+c)bw5y*oy3ids6 5fa d2cds es 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 acceleraj6h+w * c wc n;-.j(+ybivtpjftion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine thjjv- f.wjn(wc+6bhyc;t+*i p e mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of bx hsa*/yp*y4 the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws,pay4/*b* xhsy Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aboutt2 cdqh fp86) f (tia*5pxec)g the Earth af 2xtp(t*id6 ccg) )pqh8f5eat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Eah1yewrr *ofj .a )w);drth. How fast mustfa) rewh*1rj wd y;)o. the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience 0qwmvr b451a bsimulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give yvmabqw0b4 r15our answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a8v(x)6yfkrq egttxf ;:*( bw k satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whichgtx86kt x:qkyf(vw)( f ; rbe* 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 would a satellitg3j7t z+0iuo xe have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? u703j+gx zoit   

  During an Apollo lunar landing mission, th pw+qyv/b 0fdn g 5spudl9//p*e command module continued to orbit the Moon at an altitude of about 100 km. How long did*y s lwqddp05//unb +9fppg/v it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbitx r+fyyl*l0f / the planet. The inner radius of the r fl+0/yf *ryxlings 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). Wha)q. /4kbbzg(1ckigzi dsx/v: k1h m* ft is the ratio of a person’s apparent weight to her real weight (a) at the top,iqvb.xiz*/) d 1 cghz fkkm1kgb4s/(: and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cwk dfcn4 -az0 nmu s588xjgv/.enter of the Earth's Moon in a sp4km5 nsucgaz0 j8.f8-/nx vwdace 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 consfz:u7 iu ad95hists of two stars of equal mass. They are observed to be separated by 360 million km and h: dfz5a79uuitake 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale r8j6a1gyhg*,h-p4stt xoih 26hgbv n -se:3xwead for the weight of a 55-kg woman in an elevator that moves, hs2athgnhj*4 -hg sy 1bx6x8pet 6g3: owiv-
(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 a.x4) n-jl, .nstxqp8np( keaouk9 x,yn elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was these jt nu89y x-n.k(nl,aqxx4)po,pk. elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits ve )lce .yrvh2 kgj2.m/ory near the surface of a planet with period T , the density (may2lh/ .. ceomkv2)rgjss/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period fqt 4bsa:jrpd*sx4/.y0boh8*ga ey8 of the Moon (27.4 d) to determine the period of an artificial satellite orbiting 0 4p */:bdy8*go.t8qe jya4f sxabrshvery near the Earth’s surface.    s

  The asteroid Icarus, t2wk yrlkwqo9t7p)ruxc /r)v-6 on7h1hough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What ixw rcu l7-r 1kr9pon72h)kvwy)qt6o /s its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of b h5f:p :wy6yn 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very clos+2oyzc e7syfacz(0y4 e to the surascz+fy 4y z20(o yce7face of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce -ver: 4gof++;yk9jockobe 87 ucnz2gnter 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 largest m *rqh i-a+pb1d,w1 dhgoons of Jupiter (those discovered by Galileo in 1609).dhdbg+ iqrp -h *11wa,
(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 the7mqhtte;w vbyq9 /h6 , known period and distance of the Moon. we,;/h7 qvhmy6t9 btq   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moyi qq )f,ngj4b)87cnoons, using Kepler’s third law. Use the distance of Io q)n 47ibfqgncjoy 8), and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (wj91 ylr3,8d--1jc 7xvlvw c)cuep0 qds ab:swhich some space scientists think came from a planet that0ay c,wjld7b3-9- rc q us8cxlew v1v:js)pd1 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 acfyv/0abso +8ik 7 r+ jdzv2r+ band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to makiv+js2z+ /ydca0ko r87bfr+ ve 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 vikz qn a*qmq*, d nl6s.hfq+6i5ne (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the *ks,fzq6q+65 nl*hqiq n.m ad 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 g :djt1jvjg , g*u4tg4fu9vyzp*-e3 qoravity be half what it is on the surfacez:etf-,gjyv*1 t4pg*g 3jd49 v ouujq?    $\times 10^6$

  On an ice rink, two ukab85 xgt0qew pa2aj: avg3u1 :1ia/ skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individ :we 15uta2aaa8:vup 0kqa ggjxi1/3bual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelrd8jvdaya9nc .)+x b 6eration of gravity at the equator is slig v9n6.d a)daxcr+bj8yhtly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from thbfwk9 xq)uavox5 (4: nlpiz (*e Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppop:)vn x*l bkxo wza(59i 4(qfusite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yaen vaa -zcba5 a )8r+ nm2zrfnbd-;s5, k(v*iou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and inv 2*-5(ar8a) -mbz+ed vinsnzkcfb n5a ,r;aa which direction?     ----待选择----upwartddown 

  A projected space station consq2acc2p0jscb:h xn n:c g:y 3/ists 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 1.1p02:c:j2 b c/cq:s3hca x ygnn km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a ver26fut t-q t4pw9 )t-8 sni0dctbxjt,r tical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acc3 mj*ll;agv 9)6iinaamb*vwc3+zm*n v zjc 5 6eleratio b+ijl*;a )* agn 6vmcam6nvj5z39 icmzv*w3l n due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflect5e8t /,rxcf bfap ts-/ed from the vertical by an anpbt85c,/ /tsffa e x-rgle $\theta$ 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 v. zber4 +eb;sn;z7-y)92dzpox cko ispeed of If the coefficient of static friction is 0.30 (wet pavement), 7znb).ixo deybkz9;4rp;2 ovczs-e+ 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 wmd epzz(jxd53gr4pd3dk n n)/-4qs: that objects at the equator were apparently weightless4rmdw)d3g3 qd dz z/p s(-n4 :5exjnpk?    $\times 10^3$s

  Two equal-mass stars maintain a constant dis ueqf52ns hf/o22fw; nh8rqe5tance 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 r4uaad3v htj) 9adius 235 m. A lamp suspended from the cei4) uj39ta dvahling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times 6sfswq7yxyga bq . w8q:wx 0v)zqs ,83as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive morx 6:wq7ws q0s8zwq3f8 , sg y.abyvxq)e 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 Tel,3 ah:ltw bxp bwd/*2xescope deduced 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 speed of gas clouds orbiting the core to be 78x*l:wtd2b w3,p x hba/0 $\mathrm{~km} / \mathrm{s}$ 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 consn g1.yi5y-d:qp eu2b ltant speed as 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 the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the .y ugbeil5 yq:n-d21p road at A?

  The Navstar Global P,5 :k (idcp5wkn4h*:hs qtv kbositioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautic qh5kv k,w5is*t4kbp (:dn:chal ]. (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 kdpvu8 5 fmykkrqr7s *:.d(.a billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is v75(raqk.p. u ms k:y* dk8fdrroughly 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 y:ao ikx4w2m:lyzx4) zth/*ya satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km bewom4z hy a*x2 zi/lk)4:yyt x:hind 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) :icy(s/3hg2n daz;u qWhat is its mean distance from the Sg aiu(ychd2n:q3 ;s/ zun?   
(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 could actually "feeluwi db/c q3a r**z nx vu:6kbs9(*u)q:kzjg.e" yourself gravitationally attracted to someone near you. Make reasonablb s xvgak*bd(3/ :nqjwzuiq. u 6*cuzkr)*:e9e assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) a;78 -oqb x 6ctmmctmcm7)-0b3qxrqwk t a distance of about 30,000 light-years xqc 7 3twb-mqq-ct 07x)cb 8mmm6 rok;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 squareqr* ak-7 bqhnt2vo e66 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at thhetrbqon6-6v2*7q ak e midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the7,99jly y.df n/ 2hd 1ksu6plrcuo y7j Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep second noq(ndbm .dzjg.9:2t hand on your wrist watch2dbnm d.n :gqo9tz j.(?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroujp0xv e/ wy0ap0jev 8(nd in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. Wvv8( 00p0jj pxaey e/what is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trav *rdzp1u*j ,yw6usqbzkz/.4erel/ ( teling at s.y*dl*bz61k4wts/eu( pje /zrruzq , peed $ 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 whenallwe) 05 u wh:u77idh 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 radiu7u5dl iea) lw wh:7uh0s 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.$\approx$    $\times 10^2$