Sometimes people say that water is removed from clothes in a spin dryer +gwbwxt efc1c07di2 5by centrifugal force throwing the water outward. What is ec7c+0 5gbixfd 12t wwwrong with this statement?

Will the acceleration of a car be the sm /w w8ng2sakg 3pt77wame 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 / 2na78gwk7wp3mtg swspeed? Explain.

Suppose a car moves at constant speed along bld l6 y*)sl05h5fdos a hilly road. Where does the car exert the greatest and least forces on the road: (a) atl)dbf56 d h05os ls*ly 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 acting on a +kdsvfg:4 y 2+v:sm tbft7 /))pgjqkxchild riding a horse on a merry-go-round. Which of these forces provisty+gk+) m):f4v:/jpgbf2s vq7d xktdes the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the watep(ncoyaepcfv)y5zb(9w/ ;+h2 hgg u 8r spilling out, even at the top of the circle when the bucket is upside down. Explain.2f e5 b;n+9augc/ )8(chgvoz p(ywhpy

How many “accelerators” do you have in your car? There are at least three contrfz9 r8-r 7my)w*lbul0 ekl6ouols in the car which can be used to cause the0r7ou8y6 buz rmel 9)lwfk*l- car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes(e+/shbb7oi y.) k1uzvx x.cx flying 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 the normal force between his chest and the sled decrease as he goes over the h vc1 x7xykiehu/bsx) o..( +zbill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hi( geg5ofn0x8o oe m 1jk0fo;7vgh speed?

Why do airplanes bank when they turnz1gwib-+h bsr ny 3w78kzt7kr3mrf28? How would you compute the banking angle given its speed and radius of the t s+hw k3fwg1 78-rrr2nk3 z tm7zy8ibburn?

A girl is whirling aw*yqre)8 qsif 1hv 3 s6 gbna9vm;,fa/ ball on a string around 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 yard. When should she let go v 9ifvm3 eg,/y;a nqs)68ahb*w1 qfrsof the string?

Does an apple exert a gravitational force on the Earth? If so,x0n4xa:js- r p how large a force? Consider an apx pr:0-a4jnx sple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbitx il5sqnyn 1/3 bl q1nn53ys /xie different?

Which pulls harder gravitationally, the Earth on the Moou3 ve+(7 ml 27kthsmuh7e kapla(:z2 pn, or the Moon on the Ea7 at+ mpmhhae 2(32lpkz u:u(7vk 7lserth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'sf ba zo9i+d1g /t5/ alpsd(l2h(ck*sp. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side f(+llth/abia* 1 2op9 dd(k cpgs5sz/of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What tw.bz7 pqkc0xt9f;o j+;u uy r-to effects are at work? Do c+pu jt; k-0rb9y f.zut;o xq7they oppose each other?

The gravitational force on the zwr o 9lauxy(1oxngc +9no16)Moon due to the Earth is only about half the force on the Moon due to co(w g zo9alnun19 x6o+y)1xr the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largw/ sm:5 d/c.m;xpgk6f qsm-h wer or smaller than the centripeh;w-g:k/ /m5 6f .cmdqmsx swptal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (wj 9iwn) i7ls)b) toward th 9nliw)7i wsj)e west? Consider the Earth’s rotation direction.

When will your apparent wpa ajj wcnq87lag v(-mfdsd19h*73m- eight 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 8d 1 g(-fw7lsmaj mca3-nhdv* qap 7j9would 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 peri(fdj a3x)zjx;ods 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 suxa;f3jxdz (j) rface (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 runneroxuov45 g5-y l83ufct experiences “free fall” or “apparent weightlessness” between s8x55fgt uovy3u4 l-co teps.

The Earth moves faster in its orbit around the Sun ophaq1wxz51x u8dpc0 ;uw3l 3hqf1y8in 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 the seasons — the main factor is the tilt ofqwh3qdau1cz8xyop53upf xl18;h1 0 w 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 m/dk*m1j6a oaowh -f d78(hpvwoon. Explain how1o a-hjw/7d( *a kdwmvf6h 8op this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pul(2kwjt4 0 ilx6 vfbn3fl on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull 0bv fl4ti3x 6nwf2 k(jfrom 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 tjsbku-+eh7 s:x+ v3u 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its or4 j q. h(jwulp0h)hii4bit around the Sun, and 4qiul( j.ph4w0h)ijh the net force 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 exe7uvad ebgnzk.39uv e7f 72n *yrted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s7v7en7uv n.93kbegduz *yf2 a length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from ) v 1um;t vth k,mp4r*slmr/5hthe Earth's surface, and circles the Earth about lmmthr)t;m /hskr5 1p ,vuv* 4once every 90 minutes. Find the centripetal 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 accelernadzb*1gu3ea3l50c 4n. czs o ation of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revoluti4c50n.u3n *z lsaa1 d3 czoebgons per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ver r6 k,2/guf ajoe:qwm ;,rcc.,dmjv7s.a7x s ctical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 fkdwr. ;.7:xj7a, a/mqccu s2jre,smv,6o cg$\mathrm{~m} / \mathrm{s}$ 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 turn of rad udqbk)j- eq98c (zd6md *:e20 stzosiius 77 m on am6e0- i9cbje sq )u2z:q(sdkz*od8 td flat road 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 of static friction be between the tires and t fqi*4o8v /chos+vnc;he road if a car is to round a level curve of radius 85 m at a speed of 95km/h ?q 8hc;voof v nc*4i/s+   

  A device for training astronauts and jet fi7ckx5nqr(5k,s cw.vy ghter pilots is designed to rotate a trainee in a horizontal circle of rarc cksvy 57qnx,5.(wkdius 12.0 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 fk( os.3e ffht8s:8olv rom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction 8 to sk3.(he:vl ffos8between the coin and the turntable?   

  At what minimum speed must a roxf: kyc:b qd-7z )i*jkf4, pxaller coaster be traveling when upside down at the aij,c: *47 -xfb xqk:pyfd)zktop of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded o ito gpev;( 5n-:g(kueg:ey7 top of a hill ( u:k5g- yn( op eegto7(;vi:egradius =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 ww0/e1jn ver; uheel need to make for t0/uevn j1;re whe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticq4uf;;33,m wz bba/vdciv;yt al circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting tz/ yqbv;bmt3;3wcd;, fuiv4 a he bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm fr, t srth7xmkka6 j,6bao cc,2ubv8a0. om the axis of rotation is to exp k xcthju6r, 8at6am0vo b7s,ck,.2aberience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in ae3 d)fixi+v1t v; eq;w68xlos cylindrically walled "room." (See itqxv 6woilf;3v)e;e+sd1x8 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 ax;iw 1vm r4i6y circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block v4yr m1w;xii6(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 , prj:f:) iuxk mird51d2 )s0l rvyecisely this time, by not ignoring the weight of the ball whirjkmsi2)0iy5 rd l:u1 vf:)d xch revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling i6i0)tj h9sga75 $\mathrm{~km} / \mathrm{h}$ , 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:yx s .pklzn5rtv3a/ - $ 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 divii b,mzvjnhst2 m m)mnbi1*-a*ox;u7 *ng 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 com7vtbwgs g04* eponents of the net force exerted on the c4 0vbge7gt w*sar (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 area, goi)izk*apj/xclo1yh(:xot,9c 6rf 8 ghng from rest to 320km/h in a s*hzgrcfaoj, p xi6h)1 : c tl8x(9yko/emicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in d8s6xan,9 r e.c/ tljpa horizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05 ,rtx lpa8ne6d.s 9c/j $\mathrm{~m} / \mathrm{s}^{2}$ , 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,ri ry,hq,*;zz 800 km (2 Earth radii) above the Earth’s surface if its mass is ,zy ,h;rrqi *z1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g ha o2+d4wu+xqqt s a magnitude of +x 2wt duoq+4q12 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 dk+xyo wn:ui40 )sqa w*ue to gravity on the Moon. The Moon's radius is 1.74 xs:ou*40wiw+ nkq ay)$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5ybd70d 1x4zjc k;bok5gh ;y .rlh u*w7 times that of Earth, but has the same mass. What is the acceleration due to gravity near its z;.h0y5j krucdghy 7d 7lw;1k4o bxb*surface?   

  A hypothetical planet has a mass 1.66 times that of Earthtd) vf.2kfqwt1srl( /, but the same radius. What(tfq l/)r2s .1k wfvdt is g near its surface?   

  Two objects attract each other gr9ci14muxq0qk fq+1vz18wwb ;sy a+mtavitationally 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 , the acceleration of gravity, at (a) 3200o38zm-9 hnqls m l oh3-q 8sn9zm   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frommon c52l c--q )s)cqed the Earth’s center to a point outside the Earth where thegravitational acc so)nel)5 c-cqm -qc2deleration 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 mavgxb72:p hz/ 9 02c ;-vfcunr bltp(tbss of our Sun packed into a sphere about 10 km in radius. Estimate(-fcgp9 t02p7 /hvtr:nlbv 2xc;uzbb the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but it5*u25-pjvj +q g1jo/ pfuflrs now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this sta jlju*-vt uf15rp5 o/jgp2+qf r?    $\times 10^7$

  You are explaining why astou:r32muigkamf2al 3kz--m9cv ;w. a :rg +zbronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince tlwrb2ozc32.a vm- ;a mzgu: ik9u- fg rma3:k+hem 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 lo+ *1r ouamftb zfa*5 sms*el++cated at the corners of a square of side 0.60 m. Calcueoa1 5z+tff **mub*sl rs+am+late 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 258 o 4b zt w0zjr-t+lan0sknkof the planets line up on the same side of the Sun. Calculate the total force on the Eartt-5nkt420lbsw zjaznkr0o8 + h 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 of Mars is 0.38 of what iclkjb w9;vkdjjg20 4*t is on Earth, and that Mars’ radius is 3400j;kw9c0 k vd*g4bj 2jl km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fow6h,yap (oc-/f ne: ngr the period of the Earth and its distance from the Sun. [Note: Compe g: wcohf,y /ann-6(pare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of qt;ms gec.ia):sj 88ra satellite moving in a stable circular orbit about the Earth .a: s) 8mretq8 jcsi;gat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a e7ngu.z)4oc5*k9ym a -c50y bjgvi nmsatellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relativk n)*0a7o bi -n5muyjvz9cgc4. gey5me to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are nnjplkt. +-x/dqvj1g,a* 0u:b khj y 2to experience simulated gravity 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 j l: j-2q. +kykh01nvtd ,agb/njx*up 5–32.)   

  Determine the time it takes for a satellam dod0 bof,0.md+ y3cite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a heightbaoomd030c.m y+ dd,f above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched81 zi4f qsvys8 kkypk8*;rn1a from the top of Mt. Everevy1ip*8rk ;88yk1faq k4 snz sst to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, theoj.*eccsri :f35tzx ; command module continued to orbit the Moon at an altitude of about 100 km. H io :t5.3j;xz crfs*ceow long did it take to go around the Moon once?    s

  The rings of Saturn ar2l:kv b 3h2zslthj( *pe composed of chunks of ice that orbit the planet. The inner radius of th *zs:3 klhhbtl2 jvp2(e 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 rotg *slkvgtlb ++.11br hates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bok1 +t* g1s.+gvlhbblr ttom?
(a)    (b)   

  What is the apparent weight of a 75-kg a(d8nou7rlz b 8stronaut 4200 km from the center of the Earth's Moon in lrb8d87 onz (ua space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They arbyk:zuzx 3/ ux/)lj3v 3yy d2tdwn+)x e observed to be separated by 360 million km and take 5.7 Earth years to orbit about a p )n vyy3+z3zd/yxwub:d)u k /ljx2t3xoint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman8zoud9uklg m r5,b( s5 in an elevator thaosb8k9, u u5gd(l5zr mt 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 suspe0c1 dr zzr8dz9nded from the ceiling of an elevator. The cord can withstand a tension of 220 N and r0d 9rc zdzz81breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very nea rq 4)eoe9k8yprm0 b.xr the surface of a planet with period T , the density (mq0ey oxp.)9r4k r8mbeass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) 8wv y5zf( z qfblm 3,p74iah8sqf-g4vto determine the period of an artificial satellite orbiting very near the Earth’s surfacep ql874f5 4q(8h maz i-gfz3 s,vbwfvy.    s

  The asteroid Icarus, though only a few hox/gy *:uoo w/undred meters across, orbits the Sun like the planets. Its period is 410 d. What is iox*o w/uogy/:ts mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance pd9v7cvj g8z9 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 on* ;+(hqm 4fz luaf/brsce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the cometm; a/s*b(z4 huf+frlq 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 Galaxy yfv 8uukeaj7d t z:f*5m4)zx( wg5pe5 $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 ttzx- :mrh( yffa7 l59lhe four largest moons of Jupiter (those :zm(ha7yf5f9 xtllr - discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earc n(qw+j73d) mqh5oxq th from the known period and distance of the Moon. d5jw7c( m )q qq3ho+xn   $\times 10^{24}$

  Determine the mean distance from Jupiter +/vkbp*u1oqwfor 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 the/b*uq +1 vpwko 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 t8ksx;3ivb1uand Jupiter consists of many fragments (which some space scientists think came from a planet that once kub8tv si1;x3 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 o k q1 dvkzsc)7u;;r 0asw8w;gnf a band completely encircling a sun (Fig. 5-40). The inhabitantsss; wn uzk)7qa;dw; gc1kr8v0 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 an6e5ei)meyvq* . wxs 4w arc from a hanging vine (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 lowest point of his swing? His massw e5v.s qx6*w)yie4e m is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half wh (dpgk-s+urrp oj6:g 7at it is rd(7 kg-o prgsu:+ jp6on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mp,nq6.di28bvo hz.d w utual circle once every 2.5 s. If we assume their arms are each 0.2dbnh..iq8o,dp6 w zv80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appvh3 6jdm8w.acip-8 mb arent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the mawd3.i-pma6 8mh vbj8cgnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecr k6drt (q3up iffdx9h1c *+m7raft traveling directly from the Earth to the Moon experi6*rd dxhfp9 cf( 3iut1mk+q7rence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you staeaesn89 al2 i8nd on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wh 9as 8aln2e8eiich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will r-3w(br(w8bgpyc gw4v yl3/trotate about its center (like a tubupg y/ rywwgbbr3l -c4t 3(8(vwlar 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 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft0de3m1dphu;y* ue9 qk in a vertical 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 iz j,a8ecz41x : qbr8n37i iuz rgd4(da planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitat31rzgx r4dq8i :ji,zni7( d 8eu4abczional constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical bhcoku07:/df hq*(f amy anum(/*ha0o: kdf7 qfh c angle $\theta$ 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 *44g3uf ioq6kb)zlc1 1igbeors;u f,banked for a design speed of If the coefficient of static friction iuos6q),z1c*l1 4 ;b f kr 3ie4ogfbguis 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatiwsnt13 ly- k2tng so fast that objects at the equator were s3kt nyt 21lw-apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dm1z vc,bij6xlt9s5h :6 xsg)jistance 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 con-72 pmdvh,ex ustant speed rounds a curve of radius 235 m. A lamp suspended from the ceili 2,eu7x p-hdvmng 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 as1nc8nk02q o fx 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 more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Us 0 ko1f82xqcnne 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 ai sppmr8-m4a 2n extremely massive core in the distant galaxy M87,4-m mri2as8p p so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trab./h tc -p9i,vroz2gdzjj17r verses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normrvhi2,9tzogj b/c7-rp1zj d.al forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (x.q 39,wgouzh)gmjr 6 )3rmefGPS) 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 sag,h6 o re)q ru9g.3mfz3xjwm)tellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous iw4 jhx2 (04dqozb or;4xs m2w(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of aboutmzxd xr0; wbjoqhi4 (22 4so4w 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 purn mc0sykjx4t3 ;cpbf-/wg- 6 m2mo5y zsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km aby; mfwp0c3z mxs k ym/go24-n5bt6j-cove 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 itsb gtn5d1g+7v// afki l mean distance frv tgb+7kf/n1ld5a/giom 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 coulyimwdhw )q .8z-4gz *wd actually "feel" yourself gravitationally attracted to someone near you. Make reasoy *g8whi dq.m)4-wwz znable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a5k:kc wcpfmi:e6.. 9.bhypbu distance mw65. uccbihfp b.y:9: k. pkeof 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 squa4h1l,brtgv+ kzo6 bpt9ly w )7re 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0,61yvthwt)7 4kozg+bbl9lr p-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 Earthkq0nuz/9cbg 9 $ \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 acceleratio) f3toz-g.5wu +m xgvhzh ;:hun experienced by the tip of the 1.5-cm-long sweep second hand on your wzuv wm g+o;3x-) tuhh:.5hfzgrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start eb(8ij)1xmc e 9 akrn.to swing a sinker weight around in a circle below yoaex9e(.kjcb) m i8rn 1u 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 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 l86/g kuz(o15wcm1 6lub hck4r1g: sx6boe ky that a car travelikhsk/ycbxolu6r 1 546:gzeb1k1l gw( 6cmuo8ng 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 wh7ltij2 xh0;pw v gzv+6en 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 ). (a) Calculate the friction for+x p;ltzh gvj7vi620wce 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.$\approx$    $\times 10^2$