Sometimes people say that water is removed from clothes in a spin dryerprdfp )a uab 9-l;9pi, by centrifugal force throwing the wu;9id paarl ) f9p,bp-ater outward. What is wrong with this statement?

Will the acceleration of a czjc+ w 8nu8e.l qu+ei9ar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aru898 qju+ncw zieel. +ound a gentle curve at the same speed? Explain.

Suppose a car moves at constant s 5 m7q)vhhqile 6*ajecz7f :s0peed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bafism zhv ehe 0:767clq*)j q5ottom of a hill?

Describe all the forces ack o/iv:qab blox1. 8a1h: wa:gting on a child riding a horse on a merry-go-round. Which of these forces provides the centripe:1okg b8: waxq.a 1/hiv:boaltal acceleration of the child?

A bucket of water carf 0f xqae8o,kvqjw,;+cq-m58jxo z/n be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upsidjmfo0wq;xz/,8 o ,+x5-cvqk 8efr aj qe down. Explain.

How many “accelerators” do you have in yourg 0e8god-ggp a3lxm9. car? There are at least three controls in the car whicleo0 x-g g8m9ga pg3.dh can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying ove)hihee3:alh 3o -l 06li3 gynpr the crest of a small hill, as shown in Fig. 5–31. His sled does not3lileg yi )3 l:hepa-6n0ohh3 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 hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rou hb 7o/zlcvid4/c p6od,us q+;nding a curve at high speed?

Why do airplanes bank when( za+v qts7kz9o p8:yo they turn? How would you compute the banking angle given its speed and r vasoy:pk7q t9z+z 8(oadius of the turn?

A girl is whirling a ball ow. i9 ac82hz9n. npd7sdlt31ou 2jxz kn 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 of the string7l2. ddj19 z3sh azit8k2o.npwxuc 9n?

Does an apple exert a gl)g v1+ i8qqhhravitational force on the Earth? If so, how large a force? Consider an a1i8vlh+ )qhqg pple
(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 orbitab 3bel1vnib.d . 22at be different?1tv.3.b blbd22in e aa

Which pulls harder gravitationally, the Earth on the Moon 7 *6ddegv 0pd7dtr1 2tpv8yrh, or the Moon on the Earth? Which ac yg0e d17 p*hrt8d726tpdv rdvcelerates more?

The Sun's gravitational pull oz 9r:-qg7 vltxn the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for therq7:lv 9xg tz- tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more ak8pl+1 r*bwok t the equator or at the poles? What two effects are at work? Do two8 pb*rl1k +khey oppose each other?

The gravitational forcc2+t; g azz+bu l m7dq9ydb/o/e on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the m7++d9qo zl/btdg/;zybuca2Earth?

Is the centripetal acceleration of Mars in its orbiz*uv6mb.ccg. ba-18 ,fo9 u dtchtf* wt around the Sun larger or smaller than the centr,ac9vd z 6ob fut.u*f8tchmcwbg1*.-ipetal acceleration of the Earth?

Would it require less speedarqo/w 3iwl /u))xk1 w to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotar1kww/uql3 x o)w)ia/tion direction.

When will your apparent weight beg5 pdt;n v)8ob the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would )pv5bd ;o8ngtit be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be advez qnl* r 2j94hunx9bh*rsely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects f hhrbx*9n uj9l4z*qn 2all, (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 weightlest p y/qwgruy9p/a/8 w/sness” between s8rpqpwa9/yt/y/ wgu/ teps.

The Earth moves faster in its orb/ ruh:ir.jiz5 ln0me 6it around the Sun in January than in July. Is thz5u:/ m ie jlir6.r0nhe 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 of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was 8ayz9nk 4 tl+wnot known until it was discovered to have a moon. Explain howw4 +yzln 9k8ta this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger tu, y6jxnxa f c5p*2ni .l5-mjvhan the Moon's. Yet the Moon's is mainly responsible c a p.j2n5-,jfx5 *liuy6xnvmfor 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 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 1xd4mv*9,b ;ti w- rsmz980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earthin 2 ; )mnk1ptt a/kb70/jvfjz in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Ea1i7 vz2jjkt/t)nnapk 0m/bf; rth? 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-kgr2s3xl(o5 gbm+dm1 m g discus as it rotates uniformly in a horizontal circle (at arm’s length) ofl12x+ m5gr( dsogb3 mm radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400h4 n;2 ;-lp4imck/ gfv hu.ofp km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational accelgn . f; /hv4li p4uk;ohcpf2-meration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration 27 dq,a0a1hw9e/o m xoo.xbei*eb :pf of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel:a 2 ea.ibomdw701*o,b po/ eq9xhe fx’s diameter is 32 cm?   

  A ball on the end of a string ii1q o fwxhj*3jf v-oa3z i3)1vrfep1( s revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If jwq 33f11az je i-phi)1*(vo3r vofxfits speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius nmx 5xq5r/8mr08pn ih 77 m on a 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?n ri0rx/xn8pmh5 5m8q   

  How large must the c9hibzgxq 44s7m/.df c oefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of fq79bh/m4sd cz.4ig x 95km/h ?   

  A device for training astronauts and jet fighter pilots is des3 6f;lllo m/rdpf5; q(ulz2fi igned 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 ;l6 m u32 lfq irlo;fz(/5pfdltimes 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 axicm c/ xe25fz8ds 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 8 md2/5zfc cxecoin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mus gi*bb8j2a.qmt a roller coaster be traveling when upside down at theibgmb8j2.*qa top 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 ahi,y uma0u yd:*mz8h:gfm94 *ksno,mass 950 kg (including the driver) crosses the rounded top of a hill (radius = sf, kdym:u*m uham0gn:o 4yh8z,*9ai95$ \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 ) u2: uc45pdfphcll c.wheel need to make for the passengers to feec.l)cu :dpfl2u pc4 h5l “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of n8c hxlonb( af+6zci ku).v d4:/pqn,radius 1.10 m. At thx(l )n,c.4cuz: p+fhbv8ndin/ o6 qk ae lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a cener:k 2bv 2fznc.tk(8fa . p,rftrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of,:f8n r fcb ezk.f2.r2k(vtpa 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyandv tw6e/6 8olindrically walled "room." (See F86t /nvo ae6dwig. 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 air-hockedxibm594 bpd6y tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-6ixd 9mp 54dbb
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precio hkpz/yve 3ooy5b m+0f6r k15sely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In partic+0byo51k6vzyhe 5p/3 mr kof oular, 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 qsx; -jx:zha5tif4eo78joxfv2 g;-bis perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses 4)( dqfjhf2qn:cj)6w kz)n j n$ 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 vertically at 2uc .7szvdn5 ic9so;*n86p7acomycn 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 exerted oj:e n kb qh5qu)(4eg0zn the car (by the ground) in Example 5-8 when its speed (4ze j 5uekg0qn :h)qbis 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolisv mlu/h)ce.kj6 ( sup8 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what woulu6(8 u)ch vs mkep/lj.d the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circcol.k e y96r6x,bv+ jo.bazg6 le of radius 2.90 m . At a particular instant, itsxrgc 6zyb9o lv e 6.,+6b.okaj acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earths).tbx 8jlutv 4)7ng o radii) above the Earth’s surface if its mass is 1350 jx.tlt)vuobsn4 8)g 7 kg.   

  At the surface of a g-;o;nwx91pv/.lvgn r r l8phcertain planet, the gravitational acceleration g has a magnitude of 12 vpn rnhv.g9r ;w/g lo1p8x; -lm/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1n y(n 8zvdo 8xzlsz.j,:yi(q).74 . jnzv8z(8xd(z:o,qlsn)yi y $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same ma )mbta2y y.0oass. What is the acceleration due to gravi)o y.2a t0ybmaty near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, butius m)ob(,yu2bon/*g* q1di2 d3sr5hyzo *n z the same radius. What is g nearmsz2uy25*(3y*zn 1bbu irs) qo /o,goidhn*d its surface?   

  Two objects attract each o*x0i+u ) l ttxs a*v;p )0fsgo6ab4wlpther 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 , the acceleratiqt) man, dy pt;mg+,,don of gravity, at (a) 3200 mt),m nadgd,+q, ;ptmy    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wherekgsc+o ;eht+ 5g6cj* sjj:gi x2k(nq9 thegravitational acceleration due to the Earth is jxk * q5sgoggs2 6;n:k+jc+ceit j( h9$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pacyux s :fav/ xksl9(zq/eq(r09ked into a sphere about ky:aqeq9x/(( sfu0r/xzs v 9l10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star0 o8b1v)a rtizrqy0 gt/pa+ p: like our Sun but is now in the last stage of its evolution, is the size of ourgpavi:o 8r/zyp0 ) q0atb+rt1 Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space ms047l+nb/ rqa7stmv shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravim rsaqm70 sn4t+l/7bv ty 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side xkl3f* t;1/z:v6bi*bd j.smwh ceu6 z 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere b su l b.f36;m/6vbjz z* tikcwd:xe*h1y the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most orv;yv ,5q+r wx4v+t1-lz)bq du0bo xaf the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fourvb4 v)u5yxzbt,x0+;r-q q+1or lvd aw 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 ofo z.8 ,f p cr.u3vl 0w..vqk(k9iekojd Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km,3e 9z q (d.ipfcok 8.0v.uklo,kj.v rw determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun h5ip qhrhwfp5a+x i *xk.w3 6v-8s8wpusing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to twh5 avh.hik sw 83w8*+5ripxpp-q6x f hat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbi. (pjkwx1 sdt9t about the Eaxj 1w9 ds(t.kprth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above ad6h m8-w0e09ws xkct7pw5wb the Eask 9whdctxw ep07-5w a6wb80mrth. How fast must 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 experien(b1l l nz ajc+l9da:5lxku b35ce simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one rev:+jz13bx(kau5b nlcal9 5 dl lolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cirbc8ge3z6x*2li7w gwy,sb*e g2.k jxgcular “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 Ear7,g2.xi 3by gbwwezgksx g**cl 6je 82th. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have q 7god uau5 ;vi77+o;oqzt:o uto be launched from the top of Mt. Everest to be placed in a circular oo7duou;:g q+v5 iu;qt 7 aoz7orbit around the Earth?   

  During an Apollo lunar landing mission, the coy25tk f 4zeepj uek.zy+fu7a(7 y28j emmand module continued to orbit the Moon at an altitude of about 100 km. How l4j8e2kfeye2 t yy uf 7kp(75u+z.aejz ong did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that or p (fq1kuu*r ,qp8g1fwbit the planet. The inner radiqufq,f p1ru8pg wk(1 *us 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 /t;8q/bb mu zyrotates 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, q/ 8bt z;ubmy/and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of thb,qvy2f 5,srgg3km:v e Earth's Moon in a space vehicle (a) mo f3vg:m,g ykqv,52rbsving 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. Thra.hf,ct0e,x4t ( bmk ey are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betwem artk hc 4f,(0e,x.bten them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woma k0gpqfr.2/wuvm uj k-a4r 2,an in an elevator that moveg pk au-kj0m2 f vu4q2,war./rs
(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 fedx0y*1fun 5 f8meyg l4(8f 5bhno tc*rom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N an**5ylfnob8ncf1e ( y e0htfg8dxu 5 4md breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellik+q7cp b8r;.kx* i milte orbits very near the surface of a planet with period T , the density (mass/volume) of the planet;mrq8k*pbl cki.ix +7 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 f 8yhuds6qcr2) n5 g1zthe period of the Moon (27.4 d) to determine the period of an artificial satellite h2 dqz 65g)csrnf1u8yorbiting very near the Earth’s surface.    s

  The asteroid Icarus, thoughnd 2y4r7rkusy3koz2 9 ,xoip. only a few hundred meters across, orbits the Sun like th9k2ry,n 42ouo di.sy 37kpxzre planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5)lf:q2vu2z:x l5dm 0.me*n cdq d kjxi3eln02 $\times 10^{9} \mathrm{~km}$ 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.) 1ayq/ /uhljl,bmiqg5yzj 7ce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Sol )lg1.jy/b/75ml q z iha,uyjqar 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 cen2a bd7(kyae 1j2e cg4kter 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 dista m c3,hmssp17kn 14qyqnce for the four largest moons of Jupiter k7qmnm 4,1sqc13yp sh(those 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 Earth from the known period a+onvf7 4klkzo: z-ncy9, to -xnd distance of the Moon. z nk otl-coyf- 7 4:o,knz9vx+   $\times 10^{24}$

  Determine the mean distance from Jupiter for each clumr cw : b64tp*-bba*ot+aj22 vi.jof Jupiter’s moons, using Kepler’s third law+ j-m bac2cb 2jlp.w* u:vti*ab6rot4. Use the distance of Io 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 -heim.zo i d-4zx1f9 ffragments (which some d iize9ff -hx4-o. m1zspace scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "plsr55b 0ktlr nd bhz 2kg:4cfb* ky;-fe7e6* lsanet" 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, that the distash- fkn7c*g*rf t20ebb5d; z5kb4resl6 kl:ynce 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 (F) y)4kalgk kvr5 .b;nsig. 5–41). If his vg4 .blk; snk ya)k5)rarms 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 is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gr1zj1k9qpwsb-g0as9 h 75h cj)ypkxr2avity be half what it is on the sur 51syba9zgck91xj 0h)pj7qpr swh- k2face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands a zuv:k,*uov5 :u+ zicrnd spin in a mutual circle once every 2.5 5u: vi ucovz*,+rz:k us. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelen dfpkh,+o2 thgm; 7/y7cs f3lration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction ofd3/ly, f;hkn+ gt pf o27scmh7 g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directg2a o4f kbb/shw63: tqly from the Earth to the Moons o6/ab:3 wht42bgfqk experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, butggk7zw2r pfccq09* v 7 when you stand on a bathroom scale in an elevator, it says your ma9pw77 q*zkv rg0fc2gcss is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circu5p8vlnplq bw+ ap h,i80.gb2g lar 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 abou82g hlg +vpi5.blq8nbp 0 w,apt 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 aircraft in a vertical lo7j(kr(lze. r kop (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 o-lj- 99(j jqwr zsa,pthe mass of a planet in terms of its radius r, the acceleration due to gravity at its su9-a lq ( jwsorp9z,j-jrface and the gravitational constant G.

A plumb bob (a mass m hanging on bvixk5iel89q3o 04pv a string) is deflected from the vertical by an angpq4b0iv v5kiex lo983le $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If qi c :yorw8y4)dnm.3qthe coefficient of static friction is 0.30 (wet dr.34 y wi y)m:o8qnqcpavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eauk*j 8w9jv2 : hkyhe)f0px(vbrth were rotating so fast that objects at the equat:h8*ej)p( 9 u0jhkyfv wkb 2xvor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant da7s2xgc (+g qdistance 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 roundssrlbb(; m:(n0h zm h b z8yri)3fh1lk7 a curve of radius 235 m. A lamp suspended from the cslyk 3i;hmbhhb1l8zrm()0 7 b : rnzf(eiling 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 the3ks fin vj(o2*9wvsnm y9x ki50pfh)- 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 w9i*f5 i09) vnv2jk hfmkos n(-pysx3 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 Telc+.k vy8qrd0c 63 rlisescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense thcrr+cykdl 6q3s.08 viat 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 traverses ui.;z :8zvngithe 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 compu n;8i v.z:zgiare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group ow1geuhakf+ ) sszv00(f 24 satellites orbiting the Earth. Using “triangulation” and signa0e ()s0wh s1zvufa kg+ls 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 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 bi f7hfp3al,i0 u lu06kmllion km, is meant to orbit the asteroid Eros at a height of about 15 ku ,6i0a3ul0kf7lp hfmm . 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 pursuicysd, f68l0e; ieim)nng a 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 be icf 0yn, 8;e6smldei)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) What is its mean distance fhz evm*;r:lwjji,/m z 6dd.) wrom tl/:jiw)v z w d em,h.*;dzj6mrhe 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 fbv,0k -voe 15 5xikq;s flk;t would need to be if you could actually "feel" yourself gravitationally attracted to someone near0xvvq5k;,e 15 s ktl- kbofif; you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroukmeqre2k2-j,, 6m n qgnd the center of the Milky Way Galaxy (Fig. 5-46) at a distancge,k qr62-ne2jm ,mk qe of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 9j 2iuc)w2z7kvspdb 4-) b opy0.50 m on each side. Find the magnitude and direction of thkys4dzji22wb vbu- 7 )c)p o9pe 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 t,(0ln ai0uj2gcj6 /6t-5yksjfx :ql4bm wvb zhe 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 ofz+ jolf4+vb5sv*7 o b x7dlaxc18 8svs the 1.5-cm-long sweep second hand on your wrist watch? 7bsc*vozlx ssj8x7 ++8v1db vl o45fa    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arojud1di4 az 6afz .pp4*und in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishiadz i44f .*j6zdp1aup ng 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 travcv46xasbq; (0nb pzs;elixz ; vp(;qan 40bc6ssbng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotialsimz7lr :)en5e:e s* ting 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 radi*:rs )ee 7mlz:isln5eus 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.$\approx$    $\times 10^2$