Sometimes people say that water is removed from clothes in a spin dryer by centre9d9 ak.1 jabpzv(bqm ,i7 4plifugal force throwing the wate99b.pq7 dlj41e, aizvab( pkmr outward. What is wrong with this statement?

Will the acceleration of a car be th; 5 :tmqa6wz l;eywkd:e same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sdz6:e;:yka ;w ml tw5qpeed? Explain.

Suppose a car moves at constant speed along a hilly road.br. q p rm+1,ayrzi0/h Where does the car exert the greatest and least forces on the road: (a) at zh0+qbrpa1. rym, i/rthe 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 forcw7r0fz 7g5 w z2ezg9p tdc-g:ues acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accele5zgtergg 7f w092pwuc7zdz-:ration of the child?

A bucket of water can be whirled in a vertical circle without the wat x gjo:1;-diq p8mp3t0lwja1 ct:j 7kper spilling out, even at the top of the circle when the bucket is upside down. Explain83wqixjpokcj ap1 djt::;1 t -mlgp 07.

How many “accelerators” do you have in your car? jz b 4d-qojv0pl-vp;,There are at least three controls in the car which can be used to cause the car to accovb-p;v,qld z0pj j -4elerate. What are they? What accelerations do they produce?

A child on a sled comes flying ovvlr,0jy7 edw 57mf sf(er the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the 07 v(je yfwm5,lfsr7 dground (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 f9xadjzp)*u dtv9o1 6rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bairkuh9*5o o/ jnking angle given its speed and r5* ojh/ oiu9kradius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plano3fuql7 wj7bstz,d *4e. She wants to let go at precisely the right time so that the balljl,w3tqs 7 4 d*zb7uof will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earj nd+wkm6jdkiw+w g*637adq mi 8*:csth? If so, how large a force? Consider66*sna kik83dwm+ : j *jdd mqc7wiw+g an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were i3z97g uco 1dydouble what it is, in what ways would the Moon’s orbit 91 og zi3d7yucbe different?

Which pulls harder gravitationally, the Eartn)xsox7eb)czv-s+ *c: pkan7h on the Moon, or the Moon on the Earth? Which accelerates me-cas *n)c7vzbx: ns+xkp o7) ore?

The Sun's gravitational pull on the Earth is much larger p942vd+l plikthan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cv l+diplk24p9onsider 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?(:xwpx );td ky38drn dhv pp(1 What two effects are at work? Do v) (t3 dppr;18phxkyw xn:d d(they oppose each other?

The gravitational force on thpwmw 2 6dt 8(lpr*i1qm rw5qu8e Moon due to the Earth is only about half the force on tr8 d1mr(5pw2 tlwpmq 8w*qu6 ihe Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acw s7twzf7jm 6sm 1::;ch; iuilceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth? sfj lw6h i1t;mscum7wiz:: 7;

Would it require less spgt 6dpz8xril cg8.1t6 t4oqz+eed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dir.ditcg61 txt86+p o qz z8gl4rection.

When will your apparent weight be the0 jsh i3pqgd3o),clx t(w o-m7 greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accel703 3g-ph d)x(os mtj,iowclqerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lonqi r;e*,f4 gh)oewao(( * esabg 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 (Fig. 5–32). Explain how this simulates gravitb*wa,ehi *;( earf 4gs eoq)(oy. 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 “apuprbde 8x8v/oxn:7g0 g bz qj 30+jcx0parent weightlessness” between stg jp30/8:70 dvox br0uc8xg+bjqnx ez eps.

The Earth moves faster in its orbi 5 ox7u )9mt geynzm14l2plp4ct around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Eam5)mep 4xn l74gt9l zco1 uyp2rth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to ha y/mogm.*ixu;p;ry ik7ju*5 hve a moon. Explain how this discovery k .r;gui*om* iu5p yj 7my;/hxenabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eartx1 ba,ys27s5tjlf i s2h is much larger than the Moon's. Yet the21bsi s,lj5f xayt 2s7 Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves 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 1980r)e*c0x v;-wxcf0zxr $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 gswd: e w5it71acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assuw:ie wg dt51s7me 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-kgo*/bfwr .ienkkg/w 4j(v-qp ; discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed b* v/pr- ;j/kioq .egf4w(knwof the discus.   

  Suppose the space shuttle is in orbit*eucv+6zq qss 8 ony)f7 *;ute 400 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 acceltsof*e n;svq8quye)z cu7+ *6 eration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clayj ep):4),w feh8( v4ahufotuy on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s a ,ytho8u)ej4(f v4 pwfuh):e diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in av:3waz/mjs r ar:9k-c vertical circle of radius 72.0 cm , as shown i -s3v:mac w/zkraj 9:rn Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg caxmvsp( -xt,0s8) *,uhpyl bq b2kew7p r can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires axsywb *v,hme2x7p,spub)l-( t8q0p k nd 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 3(e9enu9jdn xthe road if a car is to rounddnn (ju9e93 ex a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotatehkm7njc6 pr bbn;k4q o,9/2em 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, e,9hn kb7cr2/k np; j mm4o6bqhow fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable oq r0q/am- .hzha-cebwv1wzz -we6 c(1 f variable speed. When the speed ofa -c-w/vr(z-wz weaz emq 0.hbqc116h 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 a roller coaster be traveling when upscn+2 /q,8vq- vet (ma+3 lecufkap +zgide down at the top of a circle3ncg-ez+ekca u8(q/fl2,+qpa vtm v +
(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 zttj6cw+ 6 4oathe driver) crosses the rounded top of a hill w6t+tc ao64 jz(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 minutx;w8lw: pi2 iitv :+vne would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poixi wn+2:wp ii t:8vlv;nt?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At ttu) 7(cfpdn t(ub*0r mhe low*tr((mu7t)fbu0d np cest 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 centrifuge rote5l2q*vh 72bn; ,yfy-4 lkdbh2zpq fg ate if a particle 9.00 cm from the axis of rotation 5 ,;22vheflb q y*kbh pfq4ln7 -zy2gdis to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniv/5hrpye, zci3z tw * olcghn33jn47+jal, people are rotated in a cylindrically walled "room*/econcij3 3 z+h tyg zwhjnr7l435p,." (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 3uz+g8 h wj5smin a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blocku3j g+z8msh5w (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 , pvhlg6c-nz9 4ewsi4 8lrecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude ofzl 8-e4v s46nhi c9lwg $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 gtma7)mjf 32 mt pti)r* zy349)bkwwxa 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 massezm4b0 kwb .bs1s $ 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 3(s93l3 0+h lmqh0zz9 amuxfv b10 $\mathrm{~m} / \mathrm{s}$ . 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 componentsnbqo99f4 x(m w of the net force exerted on the car (by the ground) in Example 5-8 wh on4xfmw qb9(9en 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 accelerataesd 1z-2tp7jj ;o2l:hoh: z z;zh4ihes 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 accel2zs4h d-to;a j12 ;l:pije 7zoh zhzh:eration 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 a horizontal circle of rowi 5idf5ps0a+wj;*y*wp ;s/ggzp7m vzoo:8adius 2.90 m . At a particular instant, its acc/*g5z+ izyw8 d: 0gpjfpavo; *so;s wpiw7om 5eleration 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 Eartcth +8oo- 0v9cx3 vdteh radii) ab 9 hcocdtto-03v8x+ev ove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planjmldc4xizwq7eii :0 (;ct*k , et, the gravitational acceleration g has a magnitude lme7q* d(: 4ck;xi cw,zi0jitof 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the accele s9 rrdl isod8tc8 gn.a:4o09oration due to gravity on the Moon. The Moon's radius is 1.74 0 o:.og9 8doitsarl sr8cn94d$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a byn)v: vx x q**i5qi4btp1z6l radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near ipqx 5i)61bzt4bv *:yi *vnxqlts surface?   

  A hypothetical planet has a mass 1.66 times that of Earth*il+pjec qe- ;0(rra f, but the same radius. What is g near ire (ferpqci*-laj;0+ ts surface?   

  Two objects attract each other gravitationally with ssfw2s3t :g5q 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 ( 1p8xsr6ci:of)zg- /s(fnm dohnd* ,xa) 3200 m irz f d-snf g( dpxos/c,n6ox h:)8m1*   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tomt/w2cqize5 8 a point outside the Earth where thegr8/tm 5wczeq2i avitational acceleration 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 m jmjh v 6 zv/)32o1h8cp/grsgvass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this o6/ h82r g vjv 3g1vzs)/hjmpcmonster.    $\times10^12$

  A typical white-dwarf star, which once 5kg5j f7d9urq8yj j.ye, lj7k was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is th,lj 7egk7rj9kd u5y 5yj8fq.je surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightq4c,(xe; rcavubt.)v less while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Conbtr,aecvxuv) .(q 4; cvince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of m3m k jju75nbivqa-+ fx2m:3e a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on onex72jqn fmmek 3bmj-+ a:53ivu sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the )irj n5p jj2udv01 7dqplanets 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. 5-38djj dj)27v1rq0p iun5 ). 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 o gu 8dg1+ae+gxgs ha-(f gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 34geaug 1x+ah+( gd8g-s 00 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valug*y(xy 26vem su+5n oce for the period of the Earth and its di +smcugxn*v (o 256yeystance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the E+j4f m/k h6h4r rq- p1kngn)wvx/ln7p arth at a henn/p)nwqmf kr74plxh/1hk 4 6 +v rj-gight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite)s wx:vv5o0z a into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when thvwz0 vx):o5a se release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants ar+j9trvpfa; h;y4 q i5xe to 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 revolutj v4;h;rp qf +a59itxyion. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cia0 *bsy kf,xfd/hlg, 9rcular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared 9bx0/,ly,d safkgfh * 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 hp ah7qb3b2u2 dave to be launched from the top of Mt. Everest to be placed in a circular orbit around the E3hbqa 2 bdp7u2arth?   

  During an Apollo lunar landing r;s 1ukmr*f y4mission, the command module continued to orbit the Moon at an altitude of about 100 km. k 1fyu;4mr*srHow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit thjdur -ihx rw,hh/9s-2dw-e 0x e planet. The inner radius oswjrxrwih/h -9 ,d dx-e-02h uf the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9)cpcew m .a57hal(m2n*. What is the ratio of a person’s apparent weight to her real weight (a) a(n 7lcaam.52 ewc*phmt the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75- cmh-;wka d/ lfb.o9mgg*6/n nkg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) mov ;nm cg 9makohf6l/dn -*/bw.ging 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 y: fl,uw6wpj4of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yearsp,j lw:u w4y6f to orbit about a point 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 woman in an eleva-nl+m ngr,58y4)t + dbeqxwkam :u 0ultor that movede4 ) yq0 uw+:m, lk5m ulabrng-t8+xns
(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 an elevatj0wcos9 p.lxg ; e)r9/zzskza/( hj. vor. The cord can withstand a tension o gsxarz kzvc9 /l.s)oj( 0;eh9.j/pwzf 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very sz1x adv11r dgyok49ti,ux8+mra-*r near the surface of a planet with period T , the density (mass/volume) of the planet i 1sm14arr*9gkvu ixt8d-o1 y,x zrda+s $\rho=m / V=3 \pi / G T^{2}$ .
(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 (2q dryoke8zfaml2 r 1rh)i /6/.7.4 d) to determine the period of an artificial sate1y kqz2a)//drim l8f.h6o er rllite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orx99qd2n4niu os h t- o47yzyv.bits the Sun like the planets. Its period is 410 d. What is its mean disto -io9htzn .vyu4 2syqdx7n 49ance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of n;+ qbc/yj- ivvje x*14.5 $\times 10^{9} \mathrm{~km}$ 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 w, bn-s2gt. lm4i/sznw3zzv; very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest dista-ziszzw 3g/vn, n .t; w2lsmb4nce from the Sun.]    $\times 10^6$

  Our Sun rotates about the cenzze5f8n60ft((;ozw lg-t ns rter 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 distan y. b3id9;hpbysyzy:w +u( y2kce for the four largest moons of Jupiter (those discovered by Gd hwub ;yyk3yyb is9(+y:zp.2alileo 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 kn1d9vge0smr aqpsz (p/ b-yw* 1own period and distance of the Moon. rg0d z1s1a(/ psqw*pbmy9e- v   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’sl vg/:9a nqnxl:,8azz moons, using Kepler’s third law. Use the distance of Iqzlxv 98z:n:/ g,lanao 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 consizw :bori 9lt4:sts of many fragments (which some space scientists think came from a planet that once orbited the Sun but was di w:r:bl 4t9ozestroyed).
(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 artixi7 l zx9ar / +nfbtlg+ys8.h8ficial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon).l7y x8.x+gza8/sl f hb9intr+ Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (/2cy,,,5ksav p ps fioFig. 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? s ,2i,ky sp,pa/fvo5cHis mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of grawc+/9,gbpo0masxsw . rtb eu:4 3gvh.vity be half what it is on sw9b.g/btcu. m xp3h :oga 0se,v+w4r the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grmkx:vtqf ldct99f ,ft v16w :*ab 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 individual masses are 60.0 kg, how hard are they pux:dkvvqtmff9t *lw6,t 19 c f:lling on one another?    $\times 10^2$

  Because the Earth rotates once per dasw/ jttkr8b 18y, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimatwr1jbtts8/k 8 e the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling a93yjx d:o* yydirectly from the Earth to the Moon expeyo9yd ay3*j: xrience 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 stanzsad 76e281n,yq3 yhv yawx 8fd on a bathroom scale in an elevator, it says your mass is 82 kg. What is tqz61h, 78yyeayn saf3 v28wx dhe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station co0c089pet4g; szoj ekknsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Eareo; 9j0k zp4te 0gcs8kth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43 ,i 7dmi;k5khw).
(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 accelerac:/4 br cq /q5teu+nmjs1uz,:rr f) jktion due to gratb 4sm/:u rjc cn5,/feur+kq: j1r)zqvity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflerx2/6rpd w3z fcted from the vertical by an angl /zdw xp2rr63fe $\theta$ 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 bankelonsk-ptw:s j f*5n4(d for a design speed of If the coefficient of static frict-o: (njw ps4tks5*l fnion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eartbq2sxy0)tnj gx 0 +mf7h were rotating so fast that objects at the equator were apparently weightles+0xqt7b 2g mjfn0xy )ss?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart o1-mnbmia 8cb;f 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 radxg ,rk5ym h e;wnul52jg)25zwius 235 m. A lamp suspended from the ceiling swings out to an anwn25kuh,5 ej5 mygr lz;2)wgx gle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has b p494lj+v8ccpf,2*me l vlm q jkf.6njeen claimed that a person would be crushed by the force of gravity on a planet the,4 j*nv 8fm 6 fc+j4k9.jlqplclmev2 p 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. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the pr)bj15ew/rrgf7 2pwsqka -z:b esence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no ligh2 qbz w 7r-frw/bk) s:5g1apjet escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill anj9egx,y s j8f k,lq*j0d 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? Explaing8,k es,fxj9jq* 0ly j. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes.a7;n.1 zabdr+dqw ez a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Eartz7.e1wrq a .;addzn +bh 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 billion *(*z*j zri drv*5/;p l gewczlkm, is meant to gz/ic*r w(d*5zlj* p zrl;ev*orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle p xp ren;0, ga9mon7i89jlq( mbursuing 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(re 90jmng;,9nqmbp7xi 8oal 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 +qb5lx5ok7 fgm u2jg: is its mean distance from bmkojgug5:x57+l 2 fqthe 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 ifr35b: +jkb ;cnziu x2v you could actually "feel" yourself gravitationally attracted to someone near you. Make reav 52 nc zb+jk3bi;x:rusonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) atpx h,)q.tziw 7 a distance of about 30,000 light-years from the center 7qt.z wip), hx$ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on eds3 vz8 bs lfed1;59/i,dvm wtach side. Find the magnitude and direcb 8z/ftw v dem5 1d;s9ls3i,vdtion of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the p1 sop/yzwbl) uu.px: .+gm fc)3i i,uEarth $ \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-c.y0zogk m5uz4 md 74upm-long sweep second hand on your wristpzmmu4 y5gzuk 704 od. watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing gq3 jo/v8c sb,a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle e o/qs,jbgc3v8very 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 desi.h2o4 yqt. efvgjx1b)gned so that a car traveling at s41bq.o .jgvty) xf2ehpeed $ 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, utnhiab vv/ss8w)e /q;5ilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted ;5nw8 bviah)e/v/qs son 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 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.$\approx$    $\times 10^2$