Sometimes people say that water is removed from clothes in a spin dryer by centfp4r;(o:.xot8slyl l d-me,0w d6cvu rifugal forcd4s we8 ooxvuc:fy0lr(lp -l;tm ,6d.e throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car trbjf4hp c29yc(k n 2f6xavels around a sharp curve at a constant 60 km/h as when i2hjfp2cc f x9 (n6by4kt travels around a gentle curve at the same speed? Explain.

Suppose a car moves a1il mknf 06d5it constant speed along a hilly road. Where does the car exert the greatest and least forces on the5k idm6n if0l1 road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round w :.3ptnygk *ho83yex. Which of these forces provides the centri8:x 3gyo pwtkhy.e*n3 petal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the watm-8)fboiq sr.er spilling out, even at the top of the circle when the bucket is upside m 8b.qir)o-sfdown. Explain.

How many “accelerators” do you have in your car? There are at ka5fbg tn4 xgsp m3ee,:)d*)u3zeuk 8least three controls in the car which can be used to cause the car to accelerate. What are they? Whagt 5,)nxebgez33k *suk :8pum)ef d 4at accelerations do they produce?

A child on a sled comes flying over the crest (6 oosjav7qz. of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he fes7 v.(zoaq o6jels 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 rg qb:wvtv s9:03gvp *rounding a curve at high speed?

Why do airplanes bank when they + s fmclvkdo 6(3l-sl;turn? How would you compute the banking angle given its speed and radius of th;l+smf l o3v s-dc(kl6e turn?

A girl is whirling a ball on a string around her 0wv/wi + 6 kdgobht4a,head in a horizontal plane. She wants to let go at precisely the right time so that the bbg wat60d4hk ,iw/v o+all 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 Earth? If so, 6;fl e:vuat p:how large a force? Consider an ap ;::peuvft6l aple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it pjjw9 zfe kjdd gb346-4z7 .hlis, in what ways would the Moon’s orbit be dif9 zg.73kj4-ljz dd6hb4 f ejwpferent?

Which pulls harder gravitationally, the Earth o v z96nsarju37n the Moon, or the Moon on the Earth? Which acce 9r73vu6zjas nlerates more?

The Sun's gravitational pullq )6e2 vx+ersf 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 from one side of the Earth to the other.)r e2e+sfvqx6]

Will an object weigh more at the equator or at the poles? What two emxlv+ 2 qd2lm(48c me7hk.v*pschm /offects are at work? Do theqc/h+d lv2p s* mmc(lo48vmh2e7m.x ky oppose each other?

The gravitational force on the Moon due to thbg sr0p mj::m2qwv.x-e Earth is only about half the force on the Moon due to the Su.gm:s2vj0x rpb- wm:qn. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around thob1d/0q cxudh1 2*k3loj/jo d ;fe hv:e Sun larger or smaller than the centripetal acceleration of the Eobeqodk2f ; v u/*dch3/j:ld10x1joharth?

Would it require less speed to launch a satellite (a) toward the east or (b) towc68nimckv1odwpn3e x,6 gq/f1+j vl,ard the n xq okmg,6jin/c8v1 1p+ efw, v6cld3west? Consider the Earth’s rotation direction.

When will your apparent wei.v(af.by2or6d dwf2c - f yc-tght be the greatest, as measured by a scale in a moving -cb.y(odta rycf-22 f vw6d. felevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in oy9p*yme 2j4bcmbe (,5eq d myyb25 ut6uter 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 ce6m* 5e(y ,y2me4bqybtb m2pud j9y5inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “app2alc,r uc0,vbvs a)/s*n ayc2 1-rlmcarent weightlessness” between steps.,c,calcals-)bv21c2a /muvs*0n rr y

The Earth moves faster in mda -/ajl7xz *its orbit 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 Earth’s axis relative to the plzm- * ada7l/xjane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explain v4 l,cp:( l.-k t*7dglf*zl 3wbnd ivmc( dc*phow this dis tcc *dl .lfg*pz v lc n:((*d-4,3pkli7mbvdwcovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. cvkd/ 8eub. nsv.8vy8Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Edn/b88cu. v 8.v vkesyarth 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 *j3b2i rys rn8zy- s(u 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 or*s,7pn o, jpebbit around the Sun, and the net force exerted on the Epno7 ,*sj, pbearth. 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 Nlq2eq +9h1i8z k qo/+onoc*m a is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 mec*qqo ++ an /l1 2h9q8ozkomi. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and k0e4v4iz bq r4circles the Earth about once every 90 minutes. Find the centripetal accelekvzrq44b 40 ieration 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 accelerbmwgsmf-,r.w 7ne 4i33gp0*sww8 ozlation of a speck of clay on the edge of a potter’s wheelwi - mgw4ss,lmrz.80 3 wfob*e npwg37 turning at 45 rpm (revolutions 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 ve 6.dd mywak8wxxut/ 58rtical circle of rad u.m6/w5wytax 8d8 xkdius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with6)egf7ed v:y(t 3:igpsds0i r i:xs l. which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction betw:teggs ) p0 3isdf.:v: lyrd7xi( esi6een 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 betk+1n8wz kj)v 1n 7r6bjegty 7kween the tires and the road if a car is to round a level curve of radius 85 m at a speed o7j6bn1k )v7kz8+ t nr1ewjykg f 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed hj-fk y:.bgx.;6j7s jxyzjo1to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotj sh j1jzyfyj.7 x:gk.bo;6 -xating?    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 +uig0 z:+4/q-hq7 w3 xesr fc1v oqdx-+idund a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remain+xqxq -h3uv u/g dd1 q i7die+ +rznsc:f-04ows 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 ccp2o5b2q 8k*eo,gah when upside down at the to*kc25bo qo ,h8c2pg eap 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 mas clh e2h0,ej :*i.a,uzz bd.bbs 950 kg (including the driver) crosses the rounded top of a hil*0el h,.,eabbc2z. uh:bd zijl (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter ct,8q,*meq/m pk s.)fn evtw-Ferris wheel need to make for the passengers to feel “weightlestfk) -,/q me,vwtm pqcn.*es8s” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At th arzd+tm2(pg) e lowespaz)+2r (gtdmt 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 rotate ifx/f 4i/dn sz-f a particle 9.00 cm from the axis of rotation is to experiencen4-//zxsfi df an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in+ wy+ klxj+iqf+6dq -n a cylindrically walled "room." (See Fig. 5--xkjify+n+6l q ++qwd35.)
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 gewd+osn6s 2q: jm ze2)c k1e/) is rotated in a circle on a frictionless air-hockey 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 )6w kjec:dn q12ss/+zeemgo2 Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of th,g o8 3u/f3yr,my5rp oxj f3ihe ball which revolves on a string 0.600 m long. In particular, fin3 8 hr3jyof5fgiup/rx ,m3oy, d 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 tr-3zp vso eosgpf n1w u((fxg.29-z 3saaveling 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 masseln/al npht+/ kk1 m;;us $ 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 3ml k k) (n7wuzd2tzm-:10 $\mathrm{~m} / \mathrm{s}$ . 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(i-qt.wcxbl)eoh 2 fq ;wmxevi; ; w:8 components of the net force exerted on the car (by the ground) in Example 5-8 whent.bwo 2iqqe; :(w x)fich;-vwlxm e;8 its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 5( e/uzx( nmsa+00 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 a/u+(ex (mns zhalfway 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 3i8 kidk7jj v-of radius 2.90 m . At a particular instant, its accele kj3jid8i-7v kration 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 12,8p a4;4y8pbjyb 00 km (2 Earth radii) a;p48 ajbby 4ypbove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain plj fy(0*oxsr*kw i-h3 j8ieqk /anet, the gravitational acceleration g has a magni-i3jeqjk*/y 0ok(8sh *x wi rftude of 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 acceleration due to gqwf-3b mc c(k.ravity on the Moon. The Moon's radius is 1.74 (c.3ckmfqw b-$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a ral hvc7ek+xy- 2dius 1.5 times that of Earth, but has the same mass. What is he-xk+7y2vcl the acceleration due to gravity near its surface?   

  A hypothetical planet has a masep tl ve,1d-)rxds ; ct)j2v6xs 1.66 times that of Earth, but the same radius. Whrx tx vde2 j)l6 -,tc1epdv)s;at is g near its surface?   

  Two objects attract each other gravita6 ec2wh-jl(z. tt o0eostg6 3rtionally 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 n mr)vo ti2.db+.m7cb g , the acceleration of gravity, at (a) 3200 mmt+o v.nrb2.m)b cd7i    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pckcqrlgns .,o2m hp7 u0,4 vf-oint outside the Earth where thegravitational acceleration.k4mng,ors7lp quf2 h c-,c0v 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 masse)-oam nlm o;4 of our Sun packed into a sphere about 10 km in -am 4lo ;em)noradius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an aa t54(b 0wikrg4gywk; verage 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 the surfgr;wkty(i akbw4 g450ace gravity on this star?    $\times 10^7$

  You are explaining why astronautqd i,+:we0qy0 tq-mhi s feel weightless while orbiting in the space 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 gravity 250 km abo wdq:00,iity-e +mhqqve the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calog(,)o4 n7cmzl*ouy,ftffz;mr;ef* culate the magnitude and direction of the total gravitational force exer o*luyz n f o4,rg,coz;m);7ff m*fe(tted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same s01l mj bpj*8vuide of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all*81vmu0jjp bl 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 surfdq;ws*vl1m s tq5(x/awzqb-5 e:rir :ace of Mars is 0.38 of what it is on Earth, and thev qq5:5qb;s/s(d zxliwrmr*- awt: 1at Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valu+x5d74 v kctnye for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained u5cnx y k7tv+d4sing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circbx1 px76a 7bnxular orbit about the Earth at a height of 3600 kx17 x6b7a bnxpm.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 kmt0 s1x -jgmc tg)h;cg1 above the Earth. How fast must the shuttle be moving (relative1 -m0gjc1h sgtcx g);t to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupanta1aj+ e+n if)us are to experience simulate1anjfea)+i+ u d 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 5–32.)   

  Determine the time it takes for a satellite to orbit thelglc* fx+m(ea2 :4acd Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of t*gl4fcac a dm+2 :xel(he 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 launl gf-u5 zi*r.pched from the top of Mt. Everest to be placed in a circular ori5 f ug*.rl-zpbit around the Earth?   

  During an Apollo lunar landing mission, the commandvs4 sy0j rnro6;eel+ 6 module continued to orbit the Moon at an altitude of ab y n46+;evr6eos 0lrsjout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The innoqb9oy 4): mlyer radib q4ym:o9 l)oyus 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 rotate bi7q*(g ivcp)7yb2cjs once every 15.5 s (see Fig. 5–9). What is the rat2b 7cc) vypii7*b gq(jio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-klch(81x p ue3mg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at consta8e( pul 1cmhx3nt 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 me6xs6eh)s )uuass. They are observed to be separated by 360 million k hxuu ess)e66)m and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a)g-cqoxx4bf a 2p6d6l 55-kg woman in an elevator thatx4da bqp cf-6l6g)x2o 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 suspen(rq9 :mfuwna)k zs7f)ded from the ceiling of an elevator. The cord can withstand a tension of 220 )fum wz: aqsfn 9k)7r(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 nearindh:ub8/ bw6 i+ 2ewdgz 6nb /,fx/nq the surface of a planet with period T , the densigb8he+, :x2w6i d/w /6bn ufqnbiz/dnty (mass/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) to determinemmg. ; ,zs+xuw,ur e+h the period of an artificial satellite orbiting very near thwz+, +gsux uh m;er,.me Earth’s surface.    s

  The asteroid Icarus, though only a few h r ) *p (wf d exo6crwod,blx6-/+coko3s.t)dxundred meters across, orbits the Sun like the planets. Its period is 410 d. What is d)k tf xw 6p6(c rolosw.+dd)crbx* 3xo, e-o/its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distangc / et;g3zshw99euz /ce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes veriqethe ; ) tze8i 2xo0eu-:s;py 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 qs uzexi2tt )8ioe-0: h;ee;pKepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the g4d( dq2m b pxr1yg( vn+3fy0tcenter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance h-pjjm0s0t c ;72cs ),pcpipdfor the four largest moons of Jupiter (those discovered by Galileptjc7sm d i2 0- 0c,chp;s)pjpo 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 t/od9 q+ xpdb7;nbb tu0he Earth from the known period and distance of the Moon. 7 0+ ;ubbp/d t9bondxq   $\times 10^{24}$

  Determine the mean distance from Jupiter for each oun :)wr jww lonhj0nsns xmw)q* */oy,91)6 qwf Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the v) wowso:nyw1),lqw m r*q* nshx9nwj6)nj0 u/alues 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 Jupdsmdb t/ lu+re4b3 b 93-cx3iwiter consists of many fragments (which some space scientists think came from a planet that once orbitedi me ld+ 3/-ubtr9cdbs34wx3 b 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 fhf()6f3 p e1p:cb(3 th b0xmdygmnq0form 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 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 thb0g0h (cb t3d3x:f)hp(pn qf 6fme1my e period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorgeefp,mzf a 2cxo.:xia 33gx/qq5tq 6(y by swinging in an 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 txq.o , axya:pxi3(q qm36gt2f ez 5/fcolerate 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 thei z z4 oub*.bc(:6cd(8goltq)cge; ck acceleration of gravity be half what it is on the surfoze; kbgqi ub 4go()* z8t6d .ccclc:(ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua67 fju i(tts5fl 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 thu jsif5t67 tf(ey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent n d-g;4q7 ztn(+ b)hhfn ud7hbacceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this ef()7hq7+ h hz;butn dgb4 fndn-fect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will ax lin5ld 52;lrd) jpf7,5ooga spacecraft traveling directly from the Earth to the Moon experience zero net force becausenld;,dxp if 2ll)55oargjo75 the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wj(vqe(q h8um.hen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the 8e(vj qmh u(.qelevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulo(scoi3oxv:y g, 7q f9ar tube that will rotate about its center (like a tubular bicy7oxc voqo 93:if,gsy(cle 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 aircrafti 9dhklhta;; *m;+k w8vu u5ih 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 a planet :*meyc .*4 *spd16 gywogjegi in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constant G.mg14s*6yogpcwg*eid. *e j: y

A plumb bob (a mass m cuyjnu3( g0:xx3ds (uhanging on a string) is deflected from the vertical by an xcd0uy sgu( nu (j3:x3angle $\theta$ 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 the coefficientfr6z-8)ylv zuxz* qe8 of ste*z-fr 8uyqxlz)v8z6 atic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day ,val3 )xr: 3(usdzyp cbe if the Earth were rotating so fast that objects at the equator were apparently weightless? c()ypudz: l3x 3,arvs    $\times 10^3$s

  Two equal-mass stars maintain a constant distance ay 7pqyg)9u:.touz s4(wcz vzwpzp*07 part of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lam 6 rlp x7bj*ccece52+2v-jfisp suspendedbelx6+f isve*j cr-c2c72j 5p from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the 8z(t;p* sloaa xi m)q3h7i8 czEarth. 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 a3iap)xoz tqm8 *;ilz8sh7c('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 T q yqj;:u/w4oa.6.l m 58r8bfsxpxtjr elescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense ajbr5o4 xjqm8py;: sf.w/ultr6 8 x.qthat 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 sg7gy 08 60-z .8zrc;tfs hnloz6a crtupeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (s zcn8yt 7z ga 0 l6z;rforuh-6t0c.g8c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites oroa;c8qj )613 5 zzwpc5wc cokybiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each zcq )wckpoj16zw; 5cc o58y3a 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.fy n* rz,df73e pi/dq), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 kmf 7d3dpnz*f ,.yqi /re . 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 s(asgnp7pyg 2c* q4x1 fuks k/3huttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the sate7ksxu/ f*2 1ky(pp4gc san3qgllite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) l-t5wti6k :k9n by0ul+j r o+d9(lbfh What is its mean distance from the Sun?9:lt6bd++u9 blhknrlfwik jt o(y50 -   
(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 val)z ;4ui-j qozjue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make rea4j-;zj )qzio usonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy/)p-oetk -v rx (Fig. 5-46) at a distance of av kte/x-o r-p)bout 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 ar/jlf 0 ic ley/zz;rv5;e located at the corners of a square 0.50 m on each side. Find the magnitude and direction;;llzfzc yjr /e/i0v 5 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 orbitsk,; susqhj)l;f h5tc1m tr) 5w the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.es,t7mj4-1l rlylim 25-cm-long sweep second hand on yourm7mi llrye1,tjls2- 4 wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in oze acq0ld 2:;u;bt4d2k9hnm t ,bn/o a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle everyabe;9zbmqnd: uloo2 2tch,t40 ;nkd/ 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 t vzdl w,6.pfk7hat a car traveling,fwlp.6kz 7vd 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 th 2;uqnl/p8;oy.3fgejy4.lyt0 rq) cmra5 u cilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a t;cjle3chm)4q/y run2.q0y; 5 gy 8tpulof .ar rain 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.$\approx$    $\times 10^2$