Sometimes people say that water is removed from clothes in a spin dryer bv+ ekpqu0 .vs/y centrifugal0vpuq. k +vse/ force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car tyf.b1c .y515dv w6,fgdxhda:sowz ;be the 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 v. yco515w:s. ahyd tg,w1xbd d;6ff zspeed? Explain.

Suppose a car moves at constant speed along ;s kzam vds :4(-z,llo-v8lbr 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 stretrk-;8vszb lmd,z lsa(4-v l:och near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merr 4 lfnj s;)mg:ri6xj6ag-* b lx/rv1wfy-go-round. Which of these forcesa j gln:6)f1rx i *xjbrv4 l6m-fgw;/s provides the centripetal acceleration of the child?

A bucket of water can bz3wh8ipg79i0y ep .upe whirled in a vertical circle without the water spilling out, even at the top of the cihyiu0 w.gip9 e8p z3p7rcle when the bucket is upside down. Explain.

How many “accelerators” do5if:xpojcp;u1x wc6 7n q8f :p you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do the85uqf popcwfcnx:6; :j17pi xy produce?

A child on a sled comes flying over9e)i5e v6k xjn the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as j 56)kxeniv9e he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hig4o4:),muoedhzq is 9r h speed?

Why do airplanes bank when ca2n;r+ u /rz8x0 co9lv )e(py h3:dwyasvxw /they turn? How would you compute the banking angle given its speed and radius of th8p wxl ay;/nyxs/ +u)zrcv3c:2 (90aohvdwre e turn?

A girl is whirling a ball on a string around her head in a horizontal uzvet7s2a-3,wdblq : k+wt, w plane. She wants to let go at precisely 3t:2w-bka+v,qwezwt ul,7 ds 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 string?

Does an apple exert a gravitational fo vzp)b: t2mpm:rce on the Earth? If so, how large a force? Consider an apm:vzp ): pmtb2ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woup:4np. s+* qydjdopa/ld the Moon’s orbit be dad4pjp:/oqpdy.ns *+ ifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on t nvlc,gfo,h:0ix i 06wefj, 3dhe Earth? Whi0 d0h w, :elof j6iv,,ngfixc3ch accelerates more?

The Sun's gravitational pulu.2* e3*mibxeqqb x( dl 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 oqmqe.xe3b*( dxui2 *bf the Earth to the other.]

Will an object weigh more at the equator 0 xu2;vro fj okqt*(jk7+p -cr7agqy,or at the poles? What two effects are at work? Do they opposo*qy,7ro +r; 2jcg qj -xuk tkpav0f(7e each other?

The gravitational force on thb, o,d hahz)6 a/acnh(e Moon due to the Earth is only about half the force on th) hozaca a,n hb,6/dh(e Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mltou *-3s6yqm dqe:x :gjp:9wx bzls 2pe8o9-ars in its orbit around the Sun larger or smaller than the centripetax:owe els3x2j:gy q:uoq6pz *-bd- m p9lt98sl acceleration of the Earth?

Would it require less speed to launch a satellite k z..jvbumz,y;uej-imo 0w,. (a) toward the east or (b) toward the west? Consider the Earth’s rotation dire.b;.. -i,mw jumzj0kov, z yeuction.

When will your apparent weight be the greatest, as measured by a scale inbkfmf jq b/l sxw-c/)e2c67g9 a moving elevator: when the elevator (a) accelerates downward,q)c 6kfbbg jsxec mwf 7-9/2l/ (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 outerhvkn 7ozb/ 65x space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindricon /zhk56 vxb7al shell that rotates, with the astronauts walking on the inside 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 experienfh,jea m .c7va,len5*ces “free fall” or “apparent weightlessness” between stepa.nf5 hmj7cee a*v,l ,s.

The Earth moves faster in its orbit around the Sun in ,a2xu5 7:yygj0 jkeij 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 planey5e,:0j7k2 g x yiujaj of its orbit.]

The mass of Pluto was not known until it was discoveredlgx; z:fri ;e4 to have a moon. Explain how this d ;4;zirfe: xgliscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth ih i.8oez(bol) s 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.]A child sitting 1.10 m from the center of a merry-go-round moves with a speeohl8o().zi b ed 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 5d 9-e.ztbmwn1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acczla9 nzu2d/c2 eleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exertclz 9nu2d/ az2s this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is ebu bo6ivzc 9 87jp0wy5xerted on a 2.0-kg discus as it rotates uniformly in a horizontal circl p u6yc90bv587jbo wzie (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttlek3 +mu5rlbw fi,: 4cdz is in orbit 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 orbi l+cf,ukrdm :4z5 3wbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay opjpkhx*)d u(, n the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 x)hkp jd*u,p(cm?   

  A ball on the end of a string is revolved at a uniform rate i 9+ujtrj9e ,xdn a vertical circle of radius 72.0 cm , as shown in Fij9 djxrt9e u+,g. 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 car can ryi-zhpc6* t e0 u:56cesvbkn9ound a turn of radius 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 cacz 65 0nkp e: hyv-e9s*itcub6r?   

  How large must the coefficient of static friction be bet oba wbkje-o mvr0 i:2/(ua0w0ween the tires and the road if a car is to ro a0r2oj bi0ubvmo (aww-k:/e0und a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jv3:k cb3c k4uaet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weightbk :ak43 cvcu3, 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 axis of a rotating turntable ofkd ctal).ryp;yy /x*a- t10 ne variable speed. When the speed of the turntable is slowly increased,at- . ;y/lxy)*yar 1 tked0ncp 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 coaste:t )cu p8ltsb2r be traveling when upside down at the top of a cist)u8lt2:b pcrcle
(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 (includingh4xt w7egn+.pizgazj1.m y/ 0 the driver) crosses the rounded top of a hill (radius =95tjz0e.z.g wh xyn+g/1pm i74 a$ \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 woulwf9dnb*0 ehd yu5n+x7d a 15-m-diameter Ferris wheel need to make for the passengers to feel “we5 h eb0n79+dd*nxfywuightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is wpq c7fu4;e2bz hirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension i;puf4 2 b7zqecn 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 if *ic 7hro1i.;k fc7q) /ywaipbwvb )e7a particle 9.00 cm from the axis of rotation is to experience an acceler.abocwiipwevkq )y7 /c);i7h1*7bf r ation of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled /6(eroe m3s*osgb gg t3;w+ez "room." mo b3*egeszgs3/g;ow r6e(+t (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 in77)i bv5qxe/bhg*q xs 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 aseh 7) q /b*5qvgxibx7s shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the (- ;n vyky4ocfb-dgerw+n1b(weight of the ball which ;r4cgeknvfyw (b(y- +nd -1ob revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m ;/rh nb9 3xyyl.x xgi7is 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 massejj*a v x,g.vj85 n.uhjs $ 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 e p2sk z:okw-u*vasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the e l,(0t yeo.xlnet force exerted on the car (by the ground) in Example 5-8 ex y.(0leol, t when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformlyg3 )wwpmi*k t*sp6h56 hrsz /q from the pit area, going from rest to 320km/h in a sem )gp5* * 6tkhqpsh/3rz sm6iwwicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal cirop,) 1swrk7 ircle of radius 2.90 m . At a particular instari1,ko )w 7prsnt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earw/3jwh c)awo4th radii) above wo43a /jh)cw wthe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accele j0 v;pnbykg5ym q;tmx, twj,/.7g1u 6k6vtgkration g has a magnitude of66g7, 5g,bym1/n.tkux;jg tmpt;0 k qvjw kyv 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 gravity on the Moon. T )i4nahf.n ok;()qz inhe Moon's radius is 1.7)qn;nii(n4.hfa ko)z4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tim: p cv-5j kb wsvg+o2g5(gta:bes that of Earth, but has the same mass. What is the acceleration due to gravity nbvb gg5+pw:(o 2csg-5jk atv:ear its surface?   

  A hypothetical planet 3iw9 p4k+*8wrfnkauw has a mass 1.66 times that of Earth, but the same radius. What is gw8+4nwup9fkkia 3*wr near its surface?   

  Two objects attract each othj hxs)*qmxrc .4to2h(er 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 effectivefu8ub)3, f 2teozd+bg3hm wl; value of g , the acceleration of gravity, at (a) 3200 mf+zb32l;u d 8 u3ehmo fwg,)tb    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ovd:dghc *: u0autside the Earth where thegravitational accelerationguvd* hd:ac: 0 due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timeszkf 3p j+a,p*z the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gzz,fj k3pp *a+ravity on this monster.    $\times10^12$

  A typical white-dwarf stc lrqbj0 l*(q3-mx-sn ar, which once was an average star like our Sun but is now in the last stage oqqlx(03c*-b- sjl r mnf its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightle ccpz3+ep3 lm/ss while orbiting in the space shuttle. Your friends respond that + ml33czpp/ec 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 above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are c- m s;ucn5a )itr1hf4located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sc 5nu1hfs )arm4-;c tiphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of g,egl tf)cz)k j:7( xw5snj3x zh1,quthe planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, axcghjwgkeqs 1()jz:l un,, t5 f73)xz ssuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleratior0zu.r4:hd yk n of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ r 4zurrd :yh.k0adius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun1r e 5nk:rit sac31t3m using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to ttmr i1 ae 35rkt1n:3schat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about9x5xp3cc o0b dyx+pbsa:c+:f. )hn pb the Earth at a height of 3600 kmcxnd+0h9+ca)xcp 3x: 5bs. ybpp :ofb.    $\times 10^3$

  The space shuttle releases a satestd9;2, yrrnv llite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative r2t d9,rnsv y;to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rota k 6a*(thlolc1q vj8w2rb2v 2lte if occupants are 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 revolution. (See Question 21, Fig 5–32.) q2 1lvwo2(hj cta 2kl l8vb6r*  

  Determine the time it takes for a satl eb;(p;4v njpellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one a4(lvnp ; epbj;t a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launchkwrwxo,yh*a bpy(jzne6oo -( x.2 ( ;wed from the top of Mt. bew*n;-x( joroy.k6w, wyap o z(2xh(Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landiix jmw2 (-*w+-qbh6y4tepmewng mission, the command module continued to orbit the Moon at a(bq+4 hww-jwp26 t*-m yiemexn altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of iceq*1datd 1 1gmvk4zpm :/crc 7f that orbit the planet. The inner radda1f:q11z4*7 ptd /mc kvcmg rius 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 diamet5p5+ib ez yu6zyj;z (yer rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weigu(zjey6y +;b z5 5pyziht to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4h6jk f(meo2g4200 km from the center of the Earth's Moon in a space vehicle (a) moving 2ej g6 okfhm(4at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They arebv a5rwr4* vb+o b0f)x observed to be separated by 360 millibbrr o0b+v)fxav4* 5won km 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 55-kg woman in an elevator . b6hiri bvz53that m 63b vbhizr5i.oves
(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 suqls *-33)qrj) qvnqix spended from the ceiling of an elevator. The cord can withstand3qj3-i*qn vl xs)r)qq a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbifo6pb4 t7644xefy j 2tga5mhtts very near the surface of a planet with period T , the dens4 7fp 6tatxej6fgo 2t4hm45ybity (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 determine tl68bd: t*ib*bgfp - co7lfvw (he period of an artificial satellite orbiting very near the (gb**t b f6vl b8wd-lifp:7ocEarth’s surface.    s

  The asteroid Icarus, though ondvrq0z ( 1)ous4eekj ;ly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance frv e0ujd1 (;4sz)rekoqom the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 g-q wi yfi;grb+ 6+nl:$\times 10^{9} \mathrm{~km}$ 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 orbityx 3.vih(xu3g s the Sun roughly once 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 Solar System? What planet’s orbit is nearestuy 3hg (3xv.ix 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 aboutv d/idy : 7ysuvv3zt7m r0ax38 the center 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 m6v ac*a9c3 f tzq1 --i-roocedass, period, and mean distance for the four largest moons of Jupiter (those discovered by Ga61*z9to rqd-eaafi-3cvc-c o lileo 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 Earthc/who .fnwe.- from the known period and distance of the Moon. o ecwfw-/nh ..   $\times 10^{24}$

  Determine the mean distance fr9dl5 1.lfblx6 n idsw:om Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tdw nldx69fb5. : lli1sable.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and n c,zdxv: b0;fm,g .bxJupiter consists of many fragments (which some space scientists think came from a planet that once orbited t fvb;: .0gb,,cnxdzmxhe Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form x1;ky5aj/ whm.4uuw d xet a13of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always 4a xy ea/xkm351dw. uwt j;1hunoon). 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 0h q xmy,ac0rc+fjp 91vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 59p x01 jc+0hqfrm yc,a.5 m long.   

  How far above the Earth’s surface will t c929tsdnzgqxou14wvz 7ft,: he acceleration of gravity be half what i9f2x1s4nt7u gvod,z wt :c9qz t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal a psyiq x76,p* rxfe2,mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard aref6q,p xy s 7ei2rp*,xa they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accegy 4rxsyb dltul:z5q/gd93( (leration of gravity at the equator is slightly less than it would be if the Ear9z45ll /3qd sdy: ygbturx((gth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eartb:kznf:z9p ,ah will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Mo,9bz n: k:fpazon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroo 6alw kal9zn+0m scale in an elevator, it says your mass is 82 kg. What is the acceleration of thwk a96l zna+l0e elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station c8 c3 6wnxgmle;onsists 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 efl; xng 3ew6m8cfect 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 azvg5ow8z s u4p5y55zaym q h8(ircraft 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 pl37h6qau+ass k4zvu 8tanet in terms of its radius r, the acceleration due to gravit7zu3 8a+h 6qvk4sua sty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is defew4dw u,c (k aung9,ymi- 0jv:lected from the vertical by a uwv,gujei k c9:way, n(0-4dmn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m iueq:e;al br s0:hi q3p+0ufp2s banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely ha;uq:3qpfh pe+i0 slb:ru2ae0ndle the curve?

  How long would a day be if theu lks +ki:fa-( i*n:/ds w:tce Earth were rotating so fast that objects at the equator w :si(-luafcd+/wet n:skki*:ere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintai0fe* /7 8:8secehb ;cd is5,rkytxxnrn a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 shkc+uf phy++dg/q ivt*g.* jz r*3,wm. A lamp suspended from the ceiling swings out to an angle of 17h zit*rpwqhgc+y/*v*sud ++ 3kg,jf..5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 ti ( csh,fo4z;zrmes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's.zh;cs4 z(r,of 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 Hubbl h4s7)lo+ txzze Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light o l7s)4 ztzh+xescapes). 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 and valleys*tnf vkuhf3) 2a0 ho. 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 cho02vff. )atu*s nh3kar at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positio4litr e lif-zk;p7n- 9k)l0wy ning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a fewlkif ky9l )-;0-4i rnpzlt7ew 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 Rendety) d1 5fi,hdp ,mmwu3zvous (NEAR), after traveling 2.1 billion km, is meant to orbit dy tmfu3 pi,hm )51d,wthe 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 pursuing a satelli; dyae2 s /x(pblnbt6-te 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 behind ixbe-2syn(d ;b lp/at 6t.
(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 itwaj 3d(c ;a8r-cumc3ys mean distance from tdy (c3raw;-ac jm cu83he 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 n q. qyep5q)fnnhz 553geed to be if you could actually "feel" yourself gravitation3)phfn n5q5 .gzqqe5yally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (F4h;uo, uboiw:a 1v7nh ig. 5-46) at a distance of abh b un4wa;o,uvohi1:7out 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 corz*1mm 84sbc wgners of a square 0.50 m on each side. Find the magnitude and direction of the gravitatigzmb8 1sc4 *wmonal 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 Ea/ r yp0 arxc tz(f2ov2y:6-bhsrth $ \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 yj.4d3 k+feho tip of the 1.5-cm-long sweep second hand on your wrist wofheyd k.34j+ atch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cisj 8f-pd ca:ih(rn- s4rcle below you on a 0.25-m piecep8-c -(hrjss: indaf4 of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R gf t vjqu //ub7co98p6 in a new highway is designed so that a car travelinqj6upu9 v of7cb/8t g/g 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 cl,5v l y0y m6j*9pyeznars when negotiating curves. The angle of tilt is adjusted so that the m 5ypv*yz6n lyej9lm,0 ain 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 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.$\approx$    $\times 10^2$