Sometimes people say that )bsstbk8d1qgf ( :8o )b 2a2l4qqhumr water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this2sqguksb)f4 1mb (t8 blq8daqh o:r )2 statement?

Will the acceleration of a car be the same whebr,)+c2o 8x)h*qmed9r9/rvz aofv c in the car travels around a sharp curve at a constant 60 km/h as bc))efr9vcd x9v*8ir/ohar+2mo ,qz when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at con-r;lc q1* qkp0k)hls ystant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the botto1q lqsr ;kl-pky 0*h)cm of a hill?

Describe all the forces actingc5y2,,:n/ojydc vng6* sc r up on a child riding a horse on a merry-go-round. Which of these forces provides the centripcguj*od c,sv6 ,/y 5pr2nnyc: etal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water tc49l7 yfvw2pspilling out, even at the top of the circlw9 4cyvpl2t7f e when the bucket is upside down. Explain.

How many “accelerators” do you mp(*hy7 jo5fnkyi u 7 q,kf/5 js8a2yfhave 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 acceleryk(58p u 5*njsjmq/a 2yik77f,fyhfo ations do they produce?

A child on a sled comes flying over the crest of a small hill, aaydk6e7ivc++acja2 erk;/w :s shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he a +6javarc7/e d:iyke+k2 ;wcgoes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hbbuy(49.ho rsigh speed?

Why do airplanes bank when they turn? How would you compute the banking an/j/lofh.fp/ p wk (t3igle givj(3. itl h/fkopw/fp /en its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizont*)y5 d5e ig/otv4w v ky7lh*vwe2hin9al plane. She wants to let go at precisely the right time so io4tn hhw95/ evi5 vlw*7ey*dyv2gk)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 force on the Eartu,ubk yp+l.n (h? If so, how large a force? Consider an apple (,+ubnpy kul.
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would yhtzs4yx ) ;b(s,hqx*the Moon’s orbit bexb4 *yxt; syq)h z(hs, different?

Which pulls harder gravitationally, the Eart-e.*rseb e6e dh on the Moon, or the Moon on the Earth? Which ad6. ebeese* -rccelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th+:2rgup)b yvb e Moon's is mainly responsible forpv2:rg bu)y+ b the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh 8k g():bauz czmore at the equator or at the poles? What two effects are at work? Do the:gz (uca)8 zkby oppose each other?

The gravitational force on the Moon due to the Earth i*7;zdf te7 x fa6maw*ts only about half the force on the Moon due to *z6wtxt7 fa7fe dam*;the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accea,yn.l+4 p,oin m9cfl mpr21xleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration mao 1ylfx,.i ,pn42m9 +nlrcpof the Earth?

Would it require less speed to launch a satellite +f ze(fdx7 m)m7n hi:gm.wig-8*uyfz (a) toward the east or (b) toward the west? Consider the Earth’s rotatio*ge8+n)dz-7z mgf: wf7ih (uix yfm.mn direction.

When will your apparent weight be the greatest, as measuredhm+sx j9 6v)mp4qjq 7a by a scale in a moving elevator: when the elevator (a) accejh7) 46m j vs+aqq9mpxlerates 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 outer sp q-a9ujsrv2 it:6+cc jace 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 9icr6ctj-suj :+2v qa 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 experiences “free fall” or “app :tmqo vc6ut9q - ;xr )/r.uqcegnt49xarent weightlessness” between stepcx/.gqc:qteuvx)r-m 4t9 t 6oqr 9;uns.

The Earth moves faster in its orbit around the Sun in January than in July.; iyn v*yyyw4/ Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producinyyw;*yiny4/v g the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not w: ql -0nw3a9)br okrhjk+g; pknown until it was discovered to have a moon. Explain r +9pn- h0q;a )wlj3w:b kkogrhow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger t j86r)4fsii th/l -cjehan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Crit86/h4-jj efs li)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 qk nvv+jjd; 4( ;dwa3r 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 8 f,,4i5cwe0djtxvelits orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circll8jcex,fdie, t5w0 4ve 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 exertedg r t-.8d(hgib)dj i7 rx7xrd8 on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radiusgdi8d- rd(b7.j)7hi rxx8rg t 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttl,x;qud*ks, wkkn g-6 ye+b/ife 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 orbit. Express your answer in terms of g , the gravitational acceleration at the Earth;qxf/* + 6es kdk,b,gwiuk -ny's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edgep+t1u b*cvr+iko *md, of a potter’s wheel turning at 45 rpc1* uop,k+*b+ tm rdivm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rategoqas;w- g:6 r in a vertical circle of radius 72.0 cm , as shown in Fig. r; w-a:g6gosq 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 speeh6uz70xzmh a 3d with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static zz a3h0 6x7hmufriction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the ticqux lpdgbl-jb2qup7(/ (a8 ;res and the road if a car is to round a level curve of radius 85 m at a speed of 9bculp;x 78 d(l2 jpbg-/(q qua5km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rota2 g *gbx)f3slepsgi 3,te a trainee in a horizontal2pg3 fis3g,g se)bx *l 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 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 r(bt *dstta3(yg4 st)of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turn at tbgsyr(t *4(d)3sttable?   

  At what minimum speed must a r57gxs 4hgn5z74faw mmb/ne :zoller coaster be traveling when upside down at the top ofx55 e7h 4aggfn/ bz7mwznms :4 a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 95wf-a,-1t22rpjrw*+ o ndg gqj 0 kg (including the driver) crosses the rounded top of a hill (radius =9dwwp a -n-*jfr1t+j g2roqg,2 5$ \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 wouy2x 36yc tp ./lult:(z9dxbn pld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightles l9nb2cyx( :/l ud6xpt3.pyt zs” at the topmost point?    rpm

  A bucket of mass 2.00 kg is w/asuklux+3d *o7shtb0 8m p a3hirled in a vertical circle of radius 1.10 m. At the lowest point of its mo0khmu*o abt8s /l a7xsd33+ uption 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 if a par eqp5 (+2buuwj i+:x rbidlyjoya43*1ticle 9.00 cm from the axis of rotation is to experience an acceleration oaq ubredy(:u2yj o+3 + 5b1 pwl4jxii*f 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivj zqcg8tg9i; zec/6+nal, people are rotated in a cylindrically walled "rotc cg/j qezg96zn+i8;om." (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 in a circle on a vyplf(;t ;xaxx1cm4 t3i40 xafrictionless air-hockey tabletop, and is held in thi4xfat;vlpcx40 ia;3m (xyx1t s orbit by a light cord connected to a dangling block (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 , precisely this time, 6w bgs6+3i,wdvuf: oa by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnifu ba:+3wwi66og,d svtude 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 bankr*/1su)v do ,j2vfal6w tqo3ted 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 masseqnl tc tgq(s7 29aurk+d (qy*-g7 8pyes $ 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 maneuve0wl/ xm-m vab 8qu*w711jaayvr 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 tangential9 0xdtll 6rx)r and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed tr069xlx dlr)is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, g gy36h(lh )k5s15flzqyp s0 qboing from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the tus (y51lhfqg0 k3p hzly)6bs5qrn, 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 inn wv:54 skn:lig: / so;cnyqurq96lg/ a horizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05 n /:;6li/:ns4k sc nlwouq5:yvg q9rg$\mathrm{~m} / \mathrm{s}^{2}$ , 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 spacecraf. jq(0ncg8 ce7c gs, es fei7aq80bvd+t 12,800 km (2 Earth radii) above the Earth’s surface if its mass is cb (c.g7 j8dc s0i80a7 ,sfqqgve+een1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnih--rynp3nz 1,zcbt i; 5kt/qstude bz-t1ric3 t5z ns;hp,nq- /ykof 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 Mooy a(vt wdb ;z jad4v-)mbvq*99n. The Moon's radius is 1.74 v 9 qavtmdyb z;djw(v94ab)-* $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Eartpbcuze5mggy 0pbhkb2v*-kw/ *0-u8 nh, but has the same mass. What is the acceleration due to gravity near its surfa b0*ku 2pp/g cbyzk0ewg-mb-hn8u*5v ce?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same*7)cx r1kj3bio;epgf /,bn wl radius. What is gpj1,ge3rxi bn7 w/)b;klo*fc near its surface?   

  Two objects attract each other gravitationally with a f95 b sw(tksjih)ei 47force 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 effectivxh7-r 4xvf5mb3pir . pso +tn*e value of g , the acceleration of gravity, at (a) 3200 m o.r-sf x* 5xbnimtp3 7 p4rh+v   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the h3mp* .qms5x+vhn:, ik8qq djEarth where thegravqx*p+ .s j,hh5:8vm mk3qniqditational 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 mass of our Sun packed into l-zdag570tio a sphere about 10 km in roaz -0 5glti7dadius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star 1re, 3goo+pba like our Sun but is now in the last stage of igaeb o3r1po+,ts 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 wel2:mzw) -a ohjightless 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 i:2j-) oaw zmlht 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 locaw;fzcj r+c 8+fm8j( yp xu,9x:ez-dgrted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere bjz9+j8rx,gfz-m y rw( pd :cc; +exf8uy the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lgn/ 1/5unxbj kine up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all u5j1/k xnnb/gfour 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 surfac 7 is p:2/kkh-ltgdngj,i v66inx /lx,e of Mars is 0.38 of what it is on Earth, and hn,:lt6g sl kip idv7/ /gij62k -xnx,that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for 7ci*xn- tj56(pb)f nasm bqzz.z.c* d the period of the Earth and its distance from the Sun. [Note: Comparm cn7f q*z.c bpjsdzxbt6)a-.n*z (5 ie 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 o eg.i-wbsv(w*/u 4mwy rbit about the Earth at a heimewvy 4w/bw( is .*ug-ght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite in vsauom8q:u 20to a circular orbit 650 km above the Earth. Hou2ua 80ovq: smw fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship roo j6,zupv.vr 6tate if occupants are to experience simulated gravity of. vvz6o6jup r, 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 t0b0qie3 kjd y8lj50llhe Earth in a circular “near-Earth” orbit. A “nq0e yk bld0j3lj05il8 ear-Earth” orbit is one at 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 launched froevhurofr/m*43- k; 9a6vej grm the top of Mt. Everest to be placed 4e3v;m/hk-j u6*g re rv rfoa9in a circular orbit around the Earth?   

  During an Apollo lunar landi3i+d/4crhxa xp)pwk b+aou(-ng mission, the command module continued to orbit the Moon at an altitude (do wpiub+x43+rp ha-ck)/axof about 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 zcfhef)/m3g 2m3.j (oe w;zz3curmt5planet. The inner radius of the 33 r2e m);ow 5ufjhcm/g3cz (mz.etfzrings 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 4 4brm; ju-2fj/bndfi i8e2dbrotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and 22 je-; irub bdn4m8/4iffbdj(b) at the bottom?
(a)    (b)   

  What is the apparent wenifit5y04( ucight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velu5itfci(n y04 ocity,     ----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. T4u+ k bn*y/umwhey are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each? mnuw y+/u4 kb*   $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elna7+3*xcn lftiyf 2n8efsj70hb 3s) tevator that moves cx7yfhtl 0f7)nse2+nbjft33i*8n as
(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 elevator/6z)qzeu74lbf 3m /;tclk xg ;nk*tuh. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minz76k3cu)l4blmnxe/ ; tgq;ufzt* k/h imum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits vetq6el )frz pinb5lf .y0w44e 9ry near the surface of a planet with period T , the densiy09 fz)lbti6 f.eel4q r5w4pnty (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 o 0bsks5 nhu7f0f the Moon (27.4 d) to determine the period of hu7bs00n fks5an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun li g+o 0ju2x p5m)kaqlk0ke the planets. Its period is 410 d. What is its mg5ma0lok0 2qku+jx)p ean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distae 0rmf g(e,bx.nce 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 veryfujay ,cw) wf/1w( y/y 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 a wj1,uffy)/w cy(y/w still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about thmb.zw 62me/hd e 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 mass, period, and mean distance for the four largest mn0c/ k5qny/;4qyzay0*gm jzmoons of Jupiter (those d/kqzcy0z ; myja5ygnm*/q4 0 niscovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the 4 sy cyvd ac3ey))o)*aknown period and distance of the Moon. cysy4v o)c a)deya3)*   $\times 10^{24}$

  Determine the mean d) /cs3oc ll/sd1)6ihr*lpmre istance from 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 l6pmcilr*r3 cdhelso1s /) /) 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 Jupite0u9+l)64rw6ow aqs(lo5tsqa(nkt c r r consists of many fragments (which some space scientists think came from a planet that once orbited the Sua olw +c) q5r(406r o69qsusltantkw(n 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- q pn.,tk :mtxfi+0ar "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). Imagine that this sux t,tfrmai. pq+-0 kn:n 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 t9zgfd l dsd48nkdp*3x ;,3bfhanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass iszfsn3f,89ddb;l dt k4pd 3xg* 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half vrv7rj g aj430brs.v 7what it is on the surf. s0rj a34j7vr b7vgvrace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handwn:7kcwqwkc,t1n ur 7)c) c;ps and spin in a mutual circle once ec;7) cktkn7wuqnwc1: , )wrpcvery 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 pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, thu z i4n zlaw.xy 3i-*rt9lu.z7e apparent acceleration of gravity at the equator is slightly less than it would be if the Earth 93 ualz i7 .z4xuyin*-zrtwl.didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from t /.tzhbj7h9p zhe Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppph 79j z/.hzbtosite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathr5mensjf l1b--oom scale in an elevator, it says your mass is 82 kg.--nb1emsfl j5 What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo8 2/d1yel mx dqi9of4z4vl*y fut 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 surxilqf 4v2d /8 o*md14lfyze 9yface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his 8n1avi o/aszy9j te18y ohhc81s22yn aircraft 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 w6q5ck;)y8wom* ci6jn ;wdjv of a planet in terms of its radius r, the accelerati;wj*qn6ccoid5w;k y w)8j6mvon due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a zjd (f 13yjs v63od,tt0jmt-pstring) is deflected from the vertical by an angm,06 tdvf- s1ty3(djojjz 3ptle $\theta$ 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 x +sfstuwruya;o5- h2r5q9j 3 speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car uf2qt3- s 59y5 ;ujrxroh+ swasafely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects ath5 4) t nfekr7q xbkdt2lk5zs8du3pg- 5wnj78 the equator were apparen nkrdg4q)dxz u57nkkj5 hf2pbslw587ett 38 -tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant77lme1b n b5ot 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 speedl - j-h.hj1pn+moq2os rounds a curve of radius 235 m. A lamp suspended from noj qph2- mj. h+-lo1sthe 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 Earth. Thus, it has been clai.gqxle2u.tx89s ;uni3 v+b jdmed that a person would be crushed by the force of gravity on a plane vqj3e8gu;+ibx9.t 2nsxl d. ut the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. 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 dedu(bpbdpqbho b7/ -,k/yced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which / q- y ,b7pdbpbkh/b(ono light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown in s4k ,knj84qheFig. 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 drive 8nks,k44j qher feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utw:;h0lj6+ lyq)m xoyts 6hg;filizes 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 6h:os qh )t;mw 0g;lf6yxyl+ jof 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 km, w1zvcoa ;yi4iliq :.uoww-4 5is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughl4cww1 -y4 qoi.io:u5z ia w;vly 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 satellite idf f876,neam9m;r 6kvpmztvi2 0(psn n need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km berv6vnmzfeiap, s2tmp (9f 0nm7d;k 68 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) de8q qo3i4hxo81t/r /b v b(lzWhat is its mean distance from the Sun? bziq8xb o(to//l3 d1 q8hver4  
(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 valuq pe y5v40 hzjlqli)6-e of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonablehv0lliq)j y4qezp5- 6 assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.2,fdbq toeuj5rq;t6,wj t 25k 5-46) at a distance of abow;qo,tqbrej, 26jkt5fd2 u5 tut 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each seawp: kc-1vxrbtouhh( ) ;3e 8ide. Find the magn8 hr)v(3 ;eew:akpcto 1u -bhxitude and direction 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 Earthr qh6lz8/j*v+g/forz $ \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-cm-long sw pln l1+ems o,sk15i6teep second hand onk 1o6l+t ,il1mspesn5 your wrist watch?    $\times 10^{-4}$

  While fishing, you get borewi aa) nv3; es7obz9l 0jg;i0jd and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishil e0bzaw9s ;na voj);7ii30 jgng line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwa7fah giu a)owrcr9b3 xm2+d1- y is designed so that a car travelin-)bgxcaa7 3 rof wmh9iu2r+d1 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, ths s*bqq,638d/ pcnquuik y0+e +0fhrce Acela, utilizes tilt 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 td yki0upc ncbrhs+*6 qq30+sf8 uqe /,he 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.$\approx$    $\times 10^2$