Sometimes people say t*n*bn mu(nixz:n 3.f that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wi*.n f*(n:txbuz3n mnrong with this statement?

Will the acceleration of a car be the samqmq7r76e/ns ue when the car travels around a sharp cq77 uem6nr/squrve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the cary:o 05ep/w29uu(n: y tiflobh exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) o(p2ofiytl9 uybw: no/h 5e0u:n a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-roun+a/,rp f)798ohj fqi; qxskiqd. Which of these forca) +xq9phif i,rq7soqf/8j ;kes provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cir ) .4nvrq )m/lp mukqwn1p;y)lcle without the water spilling out, even at the top of the ym)pl)4n1kq.;w p ulvn/ )m rqcircle when the bucket is upside down. Explain.

How many “accelerators” do you l7)gm0cc cl vyjaxtl(+35 9b rhave 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 th)cry7l95 m+abcvg (3 cltj0l xey produce?

A child on a sled comes flying ov7ir w8 puhy+v:kcc7u0er 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 thecr08kiuu+v7 wc yp7h: sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whenwqctnxongm9 6d;c. f751jty: rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking a:-,kq rvzzjj e9n2 yb;ngle given its speed and radius of th9vky:ebrj2znz,q j ;- e turn?

A girl is whirling a ball on a string around her heh4gqh2ynf p ;w+i)4 fwad in a horizontal plane. She wants to let go at precisely h+4fw y4nhgq ;p i)w2fthe 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 k7t 3b6wf6/ rpvuso6z gravitational force on the Earth? If so, how large a force? Considertwz f3v7r6u6ok6 /s bp an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thnq pwib*2yiic5 /k; t8e Moon’s orbit be i/inct b w*25iq8pyk;different?

Which pulls harder graviph86a ujfqe*- tationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?jef*h -86p aqu

The Sun's gravitational pull on rz5a1gt2prj-j wx7f d( t9g6 6v wgbc9the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gra59j c 1wztfb rv7g6grxpw-( 2 tgjd69avitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatnfku; u,w 8sbf u.4x2ior or at the poles? What two effects are at work? Do they ,wsbf.; x kuuiu f428noppose each other?

The gravitational force on the Moon due toh)xii 9;/ cjy8v jl;gz the Earth is only about half the force on the Moon due to l 89vhixcyg/z);j j i;the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larg5ub5o7fiyt 4m4 ioy1( lx 4pqier or smaller than the centripetal ac75yy 1oi5l 4ip4bmixq4 fut (oceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east op8 8fzhe qq3.ot 93mmcr (b) toward the west? Consider the Earth’s rotation dir z8 qm.mo3qpf83h tce9ection.

When will your apparent weight be the greatest, as meaz/hnq u;:i ydp57 cry(sured by a scale in a moving elevator: ; nqd z7(hc: rpyi/y5uwhen 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 los 9xkgfy3q)if30 8g wc)fw( dhng periods in outer space could be adversely affected by weightlessness. One way to simulate gra iqg hk8xy sw3f 9ffg)(c0)dw3vity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects 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 “apparent weightlessnexnqg1 8hu* x*a d f-j)r,zbwou)oi *6jss” between ste*) u *ji-6dqj oh*u)a8no xx 1gzrbw,fps.

The Earth moves faster in its orbit around the Sun in January than in July.hg :bt6pe57n d Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not 5b ngh7p t6:demuch of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explai7q )ey3hukpmbo 4ff:f9zzp ,(n how this discovery enabled f 4om37z pub9qyk(p) ,fe:fzhan estimate of Pluto’s mass.

  The Sun's gravitational fam(jm eied 7765i(*t ;axmbzpull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [af( z( a 5mede7mixb7it ;*mj6Hint: 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 travelinjd / 6+sv32ec)2 +c kx ./3obigegr ifqcbx7nwg 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 centripea+99u o ufdx,5v/wb m3fg-yrxtal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the E3m ra-o9 gw+udxf9u ,f bvy/x5arth. 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 N is exerted on a 2.0-kg discus as +sx)v7,8 ourso wue v(wv:we1it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. es7oru)w 1o8xw(vvv u+:,ew s  

  Suppose the space shuttle is in orbit 400 km from the Earth'hz5fd j:m l u0c3h.e+es 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 accelerationj +hlmhd:cz.u3f50e e at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the equ2 enxy iem ya5;0d22u f1bq6dge of a potter’s wheel turning at y mn ;eqdq 2xe i05uay221bu6f45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvebf:o-gl* )t40 p 2 zdnnn.phqkd at a uniform rate in a vertical circle of radiusg) q*p. hpb2 dtlonk:4fn-0 zn 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 with which a 1050-kg car can round a turn 0iay4gcq8n 2: l6xscr 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 c y0grx s:cla64in8q2the mass of the car?   

  How large must the coefficient of static friction el7,oh3o6 1nyumqy 4gbe between the tires and the road if a car is to round a level curve of radius 85 l7yo,yoemg6qhnu 431m at a speed of 95km/h ?   

  A device for training astronauts and . (jlq)kj)+eb yfre;zjet 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 weighflz .+(ekqej)b y )jr;t, 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 of variable spp, xz m;db7wu6eed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reachedx7uzw6 ;d, pmb 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 beby 1 h1zj6nf6jf27j qor*c;hx traveling when upside down at the top o11 r cfy7hj;nqx6b*2ofjzjh6 f 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 950 kg (including the 7qfe x3b ,m)c9-b3 tcfnmizo7 driver) crosses the rounded top of a hill (radius tcxbi m3 e7)o nfbcq-fz 97,m3=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-:hdwm x(*d(vf m-diameter Ferris wheel need to make for the passengers to feel “weightless:d wdfh(*(mx v” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ral-gstf/j .s8hdius 1.10 m. At the lowest point of its motion the tension in the rope supportissfh-g/j lt8. ng 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 cen jaz5lcjz w) q k(l.nial*-)k*6l)ttntrifuge rotate if a particle 9.00 cm from the axis of rotation is nl-za)*5 qti wn *tc)lza kj)jlk.l6(to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in j94jr ccal*9rr9t7d byms/7q a cylindrically walled "room." (See Fig. 5-35.s4ma9r9 lc cr qj7*j/d7try9b)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tabl.m3t yuqtj: bhvyymvu, 13;z4etop, and is held in this orbit by a light cord connected tozmuy:v;,t3yyb1 u v.tqm 4hj3 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, cf gfu d3cjir4w(gdy+6(3je1 by not ignoring the weight of the ball which revolves on a fw (jf i1rygcdj3gdcu +e643(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 if*o+z h:ucdy:.49lox)c xmng s perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses kad9bs1*)e uq.m 3w qw$ 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 evasiv5p(;)t tda ba42djtzee 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 ths;)czc.,xm* t 1adgp; bfjz y0e net force exerted on the car (by the ground) in Example 5-sgxa0b1p t;c dm)j*y;.zzcf, 8 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 h a2rsb5o: n3x )jlw3y91hrvd 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 acceleratiwj vr2 l xhda)by53 rn:931shoon of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of kksvol5 g1th7vor:)8b n w5 noyx+u,9radius 2.90 m . At a particular instant, its acceleratilxu5)ovkso7 y,g:85v1nk9+rn h otbwon 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 kju1 z)bw0mcut bw57j2m (2 Earth radii) above the Earth’s surface if its u5jwzmw 702t )u1cbjbmass is 1350 kg.   

  At the surface of a certain planet, tkv8w : iw6b-yo20 lu 2ej)b9q h3dwerwhe gravitational acceleration g has a magnitude of 12 m/u vke 2d8wqeiblh3)w0owy b j:62r9 w-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 ozi;jh 8q hnvo647nz ra7t::b nn the Moon. The Moon's radius is 1.74 znhr nb7 qh46;n 7:j v8o:tzia$\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 th 4 vy*gw+abdr2at of Earth, but has the same mass. What is the acceleration due to gravity near its su g*42 avwdr+byrface?   

  A hypothetical planet h;t2r,z ds 2 /:pi/bjrcmqin7oas a mass 1.66 times that of Earth, but the same radius. ziom7:b idnr; s2r/,t/jc 2pq What is g near its surface?   

  Two objects attract each other gravitationally with a fop2i 2rj9 4(qe6m v8 wytwa5ulrrce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration1) jm. smj0osr of gravity, at (a) 3200 mj1jr.0mssom )    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to 08tnuzrvyj subsl1nnqd vj7.0zy 56y5s:v.. a point outside the Earth where thegravitau5:v.6vj1yj n 0uzns5tn.bsyd7 v80y ql.rz stional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five /m,d7 lcfpjq* times the mass of our Sun packed into a sphere about 10 km in radius. cdl7pm*j/q,f Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was 5 n:-sokn dth5an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our -dks:n5t 5nho Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlesq8** l,*thuct 4 ik 1cdqysz*ys 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 above the Earth’s surface in termyuitlzkc*c4**,*hq 8 1qtysds of g.   

  Four 9.5-kg spheres are located at the corners ofni: i1pzr/ ;yx a square of side 0.60 m. Calculate the magnitr; y1: ixpzin/ude and direction of the total gravitational force exerted 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 t6wk+vz c:af oog0 7u4zhe same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). Tg +zc wu7o0ko4f:zav6he 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 surfo74y my kb9 hwfh-hp)7ace of Mars is 0.38 of what it is on Earth, and that Mars’ )- wh bh 49yo7hfmky7pradius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using tyi u7cm.mf6m 5he known value for the period of the Earth and its distance from the Sun. [Note: Coimmy 5 cu7.m6fmpare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satell h-26 enorafmm .mjj sk7) s)h8f.z0vkite moving in a stable circular orbit about the Earth mhzj)0. akk e6 8snof. hj )2m7svmr-fat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circularmk+1t1obwr 6odqmo c6. ojs6dt8ea0. orbit 650 km above the Earth. How fast must the shuttle be moving (relati1mowmja6 ddro1oekb .t 0qs.tco+866 ve to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spa dj485p)f)uf2j hkbo nceship rotate 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.)5jdh)8np f4ofjk)2ub   

  Determine the time izu);81 bjyih4 c/egb 0l(ui iat takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the r cuu(jii 4/;0 hlybag1e)ib8zadius 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 lau07qs tddk4,p gnched from the top of Mt. Everest to be placed in a circular orbit around th0d ktqp,s 7gd4e Earth?   

  During an Apollo lunar lrx j2aip++bor):.vt wanding mission, the command module continued to orbit the Moon at an altitb w xj2rrpa+)+iot .:vude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunkz0b tplzin6 oyk2 i9(/s of ice that orbit the planet. The inner radius of the rings is 7zoz2 l k(biy n960/itp3,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whax ;hzw*pn6gn ,l-*rort is the ratio of a person’s apparent weight to her n zo*lxnr,;w -hrg6*p real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wfb* szz7dz fuc)f178 veight of a 75-kg astronaut 4200 km from the center of the Earth's Mooc zzb * fs87)fud1f7vzn in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-st14fwp pm2y0e3b -dnhxar system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway w24yh p30 pbefmd1n-x 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 elevatormfecrcl57 dn4 f2ugr7e : 8/u:6ergaq that movgr425mr f7f6ulq e/u n:8 rc:egae 7dces
(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 ceilinw yk.askl qr 6*b0i73js *o6frg of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s mi f**r6slwsijboq a3. yr076kknimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbv2slan vh)o)b )gb5 2vits very near the surface of a planet with period T , the densityan5b2)h svvv)) g2bol (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 t2d -lncjgh1a r+7yb/c2ql 6c s9x vvso5/h5ithe period of an artificial satellite orbiting very near tl29 lao h gdr 1-tqv5c6b7/y/+5nxch2cisjvshe Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits tj-vmm. toh2c2hc6 c 3phe Sun like ththo3c-.ch2 c2v6jmpm e planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.:s x5lv4j4zrsi5o 3x d5 $\times 10^{9} \mathrm{~km}$ 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 jo/v4n:n:b +p xwunrxn6yj/0j:5t v zvery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is+/vz wnrj to5n6ny0/ u: xj:x:nvbp4j half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of thefl/ 0mnv3; zsk3ws +qc 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 la 4favmef7+et ;xgm/ atj-el45rgest moons of Jupite -+a/jv ee ft 447faxm;5ltegmr (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon.kfv cxs( 2j e5hl9)p.q e9vk )sp2.xj(cq l5f h   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitervo qro h+4:3ma5q3 lme’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to tq3 mq:4ol+vm ha3re 5ohe values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Marsnu+x p.qpbzj3-7 4mh6 spr,mb and Jupiter consists of many fragments (which some space scientists think came from .jz m3+pb4xrnm- uhp7pb s6q,a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction taju,q-*b1 wex) wro td0le describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on th , rutdxqo)0wjwb1*e-e 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 the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a f nk3b,1gt2v ykxfk// hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximuvyfk/nk23/,kbtx1 f g m speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what0 rzbp0x+pkcfxiu-7t v5 :d6v it is on the surfaccx bd5v :uvxrk+-t0pzfip760 e?    $\times 10^6$

  On an ice rink, two skaters os p9ncbbgt*0a)tp:* y;i(lao f equal mass grab hands and spin in a mutual circle once every 2.5 s. If)0b9y(obgt ns:ci p*;*lpat a we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration ofqk9r1xuri ;m :9n(blu1ez/ o p gravity at the equator9ix1:u/q 1(l 9p;mr kznueobr is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelizlw;, kajd,0rl ff)ek qou489ng directly from the Ear8fwjfqa r4dzluo9,e;l k,)k0 th to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scalezex5dfcs yglh s.- ;+- in an elevator, it says your +;sglc-- e .sdyh z5fxmass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cef(w9f m 2h.7c vkl8mpircular tube that will rotate about its center (like 92mfplc (wm kh8fe.v 7a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–scf(0;m-vppa;h8v4/ l22 etixb ijxn43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, th6:yv l(alm8gi,6 xzdae acceleration6xa :6lydzva (ml,8i g due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecte .jbcb. uow /e):+evlgd from the vertical by an angll.w ).euvj+:gb/ceb oe $\theta$ 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 u/c) bhky4ykd r;1cx+/s7 zc athe coefficient of static frictudh4k z/+by7csx c/a k )rc1y;ion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatimj s2+:iur-g /8bbzy7 o0ef arng so fast that objects at the eya fm/bg8j+o b 2 zues:-0rri7quator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0hvx; +po2x1:rbha lmvcg7by5z 8 6-qa $\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 atvsuc6* m gya2vw g2k3o.2 0zoz a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out g* c.yvg6z2awzmouvs302 k o2 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 the1 wx9imm s hz:5 vp/jj9qpmm-)iw d2z7 Earth. Thus, it has been claimed that a 2 ): zx w-md/q9mmj9 wps5jpmihv7iz1 person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the prese* vkd2 ti65 y4my1mk2 ssvx5tqnce of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this smt*1v2yidx5y2 6qk ts kv4m 5by 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 shop:2q3dpeit 3wf/ xo6b/b no(j wn 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:xtfeo ojbnwp b6q(p32i / d/3 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 Pnk v 6 p)g):eagp3tx1xositioning 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 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 antnp 1p3kea xg )g:)xv6 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 Asteroidf3cm;):j i3gpf0 xzns4 dq jp( Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroidd3s)nzji3fp m q;4x f0(:cgjp 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 s eee61rrw7.e avw wv.+ 0 vsn8fj61nndl8c 7qehuttle pursuing a satellite in need of repair. You are in a circular orbit o. w7v87d.nnr1jalv+ e6eqecew wv0 r6 n1f8sef the same radius as the satellite (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) What is i)4ge-ceyk.g + bm3,dc 8j-ggix hzu(ots mean distance from +cjmxki8 obg(34- g. u dg,yce-hge) zthe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you cu:df7l2wg .-(dpsdbe*q k *7hmds(xxould actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumption( h7:sq2 dw7dlekmd(-pxdub*x s.*gf s, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky nj ,q6b h8yh9wli;e1g Way Galaxy (Fig. 5-46) at a distancenbiq, g; 8yhwhjl196e of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m b),ou7 -0gjsvaya,dh+ofs.f on each side. Find the magnitude and direction of ga 0)-yjsd,+o, .fbhou7sfva 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 Ea vxl,k, w9pi+lrth $ \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 theo2p g ln9 rt :.ynvad9 :snx+d;xwre;; tip of the 1.5-cm-long sweep second hand nnsoe:2.lv9 w;dr;:;+nxpdxr ag ty9on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cikg27 9*l( 1yk*wm twvinpis1x0) dbuprcle below you on a 0.25-m piecen 1 sxk gp0*d2k)19bu7i *wl tvwmpy(i 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 in a new highway is desi t)9hi*: e 3z:tkkxuregned so that a car traveling at speed t9e erh)3u:k : xzkit*$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negifnf1ndg ;u28otiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the2idfun;1gf n8 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.$\approx$    $\times 10^2$