Sometimes people say(xi enx 0frz1k. -t3loz/*6zj0xuyc*na 0xdm that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statexf (0*en1cdn0zr.* 3-tlz j m/k xxxz6 oiauy0ment?

Will the acceleration+c s2l bltwp7-8zuzc/ of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curv-zz2l 7sul c+b8t/wpce at the same speed? Explain.

Suppose a car moves at constant speed alongxi 3bdwx l))d5 a hilly road. Where does the car exert the greatest and least forces on the road: (a) aw5lxd) )d3i bxt the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a py gfv-/z 2p ub3n+jtsb9+:hgchild riding a horse on a merry-go-round. Which of these forces provides the centri+t b /:hpp+n 2zsfjy bgvg3-9upetal acceleration of the child?

A bucket of water can be whir ef,znr wu9d00l 6h/kmled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaizufndk96/ew h r,0m0 ln.

How many “accelerators” do you have in your car? ,ed)9 nr,q2fn8a piepThere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acnd fnr pi),ap9,q e2e8celerations do they produce?

A child on a sled comes flyigz 9ja1b4agco /4k9fong over 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 he goes over the hill. Explain this /ag goc 4 zak9j41fb9odecrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a sx7lq *c3a,nupem4*l curve at high speed?

Why do airplanes bank when they turn? How wouldsv;tn/ spov*ngg:o0pge- s6 + you compute the banking angle given v/6 sovesng spp0gg*+:;t-no its speed and radius of the turn?

A girl is whirling a ball on a string around her head i a.tsi+lh()7 kou df0bt- s9gcn a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When sho gh)stf(7d9t .aucob +0 lsik-uld she let go of the string?

Does an apple exert a gravitational force on ths w:lsa+)7/ wt eody.qe Earth? If so, how large a force? Consider an:t /q7.w ys+w) leadso apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass weruwct):ayu+h fx.j3 /oe double what it is, in what ways would the Moon’s orbit byu)c:tfuwoh/ +.a 3xje different?

Which pulls harder gravitationally, the Earth on the Moon, ol6y8* zojb1e dr the Moon on the Earth? Which accelerates mor8 yez1ldo6 bj*e?

The Sun's gravitational pull on the Earth is much larger than the b3n5nz1omi 6 rMoon'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 tonn1mbrz53 oi 6 the other.]

Will an object weigh more at the equator or at the poles? What two effects are u6e4o o7y5n 7i 1nxwj;rm .qpq7ni8ysa7.1po57 ;q84r 7nnme wjoi uyqny six6t work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is om.fizia h+o,-/cl9nonly about half the force on the Moon due to the Sun. Why isn’/m lf-h oon,.+ 9cziait the Moon pulled away from the Earth?

Is the centripetal accs.ya 42kx o,ydeleration of Mars in its orbit around the Sun larger or smaller than the centriy o2,adsk.y4xpetal acceleration of the Earth?

Would it require less speed to u4uvhrd (a4q; vsoj7*launch a satellite (a) toward the east or (b) toward the west? Consider thev4r*vj(hu q;7su4 dao Earth’s rotation direction.

When will your appare) fi /9gnqrqk94 x5wnjnt weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the sxw99rqng j5fnq4 )/ kiame as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend /qzf9w o+bif( long periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotate(zw /of b+iqf9s, 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 weightlessnesson()yj+hmpm x/a7;rx ” between steps. xnx mhj;or7p )+(/yam

The Earth moves faster in its orbit around the Sun in Jan z02h(dnsos3bs34rar uary than in July. Is the Earth cloz 0r3rn sb23sos4(dah ser 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 plane of its orbit.]

The mass of Pluto was not known until it was diskyg4, 4m2 xy/hafrt7qcovered to have a moon. Explain how this discovery enabl4rmx,2qyyg kf7 /h ta4ed an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earthv,r8p aj+2skck+) n gzrzry.0 is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center onkv)2zk0, r +y z+jprcs rga.8f 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 i bvu tl1pt;n, 6. q(jj-ing4i1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arou4l7 mcg3f1 tlbnd 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 l4mgt lb17 f3ccircle 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 21 o ohjzxd(-/y356ibq l0 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal bjo io3- l5dz(yx6/hqcircle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle i2xdev xum-h8v 4i;(ves in orbit 400 km from the Earth's surface, and circles the Earth about oncedehm vx( ;i 2u4v8xve- 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's surface. $\approx$    g

  What is the magnitude of the acceleration /+/i rigijr0jof a speck of clay on the edge of a potter’iijig0j+r// rs wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a cst, 5bqm+w y9uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its stwb,c 95yq sm+peed 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 whi /y2bjfszo v46ch a 1050-kg car can round a turn of radius 77 m on a flat road if 6zo2j4fyv/b sthe coefficient of static friction 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 nv,bwm *07gnudj,h.b between the tires and the road if a car is to round a level curve of radius 85 m at a s, m*w7. hvjnndb0b ,ugpeed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a u4d o)7k ibr8rme6 h(dtrainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back do i6m4b rrkuh8e7d() 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 z1 2fxhxmy 5ho0cltmc3a2z 0:of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the tur:f35h h2t0c0lm 2 a1z xmoxczyntable 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 0ze6yt +ipi, edqa+7x5qr um ;coaster be traveling when upside down at thezqe0;,+diy q euitm +px56ra 7 top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (in ijdcnu hhzx*c: *0p0*5s6hoqcluding the driver) crosses the rounded top of a hill (r6:* c hhncp 0ou*shx0*dzq5j iadius =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 1dye*74p vwvr(c x,k 3v5-m-diameter Ferris wheel need to make for the passengers to feel “wver(cvyd, *x3k7p4w veightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled i:votb ,sdf + kn( ;ppge5bkpoj(xv.*/ n a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucx, e g(nt:v; .sbvp/f5*op kojd+(pkbket 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 particle 9.00 cm from tmyic8t;+(p6bu, tvpj) vz:i o he axis of rotation is tozc8itppt6(u ); +i y mv,jv:ob experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a hv9d;)1h ;yayvb a n2ncarnival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.) y2n nadav)ybv h9h; ;1
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;v xmtqf7- *y; vd5:mkftwzm 1etop, and is held in thi*f:x-y1 m;z; tqm5df mktv 7vws 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, bqq tu q)8aau7s+d0ti; 8ssx6 by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mag ds8;a78absisq0q +ttu) u6qxnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveliuwr wvoj4yld9gwd8v.mds 9 /t- ,(/smng 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 massey0 ac54):xkj-ck9 im -dtswzks $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310eg s eiv :.1s)x;biw8e $\mathrm{~m} / \mathrm{s}$ . 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 th;-qkx *4cnjy tennp43lhr) 5qe net force exerted on the car (by the ground) n t;)*xhj 3544qkec ynln- rpqin Example 5-8 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 accelerates uniformly from the pit area, gswpyq be,/,.g 3jiw *noing from rest to 320km/h in a semicircular arc with a radius of 220 m. Determpbg*w/qsi.y e ,nw 3j,ine 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 circle of radius 2.9b/q;y60 ,8rbfojj(ku 8v)g niuu +scj 0 m . At a particular instayj 6k /s; rfju b+un),jqguoi(b88 vc0nt, 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 Eal1 ouf.wap3g .lo:u9./dv sg,gq ;yy vrth radii) above the Earth’s surfa.l.:/ df ,gavolgupuqg.39 v;owysy 1ce if its mass is 1350 kg.   

  At the surface of a certain pu)koo- hebx*2h+4 *-lthnnsxlanet, the gravitational acceleration g has a magnitude of 12n- tn-hx* oko+ uls e*42xhb)h 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. The Moon's radi i * vmfkx/yoru21wuy*jqk5/;us is 1.74 *w5vr yfjuq m1*y/ok/x; 2uki$\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 Earth, but has the same mvey(f: ;i,cm.ylf ,ryass. What is the acceleration due to gravity near ityy :lmri, v,ec (y;f.fs surface?   

  A hypothetical planet has jjl2gs,cc2 h0ah.9 efa mass 1.66 times that of Earth, but the same radius. What is g neajc,lag ej0 scf.9hh22 r its surface?   

  Two objects attract each other gravitationally with a fo+-e ( md9zmrqzrce 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 accelerati)x8*zpb( zhkdu-rgbpa: x3c 8 37fikmon of gravity, at (a) 3200 m bzgdb pc-z78x hmfrxp( *i3ku:8a3)k    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ; wcabzc,6g7v:b9hq1 agfl )aoutside the Earth where thegr71 6c)bg;9 wvfa alhzaqbgc,:avitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a 2 q3s-d*fzpfjsphere about 10 kmfdzsjq * 2f-3p in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star l yk67,;xtqztv ike our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of ,qz 7xt6t vy;kour Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why +ap1lhk(2okemm(grg n4f/ ; f astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the accelerati+( f/hg pflomgraem nk(k2 ;14on of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at th9 :i2si rhgkk :z9fub7f61 xxwe corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by theff ghw: si xk:2i961bruz 7x9k other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the4m ;uty-o+ 8o vo0rduc Sun. Calculm;4oy+ t-u0 docvur 8oate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming 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 acceleration 6uldn9qn* y)lc5ze + iof gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine t*cqul+ n dyn5li)96zehe mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periodgrk313dyi mz*m *(tfc of the Earth and its dmgy 3kti*dz c(13r *mfistance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite *la90osyi 1rxknbk+ ug )e9*bmoving in a stable circular orbit about the Earth at a height of 3600 km. bi xngr)les*o9y*+ u b ak91k0   $\times 10^3$

  The space shuttle relkff p7-y -.tz )c8gityeases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle8z7i tf yf--.) gpyctk be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants aresw2xs 2t;k5k auw4lus1b - rgo+u,br7 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 revolutiostw ks ;oaxs2 r u4ru1bg+bkl2wu7 -,5n. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit ths5, vn jsj:(vge Earth in a circular “near-Earth” orb:5vgsj nj,s(v it. A “near-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 laun,gof)oy7 rxv +ched from the top of Mt. Evereyg)+v x,o7 rofst to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modu ; ugktx j s7urog3(biq:,wi(-le continued to orbit the Moon at an altitude it ;u(xi(qk:b-woj, rsg7ug3 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 ice that orbit the p,7+tvqm ldxx1 6 c3zyslanet. The inner radius of the rings is 73,0czdmx3 st+, 1lq67vxy00 $\mathrm{~km}$ , 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 rotat.,tnr 1s6mqpd es 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 (b) at,t6s dqn 1rp.m the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4 /cf 9esvfywk.wn463(ne lxc9200 km from the center of the Earth'.svc96e 3exy 9wnlwc /4f(knfs Moon 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-star system consists of two stars of equal mass. Thfg br*otfvc*ix5 : be.c0n6c4ey are observed to be separa ecbirxt6.gnf5c:ov*04c*bfted by 360 million 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 elevats1c dthya65 z)or that mov hc)6 1s5zdtayes
(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 fo.pdd4 zf,zg; rom the ceiling of an elevator. The cord can witho4 dzp df;,z.gstand 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 orbits: oz)5e lpx/h) .dxs6wuhm+ yc very near the surface of a planet with period T , the density (l5oeu dh/)+pxwm 6 s.h:) zcxymass/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 an0hi:jktiu 7*r,b 5o+f 5 p:rst2mml rvd the period of the Moon (27.4 d) to determine the period of an arti0o5k*+7 ttrr2pmhj:u svf,l mi:bi r5ficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few huvu 2c5al ro8ew-k)9a8gq6;9i aap se ondred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from g)o ou9eqir al8kap9a ;2eawvc65 -8sthe Sun?    $\times 10^{11}$

  Neptune is an average distance of j/r 6ml8fvjko0 gr4 o; 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 everp9w l5n/l p(jsf66nok y 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 jk po/l sn6 9wlpnf6(5the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about g5 w p56wmuh.mc*5;glac4zrp 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 mass, perijtlbe* p;t+zn9e (dj*od, and mean distance for the four largest moons of Jupiter (those discovered by Galilztt;l*dp 9j *ne jeb+(eo 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 o)cfl5nkzymcak*6-k ku;98d uf the Moon. *m58z6 cau-; ynu fkkdkl)9ck   $\times 10^{24}$

  Determine the mean distance from Jupiter fo,.;i 2d ;9lpal vlrxcnaq tf71r each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare tlca laf; r1 ,2n. 9iplqv;xdt7o the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmentsfgbb slxb1/t8 iuvvn. )*5g/ y (which some space scientists think came from a planet that once orbited bb/) i * yvu1v5g fln8b.g/stxthe 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 of a baa:sr;:au *tzddjj- -fnd completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon)a-j*z t;ru s:djda f-:. 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 hangib c5 o7 a1vk m5h.,oij0nxt5ging vine (Fig. 5–41). If his arms are capable of exerting anh5b gakjiv570t5.o1xm,oci 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 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity bd w( v 4/e9dtslpv2gk: eakp0-e half what it is kt9p v le kds/:de4wavg2(p0- on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutualt:(z2io vaxykw pl/i 72ioy0; circle once every 2.5 s. If we assume theixy20awozp:;kivi( 2oyl/ it7 r 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 accelera hv9n 2v-9z19xnsha kt5ad72 ghutw5vtion of gravity at the equator is slightly less than it would be if thnhk9v x-a9 hs 2vzu5 tnwg79vd5ah t21e Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance fro)o qf0 g0p7y4is:oxunm the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because thef os ) 7gyiq0x4op0nu: 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 bathrotr8) c6k:+u2 yj;qxdt,oe yeeom scale in an elevator, it says your mass is 82q8+:6yk2r,ejce xtuto;) y de kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thar1e/ux l nud 77ibmx43t will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?b3 1m 7/xedrun 74ulix$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in ,yy,r(+3*nhauue-fdo -f fkt a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet inz ( ,rzibl11ym terms of its radius r, the acceleration due to gravitz(bz y,lr1i m1y at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from tfz,4glp5r o5sm5 *ti mhe vertical by an anglri 45m*5zfm5stgo ,p le $\theta$ 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 (e.i)ztr y+ica6e +ee If the coefficient of static fricrt.+ae y eiei )+(6ezction 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 Earb-ij yk8j+( pl-i iao-th were rotating so fast that objects at the equator(+ --oi-ipj8 alikbjy were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constantmhb6i(py . bug8m vz28 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 m. A lamp sn*xug-x 5mww+ uspended fr xm5xun g+-*wwom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claim1gfi, l+8m jkoed 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. C,j8im+fkg1o l alculate 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 pref feg.q/c*xx)f(w g 0hsence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from w. *fh/ fxg)(ec0qfwgxhich no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it t a wqt. xrne*;f vr0+c;ym ijc15rz9f:raverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) Ho q ntzimy1wc;9:f5. *jecrv0ra xf;+ rw do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites 3z6y5nxys2)ml5i 1 zd5odma horbiting the Earth. Using “triangulation” and signals trlo)x2zsyd 1y556 mn3 zmai5dh ansmitted 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 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, hn4doajv v +6 26xn*dfis meant to orbit the asteroid Eros at a height of about 15 km . 6 d+j2*4fx vnano 6dvhEros 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:cb1rue7 ,3z zoaew :q satellite in need of repair. You are in a circular orbit of the szrw, o7::3bceau 1zq eame 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 yevsa o a3::op.nhq*c b6ars. (a) What is its mean distance from the a bosq .aocn6*3:h vp: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 ia dycl); dyyrxv. 7is/3dj m3+f you could actually "feel" yourself gravitationally attracted to/7dyr 3dxvd +3i;yym aj )lc.s 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 (Fig. 5-4 u4l*rp ob2rc;vod4zj) . )gmq6) at a distance of aboutz u4.j);r odm v cob*q4rg)p2l 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 eacog-a.1 we2ux xh side. Find the magnitudw-a1 x.xgu e2oe 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 orbitnjgn88f)n 0e3mzptb;6lc7 r as the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced b .vz oq1k 5/i5t r(bw q/1mou-ea2dovby the tip of the 1.5-cm-long sweep second hand on your wrist watch1v m1 ov .t5uqa dzoqrbe-(/iob2k5w/?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circ +zeuxhc:d/t6le below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with uec/:+ d6xhz tthe vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so tha)eycxw5d gb3 zsqrgq6o0 /ert 4ai*;8t a car travelinre q8/ qda5go bc*i0e643yzx; wsrgt)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, the9mvjf; 5jq objj446swjd (2 en 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 the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela jj wov4(9ejj;mbn564dsj 2f q 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.$\approx$    $\times 10^2$