Sometimes people say that water is removed from clothes in e96- gm ukprzw5n:a(j a spin dryer by centrifugal force throwing the watempnr6:a5 (eg-9 juwkzr outward. What is wrong with this statement?

Will the acceleration of a car be the evr )(ui 23ib a6jv4zrsame when the car travels around a sharp curvei 6j34r vzrvbuae )i(2 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 car ex+lc( v( m.u;cdx; d 3bgfewrg+ert the greatest and least forces on the road: (gwr(fdcx 3+(.lu ec; d+vm;bga) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. hd4hgqbbj a k ot.2e.d h1+cj- /w1(ttWhi. wh41oj a thtkhq gtbj+b-c1ed2d/(.ch of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a verz3 sp. osjymc40owu , -6lgi+xtical circle without the water spilling out, even a lm-4zsugscy o,ipjo.+x0 63 wt the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three co x-wob v4h42hrdlp4/ae- 8ii rntrols in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?8a4hrh o -4ir42e-i/l xbvd wp

A child on a sled comes flyingsvbw)6a7bp:z 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 ches:wvbapbs6) 7zt and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward d bw4/ x44hk8g8vmdnkvo8 l7y when rounding a curve at high speed?

Why do airplanes bank whey18nr9uc1 fwfhll+ *in they turn? How would you compute the banking angle given its speed and radius of the tuycn1 if+1l9h lr8fw*urn?

A girl is whirling a ball on a s ge-0rhawv;a(1 jzxo*s xl: (vtring around her head in 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 th0(1g(rlx:vvj asz;x-w* eho a e yard. When should she let go of the string?

Does an apple exert a gravitatio ry)e vqv -z( wyo2(hj6s +i3azffs2k.nal force on the Earth? If so, how large a force? Consider an apph+z sfev63sioywa q ( 2rfzj-v2 )ky.(le
(a) attached to a tree, and (b) falling.

If the Earth’s mass weredxyi2s.il*px;, iov* double what it is, in what ways would the Moon’s orbit be differen *.2so yil*dxpi ,ix;vt?

Which pulls harder gravitationally, the Earth on the Moon, 9q8/j ytybrff* q 6fe9or the Moon on the Earth? Which accelerates m8rff96y *ef 9ytq/ bqjore?

The Sun's gravitational pull on the Earth is much largeri8b/bd ngi9nae/+ 8 hu than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatbbg89/i+ad8un en i/hional pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effectyat1 n21u2z(q*6r tfjb,+-wm was d vls are at work? Do they oppose each others,+ vrwtl6zmd 1 2y bua( naq2t1-*fwj?

The gravitational force on the Moon due to the Earth is only agd8:lapc 6,a-cchoqw fikr a6+7w 2p 8bout half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from th:cpfohwcw 87,+ adg a2lp -6 ika68qcre Earth?

Is the centripetal acce cdcvb ieof8zoax4 v:qn278)4leration of Mars in its orbit around the Sun larger or smaller thanx2obai4c zq4v8vn oec f 8:)7d the centripetal acceleration of the Earth?

Would it require less speed to lau/;t abow0awy/ nch a satellite (a) toward the east or (b) toward the west?ba;oa0 y/ wt/w Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a mov+ub9gsu) m;1hl9tj)tud1en m ing elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in dt 9u;htlseu)gm)191+j nbmufree 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 inl:zbei5 1vmyl*t *de6 outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates *byv61:zeie 5lt* lmd, 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 experieq cu u384ks3cm)ecfhlx0l )6inces “free fall” or “apparent weightlessness” between 6m3csuf4 ikc0q l)83 lceux h)steps.

The Earth moves faster in its orbit around the Sun in January than in Julyaei+* 07yxsz*k q 6qst. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbiy6+*qs txs ake *i07zqt.]

The mass of Pluto was not kt1y/ cdl5kh5(q(izq f;h zo.*df:4bn * bveknnown until it was discovered to have a moon. Explain how this discov/lydnh: hq5* .t5bk(izk odbfz1e( qc*4 ;fv nery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the.;4* 1*q z rkdirv0;dauyhae6b saza) Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitt ;4d*1a ue)r;0id*ar zky aqv6ahzs .bing 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 1980 f4l :faionz), $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orby ycgpl/uxeqf o3/,soz 1i0+/it around the Sun, and the net force+,oyifslc/p q0 /e/o3zu1g yx exerted on the Earth. 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 1i . gi1but.mr210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arr1g.1bu iim.t m’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit+t0 c3,fxfylyi0bp9v z ts4m+ 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centri+mv fptz0y sixy0 3tl4 +fcb9,petal 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 of a speck of cldgim sp*p8vdd + kup +**:*veeay on the edge of a potter’s wheel turning * :pdupvsi+ p*ekdgd*me+8* vat 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved b2msty(1 d rc.vu0bba8y18 wiat a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fiy280twbaby1( uidv .s1br8 cm g. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round,xs;as-5)j;yme bgc, w jdsli3in 7n/ a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepesxsndi5;n c,a -/j g,l ;s)w7yjme 3ibndent of the mass of the car?   

  How large must the coefficient of static fri*w1;mnu ., lkg2b-pyg v-oy vdction be between the tires and the road if a car iyv.; b-g-duml*y n v2pwog1k,s to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jvuwjy+u 1w:,97 acrvps.7 adn et 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 aau.vr1 wnc+vwsdu,9: p7 yj7 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 of variable d +9ijdavx:ezr hn* / ty(e5,rspeed. 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 anvh dt5j+r/y* ixen (,d:9ezard the turntable?   

  At what minimum speed must a q1z3r9szlea .roller coaster be traveling when upside down at the top orq1 saezzl3. 9f 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 driver chvoh: 2e)+i5okn; py) crosses the rounded top of a hill (radius +k5hpcvh2en yo:o i;) =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 p9*oh1 v(gcujtt- j+z6 0wmo yoer minute would a 15-m-diameter Ferris wheel need to make for the passe9-o1(j+gy voc0*mtohz wu6j tngers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticaa8yca37ofd qjvl8 6-7qb 80mc*ffqw ql circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucq8jo7y a0mw-q 6*qqf a bc83c7 8fvdlfket 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 particlef8b78he j vwgk7nxha004f u5 s 9.00 cm from the axis of rotation is 4n hxga svfwb0j80f5ue 78k7 hto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people ar yzlg*a/ g/u 85u/rjs6g6jhc ce rotated in a cylindrically walled "room." (See Fig. y z8guahglc/gu cj6 *56/jr/s5-35.)
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 frictionless air-ht y76/ bwxs7o7r;qv pmockey tabletop, and is held in this s7pw/ 67yvmqrx t o;b7orbit 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 d+-xa w.6edos lj,tu7time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude l. u+oxs,dta76-jw ed 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 2*qzkp tpc7r tjpu: :5for 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 massem +0t*kc(xdg6oqi. ow s $ 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 ev*( r3w)t vic 8qhisxqx k-+q9zasive 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 tangentia ue7zvdct./x- l and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its sex.dcztu-/ v7peed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acceler bh yfiic 5 5-1wu.0ve55pyqghates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is 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 5-h. wyp ub cqfgi5i0 51yevh5slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.nvdlc*di(k:yy z- + 4k90 m . At a particular instant, its acceleration idd:n(y *ky-vkz + 4clis 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 (k eof7xx ;h8;cc )6jjz2 Earth radii) above the Earth’s surfao e8 c;j;z6hkcj7x xf)ce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has x:2/au.yxjbb isuvd7o/ 2sv5a magnitud7 2bxdx5//ys :ovuji .av 2sube of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 7 r6zmo(avsk:ke* nm 01.7 :a k*rz 06kvsm(nmo7e4 $\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 os(;txs,b1c4oyql /h7m7mk lnq q )x4uf Earth, but has the same mass. What is the acceleration due to gravity near its surface? qn/4 chmqsxq4y) (17s7bu;o,xml t k l  

  A hypothetical planet has a mass 1.66 times that of Eart zf5jkr ci,rv98ns;*th, but the same radius. What is g near its surface? 5k9rnf* ,j;t8cs zirv   

  Two objects attract each other gravit-.c 1 :fljw,9k4bnprc zpc)zx ationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valuy3i;b;uk9t5x gerko 8e of g , the acceleration of gravity, at (a) 3200 m8eboi;xt3 kryg59 ku;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fro1evji .ipr4 /tsk.37f+pzi a 6z2pcupm the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is 4i+pv s eui1/zpf 2. 3cz.j7ak tpp6ir$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sudj-ak ( ebmug,:5zzy;n packed into a sphere about 10 km :b yjka;,(d-zz5 emu gin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an wqsx),2ensbbh ul :: 7average star like our Sun but is now in the last stage of its evolution, is the size of our Moon 7wb ::hbsq2s x, e)lnubut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless wh vb0.+3+wj*h o:c 9 ppnv)f9gwt:w)dv s vzxegile orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince :v*+vg)ww o c gp 0v+:wjtbvn3h9fz)9 .exdpsthem and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners ifamd2hmw xdi 01.5j 4-n pu 9bnkgn67of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exngdxmfp.jdb wam07nh5i4 ink612-9uerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of zw5 ,;qh fhcu2the planets line up on the same side of the Sun. Calculate the total force on,uqh2z w5f h;c 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 of gravity a ,f n(har2 -1rfnv ,gn-gwmqi2t the surface of Mars is 0.38 of what it is on Earth, and that Mars’f21hmnaq-n giv n-rwr(,f ,g2 radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value v,g2q,tzr5 23i iyn tafor the period of the Earth and its distance from the Sun. [Note: Compare your answer to thatry2 5,z32,ait nqivgt obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cirk. u)g clm*dyi 9wf14dp,r h-fcular orbit about the Earth at a hedl.*1 ,4kdwf u-fp i)gcyrm h9ight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite 3o0j54fog pr(o aw da1into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occura04oop(ro g fdw135aj s?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate i :hao*jfqeingp :w391 p3h0q if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diametera10ipe ::9 n pohqf3w3gjiq*h 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 in x6-xwih s s)+k4m2wto orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit ss6)-n 4imh 2i x+wkxwis 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 qf : dlmt(f) v;0cssm+be launched from the top of Mt. Everest to be placed in a circular orsd:f mt+l fv(0sc;m)q bit around the Earth?   

  During an Apollo lunar landing mission, the commabx9: liv ro teuqbl40(i1gk (5at. c/znd module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around g buk:l (r1xoi/9l.bqe5 i(atvt0c z4 the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plg5mjwgc+e5 ; ianet. The innerij5ecm5 g;w+g radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fi 9o+a.crhen(k ucm0;u g. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom? c+0u(ak.o9m u;nhcer
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of the f/:xn4)sjy1vnscgl.mm+p 3a Earth's Moon in a space vehicle (a) moving at const 4p1x3mmy+ cgf )s.nsaj nvl/:ant 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 co6 9, c4mew)n qedun1+exz :gzlnsists 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 betweenqdg:cme1,6zeu x)n9 newl4+z them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight ofu9mw7s ,kng,shf 6yk ) a 55-kg woman in an elevator that move mgswu9 n6k,khf7ys ),s
(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 hand )f*ynf /f7 7(kli zzgzui61cgs from a cord suspended from the ceiling of an elevator. The cord can withstand a ten 1(/7f kuzfcfig) iy6*zln7zdsion 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 very near the; f kmnki*gh o.ai(-p0e3,una surface of a planet with period T , the density (mass/volume) of the planet iuin0hg n 3eia.* koaf,(;k-mps $\rho=m / V=3 \pi / G T^{2}$ .
(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 deter6tivwikmh6bc ats4w85i :a /7mine the period of an artific 7/:6a65ktivmwith8s i4cw baial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred m 3 nmosmz*zcwngamdyf826 (12eters across, orbits the Sun like the plan6sm8g 1z3fmz y 2acmwd2n o(*nets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag326l9*n crddyhvfoo q6 zd:c7e distance 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 very close rddl89g7n s1;a dhx.s 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” thg sdsd a7;l.r18hxd n9e 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 the center of the Galaxy b6d0rha62 v4r,4hlr z 2xdzvl $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 m(6yikq c/jb7 kq4gbh. ass, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609).yg7(qi4qb hbk jk /.6c
(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 ,rw2a. icld :y+f5ckpof the Moon. lcy.d5fk:wpa+ i,rc2    $\times 10^{24}$

  Determine the mean distance from Jupiter for ea-ai kk+l 7mj9cch of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tab-9i7k cajmk+l le.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jz3)q xn;zp y b4mpf;+-; nv t,oqtn9ifupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but zn q yitov +)f;fx3-m n,;npzqt94p;bwas 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 "pla* svods3ch 6sa)c*s x.net" in the form of a band completely encirclinccssh *3xsasv* .d o)6g a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gg8c3wrdm7zisy4, 0k dh,8 xpxorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms xy0d84 ws ,k g7,xd8rm3hzpicare capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hal;f08 /asyw fq 7f+e*echkq x-f4w du6hf what it is on tu/h+ 8w ;6fky f0ah7-c4*qswxdeeq ffhe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands an :bs lp3;h cg2jsi zeq*yqj,+8d spin in a mutual circle once every 2.5 s. If we assume th,+qs;:2 h*q j gc8bzle3is pyjeir 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 acceleratn+ d um7z/ d(quni3 5fl8ff*ugion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate th/uu d5q3mfu( g l7i*+n8fndz fe magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from t rpiyit,x sqz6lr-g3w ; dg.m*5gp x11he Earth will a spacecraft traveling directly from the Eax 3lr1qs *-d1,gym.ig; pt6rpig zw5xrth 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 ba :*8)k 6fs1fxpxl ezlfzo3i(fl; 5bhvthroom scale in an elevator, it says your mass is 82 kg. What is th1l zspx k8f b6z; :li)3vf(* 5oefxflhe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itsqdx5: t/o6dn 7pfgv3e 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 grav63fdo 5v q:gptnxe7/dity 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 (Fsmor q6 ep5a5rf)rn+-ig. 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 in terms of its radius r, the p.me1 1p7ip ytc,db*haccelerationy1etd 7bc*hmp.1, pip due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflzfj4+e/k p;+cbxqr c 2ected from the vertical by an a;z+4fb /jkc+q re2 cpxngle $\theta$ 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 spejk i/igs4jusl jb(k :p c2 .dvvw3u):2ed of If the coefficient of static friction is 0.30 (wet pavement)j4 ul di.: :sc)wji(su2vk 2j3 kb/gpv, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were3,.qfs8 kib wmz7glw 7 rotating so fast that objects at the equator were apparenbs gf,lw 7 m.izkqw873tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartjitp d 2 eqe))a-nnm),9e4gom 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 su ,vxk 8g1*cytaspended from the ceilinag8 t1x*v,cy kg 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 Et lee a( uyr.rz-t7j/i k7natvw)2s)3arth. Thus, it has been claimed that a person would be crushed by the(3 )7ruy7lz w2 -/i.j ttnaeka)tsvre 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 Te 7 jkb09azm3fjba2l/lz af-e 5lescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a bla3a57 akbzm9jj/f fl z2-bla0eck hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley scdsv0+vkkbo0n-8 i*w sw b8)whown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel hdn+kv8-c 0sib*s0k8wbvo w)w eaviest? 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 grd xen3akbp)j3+cp e( (oup 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 an altitude of approximately 11,000 nautical miles [1 napea px(()+3b knecd3j utical ]. (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 travelif z;h-k fukdqvcq4;;; ng 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Erc; d;k-;kqz4uvq f;f hos 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 p th i7:ga vp6:q0,yjppursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satell7p haji :yp:, 0qtgv6pite (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 0krp;siv u* )q d6g4smhas a period of 3000 years. (a) What is its mean distance from th6psiv)k m;40 q* rdgsue 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 w7o*d);z4sg2 n komfkyou could actually "feel" yourself gravitationally attracted to someone near you. Make rewk*koszgd 7; )fm2no 4asonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the pybm:j sef(1/n 0nrjx*a54 qrcenter of the Milky Way Galaxy (Fig. 5-46) at a distancen5f:p*r 4j sb/a1eqnrj mx0y( 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 squa9, morm pxg,-: d7znvqre 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of thqx-9r vo,m7,mzp:ngd e square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the s,w-jq*b,: tshh zg9g 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 acceleratiogorm2*hne d6. n experienced by the tip of the 1.5-cm-long sweep second hand on your wrist watch2.d eg6mh* onr?    $\times 10^{-4}$

  While fishing, you get bored and stjtmp +1obs3( rart to swing a sinker weight around in a circle below pj to(1+sr3bmyou 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 the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed sbf 6lm e511n*8ur l-r:pwkptv o that a car traveling at speed5k1nv ur t- wpme81 r6l*pf:lb $ 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 qf ii;orfb5-:e ,ey g;9 nv5s(qdtmr x77*cwjtilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the trairm7 (if bn: ; tq- 9o 7eq*;wxrfj5,c5gvyedsin 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.$\approx$    $\times 10^2$