Sometimes people say that water is removed from clothe)7fi e v6 9jwitr9so-ks in a spin dryer by centrifugal force throwing the water outward. What is wrong with t- )6vrtoiekj7fs9 wi9his statement?

Will the acceleration of a car be the same when the car travels around a shhihx1euhm s +e3w1w 4.0:qkliarp curve at a constant 60 km/h as when it travels around a gentle curve at the same sp k hlu:hi1w miqe.h +14x3s0eweed? Explain.

Suppose a car moves at cosj:t vr.-em ni+zhh( 0nstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills,( hinzr+v jt:0.mhes- (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse + i h2iw4 z0czquad87lon a merry-go-round. Which of these forces provides the centripetal a lc 8h+iawq24z0d uiz7cceleration of the child?

A bucket of water can be whirled in aqa: ag1v3q 1el vertical circle without the water spilling out, even at the top of the circle when the bucket is upsidlq:1 aeaq1 g3ve down. Explain.

How many “accelerators” do you have in your carnl v8+04h dxcobch/1o? There are at least three controls in the carn4lob8 0x 1dh+co hvc/ which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes fly6esg mo(j(h ;qing 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 des(e qjm;h(o g6crease using Newton’s second law.

Why do bicycle riders lean inward when rounding as4jmge;wyfk2p p:n 29 curve at high speed?

Why do airplanes bank wavr*8o9u)8 nseoi v6p7aiqv-hen they turn? How would you compute the banking angle given its spee9 *86vaiq7io) va8pnsr-o vued and radius of the turn?

A girl is whirling a ball on a string around her head in a hori(/1, lizh rwgzzn:egxh 0tz3tepa8 7: zontal 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 yar7 z g3n,t/:hp0lirtz: ha1xee8w (zgz d. When should she let go of the string?

Does an apple exert a gravitational force on the ar7o n3+e 8k5kt,w/r(b8ts j7lreueywb(bl) Earth? If so, how large a force?b7(t y wr,bee8k 7lwl3rob8s5+rt (kj/unea) Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass / sbuup hgdz64kxf wl2;*9qj7were double what it is, in what ways would the Moon’s orbit belp zu f*7qgkwh/; x9 62db4sju different?

Which pulls harder gravitationally, the Earth on the M3g- +q hxyqw(loon, or the Moon on the Earth? Whicwqqhy3-lx +( gh accelerates more?

The Sun's gravitational pull on the Earth is much laros9 uh+q7:71lzc8zzdios it 5ger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one iuhc8o5+ qoz7zt dzsl 1:i 79sside of the Earth to the other.]

Will an object weigh morkkn bwzz0 45k2)zodxyg o612 re at the equator or at the poles? What two effects are at worko2kzzg5r o1 wz2kd xn0yk)b 46? Do they oppose each other?

The gravitational for-x+c)ey s4fg qce on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the)y+s4-xcg qf e Earth?

Is the centripetal acceleration of Mars in its orbit around the Sunqve;*pxnegj), g4yb3 larger or smaller than the centripetal acceleration of tb 4ey,gen*xqj ; p3vg)he Earth?

Would it require less speed to launch a satellite (a) towaryh ibf9:b*(y.n c/y/navs z2h e t,y3bd the east or (b) toward the west? Consider the Earth’s rotatb.ve: /zy h s(ta*2ch ,bf nnyyb/iy39ion direction.

When will your apparent weight be the greatest, as measured by a scp ( kq9akpvz95ale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at cons(p zpv9k kq59atant 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 lon*xnxt 3pnlg uw1m1nqk6- i2 4hg 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 rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objectm1wkqp nugn th64 x3n-l 1ix*2s 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 fall364qn yv4gw qk” or “apparent weightlessness” between stepqqknw6g4 v4y3 s.

The Earth moves faster in its orbit around the Sun in January than in July.72iw3 4m, a3x txhwrmu Is the Earth closer to the Sun in January, or in July? Explain. [No 37a3m2tr ,iwwxx4hmute: 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 /aia2v0e)-rhua; ajob + 2xdzwas discovered to have a moon. Explain h za)/- u0 vo2aah xirea+d;j2bow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'sc f9llpe ;;;qa. 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 sittingc;al;e9fp l q; 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 -v13ya f jn*yu$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 i2wh sq7ul qn,6p2yea;n its orbit around the Sun, and the net force exerted on the Earth. What exerts this forc e7;2u ylw2pas6nqh,qe 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 2c0ed5niixh*(a 3 lz 7t.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.t3 (i*h5z dnxcle i70a90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfae7etuk k.s1 x)ce, and circles the Earth about once every 90 minutes. Find the centripetal stke).ke1x 7u 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 accelerati z4 af3/pi(xf dwoxo1j0jw ;h(i-9oczijo*g 7on of a speck of clay on the edge of a potter’s wheel turnin-fjzhd*oia 1p j3iczgx 97j4oo/ x o iw0(;fw(g at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is -, ;9oy ttam3*odalbnd /hrb r4 2uo5prevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If i9d ya;2ln3 * thp-uoot/bmd ra4r,ob5ts 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 of4 sbkhd:i 2 i* xq-eaz;b*h*,dx6pcrf radius 77 m on a flat road if the coefficient h*aqz *:*xi46e x,b pc- fb;sikhd2rd 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 between the tirelz3az) /*jb gcs and the road if a car is to round a level curve of radius 85 m at c3 bjgz*a )lz/a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designpu fh jk3.s45uo5.r qyqo8 (sfed to rotate a trainee in a horizontal circle of radius 12.0 m . Ifu. s8 3r fuqof.55yqhk(4po js the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of hb9rblj j - al8i4fo8:variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coeffhbbf 8rj4j8-l: o9ailicient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tr)b fl8eklnm(qwi:a 8)aveling when upside down at the top 8 e(a:ibf8l) n kwmql)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 (including the driver) crosses the rod+f a drw:i1q2uju+na8 naxxb f8h:18unded top of a hill (radx8ujudf 81b r:f+8n2qa 1idaw nxh:+aius =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-m-diametss u cf(5o s)6:ion*q i(dyfv-er Ferris wheel need to make for the passengers to feel “weightless” at the topmost poifi-yoq(5d:uci o(sssv) 6 f* nnt?    rpm

  A bucket of mass 2.00 kg is whirleasvi1bffge53wl+t5 m -fhomw/:oj7(d in a vertical circle of radius 1.10 m. At the lowest +ih/ 7w5:omwvfo35(1-f b gmat jf selpoint of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifug9vgyns6 kdhy3* ;a m9dr vi7s;e rotate if a particle 9.00 cm from the axis of roy;nam3s9*sdyi 9rhk; v gv67 dtation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled r9i3(ky1 enhj "room." (13j (h9kn iryeSee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a (eh *x 9;sp ;yo8vprm ,-dcwyzcircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block ;ye8sxy9hp w, (-m*p;rvo zcd (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, by not ignoring the weight of thel7etrt pi0xh6;i(z1) l7 bsxb ball which revolves on a string 0.600 m long. In particular, find the magn0x r 17p( bztixh6li) l7;bestitude 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 i 34 ,rfc3ys3r*m,wugl 4molql 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 masses8w8imaph ws 40 $ 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 3 8j8+mgsx/ c erwplq6+10 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net fo0q x,cah9kwgnz7.. p 8ge qv.rrce exerted on thepk . 8q9a7..0,wvgxc rgzhqn e car (by the ground) in 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 shyq w -e0p6sul*h n,.area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial y.0hqws ,nlpe*u6- shacceleration 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 2.90 m 7f22wh ry9n go*5dkjidp5s9b . At a particular instant, its acceleratfhn*rod5w22k7y p9g5bd9isjion 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 12,80talsx3cdr7 /km(3l g /0 km (2 Earth radii)krl/gx7 3mls (t3a cd/ above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceler. o7 7/u d0wv*h2g:p io ttio,)kghl+4hmrke yation g has a magnitudemu*d0hi w,poi:h tge7+.2/or4t g)o7 k kvyh l 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 tovu.i mr5(iu5h hbhk52 gravity on the Moon. The Moon's radius is 1.75 h( . bruihm2v5iuh5k4 $\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 ob 28/a zvrrp7v, yh+vaf Earth, but has the same mass. What is the accelebv/8r,2 hy+ zv7pv araration due to gravity near its surface?   

  A hypothetical planet habpdof *p1yx55 s a mass 1.66 times that of Earth, but the same radius. What is g near ito5 y1pdb*p5xfs surface?   

  Two objects attract each other gravitationall1(huaeyph. pzpd4l :/qtpg2 sriom8-; y, (wpy 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 value of g , the acceleratifl/2etbq3: aw )cb 5dpon of gravity, at (a) 3200 m 5f qeb/: 23bawd)pl ct   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point wxh: 8j;atr4ws k0d .routside the Earth where thegravitationa4wx0 8jk. ra;r:wts dhl 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 intbbx1an y dc8.0o a sphere about 10 km in radius. Est .0dc1xy bbn8aimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Suhh, j5* cbs+4r yxve;zm g6fs4);ln qdn but is now in the last stage of its evolution, is the size of our Moon but has the mass ocqh*6 gn5z44;hr)fxmvj y; sbel+ds,f our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronautsis,ihye1;48 /ws uej/a/r ffw feel weightless while orbiting in the space shuttle. Your friends respond that they thought grehs,jwysif48fr//1e;u / iwa avity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the cdcxkkpzt3 b a.3i(5a( tsw+ )corners of a square of side 0.60 m. Calculate the magnitude k(dait 3wbp)cact+3( .kz x5sand 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 mob 74r3ybz-ninst of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Satyz b7-rin4 bn3urn, 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 at the surface 667be6 1 s)l kxgtsizeof Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, 1kegis bt 6s7xz)66ledetermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period np70mf k q3k-zof the Earth and its distance from the S q0fp37zkm- knun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbid4 f visv-x 7snm:x,h6t about the Earth at a hd4vn7: fxms6i vh-sx,eight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the b ahudra9;k 6.Earth. How fast must the shuttle be moving (relative to ;9.d bua a6hrkEarth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants avzwj, 7fc0c :0h7r xfts77ecrre to experience simulated gravity of 0.60 g? Assfc7,c: vjw7zhc7sxt7e 0rf0rume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for0k(wrum u 2zl7 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 radius of the Earth. Does your resulukr7 lumwz2(0t depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fromdb:gn:y d-bz f+v.;-f wct2,tilmrh8 the top of Mt. Everest to be z-:vclntfm;. i brtdg b,8y2: +d-whfplaced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, tdv*m2eua9(y*1 zodtq uy 52hthe command module continued to orbit the Mem *uz1 utvy dqyat 5d(oh292*oon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are copb9l(oqh9 aemti9s .gjvo972mposed of chunks of ice that orbit the planet. The inner radius of the rings h9 eqls bpjot99o.(vag m79 2iis 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 (seed18*( u(evzmo0qkmy u Fig. 5–9). What is the ratio of a person’s apparent weigqy80 1u odmume (v(kz*ht to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight ofyekq.n 8o h2reb/ )8tg a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocityygboe2n88)e k./hqr t,     ----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. Theyp /ro:omr g0n2 are observed to be separate0m2 op:orrn/gd 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 womanr/,1topad,n ms3 - egz in an elevator tharzd -s,3nom1a/ gpt e,t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of abl qr6 *oa o(unlf/u8 esg((l9n elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s me6n8b ((l*ufa ulosqr9 / go(linimum acceleration (magnitude and direction)? a =   

Show that if a satelv9nd3 1 jr 4q5bl76 iljongb;ylite orbits very near the surface of a planet with period T , theno1bb 7d4n;35iy 9 jvrqgll 6j density (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 th 9,yr k4dl6lbfe period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Eakfyr l9 l4db6,rth’s surface.    s

  The asteroid Icarus, thy gvviy8,twh9 /o:ca(5bse)k ough only a few hundred meters across, orbits the Sun like the planets. Its pe cy9/vaw)5bg ( ,hs:eivy8tko riod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 7pas5)zki0 wc 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 si x i-h5.3vz:e7iodtthe Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mis:tze7viio3 .h d 5-xean 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 Ga o-pm ju,c8j.gz d-hx sbp.v)p*7 th4blaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 l jkdy8i;,xnk )vnqzv /o/3u o;ns4 xrzxh;k ;5argest moons of Jupiter (t,n4 )o5xkz/8yu; ix/ jkdz ;n r;qvnvkh3os;xhose 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 distag)il, 5n z:skrnce of the Moon. sz n )gir:k,l5   $\times 10^{24}$

  Determine the mean distance z v+s9x ua4zz1from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in x 41+azv9zus zthe 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 fragmentcfc *.-9m,n ,2upphq- u ioehls (which some space scientists think came from a planet that once orbited the Sun but was flh, cqo u-*,hem.c 9p2pinu- 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 banql sge1hi(v,wzsms3 e37if. 8 d completely encirclingiq7(s zv3 hsg. m1f,e 3ewlis8 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 gorge by swinging in an arc from a hanging vine 7gvz2b4nz x k1,bps 8h(Fig. 5–41). If his arms are capabl4zhxkspzbg b18n7v 2, e 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 bn -ph lqku-n92e half what it is on the sulh-p9kqu-n 2 nrface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grfx --6 rf.d 4qsdwd8ejab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anothedfdwj s.6x re--d84fqr?    $\times 10^2$

  Because the Earth rotates onceih t)cq4v*,d1v. jaw c d72vkh per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of at ,h4 d7 cqdvjk 1c.)v*wvi2hthis effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelho 42-ttd9f 4a +icdbuk3jps+ing directly from the Earth to the Moon experience zero net force because the Earth and Moon pf9ti3+ 2o+4ckh-pu djsda4bt ull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a y;f2.k flaru8efm g soezj/n1)24ja :bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whiy.ag funjzrmoj1f sf 2 ;8:2kae)el/ 4ch direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thateu. 5ybysxr f*3jmrg6 e(ww(- 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*ybr 3wmx u.5f( eejg(r6swy- of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aio1c,0gjgey f) b8wg- vrcraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a plan odpb 4m ok)kb7pu. bqu+vk;)/et in terms of its radius r, the acceleration due to gravity at its surface p.bv pkbmb) 74oo+ qk)uduk/; and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by eo8dtj ;e+tz)g ,9l vbq5 )swyan atw,q l e5zjs 8tgd)v)+ob 9ye;ngle $\theta$ 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 bal c;pfczk (95c uexd25su wp51nked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handfc5cxucuz9l(d1 p w5k; p2s e5le the curve?

  How long would a day be if the Earth were rotatinits f-b jd/f52g so fast that objects at the equator were apparently weightleb f-dts5i 2fj/ss?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 6-gl*j;sexz x)g/wl(gz g(k,x,wlb r 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 radijtm5s *09ofbp d:(ggesaey.-us 235 m. A lamp suspended from the ceiling. -my5ot(0ejf* gp9ds sb gae: 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 massiv;+7htg v3d(cq86zu r5 t 8okfweipx9je as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person wou e8+tpoc5thu87d3vw 9;( xg z6jfkriqld 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 Telesco,rpm9cd l1u152nng*h+ wqay z pe deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clo1a w y+hp9r21lg*m,u dnc5q znuds 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 consta5 72t wcv0yl4dl u-pg3ja+n vznt speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Wheg 7val dwzcn t4y3ju5l+0vp -2re 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 Pw r/k5ouiy- +kositioning 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 an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each sateu io-rkw+yk5 /llite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), a, awtsyi,6 pdgstypo3: : x94ffter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly ip y s,t,d4 gox3pafswy6t::9 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 sak*bzo5ku xq+rk-gh6un/c p: *tellite in need of repair. You are in a circu r u*hnz5kk6+b o:/*-uxckpgqlar orbit of 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 its mean distance fx 5:nkg9h(b2dvi 7n.)rvqk y aroa72h5).q dxrg9v: inbky vnk(m the 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 n4bqz3rvr1a1 lnog1 a.q+* ln G would need to be if you could actually "feel" yourself gravitationally aqnvlqg+l1 *a3.b n1r1n4arzo ttracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dis .beekkibnu033h*nj rs/- k5p*3xo ygtance of about 30,000 light-years fu3* /-gn p3hijekk 0x.eb 3s5okby*rnrom the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side. ic+3b4kzl+ -itqccoj *1ch. u Find the magnitude and direction of thel4it+qk bc. u+h*3zo- ijc1cc 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 the1 cbc b+6y-q p+z3imvn 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 by t iddrlma 1kiw :k3a65i:q+z-t he tip of the 1.5-cm-long sweep second hand on your wrist wat :miadr1 widal +k-53iztk6 q:ch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in jy2 .z,(7-4-q,)xsywd p mw9ilpn3 okkx hff va circle 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,4l.zw iymwf )7xsonq93x kd jfp(kv -,-hp2y line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in algy. aq3p 5gxw jrn2 *hdc)(d) new highway is designed so that a car travelg 3(pd)xa h*dwqn)lr.25 cyj ging at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt ofkxjoz*g fzt ,ib4uyf(j6 u :-zx8, n:r 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 c-iujx f,,zxgf6rt8byzo n*: u4kz: (jomfortable. 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.$\approx$    $\times 10^2$