Sometimes people say that water is removed from clothes ifon-o,0jw 2 qmn a spin dryer by centrifugq nom jw2fo,-0al force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same -,v da0ge6pn4)rj: rjwvh+b k when the car travels around a sharp curve 60b-n4 gjvkrp )dewv, :rj a+hat 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 ew1sg2tcc(z: . Where does the car exert tgcw2t: 1(szeche greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a h1whb byiu 4 b.;l1o5miorse on a merry-go-round. Which of these forces provides the centripetal acceleratio bui.b1;biyhom1 5w4 ln of the child?

A bucket of water can be wh q:9qgq kdci(,ly9)0vbd 2 zdyirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. dq(dc,2y) lb gvq9 ki:dy09zq Explain.

How many “acceleratorstzdxivb yj5uz8ddk s /.;5,8 f” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What a/kzxs5uftd zj8 ,5b .8 vdid;yccelerations do they produce?

A child on a sled comes flying over the crest of a small hilsucsg j//ua44l, 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 th/4 csg j4a/usue sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a (h3/q .q96 s )fvnt5:gdu vkjxuebmo/curve at high speed?

Why do airplanes bank when they turn? How wsmwfs9;+ (m 2gv+ pg 8 lrxk0q.zxds2nould you compute the banking angle given its speed and radius of the tl+8(sd msw+p2 sxv2x;k.mgzng9f 0 qrurn?

A girl is whirling a ball on a string around her head in a horiz4o8d :r1x36nqmy rq)m-heeqiontal plane. She wants to let go at precis8y dinmr4ex6 - ) eh1mqr:3qqoely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hd qg gz65s)f3dow large a force? Consider an 6 dgq5z3 fs)dgapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thcvdwe2nk9b m*x(2mp, / )tijr e Moon’s orbit bemr*/x2dt i)pb 9,v mnkw(j2ce different?

Which pulls harder gravitationally, the Ear hw-c on+kc5iwh9, s (q-vvex3th on the Moon, or the Moon on the Earth? Which accelv k 5q-oh+9-vw3e(chi , wsnxcerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yehaq c5t./p-b pt the Moon's is mainly responsible for tqp5-bt/pa. hc he tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at*et8 hfv xc yo0k ua/mdd24de:6o*3qg the poles? What two effects are at work? Do they ooee8dxk/: odq06g fy mav42 d 3htcu**ppose each other?

The gravitational force on the Moon due to the Earth is only abob3kb i,a8uc* kut half the force on the Moon due to the Sun. Why isn’t the Moon pulled aw8b,*ck3iakub ay from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lar jxs-6 kou,u9uk7numjq 1)xo-ger or smaller than the centripetal acceleration oxmk -xuo, u9)ok- sjj q67un1uf the Earth?

Would it require less speed to launch a satellite f-elanj g2; m*(a) toward the east or (b) toward the l* 2aejmg ;fn-west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movi3 ifi4,unon(wb:agpbp9y +m6 jn+vr1ng elevator: when the elevator (a) accelerates downwarfbp ,94pinj++ m awbu3y:6rnio n(v g1d, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in o6l2 ygf 9fb jul0;eahm b0g.h7uter 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 shlf ;j ml6g.2907bfh0u aeg byimulates 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 fx w)/lu4g w*bk /iw1xkall” or “apparent weightlessness” between s buwx l*g wi1k/k4xw/)teps.

The Earth moves faster in its orbit b 0:b/clh-l ezaround the Sun in January than in July. 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 Earbz b-l0lh /:ecth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was d(1tmqv2foq6r; s et (eiscovered to have a moon. Explain how this discovv foqer;6t( 1mqe2(ts ery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pl23aekehkmnh 3d/5 cq:1+ xj oull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravmal/jx ce h o:d135k 2hekqn3+itational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling f:3o3f8/m5bdtts t)qgfxa13hu dim : 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal accel te 80c)*rcfh lu7-kqqeration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume thf *-h qe)lk0c7u8rtcqat the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rot l ko-cei(z-ryiaa.7 k4s w (:1d9akprates uniformly in a horizontal circle (at arm’s length) of radius 0.9i7pk(dkrakslr9i4 :aoa-w. c( -z ey1 0 m. Calculate the speed of the discus.   

  Suppose the space shu-48f8fv z;5tk orjqy huh7 w6qttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal accelerationr8 74h; qo 5qhyf6jtku8vzfw- 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 os8xm1xlh pm8 zj/:v u7j.zsu/f a speck of clay on the edge of a potter’s wheel turning at 45 rpm jz :.mv7h j 8l18/pszxum /xus(revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rateed3zfm:v xhn- o * 1byy,a7gi+ in a vertical circle of r1fed ob7 3,yygi+- :mx vanzh*adius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turnrgicuo sdfp 1).b7;:o of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is f p:b icgo1u)r;7s.od this result independent of the mass of the car?   

  How large must the coefficient of etlo*n74g,vq static friction be between the tires and the road if a car is to round a level curve o7gt4,nlv*q o ef radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jetj: b/lonresqvat1 t+1e) q +f/ fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fas+ob l r:/qvfqt)t+an11esj/et 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 rotat*b1xqv;f4sxvn hy- d 3ing turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coeffi;vq fd-y1svhx4 b3x *ncient of static friction between the coin and the turntable?   

  At what minimum speed must a rou/z m vogmq8-:ller coaster be traveling when upside down at the top of a circl/: 8v-ouq mmzge
(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 rouy; h*o *n) cupu)ra,jl43tsblnded top of a hill (radyu on lsl; tuac)hp, )4b*r3*jius =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 perh7xpkhclsdd8py:7 08q+g a.e minute would a 15-m-diameter Ferris wheel need to make foh:qhcp. d+e7ag8 8lpy7ksd0 xr the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cir d2hr(c3eg fe5cle of radius 1.10 m. At the lowest point of its motion thrd ch32g 5fee(e tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotatz.qw;9 vjpdv/t *;0 kvhdue8ie if a particle 9.00 cm from the axis ofkd9h0 vvp/d*j;;.zu tivqw8 e rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in t v plf h; kdwn5cte0o0s6s(28a cylindrically walled "room." (See Fig. 5-35.s0pfwd 05so(tet8ckl2hn;6v )
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 circ ky4xe -7teu7cle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blo7e47y e-xcukt ck (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 no8ybjx/sd 3o 7ot ignoring the weight of the ball which revolves on a string 0.600 m long. In particular,syd7b j83ox/ o find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly bazl1a(47yj- .n qihb wlnked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses x9c ife8,kvxz-wdd77 $ 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 thb: j59g /ixhevasive 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 tangent1rccrta 6t+9z ial and centripetal components of the net force exerted on thec 9rrz6atc +1t 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 area; i l 55/sgi*xc/g 7w6w6buy,ptsjvvx, going from rest to 320km/h in a semvu6* ,g5s w /x7;tlwpigy/5bj vscxi6icircular 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 slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.jdix nl q4;31zx 2xet3w . pv3n-umal/90 m . At a particular instant, its acceleration is 1v1.xa in34dn3l3;jz/e2m-l w txq pxu.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 12,8j 2l. wq9leuqami60b : p68z:b,ogs fb00 km (2 Earth radii) above the Efp9bzb6 :0 sw8:aimo6q eubj. 2gql,larth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, fu+.t hze* ymuv3k7g. the gravitational acceleration g has a magnitude of y7gz kveh3.uuft +m. *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 eu1vs 1d8)9ex4 c y:lmle0mrq due to gravity on the Moon. The Moon's radius is 1.74)cyees xemv9l8 d:qrlmu11 40 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a rec hj7 7ya)xg:adius 1.5 times that of Earth, but has the same mass. What is the acceleration due to grh jx7a)cy7 g:eavity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but tuunh5ma jegainc2c/52q z4 3oyi ue -4e)8nu,he same radius. What is g nea 3 n8n2u-ag2i eumez/qoj5c ,hc uy4u5i)e4nar its surface?   

  Two objects attract each other gravitationally with a force *) i*w4v3kej2qo1jsghhd(fo 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 acceleration oftqfrxqdl skko,p:lca+se 42 5j3 u9 *4 gravity, at (a) 3200 m k5c3s sx t4 ,perdof9j2 l4qu a:lqk*+   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the xi+ 5dkf7szy 8Earth where thegravitational z+ 78yxi5ks dfacceleration 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 Senf e7q*/2snr six( p.un packed into a sphere about 10 km in radius. Estimate the surface gravixfr sp/e7(. *nq ei2nsty on this monster.    $\times10^12$

  A typical white-dwarf sw/hzecw(wg0m4 u/wq 0tar, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon w04(cuw /0mwzq h w/gebut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fp6dpiq z+bk u*ek-1bme 5)f2feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up theruep52f-i+p) 6bb *zeq1mkdfke. 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 corners of a square of side 0.60 m. i6+tp0 w .wc5gat-mh9w5 cvx nCalculate the magnitude and direction of the total gravitatin agx.56t c+w9 -pchtimvw 0w5onal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mos2)x* 9g;w+8ycrvbql jxz7 q-kn *frlmt of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four pla*wnkxrz mj xy8gq-7) +cv*;l r29qflbnets 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 acceler 4fc-kch os1d 3.v2jcvation of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass - 4 dj2sfcv31cv hck.oof Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valurf7.95 hb.l6br u7vfh owlji0e for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5– whr67bvl . lb.9r o0j5uhffi716.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the vb 9,xo0hrs.nEarth at a height h.0xbo,v9rns of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circultei; 4m)l op wk2rwg:01h 2oerar orbit 650 km above the Earth. How fast must the shuttle be moving (relative wh;gp0 wm i2t:)kr4 21e loeorto Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupaarvz8e8 p(:z81f -v*jw r .k5eztnnaxnts are to experience simulated gravity of 0.60 g? Assume the spacesn pjkv5ne-zraz* wtf.88z a1xv8re(:hip’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular .:ee 0+vwq n :k0elkmrz3nog1“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 resulwkezek+n .go0qn0 13em: v:rlt depend on the mass of the satellite?    s ~    min

  At what horizontal velocity 36j.kcodvh24eng b9 o would a satellite have to be launched from the top of Mt. Everest to be9jcdnhbk3v og 46e 2.o placed in a circular orbit around the Earth?   

  During an Apollo lunar landin 7wrqlm5qb y+:g mission, the command module continued to orbit the Moon at an altitude of about 100 km. How lml:qwr+ 5qyb 7ong did it take to go around the Moon once?    s

  The rings of Saturn are composed 4 jzi:xpb--h y/ kjyq6of chunks of ice that orbit the planet. The inner -ib/y4-qxj:zpy 6khj 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 evw05hox sfj. rde* q+/s ou4.qjo1*bdzery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) axd+o jh q4 ewsqz.0o*b1j5 /rod.f u*st the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight8t ac4o(zc2oy5 doqp+x ut8r; of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movinga(48rt o +c2ozu x cy8q;5dpot 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. They areqe 0sk9iip+ t1 observed to be separated by 360 million km and90kspe q1+it i 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 redh25t r hxuej/4/ xz1nad for the weight of a 55-kg woman in an elevator that movesu j1/hed xz4 5n2rtxh/
(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 :j p s;*;vo do+bkravxr1t12r the ceiling of an elevator. The cord can withstand a tension of 220 p* 2krb: d+rotv;oa v;rsx1j1 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 surfaj4snqoy6g1c n7 v(3t wkunh( 8s1m g8ace of a planet with period T , the density (ma(j1s8 1htn wouv68 nmc7ag( syg43qnkss/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (2yfq;fi1l0 u1l 7.4 d) to determine the period of an artificial satelliti1q f;u 0l1fyle orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lxk40ax 37 ucyyike the planets. Its period 70y c xk34ayuxis 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancv* xhi,,+tx3; owpwste 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 clos(ekj;*-60kaq zoxi xbugq8c1 e to the akzb;6ejx q01( qu*oc -i kgx8surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of th)h c ji.)zhq,yj/ rg:fe Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, an ng 5)m is83yhc v38r)i/jpzqtd mean distance for the four largest moons of Jupiter (those discg rq))npm 338i hczs8j5ytv/i overed by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance a*srd, z3hm;o3 /pydoof the Moon. dd, ay3zo ;r*msh3/po   $\times 10^{24}$

  Determine the mean distance from Jupiter for eacn ghfj;ba s,2vmn7dl29fy/ -a h of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to mv;fl nh nba-, ay2fg7s92j /dthe 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 d bm8o8cmw8w5e) wl4 uMars and Jupiter consists of many fragments (which some space scientists think came from a 48wu)8ew cbdwlm 5o8m planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "pl)x plwnv20in0g n6j o.anet" in the form of a band completjn g pvw06o l)n0x.n2iely encircling 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 icdjg7 6)pu0c 7u5a qsjn an arc from a hanging vine (Fig. 5–41). If his arms are capable of exertinq uajg 7cjscp )d5607ug 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’swtj8b* 5b) )2j 3odc8f(i cu.dim,wervf6 hlr surface will the acceleration of gravity be half what it is on the surface? )ed(b2tw8 rudicfml h bc)rf5o8 *. 3j6vwi ,j   $\times 10^6$

  On an ice rink, two skatt eit l7mo:rq-be9b8/ers of equal mass grab 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 pullinr/bi-7eq:mt eot b l98g on one another?    $\times 10^2$

  Because the Earth rotates once per day, the app b pt ygitm-3sn9-sz+5iqv:2sarent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Esvp:2t5i3n zmg-- sb +iqty9sstimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a s2 ieuj(sw js2fm3kj36 m-b hm5pacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Mob2smh 5s3(-ifkm6je2w jum j3 on pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale iyja uu0: t)br)n an elevator, it says your mass is 82 k0ay:b tr) u)ujg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wil yc tnt6bax q2x*tn)48vse)m*l 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 4* t)6 evtxxamy8n )*sc2bnqtEarth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft inl9e/7lio)bzi7oy 1x1 osep*v 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 forb f;ko51 o0sug(kjjve +7a qh4 the mass of a planet in terms of its radius r, the acceleration d bo 4q5ej+ku(vos1k7fa hj0 ;gue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertica.h j3ix b/l:4c,zv bjjai :g3zl by an an:,vbgi4 bj jz3c/i .zhl3jax:gle $\theta$ 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 isvo - bymi89,ts banked for a design speed of If the coefficient of static frictionb9 ts8- yvoim, is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast 8 7kk*.uolavv that objects at the equator were apparently weightllokvv8ak7u* .ess?    $\times 10^3$s

  Two equal-mass stars maintain a constant 5*h+a hzfiu6l4y eie,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 s2ueh5 dvnv4fjv-; 0by cokpc2-nsk *3peed rounds a curve of radius 235 m. A lamp suspend-oy f knecvp3hu0 c4n 2kbd 5;v*-v2jsed from 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 ae:,3wkz kut r1s massive 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 would experience at theutrw3,k e:k 1z 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 presence of an extr93 708 e8* uz kdesi0csi; wmhnzz8qjlemely 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 9dci 3 hs88m*zizk0nlswz8 q;ee0ju 7 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 speednit y.*joko..04 er px as it traverses the hill and valley shown in Fig. 5–nerio.* .ktp.4 0ojxy45. 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 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 skf*fomyt xl5t3 bnk)z) s 3+pmi n31p;atellites 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 )on 3+313tskkp;p5zi)y bflnmm*ftx 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 *ws rc4zaf,9;y,mny ;boidf( (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid; ,mba,;( w9*sz4ry dcfi fyon Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repairugzmes:xvds 2i1h7+(bh;k 9 0j3w jzh. You are in a circular orbit of the same radius as the satellite (400 km above the Eartzzwd s +1hhj: m(g3uxk;hbij2 7v90seh), 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 mzh*gwycv6t8: ean distance fromw6 z8t:*hcvgy 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 G would need to be if you msz6p2: vyh b-could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptio vs-:6myh zp2bns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxys545e *.sct uesl0 glh (Fig. 5-46) at a distance of about 30,000 lcs5*hl 4 eguste0l.s5ight-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 atk9 lfvukp6hw k .+fb-, the corners of a square 0.50 m on each side. Find tl9 u+. kv kh6pbk,f-fwhe magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the tj n,gm,afv:: 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 accelerationuqv9o pgkf7* 6 experienced by the tip of the 1.5-cm-long sweep second hand on yv*o 9fu76 qpgkour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a 2q0il qpeexzs ce 3 ,2y-otq82sinker weight around in a 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 y qqop 82l3e,i 2-zc2qexste 0angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R i k3zi-s./j k-;gnsc-npk6s irn a new highway is designed so that a car traveling at speesn.jsin-kk k/-;z 6i pg-scr3 d $ 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, 1xw :c/k6x-:)uahxootd 5cm gutilizes 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 comfortax ux)xk6cc-: dwm oa/ h:g5o1tble. 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.$\approx$    $\times 10^2$