Sometimes people say that water is removed from clotka4/zfsd0-zcitd3m8 jobc3 6f ; ,ltahes in a spin dryer by centrifugz83/ad4atfk s0,ctl dm6 b jzco;i3-fal force throwing the water outward. What is wrong with this statement?

Will the acceleratiow6-uy,b;kllv,q4l 4 esr7w gbn of a car be the same when the car travels around a sharp curve at a constant 60 km/h u, rbeywgqk,;w6 bl74 sl4l v-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 6ti(shg 0olydteo2t2 v0u+3athe car exert the greatest and least forces on the road: (a) at the topgo 23ltteia(d60 0v2 u tyosh+ 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-ro-bgk0bim k 7-ds hg05pund. Which of these forces provides the centripet dbgbh- k5 psmki7-0g0al acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spib nh4/p,znj2gg/t :j1zkzi-k lling ohzgktj /z- n1:jk,b n2/z pig4ut, even at 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 con78k (dmar o)jetrols in the car which can be used to cause the car to accelerate. What are they? What accelerations do they p (7km)oe rdaj8roduce?

A child on a sled comes flying over the crest of a small hill, as shown in Fp m:uceqrl9+ 6ig. 5lm+:up9 6qrec –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 decrease using Newton’s second law.

Why do bicycle riders lean inwj *9rq1aatcncm0.qu: o.t m; ra gks05ard when rounding a curve at high speed?

Why do airplanes bank when they turn? How wouldx/rx8 b:- ypnh you compute the banking angle given ypbh-xr8: /nx its speed and radius of the turn?

A girl is whirling a ball on a string around her headn;vkrd 0sp83 wvax+ro5; q; 8bm)b xza in a horizontal plane. She wants to let go at precisea 8;5np vxom 3qb;x +vkbwdrarz8)0;sly 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, how large n(qsh 8818aof up8p(mn)vc 9gfi9esia force? Consi f1p89snhp gnf c8e(miaoiuv9(q8 s)8der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s y/wnz:+tzp nkj +1qc-orbit be/z+p q:zn1nw- jcy+kt different?

Which pulls harder gravitationald 1)chelsa*0b +ydid. ly, the Earth on the Moon, or the Moon on the Earth? .h+s ebyli)*d1cd da 0Which accelerates more?

The Sun's gravitational pull on the Earth is much lar 3wct*l3:befqneh i+h6b6iwnr 2zi1/ger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational *z6rnc 2tifn6:ei 3+e3qhwwb1bh /lipull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? W6 ;ha ;oovdto4 7en8pjhat two effects are at wor 867v j; 4ohdt;ooeapnk? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only a.elj:ubxa 3dsqp ;:i *bout half the force on the Moon due to .paid ::buj 3;eq*lxsthe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbsy :)w j.v. ja u/le76rbhgzoz/t/.mfit around the Sun larger or smaller than the c. zemz w/:h7br).u .jt/vsg fojal/6yentripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) tow-dg- shy1ols9ekv 1t8 cb+ma /ard the east or (b) toward the west? Considerck1hlt9dvoa /g1m -seb ys8-+ the Earth’s rotation direction.

When will your apparent wej9fd11 oi cws:9y*s4 aog.tsa ight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the gr *wj .st9: aaod1 ciyo19ss4gfound?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space couldafgo+xg1* f1/l zzmi( 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 objects fall, (b) the force we feel on our fe iz m+xgao/l*zgf1(f1et, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free c*msgn 0av( a-fall” or “apparent weightlessness” between stepsmcag (- av0*sn.

The Earth moves faster in its orbit around the Sun in January tha a qh 2fbs*ej7r+otuk74(6om1d:octxn 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 (t2xtdb o* 7qre +mkco71 :6h4fuasojmain factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovepxp)(nv*2twt*bpen ax /7r-pred to have a moon. Explain how this discovery enabled an (v-p npp72xn*t* b )e/xapr wtestimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. vvp iq,s+.15wr, ,vm5per.t hs ni6g oYet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational puls1 .rioh qp,mgv r5+v,6sti5 wp.,envl 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 198* q)(j4v vihb+v)futn0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit a3jqi3dznfdw:;nq) t)m9a1 f qsh+ rj . sse:c5round the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth ::sac3 fjfqnqqd)imdne9h1z+w5 3ss .tr ;j)'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 2h,w (bxqv (wxv:qt+b it rotates uniformly in: qh,xvvqw( xw2(tbb+ a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from t y)tbq(7t4oncvfzkk3z.w e2 2uihw-4he Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the grav37zkvf kyo 4w(2i)- bzcqw n2u.teh4titational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a v7 .2x5868ooytef vbdvp, pzzspeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diametexv,yf zdevv t287pozb8 .5p 6or is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate e8s. 4pl5.boxjm j1s qnv.o* lin a vertical circle of radius 72.0 cm , as shown in Fig. 5-33.nlbs 4ojs*lo. .5vp8qejx m.1 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 mx 5a1 vgsjv.()sxnhw ;z13cn-kg car can round 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 independent of the mass of)hnsx j5c1 w gsan1. (vvz3;xm the car?   

  How large must the coefficient of static friction5;d wc(xnnvq,4kna 3u be between the tires and the road if a car is to round a l d(x4n qnak,53cnwu; vevel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astroj48o /gsek*s vnauts and jet 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,s*4v gso8 je/k 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 speel r*xm;lh+ v8td. 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 ;vrl8*xhtl+m off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down j8nx+ zu*v8ug b+pb.lat the top of a civbuu+g plx+z*jb 8n8. rcle
(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 teemv4z9cs9 0e ( n.pughe rounded top of(p9euzceg4 mv0 .s9ne a hill (radius =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 . 3:nmp95syej;k/ttoo an5e h a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topm ;m5 n:.spa9oeojt 3y/nhe 5tkost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1lj2c15smmdmqz zly,9zb 8j. :.10 m. At the lowestym mb9d8:1j ,.s5z2 jlz mzclq point 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 centrifuge rotate if a particle 9.00 cm from the axis o 7tv1ankyy -i)bydz7 r1/dj7 gf rotation is to experience an acceleration of -kda1 v77n/bgrdy t yijzy1 )7 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylite .s4ca 7ghxe79/bdp 4xaz2-cdup2cndrically walled "roh- 4.27epx 9 cc/sdezc4 aupbt 7x2gadom." (See 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 circle on a fe ljmr.k0h8. 1zggne3rictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throe8 .hkzmr3 lggne1 0j.ugh 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,w(j(r5tci4tera t(xfy b.jp7c)j 3 7k by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular,fcr)4(bt77 5p.j3 wcr xktiajet(j y( 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 mh)ckp o)(z)w1+1ivaj:hikri 0lr b0m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses ddp2.m.i byi:$ 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 maneu (ejda93 emtow/q8,f yver 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 tangent- 1 me/h/v ebsd7hjf5ayd 8p4gial and centripetal components of the net force exerted on the car (by the ground) in Ex 8bf/v /pdh7syeg1dj e-a54mh ample 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 unifo7f3gpu qmj ( hwp:4jgyk 4ne(,rmly 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 4 3m y4qk, phf7:guj(gjepnw(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.pq:( a1);fawp0 9jp jn8tznrr 90 m . At a particular instant, its acceleration is 1.0wf9 0(q: r1pp8pn)zj; rnjaat5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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’v me0(phiv c 5xmxlh*an 3*;cs,d.p:js gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kgm *x simhh5l3p a,v0c vc;x:.jdpe(*n.   

  At the surface of a certain planet, the gravitational accelw1;r) 3i:wazr dro b5veration g has a magnitude of5zv;a)or rwwr1 3bd:i 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 accelerassu09ni 9 h 9hgf ez3(r.k7eeqtion due to gravity on the Moon. The Moon's radius is 1.7 es(97 90h zirnhsgeq3fe. 9ku4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same mas4 l:t-oa*2 ox mw7pxems. What is the acceleration due to gravity near its o 4:xm7*-xpwoa2m etl surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same r*+u1zzuq;4 zfm bzy6ybl ;)u nadius. Whazzn u)zzqyfm*;l6b 4bu+y 1u;t is g near its surface?   

  Two objects attract rq xry l6wqs 4wa ciqleu,-.+k+4h94meach other gravitationally 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 varkes b66rxfg np k/6x,0aji2(lue of g , the acceleration of gravity, at (a) 3200 m (a2,b ri6nxep0kjs6k rgx/f6    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earzs1f4 r)dt k-vth’s center to a point outside the Earth where thegravitational acceleration due 1dzv-)fk4s t rto 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 out m0xn*zx d ,s:k;alg )piop-.r Sun packed into a sphere about 10 km in ra;:p)pxx -azo0 l*,gm .nksitddius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf stczge;1y 2+bq war, 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 but has the mass of our Sun. What is the surface gravity on thg1ez2q+c ywb;is star?    $\times 10^7$

  You are explaining whv eveq;94+z5e/cftopd,-le zy astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they cz;ze5, 9+de-fvoqp vl4/teethought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squaphj8;erj4 vj +re of side 0.60 m. Calculate te+j8jpvh rj;4 he magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of gf5)k0 bajl7v6 sxfs3 the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a li53k asl0f 67sbgxf)v jne (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 tu6mogfnn(a 16bf:q 0bhe surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the masgmu ba(660fnon:fbq1 s of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ear 9nqco:;ixyd 1th and its distance from the Sun. [Note: Compare your answer to that obtained using ocy nid;q9x1: Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of alonams8pi*u + ) 7 ulcax,00ie satellite moving in a stable circular orbit about the Earth at 78aol u lp0 ,xcmi+ neia*)su0a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into axuw(c0 +/mtlg 9; zjf.(s8ej- pusybi circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release ewulbi.y 9 0;mjzxu(g+f( 8-tscjps/ occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants ar-pu-s 5h*m9,i, bt d.dyrztz(kkq0v ve to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.h,b- tiv 0zky*kqrd,zvtpm .5-d9(s u)   

  Determine the time it takes for a satellite to oq2 )ix)utqoq(cu ugj.h *, h)orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height )ouqhuxqg)2,q *o. ct u)j(hi 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 satellit+nwu1g: mu nk.e have to be launched from the top of Mt. Everest to be placed in a circular orbit around 1 nmg:u+w.nku the Earth?   

  During an Apollo lunar landing mission, the command module continued to orfa-t f1:sp ;gsbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon tsa-f;: fg ps1once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The inq6mujy6htz.*i: n -tsner radius of the ring:*6q6 .shj zni-tmu tys 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 c8 fn4k ;.zz7o* ty7blkmn ;rc/kygt )every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) lto.fbmkyr47)z;8y 7*tkgknzc nc/; at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centek:0o9 c h f1 *akfrdvc(g8cwv;r of the Earth's Moon in a space vehicle (a) mk9 v(o wcg aff0vd*1rck8hc:;oving 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 w:18n,cn3macg9 y eqw 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 pcn9wa, qw:cge8ymn1 3oint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scal+9zmvv.3 zw vfe read for the weight of a 55-kg woman in an elevator tha+v fv3 .zvm9wzt 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 fr6io4twqw icn-u +g6m 1j1e)hrom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magncu16oj)t4g6hqnwi+- mi e1writude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period .7w0amn k -76zri91sjcfgq 6 s5hduf a T , the density (mas sfu 7r-wm6 q k7sdzich.60f n95gaa1js/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 Moo/uuzx4dl z9y 4n (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface4yzlxu /9dz4u .    s

  The asteroid Icarus, though only a few hundr zg7lqt wyupdw p:/(0y 27+deaed meters across, orbits the Sun like the planets. Its period i7tqu/ +g d7paylw2(z0:wdey p s 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dtlg*l 7w 6fl;eistance 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 yeiw: fyvxgih)/0vv4,y uw42l ears. 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 mean distance s in Kyw f4 0)vlueiwyvg 2:4i/vh,xepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about tjdjr f3c 9nqjw. q(z*1he center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, perioe)qxyi ;/2/rlcul 0phd, and mean distance for the four largest moons of upql/xrc h; 02ley)i/ Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and dis nvb(2n2m1dtkmyen .9tance of the Moon. n n.y 2nbm d192vek(tm   $\times 10^{24}$

  Determine the mean distance from Jupiter for eac,k ov:m3;h (/kyrxsn ubr1 5oeh of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods give5 kmrv 3u/;o es,koy1:xbnhr(n in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which sly;l-9jsvgimlim; (iz l1l7mg,7bo.nqbw , : ome space scientists think came from a planet that once orbited the Sun but wagzg ;bnl,9mwl:ib ,mm isl-l1jlq oi .7;7 y(vs 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 des z-c7 s5pz tc*y+jpvu2cribes an artificial "planet" in the form of a band completely 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 5syupc- t7zvz+2 j*pc 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 bb; pdsgzyt(0(r a6b 7vine (Fig. 5–41). If his arms are capable of exertibsb6grz( p0dya( 7b ;tng 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 gravi6d -e.xf,,hmngx8bud p* nt0jty be half what it is on the surfd,md 6bx xjue 8h-0,fpnt.gn *ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass gram/t6hu3 etsn- b 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 ano6u/3t nht- msether?    $\times 10^2$

  Because the Earth rot3at-s 2o7sdp z aac,+lates once 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 this effeaz a-ocd 2s3ls7,a p+tct. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the 2p wxv.ye) +;bigse7fEarth will a spacecraft traveling directly from the Earth to the Moon experiwix7fg ) 2ey;vesb. p+ence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elevy3cj kl;m:2y+(l68xqbgl qpiator, it says your mass is 82 kg. What is the acceleration of the elevator, and in 2q63 x ljmqkl(byl gcip; 8+:ywhich direction?     ----待选择----upwartddown 

  A projected space station con(u( ,g y.j01l-wy2pqtkyw*rc ezin1p,t 2e ygsists of a circular tube that will rotate about its center (like a tubular biyg1* t1y22.(lc wp,jyz k-q(e,n gtui 0wrye pcycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft y1a zgp6; (onein a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in i mi5v2 qs8g13h s,avmterms of its radius r, the acceleration due to gravity at its surface and the gravitational c2 ,vmiqsmhgv8s1 5ai3 onstant G.

A plumb bob (a mass m hanging on a string) is d3 rrybfd2571pnbci (1azf 5zoeflected from the vertical by an angp27ifc or z (nb5zab5f y3rd11le $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the l6tr+ke(mqy f8+xy.n coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handlem. (yex6 k+qyt n8+lrf the curve?

  How long would a day be if the Earth were rotating so fast r: s3;s1iapw is;d58go*kxy wthat objects at the equator were apparently 8drsia ;kpwo;35s:i*g w1xs y weightless?    $\times 10^3$s

  Two equal-mass stars maintain h 8ieqcb3fi:7 a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of;mz/w3 -cm ud kbqnzu.02:tt b radius 235 m. A lamp suspended from the ceiling swings out to an n 2dmqu;3c0.b: k tztmwb-z /uangle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed + 6njx ec3.koqhmo 2y9that 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 experienok y 6 c+.hqoejm3nx29ce 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 Hub+juy:t: k.zd gble Space Telescope 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 ofjz +tu.:gdy: k 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 trc *v,gp/lgd0 cza fj b(:lo4h-x* 9vsbyp8z6taverses 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 theo y 0 v*g/lbx-vb 8p,ld z(ft9zjaccg4hs:p6* 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 satellitel,/zekrh6 7 uqcxm5a2 s 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 apprxe/c2u 67r,qklha5 zmoximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after :3u3,w vq; u,)ezad f7byhom8zwx ab+traveling 2.1 billion km, is meant to orbit the asteroid Eruwbz783xm :z fdawvb3o ueyha;q), +,os 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 satelliqhgsq*eg0d *2u m1: kfte in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behuqg g dqf1 hs0**em:k2ind 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 ,mp6lj .fe u nj+xk.*:pwspt( distance from the Sunf*x6m jkw+n:p p.up lt ,s.(je?   
(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 b1nwg ri8xco c+9n7s ,ae if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonorsx1i9 8canw+cgn 7, able assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroumz+ .ve3talf/yq r3kc3nk 7xkkg.f(, nd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ,ft3rkkne ykf7l/.g. 3+xvm(q3 zckalight-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 im/k 06gyhedq , z9p3jat the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg masidk,y6q /h0mzp 3ge9 js 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 9j6 0 bdukw5af1kg,dkEarth $ \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 the tip of the 1.5-cm-lo/jad t 9r9t/rong sweep second hand ot a9rdtr/9j /on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arojy lzrxu; rctahat . -2h2dk*6o-+.rfund 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 angle that the fishin*trroy 6c2za.rtxhhu2af+;j -k ld- .g line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a t z qfa,s.t.d5new highway is designed so that a car traveling at spef,tq a.d5z. sted $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotgwh+g 4ni+6 bu+fgsq :w.fns3iating 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 pubgwffiq ++ 63hg .gnw:+4s snassenger 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.$\approx$    $\times 10^2$