Sometimes people say that water is removed from clothes in a spin dryer by vi02-5g4)av mtc wanvcentrifugal force throwing the water outw0 a givc)tvvwm4n5a -2ard. What is wrong with this statement?

Will the acceleration of a car be the same when the c/tx59 hee+-yn1n g zkuar travels around a sharp curve at a constant 60 km/h as when it travels around a gentl9 n xte/-hue5z ngky1+e curve at the same speed? Explain.

Suppose a car moves at constant sper ptxwfivn 547 gy*:3oed 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 dip3 *fn57ro4 wpt giyx:v between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forcps 6fiit6of2* og2 mnmo3x7 6res acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration ntx2f7* o2ro3mfs o6m6i6ig p of the child?

A bucket of water can be whi9i)p3gql ypf)u 5q4y8p pvs(lrled in a vertical circle without the water spilling out, even at the top of the circle when the bucket isq8 p l fypy5)gs(v p)q9il4p3u upside down. Explain.

How many “acceleratorkq 5pz t 66v+xi*,tmsms” do you have in your car? There are at least three controls in the car which can be used to causs6x6 pm 5 m+qzit,vkt*e the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small h/x;- pnr.dub nr wd/if2l *y2will, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he u*2l /r2wy pnx-. w; ifbd/rdnfeels 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 inward when rounding a curve at izd3-rup2k1 2oyuju) high speed?

Why do airplanes bank when they turn? How woulfsr(3*wr f 9 xcmie3u8g5s-qvd you compute the banking angle given its speed and radiw-m(esqx*v8f33g r9 suf5rci us of the turn?

A girl is whirling a ball on a string around her head in a horv4 iykzgp+. v:izontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When shovvz+ i.k: 4pyguld she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large c(wbzgui 2h gwa5*ak he94;4 ia force? Consider4w(h ag ;i2*hk4aiu 5c9bgewz an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double wa( hwm tvi8;wm;(gl j6u+5jhphat it is, in what ways would the Moon’s orbit be differlt;(5jh6 ia pwmg;jv hmu8w(+ent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Eam k*f z0h 6qhbh/pz:7srth? Which accelk/hs67hpzb :zfm *q0h erates more?

The Sun's gravitational pull on the Earth is much larger than th a-j )in8 5*o7ata hagc03aixke Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference *38aant5ao-) 0 a7icgahjkxi in gravitational pull from one side of the Earth to the other.]

Will an object weigh vhu z leo31o;2more at the equator or at the poles? What two effects are at work? Do they 3ve2 1ohuzlo ;oppose each other?

The gravitational force on the Moon due to the Earth is only abou:i a3hp8.qhyhh -7-tgwze oi *t half the force on the Moon due to the Sun. Why isn’t h:-.8 7t3ohh-e ihz yqi* wagpthe Moon pulled away from the Earth?

Is the centripetal accelerationd-g *1orzqh8x 1.idn o of Mars in its orbit around the Sun larger or smaller than the centrip1ohg-ni8r zd1ox q.d *etal acceleration of the Earth?

Would it require les b pbk e1xsf6*d b6 rl 41nnd:,su5w6t0gerr9ms speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotationsbe16,x9elw4pubrt:1dgd nkn * 0sb6f5mr r6 direction.

When will your apparent weight be the greatest, as measured by a sca 3*lvljoo4mck ,yz/1 ale 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 o,v*cay /mj 14k3zllobe 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 period:i(s rr.w5 gfvs 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). Expla.s (frrgiw v:5in how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightxsu;sf 3h4 2bylessness” between ssyuh4 f;xs2 3bteps.

The Earth moves faster in its orbit around the Sun in January than in July-f /9mm40:wx)d wivfzezu o, t. 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 u,m094edt / :of ) zw-mwvizxfEarth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to 6de1b7vmz qx- i;4sqihave a moon. Explain how this discovery enabled an estimate of Pluto’;7di b1qi s-6m zv4xeqs mass.

  The Sun's gravitational pull on the Earth is much largo:*s iobiib) (er than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of)iiibs *(ob o: 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 travelin1gc1 rg 74tosmo wcl:5g 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 acceleration of the Earthq b1w8q-jwi-kmno6xw 5* kn6d in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit i-qjnnq8 w wkd*b65- i 6x1okwms 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 hiv;k/e5 i,0 ijb(olo210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculk ibhi(5 ovo/i;je, l0ate the speed of the discus.   

  Suppose the space shuttle khh2x*( of( ),uh q*vbk*xrwhis in orbit 400 km from the Earth's surface, and circles the Earh bqu or2f,w**kv)h( xhx( h*kth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on th:ezbjry 0 4nbt::h+rj4 4hcute edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm44e+ r:uh: brbyc:0 4nzjtjth ?   

  A ball on the end of a string is revolved at a uniform rate in a venc( z+emczvv:+2x49wb8y m jjrtical circle of radius 72.0 cm , as shown in Fig. 5-33. If j mnjcx9vz(+b4+ey:2 8m zw cvits 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 turnpxr 1to9c.s9 u 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 the car?oc91s9r u x.pt   

  How large must the coefficient of static friction be between the tires and znlvlfc(4p0 +le 2sx:the road if e: p0 fcnl2z+ s(vlxl4a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astc503pm6esn *-o : qkgzrdru/rronauts 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 tre/ 3 - zcku06 r*rdnp:g5mqrosainee 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 o k0gecrb.;wws, 7 gy.4,4 ty5oalzxlaf variable speed. When the speed of the turntable is slowly increa4 ,s4gke7rczw.xa o yl;.b 50,g lyatwsed, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upatv8 r8tpum3+5 mrt.hside down at the top of a ci.apm t8 hr38+tv5t umrrcle
(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 95qhywwf)x nr9a 6+b.z+-cu 72p6xuwf v0 kg (including the driver) crosses the rounded top of a hill (rxf9zawuwhpw+qnc . ) 2u-yv66+xbrf7 adius =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-dia fw,i hiyo- *pucus2c8z,sl o7;x4 9demeter Ferris wheel need to make for the passengers to feel “weightless” at the tuc; yc7udsf zx poh*e,,o4i sl928wi-opmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle wcrg y8yn,.q)zer n+8 of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 .e)yynrcrnq+wg 8z ,8N.
(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 partic+dhdaf wdzw:z zvb4gz.-r1;4le 9.00 cm from the axis of rotation is to experience an accelerationzw1.fvzw bd:z+-h dza g4d;4 r of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoplegcbb02:/isd 0 :xe s5u9qjbew are rotated in a cylindrically walled "room." x :s 02/edq bcu5bsb0ig e9:wj(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 frictiond.lr8y. zn;m0a iv+vc bd.5t qless air-hockey tabletop, and is held in this orbiq .vc5d;bazy l8.i0r+m.dvtn t by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignogyx8w: xhlq (x*1pw.zy zfe7 5ring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of (yq xg5y81l7hzzfxwx ep *w: .$\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelin8le- lc 7 +w8kifd; y3zm)pm2hk9 plksg 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 ro )z40ezl 5z :poqlk)k:v; zi$ 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 divingr/ vpq3n1z t2b 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 tangential and centripetal components of the net force exerted on z-bcae1a5xj4-ul60 qi8 lcvh3 j7v olza( m6athe car (by the ground) in Example 5-8 when its speed is 3 8llja j0- ma el avuob6x657zq 14a(czvi-ch15$ \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, going ds -zb-gi ) 9s5q+zaq.xvsr/c from rest to 320km/h in a semicircular a z-vaz q xsqsb)d95g+sc-./irrc 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 horizont+iehp x5thz- mh:-e c.al circle of radius 2.90 m . At a particular instant, its acceleration is xc.-:+ h hmze5- iphte1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 o ql:e)zgp0lb7cp 2*4e us v*utn a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its masslt g4q:vz2pele7p* 0)* u cbus is 1350 kg.   

  At the surface of a certain planet, the gravitatj*ca joct.+g3 v op*g:pm5e:mional acceleration g has a magnitude of 12e ojt3g*+p5vm mj: o:pg c.ca* m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to grav+gf8m:(cvdio 3y*;f,nbuhfr40eeb j do d8n(ity on the Moon. The Moon's radius is 1.74 b fddoh+v e(db, (ijoc38r8 mf4 eng0uny:*; f$\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,z*-qh95bl*vjr:k wd f but has the same mass. What is the acceleration due to gravity near its surfac5-qwbr* jl9z : hfk*vde?   

  A hypothetical planet has a mass 1.66 times :r /xfkqb3nc g) /n2m+skb.,smz gju-b;vcp8that of Earth, but the same radius. What is g near its surfagm b;jxmsbg3knn/)b:/2p.zc kf vu q,8c+-rsce?   

  Two objects attract eacrs tt* m3f.qji)sr 83yh 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 value of g , the acceleration of grav1cqtt. ilhkef p2p6 n5q,)8 vkity, at (a) 3200 m iktp8ek.q1cn2, 6hvp )tf5 q l   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frl-n) *)x)g ab-idpzqeom the Earth’s center to a point outside the Earth where tdlagb))ie*- qzx pn- )hegravitational 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 So jvn sw8a/xq6w3wt)9e lbs( 7un packed into a sphere about w3 6wxeb sqts)8jn7o/9lavw(10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun ;c gj//c*dvoh but is now in the last stage of its evolution, is the size of our Moon but has the mass of*/ jh/o gcdvc; our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astroh imo-,dul/ (bnauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of dih lbo-/ mu,(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 si,92 f/bttvmgs-w aiq rd*ts83de 0.60 m. Calculate the magnitude and direction of the total gravitational force exer,aqw mvttgs8 t/si3 2b d*rf9-ted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line upefj top)p+z;68f .nv d on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assfd; p)on.ezjpt8+ 6v fuming 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 surf c;pmfy zxkw7m-7v1. 7p,f wr8hky8u nace of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mayz,wk1wupvr78f pc n h7m87;y fkmx-.rs.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for tfb-rs i71 l9)a0dj,+q,x emri g+mgyw he period of the Earth and its distance from the Su r)gqf-ibeg dr,7w,9l a1 sy +xm+imj0n. [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 stabl)3 yp-8rymylce circular orbit about the Earr mp83y )yly-cth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above thom gl/ *r 4y5*elpnbg/e Earth. How fast must the shuttle be moving (relat5pgo n4gb*er/ylml * /ive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience 3i; mmt 2ug/q+nbnmo :simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time mi 3;t g:mm2oqub/n +nneeded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takesy p d t:gyu127)bo knlgnw8 d,hji+6w. for a satellite to orbit the Earth in a circular “near-Earth” orbit.ln6ui:b ) .nw1,phgdw +kj y7 t2ogdy8 A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wou 6m fcc+q;g.ould a satellite have to be launched from the top of Mt. Everest to be placed in a ci;u6+.m cfoq cgrcular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cos40mr(yd 4m4 x,5oc,lhotjwontinued to orbit the Moon at an altitude of lcwytm 45d(o ox44rjo ,0s,h mabout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plane/g4h x* p+v p*,nazqwpt. The inner r**p a+h 4vqgnwx/pz,padius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 1w 7oym3lpz83b 5.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at thezlo 3mb7w 83yp bottom?
(a)    (b)   

  What is the apparent weight ofxp2+ ikr1aega856+lqh )nn it a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehaaitqgn i2x61 kl++8np h er)5icle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of tj 8-od/zpzs) dwo stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to z sdp/8jzdo) -orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for th j/vhu.er lq0bu4bz):e weight of a 55-kg woman in an elevator that mov:4) 0l r bbq/.ejhuzuves
(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 an eleva b 28jv5j*yzsmj3oqle 5/dh6 ktor. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitsz l v38bjmkjyd6 o* 5ejq5h2/ude and direction)? a =   

Show that if a satellite oro . ,r ttux4ub8wbh3u.bits very near the surface of a planet with period T , the density (mass/obu u .4twht, urx3.b8volume) 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 (27.4 d) to determ03a zip 6cntx4d8p n3yine the period of an d3 4xap i z3n6p08tcynartificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thou68 dqs6,kja fogh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance dojf,8 a66sqkfrom the Sun?    $\times 10^{11}$

  Neptune is an average distayfd1cu08) lo lnce 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 closebu- -e*cd0cez/ fy h5a 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 Kepler’s third law is half the sum of the nearest and farthest distance from the ayub 5ec* e0/--hcf dzSun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxyeh(0 ci02qnjf $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,5q,;9 bpgf sn5jiws*qnr**ob period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo i5gj9frn wqpn5* ** ,ioqbs sb;n 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 distanh;-s)lny 92 qk9vqgvw(ebbo(ce of the Moon. ow9b;e2svqk9 gy )blq- vh(n(   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kepo0ty3f/;bum . 2f mvy*ihhf3 nler’s third law. Use the distance of Io and the periods given in Table 5–3. Comph; .bitvyfom m nfu 3y/032hf*are 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 frovz848 ai /ifg *at-grv2fao,agments (which some space scientists think came from a planet that oncegoiio 2vza*r,af/ t -48f8agv 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 kh6j og*mhv14mojt,*n7jde / describes 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 g as on E tnm ek*mo g7vodj,h j1/6*hj4arth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in anp6b8p j7 mtx0w**mqci arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the*bi78jmxct*p m w6qp0 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 ther0tbgjpqyu rik 1*bguc(od a/7.k.9 : acceleration of gravity be half what it is on the.c/*rp ykbrggodui0u q .b (9kj 17:ta surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hanz-lg so86 lu4 ,dybnrirt7 ;uy x-m-m9ds and spin in a mutual circle once every lrbtxryz4 gumdn 8l6;mo yi-u,7-s -92.5 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 another?    $\times 10^2$

  Because the Earth rotates on+aonp*k93- xu8 ueq )acwg l1)hui6sgce 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 effect. What fraap) )+si31-q89o g*6 lnaukwugxcue hction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trsqxdmng 6 ( -i -)outy enta1:34un5ouaveling directly from the Earth to the Moon exp6te )oo4 : qnyi-3ng(5 umtduxn-1sauerience 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 b7u(n uyvl-a l1athroom scale in an elevator, it says your mass is 82 kg. What is the aul-1y( 7n ulavcceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists om/ 4i53kr:lsnd-t(md) t in jq r;azf+f a circular tube that 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 tht 3)qkdi :zr+;aimds4jt -m(rlf 5/ nne 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 in a vertica s5 t0yo--a.h*ibctk kl 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 terms of its r pp *m:0kjmfv+adius r, the acceleration dum*k0 f ppvj:+me to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strr8 r 8q*rcd;el y5a8q.she; .rpi+ecs ing) is deflected from the vertical by an angle ces.+e5c8hysqraq8 e ir l;.8rp ;d*r $\theta$ 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 of7 nfy61v)ekqxep 2pc 9 If the coefficient of static frictfckp6yn )2xe e v1qp97ion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be j w(wn,npr5sb;*4 l6aj:fcmb if the Earth were rotating so fast that objects at the equator were apparently weightln4a ww:bjns( bp6l;r*mcjf5,ess?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.s3k2c8 mqv:m*77;qkmhhx c4mrw b4vt 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 ausots, .3 tlr* curve of radius 235 m. A lamp suspended from the cs3r. oul t*ts,eiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claime/wuaucb gg u2(4x( if;v u/kf1d that a persovfxg/;u((2 u4 1 k bfwi/guuacn 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 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 Tef p5, cdabn4:ilescope 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). Theb: pida5cf,n4 y did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed nvs)a4o8q2 p xas 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) Where would the driver f) osx8 vapqn24eel 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 )xzs r+3p-biaeyw-8u 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 au -y3zsxwep8 b ia)r+-pproximately 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 Rdtbd27s c8kio.z+ zd0sy0zx8ex+ad 0endezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the ay+ 8 xd 8+ts cd70k0dizbadz2x0e s.ozsteroid 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 j.b-ut7zy4 ccsatellite in need of repair. You are in a circular orbit of the same radius as the satellite (4t4c bu-7c .jzy00 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 me*tjk b40edl3wan distance from the lkbedj0t3 4w* 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 could acg74xbnj 0;s4u.ky v bqtually "feel" yourself gravitationally attracted to someonxk u4sg;bn yq4bv.j07e near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the (g30v*q 9y bmmue n;vkMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yea9 0e3gqb *nkyu;vvm(mrs from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at w0gwc5fdqv-00z nd -yjg6q ;h5xqxy 7the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-k v0chd5qx-wqg7 wy-x0jf 60gdqzyn5 ;g mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5rary4m( 8z w7v500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep second *ff pjgnhkvg1,qnt zk .1+13vg-x7 hwhand on x 1g*3 kznjtkn .fhpf -1 +gvwqh,17gvyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing adca d 3erz (s/g6j91wp sinker weight around in a circle below you on a 0.25-m piece of fiserda9j s3gdwc 6/z(p1hing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desigb+n9zvux3;-xw-ks 1jpyxau i:b7s+ i ned so that a car traveling at spxsv; ibukyj+b+n :pi w3x 1zx7au9-s-eed $ 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 negotiatdew-:dvt-ff: :fgcix44 za 7king 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 les4atf d- vff-e zi4c:wdkx7:g:s friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the 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.$\approx$    $\times 10^2$