Sometimes people say that water is removed from clothes in a spin dryer b9nlqq;,m,v an e g(ca7y centrifugal force throwing the water outward. What is wrong with this statemena,q(q,nlem9gv7 n a c;t?

Will the acceleration of a car be the same when the car travels around o0z9x nul.eft.v9*ll2v vqf3 a sharp curve at a constant 6 tvfo.9vlevqx.* z 0fnlu9 2l30 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along 0* lr8*w 8eiw cj cu5jo9ob*eea 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 dire0*ue l85cw 9bo*ijwc j 8eo*p 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 hxtys .rc))8:kr+aye 9z+kii a merry-go-round. Which of these forces provides the centripetal acceler.ks+ia+ y)k)hrryx :iz 8ce 9tation of the child?

A bucket of water can be whirled+rfd 60.ycgtn in a vertical circle without the water spilling out, even at the top of the circle when the burdf0tgn.c+y 6cket is upside down. Explain.

How many “accelerators” do you have in your car? There are at le0( noqf z0d4zj lx2b,mast three controls in the car which can be used to cause the car to accele20 nozdlbzm,(f q04xj rate. What are they? What accelerations do they produce?

A child on a sled comes flying over the zfi1joz 22dij )yq1z/ crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and zj2iq1j/1 z fyz d)2iothe sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundinidd, zxlt-zb0 06- ayeg a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle575ab/q) u sg2porqrj given its speed and radius of the t52g q)pa/u5rq7sbr o jurn?

A girl is whirling a ball tjz7e (*0xr dson a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the strij(* 0rsxt7ez dng?

Does an apple exert a gravitational force on the Earth? If so, howrdeyid nijo;g z4 brn ;m:2qc., 21qa) large a forcecmg:er i2q1ao,.rbi; z;ydn)q 4 ndj2? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it aqky5lb kx7m 7m(-/vtrnc,.4m0egtcz: r- yi is, in what ways would the Moon’s orbit bemqnk7(yl:a x c05/tgv yrb m k.c7--remt4i, z different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon th.n1kl+ (p/k- 6ko8glafqvj on the Earth? Whic1k/- pl l8(v.qako tfnj 6+khgh accelerates more?

The Sun's gravitational pull on the Earth is muc;fm *v 5n0cwxwh larger than the Moon's. Yet the Moon';nv cf 0wm*xw5s is mainly responsible for the 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 the po80ou+k: b; uco cv0;+a.jzqccau i. jbles? What two effects are a:q.o0c;ij .v; o+jkcua auubb 0zc8c +t work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about ha48qqe,yu hqq +*t4 clblf the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eart qb +t84yq,qcle4 huq*h?

Is the centripetal acceleration of Mars in its orbit around tjyjtl :92-sea he Sun larger or smaller than the centripetal acceleration t:yl9sj e-2j aof the Earth?

Would it require less speed to launch a spl(r -qg:iy w0atellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direct0 py:iqgl rw-(ion.

When will your apparent weight be the greatest, as measured by a scale in a mov2q ylhtey kjnl* o92v mto9awt.;:*18 lhvus3ing elevator: when the elevator (a) accele 2veh unt :2.lllwo; 1oyj 9s8qv9t* 3*thmyakrates 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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be advernuu 7 5ikw -ltt)jjls;5ak20 ysely affected by weightlessness. One way to simulate gravity is to sh );njy2a5-jutlkwu 75si klt0ape 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 feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fallh lut2z5++ja r v.; zwr8odiz1” or “apparent weightlessness” between steps..vi+z or1t2u w+hd8z5lzr j; a

The Earth moves faster in its orbit around the Sun in January than in July. r(0q.)zwzv3oi rlz ;n s-g2fmIs the Earth closer to the Sun in January, or in; s2n-gforz(.iw rm 3zzq l0v) July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a 2(gciavm5 kp,rb3k 4grf/aknwm x.7, moon. Explain how this discovery enabled an estimak, .imgr,c7(b/w5x42kv3f mr kagnp ate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mom qajdld29chh )s4hh :18kdf4on's. Yet the Moon's is mainlydl1q 28dj44chha)9hfd sk m:h responsible for the tides. Explain. [Hint: Consider the difference in gravitational 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 1980 ne*1b .mmke hz*0d j1f$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 w x9si xvx 0z5)*.olvl klo/j1in its orbit around the Sun, and the net force exerted o oilv0oxx *)95jw. 1xzl/kls vn the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on.*- ;ea8bee5 agaznfe a 2.0-kg discus as it rotates uniformly in a horizontal circle (fe*8naz eea; -.ea 5bgat arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fr,ynk3-2k jjb,b xmb)e om the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shut-e , kyjbkbj2x,3) nbmtle 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 ohe0n ppk8zg.b oc ;)(mf a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dbgpe nh80zo;()c. pmkiameter is 32 cm?   

  A ball on the end of hfvalo3 )nu ((a string is revolved at a uniform rate in a vertical circle n)(vu l(fhao3 of radius 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 ct96.lctf3v sr ar 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 indes9tt3 rv.c 6lfpendent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the rb7be;sv2 , d(hn+cwzeoad if a car is to round a level curve c w,+7sbdnhzv2 ;e(beof radius 85 m at a speed of 95km/h ?   

  A device for training astronauts aj m jl00*wq/gand jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the m0g*q l/ jjaw0force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from thei-h/sgr f6j0: kko6ym axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fkhy oj6- 6 0r/k:smgifixed 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 traveling62(vjzbgn+2ouasg /aowhr ;qy4v( p- when upside down at the top of ap26( v(nba/g24vogswqyjr a;+o-uzh circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounff /n1(roajkq *n7k 0tded top of a hill (radius =95fr 1at7*qkkn0nf(j/ o $ \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);szg rrf)oa *d -8tlt minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlesfo rd8grst*l;t -za) )s” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical ci;-dy psnx1)c frcle of radius 1.10 m. At the lowest)yfc1s nd -x;p 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 8c6dm m3tgg wz2yd6d( da ,k(bcentrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of w( am6 86dg3cgdkymdz,tb2d(115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnn;p 1bxn,bg- gival, people are rotated in a cylindrically walled "room." (Sp;g bxn,b-1n gee 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 circlen 6;bowl ku:,n on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling bloc,nn6b kwl;o: uk (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 tifo n;gq;i7vaz08bu6c me, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find tn g o vu;c6qia;zf0b87he 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 e8us0wj0 ckkt033 a to0negt*hxlp (*88 m 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 massesvu qt c hltfr-7tl 5vp4d1(;uk+.n4qy $ 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 7m l,xsz 09ry)maoctbld63z- 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 tangential and centripetal componentxcf;ja *j84lx s of the net force exerted on the car (by the ground) in Example 5-8 when its spefxa8lcjx 4; j*ed 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, goingyhvv / ptr- o37cx*tz; from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial accelerah;73vzr tp*o xcvy- /ttion 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 radiusdi6dmq1r*z a , 2.90 m . At a particular instant, its acceleratio6zd * dria,1mqn is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s graviao3/ ;2pn:8fdg6f 9tgkvy ivz i9knl5ty on a spacecraft 12,800 km (2 Earth radii) above the Earth’s sf:kig/; 9pvnt 8yzl3od5 fan9ig 6kv 2urface if its mass is 1350 kg.   

  At the surface of a certain planet, thcwe hs o+6;9cje gravitational acceleration g has a magnitu6s eh+ oc9wc;jde of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on4x 58 il )gthzzkzs-:z the Moon. The Moon's radius is 1.74 li-4z8tz 5 zk)sgzh:x $\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 thaty1 ;6092kxvdtlnjr vn of Earth, but has the same mass. What is the acceleration due to gravity near its suy rl9 d16xvjt;kn0v2nrface?   

  A hypothetical planet has a mass 1.66 times ;4u:v z4tqp dpthat of Earth, but the same radius. What iv;tp:d4 4zpqus g near its surface?   

  Two objects attract each other gravitationally with anuj0xv-czqm yrv+:z8c y ( g+3 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 , th7mnk 51v p gxgsqp7c52e acceleration of gravity, at (a) 3200 mn7x p1pc 7q2m5gvg5sk    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s ceny3rmwiqve :68 pk ze;s:nmw u6c:u:(l ter to a point outside the Earth where thegravil::8u3 ve(ew 6; c :rn yup6ksmiz:wqmtational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a m ,bqma;y0 0)hkq :z2qa6h mgzeryc .7-*prq psphere aboutr.z*y;a qe 20qr-7)mamg h:c6qk0 bqp pzmy,h 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averagez0sjkanwx )k(/9h c3 y star like our Sun but is now in the la zk0 3)hx scjw9(yk/nast stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronaut 39jo)o+nf wd3rx.rfjs 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 gravity 250 km above the Earth’s sur r9 drofjx3. j+onfw3)face in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square +dt,d )e;3tyyhmh rq*of side 0.60 m. Calculate the m d3yh)h d*;tqrtyme+,agnitude 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 sh+hng u4o7ig+dz c/-xqx;he 3ide of the Sun. Calculate the total fx un +c -7xqe4h/diho+3h ;gzgorce on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration-- vtos f.a3jso+- hpl 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 hp ao+ lsjst-.ofv3-- of Mars.    $\times 10^{23}$

  Determine the mass of the Sun uy8 +y9paa 3n m2mn/wzqsing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answm+n pm 39aa/2wyz 8nyqer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving inh-a 9 ljd:;aoh a stable circular orbit about the Earth at a h9o:dalja;-h height of 3600 km.    $\times 10^3$

  The space shuttle rele f6e-ol;c ;wzyh(7p cnjfadc -:5 5beiases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (r (fw5cpnz-l-j;:5dbc7i yo6ce;eafhelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants:p7 rq(+ dpwe.gvxb0c are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 3gw7v .qr:xed +p0 pc(b2 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes5au)xw(rlc kw;2.ve ohb k6:p for a satellite to orbit the Earth in a circular “near-Earth” orbit k6)wvwkur5 pah: 2o(lbe.c; x. 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 would a satellite have to be launce*yx , t.ls-i ehby(6im61bz ched from the top of Mt. Everest to be placed in a circula e(cesyh1l iy bz*itmb6-.,x6r orbit around the Earth?   

  During an Apollo lunar land,9 5lp 7 ox,l6ejdehaming mission, the command module continued to orbit the Mpeel,hmd 65o,xa 7l9joon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of cixhixkd8u j/p:fx /() g3buf4 hunks of ice that orbit the planet. The inner radius of txibxx3i4 kj:/d/g (8 uhfuf)p he 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 nvytm knplc2z /8n49 115.5 s (see Fig. 5–9). What is the ratio of a person’s appa2l9c4 np8zmy 1knt/vn rent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fr2ksq9t y9t 9wcolqc 9;om the center of the Earth's Moon in a space vehicle (a) moving at constant velocityttc2 k 9;c 9owl9sy9qq,     ----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 oq)pma zul/xwb3 , ,w)pf two stars of equal mass. They are observed to be separated by 360 millionq x)w /m,,zba3u lw)pp km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevatyuu0a -;lrwfoyb*n( n +c6qj1or thanlw(or y;6auf*-qyb 1 0u+nj ct moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. Thg)9semr*7 ,n g(qtipge cord can withstand a tension of 220 N an9,rpgg t7nsi)(m gqe* d 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 surface o yxvej3 g53r 4hg:fq8uf a planet with period T , the densfu:ej3rxh4gq5 8 yg3v ity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 m;ymop92 ras .d) to determine the period of an 9pso y;m2arm.artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundr;ngc1v5:x tq0zw k.oi ed meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fvqoz1ncx.5t :;0ig k wrom the Sun?    $\times 10^{11}$

  Neptune is an average distance vn k;+tij cx+k;0zd/aof 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 tho21qxut.y h/)+i nvg9ga v qt,+a.ne ke Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance fro n/hx+v2it +y,.kv ngo.gaa9eq 1)utq m the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga fqxruw+x2 7zbpc616i laxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,j-zam /jl.bnz4.ay t,. zfl(kxleavn63o5 ;r period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609). y/3;lan raz.l-tvnx,k5j 4f.zab. l(jmo6ez
(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 of the Mooxmcp3 sa:y /lxgv0m+6n. 0s/vp:la m6x3 m+ycgx    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using K7(8 u sb hgegf,m.p4eyepler’s third law. Use the distance of Io and the periods given in Table 5–3. 4u shg7fmy8 (pe.ebg, 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 cr 5 :l;lm,y7biscur ll8rk+jl-9g 8 x(which some space scientists think came from a planet that once orbited therig r-bmrslc jk+l 8u;yc 5,:7llxl98 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 ot+ .;4/ q ffefhlts1e ln/f-h5mpjs0 "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 Earth. What will be the period of revolution, this planet's year, in Earth day .05h-/efsp 4f1jlhf/nfms;otelqt +s?   

  Tarzan plans to cross a gorge by swinging in an arc from a hangin)j1tt ratwg 66g 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 lowest point of his swing1t6j tg w)ra6t? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what q8j rq -v:v3e) atq2(xh,epdait is on the sudtj2 qeq, qxh a:e(av)vrp3 -8rface?    $\times 10^6$

  On an ice rink, two skaters of equal unnqcq2. (+,ke tgr6pmass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 r6,( q2c enqp+k .tnugm long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once ww/aqh8z uv4jkkac -f5g, w:; 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 fractiongzk v 4wqajc,w; u/8 -a:fh5kw of g is this?    $\times 10^{-1}$

  At what distance fro je-hy*jj0zf(z.d,jx;5 .h1 qzthqst m the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Eart jyezj;hz.ht5h,q sqt-j(jx1* z0 fd.h and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand oyn6;t3;f*nf ca hvky 1n a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directionfnhy;vn 61ta3kf* yc ;?     ----待选择----upwartddown 

  A projected space station consists of a circular mza ogr/t 466xtube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–/a664trxmgzo 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 in a)tbl+v+8t ,0fqdsqbh q 4r (bj 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+)h1n7mohi o: a/o adu terms of its radius r, the acceleration du/oh oui7hd:a)o a1mn+e to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging870,ix 7l vts8uqsmdq on a string) is deflected from the vertical by an angle sl877,mdvu8q t0is qx $\theta$ 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 ry*nu l2d vv3wz,m+us a)g .+oa design speed of If the coefficient of static friction is 0.30 (wet pavement), at what ral yv r d+.mvnwz2g)s* +,aou3unge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating slpq kp*(+ mrn4b9qnak/ 6qb .mo fast that objects at the equat bk4nbpm q. l(/qrkm*+qap6n9or were apparently weightless?    $\times 10^3$s

  Two equal-mass stars hzlp4y er,gs gy/*,d4maintain 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 radius 235 m c y: d8j,;l8bxyfcb8b. A lamp suspended from the ceiling swings out 88fbd,b ;j8c:b cy ylxto 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 h q8eewm)a b 67jo8ocb*as 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 the equator of such a planet. Use the followin87*wme6c 8oob ejb) aqg 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 Teleufk71ibcx8 4) 7 fxrmmscope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the co)k1x748mf im 7bf xcurre to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown iniz852nbhg bb bxos7; lbjo :,2 Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) 2bhbb,x:b lj8oi7; sbzg52 noHow 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 Positi bzh0-*7 uxnvmoning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of eacu*bz x-0 mh7vnh satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bilf8/jm c3m9xbfl. ,n eglion km, is meant to orbit the asteroid Eros at a height of aboul fbnje3g9 ,f/mc .xm8t 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 pursuiwtsg.*uix x/s j b4co9s:i1 7tng a satellite in need of repair. You are in a circular orbit of the same 1g coxwb *: i9/j7.xssts4 ituradius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its gy, 5ubbn95ms mean distance frb9 b5,m5uy gnsom 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 vals u4al2yk.g3u ue of G would need to be if you could actually "feel" yourself gravitationally attracted to s2sua3 4lu.k ygomeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-r5 0gryzud+r88p; gbp 46) at a distance of about 30,000 light-years fro0 bgdpryrzg 58p+r u8;m the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.2((v j lkescli()cjx d t2o8 3pq;man2 czi)8y50 m on each side. Find the magnitude and direction of the gravitational force ojc3zcvydo)q l(tpjc2s(lai ; m k 82 n2ix)8e(n 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 orbitsbfhu c84fox*w 8s7is- 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 /j*c r;j. q(.oktv ugom/- jxw*-vlavsweep second hav*l*tvguack-(ow- /qj jj .;rmov /.xnd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and starltdeonp6wl a): n(en 521vx: rvf/+gyyjm(/c t to swing a sinker 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 lg2 elynydxo5:(/entcvp+(fm )a6wv:/ n1 jrangle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway7k /0tk1l ec+ d07p1jwlzzfbp is designed so that a car traveling ab kpek/0j+ lfzwpd7t 117c0zlt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatinbbf8 ffzn90h; g curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the trackbz 0nhfff ;98b 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.$\approx$    $\times 10^2$