Sometimes people say thatzzuc,dmk, hhr2/ wntf-o5( 1 i water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statem zik,,-t nz(uhrcf ho 1w5m/d2ent?

Will the acceleration of a car be the samecn34;bp8u x kyi i.z6f h)qpu5 when the car travels around a sharp curve at a constant 60 km/h as when it travecf; n5ukxi4i .z yuh83qpb6p) ls around a gentle curve at the same speed? Explain.

Suppose a car moves at const2,jr.4f7rl ujbuvkf/ifer hr+:p+ k6 ant speed along a hilly road. Where does the car exert the greatest and least forces on the ropuf efvr:hrrbij+.742 kl6 j k,fur/+ad: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a 7mfhe;n v(ex:horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chih;vm n(ef7:x eld?

A bucket of water can be whirled f*yvnw/+ /pm f vosp84in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain.mvfppof4* swvny/8/ +

How many “accelerators” do you ha1 kc3)slg qwio9qj9(u ve in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What aq9l13koiqu (sg9 cjw) re they? What accelerations do they produce?

A child on a sled comes flying w iq2w7lh+ 2ouover the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he do72uoiww +h l2qes 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 inward when rounding a curve osv(z1(xux/0dc 9 hf mat high speed?

Why do airplanes bank when they ttmq.,( spp:y nurn? How would you compute the banking angle given its speed and radiusn sypptm:(.,q of the turn?

A girl is whirling a ball on a string ao/5/9 hiabungm 1pq1lround 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 stringmg 9q1 bop/n1 l/uh5ia?

Does an apple exert a gravitational force on the Earth? If so, how large a forcejs+f2 ;dm2 mg oq2k8tb? Con ks;mtogq2 m2 d+8bf2jsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double fj,n5bl6icp, what it is, in what ways would the Moon’s orbit be different?pjb 5f lc,ni6,

Which pulls harder gravitationally, th0;cdj l5q6myg ys;w k/*z9a zne Earth on the Moon, or the Moon on the Earth? Which accelerates6y; ckwlan/*0my q9 sg 5zzj;d more?

The Sun's gravitational pu2wo5y:dhn jdxykg:1jo9 a+lrgt(v 2+ll on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pohx(dyt:wk rn92j vg52ogy +:d1aj l+ull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effeciug /cw 8uf(*zts are at work? Do they oppose each * (c/wi8fugz uother?

The gravitational force on the Moon due to the Earth is only y. 5.uulkqgn 1+cr8 ubabout half the force on the Moon due to the Sun. Why isn’t the Moon pulled away bgrlnu 51 yu.uc. k8+qfrom the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largerf v (hi-eo2ba) or smaller- evh(i)obfa2 than the centripetal acceleration of the Earth?

Would it require less speed to launch a satelm4:z pc+b sbp5lite (a) toward the east or (b) toward the west? Considmz4 c5bsp+ b:per the Earth’s rotation direction.

When will your apparent weight be the greate felhnb8ydr/i6p s 3)he t:1be-7,j rjst, 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 h6: 7per8erlb e/dn )j3 t,j1if sbhy-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 per7w1qb-sli +9/b ouw ijiods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Considewuio+-j /1wlb9b i sq7r (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” pmr. qr)8rk6qgi4nvdo5 r v::or “apparent weightlessness” betweegp4qmqrr r:n5)v6:kdriov8. n steps.

The Earth moves faster in il69rc e .mt .e0,iz) xs6uuav6ky8wo mts orbit around the Sun in January than in July. Is the Earth closer iz.emu)ak.mx 660w68otuy9 sv, e crlto 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 Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not kts1 u 87.pjjmmz r q(ny k7x4- sa39kgj06iharnown until it was discovered to have a moon. Explain how this discovery enabled an estmnj(h 16jjsza7yk3u9rpq aix t0gr sm 8- 4k.7imate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much 3d y8a2mjx d.u7re bw0larger 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 the Earth to the other.]A child sitting 1.10euym dxrb. d07j8wa3 2 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*/ni h6hzlgwmtf i +c5 .t16pmlv +o-t0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 around;5 ,nf.kbum y4obf,ndm *ylqsg-9e 9t the Sun, and the net force exerted on the Earth. What exerts this9,g y5m4u.tsbql nfymb e, fn-9*o;dk 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 a 2.0-kg,b)9 4fupghzl;hkr u sfu:* :w discus as it rotates uniformly in a horizontal cirhhff) r ,bz:gu u4sp;u*9wk:lcle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle 7fn) f k 3ets8iw0;lgjis in orbit 400 km from the Earth's surface, and circleslf0g fn 3)7wk8s;tjei 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 gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acc7hdk;p9 7avd b ,(eebjeleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if j vpdbb,7(eha ke7;9d the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform r(e*zvwu 4j ;vkynrw7 3ate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spuew*4 vzky73r;(wnv j eed 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 w 10uvoge.ly r:pr; h(g6jv9jqith which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient h.o(gjqr 1r:90;vvgpel yju 6 of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of sta gu(m;m q88bnz+bp wdoh33;7qja+i awtic friction be between the tires and the road if a car is to round a level curve of radius3 gq(3ph; + b8aj8;qwi+wmzo7amu bn d 85 m at a speed of 95km/h ?   

  A device for training astronauts and je gz6 l8tqds/;65 2t3a zfps1pp .remjut 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 p65; 2gelu3 f8t/ rpz.qa jpsdst6zm1her 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 turnpcv 7,wojh owtx ekwt8 2n41,0table of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slid ko12hw,n7jxvc4, ot ewtp 8w0es 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 nn15a)oeh)wn*s ,ejdupside down at the top5e*) )nnjad1 hs n,weo of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (inclupky d r1mf.s,4ding the driver) crosses the rounded top oy4 .spm,1fr kdf 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 a 15-m-diameter Ferris whee3 qyv1tk)y*x 3 g js5iq.2vudsl need to make for the passenger1 s kjiu.5vq23ygs tq*yd)xv3s to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of raj m ghy+u+w+t 2pbb yx)0f6-padius 1.10 m. At the lowest point of its motion the tension in ta )2ybubph6yj-+fmw 0+xt gp+he 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 axja)u)hido+ - 5- 3,acmfysm pris of rotation is t-f) +3oam,rdmu)spc5 h-i yjao experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wall k8*sobw3cbiw i0b9 8red "room." (See Fig. 5-3s3*ibibb 8rc9ko8w0w5.)
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 frictionless air-ho0frllgbsgd7hfmk 46f5 1o( /fckey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as41b g 76hmgflodffkl ( 0sfr/5 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 nzzr+0v9kth/v eh3,ve w7-w vqot ignoring the weight of the ball which revolves on a string 0.600 m long. Iwz wq3+hv7k ,vt0vhezv 9e-r/n particular, 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 ofc pqxy*9bbuvm+ y l;.2 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 masse ij0khww01 q *od:w5fo.x,ty hs $ 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 mane:j 6/2 tmkr:x) ilxjzmc37yrguver 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 tangential and centripetal components of tye7k2yhy ,x++-xucmehe net force exerted on thex+eu- 2+x cheyyk,my7 car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 aviatn22r* 5uzccelerates uniformly 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 acceleration of the car when it is halfway through the u i*nrvz2a t25turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . A +. nos oowr4ci hwto7d/9).tst a particular instant, its accel+ .dhs4owo )7sr/ 9t.woon icteration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecrafq typ+z 7j q0b3/lqm(ot 12,800 km (2 Earth radii) above the Earth’s surface if itl(q+7q jb03zo/tmy qps mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acce)k ,/lwhlqur,leration g has a magnitud rk,wh,u/l)lqe 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 on the Moon. The Moon's radius is 1.b-rau 1a49r nu7nr1u aaur 94b-4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1d9-cirks v3. o.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near itsr3-v. cik9ods surface?   

  A hypothetical planet has a mass 1.66 times thatxs)-1wm ow5kg fy1 dq1 of Earth, but the same radius. What is mk xwf 5-w1goysd1q1)g near its surface?   

  Two objects attract each other gravitationally with a fot: d6*kn;erfz rce 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 gravitjh 9l:k3rg ss9y, at (a) 3200 m: 9g 9slhj3krs    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to +:gkx4)fucdzb1 n+ mqa point outside the Earth where thegravitational acceleration due+4q xc dmb)k:f +gz1un to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five tib3:b v2c xd5emhzw h.+mes the mass of our Sun packed into a sphere about x: 3hdbzvbche+25.mw 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarsit4/ 9ol6x. c kibl-8nl5sm vf star, which once was an average star like our Sun but is now in the lm s/5-kosnb.il t6vx9i 4cl8 last 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 astronauts feel weightleqd px*7tv7i qjq4e w.*ss while orbiting in the space shuttle. Your friends respond that they thought gravit *ieqqxj.vqd p477w*ty 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 square of side):0zs iv (gwjd3i; ujg 0.60 m. Calculate the magnitude and direction of the total izvwg)j 3u; g:s (ijd0gravitational 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, ct bmja6cng. jrrz-a/ 7h05p on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masb7aj 5zt.gmajrc ,-n6h/ r0cpses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Maslbs/ y ((wh*jrs is 0.38 of what it is on ls( jh*s/wby(Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known9 nvp1vhkpr/sw l:zu- t4 nq01 value for the period of the Earth and its distance from the Sun. 9 / p14vp: h01wqstvur-nlnz k[Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circu),v6i4rbf ssh lar orbit about the Earth at a ibrs),6 4vshf height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a c9q44wbmy2n quircular orbit 650 km above the Earth. How fast must the shuttle 4 b94mn2quqwybe moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expezfok o - 55d9v;oy:t)g /fl,ree,qbf wrience simulated gravity of 0.60 g? Assume the spacesfwr-v) g:qfey, d 5tzolok/e9b5f o,;hip’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit t7 rg;je3yeyu.q u3. uvhe Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does y 7e.uug ruqyej3v 3.y;our result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hod+q9 bdae;e 0* g/zqxave to be launched from the top of Mt. Everest to be placed in a circular orbit around tez *x q0 +e;ad9obqdg/he Earth?   

  During an Apollo lunar landing mission, the combc),nc,a:hu v9zvv1 /c nz4ki mand module continued to orbit the Moon at an altitude of about 10zcvc:z,v bkc4v,)un1ia9 /nh0 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are compo a+kje*3nvg/i sed of chunks of ice that orbit the planet. The inner radius of tkgn/ja *i3 v+ehe 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 15.5 s (see Fig. 5–9).if h a*q7tj +lcm8(ef. What is the ratio of a person’s apparent weight to her real weight (tqmi.eh a8(f f*7jl+ca) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from, va9/2nc4dhh7,djo. zf h9xu renis ) the center of the Earth's Moon in a shhdhxac.u) ode7nf /s 2z 9,i4 r,jvn9pace vehicle (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 two stars of equal s* lf36 uydaw4mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betw l yu3*6dafws4een them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman 4n+c2 xhui z8 fr,,ghdin an elevator that m 2hgh8nucifx , ,r4+zdoves
(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 fr r mu/g2d4.;8rxhwblvom 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 (mag; vh4d/ wm8 .gl2uxbrrnitude and direction)? a =   

Show that if a satellite orbits very kqeo7k(*ixl+ near the surface of a planet with period T , the (ioq+7k *elkxdensity (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 d) to determine the period :.xx1sf dum)g-e+ysz+ m owe8of an artificial satellite orbiting very ndf+exm1).smz yo :eguwxs+- 8ear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, o(8hrzvrmn jmc*b* 9p)t.nn 9 zrbits the Sun like the planets. Its bvhtz .)pjr* 9mczr9n *mn8n( period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average(t q dgqn j6hrt blrq8 63aw9925qd-m0clhgp0 distance 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 Sunv :e , ruho/0oy7imi7v 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? [ ,vi h yo7:0v7oirmue/Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about wmsc1 )p1sz:xthe 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, perioq wxhdygs-w8:+b+ kn 4lm/lt .d, and mean distance for the four largest moons of Jupiter (those dimwsd4+g +ly x8/.n-bhtwk ql :scovered 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 distancb2v)ij(c 4hdt3nn tzq43sdg2e of the Moon. 3 4nt)h32jtdnvis c4 d(g2qzb   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Ka3 j3z0l,cit oa e4l1zepler’s third law. Use the distance of Io and the periods given in Tzatjel4 0,ai331 lc zoable 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 be3vqgj g1 9l/setween Mars and Jupiter consists of many fragments (which some space scientists think came from as9 / jq3egg1vl planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the fdi/gunb 88) czs5nv+2vh d /uhorm of a band completelydz8viuu+ hh)g5n8/2 d c/bvns encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by sj67fg54n5w v:xzs 0 ptxvo).f.r razbwinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, whv7.xr0 gn 5w4 svpfjxf.56)baz:ort zat 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 ac /pl*ej emod i0h+0il4celeration of gravity be half what it is on the sur0m/e*0jlodph +ei il4 face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual ciranoro5bu 1b 48cle once every 2.5 s. If we assume their ob85u n1r4bao 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 once per day, the apparent acceleration of gravile01ch i xt ebey1b qeku6af-3y)+*elf41 ( jqty at the equator is slightly less than it would b*b f0 eqe+y11-eqkyu3h6i 4xjt)ela1ef( lcb e if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Ear6kf6o-b9xolg gor : )jth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the E6g9go 6jbo)rf - klo:xarth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a x2/dgv8 ly,qd*. ;hiy 48pv2jbh kgwfbathroom scale in an elevator, it says your mass is 8 2ibk /vd4qypy f jd2l8h;*xg.wvh8 g,2 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistsv)5ge1qm c:ir2s6 m7rq kxorwh dty2 76;2vna of a circular tube that will rotate about its center (like a tubular bicycle tire) (mre h6 22krd rix)wnv :g5 2sy1ta7cqov6qm 7;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 in a vertical 9td;cig /0x5wen u1ogloop (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 radi/1:*wlfd*rk 9wkj5:e n0 a bnphcwf u7us r, the acceleration due to gravity a:j c n9a051/hk eb* wludf7:pfnk*rwwt its surface and the gravitational constant G.

A plumb bob (a mass m hanging o3nnjb kq4(f.rb b; u)ohq0u2xn a string) is deflected from the vertical by annb k;nh ) uq4.qo (j0xuf2brb3 angle $\theta$ 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 xfl1 f.i9yhtot+o01a banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safelt1tioa0 +1.hflfx y 9oy handle the curve?

  How long would a day be if the Earth were rotating ora l+m:pn;+. ovy; cuetbwqo +k0v -/so fast that objects at the equator were apparently weightless? v a m+/+eo yl:q ur ;ovwoc;p+kt-b.0n   $\times 10^3$s

  Two equal-mass stars maintain a constant distanx0om *;dcm q30q joc1l 7vop/ice 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 roundxdmlyjp) em 1m r;4,qrvm3 0dp3k pd+0s a curve of radius 235 m. A lamp suspended from the lm0pr; ,j4yp1 d3vm ddm+)0p x3mer kqceiling 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 Earthvzxlz 27b ;nb6)nbx+s . Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator 7z b6lnv ;zxbbn2x)s+of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence4e v4x b0atk5r rci 10knd53zf 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 spek4 0axr4kbni1cz5 tev0f5d 3r ed 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 as it traverses t5+ st1/ l0gjcuscot +ohe hill and valley shown in Fig. 5–45. Both the hill and vtso ugl/t joc5+1+cs0alley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 sater;i.u n4a yvy.llites orbiting the Earth. Using “trian.4nvyry i a;u.gulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR 94+m m7 f dl7,exu9/zus zjfx2x7agmy), after traveling 2.1 billion km, is meant to orbit theam2 z f,+ s4xey9 jfml77ux9m7u/gz xd asteroid 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 pursbfb 2q(,x2 pseuing a satellite in need of repair. You are in a circular orbit of the same radiusb q2,fpxsbe2( 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. (aw a- l6yg;0fkektgh57w (2xip ) What is its mean distance frow2 gik5y-7x0w; f p6ktah(glem the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "x d,j m)8 di5dm5hg3icp *bom6feel" yourself gravitationally 8)6 di mbx5 oi*cm3hpmgdj5,dattracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) atq :fn,xq2gm l:.p9s fy a distance: fy,nl9s: 2mpqf qgx. of about 30,000 light-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 at the 3(a 14mng+m37upzd/u, hduaa t3mj bfcorners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the d3 z g (uatna 3mp/+f7juum4hadmb,31square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbit d*fyec)/3(e )geogwo:u:- itce p r2us 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 1.57yly9c cx// ab-cm-long sweep second hand on youc7yx/cy9lb/ ar wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing ac1 w3hv3ie19 hd0usnf) 4yhjcv / nfc;42xpfv 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 angle that the vs3 p/f vhn4cce jvd4in;9 ffwc1 0h1xy)32uh fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designenan5 b77c:fuyd so that a car traveling at fa7:cb5n 7 unyspeed $ 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 te4d mitq1,e)2l(aqkop6g7vz4prr9 h)m un 9f ilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius gk qp dur9,t9mo mz6alq44efpv7 )r(2en)1ihof 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.$\approx$    $\times 10^2$