Sometimes people say that water is removed kpx 1 ,zuz2d,l0ew2pg from clothes in a spin dryer by centrifuga lk ud10wp zzpx,2e2g,l force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car tranmhsmt 7d u2xg 463bx,vels around a sharp curve at a constant 60 km/h as when it travels around a gentlex36x2s47,nmb mudgth curve at the same speed? Explain.

Suppose a car moves at constant speed along a hil rj/qaw2bz v2e(mn 09/:5nip;sl xzfz ly road. Where does the car exert the greatest and lealfzbzpqm/rjseni:xn 09z 5 /a2v2 ;(wst forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wh7ts odqe2jt2 w 0cfz(e e)-3ii9 xln/gich of these forces provides thec z9x0j7ee/tg(2f3o) 2i-elq n tdwsi centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water ilxi:+b k aeepn5c)lwh7s 800spilling out, even at the top of the circ0n +i5 h:08bw lpekcias7l )xele when the bucket is upside down. Explain.

How many “accelerators” do you have gs )bvex5t,nf* g4t a7in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they4 7 5ta s,xte)*gvnfgb produce?

A child on a sled comes flying over the crest m2yt hhjnhu19dy)m :h5q*vmx x.hq770 io f8t of a small hill, as shown in Fig. 5–31. His sled does)7u njx h my0 t.vtqhi 8yx5o1dh mq:hm*792hf not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve a6 o4 fxbf4it,at high speed?

Why do airplanes bank when they turn? How w8w xqaa zo9t2,ould you compute the banking angle given its speed and radius of the x92w,o 8aqza tturn?

A girl is whirling a ball on a string around her head in a horizolmgn oqcump/6a(v18 +ntal plane. She wants to letao1(6v m p8mulg/ +ncq 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 string?

Does an apple exert a gravitational force on tr7u4ew qb 0o2qfpbwt ad4*s:) he Earth? If so, how large a force?)s0p4t aq ww d74f*e ubq:bro2 Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wu7k h6ue0 eg.jould the Moon’s orbit be differentuug . k0e7j6eh?

Which pulls harder gravitationally, the Earth on the Moon, 0hg.da tc;0u lg2zh5t 0)rmrh or the Moon on the Earth? Which acce0; 5t ag)l00hgrhz2udr t .hcmlerates more?

The Sun's gravitational pugr; h 70qc tnb5o/*rytyijwd1k2 dt15 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 pbq1t rkyd;y1h25 / c*gnrd0tjt7iwo5 ull from one side of the Earth to the other.]

Will an object weigh more at the equator or at 370ol:o e.e tbtsifb) the poles? What two effects are at work? Do they op:7 tbtils b o30e)oe.fpose each other?

The gravitational force on the Moon due to the Earth is only about half /ugiq*vqhs, 8the force on the Moon due to the Sun. Wh*q i,gquvs/ h8y isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arouni1q(k5bks)3w3 t rmsj d the Sun larger or smaller than the censjrbi3w35tk (k1s qm) tripetal acceleration of the Earth?

Would it require less speed to launch a sat/pbwz) u0as(7 qh0tjxd o -8vnellite (a) toward the east or (b) toward the west?p( vuwoz0/8nxdq0b7 h -ajst) Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a sci +1*m7ktnqqp95 tj k..dt r yv2g*jrhale in a moving elevator: when the elevator (a) accelerates dowhtt5**qtmj9.y.7kr d p2rjqgkivn +1 nward, (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 i7x3jjuxm0mne vyt*3 g/y* 1st n 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. 510*ttj3xnyjy *m3u g m /xs7ev–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 “frl5t9zuz+o 0 bue-pa(f ee fall” or “apparent weightlessness” between stepfz+aeo9ptu(0 -l z5 bus.

The Earth moves faster in its orbit around the ys rrc.ym( (:d1(spdm+ n5phbSun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is no+r((yh ry m.d: p(scbmds1np5t 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 moon. E4nvfyb1 olr5e ;*d9 ynxplain how this discovery enabled an estimate of Pluto’s massnoln 5d *r4y1b;ey vf9.

  The Sun's gravitational pull on the Earth is much larger than the Moon'9qv a6t uebj 0sf2l/mf90uwk 84d j)nms. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth tot9jfw n a8)kms62mqld 0uf/9ju0b4ve 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 c t-k+0h- jjvc1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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,p qnh5l ;tul9o p0xtdp- rm*8 of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Ear*h9;pq n xto508,rtm ld -ulppth? 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 exerteo5q.3o*dwwyk 0 x* xgod on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s0yo*q3d.x *k5gw oo xw length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space sh -s;jm*gv7y ie mhs5qly+;l* 5 o6uvfvuttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's sure m+l6 so*5vl;sv7i5jmy-*y; gfvuqhface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on thra)a66wsh inmedsrx9 g/1t:/e edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if rtiw/:asxd96 am/1h r) n6seg the wheel’s diameter is 32 cm?   

  A ball on the end of a string 4kxmb -2c/kei y2q0tm 7 9bqahis revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spee72i b9mamc-0xqy qt h /keb4k2d 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 turn of r0s8,ze yantu )adius 77 m on a flat road if the coefficient of static fric8nts y z0ea),ution between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction bh3 :z3rlx5 dnifblh/m7s5d90k er 5 iqe between the tires and the road if a car is to round a leve5qnr ls5 hm3dz :3 kfd7xbi05h/ire9ll curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilmc0o6zyhdz .f u/em7 *ots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If thee choy*dz6muz.m /f07 force 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 frcrb/qhxwv 01tlegj rpuuzt ::.*.4/ n om the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the tg4/:*nub/w ezlrpq. .u1 hxj0 :rt cvturntable 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 nv *pu 9 crw2zf0tl1uv)t3 h7da roller coaster be traveling when upside down at the topz 01vrn7ltw)2cu3puvh9t*f d 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 (includiq)y)-m,lzoec c 33cn dng the driver) crosses the rounded top qe zlcc3oy),dmcn)3 -of 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-diua-ec)qk8.i4u7w .: s blk kzzameter Ferris wheel need to make for the passengers to feel “weightless”wl)uc4 .:eask.zk7k8bi-qu z at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ver,jo t7z-eeb ec0 p0l7 m/ffls)tical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is e f t0f,70osbp)zelj ec7/m- l25.0 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 rota-y:ro fh66z*9vlex;p jngs8 xte if a particle 9.00 cm from the axis of rotation is to experiencx xr*9 6ph 6;yn:-eszvgfo8 lje an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a 2(pe; 2x 2bkpzv:x fuccylindrically walled "room." (See Fig. ek:v;zpx 2 c2xpf2(ub5-35.)
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 rotate1o mi3,c6tf 3sikhd j;i 5o3zgd in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dang, 3izm;gcs5 ij1t6 3oikdfh o3ling 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 , pq l .:es(xeml2recisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mag:m.(q 2xeslel nitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectlynmm4vn22. x5bzryl z 3 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 massesttgi io5wq g;j +wu 4xsnkiv(t.+*u.7 $ 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 d8lqydm7 w08 wciving 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 eb*fv+ r(yt 8mq- 9dal8 g)raszxerted on the car (by the ground) in Examplvb)y- 8zsad ga8t 9r* l(rqfm+e 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit areaa 2wfl; 17f7vd n.oven, 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 turn, assuming constant tangential acceleration. If the curve were flat fnf en.lvva7 wd71o;2, 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 2.90mxaa lsbjm3n.08iz ajl03e/dt *b.idpy-7 ;v m . At a particular instant, its acceleration is 1 txbdve i.0b0jp .mal*3 as n-iayd;7j3m8l/z.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 spo:y;( ev0ze hmbmu4 f+b-huv 7lmzf5)ygt 0+ cacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its masszv o+yf huz+c umyfe405-0hm(bb)g : 7me ;tlv is 1350 kg.   

  At the surface of a certain plan5s7k *8lt 0cgfi eco )qib3q+qet, the gravitational acceleration g has a magnitut3iog ) qs5 fkb+ceic7ql*80 qde 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 tzsecxl -:+3wij 0dq j6he Moon. The Moon's radius is 1.74 +x6s0zcq iw-jel3d :j$\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 o2 (tvp28wobtnxqk nzwgw 0 :vy*,4k3zf Earth, but has the same mass. What is the acceleration due to gra 8wzn qp 3onzy2wx42wt( tbvv0: *,kkgvity near its surface?   

  A hypothetical planet has a mass 1.66 t 1oesisyw68s8x;qk ;2c)ymtpz,bzm ; imes that of Earth, but the same radius. What ioesmw;xt8 s)y, 2;zpk zcm1sy;8q bi6s g near its surface?   

  Two objects attract each other gravitatio-kbbw- sr; .fcnally 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 g tk+q87lxm i1hlc/,ac ravity, at (a) 3200 m /h klxic1q,8c a l+t7m   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eartu nqh 5duz3t5g3wwl;6 h where thegraviuu hd 65 g3tnwq53l;wztational 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 mav,3 krn qp9-ox9zdj t,e1f sylf7mx 65ss of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this morx dxpvj 6k7,1lqf5s-ft e 9m,yz39nonster.    $\times10^12$

  A typical white-dwarf s32-psz6jollp, gu x; wtar, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon bu2-z op s wlgj6,3ulpx;t has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feei lhw:5t1 8mmaxtz6 /tl weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince 5xht:wi m8tm/zt16 althem 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 pk f+x+;hn9 7yielagjfm h4 /6at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravit /l ef+i+9n kya4hhxj pmf6;g7ational 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 theq),l ayd1xd v9(n :zq )utgg/j same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, dljva1 /qtgq zy(ng, 9dxu):)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 of gravity at the surface of Mars is bt5g)0 i5p0n+xxrg bl0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.xrg0xtp+)g b b5ln0i 5    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eart ifo;(47.(majzzr objh and its distance from the Sun. [Note: Compare your answer to that obtained usjo( a4.;mo f(rz zb7ijing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellit g:,gcwpf*y+w0ok f a*0(bbte e moving in a stable circular orbit about the Earth at a height of 3600 km.0fwopgcfa*+y* ke(t:g b, 0bw    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above thnc/lc c d2uepam29 +iic3 9:ppe Earth. How fast must the shuttle be9:c+pac2i 3 linpmdeucp/ 92c moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occup3q6 r+rko.bx+3c -l4uma knm pants are to experience simulated gravity of 0.60 g? Assume the spaceship’sxm.k 4rca+ql3m+r 3ok bn pu6- 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 toz,kh (ih5*jjcr w10 2nj.nklmbec5 f* orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the sur jk*l0w m1cn*z hf(h5icjbn.re25 j k,face 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.5*gkc1 mg 91kb;b9o * vdklrcmuif:h be launched from the top of Mt. Everest to be placed in a circular orbit arhu. *lkvmfkirc oc g*19;g5b1: k9mdbound the Earth?   

  During an Apollo lunar landing mission, the command module continued to ol 45jr8txu, oerbit the Moon at an altitude 4 ouerl 5tj8,xof about 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 v09p,hlzbsj0 mnu ojai(( 2:nplanet. The inner radius of the rings l sa0 pu(j(n,vi :nbo 9mzjh20is 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.fq7w.5dq yw mnq *,cbvfa k5545 s (see Fig. 5–9). What is the ratio of a person’s apparent weight t 75fv.wq4q*kanq yc5mdfw , 5bo her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg ast-h2(iaouckg i 2 gio38ronaut 4200 km from the center of the Earth's Moon in a s 3h8agu-2oc o (kii2igpace 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 mass. Thewwo8*bs5l q7+ lrc+nj8x 7 cpiy are observed to be separated by 360 million k7l+5 *8s wopn iw j+8clb7rxcqm 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 elevator) uhnsbp 5;as+8a/-dg jc(2bsbm ik7w thats8aw kc ds5u)j;nm h27bib/s+(pagb - 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 suspenq* 0k ej7n au ::t0g)5gztxpqqded from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and dgx ktaqqq07ujtz *ng e50:p:) irection)? a =   

Show that if a satellite orbits very near the surface of a planet with perig0hn bn( c8rglzk0d(3od T , the density ( d0g(khr3 nl(gn0 z8cbmass/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 theuauglj 1abw48.,q f -f period of an artificial satellite orbiting v.aq abu-j1,ff48u lg wery near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters a3qu8rnuc;g3 uatu+a/ cross, orbits the Sun like the planets. Its period is 410 d. What is its mea+3 83ru na;c guat/uqun distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc s8 i8c,zomfi9e 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 ever.gx, ki55+ 9vu mczdtiy 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distancev xt+ 5dcm.,g5iuk i9z of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of 88u k,,blxgecthe Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, a um*cgop/2+by :w rdlj5qgz8; r/ar2end mean distance for the four largest moons of Jupiter (those discoy/;m2r*webro l85q:r/cz gp2 dg+ajuvered 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 Eart rb tos8,o;idg;q4m ha )qn9q;h from the known period and distance of the Moon. q;4bm tgn9,) qahi8;rdo;o qs   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’)vw2pk 1 wj ia/,eacf;s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valu1) /iavcaw p,ejf2kw ;es 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 fragmeph-ivq o r q96,0udr0ents (which some space scienq09u -o ,h6irq0dve rptists think came from a 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 form ofsbmi81hmu :j 3 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 ro sh j:mum318bitates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fipr:qay5 ty. h3g. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximy.q h3patr5: yum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravityxwdp2 c) f-ae9 be half what it is on the surfacead)f9c ep-x w2?    $\times 10^6$

  On an ice rink, two skatu:rs /oyn 59 uf5,psvbers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and theiry uu,p9onb s5:5vs/r f 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 acc2ee1e 2nb p. rcmd7lr*eleration 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 fraction of g is this? le221rn7c eme * dpr.b   $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from tyr0te /-,:6cb+dq k cp9gu yf0r9qz tkhe Earth to the Moon experience zero net:y p9t 6 q9/0bygd0 rz tc+crkfuk-eq, force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 diw.2 idr.; f4vjuk3y kg, but when you stand on a bathroom scale in an elevator,u4w r.iddif3y2v.k; j it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station coo x ni oy(3qgc,s4s1r0nsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42)x(rco,41oy isq sg03n . 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 loop (Fsrw0 5j+ffr p xc-;5c3uw3zjdig. 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 planekd2c-e(p v: wl)v/gxpt in terms of its radius r, the acceleration due to gravity at its surface and the gravitational con ve )d/(wc-vp2g :kplxstant G.

A plumb bob (a mass m hanging on fa72a-ecouza 0w2p, ma string) is deflected from the vertical by an a aucf20eaw, -72oapzmngle $\theta$ 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 dji lswq+3c6za ak8+p 33) nfipesign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of spee p6ni3cpzf lj3k s+iaa 83q)+wds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the ehbjn) z68g+y9jkcog1h(x;g l quator were apgl(gbo 1chn9kjj8 yz;+6 gx)h parently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dist(xb q,mvmz -v7inu; .xance 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 o+rhek4 l 51 , lpbz6:sfk3nyekf radius 235 m. A lamp suspended from the ceiling swinsf:y khnk 1,6kr3e l4 pe+b5zlgs 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. Thu.ovbyzrhzd8 l n4**fk5mj, g)s, 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 of such a planet. Use mkz.o)5znfg*,ljyr 4 b 8dhv *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 thlbnnt 1-tc ei3z )7t6te Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They dtzc1nl6bt37 -ti tne)id 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 as it traverses the hill and +ute 8v9soek4nw9f,-rkcbi j1ry 78yvalley shown in Fig. 5–45. Both the hill and valley have a radius of cur1 jvurck oey+,879bwtyrfs k94 en-8ivature 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 gronm9on8u2lclo r +8 -qxup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can beo2c+m-lo 9q8xu8l rnn 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), after traveling 2.1 billi-b fod+ z.ci)nbv wh8* wg4+roon km, is meant to orbit the h r+8)i nd-4wz+b ocfvo.*w bgasteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need l 0s8c-kal/k bof repair. You are in a circular orbit of the same radius as the satellit0/ 8kbsl la-kce (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 mean distan l90o7wvrn4vp ce from the Sun pvrovnwl9740?   
(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 "3lrv91 wxo oa8 1lytd+*h (ujc u+cy9cfeel" yourself gravitationally attracted to someone near you. Make reasonable assumptwra8j1v9c dolu*y +9xy+ cuh3 1l( octions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arounr nlo 9g71u8cbo3h (xud the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30 xhn8cbl71u9u 3go(or,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 cornv p2fgojz9mi,po)e52 ers of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force i 2,)j52zfeovppmo 9 gon 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 5500ij *jz e9e)o6w 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 acceleratio4qzd xa;e l7(nki0 m:/y6vpiyn experienced by the tip of the 1.5-cm-long sweep second hand on your wrist w/dp4y7aeymk i0xi lv 6q;z:(n atch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a silpi6* te-v,ko nker 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 fiikv t*-lp ,oe6shing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new cok1lu cgo,,zt-v 6wqg 2d3a nr4r0v(highway is designed so that a car traveling agtv kr ,r(6wdo 0g,vn4u 3q c-c1lzao2t 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 wh ;63rplel1isq en negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the ce6q; seplirl3 1ntripetal 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 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.$\approx$    $\times 10^2$