Sometimes people say +b g/eoxwn n +hyibmgl0j*i-89 4r9tdthat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemeno i 9my*0jiwnnbghtx4g+ - edl89/rb+t?

Will the acceleration of a car be the same when the car travels around a ptc.xcy,k-9. yxe6 is sharp curve at a constant 60 km/h as when it travels ae kxt-yc pc .,sx9y.i6round a gentle curve at the same speed? Explain.

Suppose a car moves at constang5 i:9owb6 : oy3 .4rsg (vavx)ukuvobt speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hv bxyu5kvwgvr) : o(oo u.sg3:9b6a4iill, (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 chixs:l*,61heof k,mtiiue ecp)aa4q(;9 x x uc9ld riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleqix:;,u1auh6f kc)c e p,x4 ol 9meietxa(9s* ration of the child?

A bucket of water can be whirled in a vertical cgqj*lp8 bh+orhi(4. pircle without the water spilling out, even at the top of the circle when the bucket is u.hpo *r h+g ip8blj(4qpside down. Explain.

How many “accelerators” do you have in your car? There arecu sqg0ys kup ,/x)n., at least three controls in the car which can be used to cause the car to accelerate. What an/us , .ug) ypq,cskx0re they? What accelerations do they produce?

A child on a sled comes flying over the crest of a sma 3q;,pn. 0f0 b +uyqlnusjzy2yll 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 the sled decrease as he goquq.sbp2y3z ,nf;0nyul j+ 0 yes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle rideragey9x*nj0q6 gopz1ah-0 (m fs lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the 9tz +h 0gs3mh9( cxngha w.w(bbanking angle given its speed andw cxzgg9m3.0n (hh wt +h9asb( radius of the turn?

A girl is whirling a ball on a string around her head ww:q4b oqc u(qac0).,1a cc ioin a horizontal plane. She wants to let go at precisely the right tc1qo ,w:w qq)0c4a cb(u.icoaime 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 gravy p5ew. 8do-- e,sxheiitational force on the Earth? If so, how large a force8p. 5ehxdse,-ey o wi-? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whangouuf5 1o.5fu+p(:e/ yl v eft it is, in what ways would the Moon’s orbit be different? p:fgvn1+o/fe5oe (f5y.uuu l

Which pulls harder gravitationally, the Eart+z/u.w +mhguh h on the Moon, or the Moon on the Earth? Which accelegu+ h/z m+h.wurates more?

The Sun's gravitational pull on the Earth is much la twdtm tj. 7u7c19-bmmu nw5n./xufnsq6z :x(rger than the Moon's. Yet the M7mt. u-.mxxtn jftsu:w qc 695z1w7/dbnn (muoon's 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 e h7qyo-8 cnup;ne dkp7peu721quator or at the poles? What two effects are at work? Do they oppose each oth7 7n7;c 8pye ek1p2hpdu-o uqner?

The gravitational force on thrzwdi cq h+dcaz 2)5;*a xr-)we Moon due to the Earth is only about half the force on the)c ;wrz5-waa*hd+dc2 x ) zqri Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its a ;j8jr/4r wwl(g)i.xyp:vw x orbit around the Sun larger or smayw p ;wr)xl:8 /(gjar.ixjwv4ller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) t*pcs2 njg6 9hhs3e/zmoward the west? Consider the Earth’s rotation direction9sh /hp msg3 nezcj26*.

When will your apparentqsky 0aom(1+nm vo 9:x weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case wou+m n0svo9y1a(oq kx:m ld 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 jwziz9c 7gk-rbetnz 1r)z4 ;* 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. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity yo nwr )z- j1*i7;grzkzb4ze c9tu can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnr7lr7u0 imwk, ess” between step 0ki, rurlwm77s.

The Earth moves faster in wmn -) lmq(i(ir, *fqdits orbit around the Sun in January than in July. Is the Earwlq(fimdrmq*,(- n) ith closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto wa)7ttib :xiw; ls not known until it was discovered to have a moon. Explain how this discovery enabled awxb7;:l tii t)n estimate of Pluto’s mass.

  The Sun's gravitational p/h)cf1q8l nzxull 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 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 1.258l /fzxq) h1nc $\mathrm{~m} / \mathrm{s}$ . 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 u y133bhj5da j 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in itsvi q2ipf 0+ smqng7-)nnhwv1/ orbit around the Sun, and the net force isp0v7 n i -)nm+2f qgqw/hnv1exerted on 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 a 2.0-kg discus as it rotuo a/ pn0jii:u 8t)n7bates uniformly in a horizontal circle (at arm’s length) of radius 0.9 uj 8up0:ntniai) 7o/b0 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the ,rn1 k(tgaq:y2nm3 imEarth'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 gravitati3a r:mnmin2 qgk,y1t( onal acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edgb:uorxw 2 ux2*e of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’x2:w u2uxr*bo s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rateu 2f)k) mob(- 4szkjes in a vertical circle of radius 72.0 ( besj) s4uz)m-fok2 kcm , 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 wiv.e1r6b h.c xqp ja2ym(;qmf )gc)l0dth which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction bem 1ymrqdxpj 2.fa.qhg))elvcb; 6c( 0tween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficij-2,t hxd6uuiv yb21 xent of static friction be between the tires and the road if a car is to round a level cuj2-1ux hxiv, td2y6 burve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rot)mp4pjpjc o vv//n .3hf;4 hcmate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7h/v vcjmc4 3)fj pppnm4./h o;.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variamiw0w m- 4ekpkn (cv*9ble 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 slides off. What is ei*ww v0m pmnk4-c k9(the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be trav5+g7unp u :atreling when upside down at the top of a cur t5+pg7n: uaircle
(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 9 k /tqov1kiio:azwl;r,:i z)driver) crosses the rounded top of :zi: oa)i/1k zqi 9rvtokw,l;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 wheell7e d+qy,jjq0dl3 ju1 need to make for the passengers to feel 7eyl, + jqqj1l 0udjd3“weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle 3 pkz(a7 q;;u7osafgs of radius 1.10 m. At the lowest point of its motion the ten7u ;ap3(k7 ssfaqgo; zsion in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate ir bhdeu3c-) g91fm:has(p zh1f a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000- ) a:1(hgf3zrb9shpuechd m1 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peop,ggbqc5et4xr 0x 5 4k;orxz;p5kgbn33c a 3inle are rotated in a cylindrically walled "room."3cznqe5ot;xx a,rr0 k b34 g5 cgx5gbn4p;ik3 (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a fr:vgrw7n ikk8ll. 1nq a1f 1i/bictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cenwvgnfql.i/8lkk 1 iab 17r: 1ntral 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 thlhv x)0u,ky c)3 l htw4x0fcg4,is2cuis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In parti c240ly, g x iulf4shcxku)h3 )vw,c0tcular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelj:l7xz6/8 zpgrxmg f j2k27w mt ;3xzping 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 massescr x0(7q*wf lx $ 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 maneuverx85/ qk f2(aij:n x4ugfjtap6 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 the net force exerted on ;6jpxxaq knt; 1- nnyihs85,o/v7oxa the car (by the ground) in Example jtnvs/xpxkn -;yona86 hxoq;1 7a ,5i5-8 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 acce9(xil6 sr ifgbt(qb5:lerates 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 throug6s brifgi:(5 t9xb(ql h 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 ho-mhur90bqfcbln9 *10jqv - em;8 nc dgqrh9 o6rizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1 9e0nh uqmf1;8vbj9qnmr-glb0 *dcr 6h9cqo- .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 spacecraft 12,800 km (2 Earth 9c b2/yype hr-radii) above the Earth’s surface if its masb/yph9r2e-cy s is 1350 kg.   

  At the surface of a certain planet, the gravitatiob ;7fkfs6 ehq;nal acceleration g has a magnitude ;6kbe7;ff h sqof 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 Moy 8yb)v,z*kz eon's radius is 1.7)b8z,zvy e* ky4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiu14ra tv8kdy-px.s w; ns 1.5 times that of Earth, but has the same mass. What is the acceleration due tdv.nx 4 ;ta1p- sk8yrwo gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rbw+ini5zk /(zt*nk3 8; yee0) bcpzysadius. What is g near its/bes 0k8y n3nzi*e;wti)yb(pzk5+zc surface?   

  Two objects attract each other gravitationally with a force o, .40jv5ketbjzi nhq :f 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 ofwq 9 asnu5pcw;f27 jn/ g , the acceleration of gravity, at (a) 3200 m 7;p/9wnsa5n2 uqj fwc   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whgwvgt sjm+qy:*)x/ 8m ere thegravitational acce *mtx8) gj+/y:qsmgvwleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron stat12 n ;w yol+-:mhlmdir has five times the mass of our Sun packed into a sphere about 10 km int -l 2wmymnlio:1 dh;+ radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our) z a/zh9:yca5yms5 iyveay :e1qu)i ) Sun but is now in the last stage of its evo q)1yvza my)ia9/chie y 5ys:) 5ua:zelution, 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 weigx(jhwa h :6qo7htless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them o7xqhj h6 (wa: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 0.60 m.;h :jb )pteuz -hc v7a*ja33+hrv oan; Calcua: b37n;azvjj3 eah t;+h-*u)h ovc rplate the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line upo12u*i )z8koi )cj khy on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fo*k 21i 8)oyu oci)khzjur 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 ibo4z2 xuf 6j1qs 0.38 of what it is on Eart2x fz 41uob6jqh, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usinguq; r d3 x5u5lxt ,m,mmt. z.p8q)hxeg:e v+ev the known value for the period of the Earth and its distance from the Sun. [No tem l;5 58qx)vue.h,+z3, g.qmtmx :evpdurxte: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in amfl9 f+/h ;jfiof-1he stable circular orbit about the Earth at a hei1f i; ffm+fjlheho-/9ght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite jv 15x/xcylsr ym77p :into a circular orbit 650 km above the Earth. How fast must the shuttle be moving xc xyprj7l/v1y5m: 7s (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experienceccf91s3 -7nf)f yasxb simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fi1)fncf9s3- xa fybs 7cg 5–32.)   

  Determine the time it takes for a 3(dyxz fh8.ty lm;)ta 3-zc6f+ poeiysatellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the suy+z i(-f8fyxcza ; 3lme3 pty ho6td).rface 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 launched from lig6kp88p0b yemd m;: the top of Mm6pb:i0 yp8 lgm8;k edt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuf5:fag91o avd fsip vmz,6s 7-ed to orbit the Moon at an altitude of about 100 km. How long d s:69f7f,vi ova 5sgzmfap -1did it take to go around the Moon once?    s

  The rings of Saturn are r.z 0c0mtfn3avojy7,;dc 7 io composed of chunks of ice that orbit the planet. The inner radiua 7z0ft i yv,d.m7n ;0ocoj3rcs of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in di:h 92x( d*vyj r;gr4ogzdd1 viameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weii gd;h y94rd1 2rxodv(zgv:*jght 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 from the centetxi( ei-e er us2r5s:6/w2y dpr of the Earth's Moon in a space vehicle (a) 6 /-(25exutwpees yri2 disr: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 equq: e;;p bzs3.ug 5rgf:c frm(cal mass. They are observed to be separated bbeg.z:f; u35 cfm(rpsg r;cq :y 360 million 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 inqx yc 4br1sc6(ud; yd( an elevator that moves ;yuc61( byc4d(dqrxs
(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 fk s 9rm)yy9en28uf7z xrom 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 acceleratr97m xuyzn2efy9s8)k ion (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfhdz -a2h*t5 lqace of a planet with period T , the density (mass/voll az*-qhdh2t5 ume) 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 pec zy0p m q-dr 67jafe6.l-d2feriod of an artifil 0 6fm rqfz67-. epc2ed-dyajcial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sk (wc8u rke:pb1egc32un like the planets. Its period is 410 d. Whgc ek8 21rwk:p(eu3cbat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancp/8g u5x 5p-mfj2wqziq /xpl 9e 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 rokr(1 yf l9g7c 4xuy zjx;h8)rdughly 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 ) 4xd k y7x;u9ghc(z81ryl frjorbit 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 tkk 01 h9cfsy/wjl q.2ehe 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, period; bq*rf5. rv39kedk ih, and mean distance for the four largest moons of Jupiter (those disc.d rvfkbq* e39h; kir5overed 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 ku6g q 6sp+z -ulus5k+vnown period and distance of the Moon. us+6qz guu p56sklv-+   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usiu-ht e 2 nwkc; jkn/29j/8fe;vqwmg5z ng Kepler’s third law. Us;n e eg9w/k jc5vft-uk2;jh/2nw z qm8e the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of ma27ftz ce i-r0sny fragments (which some space scientistie sr02c -7fzts 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 "plane )kvxmch ro -9m3ap4j-t" 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 li4 9cjprkoa--vmh)3 xmke 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 swinging in an arc from a hangix/tcikh zp.83 ng 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 h/p.3 z ckh8xitis 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 gravity be halfie-u 1, q61o9ibrce fv what it is on the su uei9cfbio6rq1, 1ev-rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circli,5v m:v3ws-sp idw. be once every 2.5 s. If we assume their arms are each bp-, di s:3 vw.msiw5v0.80 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 apparentub9l f/x9gpj9dux(w1uy ,wtzw, op4, acceleration of gravity at the equator is slight(p/9u,91u ,w zo pl4d twgx,wb9yxjfuly less than it would be 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 Ee0sr y. ;nmz+barth will a spacecraft traveling directly from the Earth to the Moon experience smzb0ne;.y+ rzero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass i5 5i6jwjuxc5ns 65 kg, but when you stand on a bathroom scale in an elevator, it says 5ij 6cwu x55jnyour mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat t jld0 -a3hs3*ian1:pnieuc* e about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity as13i *e ut3a:adl hji- npn0c*t 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 (zaxsxl k/r.l1/ht2 2l u5 m-ezFig. 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 q+0n8tue vl a0mass of a planet in terms of its radius r, the acceleration due to gravity atql+0ne tu v8a0 its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected f /f6pl wb x0zn(v7j1a+k8c vnbrom the vertical by an (cf 7x/l+bn0n1pzw k6vva8bj 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 n y +:,y;k;zefcod1sx m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of spen1d ysx+ z;:y;k,oc efeds can a car safely handle the curve?

  How long would a daya;v ao;j2f/wkmi)(fj ip;, 6usf8wjq be if the Earth were rotating so fast that objects at the equator were kvf /,; ;jum ia2wiffjsjao wp)6(;q8 apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ovz uhl-* ;5 uj1i/z nx 6skl6mie/.kjlf 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 constf uu +m7ym6 */*hstjdaant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling 6htdm+u /sam 7** fyujswings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus,w0 j*wr-onx6zky4/e jr go5 kh1lc2d: 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 k5w2oje:k rc0g41o* hwy-zl/n j dx6r equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presenclbd5 89sahh2ej rfx*4ie b*:we 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 core to be5l *9:ebae*rb8 xijs4h 2 dhfw 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 valle- 2csvaj(x ky,y shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largestksv, -c(yjx2a ? 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 satellites ord8j5 e-j m7v;kep-i ddbiting 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 each sat-e-jj8 vp 5di;emddk7ellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after tq 4 c0pb/a9ks9w7pfvuraveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly vw9q97kupp/sac b 4f0 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 of re:os8 qu: ithxz;zj;w4pair. You h:z:wo8jqs; 4t z;i uxare in a circular orbit of the same radius 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 mean dis;b2x r7o hsgn7tance from the Sun?s; xg rh7bon72   
(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 stm)j*vo xmc)gz;5w3 c7 1twjq+o m2 wneed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable as g5mt c)t21wsj+o )c z7owmmv;*xw 3jqsumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46)cm o/h.+63 ojzxtl br-(kf2gb at a distance of about 30,000 light-yearfb.r(cz+2jth-/l obm 6okg x3 s 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 locate+ c(6k(eey pc.s dk)iad at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0k+) ec6s pik cy(.a(ed-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass q73(j 6sdh mx 5,edo v0/fdhqyz,h7vz5500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced 8u5g-i ub nin7q/ rjl2by the tip of the 1.5-cm-long sweep second hand on yr qj2niibl7gu58 u-/n our wrist watch?    $\times 10^{-4}$

  While fishing, you g nyaaky (iam9k g5 )66ezy*-jzet bored and start 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 angle that the fishing line makes with the vertical? [Hint:ayjm e k (ya6-i)z5k*zgyan96 See Fig. 5–10.]    $^{\circ}$

A circular curve of radius Rm20xd6d u30xmtec6l 0iwh. e b in a new highway is designed so that a car travelidmt0u6xi60mb3 d e20xw lhc .eng at 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 trainx ,q 9vw(m6)p5pvpbvr, the Acela, utilizes tilt 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 againvmqp p ) 9vv6,5pr(bwxst 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.$\approx$    $\times 10^2$