Sometimes people say that water is remov0ll;-d,o/2vz zop j fued from clothes in a spin dryer by centrifugal force throwing the water ou /2ou 0fld p,v-ljzo;ztward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a svgpxaj vwyyb(3/ 3fr x:9 (gxx61/sdoharp curve at a constant 60 km/h as when it travels around a gentle curve at the sampj/ax9 : gyvx3bvw1 o fdx6g3rx(y(/ se speed? Explain.

Suppose a car moves atp;eu;fke)7:fzh+i 45 r o-ggz:h* j xauzgh 7a constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, ( r :; 7afzjpaheg)5ohzg; :u huk +e-gi*z7x4fb) 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. W:7/. g l9wdh 4jdrqdpxhich of these forces provides the centripetal accedqdr/4dj9 p:x7whl.g leration of the child?

A bucket of water can be whirled in a vertical circle without thv2pxv)2 dpp6n e water spilling out, even at the top of the circle when the bucket isnx6)2 vvpp d2p upside down. Explain.

How many “accelerators” do you have in your car? The)-qenvkg23d3gu, 5wqgm4 ec i re are at least three controls in the car which can be used to caus5d-gw4nqg3g eui)qm 2 ce3,vke the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as st5t1 e(nowkn0t2:or4w.h z fb hown in Fig. 5–31. His set.zhfn01ob2:4ow (5rt nkw t led 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 goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a jj6w7 1 3fc:n7zt1vbcbe,ojy curve at high speed?

Why do airplanes bank when they turn? How would you p r6v5x73t+jqzc b ty-compute the banking angle given its speez tt3cp56vx qr+jb-y7d and radius of the turn?

A girl is whirling a ball on a string around her head inyiv7z0 ;g-*nmo8xlew4tg b 9n a horizontal plane. She wants to let go at precisely the rignmi ngzx*-g;ve wo40t bly978 ht 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 s+hw.bq +w6cfthe Earth? If so, how large a force? h+.qbw6 +swfcConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s or4cl1ae7:rr7opn h zqqbf1*. wbit be different?q1 74* cq7.rohalf wne1rzpb :

Which pulls harder gravitationally, the Earth on the Moon, ixfn(e,m9 qai9:qh/ yor the Moon on the Earth? Which accele9ea(imxh9 q/ q,i y:nfrates more?

The Sun's gravitational pull on the Earth is much larger than the i)rua8yr4edl4qi v isyd;) )3 Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravita e d;r)))qs4riiy4dualy 8iv3tional pull from one side of the Earth to the other.]

Will an object weigh more at the ev r76uu prn,b +xw/ew:.s w2+lrdw3m kquator or at the poles? What two effects are at work? Do they oppose em3un w 62us 7 l/ww wrdx+v,k:r.+prebach other?

The gravitational force on the Moon due to the Earth is only about half the ftvfm;/ -m (56c8eaizqnjus +horce on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eartmf/6qejnhu;8tm-s5czi a v(+h?

Is the centripetal at)k ao xh39;vmeaxya68uip.4 cceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eartx 693; .y8e p)atxa4ikohuav mh?

Would it require less speed to laund)r7- 6qmdqh mch a satellite (a) toward the east or (b) toward the west -7 md)qdm6rqh? Consider the Earth’s rotation direction.

When will your apparent wn 1m rxmu6x- a2,2aklayd2tg- (c8zn jeight 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 would your weight be the least? When wou c-tnaumx6j- 1n8 da2 gl2(azk2,m yrxld 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 i vxn pi)b6 +mq)fl+6jmn 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. Consider (a) how objects fall, (b) the force we feel on o+6v+j mlqmnpbfxi6) ) ur feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall)sz a1x sg1/yr” or “apparent weightlessness” between /x1 sag)y1szrsteps.

The Earth moves faster in its orbit around the Sun in January than qbu7 s)+uvdubw.5nc 9in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axi5c) q7 vds+wub nu9bu.s relative to the plane of its orbit.]

The mass of Pluto was not known until itlyfr;5rrju zg-4qu ,1 was discovered to have a moon. Explain how this discovery enabled y rrzfru14-u5;q,j gl an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lalqqca sw: ezt4(g (b--0p*385iefhst3p v zqurger than the Moon's. Yet the Moon's is mainly responsible for the tides. Exp 5ps eq08s a(itugfe(t *v:c -b3q z-4lq3whpzlain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 14(k9 pm j7xo27ean zj p2eafm)980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleraozbl.w p 85xz4tnh 04etion of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this forcb zz4w8opx4l e5ht. 0ne 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 ino(zp(n-pyj:t is9(d s exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at:psnn d(y-jp((o z9it arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttjkf( --0 lj+snfog8dtle 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 surfaceng -j8ldfkst +(0j-of. $\approx$    g

  What is the magnitude of the accelerationp)hxhf v n9myu7 /;x;h of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minv;xh9mx )n h/h fu7p;yute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string i) 83x p0y0iob se(qdx b5gdkd77tlezh3fs*h 9s revolved at a uniform rate in a vertical circle of radi)3exs8zq5 dgb s bh037xfdli* (hot70dy 9ekpus 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of:kjl7kz -cfv 5cusl, 1 radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent1l75j: lv czk-su, kcf of the mass of the car?   

  How large must the coefficient of static fricv6urbl-, vrh fr(4.i ftion be between the tires and the road if a car is to round a level curve of radius 85 m at a speed ,4r v frrb( liv-u6fh.of 95km/h ?   

  A device for training astronauts and jet fighte*qep :a/t ;x7cqlfr j,r pilots is designed to rotate a trainee in a horizontal circle of radiuspqtfc,a 7;l*x j/ rqe: 12.0 m . If the 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 from the axis of a rotating turntable of variabaom*mv . q6fpn r*)7b3a*uzwple speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 r)mbqv7far. n*pw *o pz*a6u m3pm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coastu yri/o6; 63wdbu9l tker be traveling when upside down at the top of a cik6rtwob ;3 uu/9i6 ydlrcle
(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 driverul /jq4 wn.7x )u:m*a- 2hjme :cfyoyr) crosses the rounded top of a hr .wy: 4muxlo-yemcq*2nj:a h7/f)u jill (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 p )lw( 0el5/)q qiqpqlser minute would a 15-m-diameter Ferris wheel need to make for the passeq)q (/swel)i5ll p0qqngers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical c/cfw5xgyez6.ik ,b w-ircle of radius 1.10 m. At the lowest point of its motion the tension izgixb-/f w5k,ce. yw6 n 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 if a partin7- k w7;yjcr lzedf0*d:0d vbcle 9.00 cm from the axis of rotation is to experience anydbw: 0 n*dd7lk-7c f0jrve;z acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a ca; -,o oymov p(pn9xyp1gkb0 r:rnival, people are rotated in a cylindrically walled "room." ,y0 ;ro: ob pyn-gpkm19 (vpox(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 tuno 3o*7qen;on a frictionless air-hockey tabletop, and is held in this ornuoq7nt3 o*; ebit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ba6z-whg:m.uygn)sca h qr16 g5ll which revolves on a string 0.600 m long. In particular, find t)6gy5 w -urs: gca1. nqhh6mzghe 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 ra;w txkk p-o2y+(wgn( xdius of 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 masses yi 0 ijkd8l5s0 *irdnl r2ty0;$ 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 diving vertica5wjyajp6e l* l:lq;.nue+ :qo lly 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 zmuxr(;( /byx4s0aj fof the net force exerted on the car (bfam4bs /x(;j0xyruz (y 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 accelerates uniformly from the pit area, going fro9u(lgbo*:7jq. q rzhqm 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, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slippin9o(jq.:gzqu7rlbhq * g or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.9vf)ayl :eqi9q 7 t50c.erwkf kg)k/xi woo3+30 m . At a particular instant,kg95 )w0 o atxqq wof)7/.keir3v ely 3:ifk+c its acceleration 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 spacecraft 12,8*abt5u9 zqw2c 00 km (2 Earth radii) above the Earth’s suw25cbqz tu9a*rface if its mass is 1350 kg.   

  At the surface of a certm;bt5nmc ha - l8 u,pta0eyepv8/(y, yain planet, the gravitational acceleration g has a magnitude yy-em at ;namcu5pl 8,8p (vy 0et,/hbof 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 the5b5tqq;: vbp e9 lpz7b Moon. The Moon's radius is 1.797:q; qpb5plb5bt z ve4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet tq+(6dosiu tpf;,f -kfn*mx : has a radius 1.5 times that of Earth, but has the same mass. What is the ;dpsffnto f 6 m(ixq-*,u +t:kacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same ra;er,, 7tp:e7x9ba afr9 y zqjcdius. Whab,ecpe;artq7r f zy a x9:,9j7t is g near its surface?   

  Two objects attract each other gravitationally with a force of h6e 7ttz,ezf: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 , 8 zb (2a0ei,q klvkkh;:yha7n the acceleration of gravity, at (a) 3200 m b8a;,elkhv knqz y:k2i0 h7(a   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside thepcbv 40vsn g a7(x6mu2 Earth where thegravitational accemagv 6b(vx024cs npu7 leration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five gsyg6 4 ;z9 /wu gb,7fss am*begk3md(times the mass of our Sun packed into a sphere abouf/s6w9gb;ge yg *m mz( bsag,k4u3ds7t 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once w.7;r 1we2)qtdlahklr6 gyn9has an average star like our Sun but is now in the last stage of itagkn9lle2r hd.ht y;1)7qr w6s 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 weighta8: 9r-a7ctcvga rcv81lr;s eg1ogc6less while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it 9sv vrg ac rc :8 ate1ocal1g78;r6c-gisn’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 av4lr h n:g5*r cj79i .dgmi b6kc19mhkt the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one spherenc m65mhg kvbi*:grl 9r1i4j7.dchk 9 by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of thjjwzu+8epke3.vq*xq n t531br fv0r 4 e Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets rpe4u.zxqvtq 53*8r1 v e3jnbk0fw j+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 accelerax do)n1o*u (zwtion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that M o1xdzwu(o *)nars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the g83d+ mjhc c/h* p-kn/ql9 loiknown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws 9/ 8m3kn+op ih/*qjdh-cl lgc, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cy8fc8q8 bpih7 ircular orbit about the Earth at a height of 3600 km. f8cyq8bi78 ph   $\times 10^3$

  The space shuttle releases a satellite into a,bki.0 ;1e+7ie/pzkv:wxtur fe7k dn circular orbit 650 km above the Earth. How fast muike ft77vr.x 1/ z n0w:eip,ek+kdb;ust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience qguc7;qkov/-tb-dq3 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 Quocq-3g vt /d7ukqqb -;estion 21, Fig 5–32.)   

  Determine the time it take7pu18hwcm: dzs for a satellite to orbit the 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 thepw7 :h m1zuc8d Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite ;pqhj2ygnrk7q *u1da;, sa8l2r tz;x have to be launched from the top of Mt. Everest h8g k1nrzq;pxd;22jy,ql*t7 ur; as ato be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oesowz w2 -m)pe 9 ((q1yskssgt)m h+;arbit the Moon at an altitude of about 100 km. How long did it take togm z t+)swo1m( kss;hse)ep 9y-2(waq go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that okr0w4s.w qyz3zd1 - uerbit the planet. The inner radius of the ri1wwusd zk -zyer3 q.04ngs 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 onctg. pnj95v8p p gbpx59e every 15.5 s (see Fig. 5–9). What is the rati pp9t.x8pbgnv55j g9po of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 kmq296t/l x w2jcir qh5m from the center of the Earth's 2ir 256q/xm9tw lq cjhMoon in a space 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 4998df *c san hf20xevfbi+mwstars of equal mass. They are observed to be separaisff 2+xwd8h*na 9v0m 49febcted by 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 in an elevuh2 g7 82 wjj fxbv0rkru;/kh*ator that movg r;uj kx22hhbkv*j7fw0r/8u es
(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 fromkyyiqyw+.o zja( (lmwc+,4w4 a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acceya+wy j44qk( +ow,wm(c. yzillerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite or/ toay(4;pxygi2v*0 satf h2bbits very near the surface of a planet with period T , the density (mass/volu s*4t;gyb(x0a /f p2ov 2hayitme) 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 pe:.:a)ezmfdl +9l ejfhriod of an artifiejzm f):lh:a+.d fl e9cial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meqr;nu3e;// * k)p(dcvn cfxk dters across, orbits the Sun like the planets. Its period is 410 d. What is)qxk d3rfne(;d ;*/cnu /c vkp its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag3fqh h4dw82w*co3vh me 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 Sun roughly+f6 q vl)oess (45,agquwwz4k once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimatel45s4uga z+oq )(wskqw ve,f6 the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gim v-3 mtx3u/t*+g vsbalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, and mean distance for the v+piza /r k2yoml 0*i92(iijrfour largest moons of Jupiter (those discovered9* i02vmr lojpir/ a 2(+kizyi 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 distance of the Moon. *ht 6* wy7 :a7vrphu3mrp6jxk jr 7hpa3pv7u** ry6k: 6wmxth   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jup qu7x6pc+qvzc6g6 3 uniter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. cqq6u6 6x+ p73nuzc vgCompare 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 betweew4 /oaewy er,mrou*86n Mars and Jupiter consists of many fragments (which some space scientists think came from a plan r4w*/om6reeow8u, ayet 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 form86m2oygi gfuyq3+g7 b7(ksxc of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make tgk 3ixum f 7yogy27+86q(bcgshe 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 27u qnl 3ho7by-fsyn: gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N7-u yl2b s o7hyq:fnn3 on the vine, what 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 su 4yxcjq)w z8 :eaz2n-i*/vmcgrface will the acceleration of gravity be half what it is o x-8zn42gc*jzq:ew vy ic )/man the surface?    $\times 10^6$

  On an ice rink, two s,z/rh zc ,r-fckaters of equal mass grab hands and spin in a mutual circle once everyc/cr,r-f,hz z 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparefyh qcch,ki bip-v,*; ./.dgynt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnf*id c,hp;ck y.gb/h-,v iy q.itude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelingr/xapizr9 i)dr+u(2 q directly from the Earth to the Moon experience zero net force because the Earth and Moon pull w( +dpz2)a qiuri9xrr/ith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand ozy7.wn;s6 2x/ zarzt w/z-gzln a bathroom scale in an elevator, it says your mass is 82 kg. W/rl -t/76.n x az wwzzzzysg2;hat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space sts ;vtb0gm ob6b*jjco1/fx ,7 jation consists of a circular tube that will rotate about its center (like *j b ocb1v jo,;g6mtsj70bfx /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 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 (Fig. 50v a3 p qv8x5/jv73atpureav*–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 radius7 yx-mxkz n*l+ r, the acceleration due to gravity at its surface and the gravit-k x xzmy7*+lnational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical mpewqj *cv(8ib4xa 9,j:msc; by anmwm4c:8 sa9bc ej j p*qiv;(,x 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 banked for a design speedzm2iw t;x)re 9 of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely h) xe;wrt2m9 ziandle the curve?

  How long would a day be if the Earth were rotating so fast th5b +pwd os34ggat objects at the equator werg3 gsodb+pw4 5e apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintatt*- f f 5 drpfw)fph:iweb)0g (/bmc/in a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds fmv/98 x zc zxrg)igab,53c)xa curve of radius 235 m. A lamp suspended from the ceiling swings o/cm 5zag)xv)3xri bg,z9 cxf8 ut 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. hji9pb6i9cmlmze*c: u *( (opklk *j+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 canh* l9luepm*(j ciiz6 kbmk:oc+(9p *j't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telesc+mw/6d df (z9caqww) nnak9l+ope deduced the presence of an extremely massive core in the distant galaxy M87, soaalwk9 dz /)mq(n +fcn w+d69w 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 be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown i at:nx y+h+z* r+y,lnoq-njy.)h ljs:n Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the ca a *zy,nts yr- +)xlojl:n.hqjy+:+hnr 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 satew 83wxp.(e6ron, exqs llites orbiting the Earth. Using “triangulation” and signals transmitted by xexoe.w6,q3w 8(n rpsthese 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), afterffzu zax047 s. traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Ero.z4s7 fz0faxu s 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 tn1h 82 5g-mc )(/;oa)axn2oc xke/lrwzp icjshuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 k)h/8xlc5o iena njamzotprxk)c/ 2 c21;w(g- m 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) Whai75e5aw uu5z gt is its mean distance from te u57gua 5zwi5he 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 actu;c ,6cyblqtll-tip/ d ll o9.-ally "feel" yourself gravitationally attracted to someone nec6t lild p -bly, /o9.lcl;qt-ar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center zly-*se ,k nb+of the Milky Way Galaxy (Fig. 5-46) at a distanc ns,k*-+ly zbee 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 corneva gj/ y+r)wc;1 zwuh9rs 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 whwuj/g+vr z19) ;aycside of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitsi.rsbs; o6-q q 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 tyk .-ceedrlcxglu6f (3h3w+1he tip of the 1.5-cm-long sweep second hand on your wc3er(-d f+1h6l3gk c xyeluw.rist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinqbg d juf)1i0jni+ 0w9ker weight around in a circle below you on a 0.25-m piece of fishing l 10gnjqu jw+9dib 0)ifine. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hclp4 id6/p: afighway is designed so that a car traveling at speed :a4c6 f/pildp $ 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 Acelkm:pz6 gjcck lsvt8i l/( / 3w.5jmh:da, 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 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 ba 8kc6 hj5jz.klc mt:s/l3 w(i:mpg/ vdnked 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.$\approx$    $\times 10^2$