Sometimes people say that water is removed from clothes in a spin dryec 6l4qm,xyeq1kk jx d;-.q) xhr by centrifugal force throwing the water outward. What is wrong with this stateme q64y;m kkxx jh.cd)xl,e q-1qnt?

Will the acceleration s(ya:lf qmmpeu6o+ *3of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels 3p qmmsy*+(ue6af:o laround a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed dgf4xx- lkg 5un3s+x; along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of + -d4gg5kxn3f sx ;uxla 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 t5vycb2-h7iv a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceciv5vy- 7b2h tleration of the child?

A bucket of water can be w r wj7 8af0le- 7m3evbm)kxg2thirled in a vertical circle without the water spilling out, even at the top o 82erl0)m7m fw7-je3 kbavtg xf the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at lea myl:nf 0( c;dvzg.r+s n0wze*xl1b4ost three controls in the car which can be used to cause the car to accebg n;z :vmy d04r1zlx(fwlo0.sn+*eclerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fi ibm)q(3x)x ;4uernr hg. 5–31. His sled does not leave the ground (he does not achiev()nui r)hrm3 4e ;bqxxe “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 3is2ik3z k(eg curve at high speed?

Why do airplanes bank when they turn? How would you compute the ba 7klhtj8dzee8(f/b n5 4pn(t pnking angle given its speed and radius of the te4bpn( fh/kljdpzt88( 5et7nurn?

A girl is whirling a ballslbmp(x5z--viowhszy l8 / 7- on a string around her head in a horizontal plane. She wan-mzov( 8w7bxzs /ylpsh-i 5l -ts to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational forc;fw5 u b7g3maie on the Earth? If so, how large a force? C 5uw;fa3mi 7gbonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whcm u,gzjyk3n k)s,a6,u5ytp be// w a:h0l-mxat it is, in what ways would the Moon’s orbit be differentsc5k tpaj,g kyu/,6me x)hmnb/ 3:0zuw, yla-?

Which pulls harder gravitationally, the Eal) mhjq d8f56n n)bg.:d*b zumrth on the Moon, or the Moon on the Earth? Whi m6bjnn g8 d)5*hu:dlbzf.m)q ch accelerates more?

The Sun's gravitational pull on the Earmox n4cud )8i qoa5;m5th 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 oqdo4 ;8 5mci5x)uamo nf the Earth to the other.]

Will an object weigh more at the equator or at thi v-mfmcmh7/ow3/(iw xaz74 ve poles? What two effects are at work? D7zfvc4hm/i/i o m(w -7av wm3xo they oppose each other?

The gravitational forc lq9(bh 62zj.f-zlvox e on the Moon due to the Earth is only about half the force on th9bzqj2ozfl( .vx- l6h e Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accritorc1: lh 3-eleration of Mars in its orbit around the Sun larger or smaller than rlr3- :tohci1 the centripetal acceleration of the Earth?

Would it require less sp0, /uu 0oaev 1vp1xery g*cj6beed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotat*ye1upvb6/j v1ogaxuc0r,e 0ion direction.

When will your apparent weight be the greatest, as measured byjb)bv 8;rt )b(t u/pcwph9q0m/ugm 9 s 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 b8 hg)qu9 09bb)t /cp/tmbj pr(smwvu ;e 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 c.xic6hs5 df2zo2 .unuould 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 o2sn 6c.fi xdu.5 zuh2the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner a3yfz 7jru1 pk; x7 9c3fa1zbkexperiences “free fall” or “apparent weightlessness” betweek17ffz33 y pu;9rzk1 a7 axjcbn steps.

The Earth moves faster in i,p-udbf p-ae-yq,b1 xala3i6ts orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor i,p1y-x 6iq-lupa3d-e ba bf ,an 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 mooft v:b0yq7qntp m88 c)n. Explain how this discovery enabled an estimftv87nycpbtq): 8m q0ate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than dk)zc)f3 b: o3m tvs.rthe 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.mr3dfbst.) c )3vzo k: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 19q2qm1d fn1+hj80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arounv ld0cqr-o --igp0 9hsd the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a cig-cs- qpvh-r 9o0d0li rcle 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 isw(wj,t/ si wm jnd1*9a exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (atwtjm9*d w(j1ani,w/s arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's 9 9.;bvyq euhssurface, and circles the Earth about o q9s.9eb vuy;hnce every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge ofrgoj;6xf 96dv/v(aj s a potter’s wheel turning at 45 rpm (revolutions/orxjv6f9( 6v;ajgds per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a v-;ebnoxsyv:htp/5a)c*tvk 7rk l0 s1ertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed i y-/ressxn1t;h :ov a7*t5 0kpc)lvkbs 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 ofl,/hou9sey, , m a9wvv radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? m ,wso l e9,uha/v9vy,Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires 0 lb i7ann3t9pand the road if a car is to round a level curve of radiusit3na l09 p7nb 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotateqdof8h: ekzm9u9p+ wbh vs;jk52, ,ex a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weighomx,h v2;s+wkqd,p e95k98u jz:b heft, 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 turg:bu2etq+ godyi2ig; qkk) 88 ntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fg;u8 2qto)d8qi gy 2gkei:bk+ixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside qo fln4tpvaib397vc)f(w28i down at the 2 i l47v89)wo n fbfaitv3cpq(top 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 (including the driver) cros9-xgvyqzl c rs8,k94d ses the rounded top of a hill (radius vlcy-q8 s,9kr z4x9gd =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 Fey.-uct 35dg heyb.e1 g(y p --5olcgurrris wheel need to make for the passengers to feel “weightless” at the topmost poing ctudy h1p l.3rue5y--c g5g.e ob(y-t?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiuo135 v,n8j-ntvnepzpc-5j; i+j z eibs 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25b-5 e-o,ni 81vv+nipjnj53 tcez ;zj p.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 centm10gi0 noq t)p s3d0marifuge rotate if a particle 9.00 cm from the axis of rotation np3saq0mg0 10t)idom is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotat6k3n zfe8xu;2 e) gykmed in a cylindrically walled "rof km g6xk)2y 3z8n;eeuom." (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 wfcd 6ardzu j8nx.j4gfgk/3s 08 ag88 ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected tod u4 gk8jnad6a80/fsxgr838zjgf. c w 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 time4 ew/0a:ygw5q nogd1h, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particuehy0g/ngaw:qwo d 541lar, 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 ibhi-q7h1 y x8 veltl;4s 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 masses7lyyv r-amae5 -d; r(zzz9i,7 eop+rw $ 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 vee- t4 aow -3y3mmm+kssrtically 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 exerteny.w kx39 k2)kmc ,njld on the car (by the ground) in Example 5-8 when its speed is nj.) kx3yw,nclkkm 9 2 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, ;,)+d0hy,3v 3ktgwpn zls , vm jijd8kgoing fros+3 gt8, )y ,vmpddhkjk ijn,vzl03;wm 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 slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle o3t if*eiq1 x8if radius 2.90 m . At a particular instani31ii8 t qx*eft, 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 spacecraf9 ayi; iir+l dq3d*ox)t 12,800 km (2 Earth radii) above the Ea*q+ l9rd3)i;diaoyi x rth’s surface if its mass is 1350 kg.   

  At the surface of a certain,y.miwz3m e4jydg4 kj )q- 9+kr3odk dhrd:h: planet, the gravitational acceleration g has a magnitude of 12 m/z9:r dmo,i ywjgj4 :rk4+)dhhmd3keq-d ky.3 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 gravitm:07l l5t:2*ksvoos w(r yerw y on the Moon. The Moon's radius is 1.74 w2wl:7emrst(vl:5 * 0 so royk$\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 of Earth, but has the same)-jrzc z+s2jq mass. What is the acceleration due to gravity near )zj-z2s+rq jc its surface?   

  A hypothetical planet has a mass 1.66 times that of Ear,-n(/ cki:1* zpjoog)rolal nth, but the same radius. Wha),co(ln /gzkor : i1-a*nljpot is g near its surface?   

  Two objects attract each oth8, lb ylet5r4ser gravitationally 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 acceleratiov hivhy+-l7 c3n of gravity, at (a) 3200 m v7cv+-l h yih3   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the nl5i20 dq;ew t u)m)rlEarth’s center to a point outside the Earth where thegravim5nt)q) ;ud wl 2rli0etational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spher3 auxb7s ike1o)3 nia vq,x43ge about 10 km in radius. Estimate the surface gravitoki i7q) ue,v1 n4a33baxs xg3y on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun butqg82g4h4t( f*wrkx 5iwtbx1 grdy8b; is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the yxgw2(tbr48 g4;w8 igdfhkrxbt1q*5surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weigh 70sxa7v jv+fstless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 25xvjva fs0+ s770 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of sid fo i2l8.fz 4uot)o9yoe 0.60 m. Calculate the o)l294oo.fiytf8 ouz 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 ,,w3vzoc+1oto i :jd oh5j+w qof the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupite,1do + qti woh+5wocz3o,vj:jr, 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 accele+q0i+grq oso4ration of gravity at the surface of Mars is 0.38 of what it is ig+ 0+s4qqoo ron Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the f,h khp1ydpvop.p93u ;4c;dca1xg;x Earth and its distance from the Sun. [Note: Compare your answ, .phdp4y3cdpo;x c1k ;ap9 fv ;1ghxuer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a wr5 ikgvg; ec6jn7z6fs( 5uh(satellite moving in a stable circular orbit about the Ev;6e gk(ing6f7 cz 5j( hws5ruarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular z(v,ss0eei5 1yh e3ggorbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rh vg( e,3e01se yzsi5gelease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are t,vpbfn9dda;k+5iqdl+ 6 h dh 3o experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and g il65vq;da,3nkb h fd d++hpd9ive your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to or1a9b)ak-8ddy5 7tg - cwqpglp bit 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 the E8 l - dpg1a9)qa 75tp-kwcgbdyarth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the too pqq gb;0z+gxer8 9ju* zl10gp of Mt. Everest to be placed in a circular orbit around the Earth? 0g q0ezrjg gz*b;uq1lpo+x98   

  During an Apollo lunar landing missio qxf.**iwmc4w/6 k,f*t vj)krbezfs8n, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around thb.6)vewkfzs 8*iqc x/fwk *r *4mt,fje Moon once?    s

  The rings of Saturn are composed of chunks of ice that orhos(g 0/ u-qh;gu jdt+zj g9*t;c r2wabit the planet. The inner radius of thg(tr;2cuwzuq+-j g0hts oh/ajgd ;9*e rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates onces1sjnb 1 2.bero6x zsx g0u1u; every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) atg.u1sb2 10 1j6;unbo rezssx x the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 42s-w;w d-1 ywxj00 km from the center of the Earth's Moon in a sw- s-jx dyw1;wpace 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 syskv g0p cl2hn.y;k h2s(tem consists of two stars of equal mass. They are observed 2 h;l2nhg0pvyck.s(k to be separated 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 i od4x)ouz-*) ia-kzkgn an elevator tha-xk -k*zd)og)ziauo 4t 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 frowpgg:f hv,e(7 g. n:s8 2denzwk/ vxg9m a cord suspended from the ceiling of an elevator. The cord can withstanng.n:zsv2gk7dx :8e( ewhgw , 9/vgfpd a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a plaht mbyzgum iv am(3um0uv b6-6el7:3.net with period T , the density z6v l i0mbmvhm( meab37-g:3yu6utu. (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determinpkj+e o3vm.0ge the period of an artificial satelli ke p+om3gvj0.te orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik( kvu 2 qcbfpc3)pf-:k.xa b;fe the planets. Its period is 410 d. What is its mean distance fro )upf;3 fva:xf bpk(2.bkccq- m the Sun?    $\times 10^{11}$

  Neptune is an average di9-- xf)u)0 qkxm iahfdstance 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 every -/t:s pe d85yxe8wlvs 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the es lsx5pt:/ye w8d8 v-sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy 5xo;uwq-o y g 2alefq+ykx+2nu ra1-1 $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 four largest moong/ rdjhz10: k uqbvq;;z4eaq.s of Jupiter (those discovered baqbe1:zr4qvj;.g; d0zu hkq/y 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 knhlds* d*tg+*down period and distance of the Moon. *dd s+*htl *dg   $\times 10^{24}$

  Determine the mean distance from Ju6gbxw tl a.t-/piter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periodg.wxt/ b ta-6ls 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 many fragments (which so 0v*;j9ph4ig+k ks xxecwm2 1zme space scientists think came from a planet that once orbited the Sun but was destroy4zkpc02iv*s +km1;w j9 hxexg ed).
(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 describee wr1 1tas (ym/aye,s49 blr-ts an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as styw,4ab 9-m (1a1/lrtseyrethe 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 2r /nztmj f3x 9bj5c8ou;lgv4 in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the loflxtz8comr;/ 43nuv2 j9jg 5b west 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 acceleratp -r;srre:nm/ hp3 en-ion of gravity be half what it isne e h rr/-ps-;pn3mr: on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass o 0 pk:yq1x*gqbrv .tuk+0f7f grab hands and spin in a mutual circle once every 2.5 s. If we a:k .0ur o+v7fk0pqb 1tx yf*gqssume 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 apparent acguyxix1wvs3 .kh)0z 05cy; yc celeration of gravity at the equator is slightly lessyi3h1 xsk0)y0 xcgzuvw c;.y5 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 Earth will a spacecrao/k8msy16qfh)wo +(u uw5xdc5+ x wbq ft traveling directly from the Earth to the Moon 5s6 /bwyf 1()wmhoxc8u+oqxd5u k +qwexperience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bk)w3fwa.. w mj7rrio db;x u:7athroom scale in an elevator, it says your mass is 8a wk73r)7fd.wjwm ur xoib:;.2 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 widg7(b6bu2 j ipll rotate 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 (revolug2jbd 7p(6b uitions 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 inqzap 7-- k/ yyp4xda*r1dld*v a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass9gez qqt x+t-q8t.l7z of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitationalgqq-te 8+qlz.x 9tzt7 constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertip*uhlc f: i397ypcuv5cal by an angu 7hf:ucy*cpp 9vli53le $\theta$ 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 speed of If the coefficient od1ifbpad3cfa0);b a9 f static fr3)pd1 9faa iab0 fcb;diction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast thax*8ocl ,+bgexyuw s-u9w yj,6t objects at the equator were apparenos ycx,+ bejw gu*,yl6x9-8uwtly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance a0gyi j:7upxbe am..iqe4+v2 /6 k(l ku6nbafdpart 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 ia:3g,xk.wl qspeed rounds a curve of radius 235 m. A lamp suspended from the c ixl.awq,3k:geiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tsw;y ozem,z; 8imes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a persw,yzez smo;8; on 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 Telescos5ij*aw eh b0.h5srejw n2ugs(; e/. fpe deduced the presence of an extremely massive core in2 ega0rhe*5iun ;bj sjwshfs w. (/.e5 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 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 am6a+fs pg e vj:(l:m6rs it traverses the hill and valley 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 largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact wiesmm f:(gj:v+a66 plrth the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 8nd3a40osav f*ie v,:i(dq zx satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,0z 8v 0a*n si:aqx,(v d4doei3f00 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 billion km, isp.4 zved dbdwjzy83s ; 0:5:ywr5ssxq meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughldss:;5 :8 jz54yrbvwzde .pdw s0xq3y y 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 ce6/ z6 v7vjhr.k9egfthe space shuttle pursuing a satellite in need of repairjv/ .vg76z 6erfh 9kce. You are 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 c*mj* yy9 .wsv- fu+n8mb2xzzhas a period of 3000 years. (a) What is its mean distance from the *-u+z8yj sn my z. mw2*v9fxcbSun?   
(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 yo fy3c x:mm2121lxuspxu could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable a1fxc 3m1 pm2 xulyxs2:ssumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around thdukb-b*ypxw. 2a(vv ,e center of the Milky Way Galaxy (Fig. 5-46) at a distance ofuk ,w*a- 2xv. bvdy(pb 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 corners of a squarr u.::edx5+ukqlmwn ; e 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fi;+k r w.mldxu5q:ue n:fth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eard*4: qwl3 m;h mscbd-,sy(xtzth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 5y, ;los klhvlh (a4q t4ki/-t1.5-cm-long sweep second hand q iyh 4ko(tsv/lt-5ll4 h;,kaon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a bkw8rj *lud 9e- ly-:,bm91,yvlsrgl 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 s9ly-lw bvrkb ds9,j8 ell*1g,-u:yrm . 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 highway o1 l;d sypbbln2 .:6rpis designed so that a car traveling at spen:1lbd o p;6lpys.2rbed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiloci xtt;ym e39n-nxo864 wr)ating curves. Them6)-eoyowx;nt8x9r3 i nltc 4 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 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.$\approx$    $\times 10^2$