Sometimes people say that water is removed fryihbs/ mc y-dv2zc,pt6 a4g0 :om clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statementc 0h6s2g4v/ ambcpt id-yz: ,y?

Will the acceleration of a car be the same when the car travels aroun+ja8gzd9i s.w w)+d-vl joai9d a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spijwo 9 da+9)zv8- jl.awg+sdieed? Explain.

Suppose a car moves at constant speed alonp; k2 pg+/zozhukcn aqi;(j38g a hilly road. Where does the car exert the greatest kc ozi+3u8jn;a hpk;2( pzgq/ and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the for;bo7k + gg8lv3vj jq hjy/zv:4*mkb4guan*w9 ces acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal jy*ag39;k hg:*v / g4 jju8zqvko+m wnl4b7bvacceleration of the child?

A bucket of water can be whirled pb- +e u k:uux,ygkq:j713w smin a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down:3kp ek7g-wm,+u s1y qj:xuub. Explain.

How many “accelerators3k,b9uzzoq fx:l9cc6yxj .h 9cuy7j- ” do you have in your car? There are at least three controls -7hu .uczj39 c6:qj lock9 y9x byx,fzin the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a i9zduo9xuvn8) 0yu my rj.*4esmall hill, as shown in Fig. 5–31. His sled does r* iux8 . e)ymj9nu4dzoy90uvnot leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high sposb pg;/ jt)w;bz-8byeed?

Why do airplanes bank whe lmyn2vr*a nwg5 05ts5n they turn? How would you compute the banking angle given its speed and radius of t sw ga t555ynmlnv*02rhe turn?

A girl is whirling a ball on a string arojc+ :sqo xi.66fq mgu,und her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should shfq,+ c6 xmig sjq6:.oue let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large ae jk/q faq k6(q+/u/kc force? Consida/c 6f(k +j/qukq keq/er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is0i fx nvmz,h 5- ;+uoi-ww(pcc, in what ways would the Moon’s orbit 0wx5om zivcp-fi (+ ;wcnu-,hbe different?

Which pulls harder gravitationally, the Earth on the1oz.i(i9ng7lev l ip3 Moon, or the Moon on the Earth? Which accelerates moreilno9.(731zpvli ig e?

The Sun's gravitatiou c5ra*.oe2qxy+ugm)c:j .w dnal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cwg*+e2ux5 d:mcaroyu. .)jcq onsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more atwsrsco0iagw+:b2 +he+xf *ixl(r /(h the equator or at the poles? What two effects are at work? Do they oppose each othe2sr+0 h/sb c:w ( xh*rxoigaw+l(f ei+r?

The gravitational force on thlc2h wcnyq2i :7r5s 9ke Moon due to the Earth is only about half the force on 52klcc h:yw7n9qirs2the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around tnkyfmk*+haohe1+n c /v;g80ghe Sun larger or smaller than the centripetal acceleration of the Ea1fnvy;n0 a+okec/g*hm8k h+g rth?

Would it require less speed toygd2 :o uiy9yf c7g1-j launch a satellite (a) toward the east or (b) toward the west? Consider cuj- 2gig19fyy :d 7yothe Earth’s rotation direction.

When will your apparent weight be the greatest, as measured bz;nbv3q 7 txor3 t+d-r2mv)bzy a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) ism3nv t)b+;rbzrx o73vqt-zd2 in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lonhge)i/gx herz/c.u9 (g periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulggc (zh/xi)e9u /hr.e ates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” orbf 9-dejhi*xm 21rz6(;fpja u “apparent weightlessness” between steps.(jbdz1p xea ff*- rih6;j u92m

The Earth moves faster in its orbit around the Sun in January tt6+.ovx;rzqff3 pl y 2han in 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 tltr6 pqf+zox .23fv;y he tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expla0gjrz ck ma9b ;65d+cbin how this discovery enabled an estimate ofb +rcg9 ;djc0mbz5 6ka Pluto’s mass.

  The Sun's gravitational pull3qo/yhvqdj3 h3dj p/:) dpwk* on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for thpdhjjdw* :d)/h3p/qov k3qy3e 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 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 dt0z2;.g;lb b2jqbz h1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ipkga)ulzm* l tp;fb/af -8)o 7ts orbit around the Sun, and the net force exerted on tglf;8a7mp/z*-tkop ub )afl) he 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-v cft0)0qf0tc hs*x0r 0nj-wv18)l 3jkuqtnakg discus as it rotates uniformly in a horizontal circle (at arm’s q fw0x1tj0*00vjqst3t -0lk rvf c c8an)hu) nlength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit-p1b xw9:s4(6f+ ejsyzxmr zy 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shutj: r zp+xye9y14mswzx fs(-6btle 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 thf5 l:wt1 jnyv b0-eyl7e acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (5vej7l -wn 1yfyt:l0 brevolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is fuw-4 u:bqigydm-/e6 revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If -4wq/g 6 e-yudbf:miuits 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 spee-vadez 3hk3g(7l3a jad with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficigk( ze3jhl 3a7-3advaent of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and tgh kjld4sby2m:m9ra;th (g /2he road if a car is to round a level curve of radius 85 m at a speed og2 t g:hrl(mh k29dsjm/4ab;y f 95km/h ?   

  A device for training astr9+ q3u c3 xd ,g6oq755pk(ij zkdpqrbyonauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her oi+pduprq3759, x(zqg ydk3c5ob 6kjq wn 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 varifv5 pest;kf 72able 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 the coeffi 5p fk;e27vsftcient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at t jypx i+g84 zkt4p4w:zhe top of a cir4py8i 4g wjk+4x:p zztcle
(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) crosses t jmw, l*ckk vuk29s:yn 7:a5+jrlls y,he rounded top of a hill (r*2nrmwl :y,l7k:v9ukjysl 5k+js a,c adius =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 4dfhtk)xu,vn 3m7l a- would a 15-m-diameter Ferris wheel need to make for the passengers todtfavm lx)un,h3- 7 k4 feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiun8yr4wd)36 iw6*4w tunwk ddz s 1.10 m. At the lndd 3)6wi*wtn w4w8 r4z6d uykowest point of its motion the tension 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 if5 nmc:y* w. pyu hr,s:ed7cz;i a particle 9.00 cm from the axis of rotay:yh ecu5r;cw n :zmsdp,7. *ition is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a gnbo1 9x93x u 2x)r7hybppqm9cylindrically walled "room."o3 by1ppnu299g7 xqxh)x 9bm r (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 on8y 5hlwihe aoe0zno,m: imn, 5ykm 5;91osw1j a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cziheno1lkymawon8,5s5 o: ,5wm9y0 mj;h i e 1entral 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 ths)px74 n dxi.dt+ .cwvis time, by not ignoring the weight of the ball which revolves on a stwvcn7.. 4x tdd) +xspiring 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fphnps, ;f*ka8 or 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 massespc.o oh8c i-fufn0 5g/ $ 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 vertically azv:wmeju y 14l.v+8pst 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 comp)i q8ru9hk1n qe .(hjvonents of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 11nhekh i9v.q8q rj(u )5$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uj zc/. j ox;cbjzefp-+j.q89 bniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine tz.ec9- qj+c. obz8j bj;p/jfxhe 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 of radius 2.90 m . Adu7 ,4yi1 ay er,bh:ymt a particular instant, its acceler:abhy ,r1 ,m yud4yi7eation 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 12,800u(74ybj xi2: v7kd3twwwe x7s km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. 374 swub27wj: w(ykxixvt7ed   

  At the surface of a certain planet, the gravitational accepchatqi8; de op* k2,e:en/ (wleration g has a magnitude o o/:a( nqted;e8w ci,ph e2k*pf 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's dqrf og5 -fm.hbc13z:radius is 1.74 3g .drfzc b :f5om1-hq$\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 thgd)xza 1t yj; g*9e0lcat of Earth, but has the same masej*9)z clgt1daxg0y ; s. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timeq+ygg i4 8ky.ip,if 7fs that of Earth, but the same radius. What is gi7,4ffq ipyygk8ig.+ near its surface?   

  Two objects attract each other gravitational)g 0-usmfm39r jw: jvb0tyu z,ly with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, azu:y:t,8n5hjj 4bbv(debtm/ t (a) 3200 m jz8uh(/ j:t5bvt :4,dbmbyn e    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from th(f ond7j ie5blc*s+(ue Earth’s center to a point outside the Earth where thegravitational acdoe(nbcs(57*i flj+uceleration 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 9/ fzicigg .tvlk*6 e7mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this /f* ltgkc7g9.i ivez6monster.    $\times10^12$

  A typical white-dwarf starnvm(jx xzs)+9ipr48kvp4sm 3d h1 ,yc, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on thiv+z,d1rms4 (sm4xn8p c i3jk xyhv9)p s star?    $\times 10^7$

  You are explaining why astronauts feel weightless while ou.t.dg9gc m lx3rg01j rbiting in the space shuttle. Your friends respond that they thought gravity was jugj1xrcgt 03 mu. dl.g9st a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calc mzyyc8i5u8ay+h t,y6ulate the magnitude and diray88yz +cihm yt5,6yu ection 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 lineb62i5mg,ursp.2 ;jvpq5-l rhg i7 pt n up on the same side of the Sun. Calculate the total force on thgns2jm ri6gpt lu i,7h2. -5prq;5 vpbe Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Marsuq55+h*)l tfq5k1c ,mgay upm is 0.38 of what it is on Earth, and that Mars’ gq+ 5ktmyfp*5 51 ,)cmhaluu qradius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the peri xydjgc)+ ;en(fp yeuoxm:4o 821jy,xod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exampjx jun xo4( 1,cdm2xf+8;e: oyyy)eg ple 5–16.]    $\times 10^{30}$

  Calculate the speed of a satell gcgte l3crab,om4s wt6a6860ite moving in a stable circular orbit about the Earth bc66m8 g3ag6r wso0,ta cl4te at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circuun4c2uzs zf7ze mx8h4: 6.vbular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) w uc.v7 z8 nxhszzfmeu44:b2 6uhen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expergqm4wf/z ;4wd ience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, andd4w /fm 4w;zqg give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite t-( jk3znojv6 q4 n4ntno orbit the Earth in a circular “near- vk4n (ztoq6jjn43-nnEarth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have tohx.m+ lf5gz zfk(5 cs) be launched from the top of Mt. Everest to be placed in a circulg (f5f 5lm khs+.z)zxcar orbit around the Earth?   

  During an Apollo lunar landing )5gbm m- mgx.cmission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take tocm)-xm5b. g gm go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that0;5dfel6 ;pmjo v w da,hu6*pw orbit the planet. The inner radius m5 w d6fouplj * ,6ahed;0vw;pof 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 diameter rotates once evhavs+x (vjny9nyje z+o*5i+5ery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weighn+si5vvae5 yy(z n jho*jx+9+t to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg2v ive(j+m06a -x cxdb astronaut 4200 km from the center of the Earth's Moon in a x v2ma(0xcjv-+d6 be ispace 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 twopkvl 7f-4h,r l stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the pvfk47 ,h -lrlmass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a f;i j)an y+) fasgf3h01 prcl055-kg woman in an elevator that movesf0al0 )1sj acf; rp)3nf+hgyi
(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 4lpc 5iid*g)xs-8o 3nyh)mpncord suspended from the ceiling of an elevator. The cord can wns5hy 84)x p-p i3*)imcndlgoithstand 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 orbits5/frhblb z8 .7 qrg1avr u8+bf very near the surface of a planet with period T , the density (mass/volume) of the plrf5rzgh 8.qva8ubf1 bl+/b7 ranet 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 Moob)x)jel ,wsk e7lepr v6/.eb 9s*crh0n (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s srh xv 0j wse*,). /6 ee79c)lslkrbepburface.    s

  The asteroid Icarus, though only a few hundry4 .)jrw ;-oq:jmubir ed meters across, orbits the Sun like the planets. Its period is m-br4u r.y);jwj: qio 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4l i.i h4j;,sbp.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 rae-jso)teuu 0mgi zdv9 v--t8o- ; /xthe Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the c;vm x0o--uiou ta )e t/-8gr9eszvjd-omet 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 Galaxy -:vgvbdx9h)lh 9ku 9l$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 fc+v;hcl wk p9;or the four largest moons of Jupiter (those discovered;p kwh ;9vclc+ 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 /itr, 5nzgvivn)*q*n Earth from the known period and distance of the Moon. )n*nni, */vzvi5t rq g   $\times 10^{24}$

  Determine the mean distvuixx82xsz* +ance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valuevs82+ xux*zixs 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 Jup a-q8cexf. 5gwiter consists of many fragments (which some space scientists thinf8 aw .-egcqx5k came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the forb( i -vn4c 3r6;f-fdd gq:mppdm 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 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 revolut4i vd(3dd6m f;r npb-c:fq- gpion, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vt3/s-jj r9r(txz1nt j ine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is thejtrj 9zst n1/ jxtr(3- maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the a4,/eq0 cfq )kanlj9kicceleration of gravity be half what it is on the sur ekj94if nkcqaq/0,)lface?    $\times 10^6$

  On an ice rink, two skaters cg lp;cr rb;.3of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anop.crrl bc;g ;3ther?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration og cs+t*cvp e1p*)n2nd f gravity at the equator is slightly less than it would b g*d e1)ccpnvts2+ np*e if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the E p8mq- ea+ upm ,gzzcci, 78;9k4nmmpiarth to the Moon experience zero net force b8qgm,m,9 z;-pim p+m47np zca k8iuec ecause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand o;d sbax k9+i1hn a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceledx 1sa+;kb9ih ration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotaw :6xdv6 qea:tte 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 e6awxt: : qd6vspeed (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. 5–w1dzt3nq qumf*-d99l43).
(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 mab8 owv 8twg6 wa9fos/0ss of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitation wov9f 6bo8/awgw8t0 sal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by 1j k 0sudx34xdan 4ksdj d31uxx0 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 banklv2;pi:q u.;flrf.p-*d p5nmx6ypaj ed for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of spey ln;lvr5.fdm u*p-aqi : .fp26px;pjeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at twy+ 0oqpi -khpx1d9g *he equator were apparently 0x*d+w y91 -k hoigppqweightless?    $\times 10^3$s

  Two equal-mass stars maintdvsel0tm +u(j/1 1tmmain 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 a curve of r,es kj(hc5sz1 adius 235 m. A lamp suspended from the h(z kje5 cs,1sceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as bio5v5,b(sylnx: a,p massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet yb,b( 5op,inx:va 5sl the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use 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 presence of an ext8swvzmrm vb9aj )9)0l.coe * premely 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 orbitivp msvm0wr) *.e)9c89azblj ong 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 ps0 :(f1izt, f)tmyfr cwu 1:jand 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, f tz)(wt1uj :fy fpc:ms10ri 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 groupq3cj rc qhx4i0tke5:/ll s- i+;:qe qj of 24 satellites orbiting the Earth.3:crhesce4q/;q 5t i -llqx0j q:ij+k 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 satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after trabm48d x 2xgjw 9xxf1hs5z (za0veling 2.1 billion km, is meant to orbit the aster5bgxx0j 2f98mdhx4 wx1 aszz (oid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuingth85tr rzhba4va796y a satellite in need of repair. You are in a circular orbit of the same radius as the sb6 ryvtta4z5h h9 r8a7atellite (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) shylp2z- 9 8xelpq);eWhat is its mean distance from the Sun? plsze;-8yphqe2x) l 9  
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" bdms ro .2j+78jlc8dftb x9.h yourself gravitationally attracted to someone near you. o bjj 8c7d .x2mlhrd89t.+sbfMake reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fiw4 csngsjl4 64g. 5-46) at a distance of about cgssjwn4l64 4 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 lwlt/8i jz p2u/f4zuy 8ocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg m4 zzuilf8ytw pu 82j//ass 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;yq)savgv y23-jbwbyxt2 .+/aywvu 6 the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip 8:go4cdij1xnvu4(l(q ti 1 j wov3rh7of the 1.5-cm-long sweep second hand on yo7v1 h 3ivdjog1x8w4:ur(n o i4(ljcqtur wrist watch?    $\times 10^{-4}$

  While fishing, you get boro.a faav3(nm6g/ dz cwbi65r (ed 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: See Fig. 5–10.]c fdni5a a/6 wabrmzog(. v3(6    $^{\circ}$

A circular curve of radius R in a new highway is designed so th,rgoct4f r 7x+at a car traveling at4t crxr,+7fog 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 l dc,ag(s(9sktrain, 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 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,c9ds gla(k (s 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.$\approx$    $\times 10^2$