Sometimes people say that water is re.z3ujkbo3m+cx-g0 to b-rx ,amoved from clothes in a spin dryer by centrifugal force throwing thzco-0ra-mkx+ g., 3t xoj3ub be water outward. What is wrong with this statement?

Will the acceleration of a car be the sxfr5y1wh d vk+ 4-n t; tl2tlr:yx21adv5d,vn ame when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the sat2 wrhn ;lnadyf5dv:tt,vx1ld2yk+ 5-v x4r1 me speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the ca;efg1ak yz5u jvj 8.b1r exert the greatest and leavab.1jj8 zgk15 ;f uyest forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-gr9vcm9h;;qadv 1 n.f.lc u n8wo-round. Which of these forces provides thel;r. q198unmhcvv. d w;c fna9 centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wfn c yk6m-aenq)g9uvx44l+o *ithout the water spilling out, even at the top of the circle when the bucket is upsi c)+g*v-a x6knno uyqel4m4f 9de down. Explain.

How many “accelerators” dfzqit*b3+0 9- t82zfoi r2er c.a azalo you have in your car? There are at least three controls 0za carb.i+i *q92rtef8-lf 2o3t azzin 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 cr);cnqu0lqq w3 est of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chescw0q 3lnu);qq t 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 cu/2ycpjtis3 35w (uvo*gcqb i/rve at high speed?

Why do airplanes bank when they turn? How would you compute theg61 fgy6zr p;w banking angle given its speg z1p rw66fy;ged and radius of the turn?

A girl is whirling a ball on a string around her wn2aq y5/8rz dhead 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 she let go of td aqn/5 rwy8z2he string?

Does an apple exert a gravitational force on the 7 zvi-xuq5jq( ;vg/,p td*qvp Earth? If so, how large a force? Consider an apple dj -pq/z7 x,gt;pqv*vivuq ( 5
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wo(7pz4oz.hff4zap l)om :f/l duld the Moon’s orbit be4a(p)l/ 7zfpfzzfmd. 4h :olo different?

Which pulls harder gravitationally, the Eaosu o((3yc, b s q:;fq)fwc3warth on the Moon, or the Moon on the Earth? Which sqwy3f ab(oc ) ,sucwqf(o3:; accelerates more?

The Sun's gravitational pull on the Earth is much larger than the/ +k ufjph66yf Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenc/y6h k 6jfuf+pe in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two eff c+qfz rz43nkitw*n06 ects are at work? Do thi ctn *rn3w6qz0z+f4 key oppose each other?

The gravitational force on the Moon d0on+q2 ho.ufolc 4uz 8ue to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eao fhcn4o28q+.0zuo l urth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger oi/j s;h bieym9m/h8f(r smaller than thm;ih 9h/ /by8f(mijsee centripetal acceleration of the Earth?

Would it require less speed to launch a rdor9 v6v,7 3zbjyqj *6ofq:e satellite (a) toward the east or (b) toward the west? Consider the Earv7eb r6qqd*3yv fj:o, o j96zrth’s rotation direction.

When will your apparent weight be the greatest, as i;bmo)t lxd9gp8;b; h5wmc1xmeasured by a scale in a moving elevator: when the elevator (a) acceleratesc;x 8)5 ohd mgpw;ib l;btx1m9 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 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 spac q b ijqq9 uuj0;mcgg:szh58-:e could be adversely affected by weightlessness. One way to simulate gravity is to shagmhb;zqc5 0g u::j9quji s-q8pe the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “02 /v1hu alx(q7iert br(jh6ufree fall” or “apparent weightlessness” betweejatxr2u6l7 hvr /((hq0uib 1en steps.

The Earth moves faster in its orbit around the Sun in January than in Julyl3; :adycu6 (b mus3wtem ,z:r. 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 axis relat3ry mu 6:3e u (ml:;cswa,zdbtive to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a m7)xqzn i qe,9yoon. Explain how this discovery enabled iq9nzx 7q),ye an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet ttmt3w:q9lv;*kx.k a c9ln kwh*cf :k-he Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.w:-f9 k9knlxmh*:3 vawl*t.ck qk;tc 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 1k*m 1;mbr *m ntn:hmayo+w7;j980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 cx i .q5z4wpd jjv/)+ny: up*xits orbit around the Sun, and x ijw/:p.*dzjux )+npv4 5qyc the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as /hcukt bkhjf;;s /l19 it rotates uniformly in a horizontal circle (at arm’s l uk9h/bh j/sk1;tc lf;ength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is-k8k*:: sa irsh *kspk 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 shuttlek-ai*pksshks:8 k*:r 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 . zk1i7byv +-qgjw9u*pd*troclay on the edge of a potter’s wheel tr-71 pjou*vybiq+d9. *kwgzturning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unifor d . sw26r8qna, c/(ehrmb6mldm rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed lndm,a/ h.c 66dqm( s8eb2wr ris 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 1p0/39-97 q 9eco brnbsis 3gidb kx3d+egkzucar can round a turn of radius 77 oxb93dbi i0u7gbn r9qe+zdp3e1gs-kc 93s /k m on a flat road if the coefficient 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 betw rtwe9a;2eue3n2d3-+ unx+jhr ngm h :een the tires and the road if a car is to r :r3ghuuj+2 x2wee+9;mnn3tn-r ade hound a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed teo :4rd.6cpcx/f oh4 yo rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her yx4cd/.f6repoco:h 4 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 oq wdhh,.. d7jzf variable 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 coefficient of .7 dhwz,.qh djstatic friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when ulu(3) gl -daomxpzt.8kwti /+pside down at the top of a circlo i-.w ut3/t8zlalmd+g pk x()e
(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 mas:cwls7b 9f:;wmi-p+ti; vq2jima g g+s 950 kg (including the driver) crosses the rounded top of a hiv p f7s gm -+:ljbci:qg;iwwt2;mi9a +ll (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter i+ lhnh1c :w0i ; zxd84ncz3n1h *alktFerris wheel need to make fd38x:wna in*1c;zh4lich l + nh ktz10or the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of vm 5ghr9 l(oc+ 5qtxq9radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.qlmoq59 5vt9r hc+x( g0 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 particle 9.00c c;+8i s,rnnzb 6pwd/ cm from the axis of rop,8n cri+ ;zc w/bsnd6tation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c , ox,zb9t6cmz ml4,0rztmcgk8el o xp1q9,6oylindrically walled "room." (Se q 1oemz,6b ox0t coz,,6tck99 mlpz,xr4g lm8e Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on mgr0+mpt9y7u8 z0ube a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling bl9m egu 0y7+zmrbp0tu 8ock (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 t/z1 n 5taw--s/z/w2m qkdlu dhhe ball which revolves on a string 0.600 m long. In part-wz2auns/ 5k/qmh-d1tz w/d l icular, 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 t6cs tw8 ryh6oi 6hv+e7e.nqy/sgf23perfectly 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 ;e0pm3mnf8 6hwaa ju, ufpy4;$ 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 l(nz r0q* rf4v4qx f) kqp8d0mmaneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal componentsb n-,ihf w.1zv3xy/u.ffq m0l of the net force exerted on the car (by the gro- f0 qumy.v./ibx1hz w3nl ff,und) 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 acceleuf hrbzkv6bsm/ w:-7h6d x*t5 rates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static frictio*h6h/r z dvbx wf6bks-t:u m57n 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-so8f vxab/- :;onz +7qruycw of radius 2.90 m . At a particular instant, its acceleratios:va+qo-7zf c;-8xb norwy /un 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 gvs vp,a sy8) dip8y*)cravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s suriya*)v8 py dv)cs8 p,sface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g h8mp 9 t+qzsd)pas a magnitude of d8p+ zpm9qst)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 accelear)-l *-d5lsbfrdm 8tration due to gravity on the Moon. The Moon's radius is 1.74 f -atrmlrd8-5*s ld)b$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5tjamqj;9k. 6.hy.q ddj na9z+a..c ca times that of Earth, but has the same mass. What is the acceleration dun .tj j+qcyz. .aa;.maj cqad 9.6dh9ke to gravity near its surface?   

  A hypothetical planetg d*t5 u v.a7s dsdpio.s;0(yg has a mass 1.66 times that of Earth, but the same radius. What ut *vy a(psd.7dd5i .gs;o0s gis g near its surface?   

  Two objects attract each other gravitation(mj (mvvxd o.tu yob*zj snb/5*(;m.cally 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 acceleratiol t-u+ *riqzh;yp*zi 4n of gravity, at (a) 3200 miz lq*+pu4;h*t- zriy    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from t4zef5j/f;r 4mmu of.w he Earth’s center to a point outside the Earth where thegravitationam5r.fzmow ;44 ej/fful acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has mtbf3wxq q69w 6r h6u)five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfwtumq9q6x 36)b6 rwhface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was v )2lk;m(fkb qan average star like our Sun but is now in the last sb 2;(q kmlfvk)tage of its 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 ,kba8(di0rme l f.vn- feel weightless 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 accel .e80a dbvk,rnlmi(-f eration 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 sqwtgw0z tkf9v/sj/.n sk 1o8 p/uare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerv t98p/w/ 1f0kg.ztk js onsw/ted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the7t 3vx)6;gn s n)7 a3imhwwexm Sun. Calcunnw 7 x) ;3mv)g ix7wem6s3htalate the total force on the 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 Mars is 0.38 of wha6r2pq6skcc ( st it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Ms6 6qs2cp crk(ars.    $\times 10^{23}$

  Determine the mass of the Sun using the 0grz0y)+7 hjyqsf7 br known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]rbs fyy)7+7 gj0r0zq h    $\times 10^{30}$

  Calculate the speed of a satellite moving inp(uy8v unu+:9 gn3q5kk hfh. n a stable circular orbit about the Earth at a heig9kuq5upghn.:nk( yn8 3ufhv+ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovefl :pwja kj4*5 the Earth. How fast must the shuttle be moving (relative to Earth) when the relef lj 4kp:wj5*aase occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan+q sftr;ho1, 9z()dmdkl0y( 8i;/hslkclchb ts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter iskht8c9 d,kl/f( s(;h+ comqslzy ;r10dh)lib 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time iflfjvyz6djcf b (i:(1 ,9y /fmt takes 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 m(19dfj, zff/6y :cb v(yjflismall 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 t(i1gto( *zt n6a hbq*yo be launched from the top oibzny 6hqtg**t(1oa (f Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contin;rbql8mq9-g6y1 ld rrued to orbit the Moon at an altl 19r m 8brq6gl-ydrq;itude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn ard z5 wg1v hht)lk-.oh:e composed of chunks of ice that orbit the planet. The innz)5-1wlt hkdg v o:.hher radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter nryx--sh t8c6tvg06lrotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s anc - 8rtvx6h0ytg -ls6pparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a9d 0wnn4s t1ku kmd2/f 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (n19mnk/d0 dk4uf ws2ta) 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 ofp:y1*k woa ny6 two 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 mass6k*wy pn1:o ay of each?    $\times 10^{29}$

  What will a spring scale read for the weightn*lgy79w a/ frfjeso*f2e0y1 y d) g0w of a 55-kg woman in an elevator tha) s70dfae j1/ff9yegw*nyw rgo2 yl0*t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an ele1onp-am.(dies.acfdvp: 1w 0vator. The cord can withstand a m:s1 e( po dan-.fd.1iv0pcwa 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 orb/o(rre suc s-j.qa*0aits very near the surface of a planet with period T , the d/qrssja a( ue *.-orc0ensity (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 pe*e9-k6r hstwx f0smr/riod of the Moon (27.4 d) to determine the period of an artificial satellite orbif9x hwe0mrsrkt*s-/6 ting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred 0s ll0obp0w/i8 (qxqnd2r1lu meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the dsqxrlbn0(0pl21 ilq 0u/8 wo Sun?    $\times 10^{11}$

  Neptune is an average distanc(ndpfy j.h,hqi 6 c9 t9j5pdv-e 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 on5(oymq h0 vt.zce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Eqh0mt.( zo y5vstimate 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 cen1/ u5deydw w3pter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest.fe1hmx4 uy0f moons ofyxmh u4 01ffe. Jupiter (those discovered 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 thm41b05cirk4ot1 k qd + ,dxabme Moon. c 1art0m+ 4bo d1d xb5k4mkqi,   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons61vf+k (2++wfveed ivy2r u *cj yxj.c, using Kepler’s third law. Use the distance of Io af.x reyv+1kyjui (6fj e+vd vw2*c2c+nd the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmentyfkk38 7)ojxd s (which some space scientists think came from a planet that once orbko8) dj xf7yk3ited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a b vzpw479 da0inyu .qa8and 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 0q a8a947. dip vwnuzymake the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a haflmrv-jp5-hpp/*2 iinging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, /jl5fmp -hp*2p vi- riand the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be ha8w3nk 46vnno qlf what it is on th68vn3w qo 4nkne surface?    $\times 10^6$

  On an ice rink, two skaters of eq5lp-hdcp. lo,ov/ u)oual mass grab hands and spin in a mutual circle once ev c-p, u)o.lo/hpdvl5oery 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 apparen ic0pbqhr(jb p4*,l38) lx 2kg4zfcyot acceleration of gravity at the equ2x ll0z)cof bgr3k( pih*q ,84p yb4cjator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earw +w17le.kmr: ,dziieth will a spacecraft traveling directly from the Earth toiedeimkwl,z.1w:r+ 7 the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, b( fzsdo6q 8nr*ut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the*d f (8q6snzro acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cir)13tnjmmv1 okl.3 mndxt .4ekcular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter om.jk ttmkle1)3x1on3 vmd .n 4f 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 aircra1 nj2n1no.r,/sdq.e+ dwp oyydqg: p8ft in 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 for0lk6 6;hrcr;2y c tvnw the mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and thr0c; wcv yr26;k hn6lte gravitational constant G.

A plumb bob (a mass m hanging on a string) is(k: wm.rn+n) fqr(vb3tmi of7 deflected from the vertical by an atikr. mof3f )bqmv7(: n(rw+nngle $\theta$ 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 coeff3 -yjr ,) ;wjc)m3jgy a(s;:ick htttmicient of static friction is 0.30 tjaw:t hc); mm) ;kg,jyyc(rt-3ji3 s(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 fqcnngjztux 31xn+x5b /l; wf+u.l: 3 fast that objects at the equator were appan+z5t wl xgx +q3u ulnn3fc1b/;.x:jfrently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ox 1,)xcy crr ) 5l5,m +ikqb892jj0tronhaso rf 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 aty6a 3+:eefv/ff k:ec- m)xp7 9twiquh a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle oyief+e:/qa6h:p mt-9 xcewf)f 3 v7ukf 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, 0+8r2iptq pdoit has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of suchi02qppo 8+ dtr 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 2b ix au*be pn8w(rtbq+b+8; xan extremely massive core in the distant galaxy M87, so dense that it could be a black ho( ie+xnt8r ;8bwub+abxpqb2*le (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 constasqeiu6zugc5, em8(jo( o nz)-nt speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of cogs-ue, o6zcnz) (mie q 8u5j(urvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positip azur vig,7e*lra00y*k d-u4oning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be de4*vpz0a agu7d uk 0* eyr,-irltermined 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 travelin--gwdcwti ;ctqc08)r ) mz gh.g 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . iw t-cwr)thmcq gg)8cz-. ;d0 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 krh 91mo7tt( bshuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earthkt 97htmb1( or), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its un)1ad1.0 waalt0q z;* eaq5cb8xzel mean distance from theaat0z ) l un .bd8aq;*0we5aezq1x c1l 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 wo3aal8kajz/qr y* saq ui31:j5uld need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable asuk:yal i*sj/8r ja3 5az3aqq1 sumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around th: )jkfvgigh i0v.,a a1e center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lightiagvk1 0.a:fg)vih, j-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 square 0.50 m on each sideej.:zj kbe ucr*z )*4ay8i 5pn0(vvqa. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sivzij5pnb*q. ycr:eekj ( zv 4 8)*a0uade of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5;8e fby2aysex tx-l+3500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long swee(h32 j1hom ggj 3bh3erp second hand on y3 ob3hgm ehgh2(3 r1jjour wrist watch?    $\times 10^{-4}$

  While fishing, you get b64xtncxow8id 2w1; wzored and start to swing a sinker weight around in a circle below you on a 0.24x2wdn tc1o;x 6ww8i z5-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.]    $^{\circ}$

A circular curve of radius R in a new high4jzx7brx )7m bway is designed so that a car traveling at speed x b z7)bmr47jx$ 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 Acel i,y(9er5fx+ dmws7 mia, 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 (afi,wx ( di9m +ry75sempproximately ). (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.$\approx$    $\times 10^2$