Sometimes people say that water is remtyuv py/+iry750fs)e/h tm v 5oved from clothes in a spin dryer by centrifugal/imp0 yvht7/5vy5r fety)us + force throwing the water outward. What is wrong with this statement?

Will the acceleration-qw -t9rkgtd. of a car be the same when the car travels around a sharp curve at a constant 60 km/h as 9krt--qdwgt . when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where d,g,oj o nj v.dgz34st2pvk7 u,oes the car exert the 4o7z.tvj,ng, gv od s2p3k,ujgreatest 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 forces acting on a child riding a horse on a merry-ga: t b2js.*j:+ lnm83+ldj s ixmdjks0o-round. Which of these forces provik+aj+mm 3nlx :s s2:0*i8 ltdjds. jjbdes the centripetal acceleration of the child?

A bucket of water can be whirled in a:b c bl1aehq2.c4 m6ev vertical circle without the water spilling out, even at the top of the circle whenlb2e:vch4 1 .embq6ca the bucket is upside down. Explain.

How many “accelerators” ;s(r8db. w-i0ek mq ikdo you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate0ri;qbm wesd-( ik 8.k. What are they? What accelerations do they produce?

A child on a sled comes flying overvjus58oo (* sy the crest of a small hill, as shown in Fig. 5–31. His sj5uv*o8sos y( led does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders len vfa0)ml8bi b.s+7h nan inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compu d 8)uhylv1f/ute the banking angle given its speed and radius of the turnu y8v dfu/)h1l?

A girl is whirling a ball on a string around her head in a horizontal pla(gy j1* stxwzv:e5 m9une. She wants to let go at precisely the right time so t (1yj5 : mevzw9xt*sguhat the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large 3x 14tk5xlp gga force? Considgpkl1xtx45 3g er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ku:e b8jmg)cl bq22 wwzs376t ways would the Moon’s orbit be differenbbl7ge6wm:wt)s2cz3 jq2 k 8ut?

Which pulls harder gravitationl9iw5s/nc wmi5 q5f, otue s2y0;j5qpally, the Earth on the Moon, or the Moon on the Earth? Which accelerat osw tmi52necy ,/ipjsq lw55q5 09;fues more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. y37d9lkpu hl ;7* aizoYet the Moon's ydi*lk7p 7o3l9a uz;his mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more aoj1;as*s n1 9ior* vtht the equator or at the poles? What two effects are at wo si*aotns*; 9hv1oj1 rrk? Do they oppose each other?

The gravitational force on the Mox1ey3 cs-zwm;l9or8m on due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t83-x r1yzms mcolw; e9 the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its -rth:rivstc5s1piw;8 j) q o .orbit around the Sun larger or smaller than theo: tvi8)r .j;tsrp-w q chi5s1 centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east oksgoeiyt 34s7val ;. 7/::jyxf h+f oxr (b) toward the west? Consider the Earth’s rotatioja+hxvf7:4/kgl7. yt3 e:;ixfsyoo sn direction.

When will your apparent weight be the greatest0t(c fc26rjaje:pc;d*-nyg4rr exc ; , as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) ;recnc;p0*(ae tj:d c2r f j4cg-rx6yaccelerates 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 space could beuqh3oq lw2jj9)x ;s8;8dj lxhz 07lvm adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects f7uq j ;w38s 9vm;lxhohdjl8 2 jxq0)lzall, (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” or “apparent weightlessness” b zv0d 48yqtkyo6ztn flu a0l43m+yh55yf:w g4etween stepsfuzg0z4o5t ly:t4 yalwnh83406md f+q y y kv5.

The Earth moves faster in its orbit around the Sun in Januj3z w,,5 ubdlfary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in produd,l fwu5j,3bz cing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto waoduxuj/e690xz :xsvk/tea hk* sf,nl8; /qa2 s not known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mdh*, tlzxv 6 /xuu:;s9 xf8/nosq/ 2k kajee0aass.

  The Sun's gravitational pull on the Earth is much larger)b nq.glj e:d, 6btq+p than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25e.:,bt) lpb6+d gqjqn $\mathrm{~m} / \mathrm{s}$ . 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 1980 jpnp+cadi- 5ik p.7:e$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ar*4f ;vjl+/ kzgpsu*gjound the Sun, and the net force exerted on the Earth. What exerts jupk ggljs +4v* /*f;zthis 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 objr: ib1)j bbz:0eh)210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizont )b) hbibbz0: e:1jjoral circle (at 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 surface, and ci,-g;x iuuu pawm (ohbk 7oz2vqc2s0*,rcles the Earth about once every 90 minutes. Find the centripetal acceleration of ivqsu0-uum;bkowx22(*7g, ao ph,z cthe 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*,1koz1 vh.f dovrk.h4vx p3e the acceleration of a speck of clay on the edge of a potter’s wheel turning atvke* ozp..3 vorv ,hx1 1kdfh4 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 uniform rate in a vertical circleal5d5 rmi.re 9 of radius 9mirr5a5 e.ld 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of rarrewes6t9 z30 dius 77 m on a flat road if the coeffic6t 0z esr39ewrient 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 t v75att;mrxz)he road if a car is to 5ta7 ztrx);vm round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotp. ug*m il/l,7dk 2 i;fzjt5boate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back isd2,/g*. i5m7lj; bzf iu lotpk 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 owlc4vo-70 pp ;+jkfg pf variable speed. When the speed of thkj o7lcfpwpg-4p 0 ;+ve 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 static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down p0 3hzesier1nd 1y c4+at the top or40dez13+ y1pih esn cf 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 drivb-l+luq6q1i pbvq dk+s9 fh,0 ql:+ojer) crosses the rounded top of a hill (radiusvk0+ipq:b qlf,16hlo9+s bql +jq -du =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 Ferkpvb n-s6 -7jhris wheel need to make for the passengers toh-7s jb6vkn-p feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whhwxxp g 0(cw rf5j2rx k,8,i3r(s teb8irled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in thxx w8fg5(8h werrsix,3jr0cp k t2( b,e rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if eu 6j.ehrs6wl5.kq )ka particle 9.00 cm from the axis of rotation is to experience an acceleratiokw su.jk 66).h5eerlqn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrica/fcfu3em 7mtrb -yoy0:*9 en w 2pu1jolly walled "room." (See Fig.m b- jee* c:21 y3fn9uom/t7 puro0wfy 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 t +)60srocde(yp +epson a frictionless air-hockey tabletop, and pcot0rd( e yesp 6)++sis held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not igonxab2zv );ibk 6b,h4noring the weight of the ball which revolves on knb; ,b4 oz iaxb6)h2va string 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 for a car trav-esary5/w8 y;u w7n/b(mn +0o*ma9u ftdf orfeling 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 3we:3uwex30w sb.t nlye b9 f-+mddt- $ 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 disk (vg;ud4s+q ving 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 tangentialh:*lqfn33*usazo 7gl and centripetal components of the net force exerted on the car (hlu33l:* n 7g zafq*osby the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniforml vwhx z426;klgy from the pit area, going from rest to 320km/h in a semicircular arc withlwhv;4 xk26zg 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 horiy/eqd,o)xk dyh-w/-3lywxlu: qxi cj5 q,7o4 zontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.0 3h,xl jeu o4ox i:wdk),wqy5lx/7-q qyd-cy/5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 gravitkwlwtv q8q:d+s n:: o+y on a spacecraft 12,800 km (2 Earth radii) above thent w:vol +:ks wqd+q8: Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accele:j:bg .ojbr2 dration g has a magnituog: bjd2.b:rjde of 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 gravinq2fbgq n)f 05vdd-rva w+2+tty on the Moon. The Moon's radius is 1.74q- wdv25bd n 0f +avt2nfqrg+) $\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 makv3ku d)(y ospgn671j5:qs ezpch77gss. What is the acceleration due to gravity near its suz g 6ok(v 5kqy h)ss:j 771c37gepnduprface?   

  A hypothetical planet has a mass 1.67jt6 gk.x0+gon(/vkm:hm zr m6 times that of Earth, but the same radius. What is g near its s x+o(gm/rt : 6mzkvhjkn0.g7murface?   

  Two objects attract cure ;.b 8*hcv1dlpe9 each other 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 acceleration 3*pu. sfrt*i/*.bhzv cjqsc88rlra*of gravity, at (a) 3200 m c 8 rzj3lcbu pvqs* *f8r/h. i.ra**ts   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where87ky*at)l f ze thegr)l 8yefka*z7 tavitational 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 S :es:,z8)fl2ruab jo vuk ;;phun packed into a sphere about 10 km in radius. Estimate the surface grarj2u)z:;huk p:8, ae; slvof bvity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was ymi8fccx0yuuj454hca7u9 -w9 ge+pyan average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the j-m 8 cuwg4ci9cu 4e py 0a7h5x9yfy+umass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fey m8i0f8xan..xh2we-k ll2g t el 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 accelerationl. t 0wnxhx2 8.amf2lg-8ye ki 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 squ ao va6 0iiory b/)ly02,qx3iuare of side 0.60 m. Calculate the magnitude and direction of the x , lo)qayau 3 /ivio0r2by60itotal 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 planetsqcw; hbo4ib4+2-p(a cbb ;oqt line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The mb(tb4o2o;p-h;cbc q bwa4q +iasses 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 what051-n /rbjgbo.e gizx it is on Earth, and that Mars’ radius is 3400 km, deox-/5 ibr1b je0nz gg.termine the mass of Mars.    $\times 10^{23}$

  Determine the mass of thevy6xmaw-c+807 8l 6dhh flrsd Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawsxfmd a+r0 6-l786dh v chys8wl, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellitemtse,ls05n4 ab f10a f moving in a stable circular orbit about the Earth at a height of 3600 ks0ms5, t04f aflea1nb m.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbi3gwqc ,4r7ziz5f -ojkt 650 km above the Earth. How fast must the shuttle br 5gzjzq-i7c4 k3ofw,e moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupanaxsr: 2h8b7m p 2ob ,pr9r*qatts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer ahbq *mba9 7a p or8x:r22t,psrs the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satu:m4 5 j l9o9upxu7k *fhex,sxellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellitx5f 4uu,*9ho :xem9 upxlj7ske?    s ~    min

  At what horizontal velocity would a satellite have t fyx(y7aree8s.99z qjo be launched from the top of Mt. Everest to be placed in a circular o erzfyys(qax87je.99 rbit around the Earth?   

  During an Apollo lunar landing mission, t+63*ftqq ek4plmkd *dhe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take3k e*q6t k4p+l*q dmdf to go around the Moon once?    s

  The rings of Saturn are composed of chunks 4s-l uv73o imsof ice that orbit the planet. The inner radius of the rings mus7o lv3-si4 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 every 15.5 s (see Fig. 5–9). Whateo bl d,9fknzb0, gk**mjr5d 2 is the ratio of a person’s apparent weight to her m90ddk 5bo k2,r*n efl,bz*g jreal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg as*.nfat n uy)r7tronaut 4200 km from the center of the Earth's Moon in a space vehicle (a)a).n rutfy 7n* 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 nni9h p) ejor zu-i29-:uyv*s-star system consists of 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 massruj e299 y -sovpnh-)iniuz :* of each?    $\times 10^{29}$

  What will a spring scal/)i.c 4hx: wcetk (kdre read for the weight of a 55-kg woman in an elevator that moves )(xedk/kwi4c ht .r:c
(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 dk9ml7f5 l0ss of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitudes m7f0d5sll 9k and direction)? a =   

Show that if a satellite orbits very near the surface of a planet withe77beldvt (. a period T , the density (mass/volume) d( l7ba.e7 evtof the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the pzmo/ sf1b8( 0hxe;*vr*h ukb meriod of an artificial satellitvxbmszubf/r ; *(km1h*o eh 80e orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sb3ilt:08dp 9g6a ekavf8 0hy qun like the planets. Its period is 410 d. What is if8:8iav039kt0 ql pg6ydahb ets mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 x3scrv) ;*(k cw+eya rv owl82$\times 10^{9} \mathrm{~km}$ 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 9pao 9(xkhkn176 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 (xk1 9nho9pakthird law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of z nsei 69wk71 xy9o3gowyp6 w*aaf,h5the 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, a1rhc0052 g yg)edfjdyoi 8k/and mean distance for the four largest moons of Jupiter (those discoverefd5kcra /h80 gj)1 go 0iy2edyd 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 themd0j : *sr+smg Moon. sr jgm* :smd0+   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of4mzi:nkhso6 ;2n9oc,c f bd4m Jupiter’s moons, using Kepler’s third b4; nihz4km,c d62: f9o scmonlaw. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and ph ckd,:7ic 7kJupiter consists of many fragments (which some space scientists think came from a planet that once orbited thp7:dc,i7 h ckke 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 c2jde-i6h qe)r.wfw; form of a band completely encircling a sun (Fig. 5-40). The ij;weewr . icfdq2 )-6hnhabitants 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 revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging i,/dj 1-aj eoebn 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 1 deb,oj/ aje-the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of g8avjcpmef 5b5v3iqd 6fc4:nh5qs 3)s ravity be half what it3 6qba nvfshc3s dfipj5v4e5 c5)m: q8 is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a ojdbb 0+588r bj4;trfsnqf8 smutual circle once every 2.5 s. If we assume their arms are each 0.80 mj48js0ffr 8q 5sbb odt+bn8r; 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 appa *cebrf+rv8h+2j (yzwrent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnit( yhjc +v8err*2bzf+w ude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travmv m/m2wleboo zmdq4 )g0 f 6z3kt7gn,wrr(- .eling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull wim v gg7-(tmdz wlef 4z2bo3nk ,omr6/r).0wmq th equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand ojhwwy3 90 pvsrw6y4( ,:b o1hnb33vg jefq 2ekn a bathroom scale in an elevator,sv0wo,3 9y426:( yjvewe hf33q b1hbwgpn rkj it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of *oe*ae4zozx8a circular tube that will 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 (revolutions per day) if an effect equal to gravize8ox **oaz4e ty at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hiad88: ;c ,nslozv8fr ss aircraft 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 for the mass of a planet in terms of its radius r, thevsoq a (d7vi;8 acceleration due to da;vq 8o7(vi sgravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a str p6 ep:4 cfd3dcx;of-iing) is deflected from the vertical by an cfx 6o4ec; 3:fpddi-p angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of c*b r(*0 g p mxkv06dbof/wd9vstatic friction is 0.30 (wet pavement), at what range of speeds cap6 d*d0bm0gvv o cf9r*k/xbw(n a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that ovr/8el9d5c x5( d( o0zixlvat kt.tz2bjects at the equator were appov(cz52x5vt 0 /9(rleai dzxl. td8kt arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cox99r8bxgj* ut3q84q ifc w7cq nstant 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 constvi-s5w-k a)z ek1t- 4whk ngf-ant speed rounds a curve of radius 235 m. A lamp susp-kk4kf av-i1st ewng )hwz- -5ended from the ceiling 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 massivec gx j9los.mv dk3y0ce0mw 7shl9e*,) 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 m9c3j*vc9l7y lse0mewgskd ,ho ).0 x '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 w 2 cl a)d*n(.jj)kqkxpresence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escape)a c.)*w(kk j qdnj2lxs). 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 sppp08qq )rp g61k4 stkmeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill ankpp rkg418 t60qm)spq d 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 with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 sate(zyo s5bi 4brtur.5;+ mr5bozllites 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 centimeterstb.4rzymir+ zb(oo r5ub 55 ;s. 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 traveling 2.1 bilga(;-1*b yinqgx+o-quu0.n uxp5 i0u sxkq:u lion km, is meant to orbit the asteroid Eros at a height of a-; y-q(u.kp0q u isog5g+uia 1u0x*xu nxqnb :bout 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 shuttlen qp c9zacz2n :ar5sjbq m i**x.(88iy pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km c8s(2 xzqaj9q*a.nm *5:ib8 irz cpnyabove 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 30 u e2yaqjacj ;a/y5 n9q(e35r7/stcnl00 years. (a) What is its mean distance from the Sun?syt e(a;/jnauj 27ecaq5ylnq 5r/93c   
(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 actuall 63re(2q ypstjyc(qe-p*ek5y y "feel" yourself gravitationally attracted to someone nqq ee 5s2yypertyj36p *(c-( kear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Figpk3rz ko9t :pbn- rz/b1b98je . 5-46) at a distance ob8ek39p-tb9 n jo 1 :rz/brpkzf 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 square 0.5k*/be 0l8 gxhs v(x5u6t6zoob0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.s 6xb6(v e5hog ukb*zl0txo/ 80-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 j+*q::1 wdf;uue0o luw zuu6hthe 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*hq*9 tv:5r t)gyiuyx experienced by the tip of the 1.5-cm-long sweep second hand onqt 9t)x *uhy5 *v:igyr your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a y 6v1t5*qxwrlr5et*ba)wyl1circle 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 w )bavy*ly1e1lt*q5 wrt5xrw6ith the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that adws rx b35b9d: car traveling at spe9 dx3 5wrs:bbded $ 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,f;gq0iv8 nvdc c c13(v1km ts)k5wye4 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 yginfvd5v134wtc81kkec;m) 0q (c sv 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.$\approx$    $\times 10^2$