Sometimes people say that water is removed from clothes in a s 6 hzp,7c7.az q dfpwfl1vycq wt7;78kpin dryer by centrifugal force throwing the water outward. Wha,fkw76yz v7faqp;dw7 qcc.lzp h17 8tt is wrong with this statement?

Will the acceleration of a car be the same when the car travels around0 xpy,7rd ngp) a sharp curve at a constant 60x pypdg70rn), km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constanf 2us/r2tt+ vlcor9a1t speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom o9 to rt12c+vrlua s2/ff a hill?

Describe all the forces acting on a chi *5(uxlhkw w1u6rq gz-ld riding a horse on a merry-go-round. Which of these forces provides the centripetal acceqx- u5u (wwhr1 *zklg6leration of the child?

A bucket of water can be whirled in a vertical circle without the waterudxhu(x + )5ds spilling5xsdxu ud()h+ out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Therqvild.l mx8aiih/,gj87/w3 iut.*s s e are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations di7vj. wm* s uisa h/8l8d3ii,/qxtl g.o they produce?

A child on a sled comes flying ahg n:cptm.: 2 7hegkz;8wy7pover the crest of a small hill, as shown in Fig. 5–31. His sled doggc pa 7zt27:hymwekh8p.n:; es not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundinge akno-4vm) lv4- b;uk 4h*ydq a curve at high speed?

Why do airplanes bank m (v *((darwz jevs7s9when they turn? How would you compute the banking angle given its speed and radius of thesa9s wm*dv r e(z((vj7 turn?

A girl is whirling a ball1rb)qm /l(mucoqi*6dw 2y s hc g9v/k6 on a string around 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 shokq 2*wmu rc ib 9cl6dhy1qvsm/6() g/ould she let go of the string?

Does an apple exert a gravitational force on the Earth? If syy-v v+co p1,mo, how large a forcevc +yv, -pm1oy? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in b 1igt(gkaoo y t,8b:fe0/m-gwhat ways would the Moon’s orbit be diffe ko -eb( f1:aty igtg0gmb8,o/rent?

Which pulls harder gravitationally, the Earth 6 6 )f h:a ka45t1qqbhjctcza:on the Moon, or the Moon on the Earth? Which accelerates :qhb)a:c ak5f1aqc tzth 466 jmore?

The Sun's gravitational pb x7ne+q9a/z yull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in grq/zx7y+bn9a eavitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects +;yrzhn*h q9i are at work? Do they 9+*zinhq; ryh oppose each other?

The gravitational forcrl)jn8x3w y :oe on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled aw n8o3xl:w)r yjay from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or smur8n i/0ua v)jaller than the centrn/8v airj u)u0ipetal acceleration of the Earth?

Would it require les; gq x rwq42;r/gzp(h 1xgx(yhs speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Ea2;g4w r pzrq1x(hh/(ygq xgx; rth’s rotation direction.

When will your apparent weight be the greatest, as measured u;q7 e4ap:faeby a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant spe4a7ea pu:fe;q ed? 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 spa nsub32kcr03o ce could be adversely affected by weightlessness. One way to simu3k s23ouc 0nbrlate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner ex9f) f nt9llcpmi5)2*.yryprc ;uun 2 zperiences “free fall” or “apparent weightlessness” between st);m9pnf c frtp 2 l)u yclunyzi95.r*2eps.

The Earth moves faster inq6ek57kw/noags x +v/ its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing th oqn5/v+xgks 7ek w/a6e seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explain.yn 8 eczdm)h+yq6+2- nlxw(fg8amm au.y k8b how thilmgm uc.naqz68) 8nyfk2 h(-b8a.x m+eyd +wys discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon/smrz- , oy*gt's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitao mrs/t,z-*ygtional 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 1l, ftio2s(1iswn41.zxysp)j l ,- m qy980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetani2l 3u xb, kmee .;(gfts7 myf+lhs(.l acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume thy;t.g nklsf +h m((mue3s.x2fe,il b7at 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 nem:3k o*-lgs 9-acwlp qp(0c*c9zts2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the sp-9 pg-k wsa e(c3l9q cl 0*tpocsn:m*zeed of the discus.   

  Suppose the space shuttle is jvgmeidrn a;14yf/s*4p94 gd in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleratif 1rji 4ng/* e4pv4dda9mgy;s on of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on thp+jrnu). xst a )1t- 0 kizgx/1yh1kfoe edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter i kxth 0f-rkiu sx11/ty)jpao+. )n gz1s 32 cm?   

  A ball on the end of a string is revolved at a uniform rate i aakjix *v1ucn*3i 7n+hua .*fu 1ej2kn a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If * 7n 3f*ucauh1 xiv.ak ijn +u2ja*ke1its 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 *46ezuzatr8 vg.5 y1rb8z i ptcan round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Iszrtebutz8 zr*16 g4viapy58 . this result independent of the mass of the car?   

  How large must the coefficient of static friction be betwen hnz.0.4qn;ct6il q een the tires and the road if a car is to round a level curve of radiuszt .inn .q0l4;qc6 nhe 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilo0)fq: 6q1wnt gzzr9l 2f ky9fits 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 :9fwr qfy1l0)q96f z iztgkn27.85 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-wxrp mv v1l/da (1c0f turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixem-(vvlfc1 xarwp 10 d/d 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 hjs;kp-d xv. 6a roller coaster be traveling when upside down at the top of a ci6hxk vj-.;sd prcle
(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 r;v3ajrrq b84e8o o7uc(0i gq) crosses the rounded top of a hillur7gebc0ojoiq ;8 ( aq4rv8r3 (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 Ferris wheel ne/s vw6 68uj,x*xjx bojed to make for the passengers686 j x,jjouvb wxxs/* to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 xgchof/(c3;1f +)t (utm twiekg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportingo(tf fh+1txu; gc w3e( )cmt/i the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm frd7y /v b8ejiw-yqa1r9om the axis of rotation is to 7 d wb8yj-qe/a rvi9y1experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivadgki2tl1k+d3*pt4d ;r ftdh3l, people are rotated in a cylindrically walled "roo4;r3t12d d+kkd tilphf dgt*3m." (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 roan(qb 8yp/cpwo //*l otated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling (aboy w*o/p nlqp8//cblock (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ba :ndn *dgubunp06p-c9ll which revolves on a string 0.600 m long. Inp-n6n g:nbd d*u p09uc 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 1+nk efpz *s4ea 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 ag.ocoyi2 8n. $ 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 at 310c lti faba(xb 03e+0o4 $\mathrm{~m} / \mathrm{s}$ . 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 cent,lmusj4.j sz -ripetal components of the net force exerted on the car (by the ground) in Example 5-8 wj.s s- m,4jlzuhen its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pitxmrp1avvm( lx r 2-fa;d+(6ql 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 friction have to be between the tires and the road to provide this accelerationa mf;qlp(2-( v 1r mldrxx+6va with no slipping or skidding? $\approx$   

  A particle revolves in a horizonm2jua 2- jav iy9 0xktut-pv*/tal circle of radius 2.90 m . At a particular instant, its acceleration is 1.vuta2-jj*/ 2mi - px0tyv ku9a05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 6k7 6l696yip+ ja4xkw adjdxca spacecraft 12,800 km (2 Earth radii) abovecpx6x6i 6w7+6da jal 4d9 kkjy the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certj64+sr c7 xx8jt4xai,+ ukfisain planet, the gravitational acceleration g has a magnitud+ifx47axt,4js s jxiku8+ c6re 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 accele61t.g 9ih9x1k7gk0s jepe ti ik1naz3ration due to gravity on the Moon. The Moon's radius is 1.7ts.hzkkgie131j 1 0knxapti9e6i g7 9 4 $\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 Eaxugx (:/cpd h7rth, but has the same mass. What is the acceleration due to gravity near its (:u/7xp dxchgsurface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiuskn1w i w.iyb( *q;tzz3. What is g near itskz 3w 1;ibz*(. intqyw surface?   

  Two objects attract w 5jubw6nxpx196ok 3beach 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 of 9;kx7sy o9zxcwt8 eu)gravity, at (a) 3200 msoukcz7wx9 t 8e;9y x)    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center zd g5 6jtjp:m/to a point outside the Earth where thegravitational acceleration due to the pzm6g j:dt5j /Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five t4quq i7cdfk8f9l(-i wimes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monste 9-84idqc7q iukfflw(r.    $\times10^12$

  A typical white-dwarf star, which once was aqtv /iyn:b 3kk28d d+xn 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 s dxnqd: y83k2bti vk/+urface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fee. u2k(d(kg5 qcfwfe t2l 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 efdu(g(.kq wct2 5 kf2acceleration 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.2qch2rgddd5)-f rlw1 Calculate the magnitude and direction of the total gravitational force exerd2rcld)d r 1wqh-g 25fted 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 samg4e/ilgf:*k7p j5ez ve side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets4g*fk5g7l /j:ezv ipe 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 d kixu,4tyj 7*oyms;5of Mars is 0.38 of what it is on Earthj 45yuy7*d xtskm;io ,, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Suue3n ewh ky0.f:t)*fdn 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 :ufnkw eh*0edf3y)t.’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit w60mqx imw+ wpfl8x57gx95m xabout the Earth at a height of 3600 kx li5mqxmp50 +m7xw 6 xgf8ww9m.    $\times 10^3$

  The space shuttle releases a satellite int( zae8 *dpfz)vo a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? dev)*pf a zz8(    $\times 10^3$

  At what rate must a cylindrical spaceship r; b)27uts)3 9snx ,y ksthyfduotate if occupants are to experience simul7n yh ss)k 9)2dusxt; fbyu3,tated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to or ( r-hd0uxzw*b cjf xlz+c;h(8bit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which f*-l0d xj8u (wb r czhhzxc+(;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 to be l 7 *u8fv;c:tldum+jok aunched from the top ovk*tmljuf7o 8 :;c+udf Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oaf(t;tx(x3/sm /yt1z(fuo r f rbit the Moon at an altitude of about 100 km. How long did it take /(f mf 3/xrx;1yttfs (zt(au oto go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plane- kq ;x3mo- 8dlrwsp-th9sdy2t. The inner radius of the xh-rs-lq d9 y k;p8so-tdm23w 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 di7r 0t jgm,zcddu)/c b3ahru/2ameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the to)3j/c20tdcud h ,rmbraz/7g u p, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronau vk2;i0n5awwv t 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constaw 2vvknw;0a i5nt 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 it 5kz :d 81z)yc*roegymxy6 4system consists of two stars of equal mass. They are observed to be separated by 360 million km and takeyke6r5gcomyz y 1*t :4d)xz8 i 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the we9;lio 0dj b azt)6/njpight of a 55-kg woman in an elevator that monljpdz9i6j tbo/ a)0;ves
(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 of9 th b1*u/+oxy0pu zyc an elevator. The cord can withstand a tension of 220 N anz/+*o1 yhtcxy9u 0bup d breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surogl+ vq17wz.vecq6x npy8,; 5yi ph)s face of a planet with period T , the density (mass/volume) of the planetxyvh e ;.+pn7)zg5qwo qp,18vlcs iy6 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 kno;:c jp3e:o :ci zktl4)jd8the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’scc:jd:ktnoikj e)p3:; o 4 zl8 surface.    s

  The asteroid Icarus, t1ih 0vbarcbx a62kx71hough only a few hundred meters across, orbits the Sun like the planets. Its period irhcxi a vb0x1261bak7s 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o wnb-g f( :0q3kejekel7o:a )rf 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 2koz1u fklfs;m ph4):the 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 comet flpuk;fh1 )z2s4o f:k mrom 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 ctas8g t0/ )mkq*wjgt6enter 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 mo/zqzdy q1,yjdxj-wtl 4 02 8qcons of Jupiter (those discovered by Galileo i2,1y 4zxdq tl0c/qyj jq8dw-z n 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 qrya.;3w(;lnwsza z i6 2ls k5Earth from the known period and distance of the Moon. ;2qs5n s; 6w(arzaylk.i z3wl   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usinmtvr7(hy j +i0g Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to+ try70mjv( hi 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 gy bnl3sw/( ,+ zzos0nmany fragments (which some space scientists think caml zn0ynzg,o3b/ + sw(se 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 405 k7bxaw5wix)d+ +vb5l zjvh4abqe describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is alwad4bkvavb5q5h0)z w5lij x74+e wb+xa ys 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 in an arc from a hanging vine (Fig. 5b8 h r5ntqups ofg.7 )w0gk,9w–41). If his arms are capable of exerting a force of 1400 N on the 9ton)wuq7rk50gbpgh8 f.,w svine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface willc3 v prryznr74qf0+/cctbi9 . the acceleration of gravity be half what it is on ivccy+.z b73t rp0/fqnc rr 94the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab ha g./te da)xpo1nds and spin in a mutual circle once every 2.5 s. /)1t.pdeago xIf 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 appa;w31juax blb0 ukrc3-rent acceleration of gravity at the equator is slightly less than it woulduk j ;wcb31u-3rbalx0 be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrayv7h9xj.f p4 wft traveling directly from the Earth to the Moon experience zero net force because the Earth and Mxvy9.7 p4whfjoon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kgzn.k.2r 73emfk zyp :f, but when you stand on a bathroom scale in an elevatormz:7k2r . zn3efp kfy., 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 consh, /9oiqu n h87h6dj;84hows bdfih 0nvyb 6q0ists of a 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 db6no o 4 dqi0nyhb q8 9 ;h68uvfh0dihh/,s7wjay) 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 (Fne3aut l 7k9)ix nb wgpb ,4o7.mojk.3;ftb k.ig. 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 lqz i 18o.p or45fhpoi93rthwl d*x7-its radius r, the acceleration due to gravity oirz8 hw9p3ot* x1i4fqdrph-7l .o 5lat its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertea7)t,xehd*7g- fr hy ical by an angl*grthdyx,7 -e 7a) hfee $\theta$ 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 coeffinhelquwco d-he 30 );c* 6f/dh3hwkw; s+fu8tcient of static friction is 0.30 (wet pavement), at what range eew/hhw+d w;uhs f)u tk 6;qoc-n* 3d0h3cl8 fof speeds can a car safely handle the curve?

  How long would a day xj4khg+cv8 3kbf jj8 :be if the Earth were rotating so fast that objects at the equator were apparentl3jb xjjcf4kg:+8k hv 8y weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 1yn26sgu9e k9/n iwzi$\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 consgtj9v9 a xb s(:8ycio: vum+.etant speed rounds a curve of radius 235 m. A lamp suspended from the ccoeg8m j(xv.s +:viy9atu:b9 eiling 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 ptxo1v.t u0xj- ,kg;y massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter spy0; o.uvtkj x 1,x-gtince 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 Spacsw5(ihkc ;2 rde Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which rciwkdh2 ;s (5no 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 constancxode m7,t hkl-*6y)ft speed as it traverses the hill and valley shown in Fig. 5–45. Both the hi-m) de ctyo*f67lxkh,ll and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System x2qcp/n t k n1+z588aoo:r ktvo4sl v0ubpq33(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 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, allouo3 10 qrppvbt8s 2:5xvoz t/ 8aklockn q3+n4wing 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 billion km, i)f ejfwe90dh*9 qqcn)s meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40f9 )qncf0ejw e9d)* qh $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 purc /omxw3ne:.k suing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but mx w.c3:/keno25 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 perin pfujy9 e*dc((p(h vter2g, .od of 3000 years. (a) What is its mean distance from th 9njpt.g(up2efe* r(,y(vdhce Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuallylz+1y q, 2lr6go cl*pq "feel" yourself gravitationally attracted to someone near you. Make reasonablerl,yzc1+ 62lg qqp*ol assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxyrkqn3+f 8hf,m3c: wl1 owyyp4 (Fig. 5-46) at a distance of about 30,000 light-years from the cent1cwoy8f, +wk:3ryplf 4 qnmh3 er $ \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 squaa5 :u av: ohb*mitz .8a4ymo rv1-6sivre 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass place1vt*a 68hiz5.ayuim b-: a vorv4ms:od at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the9mtp7e /hq*lmx1m9l 6p8nizz 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 1.53 or+3tavsx2+riii wm0i0j7 sq4eo0t -cm-long sweep second hand on your wrist w s emrj2+0ov ai7t3iw+0st3xr0oi q i4atch?    $\times 10^{-4}$

  While fishing, you get bored and start to swingr.kca qti5 s12 a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle eve.k i 1t5csr2qary 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 ne v64 h-ks ojtw w b9u/n6tt4avmtf,3i5w highway is designed so that a car traveling at bk4/w9tmut oj4,ift a- tv5hwsv636nspeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negog pg9r h ydq7j 9k47ledpe//-rtiating 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 f/p erp j9qddg9k77yhreg/-4leeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$