Sometimes people say that water is removed 8e( g wqjda dq2 dsttgh.2+,l6from clothes in a spin dryer by centrifugal force throwing the water out8 62.eh wtgql+d2 jts,(g adqdward. What is wrong with this statement?

Will the acceleration of a car be thwoy r;bjc- e3,e same when the car travels around a sharp curve at a constabr c-joe y,3;wnt 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constx-0iq oe-ny7s8t e uf8r41xjj ant speed along a hilly road. Where does the car exert the greatest and le8e7r 0x8-juio 1fej4nx-qsy tast 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-go-roug7u ym 1 eff,2g8a7n:gs nvp;wnd. Which of these forces provides the centripetal acceleration of th8 v27 gn pmgw;7gsef uafyn1:,e child?

A bucket of water can be whirled in a vertical circle without the water sp)v k3c:31we l8yc znqpilling out, even at the top of the circle when the bucket is upside down. Explai 8qly3c3kv:p )w 1cnzen.

How many “accelerators” do you haveos-. ircs2;i m in your car? There are at least three controls in the car whic i; simsc.o-2rh 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 cresmv6i9w yap* j2t 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 chest and the sled decrease as he goes over 2* jvy69mwipa the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders leeau2 a ma42;,fprw k+dan inward when rounding a curve at high speed?

Why do airplanes bank when they*q3e4 zql-pb4 q (fdndqk)3tf turn? How would you compute the banking angle given its speed and rade3nk4 pf d fq*bt l3z(dq4)-qqius of the turn?

A girl is whirling a b0o nilxov,,pbn3ib , u8 i:wk3all on a string around her head in a horizontal plane. She wants to let go at precisely to vk ,libb33xi0wnu pi, o8n,:he right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a ga 5wuzi1 eb.2w/d7 qnkravitational force on the Earth? If so, how large a force? Consider an apple qnwe .7u/zwd25kba 1i
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wh+5ed * kc,j+gel:fwi*xse y)h at ways would the Moon’s orbit be different ice 5g ee)+,: *+hywk*dslfjx?

Which pulls harder gravitatymjm) n-3 hxpp 04cz2, yt)kwmionally, the Earth on the Moon, or the Moon on the Earth? ky hw4c )xynj-) pt3z,m20 mpmWhich accelerates more?

The Sun's gravitational pull on the Earth is much laryi:o)v5j zj/f ger than the Moon's. Yet the Moon's is mainly responsiiz 5 /)jjyfvo:ble 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 at the equator or at the poles? What two effmbz81c z,k3 t6mtn- hwects are azw htmk1bc - 3zt8,nm6t work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about skdmt2 fb p cts-),u,0half the force on the Moon due to the Sun. Why isn’t the Moon pulled away f )ukb,-p ,t0t cfmssd2rom the Earth?

Is the centripetal acqit8xdcs8rv by 19b) /celeration of Mars in its orbit around the Sun larger or smaller than the centripetal a1y/) bi 89stxvcd8qbrcceleration of the Earth?

Would it require less z 9)8vklr az8( xj:enktdh6) ispeed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’sta)zik8 :v n l 9x)rhe6j(dkz8 rotation direction.

When will your apparent weight be thejg in:v-lz-4g greatest, as measured by a scale in a moving elevator: when the elevator (l giz:4--gnv ja) accelerates 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 space could be adversely affv93fb(,jyq qso)jt,mected by weightlessness. One way to simulate gravity is to shape the spaceship like a cyl,ms,v jbtq(q3 j)f 9yoindrical 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 “free fall” or “apparent weightlessness” b -/e.eyl(jaxc qmu7pl;6fx c9etween styx.j/cq-f au6pl xlme( c;7e9eps.

The Earth moves faster in its orbit aroundjx(a2jidg-(vn q 5 52owmo f(s 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 the seasons — the main factor is the tilt of the Earth’s axis relative to thn(( wmj s5g(a22j 5qd v-oxifoe plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon.nfynt6.u9.wi1x fh rm6l,a/ x Explain how thinth6ixrn,.19u6m/f.y xwf als discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitationai k0yez 8b5wwwm8+y s.l pull 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 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 1.2 z. +k8iweyy0mbsww585 $\mathrm{~m} / \mathrm{s}$ . 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 travelini( y,0b /uxqug-n ake+g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acce baeh616ce4x3o he1um01ip mdleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts th13 hmu6oa11 exbhp e4idc6em0is 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 bm/ku bg;o(x u1cu7c+ on a 2.0-kg discus as it rotates uniformly in a u 1b+ou;gb/m (cukx c7horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is d*mmbf- dzafnmk7m 5 b/8f3b- 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 shuttle in its orbit. Express your answer in terms of g , the gravmz8m b/kdbdnmf -amf5b-* 3f7itational acceleration at the Earth's surface. $\approx$    g

  What is the magnitudk(*0o cdynp-me of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter i omcky*-d(n p0s 32 cm?   

  A ball on the end of a string is revolved ajmrc: e. 5cvk1a( bva-t a uniform rate in a vertical circle of ra cev 1m:jcb5k-a (ra.vdius 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 a1 vm lj1z/kdnj;9r)g-r btk4y turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the masslm rg1d1z4bt/-n v) j9jr;kky of the car?   

  How large must the coefficient of static friction be 8jcokz(h 0v66k)ixd9g9ymnh wc ic74between the tires and the road if a car is to round a level curve of radius 874mz9 hykk 6j9(wc8)cidnghi cvo60x5 m at a speed of 95km/h ?   

  A device for training astrondxrw 2m oya tnr. 15frpw3*2m-auts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?narxf 3tw5-*yomrp m.1d2r 2 w    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 :z*8uvi 7b54bupk snvthe axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm 5bi7vv * 8un :kusp4zbis 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 roll7 7ak k ymywsu6w9s48q9utva9er coaster be traveling when upside down at the top of a circkk a9yyssm8w a 99v77uq4 wu6tle
(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 (9f: taghj o4 h:-s0ergun9ld2 including the driver) crosses the rounded top of ae 9df 4s0gou j:9nthga-2l:rh hill (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 Fer-p7h.r y7hcpk ris wheel need to make for the passengers to feel “weightless” at t-h kh.yr 7cpp7he topmost point?    rpm

  A bucket of mass 2.00 kg is whirl* ,faae7 lpm8ved in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporti8pma* e vafl7,ng 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 9.00u difdp) wh,q,;r53 t8chklk2o;lq f1 cm from the axis of rotation is to experience an accelk fpu ;dqkol 18r,);5cl3,t2fh wqid heration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cydugfm78sl 5xu+rp8 xb8 p7q ;glindrically walled "room." (See Fig. 58+5ugg 7xpf ;qblx u8dp8s7 mr-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 rot d:q1+fu8 z x..iss-f ijvti:vated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central ixzsui:+jq1s8 ft vfi .:d.v-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 ts ( w;1aqitgg-7c wh.nhis time, by not ignoring the weight of the ball which revolves on a stri1tn.agw;g(q 7wch is-ng 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 2xunrucs .c/ik:n vx 943wgumn 324ni 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses g8lm.jzb c:b iy164 wf$ 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 31vy l+*pkx6ey30 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exertedz6fxf2q 9 zoy/d3f. u5.loeop on the car (by the ground) in Example 5-8 when its speed 6q5z fyz. 9ofof /euo2.px3ld 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 pit area, going fr2f0rusd s30+k xnip+w8oigr-om 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 frictiw un03sr i2+0+8- kdo fxispgron have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a mm1bhsox1k b 5en9p8 g)rw8r1 o;ie2 mhorizontal circle of radius 2.90 m . At a particular instant, its acc g8emkr92n1i)b 1woo r1emm 5hb;8sxpeleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on j jq7)n;rl-ksa spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if itsnsq7 rlkj -;j) mass is 1350 kg.   

  At the surface of a certain planet, 3f +3v j4ypbvaf7cn(ythe gravitational acceleration g has a magnitude of 12 mjfc 3nbv(4vyapf7 y+3 /s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to 9gm-f 7b x8, cqpcdq-rgravity on the Moon. The Moon's radius is 1.74 q ,- cc9mr8dxqb -pfg7$\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 thatt m t(t2hdwz6. of Earth, but has the same mass. What is the acceleration due to gravity ndh(t 2zt.mt6w ear its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiusxi nxkbp 73. twb.gtv,. gxngd. )4rr+. What is g near nit p.x b+rrxbg7.x nv4)g. d3.,kwgt its surface?   

  Two objects attract each other gravitation-v bz0 f,vdrn(qfy, .fally 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 effectiveptz +99gry92x,znrsc value of g , the acceleration of gravity, at (a) 3200 m gtrprzx2+99 9sy cn,z   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center8z v91*h8fineh *dwp o to a point outside the Earth where thegravitational ozhf n9**8phvw i1de8acceleration 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 5yc,g8e bv/m/jy ;e;yakqu e6of our Sun packed into a sphere about 10 km in radius. Estimate the s;5uycbye; gq,vyekme/ a 8/6j urface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an- 3 ouj)cz,pmouqc-+v average star like our Sun but is no-qmcou+j-c,zv)3 p uow in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fef d; bj n+tpfb;+lpcpy8( *va0el 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 acceleration od(t ;vf bp ab+;n yl0j8*p+cpff gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located ajwk*uz12x o-yp45yo hp:j2jk t the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphe-pu2 k1 jowj 2xpyz4*okyh5j:re by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years k0ad +j 69bs5-yg6(txcb3s /gzc ygcs most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all cb-3(s6zg td/s+ggc 9 0bck5sjx6a yyfour 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 x+ i: 08ggx2elbenr2s is 0.38 of what it is on Earth, and that Mars’ radius is 34+ :sgb2grl xen20i xe800 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for fvz;0 e7)v ugqthe period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Keplereufq7v vg0; z)’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellit 5fegah)q sw;7e moving in a stable circular orbit about the Earthe) gfqwha; 7s5 at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circularfg0u j.l9nj 3f orbit 650 km above the Earth. How fast must the shuttle bnj.lfj3 gu9f0e moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate ,v - gb: x-chwcd4oi+rif occupants are to experience simulated 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 Quevhwio- bc,x-:+r 4dg cstion 21, Fig 5–32.)   

  Determine the time it takes for a jg )jusu/a6e: 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 i/ j6gusuj e):as 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 c.7uj5,rrsj0sl d6yg to be launched from the top of Mt. Everest to be plarly.507c ugjr6dsj, s ced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oq5sfik sfmiosmvie4 5 r*-.67rbit the Moon at anrk*64-sf io feqm5v7ims.5s i altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The i,o +yygdo 6jbf0.e vq)nner radius of the rings is 73,06b o)yjvqe og,0yf.+d 00 $\mathrm{~km}$ , 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 dyd:fyx+4nkzgp8 b2tz ,a+ r2niameter 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 top, and (b)2ydt+nzx8 , 24 yanzrpgf+kb: at the bottom?
(a)    (b)   

  What is the apparent weighz/5z0vxuo :jt/8u hqi: tcr b:t of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at : v/bhtuz8ir0 c :t5quoj/:zx constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equaly*o,wmtf xq, ct,)w/s 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 mass of each? cy/wf *,, s),twqxo mt   $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman 1gk(; l1:ameh w,txpzin an elevator that movg11km,leth (pz;xwa:es
(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 r +t,he sxi3ue,w: .op0xa vp59 mq4euan elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevatsu5, +4 x0epeqvir xt3h:,9aw.oump eor’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wi ,7qt*9 yd, osf6ufhtith period T , the density d*,f9siyof6,tq7th u (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 pep xe6,jq(gv aco1er(1dh- t-kriod of the Moon (27.4 d) to determine the period of an artificial satellitd(xtoq-c61(-ghep 1a e,vkrj e orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, ordjo3mfn .llx 9 8ye7 9t2y1qebbits the Sun like the planets. Its peqjy9xebet92 8m3nfoy.7d l1 lriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o y;b.ip4kxw4 kf 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 rw;rfkuq 8e m;cx(b:g+oughly 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 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 th ug+mecf:b(q 8; ;rkxwird law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the *bj/7 x0-i eyanq7t0blrf)+a6 , vj ppgxxli0 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 distk,pj z,*5lp pmaw,dh 3ance for the four largest moons of Jup*aj,p,m3h 5d,wk zppliter (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 hgqoktf, q3.eldtym i347t8 041jo njof the Moon. fdt 3njoy0l44 iq,18ehqott3g j.k7m    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moo cuylo6gjz91xoy3ijzuf*c;98 *j x +c ns, using Kepler’s third law. Use the distance of cxl ;uj3zoof9 cy96ju1*8ix*+jyczgIo 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 Jupiter consists of many fragments hv shkz (258iu(which some space scientih uv5zs2 ik(h8sts think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in thxqy) iydb41vx2nw;8gele2m3j q p 5f 3e form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as 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 n2qxpb43iey 2 1qvy ;gwdj5eml)8xf3the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vix7 j56ibmqif,ulf 7.gne (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 mibf6 xmu,i. fgjq7l75ass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerat9n:y v o2kgvb42h/ugi 5fq a1zion of gravity be half what it is ono21 kv ygfi5vzh2ub:qa9 4n/g the surface?    $\times 10^6$

  On an ice rink, two skaters of ir0-rh u n5sth.l aea:84zh2eequal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anotherzh u .854 hhas0 :rentra-le2i?    $\times 10^2$

  Because the Earth rotates once per dl9 g;kcy+mwni9fz9niwhx-x,(ns* :n6fds9 j ay, the apparent acceleration of gravity at the equator is slighnm iidjs+n :- n69lx xfs*gyz9w;(hw,fn 9kc9tly 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 Earth w,ymt:(suzc1mq jj4z -ill a spacecraft traveling directly from the Earth to the Moon experience zs jy j:1mczz-t,m4u(qero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand ogks gl7 in.f)ns1 4h3in a bathroom scale in an elevator, it says your mass is 8 )gignn.3k41s fs 7lih2 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tub1y7;atsbva1 f/ ; rs g90yhjqke 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 equsj09 t7h rybsy1a gf/; k1avq;al to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig.fqqz o 22i5jc. 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 c *jw-;h3 /ec5bwujfw so+(wjr, the acceleration due to gravity at its surface and the gravitational cs;wewu-j(+ww h*oj3/ j5fbc constant G.

A plumb bob (a mass m hanging on a string) ib+wb,7 l(ato js deflected from the vertical by an angle jo7lwtb(b+,a $\theta$ 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 forn *v-0hjqg c/to ng9-plvzf31 a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what ra/0jvvg 1zc 3hgtfn-*pqn -l9onge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obj2w0 5wcj7 x 2kyll,5 1bxpho 6ig6ucayects at the equator were apparently weightlessxj u72bwhw62 5lcigla1x, y0pcoy6 k5?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apar x v46oilhbm49t of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant spee8m3 +(mdl levtd rounds a curve of radius 235 m. A lamp suspended from thed l3+(te 8vmlm ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320ej 1gugfc4(oy f5/4,rp x)jkf times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's.1e pxkj f(4ggyruj5ffc 4o/ ,) 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 press (ea5-3xagwk)z3fc+g/pzuf v(und (ence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiti)d wua5(fpkcfazx 3-uv(3+neg g (zs/ng the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traveo5s x561k *8nx wldj.c uxf/dgrses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact wit us n65xxdxjg1lkd*f8 co5/.w h the road at A?

  The Navstar Global Positioning System (GPmv z; :jtl34l n;gpk1kS) utilizes a group of 24 satellites orbitink1;:mkzp3n ;lg jv4tlg the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 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), g b ms2d9x0jf1after traveling 2.1 billion km, is meant to orbit the asteroig sxj192mf0db d Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pul7ni ;sk: pjh+ms *he1rsuing a satellite in need of repair. You are in a cipk1 l: sen7j;is hh*m+rcular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean 7z4hxou*;g/kv+3. 0gjmttvh)f su lp distance from the .hkgt)0u4mo+x u 3zfh sp /gvt7j;*lvSun?   
(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 .h0gsna;n 9 0re i8d:fcs h5oxcould actually "feel" yourself gravitationally attracted to som8ih ahn0: sex9c n5 s0rgf;od.eone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a (fr8mgc/v:o9w;t i) k6h k rimdistance of about 30,000 light-years from the ce rgicwk f9r mm/hok 86;:)vi(tnter $ \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 squaru bgnl)h4 b/j0o; (l3we;fumne 0.50 m on each side. Find the magnitude an4um ehwl 3gub lf;/b( j0);nnod direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits+w6 l+njadw+/yl 2av l 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 dr6wnni .ws wju.2 1e5of the 1.5-cm-long sweep second hand on your wrist wjrn wnusiwed521 w.. 6atch?    $\times 10^{-4}$

  While fishing, you get bored and start to sw 1+ dqq i*q(6oukzrry e556iuring a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makesr 6irk5uqeqq*+r5uo6zy d(1i 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 highway is designed so that a car trave-tv/oa lv i ee(7owd*xgv:w 6-ling at speiw ta/- d e*vxelv7og6v w-o:(ed $ 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 trrfd -q+2 cs/4) jjlxqjain, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximateljj +/d- jf 24qlcqs)xry ). (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.$\approx$    $\times 10^2$