Sometimes people say that water is removed from clothes in a spin dry h:(0xb1jmh20 er2czzxcne d7e/3thzer by centrifugal force throwing the wate2zm :ex 2/0tz0jn7hd1h3rchcee xz b(r outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels aro 37 4kgdg5 i.w)-cltpcnd:rnlund a sharp curve at a constant 60 km/h as when it travels around ):lw ngctp3c.4knd i lgd-r75a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alo;jl4 uz6-2elo sam c4ing 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 tws au4i;l-elm 26ojzc4o 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 merr 9 r4tvmci:w1x;u/oo zy-go-round. Which of these forces pw4;omt/1cx 9rizo v: urovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without 4,bv5):f5morgtdr4i0jmduv the water spilling out, even at the top of the circle when the buckefuj:5vi4m) vmt,b odr 05dg r4t is upside down. Explain.

How many “accelerators” do you have in your car? Thgxkxsb y;5tyo79 6cqx(4zvn p ig/. -here are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerat4gt9y5 7z-sq.vo nbgi(c xh xk6p;y/xions do they produce?

A child on a sled cou ahc)8h9w i1e-q aq7br5crp )mes flying over the crest 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 w7-hrh c1)eaqc 8p5ur 9ibq)aforce 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 leaoobx. 1nx1d kc7.0j nmafaay4yvp(0gz*) l 9sn inward when rounding a curve at high speed?

Why do airplanes bank when they tur0:e;js,-ro q qk yw./g3f udfgn? How would you compute the banking angle given its speed gr/jgwo :0uqq,-fe.3;s dykf and radius of the turn?

A girl is whirling a ball on a string aroun /v-6m0zq u9ljd0plig d her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the jg0pl/-im v0dl9 6zuq string?

Does an apple exert a gravitational force oc//w6 bl36 l5n7bdq7t ffolccn the Earth? If so, how large a force? Co6c3b n/6d5wclf 7fb 7lcqto /lnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wayf +/6bkrj jx.ps would the Moon’s orbit be dxrfb. +jkj 6/pifferent?

Which pulls harder gravitationally, the Earth ) 6c6koy .7:sy xgrdhbon the Moon, or the Moon on the Earth? Which acceleratesx.:6ok6 b7 ydrhys)gc more?

The Sun's gravitational pull on the ver. 8j zbs0)ko nn58dEarth 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 thr s nobjvdn5z.8e 8)0ke Earth to the other.]

Will an object weigh more at the equator or at the poles? Wha 29dj:depqh97nx -.p,gr mhint two effects are at work? Do they oppose eac7.p mdxnh ,dp9:9nher gj2-iqh other?

The gravitational force on the Moon due .22*mqc eaa/ h 0fehxjto the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled awa ex e /hmcj2*hqa2f.0ay from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun large b 6g+hk jfz3i+d( y2jxcg9,rcr or smaller than the centripetal acceleration ojzf,bj g k iy3h x92g6cd++rc(f the Earth?

Would it require less speed to launch a satellite (a) toward th(1l:zit8e6f ouus sp9i hjh : g;+cax1e east or (b) toward the west? Consider the Ear9:h:xf iioz6acujth +;(e1u8lssg1pth’s rotation direction.

When will your apparent weight g6jh8o. rv+s pbe the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerate h osj6r.8+vgps 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 outerez8vb 7-aec( v space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates,7vcb z8a-e ve( 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 weightlmxed jw pg hka9s g4g ,d;+e2c90wx,)hl4oe:pessness” between steps. ad 4+c2x mgw4h9 pxo gsk:;hjwpl,)eee,9g 0d

The Earth moves faster in its orbit arounnjnt4tpar9jl gn*-, 6 d 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 the6 ngrjl t9 j,-pa4nt*n Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered tixkc/m3py pd24 c h/7vo have a moon. Explain how this discovery enabled an estimate of hy/kdpv c4p7mx2/ci 3Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the co+bn8l4 o 0aiMoon'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.c onb 804a+loi25 $\mathrm{~m} / \mathrm{s}$ . 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 travelin u 5lqtjjdy6 g*h)9u5d)yzf q,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 acceleration of the Earth in its orbit aroun+x8xm.ml ej6k d the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbimj6e+ mxx.k8lt is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg dtyt77g+h; pl giscus as it rotates uniformly in a horizontal ci hg+l7tyg7tp; rcle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in jx4g*x q7 ,ddss, qtaqm;* 4cworbit 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 jgd*,, x7q x *mds4 tcqa4;sqwof g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accele/e + otl(q b:vyn)lb3tration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diat+o/b ly(v3)e tnqb :lmeter is 32 cm?   

  A ball on the end of a string is revolz-pd1ivg25fww6ucwto: n8 ,ived at a uniform rate in a vertical circle of radius 72.0 cm , as shownp of d6 i8wc2,tww5v1iuz g-:n 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 turnb)hg0.t6;dwn :ly pyc of radius 77 m on a flat road ydlg6;.) hb:wny0ct p if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient ulvr* fu9qc8 9of static friction be between the tires and the road if a car is to round alr98cuu fqv 9* level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts v).vw)hx )j)h u1lkbqand jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the forc)bkv) .lu1q)x h)vh wje felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axi1)riwounv:pfx 17)tos 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 is reached and the coin slides off. What is the coefficient xpvto7)or:wi u f 1)n1of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at t:6wqx9xca xo-h.xl* e he tlq*9ex6: .woh -axx cxop of 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 driver) crosses the roundeds9 :d03ds uxbiddcapu,rc- v*km2-n7 top of a hill (rad, * cuuiv3 dsc -2dkxsa9rnpmdb 07:d-ius =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 sgt c::/ ppm.zwould a 15-m-diameter Ferris wheel need to make for the pa:p /:zpmcsg .tssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 q up1 5;cvi5efkg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buci 51pc 5u;fveqket 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 partwu2 tr4;-- icw9i )u p nnpn89 .nm(dstebykp1icle 9.00 cm from the axis of rotation is to experience an acceleration of 115,00w.ins cnbniuprnkt9 4etpyu 19; -(m8-w 2pd)0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricyk5s:g4br+ y; y7 hiddally walled "rody :4r+y5ybihg7;ks dom." (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 rotatedqz*exi;6 ma-zux2p+ w in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dang*mz 6a qi-w;2 ux+zpexling 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 ignorij42xw4 zdord;e s72isv)+dj wng the weight of the ball which revolves on a string 0.600 m long. In particular, find the d jw;4rv4z)2d+sesidj27o w x 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 1)s7q+/smxoqm(5 jq/ d(4ityfrf tt 6 qol7aem 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 massesxxm0ib4jy vzqb;*fv1x,ib3u*mmj1 gt 8m38 s $ 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 310q7i wk,0sgh+x9dv4n( vqq 4 vw $\mathrm{~m} / \mathrm{s}$ . 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 rkgo9o o* *ndq8 v-c,.hmr;dx components of the net force exerted on the car (by the ground) in Example 5-8 when its speedxovnh*d 8o -.rqrcgko;9* d ,m is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolisp0bm;e/7saaovvh ni)t2 ks8; 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve kaost;esnp;vm /h 2 )v0b87ai 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 horizontalgv:shr k83 f4w circle of radius 2.90 m . At a particular instant, its accel:rhkv8 gsw 4f3eration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraf.hc3vqej ; j kj9vo8x9t 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 133h xj 8v.jo;e9c9kvq j50 kg.   

  At the surface of a certain planet, the gravitati-,cxrqo -*pt7s*k b xronal acceleration g has a magnitc ,tsbo7x *xpkr-rq*-ude 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 acceleratkz/e; kpg3b l p/29ouhion due to gravity on the Moon. The Moon's radius is 1.79oezuk/kh2bl pg3 p/; 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 Earth, busz3p 3gm lz66sg0ykvss 6 ;zl0t has the same mass. What is the kss pg m zv60zsl36y 0lsz36;gacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiu.l8xcei17ia e s. What is g near its sue1a.l8 xicei7 rface?   

  Two objects attract each other gravitationallykofka ;rr5n5(wgfm9)qnd6s:/ (z m od with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) dh*-x+hjg w7 pv v+9cq3200 m hd h*vj c+ 7+gw9xpv-q   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to aw3 -h4rpl7rd 7 m5o*dou0 utku point outside the Earth where thegravitational acw04ru 3h7om7td o-dkpul5* ruceleration 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 Sun pad oj;e7k20xzo cked into a sphere about 10 km o 7kzd2x; oj0ein radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an aver qyu7a;w( 6dc d0vvb,eage star like our Sun but is now in the last stage of its evolution, is t ,0ddcue;7wv(y qavb6he 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 feel weightless while orbiting in the spac-z-c5d 1en 6dbvtsa*ie shuttle. Your friends respond that they thought gravits6 e zdv1i*dt cb-5n-ay was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the cog *wzf6i9ci9wbcz.-lql 9cu2rners of a square of side 0.60 m. Calculuc c99izq. cwz6wli*9fb l2g-ate the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the samj0a :we.ebp4tt1a 6wje side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuwj0 ta64t . 1jbee:awpming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface9 ,yz ybdhu5 yv+n69nu of Mars is 0.38 of what it is on Earth, 699uyvbny hzud,n+y5and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun u ube -um:jgj+h4 x:b,vxstj3:sing the known value for the period of the Earth and its distance from the Sun. [Note: Comxj::j, bu3xm4t g-: ujb +hvsepare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular8vtpwx7k, h (sxd+hp1 th,c s+ orbit about the Earth at a heigh, k+hx h1xc h,s v(t7+pwt8psdt of 3600 km.    $\times 10^3$

  The space shuttle releases a satellit 4og (w +y5b8tcxpaz9qe into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relativw xybc48q 9p5 tgoa+z(e to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaxfc;o6 pqn( jib-1eh 2ceship rotate if 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 Quest-jf i2;n6c eob hp(qx1ion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbitqe dn ,c iq/xt;5x*jik) e,y(l 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 ixc,) ti jn,/qylq;(xk*d ee5the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal vel (d,om9.::1 wntshjetyyl9tf ocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Ea fy:ttdjmytl,( n 9:.eo19s whrth?   

  During an Apollo lunar landing mission, the command6t s jz(ikm5.x0m abo2 module continued to orbit the zijomm6x abk.05t( s2Moon at an 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 te o/q4hvfs /n3he planet. The inner radiuse4n 3h/sv/fo q of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in 7euzp vzw; ;ozfbk14: diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s a 1ubzzv7k4w;o:f z pe;pparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 42n9p ilhq:b o2*o ,y7iyr(gmz. 00 km from the center of the Earth's Moon in a space vehicle (a) mn ybo 9zy7h,g( .qprlo:2*i imoving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars +xs6sqc, h fq0of equal mass. They are observed to be separated by 360 million km and take 5.sx,06c+s qqhf7 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 weight of a 55-kg woman in an ele;sll zq ;9ln81 rxqj)fvator thatfsqx nlqz ;j;)lrl81 9 moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an-9a3lrpzd mh2eliqvc 4hn/- 8 elevator. The co8q4cl/ld p--zr i32vaen9 hmhrd can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface g*ak/ f s/0abvof a planet with period T , the density (mass s/fagabk0 */v/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 1f, 6szeohj*phsn.2g the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near thj 6 ef so*2,.hzngps1he Earth’s surface.    s

  The asteroid Icarus, though ond3*1 kyi3jh ;6jk )vcl bqg/qsly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fro)j/k 6dv1 lcjysq*3;bqh k3i gm the Sun?    $\times 10^{11}$

  Neptune is an average d52d swleqz h8(gbr ez./aq b3)istance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits(68mx0pdx oyr thn)9c 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 from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean disrp6(cy0 xomhtnd)x 8 9tance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gals+w7vmw/fwso9 .*vp 8mar +zsaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 laq7 g-myac/4 sgzr4ro;rgest moons of Jupiter (those discovered by Gqsr;ymz/4 -4g rg7ocaalileo 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*l.e /;1y vk(ujnubbp known period and distance of the Moon. u(/*klpb bn uj. e;yv1   $\times 10^{24}$

  Determine the mean distance from Jupitezr,b 1j t 3o9nqiw:*v1co)lczr for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare t)l1o, ncbwz:* r v1 qz3tij9coo 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 4g1v2(/u97 .q3lld nrf8tzdst qun nqJupiter consists of many fragments (which some spacl.nu2vq( 3z /gq18t qnu47 fdr s9tnlde scientists 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 a 91ed kzy7zwg)0o c.ocrtificial "planet" in the 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 9c7 k czo0zd)gow.1ye 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 a,*u yl rf9*l w1 cd0why jslm39:ot.jxrc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tol:cd9y,um 3 9yr1w*jxw l*.0 sjlltofherate 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 g2 clqt*p( njy/ravity be half what it is on the surface?2 l jctnp(/*qy    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual c46 i9,c+xgfk. lw, oih8fpnm qircle once every 2.5 s. If we assume their arms are each 0.80 m long and their i wnclmfx,i .,+ 6k9fgqpio84hndividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravitnjb/r9 uoip :78kebdi48b4 epy at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. Whati:k ridu7 8bb b4jpp/8 n94eeo fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directvbr5 23m (giluly from the Earth to the Moon experience zero net force because the(mlu52 3 bvirg Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, ga7x1 -cgb d;c)cehll 3dx+ry8r ;wr9 but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in d7cyhlxl+)a-8rc r;bg 3dcr; ex19 gwwhich direction?     ----待选择----upwartddown 

  A projected space station consists ofd j /-8g/bch )t(qyuuf 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 day)bg/f y( t-juh8q)/udc if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4tav o+ckh):6 b3).
(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 radwk6ld- :xr/m(eu udw407 rdt be 6b5ngius r, the acceleration due to gravity at its surface and the gr0lg6x6 /u 7r bd:rw(tdmnd w4b -e5ukeavitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from t yopp.g .rr:o6he vertical by an angp6yrp..g ro: ole $\theta$ 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 colmnn f -8j.6giefficient of static friction is 0ign6.jm8 nl-f .30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a daynb /zq8 - rxygeor57/g be if the Earth were rotating so fast that objects at the equagyg or /q58reb xz7/n-tor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant d pblt ql:3c:*mistance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve f vv.a+kf)ocf3o5x+gvb3,+s*lah xsof radius 235 m. A lamp suspended from th+bhf3vf+las).,c 35v*axkxvs og + f oe 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 massive as the Earth. Thus, it has beavfri i:1b swse*elqxcr*jf4x .3fw,:e4q, 9en claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a p4f ,e4ilef*awqw1x, ssvrx*q 3i:e9 r.b f jc:lanet. 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 ( rjj(bdpkq+ :2ph1o7xmt. dxSpace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole jrh 1p q x(mbx(tj:d+ 2kd.p7o(from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valle .t.4x dh(wncoy 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 wondc(h 4.t. xis 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 (GPStiadwhu h1l/kj r5u.h22jh6 - ) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receihu 2d .r6jatu-i jl5h 2h/1whkver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travelin+g69; bu9)rgh-, ,oovl)w mm hwlqep ug 2.1 billion km, is meant to orbit the asteroid Erg pwvo l+,b,mg-ur em;oq lw)9)h96u hos 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 pursuing o l6*rc:t-o*nf; 2msrx8tmt k a satellite in need of repair. You are in a circular orbit of the same radius as the satellite xoto-:*6lts 2* rrc;mkt nf8m(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(epm/zh 5 so;m is its mean distance from th5h;pm mes (zo/e 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 l6a jh-w(,enabky.1 pa 0arl8if you could actually "feel" yourself gravitationally attracted to .1kaa 6bhlw 08,r(a aypjl n-esomeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center9r 009wp lqgy ksw+m9l of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from th9 0gp wql09ls 9kmywr+e 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 .jdpup)(dx -rsquare 0.50 m on each side. Find the -dx.)r pjpud (magnitude and 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;qutez a,t02x kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the x;c3 1w.ikfery0h x5 u1.5-cm-long sweep second hc10kyr5;3xxiu f.w heand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start*ajcjx x 80*x p;ujjk83 8hwcm to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight x a*j3mj8jxwc khc8uj p8*x ;0makes 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 vk 7y :zl5ckth)b(;i sthat a car traveling at spebt7lkskh 5z )ci(v:y; 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 train, the Acela, utilizes tilt of fg/b+n4-fszbrrd+b ; 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 cg s+-z4fdbrb;b+ r/nfurve 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.$\approx$    $\times 10^2$