Sometimes people say that water is removed from clothes in a spin dryer by cent3u 1v0 s.ow;0wp)8z eaqyrebsrifugal force throwier13ea0w0 z obq)sp8w.svu;yng the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels arou:og)e ;b1wmkb1q )f0ppduq1 knd a sharp curve at a c1pow )1 ;d:1qk0qe)m kupbgbfonstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant rlxya5+yiwe 5c* v3h, 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 5l yey5ax*3c, iv+w hrof a hill?

Describe all the forces acting on a child riding a horsk+ r4x9xnmal5uft25b5i:e //rfc dr oe on a merry-go-round. Which iru 2oa e5 m5bt:9/lxk5+nrdf x c/fr4of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillinge8eeay )(i. ryxb m*l1 out,ex. ry)e(b* i8e1yl am even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cont.je w:2;brdln rols in the car which can be used to cause the car to accelerate. What are they? What acceleration;ed 2jrnbwl.:s do they produce?

A child on a sled comes flying over the crest of a small hill, as sr0d8n h7g/k gr pd.j5smg+ch1bu8)y ltlm 0(lhown in Fig. 5–31. His sled does not leavml7kd08sch+hjbtymn rgdr(. u8g)0 g1pl l /5e 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 inwa,z2av231 9)q ttcuxhvwhv+nxrd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you comput 98vf psd larylo3b634e the banking angle given its spe 6rl4bof 3lvsy8dap39 ed and radius of the turn?

A girl is whirling a ball on a string48klzx5xyagk am 0)/x+/ga co around her head in a horizontal plane. She wants8zoxag lc4/k5 x m y/+a0)xagk 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 string?

Does an apple exert a gravitajdh 4 u/lk-nl vm+53oktional force on the Earth? If so, how large a force? Conside/5kou d+l43km- hnl jvr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Mo e *cb/(s.zkwx5:9lh,ew elpnon’s orbit be differe,bn/ z5k.9eew* wl:pes c(l hxnt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon tbh 9hvutk1sy(z 06.e:y.zar,s se y .on the Earth? Wh rs.z.zh t1 h.at(ysee06skv9: byu,yich accelerates more?

The Sun's gravitational pull on the Earth4 ;g(; jzufahuh (rwxtk/ 3)kr is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatxj( ru/hgk)h 4(ta3zkuf; wr;ional pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poleunwsoq2. 4* po- +furpkf7q. t43 diwds? What two effects are at work? Do they opposenwo7-f+u*o .s.p wrq2 3iq ddt44fpku each other?

The gravitational force on3jp8p hiz4) qo the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon q izh34o8)jpppulled away from the Earth?

Is the centripetal acceleration of Mars in its orbdppj l-l2-aj6it around the Sun larger or smaller 2jl-6pl jdp-athan the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) t2zwqryxrp ;f b y9hf(31 ;/yfcoward the east or (b) toward the west? Consider the Earth’s rotation directionpc3;fyrz(1 yff ;hy92/ bwrqx.

When will your apparent weight be the greatest, as measured by a scal trj9z.,7:oa(tr :lvd,4va y1u eelgje in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) movesjr::7a , oy taz4teg9l urv,ev ld(.j1 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 ad :elpfbg4m:dd4e gsw, 0d2+rffected by wed 2b0,em 4rd+4dgpfslw ed::gightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects 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 weighq ftppn n .zmq3)f8+1ptlessness” between stepsmf1 ptq z+)3pnn.8 fqp.

The Earth moves faster in its iim+jj)6/afvxvz7 k: orbit around the Sun in January than in July. Is the Earth closer to the Sun in Januv af)6izv/7 j:i+j kmxary, 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 the plane of its orbit.]

The mass of Pluto was not kno,:+2l2licrwh8mb ja rwn until it was discovered to have a moon. Explain how this discovery enabledjrilca2 :r,bl82 w +mh an estimate of Pluto’s mass.

  The Sun's gravitational pull y,2rvx2v6 g xm+k ;nlpon 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 pul6; gk,xlx2+2yrvmv np l 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 travelingn,pz q8ks 6fg8zh-wq6 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*8o, -kfclqku acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts thi cu*,k8o-qklfs force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates jgsnr5w+x42fh 6sy7zuniformly in a horizontal circle (at arm’s lenhzx6fy nr7 j ss4g+52wgth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ci;+ef) uz7a7c216s fmee bcfuh rcles the Earth about once every 90 minutes. Fi;fu uch mc 1e7fz7 fbese+6a2)nd the centripetal acceleration 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 spezdkc8ibmym7 1yz-( 4e ck of clay on the edge of a potter’s wheel tuci4 8(b-y1y7me kz dzmrning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a wo:8+ wpcmxj.0 rr n(e7p :qznuniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-338or.z0jwe:x rm c7+:nq p(nwp. 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 ca2lbvafnvk/-o27 r * exn round a turn of radius 77 m27/-n2 v orvkxlbaef* on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the r 6f,7(k spqi5r 3vt6w7 natcpsoad if a car is to round a level curve of radius 85 m i a5w f6sp(6 t7 p37qtks,rcvnat a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots ikv+b(2*p xhj w a.ajrd1:p: eks 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 fastp1hpk:b:+x e*rjw2vadka j( . 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 rota3)x7vma8wju uting 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 of static friction between the coin andjx )7 3vuam8wu the turntable?   

  At what minimum speed must a roller coaster be tra ;wsoce*7gqj; 8skt,rveling when upside down at the top of a circle q ;j rwstogk,cs8*e;7
(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 driv(n c 9hxmk gv.5ycww4;er) crosses the rounded top of a hill (radi4(y9 chwk vgwmx .c5;nus =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 p/vu3,j jm ls)tu7ad j)er minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the top,7v3m la)sju)tjj/ud most point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiuok77g hc3. gqe8sw7nbs 1.10 m. At the lowest point of its motion the tension ig chw7s.qn8gb k377e on the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from tb91*or j qdrja .g*em:w b5l,dhe axis of rotation is to experience an acceleration of 1w*la9orbj*1 qd b5d: j. egm,r15,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa ude0fwyjr8 ::lled "rf :ry0e ujwd8:oom." (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 rotatedc g5ta(s:,vq k 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 hole as shown t:c5vks gaq(,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 .z7d g(ildz6h time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of 6ihl.ddzzg 7 ( $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 bankedzem;sff 40o m8 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 masses2 kj0qyrulbv7dk.) c5 ( zau6b $ 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 o5lfzwtgt 5az /t9eo0/ s,(;qndf2jv at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripvb37 zz*u xc zup1n5/ietal components of the net force exerted on the car (by the ground) in E37uv ci1unp5z* xz/z bxample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit kk19mst2ff*earea, 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. Ik fsekm *f12t9f the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 gooulg+6u;w 9)i3wnp m . At a particular instant, its ac ;9gw6p)iuw gu lo3n+oceleration 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’2+ saq+- vrv8ebgzi5o- )ltuv s gravity on a spacecraft 12,800 km (2 Earth radii) above th+8g 5etiob vv +a-2- qvzu)lsre Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratior1-nt/5 hbv jrz ((zumn g has a magnitude of 12 m/j um1hrbz v(nr-/(zt 5s$^2$ 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 gravvutd ga;7sfd( m279qlity on the Moon. The Moon's radius is 1.74dq; v7d sla2utgm7 9(f $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 t:jtwa 4t:v bd:imes that of Earth, but has the same mass. What is the acceleration due to gravity near its surface? :t4vwt baj ::d  

  A hypothetical planet has aw l5ctk e qa4amh02*5n mass 1.66 times that of Earth, but the same radius. 2 e4k0q*h5 c5nwamalt What is g near its surface?   

  Two objects attract each other gravitationallyhyqzt dvvk6g uz )m rfq81,m/:)rd8e 0 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 voezlb7jb k0w 9 ()*qsralue of g , the acceleration of gravity, at (a) 3200 m*zj( )eqw7o bklr9b0s    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cent7u4y4ir*m3b gkt+ gdh1gzf/f er to a point outside the Earth where thegravitatio7 g3h4rbkf +1 gfgy/t*miz4dunal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our,big3 fa:s/i vjk0, qt Sun packed into a sphere about 10 km in radius. Es bf0v,:q3ts jiagk /i,timate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star lid6i o-jr7x1xol 60brdke our Sun but is now in the last stage of its evolution,xoo6ddr7-0ix j lb1r6 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 astronautsb nhrto;+t /t4 feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourso ;r4tttnb+h/elf 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 corners of a squarral1 q +kke8wf 22y; v (4gwclwz0:goce of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sph 0e2 ryo+;lwl8a(wgcz2q4f kk:w1g vcere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side7 oc n4lvql1;v of the Sun. l4n;1l vvqco7 Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The 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 accelerb* oi8d37s zrsation of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is*rbs8i os7d 3z 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of tb8h*d 5;xlt/.uoc x-gg+ p m j8yqfc,she Sun using the known value for the period of the Earth and o;5gx y- .8,dlg/cuptq 8+xb mjhc sf*its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stad8l -bspd/mwg, 2s .peble circular orbit about the Earth at a height of 36dm.8sw 2g,/elppb-s d 00 km.    $\times 10^3$

  The space shuttle releases a,bi cxa8y8mo, satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the r,88 m y,obiacxelease occurs?    $\times 10^3$

  At what rate must a cylindgvt9d7fu m-:r rical spaceship 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 nvr7t uf9-g:dm eeded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes f/d(fgl dxno7 7or a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass ofldxo 7fdn7/ g( the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched frfv0o t3eqn v8*om the top of Mt. Everest to be placed in a circular orbit around the Earthqt vf80n3*oe v?   

  During an Apollo lunar landing mission, the command module continued toe sy7um+;xvppv+4nm4 ldj+;a orbit the e 4v7uj;s apv+m p;+nmly+x4d Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are compon7ydrj6 fm8xmw *p ,j6sed of chunks of ice that orbit the planet. The inner radius of the rings pjx7rmndmyj *8 ,f66wis 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotatesfp 0bz2m1 u/rd 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) au12/f db mp0zrt the bottom?
(a)    (b)   

  What is the apparent weight of a 75-q (xivc4abuh icx(,tdqx )(:m,ok/u, kg astronaut 4200 km from the center of the c q vmd cah,u(,o,u/(q)xi :txx4i(bkEarth's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass.fyp/ 97zy/o*zz .k ubt They are observed to be separated by 360 milliont z7zy9*/uoy k./pbf z km and take 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 weight of q d*czybd 1xi5)i:+fs a 55-kg woman in an elevator that moves sdi fib:5xqc) dzy+1 *
(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 2r r +1jix/ayiof an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (+irix a1/rjy2magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet w *5ufkit;6bg8 y01 qtxkd81 mwi(bd jbith period T , the density (mass/volume) of the planet is 5ifbdjm*1 bb 61;uqty8dktik(w 08 gx$\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the per pt xl0z oncfo1sd7x *j)u7-6kiod of annod7p t)l10ckfu s * zx6-7ojx artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metep;k0 o9*u/tzwhw387e vp xponrs across, orbits the Sun like the planets. Its period is 410 d. What is its mean d zp/ we*upo0k8p3 ntxw9v;oh7 istance from the Sun?    $\times 10^{11}$

  Neptune is an average dp5x c99g5jdrabc;d8apv/*o yistance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. Itk vy6-c/- flkk 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. /6k cyflk-kv-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 center of the Gewaq ti 5k4dbfvzb--s e19.6wmhh+f) alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distaz7 s5o wt3/qjjxf 15e.yd q/)xcrtrn9nce for the four largest moons o/5z3jjyq rw.o1erxxqfd/ 9tctn5s7) f Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Ea kgeumlfuvp2n*;w/e 52 h bbt1 r9f9f(rth from the known period and distance of the Moon. pte9u u; 9f (rv1mbk2f2/hg lb5wne*f   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons43g3c e4ue8r5sdp xqs, using Kepler’s third law. Use the3cs45q sx edup3 r4g8e distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fra ) :gw:wb.yl0pj qcum7gments (which some space scientists think came from a planet that once orbited the Sun but wa::u mj )q.0 lbw7cywpgs 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 yay1 y78, pl3b0k1gwdbplcm+ 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 always noon). Imagine1 0lp8gckyp3 a1ly7 , ymd+wbb 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 go d k t+sv9d7kvn4t+g+urge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest ptdu9kd4v+7 kg +v tns+oint 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 gravity be half wsvu;:8iwziw 7 sof5 p6qzvz61 hat it is on th6 fizzo6;qps uvzs5v 7i:w1 w8e surface?    $\times 10^6$

  On an ice rink, two skaters of equal 5 ajez-n9lqzj:5d; eymass 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 e9- qn;adey 5z :lzj5jindividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotate0nj2penq q :md4qlg18s once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fracp04 g2q:nq1eqln j8md tion of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelinc+p3k .io6jd lpv b3sx +:na+yg directly from the Earth to the psn l. a+x3:v3oj+ i+dp6 bykcMoon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scaj920d o- ekrdyle in an elevator, it says 9k-d02dr ejyoyour mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists offe8+o umxm0v . a circular tube that will rotate about its center (like a tubu.0f+ox8vu memlar bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to 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-t(6ac5 lqonf,p xh8n loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for te3-fz7q lta9 v*gpxn,c y0(bt he mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational ( l tep3ztgqcayf7b9- v0x* n,constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verv y+0mgx aoh ym7m+65itical by any7+ygx6o mv+i hm0m5a angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a designok 5q(d;lo4+jlxqhv * (ls8rh speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a cao dsk5l(v4 l* +8jq;lh qrhox(r safely handle the curve?

  How long would a day be 0vr.3b mk (u(sp;8wvr hbqoe rzt):p+if the Earth were rotating so fast that objects at the equator were apparently weightlessb;vp r m8zokr+rev()pt0hwb. u:(q3 s?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance avtt/ 9r2 ei 7 6xkhm/w:9dgxvfpart 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 curvel6q t;h /0i ttc :d*cgs-sh,nd of radius 235 m. A lamp suspen*tn cs t0q;h-sl:id/h6c tg d,ded from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tim9 )laa5tu mlxw3c0 oksbgg 455rovx(*es 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. Calcula 5x*5 uc(logswrxaa0k35 4t l9)mgv bote 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 presence nr*4pcjg*5e(*4v: mzd gl roj of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapesg5 4nm4 jojg :r**p lc(*vzdre). 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 t4 (ad zg;y5mr/q*wibit traverses the hill and valley shown in Fig. 5–45. Both the hillqradw m(4i/5t by*gz; 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 (GPS) utilizes a group of 24 satellites tp i)l6s0pe n-:gnkw+ 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 fln6k0 p) :ew i+tgspn-ew 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 traveling 2.1 billion km, iwih;v(89zw3 5yttgios meant398gyt itv owwi; h(5z to orbit the asteroid 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 pursuing a satellite in need rrl2t7t3te:u2s4 f wnof repair. You are in a circular orbit of the same radius as the satellite (400 km above u7t2wlnrfrs:e 2 tt43the 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 perio 0rd3 jonrkq0kf448 dgd of 3000 years. (a) What is its mean distance from 8d4rr4n k0d of30kgqjthe 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 an yv .g38+(qmorz6dy could actually "feel" yourself gravitationally attracted to someone nynr3.+qmz6 vo d gy8(aear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the M* q9xjm0oddlyox - 4q4ilky Way Galaxy (Fig. 5-46) at a distance of about90l*dx4od-y4m qq oxj 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the vaq7 lth.u1+(gmz*.ns jp vca+q .i/ ncorners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational forccmat/sgn .jqin(l p.u++ q. *zvha71ve 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 orbitzo f (q*onn39x/7 ogues 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 th./w7hj ozu2j ke 1.5-cm-long sweep second hand on your wr .jowj k/h2u7zist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sh*sjang /ei+ wljzyud 0;; gtg:o0l+, inker weight around in a circle below yoz jd g y0g:/+e+ s;a0ln ,*;hgowtjiulu on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes 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 trav*+ayy/ q sv-pq/j opg0eling at speedps*/+p0 qqjg/y-oa vy $ 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 Acembvhpp.)/lx ;la, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjuste;p b )ph.xlvm/d so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train 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.$\approx$    $\times 10^2$