Sometimes people say that water is removed from clothes in a spin +qv5eb, p7 7jyd xl.pjdryer by centrifugal force throwing the water outward. What is wron7jpb+pjq5d x y7.ve, lg with this statement?

Will the acceleration of a car be the same whex*81hew)om t49w qiibn the car travels around a sharp cu8m* hiwt)q 9exiow4 1brve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does th6f. )d wxtw4*mts.qb0n6tgy m e car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two htw0.t6*fmmxt nw6.q4y gd)b s ills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a ow ;vebf;hx8b8 vyij6+ b3t(o merry-go-round. Which of these forcesb + bbvt (w68xe;o38fjyhvoi; provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water7a e6onmg ,l9m spilling out, even at the top of the circle when the bucket is upside down. Ex,en mmgaol 769plain.

How many “accelerators” do you ham0 84btb, r(ssn vjx.3w rycz/ve in your car? There are at least three controls in the car which can be used to caus 3jtn m8rs0 rc/w.bx(ys,vb4 ze the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smar t1 2a p))rokifw6l.jll 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 the hill. Explain this decrease using Newtar jt)pr k6l)i2of. w1on’s second law.

Why do bicycle riders lean inward when rounding a cur786 fkx4z evoeve at high speed?

Why do airplanes bank when they turn? How would you compdprk 9m9,r,kmy6dcy9 4 zsw)w ute the banking angle given its speed and radzypd, wc rrm99,9)m ykk6d w4sius of the turn?

A girl is whirling a ball on a string around her head in a horizontal planz wuik6 7nelin:55cs.5svh ( qe. She wants to let go at precisely thesun hsw5n5.i:6 cz5vqilk(7e 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 gravitational force on the Earth? I 6blc1 tk y8t0:be*eecf so, how large a force? Consider an6e:1b0t8 ct*eek bcyl apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in 7t k.y,of pj,zd9a- cunph1 ezkm13 4twhat ways would the Moon’s orbit be dimp cktu 7-hd9oa 3n11zjf e.yzk4p, ,tfferent?

Which pulls harder gravitationa429f q(4co,hs sjhfxjlly, the Earth on the Moon, or the Moon on the Earth? Which accelerates more4hsx cfo4,(sj j9qfh2?

The Sun's gravitational pull on thc2srplj i5nd72ur00 fl*q0tre Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatilpq r5r0nd 7 0*lci t2f2jsu0ronal pull from one side of the Earth to the other.]

Will an object weigh more at the equator or rp,* zu/3g jdsat the poles? What two effects are at work? Do they oppose ea 3,rds* /gpuzjch other?

The gravitational force on ,k ynk9k7vi 7jx ; h j9tnbqv)que(p*6the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pullp n xb9jikqe;)6h*k9k qvju(,77nyvt ed away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the S+i.vno+b .g gfun larger or smaller than the +f b+inv.o.gg centripetal acceleration of the Earth?

Would it require less speed to launch a sateyh(:7jts8a b 9e0 pzndllite (a) toward the east or (b) toward the west? Conside ahy :90p7tnb edz8(sjr the Earth’s rotation direction.

When will your apparent weight be the greq w4dyca- 4eabjz4nh*, (r5ha*wj v/xatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is(4x4n*e5ja*/w -brdh4j a,w vazyqch 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 spendih2o)9xi u9c 31ngz:+z wuwkb long periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shab+ uu kxg: w1i 99n)ohi3wzc2zpe 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 we( i nntw4fn6;3q5kfrbightlessness” between stepb; 6 n(qnwfikftr34 5ns.

The Earth moves faster in its orbit around the Suj6;lxbmg1zw 4 n 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 gz4b1x jmw6l ;— the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was iw.q8x a0ch5 y+yurw4not known until it was discovered to have a moon. Explain how this discovery enabled +5awh.ic84xrq wyu0 y an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ear27;djn-v tf1d ol e7z1 m3f0da6vtzgsth 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 wi7 daz213svvfg e -1df60djlo7mz t;ntth a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 7eey*yl u/ wqzuk8v30 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 around thz;,taw5 0jxlhp9+ ed t)y2 oume Sun, and h+w)0plztuot,ex; 5m9j y2dathe net force exerted on the Earth. What exerts this 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 exew5e1 fso: dw,nrted on a 2.0-kg discus as it rotates uniformly in a horiz:fwnw d5,so1eontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from tqjcsiqi92) e-he 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 gravitational acceleration at thecqj ) qi-i2s9e Earth's surface. $\approx$    g

  What is the magnitude of thqxxw smy*),e9e acceleration of a speck of clay on the edge of a potter’s wheel turnxx, wm9q* yes)ing 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 uniforfc v pg5aa*8w.(zuqj7:cl *yxt zad59m rate in a vertical circle of 7vja g*8p*5xczfwt l (cya9 zqu5 .da:radius 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 whic; h/u 5j7*hgtt :nzsbopr1w :ch a 1050-kg car can round a turn of radius 77 m on a fl7h w5o /bs;*r puhg 1:jnttcz:at 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 snnj fv2icc -jm1xw8 fx vm n43s:c7,z)tatic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed ,sv 4x j-f1 )cfm2n:in 3 v78cwmzjcxnof 95km/h ?   

  A device for training astronauts aw;bcp2 n6n+g7q-o) 5kfgags hnd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force fel 7sg a);kn+-gnq hopb6w2f5gct 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 axis of a rotating turntable+hiq6y q 9,kpmu( k)sy of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable )u kk,qqmy6 9s+( phiyuntil a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coastkd 9;h +ascz5xer be traveling when upside down at theh+z; dc59s kax top 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 l4cg935 vecit rounded top of a hill (radius =9clivge9t 54c35$ \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 F /jh1xie v-.h4mjr* zaerris wheel need to make f.h1*zxei 4j/ vjharm -or the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radi/u pv3vn 67jb j;1nlfo+cpdc2us 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 Nl2 cjfd/n+ c;63vjp bou7 v1np.
(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 f6g20hg*y pcu : xpdw:urom the axis of rotation is to 6u :hggwupp0x : y2dc*experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatedupku ,8w4c9qw 27qaeh in a cylindrically walled "room." (See Fig498 qpquawew, 7c 2huk. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated tr/cu:u /bfp) *fsi x5in 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 )c/uub/t)r5 i:sf fx p* 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 , preleth)z z j( ,5wexbf4ej6 +x*jcisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of xefwxzee),6l+*tb( z j 45jhj $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 ra( gwk7 *4ew v)gwojj7sgtnd;6 dius of 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 -9iui(wck)p r :bbjn e-g:(kr$ 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 310 )uwzhy gl(zt-61 zzv0$\mathrm{~m} / \mathrm{s}$ . 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 niu*x5 1:uvxo0fa ubi9et force exerted on the car (by the gb*iu 1 :u5x9x f0vuiaoround) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area+2p*i9aehf tz, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires a+9ahi*zte f2pnd the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particula 1by;fgxp8/yljtg/efxb;5 u ,r instant, its fjb tlp5 fx,ug;yb/8g/1y;exacceleration 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 of8dnr+s8.e3* ohybqvv Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above th*8orv . bnsed+q vy83he Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitation h4arheo: df.0al acceleration g has a magnituderdh o.04:h eaf of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. Th9yf1fduw6 v8 r hae3m-e Moon's radius is 1.7w 896 hv1ef-rfuma3dy 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, but dg 1wbo+ dsp:;ich,g (hww0p(has the same mass. What is the acceleration due to gravity neag(bdd 1; wgwwi+( opp:hc0sh, r its surface?   

  A hypothetical planetsgu/ qp1tr.p* has a mass 1.66 times that of Earth, but the same radius. What is g near ir *t. gp1sq/upts surface?   

  Two objects attract each other gravitational o5pofo: v/x,ily 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 effectpm 72w0fp6uhz ive value of g , the acceleration of gravity, at (a) 3200 m pw0 7pu26m zhf   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside dk3o-t w9y+fyh9tc:x the Earth where thegravitational acce9k tyfwh3+9xc odyt- :leration 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 5)ngzsx 9 wov6mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface 6 g5vo nx)9swzgravity on this monster.    $\times10^12$

  A typical white-dwarf mgyy *9w:i ee1w)dk.pstar, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on th*w dygei1p)k y :mw.e9is star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the sy 8ux1fv2;m /zb2k8vdaf 3m(ju h,l qzpace 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 of gravity 250 km above the Earth’s surface in 2 mzf2jxf av/3m vlyu(qz;h1 b8d8ku,terms of g.   

  Four 9.5-kg spheres are located at the corners o vaj/s6sj41t v*w0kcab/c d .nf a square of side 0.60 m. Calculate c0cdavjjbvsk6a4/w*n .t/1 s 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 linemf *6ix- vl/bvh57wi gc:z*yl up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Satur:* *6mcgvy i/x7 bl-hlwi5fzvn, 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 acceleration of gravity at the surface of Mars is 0.38qnn6:*f c 6tlj of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of n:6jlq f tn6c*Mars.    $\times 10^{23}$

  Determine the mass of the Supjz)xyzg0j 9+n using the known value for the period of the Earth and its distance from the Sun. [Note: 0j9y j)p+gxzzCompare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satj)7e )kykw80dckfs:(ddyda1 ellite moving in a stable circular orbit about the Earth at a height of 3600 kmk0f7ad d8k ye())j:dsy kw1 dc.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovwu;uev,yv )dkeq18 /r e the Earth. How fae k/ ,eq8d)uwuv1;yr vst must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to ex7)p c4e-)u 8 nxcf1q2tr nakkzperience simulated gravity of 0.60 g? Assume the spaceship’2)knq-c7nf utcxrpe z a84)1ks diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “ntmmejiflj-h4pi t o t-7j3)-+ear-Earth” orbit. A “near-Earth” orbit is one at a height above the )pmj ht4 -3t ij+l i7jmoe--tfsurface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitpftn0xg88 s. oe have to be launched from the top of Mt. Everest to be placed in a8x fnp.g8ts o0 circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oxk0yiaii)c0s( 7s e:erbit the Moon at an altitude of about 100 km. How long ds0:sexk(ii)0a ye 7ic id it take to go around the Moon once?    s

  The rings of Saturn are composed of chunl+q v(r;r spw(ks of ice that orbit the planet. The inner rpswr;(l ( q+vradius 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 diameter rtyg-y 3ukexz1g62h g(otates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent we3 gkyg zh(xutg21-6yeight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weighttxt9k,f e0 9pd of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space veh9efxd9tp0,t kicle (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 stega.1v,teuc0 3o4 m /vgyif* /yvd x4qars of equal mass. They are observed to be x ,ugvtiy3vc.q/f y eo*d g401mv/4easeparated by 360 million 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 weigc qj*mg.xcl90y3o4o kusfs *.ht of a 55-kg woman in an elevator thaty0lg .4 ofsck*u*9sj mq. co3x 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 elvv2p ,y0v(yd 4e ,j;f gifw(bzevator. The cord can withstand a tension of 220 N and breaks as the elevator acceleratewvzdi pj vf( ;,yb4fg02e y,(vs. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface w.za5s go*heah+k8d 0 o*)sqrof a planet with period T , the density (mass/volume) of the planews g0 k*q erhh8aoad)s.+5*zo t is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determincajup1ve 0wq;p3vj3wcb827,0o(7 ml hqspp me the period of an artificial sa3(wa c0m;p0ou3 h,8 svb mj2ppqvpl7w cjq1e7tellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitike:*cmq;b(qoub8 (bre jk)h0a r * 0wp/vdc. s the Sun like thkduc( *jh*qb;/8b rpw:re0 qko0 av.e(ib )cme planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dm92wy tzskcgd 97.nd3./ a tlkistance 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 roughgwnin/7 7p4nqo y 6oo5-)eykuly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimatey-wgo6nk5q77on/)pi 4o yenu 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 third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cey 0nmdm: 1t(ointer of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, anbc9*btgo7,svu 3voty:pc q g8)c.c b8 d mean distance for the four largest moons of Jupiter (those discovered by Gali:b7,3*gbocp u .tqc ov8c 8gtvs)c9byleo 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 o t6a;pppumi:60ch; h the known period and distance of the Moon. 0o:66ih hpp ;tuapm;c   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitgx;. yvryq:ld-t-)j *4enajcer’s moons, using Kepler’s third law. Use the distance of Io and tdjcnjxg -:y;4.) ryl *avte-qhe 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-thyknd 5 muo3/i ,x0v Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroy - i/x3ykmvu5 th,odn0ed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band (8z(jho8n7we 6vqix xcompletely encircling a sun (F8j6 hx7qnwvz(x(oe i8ig. 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 the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hay+jw g6j)u .hnkxzn/1nging vine (Fig. 5–41). If his arms are capable of e+n) k w.hj/ gzu6n1yxjxerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Eart hny(6zd3 v3ash’s surface will the acceleration of gravity be half what it is on the surfza 3v3s6n (dyhace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spis)p w:8st:q 8dbjs/zcs9lg)sn in a mutual circle once every 2.5 s. If we assume their arms are eachqz/bwptl8 ds:)9ssjg :8s cs) 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerat r-n)zl+m( 3vca)1peorl5yd7*cvb no ion of gravity at the equator is slightly less thb( c co-n)5r e 71y lvmn+zlp*)or3vadan 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,ylz:g2(adl7-wlie e.lp r j5 the Earth will a spacecraft traveling directly from the Earth to the Moon experience zerlag- l2ljyrz l :.(,e wdpei57o 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 stan b-pg,qb.6goqh. qgnep+ 6:jffu p6-pd on a bathroom scale in an elevator, it says you6bg.q 6pfj,q eof.qg -gnhup: 6ppb+ -r mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube gq8msen)hsq t4+r4.ji7 pk 3e 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 sph4sep j43si 8r7qtq ek)mg+n.eed (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 foi8d wz 5c; 38x 3fouthzmj.9a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its r2-,5ij9pdpcyx nxe 7tadius r, the acceleration due to gravity at its c5d 7jx29 - txppiney,surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflef eon8of+ udv4) 5pd7mcted from the vertical by aopf 8nm) edf do45+7vun 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 banap4 7ezom,4nqked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of me4qozna7, p4 speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the.gu wn+ ji em1,nn45kp equatp i+ 4n1en.kng,j5u wmor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dist7 1egwgl04 edzdesn;4ance 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 of radius 235 m. A lt ms:;- o3dueyamp suspended from the ceiling swings out to d;tes-:uomy 3 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 been claimed txifb-*p22f2oyev :y(1 bin z* /dwso mhat 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 *xn(iyfmysd2:ob wfvpe*1z2oi 2- /bof 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 Hu .xhi8wu, .mn7zq)l mtbble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did q)8 znxhm,w7t ..lmui 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 i+0u 3tgv/yy fhr8/i.gwiob3 as it traverses 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 ctyyf/w ubih3gv+ii0r/g83 . oar 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 (G6.0ma6( 7fa 4hc2kczgthq icfPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determhiq02fa74.(mzfchk ca ctg 66ined 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 traveling 2.1 billips4 5 yptn9+2mslb.cjon km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 4pb52 jc4ny mpts+.s9 l0 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 ne:0iaukb 3b md *p-;8t 6fqmbmved of repair. You are in a circular orbit of the same radius as the satellit pi-u:k tv* 0d;6ma3bmbb fqm8e (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 distance fuz7ae s6w n1ht3yv9: yrom the Sun ys3za1ht6nw: e9uvy7?   
(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 wos) / l7 4ncv.ksroz)ozuld need to be if you could actually "feel" yourself gravitationally attracted to someone near you. )z.rs vs)cozk 7l4no/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) atz q9/r7dg0rqm a distance of about 30,000 light-ye 7r0qrmgdq9z/ars 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 wpu7 k7;m.fdw h2s z3zlocated at the corners of a square 0.50 m on each side. Find the magnitude and duzz.77kw fm; hs 3wdp2irection 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 th6 pa1 aj-/ lwog.izf)b23zlgqe 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:p6s cdvrk3 j60ez7 vsgp: q;b(kc*re by the tip of the 1.5-cm-long sweep second hand ovec6k:k c*qspzedr rv03 ;p7s(bj6 :gn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wei3fr2 (q(u edpzcv ,krk 4-7pahght around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10u a3kepkqrc2( r4 p -fv7,zd(h.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travei9e28r8xdyr 5ptg v9 nling at s9gy end 528r8r9vptxi peed $ 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, : ouv5oujb*,mu m hx5ku5wi0(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 m ohuu:ku5x(,jm*wubov i5 50force 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.$\approx$    $\times 10^2$