Sometimes people say that water is removed from clothes in a spin dryrwbc8 xzsli b82-p yun(m:-k8er by centrifugal force throwing the water outward. Wh lrbc8ni z8pm-b:y u-(wx 8sk2at is wrong with this statement?

Will the acceleration of,r)wscp v48vhhtc14 v a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it trav81)44 cvpcvthw,rv hsels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wh/rlbqy*zsw7 4 ere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a diprs/b*l7 ywzq4 between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acti2+nmz3i2y g oz fb4l(fng on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal + z2 fn(ymoblf43gz2 iacceleration of the child?

A bucket of water can be whirled in a vertical circle withouq/vjz70c02w3 hwkc hctpo), yt the water spilling out, even at the to 7zc ,j2ck/0wopvyc w )hqt0h3p of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Thetef* z7booy 74re are at least three controls in the car which can be used to cause the car to accelera7t74zfeo b*oyte. What are they? What accelerations do they produce?

A child on a sled comes flying o g lz1,1cuhu 7bcqebpj1.z)(lver 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 force between his chest and the sled decrease as he goes ju l ghzl.1)7c1 ,pbzbe c(qu1over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lifaixq+osf96y g,6zq- zu ab5*c(qidc4/x 1zean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the z1 ;yx t*cy kx(dj9)lz5unt;obanking angle given its speed and r; dzku y 5ctnl(9z;yx*tj) o1xadius of the turn?

A girl is whirling a ball on a std3ugun0 *i+wt 9n* rkpvl/s i+ring around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of vndu*ngl09 +k3 siu/w p *i+trthe string?

Does an apple exert a grajm.+p cb; v2iqo:0xoo vitational force on the Earth? If so, how large a force? Considerx +ioqb:p0m;o.jo2cv 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 Moon’,yuuybsxuj r6k q 0rye) 9::b;*jlj a,xqzq 0*s orbit beqxryyruazy jb u;)b:, lsx*e ,kj:0j9 *6q0uq different?

Which pulls harder gravitationallyebx, 8 ;eu sb5a1w3mdphbosw2 4 zki,*, the Earth on the Moon, or the Moon on the Earth? Which accelerates morpw1dbz3 ,ms*e2bau4s8 h w; xob5ke i,e?

The Sun's gravitational pull on qqgq yjeu4,sn4e/42dthe Earth is much larger than the Moon's. Yet the M/ 4, g44qnqey2eqdsjuoon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh morqr,6vgh 8m3 3i2axyo3eys 4eluw 2d:qe at the equator or at the poles? What two effects are at work? Do they eh v223uoa ,s68 qeqgwrly: i3xymd34 oppose each other?

The gravitational force ono+hec 3kvrr 9/m.:vll (kp- ub the Moon due to the Earth is only about half the force on thl/vv:kr3 m.rclkh -eup(9bo+ e Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or sm kw wy6vl970-fg/qaxviy11e taller than the centripetal acceleration w0y gvq7 k1l/y6-aix f1vetw9 of the Earth?

Would it require less speed to launch a satellite (a) tooo7j7s st:.yw ward the east or (b) toward the west? Consider thso7 :7wyj.t ose Earth’s rotation direction.

When will your apparent weight be the greatest, m,rz9,bc4/ uh0+ )y)wjuo lswkkn/bqas measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accew,kqsz+,9u / uwb 4y o/cbj))nl0krmhlerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected m+wduvcq,6;wi0)p qc rpu5 k- by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the as m;cp05qww p+qk-6)v idc uur,tronauts 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 1h:d70zek 7s 0wmnzrn-4 ufjdweightlessness” between s 47uwe d1:r00 hndznzjm-k 7sfteps.

The Earth moves faster in its orbit around 71kj goste0k9 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 theg 1k90tjek7os tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it gy ; org/uko(n)b+6mawas discovered to have a moon. Explain how this discovery enabl r+og6 gna)u; kmo/yb(ed an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much cqehpn hk6cwo4 7s- .7larger 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 othew76chh7qpc n -s.4koer.]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 travelin;et5m6b,an-*oefu)4 zq ugw u 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 arounddkz8nb; qylo 46a.6wpi p*gf- the Sun, and th66o bg 4pqd.z -p wfn;kyl8*iae 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 exerted on a 2.0-kg discus as ie8fj n9p u64tr a.r5ubt rotates uniformly in a horizontal circle (atr t964f8 ur5up bjn.ea arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 kmtam5-rn;nbm h-- (c-l a6vzdclqv8 b ) from the Earth's surface, and circles the Earth abou;ln 5-qmac-acrv( v bbm-l n6dz-8t )ht 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 the Earth's surface. $\approx$    g

  What is the magnitude of the eop+l,o1 tm8 x;mrs1p acceleration of a speck of clay on the edge of a potter; e1o tsmpo8,x m+1prl’s wheel turning 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 uniform rate in a vertical circleh :+hyz:7 6es t0oqqfg of radius 72.0 cm , as shown : 6sqe7zhhg:y0 +tfoqin 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 tum9iz(sg33a o dnk*k r4*h+ md4)spinurn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the m*3prd9od gki sam4 hzsuk(i*3mnn+4)ass of the car?   

  How large must the coefficient ofazgtmkt:ju yau+dj- ()0p +l; static friction be between the tires and the road if a car is to round a level curve of radius 85 m zayk+tup+a 0 gd: ;m(l jt)-ujat a speed of 95km/h ?   

  A device for training ast cqe) 4q4tgza p as6joo33i2,pronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, hoaqp4ezqt op6ag jc42 o),3is3 w 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 r3ysdm:ynub;: otating 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 frictisb ;u :ny:yd3mon between the coin and the turntable?   

  At what minimum speed mgyt3ee4k;h :d ust a roller coaster be traveling when upside down at the t3ey4 thkged ;:op 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 dlr8r mrdq (j4xmjnm//b)k+l1* 80v bo6gxre mass 950 kg (including the driver) crosses the rounded top of a hill (radius =95e qmxk b/)( rr6rl08bx8jm r*dm4 o/+nvlgdj1$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel needph4bud ndys x( 34q w//b16wsm to make for the passengers to feel “weightless” at s 4//4 ( mshp ndb6xu31wqbwydthe topmost point?    rpm

  A bucket of mass 2.00 kg z68pxlc*ed ,co d:n26jmx d i(is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion: pl8dx2 cejo xn6*d(,mzicd 6 the tension in 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 c)tq,-w wqp xvkvy+;k; entrifuge rotate if a particle 9.00 cm from the axis of rotation is to experiencqw ;)wx+tq y-k vk,;pve an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peo zwjmfr6) uc(/ple are rotated in a cylindrically walled "room." (See Fig. 5-35.)z )rmw(fucj6 /
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 in a circle on a frictionless ai 05rv kqla+34j)t hy /elnu8uyr-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centra ra3 y/qu)eh4lljykunt805+ v l hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of tdu thtwzn*0rfm*+4px 0,l+a she ball which revolves on a str,fzm0 sanx+tur*hw+ 40pl td*ing 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car trave sax*5y5o3bui1m gd9cling 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 (jk/+smcir8/p: ) yc90vfh 2cctbulb $ 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 2va gmv6ocrk8c(bj,(yw) k4 b $\mathrm{~m} / \mathrm{s}$ . 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 ofuqncw (ml76u/6j wdmk+0 zv3 a the net force exerted on the car (by the ground) in Example 5-8 when its speed is naq/7mcm (wwkuz+d0v6ju 63l 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indiana w d41:;s-*nhsk hjepipolis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular 1h- ;e* s:d4jki wpsnharc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.9wvd y/mm,tsu*sh(g/)0 m . At a particular instant, (/d/gms*)wm ,yhv utsits acceleration 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 spacecraft 12,800 km (2 Earth radii)pgocn whainv6p.r x(q+t*, we452 vv) above the Earth2vpoxn+ .a vw6 * 4pvrt(wi)ec,gqn 5h’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has dp )y3* tyyd)jged9-g/ra-esq ue5m/a magnitude of 12 td-eujds*/a 5r9-egegd yyy/ q)3p)mm/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. Thfmjut 41cchqy1y:2 ;9dfgd w3/eb; kde Moon's radius is 1.74 c;b31mf1:/gj h2tefyd q4dkycu9; dw $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has i:-uqkbdnr, r j*w)ugw/wd3 90ji oy.a radius 1.5 times that of Earth, but has the same mass.:03drww)nbo/-qkd .g,uj w *j9y iriu What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiu yn1fwbmlm;34s. What is g near its ly3 wmm1;nf 4bsurface?   

  Two objects attract each other grav a:,(m na7e3qge1ktkuitationally 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 gra;*- p aurq0xgg;jv,wn ,6kh idvity, at (a) 3200 m*, jrh0,dwk -pv6 qg ux;n;iga    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Egceut1t3m : ,qw33k saarth where tmte3 13 :akusc3t, gwqhegravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five t9ujnhp/uj2, fe* i +0owxg6pjimes the mass of our Sun packed into a sphere about 10 km j9f 0+/j, xnup6epo*h jw u2igin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is lfm 2gl4zqk-47bpph5 now in the last stage of its ev 4p-fpq 5z27lkbmlg4holution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlesm;p6 ,ywj)*4i 7 d sivqdd2yihs while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot w,y vimiqy2pd7*6 ;)iw4d hsdjeaker 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 ak0fs :;vzeq 0bt the corners of a square of side 0.60 m. Calculate the magnitude and direction 0f;0 kbszv:qe 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 jj fm;ijz mv4;jb0 5-nmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuminb0- j j4mnijj5fmv ;;zg 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 gravkb2h5frvm.a+ iw.tlv03 td8 bity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’afi+ 2tr.0wm 85tv.3blh v dkb radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valul7jn *-v:bmqx) o:(asi/aqr f e for the period of the Earth and its distance from the Sun. [Note: Cqa-l)b ors* /xm aq:n7f(vj: iompare 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 jb dc2q8t7ulvo u;n0 +circular orbit about the Earth at a height of 3600 kl 8n0;jtob2+ du 7qucvm.    $\times 10^3$

  The space shuttle releases a satellite into a circular orzk6:: xt hj39 vp8arcobit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) wp6c8o:akz9vx:h3r j then the release occurs?    $\times 10^3$

  At what rate must a cyl,hz2huy)d2y zvq8-9hqmmq n 4indrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and giv8qzh9 h,2 m4d-q y hnumz2yq)ve 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 circf uyj/ cia*)u-ular “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 you )/j* uiau-yfcr result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite haw;qzoi2 6ga7+ c6wqlcve to be launched from the top of Mt. Everest to be+cqwc lqg2 wai 6oz7;6 placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, therluogm yr80 .7)co lr4 command module continued to orbit the Moon at an alg)y m7u o8llr0rr c4.otitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. T +8ya0pn-rf uqhe inner radius of the rings is - 8pqf 0+yuanr 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 diameterhhf a4ir,l92f rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, an4,fihh9 rla f2d (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of thf atgvfn:5q2(h 4wd(+kfc4pl e Earth's Moon in a space vehicle (a) moving at constant velocq:(( fnc f5h4kg4v dw aflp+t2ity,     ----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 hirv+ qwofa.3x6m:-y of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway brw3ioyx mh a+q.f6-:v etween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg gj*zk/ u- a0zyx,ke, ywoman in an elevator that mov 0kuzk,zg/-yj y* ea,xes
(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 fr )6k* qdb b0y1-ep)ppvnixu30 x;drn wom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration ( p 0xb)ev)udk y1pp0-d;wnbqi3 x*rn 6magnitude and direction)? a =   

Show that if a satellite orbits very near th xi71dh i9 pkj-mkshe4op9l*o pc8 )k*e surface of a planet with period T 98 -cexdphk h) *7 k* ik4imls9oo1ppj, the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.422x87l.7e0 q o lnmqafmldb/d d) to determine the period of an artificial satellite orbiting m77aeml2xo2 0q bln.dl8/dqfvery near the Earth’s surface.    s

  The asteroid Icarus, thous+z ,6izh*dnhoj8oinfsh slg) .317 g gh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean jh l+ f7hs,)* so .oz6g8nnzi1ig d3hsdistance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of wq4*fngbba-0 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 eve3e/h-1qvum xyry 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distan/e -mvhu qxy31ce 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 center of the Galaxy o m:,ykq/s/d) suom*s$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,eo 0tcv3*dx i four largest moons of Jupiter0e i t*x3vodc, (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of0 blm0ic9tu *m the Moon. 0m 90umlbitc*    $\times 10^{24}$

  Determine the mean distance from Jupite6 ky8ww8 oa3x6t la:zfr for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Co:kxtwf6a 8a863ow zyl mpare 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 mad-gbj dxc;;5 kny fragments (which some space scientists think came from a planet tgd;x-5bc k jd;hat once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of ) njv+dtr,p+ ra band completely encircrn)+dp j,rv +tling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging8mpoo(o )7oy 7ngpo0w 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 thpoo(0noygo p7 o8 )7wme maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half m4rx7a/if (ze what irfm x7/iza(4 et is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands/wb tapax+ou 7u8 p+;r and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are tp;wb ux ao7 p+8+aur/60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration kdy/uta1g:5-sl p c3e of gravity at the equator is slightly less tha-cdgt 1ps eya/lk3:u5n it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraf0zrlp e ig/1no0 e8wu(t traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? i(0/r1 8wog 0euen lzp   $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in a6zzmi9vd*bv5+fv2,g ngs x-d diz9+r; ias s8n elevator, it says your mass is 82 kg. Whav*9+gi,dig;9-av 25sbz i srsd n z 8vmzx6fd+t is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wiqw /(t lbhm *l:up) h-o-i(v kkqg9zt(ll 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 rv(9pot (b -q)u*(gwz h /ikhlt-kqm:lotation 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 verqmk96z7qx( a(v m/xmrtical 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 eep*ls6 qqt)ele7bf+ nuz(+;h q7 f+oof a planet in terms of its radius r, the acceleration due to gravity at its surface 7n ef; ) +(uql7lh+be+poqf6qeet *sz and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertica,rz /fa (jima6op.n:rl by an annroa/ j p6za(rimf,:.gle $\theta$ 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 the0mn0m8u13 o6trbthsc coefficient of stahn0tmo3 s60r b1ctum 8tic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eartkrs :jbcij 0pk5 m569kh were rotating so fast that objects at the equsjib j906ckrkk55pm : ator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance ap--qc.0o1 ox -enbi ptdart 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 cu(st,czv)4 y4z+3 (m(ayroi bow a dsj*rve of radius 235 m. A lamp suspended from the ceiling swingsa+b (4d3ay,*z( yo o(sst wic 4)mrjzv 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, +eeff- .kkvg gukhh10xw3t8( 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 suxk+hghft.0k- k 8( v3ugw1efervive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of aphftt3czniwd *0 1*6 un extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no ligh3zinw0t6hd t**f cu p1t 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 valle98vy7y4nte 88z 8dwl( a lbkvyy shown in Fig. 5–45. Both the hill and valley have a radius of curvature ay l48k798wzty8y lvbne8 vd( 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 (GPS94 uura4u);v3ftqndzu ef q0 :) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of ea:3 a)v0rquu4fedtz 9fq 4; nuuch satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR),hsw-oicje22vn+ 1 d9y after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 9heo12ywi2djcsnv- +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 spa r.25vo,9y ) gtdmi6zu yy+tuzce shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 kri6yo.yt, guyu+) m z5z9v t2dm 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 3009 e1t)j tfr yxyk)6ur.0 years. (a) What is its mean distance from the Sun?t fy6)e1 r kt.y)xju9r   
(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 3p ,./ 0gdnxk9hswnb jto be if you could actually "feel" yourself gravitationally 0jh ns3x9/,d.gwpbk nattracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroun+h s7gh *9xq 7k asgbny*g)xw4d the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from4hgg *swax77x*q g+k) bh y9ns 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 corners of a square 0.50 m on each side. ,ra3/h pmc d)cFind pc/h3a d r)mc,the 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 5j 2ob93qh((j0p eldn vmv,e2c500 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 th. ngth4 9p*,nnj v7y lqiufw-7e 1.5-cm-long sweep second h n-* ti7gvp,lj7 n nf9uqy4.hwand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and pk59e/vwqggl0:j 3 b ystart to swing a sinker weight around in a circle below you on a 0.25-m bwj59 lv3k:ep 0q/gyg 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 ca 8 *a6p;w:e,wdulmy j6d/cxx sr traveling axdxa 68w6ue/,y*s; c:ljdwp mt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when u28cm: ljss*fnegotiating curves. The angle2 lfsmcsj8 u*: of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (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.$\approx$    $\times 10^2$