Sometimes people say that water is remkfm j z -xo zfrr7y(6+sg)),mroved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with (z,7)ky )f+grr6zmm ojx -sr fthis statement?

Will the acceleration of a car be the same when the car trixnx xm6q1/53z m2wlfavels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at x3 x/1 iwfzmx2mlnq56 the same speed? Explain.

Suppose a car moves at conswue6,p my2f2 btant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the tb2,ep f m2uwy6op of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-0w xkom 6vwo/, mz0he/go-round. Which of these forces provides the centripeth /mzoxwkw/v0e60m o, al acceleration of the child?

A bucket of water can be whirled in a vertical circlebn65 +d a rmhze:q*5qy without the water spilling out, even at t*ehrmq5n+q5 a6 bzd y:he top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are zug.dyv8g c.lfr eu*jbi ;g u2m287m, at least three controls in the car which can be used to cause the car to accelerate. What are they?l.fy8mu2i de7.z;,*ggcvr 2 bj 8gmu u What accelerations do they produce?

A child on a sled comes flying over the crest of )1qehwi+slc,d+j a 4:z1ae rna 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 decreas) q sech1,azd1+ jr+l:ewa4i ne as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwar k/ ; 9fekapcg.qary o;fd08.dd when rounding a curve at high speed?

Why do airplanes bank when they turn? How w mofsw+(nc47mr3d-wd ould you compute the banking angle given its speed and radius of wcs4d -f wm r+od3m(7nthe turn?

A girl is whirling a ball on a string around hpn3pfifw,; 1peta*g)x 8ak m0 er head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a tnax0ia3)* f gwf8;, kte1 pmpparget 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? If so, how large a fobdi/ :ah/tvkq s)ls3;rce? Consider antd)kv h/ i/q;sb :3las apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whajlz6 rjz,l s9.t it is, in what ways would the Moon’s orbit be difszj jrz,l96l. ferent?

Which pulls harder graviu ji8tie(oo *elk7:s1tationally, the Earth on the Moon, or the Moon on the Earth? Which accee ijsto1(:8il7e*kou lerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th )p 4t* bi0ah/0nresyce Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of thitey/* c0)nap h4 0rbse Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects ap4 k6 l:liy8vcre at work? Do tvcpy:l k6il8 4hey oppose each other?

The gravitational force on the Moon5u joa kt : p:6kk*qdud +y(r)9mquv+i due to the Earth is only about half the force on the Moon due to the Sun. Why ikv iqa:+*tukpdj ry ukdo(m5)uq6:+9 sn’t the Moon pulled away from the Earth?

Is the centripetal acceleration ep0q8xdx (v.(bxrhpp6yq5/u of Mars in its orbit around the Sun larger or smaller tha6qyr(xx8 hb0pe5(udpq. v p/xn the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite ( vh/4izx5shi 9a) toward the east or (b) toward the west? Consider the Earth’s rot5s4iz vi/9xhh ation direction.

When will your apparent weight be the greatest wekts4mx6+k c2c65nr, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case wo6ske+6wm42r txc ckn 5uld 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 pmn mczzc79qb c649ye* 0bqpb; eriods in outer space could be adversely affected by weightlessness. 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) p0qb9bb 46zceqyc;mz *c 9m7nthe force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runnerbe1 7)v)mskyyk 0b /oq experiences “free fall” or “apparent weightlessness” between q 0oykm e)vsy) kb1b7/steps.

The Earth moves faster vp:-wbvmoq4wgy) 94 e in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its gvopvm e44:9yb-wwq )orbit.]

The mass of Pluto was not known untu(59our skzy) 1.hjdyil it was discovered to have a moon. Explain how this discovkuhz.9o)1j u y5(rydsery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's.u14 ogguc)p8 d 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 centeu)g1p8go ud c4r 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 traveling-dklzyxwlre 5 n(pakz1;s3+ 6 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 t+sqw/75+ s 1xzuhxta khe Sun, and the net force exerted on the Earth. What exerts this force on the /t+zxxkw a5s+u1 hqs7Earth? 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 ropjouf r0dg lk+y 33pep794y u5 oo2f5fnah(7btates uniformly in a horizontal circle (at arm’s length) of radius 0.9oap5ofo2 03b r7f3 yup+k dl 4pug79f5hyn (je0 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circl51w7o hq 33)7p uftyn 0x:;whrxsyz dwes the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in termx35 1q7ot7 rn0fsd3yzh:)ypw wx wuh;s of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on t m/y.hiuvn 0n1he edge of a potter’s wheel turning at 45 rpm (revolutions per minute) ihy./mn0 un1vi f the wheel’s diameter is 32 cm?   

  A ball on the end of a string is / qi9ytcdsk8;3 z(zxjr-nk/b revolved at a uniform rate in a vertical circle of radius/bk9(z; 8z y/jk cdqt nix3rs- 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car cvruhf g)z+/*x an round a turn of radius 77 m on a flat road if the coefficient of static friction bez/ fgr*h )ux+vtween 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 te6eynb ktrv834h5o9e9ui; c mhe road if a car is to rounc;9 o6h3ym5ke9u4ee tn rib8vd a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training asf 8 a njo5ipge(bwpi,dl9q ysg*q6 -/)tronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of ra g gb,( odp)qy pslw9 e*8njfa/iq5i6-dius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm8v+nygt0lbf( from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is gfny 8 (tb+0lvthe coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a l+h )6p9v5hv1jrzp x croller coaster be traveling when upside down at the top of a +9l 15rpvxhhjv)p 6 zccircle
(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 ttctu juw u;vu/)u -nn43 h7hn:he driver) crosses the rounded top of a hvtcht; -uu4ju:n nn h7 3/uw)uill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Fet,n66 je 8vi20)l qwjqvo+zdrrris wheel need to make for the passengers to feel “weightless” at the tot,d)jel 80vq qr+wv6ni j6oz2pmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. 2,vvixd u1vca64adge jc--.dAt the lowest point of its motion the tension in the rope supporting the bucket is 25.0 Nvdadax1i,vg6 4 e.ju -cdv2c-.
(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 centrifu+n tsz8n r+o/rge rotate if a particle 9.00 cm from the axis of rot+z+r /rnotns8 ation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrictr z hagb1m)5 m1lf;4tally walled "room." (See Fig. 5;r )f lhgm 1t4bm1azt5-35.)
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 in a circle on a frictionless air-h*nbp7- coir-a .l 9pb31gvtkfbd 8;hrockey tabletop, and is held in this orbit by a light cord connected to a dangling block (massb;-r7ph 1pdg iof a-.rk3t*b 9l8nvbc m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring t +bu4 3xgnzi0sd+z)yzhe weight of the ball which revolves on a string 0.600 m long. In particulbxy 03isgzu znd4)z+ +ar, 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 ra5da yz5 ;mlhgg3v*hbqwt5/ ) vdius 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 massese 5x t5f6s;prc $ 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 by2r v:s5l-xkb8 j atfn:q)lcj,7 jfr;i diving vertically 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 tangentiafevt h9xnm/h v /,7*uql and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its f u 7hevm /,hq/nv*9txspeed 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 /ffj qd 8z/:pe nj1hn1area, going from rest to 320km/hjn f1q/dj/8fz enph 1: 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 and 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 particular in pz7y 64qs, hnsxg*ohc;( k.a d :yvmm*t:wjb1stant, its acceleration is 1.0yx(: 61 ombc; qd4nh*apv.*wsjgmyk 7s:zh ,t5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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, . 7cuse4wsvve;6u,u bs,xgt: 800 km (2 Earth radii) above the Earth’s surface if its u;ubc,e6tv,s 74u: swex vsg. mass is 1350 kg.   

  At the surface of a certain planet, the gravitationa q3 z:6p/ye/p9sm 7ismzkrdt -l acceleration g has a magnitude of 12 m/sz9:t y/e7k3rs mqdp6-zm/i ps$^2$ 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 r )ci.6. :ha(ibtnia 8qbye(8 pfj9z rb6p,pdMoon. The Moon's radius is 1.74r9 pj6eb.,pd r6ahi :.88bitpi aycn )(fzb(q $\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 hay4fli xj-kpr;zx a)q9 4oub11s the same mass. What is the acceleration du1qyfx;ouxp1 kbj z ar )i49-4le to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that ocu8 vwzz1(rr -f Earth, but the same radius. Whawzcu-(rv8z r1t is g near its surface?   

  Two objects attract each other gravitationally with a force of3b s/k1ruc ac3ncxe84 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 mq9 nva- b+wyxbl,rs 29y n x+svb-b rl29,aq9w    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside ta k;q1zrm bz*opf6 kn15/o kd9he Earth where thegravitatiko5p9/qk zokf 1zr*1dmanb; 6 onal 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 gzfb)sw173fe our Sun packed into a sphere ab z sfbw7gef)31out 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf stv8g0v yc ;4ffhar, 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. Whatc8 gy40fvv;h f is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spaqe ; 02lcjg5en e,(jqvce shutt lje5;n(ev2,jcq0qegle. 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 terms of g.   

  Four 9.5-kg spheres are located a u(d+6fioh p*at the corners of a square of side 0.60 m. Calculatu ifdpa( *6+ohe 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 vao,exx 9;g-e most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four xo9g, ex- v;aeplanets 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 ieygx)f uu:w *mght--6 s 0.38 of what it is on Earth, and that Mars’ radius is 34 xtegu*--g ):ufyh6mw00 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun u428t lvu9 o 7e(uameo2 .gqek)cxobh6sing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obta g8k6leooquve(7m2oa4 cteub . 2)9hxined using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moy( d*cgwc4*wt ving in a stable circular orbit about the Earth at a t*ycgdcw *(w4 height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km aboqah+t*t 6r b+eve the Earth. How fast must the shuttle be *+et+ rt qh6abmoving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expe*11rkknyyyu3 /zj8 1o akk5tnrience simulated gravitykk nn/yky8u531j tak y oz*r11 of 0.60 g? Assume the spaceship’s 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 take rj-oa:2 0.mex, zxkjxp-qoo4s for 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 oe:04ozj m ao-q.p2x-xxro j,kn the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fromgouv4cx os4)u4n +r6r (x4ybr the top ocx +44v4s(6r)obg xyu 4uo nrrf Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo luna q8da2dzl/)8 qa9of*cw c/bn18wfwxr r landing mission, the command module continued to orbit the Moon at an altitude of about 100d/c ) zo /9rf wad182xw8blaqnq8wc f* 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.xhuaj368a( kt The inner kjx8u (hat36aradius 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 rotates once every 15.5 s (see Fig. 5–9). Wha8uh5 1orxt+ cd x7ov7xt is the ratio of a perx87o h rx 517c+vouxtdson’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 qg(mx.xucj-v e6ex66. b 2sepkm from the center of the Earth's Moon in a space vehicleeqv.6ejb62 exc-(gsmx.px u6 (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 o z,shi.af+ibh, 5zf ;8xqz7kuf equal mass. They are observed to be separated z h+fs z7, ,a8.qihx;kbi5uzfby 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 weight of a 55-kw *( /sm* + y.uh;79hhrl3v8ijkdbhlzbguzn1g woman in an elevator that movz7+u hm.yzv*uh w j*slr9d ibl3h;g(k/b8h n1es
(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 elevator.,dkcf(wigv+txd7a g-vx+z ,pq3zf t7- n*0nx The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceler7zwt +vn0,(k dic xgf37v*, + nxd-a qf-txzgpation (magnitude and direction)? a =   

Show that if a satellite orbits very nem o43ztznd prnt wq31*lv*(g/hoa e+7ar the surface of a planet with period T , the density (mass/volume) of rntt*qp*1wzo3d / 73la h no4 evgzm(+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 (27.4 d) to determine the period owb 8p(c a3jcx)f an artifj )wx cp(3acb8icial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hu8dnpo -ri 13wf:shh m 5o8y0cnndred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from thefdo-n:yh5c3nh1i8rp0sm 8 wo Sun?    $\times 10^{11}$

  Neptune is an average distance op/, o3v 96,a.hoq hxbsfvn7jh f 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. It come81 xehi+ vgmw-s very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar S-e+ h xvmiw8g1ystem? 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 z. c:(dg9-0xgii jd al1bbyt5Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 mas1pygb3an); lb cyw 4+zs, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo igby+ zb34; cwya 1lpn)n 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 n os iyz7s o4m:2myew++k( s-mdistance of the Moon. m 4 ozm(ksey+w2-i :sn+ 7myso   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moonht1* zd+y4kcms, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–y *4 +mkt1zcdh3. 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 Jupitv4scwx x eq,- ef0q.lij2z6*ter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was dezce2 w t,is xl0q j.f-v*ex6q4stroyed).
(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 desc tn)u9i-zh1 oxzw3x 5fribes an 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). 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 9x i3 owuzfx)nh-5tz1 be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from -(j a q(rnil+wa hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine,(ji- rnqwl( a+ 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 Earb;*eg0 q hpr e( b-+v4h-usipbth’s surface will the acceleration of gravity be half what it is o ehp-v eb0-gbsb4;p q*rhui +(n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hanpc+nt u30rs.yzljs3 8 ds and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and the3ns0 ujsr3pc tzy 8l.+ir 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 acceleration of gras 8 tk.qg0p,ch4 iwn-q(x n6rhvity at the equator is slightly lx k6 hqp(i0.hq8n gwn,4-r tcsess than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly frome8i o/ 7xh7r 7mrtq1lo the Earth to the Moon 78ilt/7xeom1 r7qroh 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 yol :y;u-o-sew/ho8ec bvfr e3cr(c 8z4u stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whi:;bvceo z rw-88 4-y rflhuoec3se (/cch direction?     ----待选择----upwartddown 

  A projected space station consists of a circular qi 32zjwcyti z76w*ei1 +va-e tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g -wt3 w ezii6vq +ay*ji17e2zc) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft inbdsjfo03-/cc a vz78y a 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 )z v-f. v;3pklj(lbu +n *f i8eke 8nddfb-vj,of its radius r, the acceleration due to grfd*bfez;8n j-n jvli-+l(.u,k pkb)d3vvef8 avity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectedhfldej03 j.u9zlt +gk. ,*ao.hhp/rv from the vertical by an angle hfh t,.p3e.vdr +l/ujzla k9.*hjg0 o $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficien:lz 1 n o 16+ovq77qpan2sf*edlqs2eqt of static friction is 0.30 (wet pavement),n 2pso*vlsfe 2+nq da7 z1qqq:e7o 61l at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects+n+mfna*o p-x at the equator were apparen++x no*apfm-ntly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of)e hlzu(y zp,. 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 speedb gxjr (f+0m 3*kgn9te rounds a curve of radius 235 m. A lamp suspended from the ceilnkfr+* bgt(xj0 9gem3ing swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the mb0+04 ptcho3b ri ywg 59u3rxEarth. 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. Calculate the numbegwx5 0yr0bb ot9m ur 4h3+3icpr 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 presencgy6.y:u* vmef e of an extremely massive core in the distant galaxy M87, so de6fvemyg u:*y .nse that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shot0 pv2dr+5ak( f q*wrfwn in Fig. 5–45. Both the hill and valley have a radius of curvature +rrw205fkvdtf(ap* q 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 Positionin5ee/ a,(o+mg;fkf 78:sxbfi.cf dr) lwp a)thg System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satelli;b7gekdrfx 5 f l sw+/( ,phaaet)).miff:oc 8tes, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billi 72yg34 2ixv kc3fk/vvun),n3docn vuon km, is meant to orbit the asteroid Eros at a height of abou,nduokxf223kcn3 4/u7g)vv vc3vy n it 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 pursnwt t-emgd 4c7m/h r3 9,c)(lini h0gcuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above tnw ) g/ ml,cm3hhgiedctr 9c04 n7(t-ihe 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. (mjh6ft+f*bp yru o yh8zj;0.7a) What is its mean distance from the Sofp yhyu j.h076z*jft m r+b;8un?   
(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 valh +.5 bp6f//mmszzrvc ue of G would need to be if you could actually "feel" yourself gravitation5zmfhr6m/bz / cp vs.+ally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46x 6utdvl03m jky+kz;9) at a distance of about 3k;mu+k0zylx 6td j9v30,000 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 corners of a square 0 .zcibefk)-h 0.50 m on each side. Find the magnitude anfb)z0.- hce ikd direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg or 8ep(kbfjqxk 4r/2q )rw:jkls 0.rq;vbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long s . gt 4gvl 4zs1))y:plxa2xsteweep second hand on your )xs gv a:z4)ygset4p1 2x.tll wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wvi z j1roia/5,eight 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. 5–10io1,i zvra5j/ .]    $^{\circ}$

A circular curve of radius R in a new highway is designed s 31l0sfr8dvni o that a car travelini8lr13nf vd s0g at 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, thj: d xcs2p v52mfin3y/e 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 accelerationfm: 5y2 2jxspdvcni 3/, 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.$\approx$    $\times 10^2$