Sometimes people say that water is remov n. xj y)oh:6vbld,ae5ed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with .6,vaejh bndl yo5: x)this statement?

Will the acceleration of a car be t6y8jngy+ b 9g x 9*wzx*km+ok ojwyv45he same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.xj w xm 5 kooy+ 6+*vnzg*y9gbj84kwy9

Suppose a car moves at constant speed az4m,lpyy yk .)o(kqd 7long a hilly road. Where does the car exert the greatest q(yzl7. yp 4kky)dm,o and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding alzway ,y0exr ) e/rzyj m583,a horse on a merry-go-round. Which of these forces provides the centripetal acceleration 8lyz3r,eyz mwe)y , xar0j /5aof the child?

A bucket of water can be whirled in a verticalb i wfb04zn) qc; 8f/n4(xmhac circle without the water spilling out, even at the top of the circle when the bucket is upsnif8ma4(;hq)zcx c40bn wf/ bide down. Explain.

How many “accelerators” do you have in * ,/pp)gtzhg eyour car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelep*gzt ge p/h),rations do they produce?

A child on a sled comes flying over the crest of a small hill, as s38 rf0m oyw o(ockks*(hown in Fig. ows 08*kfyromk3(oc (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 Newton’s second law.

Why do bicycle riders lean inward when rounding a curvxx jdj)hf()l-/auoy+8lv s 9ze at high speed?

Why do airplanes bank when they turn? How would you compute the bal s08+bv+bhi pnking angle given its speed and radius of the tur8b+psi+b0hv l n?

A girl is whirling a ball on a string around her head in fxu4vo/5x3 tya horizontal plane. She wants to let go at precisely the right time so that the ball will hit at4f uv5 x3yo/x target on the other side of the yard. When should she let go of the string?

Does an apple exert a g,gft f)n*j ,vm+5ace2 r5zad, -d orukravitational force on the Earth? If so, how large a forcekzm+foae-gatrj curf,) * d5dv, 2,5 n? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouldd y+,oh9dvl5o;a rg( n the Moon’s orbit be differena dlg,oy;o(h5 nr9v+d t?

Which pulls harder gravitationally, the Earth on the Moon, or t*gmr2l6*rrfl+4 kih83nusnry z +z . bhe Moon on the Earth? Which fkr2* b*3ur.znnlhg+ r+l 8i64yrzm saccelerates more?

The Sun's gravitational pull on the Earth is much larr r4r/8f,ix ujger than the Moon's. Yet the Moof, x r/4rui8jrn'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 more at the equator or at the ppky,3wj0 xr,l)zr q y2oles? What two effects are at work? Do they oppolryr ,q )jpk w32,0zxyse each other?

The gravitational force on the Moon due to the Earth is only about half the for 88ze9 fgcvx8qjz 2a6jce on the Moon due to the Sun. W9gc62jfz 88x vqje8azhy isn’t the Moon pulled away from the Earth?

Is the centripetal accelerats6/1 vv /mt9 myjpix4xion of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?6jixy p1/ v9xms/vt4m

Would it require less speed to launch a satellite (a) toward the east or (deo; o1k0h-f8af6dxmb) toward the wefx8 a;hf6d d1 0omoe-kst? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as m8 irjgm/he9w+easured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c9rh mi+8jg/ ew) 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 perioli5;pge4z vi elrlin 1 l(v38+ds in outer space could be adversely affected by weightlessness. One wel+n51(3ri 4p 8izl;gv lvleiay to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appao-rhkgkc0-w/ 7yu e5lrent weightlessness” between steps.uwc- k ko/eh57l-gy0r

The Earth moves faster in its orbit around the Sun in January than in July. Is t):f :5tkldrl83rf4;p pcib tdhe Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in td8:p; tbdl5)p:rl kci r43ffproducing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered toc i:9vrw 7f;dx have a moon. Explain how this discovery enabled an estimate offrc di7v: w9;x Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the ehr w3,)j6pgldv k -hspv ;av8);e+s eMoon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational p vjs3evagp,;;e- wdps )k+6)v8lhherull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980nzogmp 03x5fll d32zpv4s j *4zi2f0p $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 +q wdzyyl8-v3smso..whq1c bft 3/ 7athe Sun, and the net force exerted on the Earth. What exerts this force o+ tay3q-o.fw1cd. s8wymz37lhv/s q bn the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotatesc(8 k1lz54g 9fb; ztreafktu; uniformly in a horizontal circle (at arm’s length) o 8fg9(z 5fk; 4e; kbtczrl1autf radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400-u ;)hd8 mtnqf km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetdhqm8-; f )nutal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of ad-cgwk3 3uzwjlg gjo .:z-l70 potter’s wheel turningjo3gjwcd ukglw:-03zzl -7. g at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved a d5+lk fmgp.ptxa 0.t1t a uniform rate in a vertical circle of radius 72.0 cm , as shown in.+ltfdp m0p1g.kx5at 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 spee8)6ofk fq 8hoid with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent8i 68koohfqf) of the mass of the car?   

  How large must the coefficient of static friction be betweeh *y1(cs8k l pnhrv:qv; hpi3(n the tires and the road if a car is to round a level curve of radius 85 m at a qy h:h3 *1pvi p;8rknv(lcs( hspeed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designeqp/:vwvbu *v( d 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 weighvb/*u (vwqv:pt, 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 of variable svkx;z qmsa0;zuv38;3tnt 6 ggpeed. 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 z;g;6 ;gkav8q0mv znx3st3utcoefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster b 8ui4sf8buyzrorj2r2.e , x3 ke traveling when upside down at the top of a circle r4.3r 2 x j88b,rkeouu2iyfzs
(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 95*ke2c0l/,oz nisg 8e o0 kg (including the driver) crosses the rounded top of a hill (radiu zikonl/e,*8 02 oegscs =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 Ferris wheel need to ic -ni:+lymj3+ iyz7emake for the passen+ii3me l:j nciy7+z -ygers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At thca135nm +fi fmrj w9v,e lowest point of itfc5f9w+v m,am 1i rnj3s motion 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 ce6fuc/cy.g59niv d k7 antrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an v/yaf5.nd i7gc9kcu6 acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people ar ;ftwqjnu3dmhpu 15 rp,b+ (n5e rotated in a cylindrically walled "room3, fdh 5(w 1;5 mppunjqbnurt+." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated9jaf .9iuo dn- in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected t.f9 iau9ojn -do a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this t )t ltnh- vrzv99tfp84pg44c**nhji kime, by not ignoring the weight of the ball which revolves on a string 0.600 m loj f8 4*4ic tkttpgz9n*9lp nvr-) vhh4ng. 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 bazzjifd :n0 r4(/ne..nm moii 1 i7;kkjnked 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**r l14n o5gyix-q*enf/h tjc $ 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 ;)k4klj y, akn7v3r2o dcoak7310 $\mathrm{~m} / \mathrm{s}$ . 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 ceu+uwrvhb*tz uc(3d am9 76pf6;v uhg.ntripetal components of the net force exerted on the car (by the ground)(6+u 9g.t; hrw37 d*f6bazuucmvph vu 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 n*7an/;e hqopthe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between th/a;p o7en*qnhe tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of kk ,e:zca bm2 5gyln,0radius 2.90 m . At a particular instant, its acceleration is gaeck zmnyl :bk2, 0,51.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 o r0b.p,cvblp- n a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.b pp0,r .-lbvc   

  At the surface of a certain planet, the gravitationaufc)i zpfkbi0v17av(8* hai7 l acceleration g has a magnitude of 12 m0zk a*f7hcb )fa8u1vv p7i(ii/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 2)y.(tos5n02u/ qw eih mi1p nx*z+aaac)vh mgravity on the Moon. The Moon's radius is 1.74hhw 0x 1v)amqi/in o+(*2cyesaaumnp. 5t)z2 $\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 thue2;/othp4 ypat of Earth, but has the same mass. What is t2/y ;u4ephopthe acceleration due to gravity near its surface?   

  A hypothetical planet has a mas(yrn tx8()wniw cg6g+u :hv5g c+npn5s 1.66 times that of Earth, but the same radius. What is g near its surface?vgg: hg85 c56+(ny(puc wwx+nin trn)   

  Two objects attract each other gra xr; qs 99)nj3fw:*yepocvearj le78 ,vitationally 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 gravitqby- fhnrlfzb 2xzv2;e 00,3sy, at (a) 3200 mzy,nvbq0 0x h- 2 fb3rszf;le2    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ly:k orb/+/ hii6pl,i outside the Earth where thegravitational accelerbo li/ir+,y ih:kl p6/ation 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 ouazv.4raul4 +v w0 :eylr Sun packed into a sphere about 10 km in radiusy+eu4v 0vlla z4:wr. a. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whx.7tt*bpnqc k7,x9 wjich once was an average star like our Sun but is now in the last stage of its evolution, is tb*t7w.tq cpk,97n jx xhe 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 astron 80/hwkn j ra3p2tsxppkh oc.bg8+jl0b/.7 nvauts feel weightless while orbiting in the space shuttle. Your friends respond thx 8s3p/cph8a.jn r/0ktwn jkh.0lv ob+pb2g7 at 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 ;*m6dc/ 7hrtu/vh4x c ufue.fat the corners of a square of side 0.60 m. Calculate the magnitude and directio4huv / *7fxc uhderc. mtfu;/6n of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the w8 .hxapgk+q5l y,,6nvguak9Sun. Calculate the total force o kavnh,xg+9 yw6k aql.5gp8u,n the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity cb13huh ) tqv:i um53yat the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is q )bvt c:3u3yhum51ih3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value f 2ifnk0cq;b)o zho w/4or the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laohn c0q z2f/4;w)okbi ws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cmdtl 6h3q,o d8 ,f. o;onnsd3wircular orbit about the Earth at a heiofo ,qml,n3d; d8on6t3 h.wd sght of 3600 km.    $\times 10^3$

  The space shuttle relxuh-f5c2 zheh x1)f h,q.m:loeases a satellite into a circular orbit 650 km above the Earth. c:hh, x .u-o 2q )xm5hf1lfzheHow fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical2z v+-+ipilvo1 bz:w r spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.w po izr v:+bliv-2+1z)   

  Determine the time it takes for a satellite to orbit the Earth in we+k 4*za*gx;)v iwa qa circular “near-Earth” orbit. A *k) ea+*;vqww4zg xai“near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite havn 2,n8v-98uszw lab h/eremd4j1m zc+e to be launched from the top of Mt. Everest to be placed in a circular a2 8l+s8ne j-wncmh 4,rd/z1 m9 vbzeuorbit around the Earth?   

  During an Apollo lunar landing mission, the commatpa8um7 2 4umsnd module continued to orbit the Moon at an altitmatups84u 2m7ude 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 kb y 7-9+mwddgthe planet. The inner radius of ty -dk+b7d9m gwhe 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 (5iwqv wkj1/n5dhbctz9/lsf 0;1 s: u esee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at th/t cvwne:;j 5wsf5k d1qi1lu9hz0b/se bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from th ;pu 6l1ukqk.hwed a3(e center of the Earth's Moon in a space vehicle (a) m1k k6;.qa(hel3 w dupuoving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. T n8ywdc+gh ):bhey are observed to be separated by 360 million km and take 5.7 Earth years to orbit abodb8+wgn ):hyc ut a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator t+ch6- svdy n.qhat mov .cnvsyh-qd6+es
(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.fxnqm5.af6bdd /gze/d (q 9zat6b,0p The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eqgdn 6 5bxama e .9f0z/6/q fzd(,tbdplevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period T;v)vxy2 (p-q3fsinx z , the density (mass/volume) of the plans in)qxf 2v yvx-p(;z3et 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 determi n)v4y)v) v0xjin;qvo ;czwb3ne the period of an artificial satellite orbiting ic)znjw )v3o)vnb;;x4 vy0 qvvery near the Earth’s surface.    s

  The asteroid Icarus, though onl +vj 0 zp/ 5o:nmanjr3u*ogl2my a few hundred meters across, orbits the Sun like the planets. Its :+ng v m*jnjrul 3a0 o2poz/m5period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dista6b c h-kib*/vance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 yea ,.lf+tdx 4mkjrs. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distanc.dl,+xtj4 fk me from the Sun.]    $\times 10^6$

  Our Sun rotates about the center odpj z, t4v8:,mvcj. ilf 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, and mean distance for the four largest moons ocs*g.0emhp 1a f Jupiter (those discovered by Galileo in s0apmgceh .* 11609).
(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 a678n55dm pwo 4a;w6 bqlzu rq,eihm p+o.;xslnd distance of the Moon. mo indsbuplwpe 6l +;x 5;.oqmq8 harz75,w6 4   $\times 10^{24}$

  Determine the mean distance from Jup9ai 3r -dg:*iw f+ptewiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in twg df-etr9a+p:* 3iiwhe Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frahpf*gg+/og6 t gments (which some space scientists think came from a planet that once orbited the Sun but was desggo6/hpf+ t*gtroyed).
(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 artifc09an/ vn-xdb n.v7lx icial "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 gravitycv n. 09d/vxnlb7- xna 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 hanging vine (Fiuy jg ze3*06g w.f;xg m5e bjcqoe2;j7dig *;tg. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.52toi* g3.egg;ubwjgje j;6 m*zc e;dy x7q0f5 m long.   

  How far above the Earth’s surface will the acceleration of gravity - l:7 8qmakhvmv ku ;bo4;j/zac z;,nsbe half what it is on the bav-4;z qn8l,oukmj;vhm;: a7ks z/c surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsn//3sd2jwb.ak 5 ne v kcb;*tr and spin in a mutual circle once tw brc*5skkv/3 ab2e;.n/n djevery 2.5 s. If we assume their arms are each 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 acceleration of gravity p40t)ayg1jh(2 oa b3fyy 1hfxat the equator is slightly less than it would be iy(gjahph3af1bft y 04 2)1 yoxf 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 Eqear v/)7mtl/lzw u)+ arth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposi //uar t +qml7v))wzlete forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a ba d2v8zj*rf;ng8whm5ut -t eq6 throom scale in an elevator, it says your-t fvjemq h8;g5rwu 26*t8nd z mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists 0 6 eugwstp y9cl*cil3s1 p3k3of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed 3cs9i13 u sc 6wlglt*kyppe03 by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vert :j0;d+p2hva+p: xop05cutum to6tm cical 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 radius r, the acceler sl8ufwjghdyh6-dji;- uoa(*t*u k24 .k olr7ation due to gravity at its surface and the gravitational constal-j dwk*lhau7hdyrj;g - .s 8kt(o2i u6 4*oufnt G.

A plumb bob (a mass m hlz7h + xcn o0+b1*,7zwagpz spanging on a string) is deflected from the vertical by an ang+ppzz1chwoz0+g a7 7lsbn x*,le $\theta$ 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 isa, 6:vma14 jguw*lx/ b j jnw;o6:jtoh banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what rangel4 x1m:j ;wauaj66 : /o,jgbonwjh*vt of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast thaw:j w3zob nvj3of*x)- qlzu 67 im7 ybgj0*cn;t objects at the equ: y i;*jwzojbbzn)w6 ngvl0jx*77- ou3mfcq 3ator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of w lnc*t(u e+psxt 8/:x)b1cw v8.0 $\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. A8na2ct cfdgb mgz:,2 1 lamp suspended from the ceiling swingna ,tmz8 ccdg:2f 1gb2s out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has berul(rsm:e)dkxk 0 * ;ven 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. Calcu * d0:esxklr;u rm(k)vlate 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 deducedznvo -9ws4g/ r 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 this by measuring the speed of gas clouds orbiting thezr4wo 9-/gnsv 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 hit 4. pqui d:cl) m949,kfflsi7xdf/ jjll and valley shown in Fig. 5–45.7jc )u:9d4/lksfijt4p i9xq l,f.fm d Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizxaq4orjdyk spxq(je(s.(. j 3v m: ::ags l-a,es a group of 24 satellites orbiting the Earth. Using “triangulation” and signal(q 34l p-yxdv,rgaokaqj.je(:j(m s:ax: s. s s 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 each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 syc40z;dx i2wbillion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughl sw2icz4 y0dx;y 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a sateluexr/n/ pkzzn 7)3e2 jlite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the rk)/73zenxz2 ej n/upEarth), 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 diskex 8, xka e,h7l;g5obtance from the Sun e,, xgha5 lebo87x;kk?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuajefw -; a1b(tqw;gbr yv r7q1-lly "feel" yourself gravitationally afe wjr; ;-q- bw(1b7q1agyvrtttracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the M3lc/7c(z3yuye j w fncy.t4 n0ilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from u y3yn4./z w0l(n fct7cyc 3ejthe 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 corne x:(kvx 9.+so7wzbejxrs of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom jvk9b(7wxzx+ex:o s.side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth j-r,fclf s9p x uq*arx5i,5m+$ \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 64acw.cd.1vt3 j4-exnubv ak e 1.5-cm-long sweep second hand on your wrist 6d.cvjx -e1u3vct 4 w.4abn akwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swi*jt ehdv1+8o1zklo2- wk aydi lim,),ng a sinker weight 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? [Hi2oeo-8mwz*kd 1vi1laty+,) i l,hkj dnt: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a cae2so d392j cwqr traveling at speq 2d3j ecow2s9ed $ 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, utiliz sg kv brw fh:.g,tcu*(c;oi*ug mu645es 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 f(u; 5u .,ivucbg6c:h*k *t ms owrgg4force. 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.$\approx$    $\times 10^2$