Sometimes people say that water is removed from clothes in a spin dryer by cek mcnbdm 6.68antrida 686nkb.m mcfugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same w ,9fbkd (/3jhe i.bqgphen the car travels around a sharp curve at a constant 60 km/hj g3.i(p kbb e,9f/hqd as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at 2uln ow4dq7y(constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (4 7oq2wyn l(udb) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces tss2/kmw+r+cjy,a p/ acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acms kw/s2+y+c t,rap /jceleration of the child?

A bucket of water can be whirled in a vertical circle without the wate5zn-8 n o/lj ;drbcjc,r spilling out, even at the top of the circle when the bucket is ups/odnnj rcl ,zc b;-8j5ide down. Explain.

How many “accelerators” d *lth-s r-kwv2q yc.knd:1b5to you have in your car? There are at least three controls in the car which can be used hsl: 1 5t.krvdw2qtnb-yk* c-to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes jie(gr j);yfz: u ln (kfz+m813jcxf+unq1v; flying over 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 over the hill. Explain this decrease using Newtonnz8vff)cgk(m:irx( y;1 j e1+ qn+;ujfzjl3u ’s second law.

Why do bicycle riders lean inward when rounding a curve at high sg:6 ejl2 ;kbfas)uts -peed?

Why do airplanes bank when they turn? How would you compute t 9 o* kde dr/rb5p3q:pkg jag6b l19spk*oe-6uhe banking angle given its speed and r 69kddpkrb95- eg*elsuqg6:o3pb jkr/ 1oa p*adius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. S)d i/ dfg m7r+kn:b)rbhe 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 shoulr+/f ) kmbng7:)ibddrd she let go of the string?

Does an apple exert a gravitational force on wg+ me1.7qk*:urbw 4tou u-dh the Earth? If so, how large a force? Consider an appluu 1k. q4tuor-me:h+ wwd*7gb e
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wo(;y4xs55lqgl z*sx zs uld the Moon’s orbit be differxgzl x5s z(5ys*qs;l4ent?

Which pulls harder gravitationally, the Earth on the Moon, or the qo)cvqzn+8c2vm4e m0 Moon on the Earth? Which accelerates m0qevmz)o4 n +c2q 8mcvore?

The Sun's gravitational pull on the Ea6 t57; 5u9jm qy bbgp()dxlwhzrth is much larger than the Moon's. Yet the Moon)q(p9um 5w hdg56 bytl;jb7zx '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 thewzethqdyxk4 u cp)2p8a9 qn,rv5m (/6 equator or at the poles? What two effects are at xp5dvta) ymrnp46u/ z,wq2k e(8qc h9 work? Do they oppose each other?

The gravitational force on the Moy*hp5/ r;/luu g/dkqtvj4e rku7*rn, on due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earthe k*r *rq7,5djh nult/ uk4uvrgp;//y?

Is the centripetal acceleration of Mars in its orbit around the Sun lt dyv0he g70x:arger or smaller than the 7ed0vg0t:y xh centripetal acceleration of the Earth?

Would it require less speed to launch a satolws-g6(bkbb2( wg6k ellite (a) toward the east or (b) toward the west? Consider tblk w-bb( 6osgw(k6g 2he Earth’s rotation direction.

When will your apparent weight be thqc4 t -xchu-,he greatest, 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 would your weight be4hh-ct x-c,uq 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 bem2+b,4t uoi pt 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 falbo,4pm+i2 tt ul, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “f8j/7 i5k lk9 dr/,l exhxop-ycb6hum ;ree fall” or “apparent weightlessness” betweenm, /y8dk - 7jh;lc/bhep6rixo x9luk5 steps.

The Earth moves faster in its orbit ar8.i aem1rj6m d21kp llound 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 .8 kel12 jmr 6dp1alimseasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not kp8dy v0lq9i+wnown until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto9 v8dw+pyi lq0’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's..w8p73rs pj8xxynw f) Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of7pjny8)r8sfw.wp 3 x x 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 travelinglsh.:f fx nb) 8f)4dbi 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 d m2 hy 9iup92jdgdvdt64hfk y8j/x,w66h pq9 orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orgdpt d6y/82ifuhy2mk9jdw9, 9hq46v j h6dpx bit 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 diu9.. zvzabn+qpj,wy v,).qhmscus as it rotates uniformly iv.whjv9+,nq pbzum, az)y q..n a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eas v+get5c6 b-:b-siwx 33l wsfrth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the s e swi3s6lb-bx s:5 c-wf3tvg+pace 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 o7xmzu p mi rklq2j-cuim;(,1/f clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is j1r ,x/uzmi27q c p ;u(imkml-32 cm?   

  A ball on the end of a string is revolved at a u vc tglszu3r482*x d1/:lbndgniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is u4l8g*rt :s1c / 32dxzlnvgdb4.00 $\mathrm{~m} / \mathrm{s}$ 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 jg67qheyg6 r(ofi4hg0ui6 , nwhich 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 indepe 6j r067yhgqfi6(i4 ,uggeohnndent of the mass of the car?   

  How large must the coefficient of static friction be betvj5r0; xgpn v/amik 7(ween the tires and the road i /k(; a7v5 vpmrxjng0if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desiked 1:f 5.zngv-dr3yvgned 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, howd3:ekd vgn -fvyr1z5. 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 xo5 rg) javeu ohy*c5.gd:8 io)92rc,8gtjx rfrom 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 ,*2g)uodvx e jc8: xy.torjci ar rg5h8g )o59rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelixoq45x -)7 kgu;pboj wng when upside down at the top o; -xx)okwgp 7u5o4jb qf a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including tw776t3pyxjge bz jd4/ he driver) crosses the rounded top of a hill (r7j7xwt6dj p /be 4g3zyadius =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 mhij5h 3 lw3rnx42ni8 qake for the passengers to feel “weil hh4rqjw83i5n2xin3ghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is xe4rk6x p2hox *ry45bwhirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in t2y*4rxhr p4 kxxeo5b6 he rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 4z 8 jy2/zsml pse-q:y9.00 cm from the axis of rotation is to experieme-4s8/ z yl:2pzy sjqnce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people aadukh6-1)xn are rotated in a cylindrically walled "room." (See Fig. 5x adn)16hku-a -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-hockey tab kici k267ei );/ryhvpqq,n f 9n;x)vhletop, and is held in this orbit by n; ; ik26q))x7fkiyv9 iphc rqh nv/e,a light cord connected to 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 time, by not ignoring t0t. 7y mxfw6wehe weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude ofmxw y6e7w .ft0 $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 foo*5k,2-ewha 6/ixl :icr /gc2auujn ur 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 9gso1ujxr ba*:je*-r $ 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 divnx6by:eej; p+ 3bc-oning 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 tangential and centripetal components of the net v 6 r 6t6p8wdklu2;zhf8qv;h mforce exerted on the car (by the ground) in Example 5-8 when its speed is 6d;p qrhwl8 u t82 mv6kzhf6v; 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolisb x 4wu 6l,brx47c-xae 500 accelerates uniformly from the 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 tangb 4xlbc we7- ,xr6xau4ential 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 w+ye-wcw akgo2o xvl v,-1r:1radius 2.90 m . At a particular instant, its +gw1xlyoow-1 -kvwe2v cr:,aacceleration 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 3n4h:o lcrzu -spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is : -zh3lr 4onuc1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g haz(1t3t 1 urbsit(bt*hcrzf / 3s a magnitt33uiz1(tc h/b b1r (z*stf rtude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is m :znjwp7wa6c4f a .llbo ./fi:ti*,m1.7 /wa nbimc 4z fjafi .6ot7w,l*:mlp:.4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.nxlw9 r/ aq8l-*/ p1nv5va tlp5 times that of Earth, but has the same mass. Wha /1vanl/ vl5pqn*-9xt8lpr wat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiusyk5o w;p zg(e9. What z9;w yp ego(5kis g near its surface?   

  Two objects attract each other grawea *-crer,ntm,a, z: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 acce3k((sx) cu cr*qgd wj1u-crj;leration of gravity, at (a) 3200 m xg)1w ck (jur-q (*uc;j3cd sr   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poin/q9vwm sdc-nltacv p m;z+m- 4h)39(hkcum 7et outside the Earth where thegravitational acceleration due zpam c-/vhs97 (me+ 3ckmc;-l tnqmu4 h)vd9w to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron st57m nqu5pj.myw, 3vv 0wxn.e bar has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this mo3j.e0 5n5wv.um ,xq 7b mvpwnynster.    $\times10^12$

  A typical white-dwarf star, which once wmy ,x 72y1rklmcf1m+c as an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surfm, ccm+xfylr2ym1 7k1ace gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightly+gjfa 23ync0 ess while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculfcnay y20g +j3ating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square ,sx06 b iux,v:qt/if/ ytbi;oof side 0.60 m. Calculate the magnitude ,/ ,tbt: 6x vsuioiq; 0fyxib/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 years2;ay c.wyp 32p0ii*u ut;pouc most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiterty32pu.u p;2wp0iai;uo* c cy, 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 at t-uixi,y/ g/ksebbqh/ +t , .gwhe surface of Mars is 0.38 of what it is on Earth, and w+ths/ bq.g/iiyg, ,e- bxk/ uthat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perio )-d48 gtnwe3gv8buoxd of the Earth and its distance from the Sun. [Note: Compare your) b-8doeg3 x 4vwgt8un answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable nu;qnznd)qq 8b:cpq kk1 43 :qcircular orbit about the Earth at a height of 3qq upq d8z b3q4cnk qn:;k):n1600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Eae7*81fcvi x;ep2y etp9 vad(i rth. How fast must the shuttle be moving (relative to Earth) when the release2 t1 f;*eeva9pi7(vi8d xpy ec occurs?    $\times 10^3$

  At what rate must a cylindrical 0ja;wmw uzyvk.ag++ 1spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer asmag vku 0.;+w+a1 wjzy the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit llb-m.ga 4 *edn4p;izthe Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface oenlb ; z pmad4i4-lg.*f 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 have to be launched from the top b7sk7ni8;v6f2qbs0rvb tu (r d-rl l+hu 5;jpof Mt. Everes0tpih j;v+;s bbv flb72n5- r(u7 rk6rsld8qut to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oux6s. ;506yp jvb cv+hlc. oafrbit the Movs .xyh5 l0 fa 6pcuc+;.vj6boon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed gz) x3ounnobc r6:1q1of chunks of ice that orbit the planet. The inner radius of the13czq:u)6o n b1gxrno 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 ever0c ;uxg 3ouc3iy 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottooxgui0;u cc3 3m?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km f p9k0apsmo1 clop5 v ts92)la5rom the center of the Earth's Moon in a space vehicle (a) moving at consakop592pms1t 5l a9p)v c0 osltant 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. They apml+noxowa2 z+/ 5w5p 27:a eouxavf; re observed to be separated by 360 million km and take 5.7 Ea5v 7p a:ooxnlo2u/52f w+aez+ xmapw;rth 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-kg woman in 5uz1ecr* b7dtan elevator that moves*crte5bd1 z u7
(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 skw ; x(evxz ;r a4nibgrr9567)p4qypyuspended from 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 acceleration9zw( )xr;yap;b grv6y5xp ik e74rn4q (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet widjj7 146e blc*dyxa xi0 v(q7zth period T , the density (masscl4 * 0 7z(7jbyjxx ddaiqv16e/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 Mq 6tln+m qs(qz.el43k l07axw oon (27.4 d) to determine the period of 0l4qn7s w m x6+aelqq3z.tlk( an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metersv; *u .g fucfn )rw)(yhtlk3x4 across, orbits the Sun like the planets. Its period is 410 d. What is its mean distanc )fuc*tu(3n.grlyv x w4;kfh )e from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.v*1 /hw-x sgeo5 $\times 10^{9} \mathrm{~km}$ 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 c9pcyr ji/4ppmnch e 637:,k rroughly once every 76 years. 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 hal4, /jnrr7yih9 mpppcc3c ek6:f the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cente:da ymaa)4do55e n7 u3+ztqner of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period rfw gz3niju :l2-2uheh;; qy*, and mean distance for the four largest moons of Jupiter (those discovered by Galileo i;jyf*-ui 3rh2:lguh ew2qz n;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 distanc(d/ n2lsdn v66qiw wbr7l 8 u6akj;a)ye of the Moon. d 6n/ 7 y(vnqauk6rdi6s82wwj;)l bla   $\times 10^{24}$

  Determine the mean distance from Jupiter for eacht+e83 wu mro;1z 93vxrxb/ael of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and tazmbt; v 3u13r e8 r/wxoel+9xhe periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt bet pe4oe3sz: su;ween Mars and Jupiter consists of many fragments (which some suo:p;z3ses4e pace scientists think came from a planet that 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 artifi)mxij 9-z wmdjx;9pd9 cial "planet" in the form of a band completely encircling a sun (Fig. 5-mwd-jxzdpi)9m;9 9j x40). 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 swingi:hz c2itecs;z uste -9o*iw95 u1*f ying in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at thtzh-9ee;f ui5s1:i**yi9zocus 2ctw e 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 hd(rad.(oq x1nalf what it is on the surfd1((oa x d.nrqace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab han3ok m sz+4m)oxds and spin in a mutual circle once evez s4 okm)+omx3ry 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 a iaw0so:rh. v.df.fpcv f 57;tcceleration of gravity at the equator is vhi: a. frf7o5.stp; .wcd v0fslightly less 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 fro ni+r0q6rdv3+ hvqz13q*yajwm the Earth to the Moon experience +0 vnd*qqzw1r jhi6aqr 33v+ yzero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 k+o vfz.ga:1e dg, but when you stand on a bathroom scale in an elevatoo1: fzegd. +avr, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statiobhx gn5+b*u9gn consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a dgbn+ h5 x9*gbuiameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5vv8j1c 5i kv5x–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 ofz nf ytcy;ty)p8l /+.h a planet in terms of its radius r, the acceleration due to + fttznhp/ l.yy)c ;y8gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve cme0cn 42f)g wouo-k;rtical by an anglk0 o e mof2uc)c4gwn-;e $\theta$ 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 nj vpf;t. rh;z t5h:wx9;z, nuof If the coefficient of static friction is 0.30 (wet pavement), at what ;un; : vzthh.r zwpfjxn;95,trange of speeds can a car safely handle the curve?

  How long would a day be if the Earth werej,ufrnhq,;tdw iu :h; 5 p.*og rotating so fast that objects at the equator h.o;q djwn :r*5u ifutp;gh,, were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a conf:fg+-7bl b iz1cpzig9vd 1 -jstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp su- ((ob: p.zo s/uy5hytdh4vn lspended from the ceiling swings out to an angle otbhvos-y(ndz:. yl ou 4p/(5 hf 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massiv ft1ir u0 kpx*2gtf+022 u ofro2f8btce as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of 2u2tgfr ki20 rc1b8 *20ft+u fofoxt p 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 vj/ 7i 19qe tojvf.y,fc d;s84doyzk6 an extremely massive core in the distant ojcqk; 1y9 yos4fv8fez7,t6.vd/jid 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 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 shown inq z6c.a7s nl (epbr41k6q,xzb Fig. 5–45. 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?6zcebx7qb rap4zs.k (6nlq 1, Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites or9pl4)g p 5(7urspg q7gljvn,rbiting 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 evenln v)ru74pp9ll,sgg qrj(gp5 7y around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is m(yo bo 5c/znerq,* l7leant to orbit the asteroid Eros *7zlb c oyl,onr/5qe (at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in 2a8x1lj tm fpe7(qr l)e*1gijneed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 2rj8p21(qt) 7iljf x ee*ma1lg 5 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 yew()qm * cuq1v2,wd r 0a6jwqjyn8glh-ars. (a) What is its mean distance from the ald h,6)8r g qqw2 wucj1 -wq*0(yvnjmSun?   
(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 actually "feel" yqh wq9 awu4wz+gm3cm / vb::j7 qbk(,vourself gravitationally attracted to someone nearj3 m,4 qb hzwaq+vgwmb7k qcw9: v:/u( you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of t. q35 (dhaau- jffv8qzhe Milky Way Galaxy (Fig. 5-46) at a distance of a q5 zaj vha-qf(3.ud8fbout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are uu/x)u1wq4pxxo ro8* located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mpw x/x 41uouor)q8x*uass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 55*5 yr9vy6d/5 gry b4t k:jetvf00 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 experienced51wel a)rg 2d*9ldfkl by the tip of the 1.5-cm-long sweep second harl1l 52leak dw9 g)df*nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ,x k6.hw hvsv.qmkx 55around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle ever v 5s6v.,h qkxx5hkwm.y 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 8l bw 1vc,wevf7 /fe7s R in a new highway is designed so that a car traveling at 71fvw8s/ le,vfbc 7wespeed $ 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 til-ems y28rk8vs bl2u k3t of the cars when negotiating curves. The angle of tilt is adjusted so that the main force ems rbk2y u3k28v e-s8lxerted 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.$\approx$    $\times 10^2$