Sometimes people say that water is removed from clothuhabyv1 qt nkj2q; +20es in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statement?2 j u+h2;vqb0n aktqy1

Will the acceleration ocux,./ gmjwivn-2-pma u/dfnb *jc2 6 paw.j 3f a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curvnunjjwc bmdi6f a-pm p-32/,j.vg2ua* .cwx/e at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car ex v lhj.pb4s-h1ert the greatest 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 .4p- hjb1hs lvbottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-r; h7k3rboq c9jound. Which of these forces provides the centripetal acceleration of the cc qk9r;ob7j3 hhild?

A bucket of water can nvmg,a a*v;2vw y6lk4be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explak6v;w ln,2a4vm*va ygin.

How many “accelerators” do you have in your car? There are at least tzmv zltn1748 hhree controls in the car which can bemhl74zzt 1v 8n used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes v9drpg2u jw9t83 ar oaxuf:r8l vy0;1flying 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 thelrjg3yw89 :f dpovu 098u r2avx; 1rta hill. Explain this decrease using Newton’s second law.

Why do bicycle riders le-1qshz**n xb7 iri.dean inward when rounding a curve at high speed?

Why do airplanes bank when theywa(u38z pn w9f turn? How would you compute the banking angle givepz(83fnaw 9uw n its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.-;o i 9d3guy9rlx ;zuv She wants to; diyzgo vu-39url x9; let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a5ks- qu wm (v l:blnc6)io,eh/ force? Consceo56 kuv hmq-(bwl i:)nl s,/ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit ,ao 4t i:wm5 (lwvburd0m-u1 (ub;xl obe differt : rob( owmx mvua;,4(u0bu1l -id5wlent?

Which pulls harder gr7y n8ug +ez/gpqfb,4 ravitationally, the Earth on the Moon, or the Moon on the Earth? W zg+ 7erpnu8gfy/bq4, hich accelerates more?

The Sun's gravitational pull on the Earth is much larger thcjrbl 6w zvr*8 ;1qjz;an the Moon's. Yet the Moon's is mainwb;zr c*q1 8jl6z; rjvly 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 poles? What two effects are)n9h.nwebbh:-b3 8 sv sjjb.h at work? Do they oppose eacw.hh:vj 3hbsn8n bb e)b9.js- h other?

The gravitational force on the Moon due to the r(4 .m eylm:4fkyp3bx Earth is only about half the force on the Moon due.3pxmreb lmfy y:k(44 to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger ord,c 1arohqiv/i u x7t3- eln07 smaller than the centhlx-u7 i d /7oact01 3reniqv,ripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward e 26v(,71pl nat1dbc hleujz ,the east or (b) toward the wdv 1b zult2ne7,6, c(eja 1plhest? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured be ck +:ms+;cwed)ht/p y 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 be the least? When would it be the same as whenhe+kmd / e:p)twscc ;+ you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affe,4sbon *8qo grp( t fg yvr:fa .-,cm*ow.zf,kcted 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) o* ns pamqto y,ff.g,z o( cgfkv,-b 4wr.:*8rthe force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiencesr:) tyy4 mrau8 “free fall” or “apparent weightlessness” between steps.urm) :yt 4y8ra

The Earth moves fasters vqev3 r6qw7o;.9xfc/0ffk0 ei5 bvm 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 it e.iv0 qosr09f67mqbvf/e vc3wf; 5x ks orbit.]

The mass of Pluto was not kn ohyw)7cdm1s; 7ztfb ,own until it was discovered to have a moon. Explain how this discover; sw1hcz),dby7tmo 7fy enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet thiab( 9eqj;xmlf. gpm4+ vp f90e Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gralfv(. aqmxpfpib e+j 0;9gm49 vitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves 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 3e6i92qsey+fl ca0jl1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelihie/rj7 5sg+j p s3d3eration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earthi dje5ihr7/p s 3+gjs3'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 rotfeq aouie 65p:lmyh 7 8t,fw-r kov(,9ates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. a 9lwf5mr, o6y-ukv:e7teh o( p,8qfiCalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eary*oys yl)m48 jth's surface, and circles the Earth ayy4oy )s*jl8mbout once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitud 2*5 j9zewq xmhg)dg1ue of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpg5uh1w*ze2xjgm 9d )qm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string isffbgat:,+. gfxzaci i31 1ms5 revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. ifa3:x.zf 1 gibtscamg+5, f 1If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can +rz aj 0jdyb:(ixcu;0 round a turn of radius 77 m on a flat road if the a(dyx ;b j0+ijcrz:0ucoefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fri9)bf.qnf )b:plq nnb0 ction be between the tires and the road if a car:q)qnpnnb b0 bl)f .f9 is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jeslfwqn: yt+pd:/j ru lox 336;t fighter pilots is designed to rotate a xf/r3d+l:jupoqnyw 3 ;st:l 6trainee 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, 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 turntablv+tvy9e7.7oz4vdit * km 8iaye of variable speed. When the.kvda 8ey7tz*yiovt49 m+ 7 vi speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be trave: ey,g3-hojlsling when upside down at the top -3e, :h olysjgof 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 x gycq410ga1q mass 950 kg (including the driver) crosses the rounded top of a hill yqgg acx1410q (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 Ferris w3,1j4 (fptjs u b5i3ah4 is.*w blgaijheel need to make for the passengers to feel “weightless” at the topmost poinsfgii(* , ajbij4 5 w3pb.3ljshu14tat?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle .ny h :phsns5e12 k*v c+pjwc4of radius 1.10 m. At the lowest point of its motion the tensjesns* cwpkv:5+hny h 412.cp ion 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 centrifuge rotate if3dz trak :*tymh8.wk3r*k- umx /w e4v a particle 9.00 cm from the axis of rotation is to experience an acwz 8rtmk. hr4ya v3 /w kmd3u-e*txk*:celeration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrrbie,05c a/aft7my*qvoif1 s57 hwl (ically walled "room." (See Fig. h1co*l5 ifwv arm77sft q ,yi/5ba0e(5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in bnphrimt72vq(ta,3: a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected toh2tmvn:q(b3pi tar , 7 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 nocmpxrk0hqf : z4o q0+63 *x/xxmn qa*it ignoring the weight of the ball which revolvemqx*xxx0 p6a /h+koqcz40i*m q:3fnrs on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectl g.mabu+i-)yrl eeg;l z k )t6on5xld: 8w2i8cy 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 masse zggvi03sof 2(s $ 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 verticalpewzof+rg(j 5r n;h8l w iyt.;p ;(ru:ly 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 force ez i4sz 2pm8:rwxerted on the car (by the ground) in Example 5-8 when its spee4rz8:p2 i mswzd is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acce 9hcnc,k1fet, lerates 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 tangential acceleration. If the curve were flat, what would the coefficient of static fricti e1k h,n,tc9fcon 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 29l h0426a b ixev c*o/nfci-et.90 m . At a particular inv c6-4x t/bioeifae cn2 9h*l0stant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 ieq6w6,a h2 u2u3z r6pjum)zkEarth radii) above thez h )z,6eqk6aru6 p2 iw23umuj Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planmq rh80k .+7 wedxq6woet, the gravitational acceleration g has a magnitrqmo ek.d7+wqh086w xude 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 Moonl9 hf2o.hy3is nn2co 0. The Moon's radius is 1.749ochn3nlo2.f 0i s 2hy $\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 has the same mql8e ;9wg fg4fass.ewggfl9;4 q8 f What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,1wg i8v u2,r ux9kxdb2 but the same radius. What is g ne b1kv,dui9w rug 82xx2ar its surface?   

  Two objects attract each other gravitationally with a for;mw*gl 3p b2dmce 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 graviu n3-zb(kwue-am nppv0x/ ,*dgpxw :)ty, at (a) 3200 mnpe(mu du0-n,/xvkx * wp:3zbg w) -pa    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eap1at0icy awi7 dg h/nd q36)z7rth’s center to a point outside the Earth where thegravitational acceleration due tozwhd) cpa/1i7 tqdn7yi6a0 g3 the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivxet 52rja 26dqe times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity xt6 dja22qe r5on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but f4 0tmijafl(,pz:/d ;vacz i(95fzvp is now in the last stage of its evav za(;,p /f5 ti4: (cvjp iz0fzf9ldmolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel wei6szwg u 6kz:wy 9cf4fkh8cb* 5ghtless 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 s8fch6zk* 9kww zgu5 64y:sfbco by calculating 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 squaredxe) ux;, q3.mfsuhu1uw : 4yv of side 0.60 m. Calculate the magnitude and direction of the total gravi d1;)s uvuh4m,ewx:uxf. 3yuqtational 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 S ryu o2f+a- 1ywwj)9.vclvw9cqr+av7un. Calculate v2c a aw+qrwy7y)91o . w-vufjv9lr+cthe total force on 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 at the surface ojias* ,h1/ h8x,jogik o3pk)pf Mars is 0.38 of what it is on Ear)oa kg sk/1,op, h*8ih3 jxijpth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for,f:ag ja7s 4cn the period of the Earth and its distance from the Sun. 7 c4nsaf:a,gj[Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a w )np)0a )/mo7x7g5xiy4pyjlbfph8 nstable circular orbit about the Earth ayba8xpgn 5f))7p mn yxwj0l4op) ih/ 7t a height of 3600 km.    $\times 10^3$

  The space shuttle releas.(j7(t/mpa+s b:i z3m f frmives a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occuria/ : ipb+mm7.(s(tf zvj3fmrs?    $\times 10^3$

  At what rate must a cylindrical spaceshipx m:j+4 gr4sxii4( p)tovrj .a 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 4p4 rji ximjtaro.+v)x4sg:(revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circuln-n-nc5q gxh3b s.4 yjar “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very smnn5hbq .-y4 -sc3gxjnall compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would t c mm92,iamp(a satellite have to be launched from the top of Mt. Everest to be placed in a9mmpa, 2ictm ( circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continimk*8e6-z-5 ny imd5 d7trucw 0k1dpq ued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onc8dri d 5 m56-k7qkn *metydw1i0 uczp-e?    s

  The rings of Saturn are composed o1c5 (ad; k a3affwxh8i5j)lquf chunks of ice that orbit the planet. The inner radius of the rings is 73,d3uaaf)5 qa hclw 5i;(k8xj1 f000 $\mathrm{~km}$ , 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 diame9 + ch2lj)oufzter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top,czlf9o+2uh)j and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the c zjti d6hnm pmr -7sr0581)iksenter of the Earth's Moon in a space vehicle (a) moving at constant vel8d5rzr-snii )p j t0h7s6k1mmocity,     ----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-stari4ay9iwe;u nwi6+uej-l iy+a3a19 yv system consists of two stars of equal mass. They are observed to be separated by 360 millioniu;il-+6 3wa uyiea v+y9nw 9ay4jie1 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 the2l hk* dv(u0p2ugu n;jhh .,to weight of a 55-kg woman in an elevator that moves0l2 tn2jhu gkd *uhv(o;.uhp,
(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 cej -u1b4xkkz0iiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accele04-z ikjkbux1ration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period T 2deukqek7(. z , the density (mass/volume) of dzk(eek. 7u2q 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 Moonuf* bzk-py7g9b zupnsr.( /s+ (27.4 d) to determine the period of an artificial satellite orbiting very near th(n7ursy+pkb*sp- z.9 /u fgz be Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acros8yseemq0t:a* s, orbits the Sun like the planets. Its period is 410 d. What is its meanq8a:0et*se my distance from the Sun?    $\times 10^{11}$

  Neptune is an average 9k9zwjjo q1e6* 4yhxbdistance 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 *y c2lveu+j/ofr/g-m the Sun roughly 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? Wh fu2m/+ egr*-yj/o lcvat 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 kr69-oazq jb .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, and mean dis/fs./ h1nbn;5gw p4wpvsi ::gxys v/ jtance for the four largest moons of Jupiter (those discovered by Galileo in :g xv yp/1bfnw/j5vg/:hpis nss4;w.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 distan n7gk31bc2 -f )wfjuncce of the Moon. cgkn )31w- n b7c2ffju   $\times 10^{24}$

  Determine the mean di)mj g)/n5/u0 rt2bqsjnhj) spd2 -r ojstance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use ths/sj/5hbpor n rdj g)mq)jjt02 2un) -e distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter c1z*;gddt7wy o s8i:qwonsists of many fragments (which some space scientists this1*7w owzigy 8;d:qdtnk 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 artificial "planet" in the form of a band xo2al(fv l1mva*)0 *b 7br1sy jyels/ completely encircling a sun (Fig. 5-40). The inhabitants live on the1vxss07al1e* l/ fm rjayv)l y(b2*bo inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanginmv;/ ,s u7bddyhso -xk1ah+ b+g vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is thk1xd+ ,7 ao ssmb/hv-;u +hdybe maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gr)xo6uhf;.mq tavity be half what it is on the t.qhm;o)fu6 xsurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and vj2 25nmf7 abaspin in a mutual circle once every 2.5 s. f7na2bmaj52v 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 once9 9;*xboz p,nxxk: ig7ydorq/ per day, the apparent acceleration of gravity at txxn9p oyo , ;q gxz/d*9rb7i:khe equator is slightly 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 sp dl6cv--d7e:hbph7vk+ k pyxy( aa8l.acecraft traveling directly from the Earth to the Moon experie.b-p h vlh+7 kyd7ekxa :d6vlyc -8(pance zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bu.q am*ysx* 7-j *hlooit when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direa*qi7y j so*l-mho x*.ction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that c1*+4 dznz7v-7odexq +ugatt; nc 1xh 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) tdg+4 1ta*hu-zq+vc zxdcxn 71eo;n7is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loo o0(ao,r8y.i )n )wdln4h5 cr calm;gip (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 plb4q5)sq4 boc xanet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constaq 5 4o4bqsbxc)nt G.

A plumb bob (a mass m hanging m .+82td nfz2bpz-icw on a string) is deflected from the vertical by an f b pn2w 2d+mic8-tz.zangle $\theta$ 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 qga3(eidyj/ 2 the coefficient of static friction is 0.30 (wet pavement), at d3ia(2 yg/q jewhat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast.m bv 8)ve m-rib,j5sscuehq3/1 -e ck that objects at the equator were a -q8vhs icmu.- 3) 1 ceekmer5jv/s,bbpparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a ,px jofiffu j fct,+a8/* *3xqoy- d,rhkk2 t0constant 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 r0b**jyzlf peep *m 1dys)7y+. A lamp suspended from the ceiling swings op7my *fpy 1j+esd0elry* zb)*ut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times aad/umm*id3 3,scxh e +s massive 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 sau3m+3,hec i* /ddmxsurvive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presenc wly;*yl(x6o :xkb. vwe 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 clou wx;loklx.*6:yb(v y wds 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 (yrgf5 vq( :)ve(ifuq in 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? Explain. (c) How fast can the car go wgf((q v:)5(ifru q evyithout losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizehp nxh+ y9h2vg-q(ro )s a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth yxn-qhpvh9 gor+h(2) 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 billio99 c. i(,tjr cw:zdpfdn km, is meant to orbit the asteroid Eros at a h.9c dfzpwj,c :di (rt9eight 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 9cc 5d7y2+,3aon ty u,hrfjtppursuing a satellite in need of repair. You are in a circular orbit of the same radius ,j7y23nu ar9 tp+cct ohf5d,yas the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distj0zbdtaf1ww 75 s,fv g m:ly13ance fr:7swb3jy 5mgz1v wd1ft 0l,af om the Sun?   
(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 of9dee3y jpbd96,09 pnjh;gm.dhe f i w3 G would need to be if you could actually "feel" yourself gravitationally atte,9wndjj9yp 9e ef3 hh;dipb63g0 d.mracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of theao(2l3/eenv w0xkez /hr ob(5 Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center 2h k 5n o(b/el(o/0vz eewax3r$ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m onfqj)s2 w y ;zkq5 :-yl2kw-tst se9nv1h*pnv . each side. Find the magnitude and directnfz2 n sw heq y:k)ptt - l*vsj1-qs5y.k2wv;9ion of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits; hjxf7l0l4iq 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 experx * /8tjl+or i9t9bxnjienced by the tip of the 1.5-cm-long sweep second hand on youxbtjlrjt* x/998n o+ir wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in xeqp6i5 ah(o16h3 fdsa circle below you on a 0.25-m piece of fishing line. The weight makia fo361pdsh 6hq e5x(es a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hig wijbk;p19lc ,2(h+a p. amggvhway is designed so that a car traveling at pa bj;w +(mp9gg,k2 ailc1h.vspeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of t /jr875zbb.oo bj*vzfn n14 vxhe cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers5 7/48bb1*oonr.njfxvb vz jz , 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.$\approx$    $\times 10^2$