Sometimes people say that water is removed from clothes iehwvyw ;7o1ef)2*oe f n a spin dryer by centrifugal force throwing the water outward. What is wrong w 1yoef 7 hoe)2*fev;wwith this statement?

Will the acceleration of a car be the same when the3io,f bs*eza-p/gjoh;m/g5 g car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explhejoa; fbz gm35/pi g/,*sgo -ain.

Suppose a car moves at constant speed along a hilly road. Where dod s9v.kj rw sj+ov-+8res the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip betwee8d+ rsjor9 -.w vjsvk+n two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse w2ysao5 jm i78bx .ryd ivk:)9on a merry-go-round. Which of these forces provides the centripe m)xajsiv:ywod 8ik2r.97y5b tal acceleration of the child?

A bucket of water can be whirled in lx.n6aa)5r7 9h m6vjtw . btwva vertical circle without the water spilling out, even at the top of the circle5 7m) .xwtal9. jnb6 6htwvvra when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three contrg.xtxx*8t1ac* ex0j gols in the car which can be used to caa.x1*c tegxx x*g80jt use the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying7 edbp; qt5sd5 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 t ;sb5edtq57dp he hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at 86oj3 2wuh4xnwe3 h uyq j9fi1high speed?

Why do airplanes bank wxo9m- i0l 4omn) (iht5 lqf/fphen they turn? How would you compute the banking angle given mxfo 5(ip9qmti4lof-hn/0 )l its speed and radius of the turn?

A girl is whirling a ball on a string around her he 41cim+cuik4;; 9quiea 9 vp3l t5gioead in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on c g 3il;q1 eo49ii5+4mvcuike9at ;pu the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth?1o.4 e30lz ueb7uiq eb If so, how large a force? Cob3 equu.1zb0leo4 i7 ensider 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 Moong/kr oh)fe qftm 605z:’s orbit be diff :go6et/ f0rfzhm)k 5qerent?

Which pulls harder gravitationally, the Earth on the Moon, ov-e4l 9q nlsv*r the Moon on the Earth? W l9-v4lsvq*enhich accelerates more?

The Sun's gravitational pull on the Earth is wwgop;*y/lh:j5x s gu+i8n (y much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of h/ *x nig(;wy wo8gsj5y:pl+u the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are zpkxeo5a s1.0/:xq rrat work? Do /kxrs 0e:5.q1zax rpo they oppose each other?

The gravitational force on the Moon du )aref f6c:vn6 1h-cepe to the Earth is only about half the force on the Moon due to the Sun.:fc p-n6efvae1h 6)cr Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its or r r./ i ;m3ebayc9jjvk4 ,prs38svr.zbit around the Sun larger or smaller than the centripetal acceleraticsv,r;rjze4j.i3m rk8 b 9 ./3sp aryvon of the Earth?

Would it require less speed to launch a satellite (a) towa vwouw)a+8 xq qtga+29rd the east or (b) toward u a )a+2wx89gvtwq +qothe west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, a8 ix9f.0l mres*q; -xd6x qubxs 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 be the least? When would it be the same as when you are on th 8e6x9fs xix-.xbmu;*qld qr 0e ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be advmb/mq:z0nn3 ce+ lw w2ersely affected by weightlessness. One way to simulate gravity is to shw3:be 2c+z nml/wqn0 mape 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” ori e db60pq kd+i21s 0gmko8-ff “apparent weightlessness” between step-dkg2smfk0f61p0 ei+ q dib o8s.

The Earth moves faster in its orbit arounvmkr4 9y*n z4srmh* 2wd the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbwn*9v rsy2 4mzr*kmh4it.]

The mass of Pluto was not knhsm , hi8g;os1own until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluh ioms,gh 8s1;to’s mass.

  The Sun's gravitational pull on mu)qhnjr i 1y8qbp3nm6 6) c:vthe Earth is much larger than the Moon's. Yet the Moon's is mainly respon6q h)u)m83n1mq6bvj nir ycp:sible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the 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 1980 wf -* hgtmn21e$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 )- jgk;e:q;p: xtjp lkacceleration of the Earth in its orbit around the Sun, and the net g;lxe)t-jjpkp:: kq;force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exer 0iwso-;1rs huted on a 2.0-kg discus as it rotates uniformly i0iowsu ;hrs1- 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 Earth's surface, and ):ob m0, g ptabxevv50circles the Earth about once everyg vbt v b:o,aex5)0m0p 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleraqxu ez5:a*c1 ytion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions c5yxz*ua qe 1:per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ve+fe1(s kj;vm;sw0e+7e ev n vurtical circle of radius 72.0 ;en+m0vufv1( wesj+e7v ;kse cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kgiyp8rp*0t4 p:( hk lyf) zgu+a 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 independent of the mas+puyfz:kg)yh p( 84*tip 0arls of the car?   

  How large must the coefficient of static friction be between the tires andfjikys;3 hb,wiz cm8 4ud-23v the road if a car is to round a level curve of r-i f,3vcuji28zbw3yhmkds ; 4 adius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate ezd ; l0*vz s.mdp-ky:c2zj s;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 j*zcz pze2vy.l;-: s km0s;dd, 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 t8eef-hf8i o*g he axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntabh8-eofgf i e*8le?   

  At what minimum speed must a roller coaster be traveling when upside down lkl odq038 p )9f.mgdkat the top of a cg 0 kl8pkd)3mf qold.9ircle
(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 the driver) crosses the rounded topvi:6zgp)xry)kxcb- 72 /b* ofkpl(cm of a hill (radius gp27 6kp)f* lxykb)iv xr:(m-zc c bo/ =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 nee:nldnof 8vgbs4 4fz:i mzv+l m), 4jo1d to make for the pal +mvvnznf4 f j8z,g d)mob14:s o4l:issengers 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) bcwpqqb/1l/. At the lowest point of its motqw q)bcl// 1pbion 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 centrifugdo w;wrllx)r /wi s,81e rotate if a particle 9.00 cm from the axis of rotation is to ,wirl/w 18s lr)d;x owexperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a j-jxkd.w 22 +cbhny)vcarnival, people are rotated in a cylindrically walled "room." (See Fig. wx2b) hv +jd.k nycj2-5-35.)
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 a mizpnn co-8r7y- *ky2q u4ffh-z: : tvcircle on a frictionless air-hockey tabletop, and is held ky z2z4nc-:-8*n-:q ipfm 7uv fyrto hin this orbit by 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 timp57yk9 iwncco)j.uf n2 +8 ngle, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In7kn c)5ncing8l.y +o2w jfu9p 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 pemny: r* 6eww6vrfectly 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 massed)5to9tf wg)ls $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310 c1igw1 uajvl s8v3/c5$\mathrm{~m} / \mathrm{s}$ . 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 comp1qm e)fx;nnzbj8f;ic u:(5 ojonents of the net force exerted on the car (by the ground) in Example 5-8 when its speed 1m 8iocn5 j:jzuff b(enq );x;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 theqqk7 w1(ozaz lz83)0trb of 4f :u4fik3lczi / 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 the tires and the road to wzo:0qi(kbk8tz1)/f4a37 q3z cl4 ozi frlfu provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circ s0fmox1ou ,p;le of radius 2.90 m . At a particular instant, its accelerati;,fouxm o 0sp1on 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 1g lbk.dp 9p.c02,800 km (2 Earth radii) above the Earth’s surface if its 9.kcblg 0pd p.mass is 1350 kg.   

  At the surface of a certain plaxq +n),pm e ym:ju0 nnzl)v+3mnet, the gravitational acceleration g has a magnitude o) mvp m3u0xj qnz):yn++el nm,f 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 1qjjxi f.3;ixfq)mykr5 2w hp17 gtl)the Moon. The Moon's radius is 1.74 ltqfj1xi1qjh)5 w23 yi)7mk;f xpg.r$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hasznv 9nh 7lnca g(d;jl9nn(+e - a radius 1.5 times that of Earth, but has the same mass. What is n (c h nn 9n-9vdgl7+ejza;(lnthe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius.8ph. :s,yok47 ymq,enfbz(rvur-em 0 What is g near its spom mkqh8rv r enzy40-ef :u.(7b,ys,urface?   

  Two objects attract each other gravitationally with a forc( gx mhskh7vxuxf0h-7 lt5ay2y ;, tn2e 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 a yx63 ;eehd85ht:apokyp95lacceleration of gravity, at (a) 3200 m; t83yl659:ahppyex5adh e ok    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fq9 26xvai*o/ ogw ba)mrom the Earth’s center to a point outside the Earth where thegravitational accew29 *q6xaogv b/) omialeration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star ha hruyk22t ko2 ;tbv5h-s five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this mon2yrtthuh2 25vokk b- ;ster.    $\times10^12$

  A typical white-dwarf star, which once waa4. cpvugt. ; zrjsb j-*9s3ews 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. Ws w vb.zr9tg4p*.j3e acu;j-shat is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel wemg2j he: ;c7cy3m geg,wh 0bs0ightless 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 calculating the acceleration of gravity 250 km above the 0 m :03 hjcw g;7hecgmseb,2ygEarth’s surface in terms of g.   

  Four 9.5-kg spheres are located a( 4 b/s y)gzdsd+oe7lzrc lp,97ele5xt the corners of a square of side 0.60 m. Calculate the magnitude and dis9lex /z(,zby 4dso )r+g ld5plce7e 7rection 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 planets6 ktp,px/p5ij line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The pti/6pkjxp ,5 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 surfac*w -: + qce(7 lmc.y2iqeoo l0rxatg4ke of Mars is 0.38 of what it is on Earth7l-i4y. c+ w(lo:*tcqeo qkrge 2 0xam, 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 forzmbmr (.)j 1 6trm4izv the period of the Earth and its distance from the Sun. [Note: Compare your answer to tbv. immj 6rm(4zt1)zrhat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a s9i kgqgjz;nnl p+d(: 9table circular orbit about the Earth at a height of 3600 km :9dz n+ ig9lg(j;kpnq.    $\times 10^3$

  The space shuttle rele;a7 6qgh tdbp.i;q* qbases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relt;*qa;bq.p6 qigd hb 7ative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship;e6uaz:3)r npeo5wty 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 3 rnue:a; 6)5p ozetywfor one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular jumy+8a/w 1 -hwml, st“near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on- +jl8/msu mtha1wyw, the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have 7l5e: ugd 5o1xog:v+yx g 8empto be launched from the top of Mt. mo8pyg5ev :15goxleu7+dx g :Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, g8 d )adwhlxw5ss(+yifmq0v9ca 7-.a the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the -shiqw5)g780dswc(9a xfa +lvydma.Moon once?    s

  The rings of Saturn are com51wtn nq,zf9dposed of chunks of ice that orbit the planet. The inn 5wz1,tf n9ndqer radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotatequ6ffp 7,m txrcu *ud37 ;n)gus once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weigh;)nfuq f 7u, g7uudrxc*tm3p6t to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fromkyaao .2):sak the center of the Earth's Moon in a space vehiclak )ak:ys .2aoe (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists ofussyc 115n:d /8ozk )zfoen.s two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth y8o.do s: se/ynn)51 kcfzu1z sears 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 an,ghgksv*k+ y5)v 2c: iwt xky)4k 9aji elevator that *thc gk gi 54i y2vk)ks x+:yw)ajv,k9moves
(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. y(v;c j8 pedl, e65jab) c.5ot6xviwuThe cord can withstand a tension of 220 N and breaks as the elevator accelerates5j .tpoyj,86ev xw( id;vu6c cla eb5). What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planexs3g i,.t-4at 8 eunm k-h0mupt with period T , the density (mass/volume) of the planet u-3n4.kheu- smtixp 8m g0at ,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 Mx8d 3,;5 fqmmqi+eym coon (27.4 d) to determine the period of an artificial satellite orbiting ver8ymc ;mqqd+ ,mf 5ei3xy near the Earth’s surface.    s

  The asteroid Icarus, though only ai .f /dn hzg,4 8egdeh+wvkc73 few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean dist7gezfh/ ,d+hnd3v4g.cw e ik8 ance from the Sun?    $\times 10^{11}$

  Neptune is an average distance yp,+vh5d z+m b0seosoq-9o ,zof 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 rqhm)30 t8sx4q,o9m1tahsg vq oughly 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: Themot8a)q4q,9s3t1x smhh0qv g 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 cengahtrcwfhk 9 (u771l( ter 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 m)exyr dq, g(9g9zt( 2(lcj meshvvu. :ass, period, and mean distance for the four largest moons of re9 gszjmy)l9chxvg(ev d u,t.:( q2(Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of u.ogb/q.g; sgmloa-4the Earth from the known period and distance of the Moon. u-oqmo glag;. sb/ .g4   $\times 10^{24}$

  Determine the mean distand)g7cre7d0 n u/) iwvsce from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use th7ncrw /dvdsgue ))70ie 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 consists of many 6d/,.cw(cc )ufz(g/cav askbyrj /9 gfragments (which some space scientists think came from a planet that once orbited cwd(cczj u. r(kvcyga9,6/g f) / s/bathe 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 form38 b*8br5xhybfl .w bi vy ,bg)jelw,2 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 thexbebybly). gl wb5,vi, 88 whfrbj 3*2 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 fromld 3vzkc )ljga. 3s42m 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 the l. sgaz3l4l3kdc)j v2 mowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface wt+6jw 26gjnfe t3igb0ill the acceleration of gravity be half what it is on6 f2 6+wtjnbg3iet j0g the surface?    $\times 10^6$

  On an ice rink, two skaters of ef()dj m::;r7 9xcjnlis 0zs wqqual mass grab hands and spin in a mutual circle once every 2.5 s. If w:zx mr(wj di sq:) c7;ljs9nf0e 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 reywpbkr q-j38svv+vgk rpp)2 /2w 8i*k7o;ncceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimat-vwr8jyp8/k 2v kep+sn*r)q 72ov;3pwkb rgi e the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from tai tq 9*sn,y6g9zp) p jyn0dm:he Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force becaus dysgz) ynt:j6mq9p09a n* ip,e the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in anon (4 zxl9/ 1li12aq9vkkda hugo(as. elevator, it says yos(h94av1a9uk xnqkz a12l(d /ool .giur mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will wut 1-)f.m ;c mb1mm l1egbbg1rotate about its center (like a tubular bicycle e11bcm;1mfb).w 1b gmlu- tgmtire) (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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verbt2) 9pe :9hhouv0 (zi,k6ctrp(o wrrtical 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 acceleraf u-0s,arwtrj4 agy5*tion due to gravity at its surface and the gravi* af,rjutyw4 g5r-a0stational constant G.

A plumb bob (a mass m hanging on a*fdug5g g 31mf*zz+0ueoas 9f e9z .nq string) is deflected from the vertical by an angle 9 +*f*95m.3qe0 dfg sefg1gn uzozuz a $\theta$ 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 bankedq57wgrn e *tyt*1u1riv* 7avq for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a c1gqe uiw7*v v yat7qn1r* t5r*ar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objescjx3s;e 6anm z:fp64 cts at the equator were apjs 3mzp6a x ;6n:f4ecsparently weightless?    $\times 10^3$s

  Two equal-mass stars maintai5 ,rrmdz6my+x. d6b 8h)uixb jn a constant 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 om*zt/a8 fpi(y ,u x5p235 m. A lamp suspended from the ceiling swings out t(*xzu5, ti p mo8/fpyao an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mass.;on39j*oogz ui ze5 aive 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 caouea5 zjn;zi.*g3 o9o n't survive 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 vd839kd1kb s1p2vsv gpbe mrl*8)- ht 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 mea *sr9bbvv 2s k1 vd8leh1gtpm)k p8d-3suring 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 vall mbf :wurb*5j+ey shown in Fig. 5–*rf+ wm5jbub :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 without losing contact with the road at A?

  The Navstar Global Position vg42h 17exif*xf y-hjing System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical milevf ygx4efh1 72ixh-*js [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 travelingi:rgkpv. e :2r 2.1 billion km, is meant to orbit the asteroid Eros at a height ovre2kgi:pr . :f 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 needja6kch3um - bp;x2 8os of repair. You are in a circular orbo-2x pm8sb;akcujh63 it of the same radius as 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. tjzg--hc um.rzd x 0q)e1n76b q(e9fl(a) What is its mean distance from the Sun?fjd0(x7 b)-lzh em.9-e6 grtqn uzq1c   
(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" y*c g2,tioqg(+ kwpxtw a.j)ck0:;e lbourself gravitationally attracted to someone near you. Make reasonabw20(ckcox.gq ;jke ti t :wbg* ,+l)aple assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of--tzpe g6 uj1l the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ligguje 1zpl- 6t-ht-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located av)fyvo + vo h90c5kh4pt the corners of a square 0.50 m on each side. Find the magnitude and direction v vk 4)+ov5pfohh 0cy9of 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 the Ea y 6jmusqk+aix/ c+a q+*cp.znb gi/0:rth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep s( ti .l 9pp-ftqi .,6ba:mdmesecond hand on y-tdspm:6 , ie.(9t ifmqp. albour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cirtas+c tgyq389ld7/ gpi/eda2cle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fisa2 /tda8y7 cd3e lti+g/9pq gg. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed fueti+bep(eb( 1fdl+3xn ( k 1so that a car traveling at st ke13u+bdp(b1nefi(+lf (x epeed $ 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, 4b 5xjo:4ykrx utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consior:x4 yj4b5xk der 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.$\approx$    $\times 10^2$