Sometimes people say that water is removed from clothes in a spin dryer by1c/b(mhuz y r0 centrifugal force throwing the water outward.bmzy0c h /(1ur What is wrong with this statement?

Will the acceleration of a car be the same when the car travwxiy3 9pq(vng7 foqf/9a16 pxlfq l18els around a sharp curve at a constant 60 km/h1fy i w9p/ l 18xg6a(fqlnqpqf7vo39x as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alongq l()eec4fz6jdi3h7f a hilly road. Where does the car exert the greatest and leah76eej i4q f zlf3d(c)st forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-s/vg*uexdn+ i h -jc97round. Which of these forces provides the centrixc n-gi9 uj s/+7dvh*epetal acceleration of the child?

A bucket of water can be whirled in a vert/-)cy,jpj;jhr. ausq0;i d2 tgs7l vmical circle without the water spilling out, even at the top of the ;ah;-jg.usvpd / imc,7j0tjyrqs)2lcircle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There +5yugsfhn,*c::4p xa6v6iq(tuu uhyare at least three controls in the car which cf 6apgnixv*uuhu s, tcuq:(+yy46 5h :an be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyi ir605 kz;ychxng 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 Ne0z kc; ixyhr65wton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speed pjh7.y v: f8//rm0 xlgpb1noj?

Why do airplanes bank when they turn? How -x2eo2lq9ip4zixsa7 zzu5sh8 * l)bg would you compute the banking angle givuo)* slipg a87q hiz5-zbxe 2sz294xlen its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a ip5t-gi(b)dv;6krql na e 0(jhorizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side(n0bgj -a6i(5li ;qedvk t)rp of the yard. When should she let go of the string?

Does an apple exert a gravitational forc p wjgi7j5z4i q-03 gns,j4hsre on the Earth? If so, how large a force? Consider an -jw0g zr 5,ps7q34igh4jnsji apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass weeppic pda1ii06, +k 4dre double what it is, in what ways would the Moon’s orbit be diade,kp0d6ip+p c 4i1ifferent?

Which pulls harder gravitationally, the Earth on the Mob -jn1qk2t*.;nh v1 oo truwo+f:rf* gon, or the Moon on the Earth? f nroouo1w:j2r*tf1;. +bt*nqh-vgkWhich accelerates more?

The Sun's gravitational pull on the Earth is much (v4xz v, zj-mmlarger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Himv,xjzm(v-z 4nt: 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 aj0n/6j rh+ppi4 9r ublk/4lawre at work? Do lpr0kwlurp+/6hij4n 49j a/ bthey oppose each other?

The gravitational force on the Moon due to the Earth is only about nrtt/6q-) c 1tfr roq2half the force on the Moon due to the Sun. Why isn’t the M )26 rt1cr-o/nftqqtroon pulled away from the Earth?

Is the centripetal acceleration of Mars in itm6/h fq;3 sck3wnsnn :s orbit around the Sun larger or smaller than the centri6 ;nqks hfn3 3w:ncs/mpetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east o;, de(f ru/lt7u6ig rgr (b) toward the west? Consider the Earth’s rotation directifge , u(d7;r tr6g/liuon.

When will your apparent weight be the greatest, as measurenx0a/vb0q mqc/xd --pd by a scale in a moving elevator: when q0acmd/x 0-nxbp /- qvthe 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 the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outery/r o4rrghh d71b )ylv6i bj:- space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) a-/1: bjor vyb dhg6 )li7r4hyrny other aspects of gravity you can think of.

Explain how a runner experiences “free f 7k3h611cozdphtj q7aall” or “apparent weightlessness” between stept3h1cozqj76ah7dk 1 ps.

The Earth moves faster in its orbit around the Sun in January thax vzqoc;b5,8gn in July. Is the Earth closer to the Sun in January, or in Jb8,gc zx;v5oq uly? 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 orbit.]

The mass of Pluto was not known until .ymk5m/b0+abg)0b bwxuot m6it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mtb u6mx.0 0bymbb mo )ka/+w5gass.

  The Sun's gravitational pull;midy)5yhv+ww n d6lr/y b*/w on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsi w;yylddn+bi 56ww*h/rmy /v)ble 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 7*7 wrn++hn k*hlmwrj $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 u((t4x zt 6q(h/vwe ygEarth in its orbit around the Sun, and the net force exerted on the Earth. Whawutv6zx4/y( (t h(geqt 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 exerted on a 2.0-kg discus as it rotates ds26v f7igxw o4ur4g: uniformly in a horizontal cir4674v r duxw isgf:2gocle (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 suo8u ; -hn1w/hgpwsh:x.p dm 2jrface, and circles the Earth about 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 h;s : / jdxp8 ow.hhm12puwgn-surface. $\approx$    g

  What is the magnitude of the accelera bcgxg6/wwzrm34py y ; 2l-.jmtion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s;xg. w26zbyj wr cymm-lgp34/ diameter is 32 cm?   

  A ball on the end of a string is revolved at a unifo uj7 p0swqyayn3)w -e8rm rate in a vertical circle of radius 72 8 y0npuw7yews-a3qj).0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius 7/r*biv0n e-hl jzpt0gm .x*1w7 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the massetn 0-x pw l0j*.imvh 1b/*rzg of the car?   

  How large must the coefficient of static friction be between the tires and (tr, mpotjmi n-wn.:xja17 4g the road if a car is to round a level curve of( r7.j:im,jw1oa4nn tx-pgtm radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is32mc)j*m ,9z/o0n6ln2in hvdv l srel designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on h /22jznn i0 9he r6c)vsmomvll,d*l n3er 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 rotatinjasn * f q)tg9bjr410hg turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a ra0s9jfb gnq)* jrh4at1te 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 y (eeon.p6b .ttraveling when upside down at the top of a .6eb( n.poty ecircle
(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 08 fn1ew8ntdfpm0bi) driver) crosses the rounded top of a hill (radius =95w00ne pf88dt1 f)ib nm$ \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-dirni1 a7j wgy:3ameter Ferris wheel need to make for theagj73n :ryw1 i passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radizs)ex (jdn;h1aq4 wo q1/b.v cus 1.10 m. At the lowest point of its motion the tension in the rope supporting 1qzsn4c/.1e)(adb jo hxv qw ;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 9.00 cm fr ,(g g*5 u(eq spr;ftblewcm9(om the axis of rotation is to experience an as(;9 u*eq,beg( wl m(5pg ctrfcceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatq ff2 tvm2gq2w06tf:/1 mx1t 3siigyced in a cylindrically walled "room." (See Fig. 5cf12qygi 6g2m/1 xt w q:fi30ttm2vsf-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-h)rr0be;n uw6arc+ c9h/bbl) eockey tabletop, and is held inh/ 9 w+c;beb0aur 6)erb ncl)r 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 time, by nrnn9ja2r24 tmo uu +ck)9ifi2p q75drot ignoring the weight of the ball which revolves on a string 0.600 2ud 99 prmu nnr+afki5i o24j)r72 qtcm 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 radiustjv1kn2mlf:i,2zp6- f rb9e r of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses g6pgdw u vq thc1d scpx9+7l3o/ /yk+9$ 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 jk0fye *3kkxzjy5r c5 .u6,ws maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetauu6f093p3thk- 0 e.yh )cdhi wip( ryxl components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15whii u.6 9t)x 0 yp3pd fe-ukc3hh(ry0$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates u-rhx 4vi77k qnr,; ghtniformly 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 wvinxg,rr 7h-4 t7;hkqould the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a paro9l(fm1 s9)elvfsn h)ticular instant, its accelera1nhs)9mf fv eol( )s9ltion 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-0jzqb(+ jnhc uze+( f zc9q2f 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. q2u czjhf(czq+z 9j0(b- fe +n  

  At the surface of a certain plaalsx*+wmrm4a;r tt*9 u56 6e ;diqe utnet, the gravitational acceleration g has a magnitude of 12 m/s*eu ;i6 +xtau*e4s 6 9a l5rqtm;drtmw$^2$ 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 j 48)dakt.3c 5xf4f*1 wjr xbsswh; ikradius is 1.743f)x ;ah44. w * b5fswitdjrkskc1jx8 $\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 that2 yg) ew2 enuthg3mn6/ of Earth, but has the same mass. What is the acceleration due to gravity near its surface? 3nemwh2g )ye/tn62u g   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samdqpn6 jbm*)q:+wq-dq e radius. Whanpm+qq 6 w*bjqd:q-)d t is g near its surface?   

  Two objects attract each other gravitationally wiclm;r9 ; 7wjpcbd9yj;psc c1 5th a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at s*ao*. cb,,s /vkfazc(a) 3200 m bs.c*az ,sfck*,o/v a    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where td4h c9tt6f ; gifu,.qchms c58c -hck+hegravitatg- .csqit ck;c5mcf498 fcdt, u h+6hhional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times qwd l3i5;x2u5 9goja9pspk2 lthe mass of our Sun packed into a sphere about 10 km in radius. Estimatjq25;d3w5sl ka 9pg uo9lix2 pe the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was 4a7n/;97 lo jvwfb bcgx3rhg(an average star like our Sun but is now in the last stage of its evolution, is7vbjf l7nwgo;garx 3 /hbc49( 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 weightless while or9p2) jb)+,ap sobpiixs4o h a2s/gs1abiting in the space shuttle. Your friends respond that theygjp4b 22i x/,p19h+a a)ipbss)as soo thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the culi0mwll-e x) )zoo,uh8( yc9orners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphez-)(ll u,il9uywho 08cm xo)e re by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most ofwwh 2jimn; 6g, the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venwhng;jwi26 m ,us, 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 omvi)xp i4 .jvz3y:z wa5m x77yf Mars is 0.38 of what it is on Earth, and that Mars’ radius )yii:ymvzx .7x7v3 mpzwa4j 5is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the yt 1)sb1sizx)Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Keitxs1)1 )zsb ypler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a swl4z3gd3xl a- r)t e(ftable circular orbit about the Earth at a hee-w (g )zx3a43fdltrlight of 3600 km.    $\times 10^3$

  The space shuttle releases a satelp 7.bf )up9cr1e+mgmx lite into a circular orbit 650 km above the Earth. How ufgpcexr7+mbpm)9.1 fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan(o u,a maia6)10 d197q ouvtb bd2*twb*dsx kdts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Qs *qv11 )ktxdbt7dudai ,a0o*6abu2db w9 (om uestion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in jt04 n9h0up gwytff,ws/ 6x)p a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the r s0,f)x/t jy0 tnpp6hw4gf9wu adius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocit9x zap :y3yga(8h19v4haj5 mzan tac9y would a satellite have to be launched from the top of Mt. Everest to be3vya :pangacah49 599yz haz(1mtjx8 placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module s f+xj,uqi25q continued to orbit the Moon at an altitude of aboji qsu+xqf,5 2ut 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit /) s3p ckdh:ac;qmbb ,the planet. The inne ;3,bqcd a pcmhs:)k/br 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 diametent0yc.b+4lbqb8 r fz: r rotates once every 15.5 s (see Fig. 5–9). What irf0+8qzby:bb.n4t lc s the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center o+k.gf+i .k.juhn0fl l0yp3 yif the Earth's Moon ink0.hly+ .+ fjp n3g0ifkuyi.l a space vehicle (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 l t nd,8ma;vhxi:0q+v-star system consists of two stars of equal mass. They are observed to be separatedv 8mnlh0qi;, + xtvad: by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in aslb n02qs; vh-n elevator that -0 sns;vqblh2moves
(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 suspendeq iyy-uv.1d b h0d3-0s:enlsad from the ceiling of an elevator. The cord can withst hl0 1:3-.edbvi s naduqyy0s-and a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbit 3 nb3nbrh(bq: i*w0sqs very near the surface of a planet with period T , the density (mass/vob 3i(bnn:hq3 r0*b sqwlume) 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 Moon (27.4 d) ebi8a7 tbe8,b to determine the period of an artificial satellite orba ebe8b78bti, iting very near the Earth’s surface.    s

  The asteroid Icarus, tn8f 3s9 2jd;wr,9ny mfgt eu;nhough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distanfnjn9;e39; n 2dr, fyw8stumgce from the Sun?    $\times 10^{11}$

  Neptune is an average distann:1xpow bw(h+ce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very cdd 16t* fp ep.iv5+pzplose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet f*d e pp1ipvp65 ftd+z.rom the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of or+b vb:6gzw6the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four la2 +qhim(3 omqnrgest moons of Jupit3q+hi n2om(qm er (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 the Ea,nb *w 006twkdxa 6afcrth from the known period and distance of the Moon. a c,6a 0*kxdf6w0nwbt   $\times 10^{24}$

  Determine the mean distance from Jupiter forc63eaxiph x*n c0k wazj 7u2,6 each of Jupiter’s moons, using Keplerpk3xa x7 w uia2 n,c60chze*6j’s third law. Use the 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 ofw94y/gpw ,tjdh/kilzl,8- j l many fragments (which some space scientists think came from a planet thatjgi/y 98w ,lzlptwlk,-jdh /4 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 "pla8a21mazp2njucn:t6f n- z1qcnet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the pe68a1z-2c 2mza1 t fnn:qcpj nuriod of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging i h(c2 y udo./5hfc*usnn 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 the lowest point of his swing? His mass is 80 kg,of5 c (/nduysu*h.2hc and the vine is 5.5 m long.   

  How far above the Earth’s surface will t;f)gle x 6 yct;h,7ogkhe acceleration of gravity be half what it is on the surface? f,)kl cy;;6ghex7g ot   $\times 10^6$

  On an ice rink, two skaters of equql:a0p9pw q)z al mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual maqpz9):wal 0 qpsses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra)21puf j0kvol vity at the equator up2 ljk0fo1) vis 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 spacecraft traveling direc dv7z1 0jkvc g2d:lef;tly from the Earth to the Moon experience zero net force because the Earth and Moovdf0d:j1k glz;7vc 2en pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a ba+(*mb3p rfi zwxptxsk-:b3 v,throom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, rf : +3bpkx3z(xt-swpib,m v*and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thatds0iz4 9zo 28gup dr,r will rotate about its center (like a tubular bicycle tire) (Fig. rudio280pz4 rz9 gd,s 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 vertical loop (Fig. 5–43).32sve x0je f7u
(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 accelend/k7 bk7aq5x xrc -5nration due to gravity at its surface and the gravitational- d7xcrx7b5/n 5kqn ka constant G.

A plumb bob (a mass m hanging on a string) is d s/ma rw7)wfz;/ v ra5ufsdti(;o25ndeflected from the vertical by an ang2artw;od5)s/f5 s7i(vad / wrz ;umnf le $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is 7+z6fq* z*signg c:kvbanked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at n*g:z*qzkfv c+67gis what range of speeds can a car safely handle the curve?

  How long would a day be if -;e izfn* )av0dicuv.the Earth were rotating so fast that objects at the equator were apparently weigh0u v ;a*dcvz)n- ief.itless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 *ud ob/bat(7xhy 0vx2 $\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 constajj*+h, w3 xjrn :3srjn8k,fghnt speed rounds a curve of radius 235 m. A lamp suspended from the ceilih ,jfr gh j3nnrks:3 +jj8x*w,ng swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive ay d:2if)a6)p /yst75btxucz 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 g 's a person would experience at the equator of such a planet. Use the following data txyb5s7 2c /6itaf)zd:ap) uyfor 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 pres gl0 d2byupymj-ny kiqn 3aw7)09ha9-ence of an extremely massive core in the dista0y yn9 iau9hgnmq--w)2j3yldkb a0 p7nt 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 )eb3 9d,gwj+:yfhu pk o 34qimtraverses the hill and valley shown in Fig. 5–45. Both the hill and vallek)qbd4ye+3p mji3hg9, uow :fy have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gpp jxbk5/ ,gizs+v7-m roup 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.”g, mv+ sp57z k/jpx-ib 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 billiono8o*brzon blad/w ram n2+-60 km, is meant to orbit the asteroid Eros at a height of about 10wr-omnazar+o6 lb8n *2dob /5 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 need on k:y*2sltzhg 5:f4f1tcv l(of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind ithk2s:v t *nl(5oz1c:fy tf 4gl.
(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 jv,q+hchscp ;3-)xdy r:6mu phas a period of 3000 years. (a) What is its mean distance fr+ cud:;h ,hm cjv-xs3 pr6)ypqom 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 of G would need to be if you could actualk2:wud ypjz*n:) phw04e- lp obmfarkv88 ;4uly "feel" yourself gravitationally attracted to someone near you. Make reasonable z m:d :bu wl*kn)0rvpfh8 k4j o2ya-4;upe 8wpassumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gal6b5nx1axx(ee b(y5a d axy (Fig. 5-46) at a distance of about 30,000 light-years from the cent56e x(ydbna xa5e (xb1er $ \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 0.5pt okvi5*t k. :cwh*j50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg masso.cv5wpt hkk j:*i5*t 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*u bgwpc+*en, the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of th (yocb/; dl9phftviej.d 1+ij ga.a2 9e 1.5-cm-long sweep second hand on yi e v21;c +(a9fl.tpajgdo/.i bh d9jyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored0eblb)0 v5vzht( qwb, and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vbw) h(eqz tv0,0bl vb5ertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of rxg )tk6rwcy(t9bj 03nadius R in a new highway is designed so that a car traveling tk ygr(0t3w)xj9 nb6cat speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Aceue24 v;x)f2x9r tadzn la, 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. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the ;xv9242 zfa xtunder)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.$\approx$    $\times 10^2$