Sometimes people say that jeu0ft3j 1zbgmyx)8b++cx+nk:js+ rjq/e s8water is removed from clothes in a spin dryer by centrifugal force throrjjjsbfet+03+:sgcx)/81+ jexb +n yqkz8um wing the water outward. What is wrong with this statement?

Will the acceleration of a car be th.hdh9q r/ p9lo6 hw3/rab 5shse same when the car travels around a sharp curve at a constant 60 km/h as when it travels aroundp5q9b r/h3hsl9/ d oswahh6r. a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly 8; 6xy/ f oima tfzc+5f(frb1m-pv*x froad. Where does the car exert the greatest and least forces on the road: (a) at (m;f8cf 6p1tfxbr z-of 5a* xiv+fym/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 ridinq1 ux/y4tw:y0vn hpvb jq**; rg a horse on a merry-go-round. Which of q nj w0ryy;x1h*:/vq4t bvp u*these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without 9h2thgcz fka3qvr( -;the water spilling out, even at the top of the circle w3qf9hht rc;-g v2akz( hen the bucket is upside down. Explain.

How many “accelerators” do you have in your car? s yfi s-pll7+c ;tqn8*There are at least three controls in the car which can beilssl+7n- ; 8tpf qy*c used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in joxzvk6/. -+g ys ra3kFig. 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 Newtov. s-zx y/ka rkgjo63+n’s second law.

Why do bicycle riders lean inward when vdip 3,vc. bd1,mdnp.azyi .y +c1(gbrounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking ang-1dd; 1 h 5xvdik vna6h0cl9afle given its speed and rfi5kda c0dh1;ndvx6l1 a h-9vadius of the turn?

A girl is whirling a ball on a string around her heakn/h(l bx,r1ad in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side x,ab1 (h/ rlnkof the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth?m;m/;/ xy duueqcp,*k If so, how large a force? Consiqkd /em;pmu,;uc /yx *der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wh1:kb -o: a/tzh*vjebo at ways would the Moon’s orbit be diffz *o ehbv-/:k:oj1 tbaerent?

Which pulls harder gravitationalurr33uz3+ cp f:utdl,ly, the Earth on the Moon, or the Moon on the Earth? Which acceleratesdru zl3u ,ptfr:c +3u3 more?

The Sun's gravitational pull on the Earth is much larger than the Moonzxk66. q 4( p.hzvwcxj's. Yet the Moon's is mainly responsible for the tid .k6qzcjvxx.4hpwz (6es. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equato/.cq qy 8 :ivagta4jyt+ itb8)r or at the poles? What two effects are at work? ty8qj.+iq:cibgav4/ya t )8tDo they oppose each other?

The gravitational force on the Moon due to f g4,son7u0npr 7s6wzz 6ub;gthe Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from ,6 zfu7gwgbzn s4 uos 7n60;rpthe Earth?

Is the centripetal acceleration of Mars iy),jk- rbr4c rn its orbit around the Sun larger or smaller than the centripetal acceleration of thek-,b 4r) rjyrc Earth?

Would it require less speed to launch a satellite (a) toward**pov.-*ojfu 6v 3f l*y mmzgxvn,+vy the east or (b) toward the west? Consi vx*-o 3of *p m ul.y6*+fzyjn,vvvmg*der the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale slkj*j/fwj6 0v *epb;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 wolefj ;*0 *j6kpw bv/sjuld 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 bylf +ue5p1czj3pxj 9ae8d:(in outer 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 c :f3(8bd5 x+uajz9epy ple1j 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 fat 9p+g: soxu;sll” or “apparent weightlessness” between step t;ous+x: 9sgps.

The Earth moves faster in its orbit around the Sun in January than in July. Is+ bx 3zty dfqqs(odk6g*50 cy, the Earth closer to the Sun in January, or in July? Explain. [Note: This isqdgc txy(of,30+s *5zbd6yqk 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 unt; 7m91mjo;lpg m ald3pil it was discovered to have a moon. Explain how this discovery enabled 1o7jm;a 9m3d mgp;llp an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Y8tdy:0 y 3qqbdet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to q8y3tb d:y0dqthe 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 1980j1ai-bk ii+czo* .y1 u $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centrip keu,-8* 44e rocgwxkwetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Ew* u4kk 4x e-ocrgw8e,arth? 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;6rikw /cm,: tln fs.vzn:6 jj discus as it rotates uniformly in a horizontal circle (at arm’s length) of radiusj6m 6 ,ft:/v;:nzl cjnksiw r. 0.90 m. Calculate the speed of the discus.   

  Suppose the space shutt+kl7vvjh 1l 9ra 9szx6le is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Fin sl 6jkzv91+rhl a9vx7d 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 acceleration of a speck of clatu7,gnyp o (9ay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diame (n79,ayputo gter is 32 cm?   

  A ball on the end of a string is 2m x d4s4+ ebky3/jwl1 g/7yog) cewnnrevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown ikyem/)l3w+wys nxn4o4 g g cd1eb72 j/n 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 s4 rchq23dh /3hox8u)-jh ha4 z hbdac8dx),hwpeed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the c-3h)zax83oh 8q2wh4,rchxa jhd h bdh4duc/ )ar?   

  How large must the coefficient of static frict5 voha1xr5bl: 13/t 6ocknhcg ion be between the tires and the road if a car is to round a level curve of radius 85 m at a1 anb1hr5xgh vt :c 6ock5/ol3 speed of 95km/h ?   

  A device for training astronauts and jet fighter s;k*f,yas +p9 (drip:m88(3d lcedtp jq (qqtpilots is designed to rotate a trainee in a horizontal circle of radius (8s*a(d;micy3pp: +89 qk,q ( e tt lrfqsdjdp12.0 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 turntable of variable spep7sm* nzw9rh *i/g*dw ed. When /rmwshw gind9*z7 *p* 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 turntable?   

  At what minimum speed must a roller coaster be traveling when upside dow7ct *v8d sbwijt*.y c*b6lp k.n at the top k cvjb78tylp dw 6*sc*.b*t.i of 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 masswxih qp3d j-.c mhzq c3(sx;,, 950 kg (including the driver) crosses the rounded top of a hill (radius =95zcpi c, h3s. 3qx(hx;j-qd mw,$ \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 va sg9etnvsd,k- *40kper minute would a 15-m-diameter Ferris wheel need to make for the passenger vadn0-g9s4 ek*t,kvss to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical1menyts8 wl.8 h48gyrchtv x4h:2+c8 zz ri j5 circle of radius 1.10 m. At the lowest point of its motion the tens8y:8 r .x2hhln58hw4irs jz+tzm4 c ctyeg81v 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 centrifud *w(dq s4y 7idcq7*unm 98bjjge rotate if a particle 9.00 cm from the axis of rotation is to edu(j*q89nwdy*j qs d7cbmi74xperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylind5k o*8zt xo2yerically walled "room." (See Fig. 5-35.*2k oozteyx8 5)
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 ro34gjs n0*z6zw 9kgty )a4 vkuf :0fkzgm7q8bwtated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) througsw* qzf7fzy4k ank0g8bmvk 6t4)ujwg 93zg:0h 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 t, 3klrz* yk4:tr(+cto0 6-nlj ywr mini tl*9this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular,9icr0j+k* 6 (*4wr,lty o-l:n3 i zkt lrtytnm find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a /wd5ehk j h:qhp*w /6e5c7skhcar 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 wq)*-8ydd-hs4jmw u vs $ 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 evas+04y nv sc;opnive 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 centripetal components of trhk( ozki9)clf4 l m69he net force exerted on the car (by the gro9 ckrz) (4 iflmolk9h6und) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going eci+hu 5ip slw5:*x( tx l4)azfrom 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 lphiwx 5eu(iaxzt: 4+s*c5)l 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 d6 t7twa:jm)gf;w6 ) fywyxh8 of radius 2.90 m . At a particular instant, its acceleratimg6a wtf w;yf)7: 8 wthdyj6x)on 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 Earth radk( 0i4 hikju.uii) above the Earth’4jhu i0k.ik( us surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration-z0jr ohbi3cuf 4m-4 mtz7ob/ g has a magnitude of 12 mo ot-hi0zfjc4b -r743mzm/ bu/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius ish)ock 6ef 6s:nhh3o .z dzs2a) 1.74z:zk eo. n6hhc 36))soafsd2h $\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;csoqrr/ f,77/bcgal a2l qb9 same mass. What is tb/crql grc/9qo;a7s7 fa, bl 2he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samnxk/c,r),p88wf vklf4s-q vue radius. What is g near its sv/f8rp) xflcsu4vw n, ,q-8kkurface?   

  Two objects attract each other 2is8olo7r(7wxuv-uv gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of n /t9fu 6lp6jhaj,-4 vyihjl1 gravity, at (a) 3200 m pl /jn-16vyiu 4h9,tfjj l h6a   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outllk9a lm q97dod.09 uzw u()xrside the Earth where thegravitational accelerau.7)ax9 9orlk9lduzlwqd ( m 0tion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pac4gdts53 k(: sfnua-p*(im bve v4/tcrked into a sphere about 10 km in radiugtb:ev-34smpsk*i( 5cdf n4ra t u/v(s. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like o-rnt:fv**c xy ur Sun but is now in the last stage of its evolution, is the size fytv*r:x* c-n 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 orbiting in the )xo78f )z u khmc/(oijspace shuttle. Your friends respond that they thought gravity f m/h)ooj7xi (k u)c8zwas 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 corners of a square of side 0.60 m.d(ry)( .qiziz Calculate the magnitd()y z(iqr .izude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side)3 nh i bp0h4fxxs)v)vx)t(fp of the Sun. Calculate the total force on the Earth due to Venus, Jupi )v)xfxt3h i(4vxhp0)bpnf)s ter, 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 of Mars is 0.38 of wha9evd *h uiworfwyu/o4+p2 *bqp; 9g /zt itobodu */pzf9r 2u;p/e y igv+q49*wwh is on Earth, 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 the period ofo8-nee z3r: gb the Earth and its distanboz :e8rng3e -ce from the Sun. [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 swdid*w*v u: :a stable circular orbit about the Earth:s*ddi wvw: u* at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circuleh6 kh-4 lu)/ lomtac(ar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? )ut( -lc e4 khmlah6o/    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occqak5fsd2u 6z2 wm9a6*yb/ah nr.dicoo) .*b bupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fioa. 2wn*i b/b.mf a56 *u2k)q9 s hcyaor6bzddg 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in si kavnc,ftze; el41 +e7ook6n*9lp*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 reolz9p vn+t,a*f4n 1ke *e kl so;c76iadius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be7 re wu6zp+k0a launched from the top of Mt. Everest to be placed in a circular orbit aroun 6ue pk7za0+rwd the Earth?   

  During an Apollo lunar landing mission,,7s+r2bvqtsaff4) a m(cy ik* the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once? tkfbc 42r, ayfm7q)v+ss (*ai    s

  The rings of Saturn are composed of chunks of ice that or knyq up,,p1xx 3tf;l(bit the planet. The inner radius ;tqp,k x,l3p(1yxufn 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 rotates o at sl,dpc3/42b) zqlu/e;bwence every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weig)bteb,ecl u 3a/2 ;lq4p/zwdsht (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 cente9-rc r5h0 iwwpr of the E - prwr0cw59hiarth's Moon in 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-star system consgz38 x.rjs 1a (vhqz)hists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit abou hg. 8 jva1sr(3zhzqx)t a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of8frrjdsv,g )77qs)mynsez(z0( zae)i h/9 to a 55-kg woman in an elevator that moves 8avj)dq o)m7z)hgi(z7 fr 0es(t, s re9/snyz
(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 sq;9f ked42 7s cmbz8xwu6yc 4vuspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as thekd2;y44q uew f s8 x96z7cmcbv elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfaty a (j89lnt )fmsdk5.ce of a planet with period T , the densitdm.n)j( ysltk5 t89 afy (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determin k1(qwbp.u2 yoe the period of an artificial satellite orbiting very near the Earth’s surfaceu1 wby p(.ok2q.    s

  The asteroid Icarus, tho 5bfud0l3s ne0ugh only a few hundred meters across, orbits the Sun like the planets. Its period is 41b u0d lfs5ne030 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dist)dkxz9ns okum8276lk ance 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 everye34 o+m -j0kgyr ivo1d 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 coo430rge kmv od1-iy+j met from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cso r8-sf5 7( +fknaozjenter 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 distance for the four lar hgl vmsqd7b0q *u-/b:p q:1nsgest moons of Jupiter (those discovere7b lvs:uq-sq/gpqn 0*m:dh b1 d 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 Earth from the known pes,hdm2l ba ,5oriod and distance of the Moon. b,25moah ds,l    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, , ax olygr 7s.6xjp22vusing Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compara gsyopr6 x2, j27lxv.e 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 fragmeod6cqrt)t/ hd/.:gd xnts (which some space scientists think came from a planet that once orbited the Sun but was /r:6/thogcdd dtqx) .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 ea)r9b ekjku :rmz; ibg6rj115 1i:swa 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 gravi z ku;wb6 r19ek:isj:)5 i1mergarj1bty of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a:*szig t/4uf e gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerti ig*esfz4t :/ung a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface wg vc4 ,g:z cw/klv8:xdill the acceleration of gravity be half what it is on the surface?: xg c,gv84:lv /ckdwz    $\times 10^6$

  On an ice rink, two skaters of equal mass grab4hst zu2)5fa n 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 masses are 60.0 kg, how hard are they pulling ht5f4z)u2 nason one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of g cp.8 dm/lu-sjze6 dx4ravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effe dxdzujl cem6s- /4p8.ct. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from th t7zavm7gc/cjn*)7yl ug:lo+e Earth to the Moon experience zero net force because the Earth and Moon pull with equal anzgcc7vo:ljy)g*nm / u7lt+a 7d opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand n ;k qt *pj6ov7k*ti:yon a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleratij:6 p*ntyvt7okkiq;* on of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of io/r-kx(y(7l pwgw1 s a circular tube that will rotate about its center k-/yl(i (owp7xwr1g s (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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lj/m7kewen : * /c.dyf 6g/ /dgrz;mgdioop (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:c u 8pgzrt6;s of its radius r, the acceleration due to gravity at its surface and czs6:g rup8 ;tthe gravitational constant G.

A plumb bob (a mass m hanging on a string) e7y76t0pl9pzy 1au heis deflected from the vertical by an an9h1el 0p ytuypze7 a76gle $\theta$ 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 designtmvhn;hv-f3sx 4j 3e2va3zp zd5+ca ; speed of If the coefficient of stavade2v3 j; czm s+z 54vn;af3tph-hx3tic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so h0pd)ejngg4d(r*ekctd: , r *fast that objects at the equator were apparenje4nr :d e(dgc **)gr0d k,htptly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 s;j wy5n:697mv abvf+z ge0* a)jpnwoc4pe0u $\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 spee5 p0bse6/zc+jyzhov pem( -/hd rounds a curve of radius 235 m. A lamp suspended fbezp/h-socz + hp/v(6 y 0m5jerom the ceiling 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 as the Earth. Thus, it has been bs:/(zxe(swcy dmtf ;0c;w q4 claimed that a person would be crushed by the force of grezbcwy(xq; /sc f:m 04w (d;stavity 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 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 Spacez9kj.qc,wg+ 2ap z3 2k;zkx j/6oa7muokx vl1 Telescope deduced the presence of an extremely maok,p3z uz; aq2mxv+k.6cok j7kx2j9zaglw1 /ssive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting 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 hi ;rksnly)tq1b + 52ea0cea2 as it traverses the hill and valley shown 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) hl21 at er5s2yibc;0kq)nea + How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 82ok49lndce c24 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 al 8 lekdnc49c2otitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km,kb0vz1c46c1 7l/zo p(* ng5p bwmmgd n is meant to orbit the asteroid Erol415nv1kz/ z6 dm7c( n0bp gp bomgwc*s at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttlc ur(5y3efd) 3 eyvrd6e pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the sa3ee)y yvrf 56u3 drc(dtellite (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 n- emh7;w04dc5jqxi vq67jefits mean distance from th5q0mj v ;ne whx6e7di 7q-jfc4e 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 actu +mtxjn1 9n9bgally "feel" yourself gravitationally attracted mtjb+1nx9g n9to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milyz2 s7uus tg;nr14jz9 ky Way Galaxy (Fig. 5-46) at a dista4un7 zru92 ;ygtjszs1nce of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50) *ycnl -cixuc bv8gj (5idc:5 m on each side. Find the magnitude and directi-5 )djcbnl i y cu5*x8gvi:cc(on 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 tu3 3q, iz1fgmphe 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 thev:njbtlbb rcq.m f2bdy /-84 2 tip of the 1.5-cm-long sweep second hb/n -b.rq2l:bdybm v2 t8f4jcand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored ubr*,zv72qu:k1 owat 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 vertical? [Hint: See Fig.k: qzu w1r7o2 *,bavut 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trave bxr)lnklw-:7ob-r;x be .z(slingszrl-en-x)x.:b7wb b(lkr;o at 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 Acela, utilizes tilt of the cars when 1d*j :gs8wyu anegotiating 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 exper:gys*8j 1 uwdaience 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.$\approx$    $\times 10^2$