Sometimes people say that water rxo3-r 71u,awl8orw :hqhf d6 is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with drr3ou7:fwaw6o- hhl8r,q 1x this statement?

Will the acceleration of a car be the same w;icj*zopo ;wvqx c+))mo ,r zc06 *bxyhen the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the samebxw vrc;,mczy xo*)oi+p 0j zqo)6c* ; speed? Explain.

Suppose a car moves at coltn /2shz(p*a2e h;ymt3 z8fm nstant speed along a hilly road. Where does the car exert the greatest and least forces on the lhp ;sntz hmezm 2/8*(yaf 23troad: (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 actingwv82 w(mey-)ja li1lg on a child riding a horse on a merry-go-round. Which of these forc1ljg)ymi(w -w e lv8a2es provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertic6oblqi 4fg2.sal circle without the water spilling out, even at the top of the circle when the bucket is upside down. q isl42.6o bgfExplain.

How many “accelerators” do you have in your ca3f lw wozg.2ip0,p+ezr? There are at least three controls in the car which can be used to cause the ca plz2i0.+p, gf 3wzewor to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, a*hn7 zs2z obeq)rn0f ,s 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 ar)q02 fz*n bohzs n,7end the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders leanwhn+ 2h)w/( gc)e.c5cjfm xay inward when rounding a curve at high speed?

Why do airplanes bank when thfs (4f575 qq1xqh vntgey turn? How would you compute the banking angle given its speed and rad5q1 7hfxnv g fts4(5qqius of the turn?

A girl is whirling a btrgp z2;2in jgotu3 v.k.es;*l/r y3fall on a string around her head in a horizontal plane. She wants to let go at precisely the right time so t 3zor/tf3uke ltrjv2.ng p i.sy;2;g *hat the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? i0+o n q*c(yrwIf so, how large a force? Consideio +(rwc0yn*qr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tczh p fy6q(7j; y+rr)jv1 hh/o- glnm4he Moon’s orbit be differenoch )vnm;jz7(y rh/4rhl+yj6 -qgf p1t?

Which pulls harder gravitationally, the Earth on thetz*o+mzbke4br-d( j szk 1l,i 7zs)5 u Moon, or the Moon on the Earth? Which accelerates mbe7 kdt4k *u -smzz ,zj+ls)rb1o(z i5ore?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th:cuid83z (i ebe Moon's is mainly responsible for the tides. Explain. [Hin (du8iec3bi:zt: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator3n y7,w,dtm ,hkqpom) or at the poles? What two effects are at work? Do they opdm3ym tno,k,w,p )7qhpose each other?

The gravitational force on the My ; /3x 96*w xkfkhbbgsutnk,/oon due to the Earth is only about half the force on the Moon due to tkgk knufs/ w*3t9bx xy6h;/ ,bhe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lacu:9bjh;e1he 3ole le5/jp.z rger or smaller toeeeu:/ 5bhe.cljhz 9j; 31lphan the centripetal acceleration of the Earth?

Would it require less speed to launch ab3ii v--ww0z ok, hcn)k1 k a:ge;jgd2 satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direct ok iikb 2-wjgd)-v; 3k1w,zg:h0 cenaion.

When will your apparent weight be the greatest, as measured by a scale yz4 4- x+f9sh xcezmh(in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant fcz(he4h4 xx+msyz9- 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 outer space c:ti)jlb ijp.xo 4+ rp;ould 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 thisjjrl.t4 ;obii) :+ppx 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” or “appareh7 yl5i6qy np.nt weightlessness” between steps.7yq l6hni.yp5

The Earth moves faster in its orbit around the Sun in January tha02obmql6-( tfy427ey1 fz tx0osk)0 yb t grgwn 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 relativeytof7(rm fw k40s y2z 6-e0gqgtobbl0t2)1 xy to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explain (ia nsg+kk* ;sohnv;7,o5atg how this discovery enabled an gi;avsns n o;o*7,5+ t hkgak(estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the12 z1u;kt dj.)bkb qz;b4e pqn Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earthkbd 4)b;1 2ejq 1ubtn;.pqkzz 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 +d. *jbac/at iflwmi kd6 ;47c1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratio ul0goc6 a(ez be.+c9hxuu38nn of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.h+n u6u.e8ec9cug a0 zb(l ox350$ \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 exertq +qsi/wj(go7ed on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. 7 sqgwij+/ o(q  

  Suppose the space shuttle is in orbit 400 km from the Earth's surfac)1gc erti2v8z e, 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 gt82g1rz ie v)c , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelecf ud2q2tt5 +pr(ar6d5 yt5hzration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the w(+ 2 y5da qtdhcr6u 5tzfrt5p2heel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rz oaeatj52:e8hya+t:1r a 2t fate in a vertical circle of radius 72.0 cm , as shown in Fig. jz :a 5fae1traot2y e+2:hat8 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 c5.i;kxu9 jpy77 m on a flat road if the coefficient of static friction between tires xck pi 5u.j;y9and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires an:gwlvo g+fqc l2)m++ c. mpy8hd the road if a car is t mq +hm2gco)ycg+v: wll.p8+fo round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilotsd6xkwad wj9i lj6 hdx 7:+26rs is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotatinx6+d sw adr96dj wj6: 2hlkix7g?    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 e(6t) e6a o wlpn1n:,c,+;rwcneugsh axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntasth;agle,en p+,we w u16 crn() con6:ble 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 downeqw / lnb:2nuc8b3x ,h at the top of a ci e2l,cnx/ u83:whbnbqrcle
(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 t0lo nqz)r6ha42c1zmd ( j7fkt he rounded top o)fz7jrh6zlm qkd4a02ot1 n c(f a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris 10to2f/b dnaywheel need to make for the passengers to feel “weigh2ya1 ontdf/ b0tless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirl57:xp7t lpu-z+ofgf d0fw1ulg zxx4 ) ed in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. uo:f x fx-)+7lt4 lpdwzx0fz u75g1pg
(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 frq+ubxg 5+imnk .e wym .y)d+w.om the axis of rotationm uw.wd . +ix+k5 qygmb)e.y+n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot d0bsparvtsz8) *ce4k* ;0 ebwated in a cylindrically walled "room." (Seesbc4ept00ardv ) ;s *8ke* bzw Fig. 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 f4njcr 83:bq na circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danglirc8q :4bn 3njfng block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight bxyqv/ 7o*0zk of the ball which revolves on x /70vk oy*bqza string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car lm/ kh zxp4(;x m3dc*ytraveling 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 a nhwfdezd u*(2g:04o $ 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 o 5)xto y* e3cpc;yfvbcmz6q,z l.(z3diving 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 centritpl xima-5r;z4d geybip) v ;)v; 9q7npetal components of the net force exerted on the car (by the ground) inzxv qienr7-v;a5;ti)l; 9 4g pmby pd) 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 frvau v 4ays-:: zj pw34hjm13plom 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 friction4w4 mjvy1pjl z:v3pasa:-u 3h 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 particulab/zmxt+ , k7rrr instant, its acceleration is 1.05x z,7t/k +rrbm $\mathrm{~m} / \mathrm{s}^{2}$ , 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 rad 0-( h av1wzl:o-kt*pd;e uhlgii) t-; we0zl*al -hogvuhp(1 k:d above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerahm a*w6dgt.2/jzf yc(tion g has a magnic (.h z2* f/gwmdyjta6tude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravi3ph;k-:p *hwn np:fnm ty on the Moon. The Moon's radius is 1.7hw3h n*fp-nnp; : p:km4 $\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 u 6ojn6j, spg4ly;rr+Earth, but has the same mass.r6p;,jo+lsn4r uy 6gj What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the w-28h 6io)ojva:4b- zmu,ne6ojd urv same radius. boo-m4:2zu nve6or hj 6av8)ud-jw,iWhat is g near its surface?   

  Two objects attract each other gravitationally with a force xf8q75 5uqqnqhp0.-sq f q3qg 50zbg iof 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 (cnnqp)518(c gf yd *bjq )mhnk3.uqm du5.sa6a) 3200 m3d f.u *cdugq nj ()5hysmp)68nqkqacb1 5n.m    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wzdinw 2 i+1m7qjzwt,xdg:-1o here thegravitational acceleration due to the Earth o z-1g1zdw: , 7mijxn tw2+dqiis $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Symnm it2*m, 6hkirr -5un packed into a sphere about 10 km in radius. Estimate the surfacem6 kiitr* 2y,mr5nmh- gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an )xmw(a usgo ,,b,9eqfaverage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface(o9)aw,fm,xu bs,geq gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting x-lcq;g nxuzv* (7:nx *nnz5am t9z-zin the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them lt5nzqa:--xzx;* 7nv(g uzn 9* nmxczand 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 txey jr(/f;i5x z (dpgs1qm0ny2rm7o )he corners of a square of side 0.60 m. Calculate the magnitude and 2fr 5 0j(7pq;)mx yoz1snyergd/xmi (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 :ao*cgh hhg) l 0 q.caaq/b-x5the planets line up on the same side of the Sun. Calculate the total force on the Eoa)h*. hggxca -h bclaqq /0:5arth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars isygw7 7 x6r/lhp7e4lw9gbrn4khy / hf, 0.38 of what it is on Earth, and that Mx/ph9lkg77/bnhlhge w7y6f4 yr w, 4r ars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value xm)susto *++k for the period of the Earth and its distance from the Sun. [Note: Comparextm* kso)+us+ your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a staba o34-wc m)z*7o;btlzo0h3 y8rdxo1l eow.ey le circular orbit about the Earth at a height o o-a0x7 4z o *.y e1 )8wwlobroozel;tm33cdhyf 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into augz-i 1j 7z;yi circular orbit 650 km above the Earth. How u7z-gi1;jy izfast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantsv* cii tyue,1w/mk*p ls()my3 tj(8 pl are to experience simulated gravity of 0.60 g? Assume etmwiy8mk pi3ls * c(jvy/tl ()* ,1upthe spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cao)amrk59c/rj a* fmrsk; ,k.ircular “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. Do r*k.5)a,srmmkfao /r a9;jkces your result depend on the mass of the satellite?    s ~    min

  At what horizontal vj y f1,k wu2(cz:rkf3lelocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Elfkcw f 2r3,(jz :1kyuarth?   

  During an Apollo lunar landing mission, the command module c by+4i 2-kcn5w7vt rtlontinued to orbit the Moon at an altitude of about 100 km. How long d 25k wcyrtv+ibtln- 47id it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planezstcz-68rk5b3nj ;(cgl /a r gt. The inner gk(gr5 alr3 tz6/j8szn ; c-bcradius 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 once every 15.5 s (see Fiz( ,mqko3okza v9qu6( g. 5–9). What is the ratio of a person’s apparent weight to herkqa69(zz q ,kvom(ou3 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 of 8zyd/ 8rq6k4l*6o/r+jj lf +qi : kbk6nfzphx the Earth's Moon in a space vehi 6y pq:f+rjl86/hjqknf4l z8kdi /kx+6 r boz*cle (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 coirns *cadlh56p44pi *nsists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway bs6 *n *hri45la4ppd cietween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman intqijj5 7-pjp6l9 nr9b an elevator that movesb- n6j9l 5irjp7jqpt9
(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. Taf8nnl,2 )ja ihe cord can withstand a tension of 220 N and breaks as the elel2n8j fi,ana) vator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface ojrg 3 m;k5gkoqa r72-uf a planet with period T , the density (mass/volume) o 7 k2o5r;mjrqk-3ug agf 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 determine the- tb b)t0rg-c nt8f.9be6 hwag period of an artificial satellite orbiting very bc.gra9-w6th- gnb) 0t ft8benear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits mp) jxd* y8 :pc y.tblk*0wi-kthe Sun like the planets. Its period i kmdby *p-).*tc y:xji8 pwk0ls 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance jk/* 7 aw*deagl zxn80cid6yz2) b5fa r; i0peof 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 everyna + 6w6gcdy6dsm2 a)p nd5:my 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 wy:6c+ nmaspw6n y2a)d6dm5dg hen 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 thsw j8.6e biuj.e center 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 distanc n:)(m gg,oihznd* w/b *mfe2ge for the four largest moons of Jupit :(if 2n m w,*d/gngoebzh*mg)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 Earth from the known period and distance of the Mo9wu;s/n6g-vb1ezhve u 5;v:y4ym bgoon. /u vo-w u he1gvv4:b gy6z;mn9b5 ys;e   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kep(, dqz)o,n/ ekb6hqysler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.k,bq oh 6e,s/ d(qy)nz
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars 9/ o7gwyt:q dnx3ew1fand Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited thqnf73/9yx:e t dwow 1ge 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 "n ot60 i:i,tl5 iti8mbplanet" 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 app0 tl:niit o,m86ti5i barent 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 a94zy gctw mmwby:3-c7rc from a hanging vine (Fig. 5–4t 3 z-w7wcbgy94m:cym1). 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, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the8a/7hop klq* h acceleration of gravity be half what l*po7a /8 hqhkit is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equrvqa3v7ia+dzjc. pp 3n)s +/l al mass grab hands and spin in a mutual circle once every r).33naqiz vv+7+dp/s lj pac2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravy (-b52zx,sy;mnko6o )8mzygfdy+wi ity at the equator is slight)yym8zoykw g y-m6f+ x sb(id;,ozn25ly 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 wi (m6xd b);,k xk2r:t1an pqayvll a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull wk ,pxy:tavb6 qmr ;kdn)x1(2 aith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand o v/0imlzi9teb s0ebr t+rf-swl+8,/kn a bathroom scale in an elevato-zkr+9e we r sif/0ismtvl/l t,b08b+r, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circu qg9(wx60oat ular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube h ux60gwao9t(qas 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 aircrar45c ez1pyo1 bop8gq 6ft in a vertical 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 ra-lu.ywi cu3 9k; b*owmdius r, the acceleration due to gravi9u-.c3w*u ;m lbkyw oity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on ih(c l0.cy72sjgi ;u jlxf p21a string) is deflected from the vertical by an ang2ug y(7hs12cfl. 0 c ;xjpiljile $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design spu/dwa (7k-uy veed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle thdu7/-uw vyk(a e curve?

  How long would a day be if the Earth were rotating so fast that objects f0qqqowm m+v+)q4or jo 8 a0+fvdf+8wat the equator were apparently weightqfqa ovm+f0o+0w +8)f v8 4 +wqrmdjoqless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distan-;u oqq)ec r 4nk:bk7zce 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 constah4e u/) 7-s,fiuip usdnt speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle o)-f,idh7 i /u4suesup f 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 3209bcd4 lqs;0j3xtz.om gr-n *n times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few dbtj9xq*ro -0 nc. ls43;nz mg 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 Hubbnd,j j-tt,jf-w4vig * le Space Telescope deduced the 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 measuring the speed of gas clouds orbiting the core *4jjtg w-vj-,td ,ifnto be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown orqwf5js9d(z6fn*rik b 4 d 6a.kr.q- in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the d5rfdb4*.j rno9q-sw.k 6r kzf 6ai q(road at A?

  The Navstar Global Posit1(73r.ed+td(b 1nt/ ks4 vbfwj wil uu xo9e*zioning 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 acu i3/ lnbf9 dtxb(e1.oj urz7k4e+(v wt*s1wdcuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), afte ycjolb p118f4r traveling 2.1 billion km, is meant to orbit the asteroid Eros at a p j4f1cly8ob1 height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repd uk:ne+n.eio*;zz1 g air. You are in a cir ;d1ognenze. ukiz:+* cular orbit 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. (afw fcnnwpb rgy v4+ 9i)sm+ypp 3,*l4)) What is its mean distance from the Sur+ mnf9c),vlpf)+wpy n4s yip*gw4b 3n?   
(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 couce41rcwfxzb) 0 1 y1vkld actually "feel" yourself gravitationally attraf xv y41c1erk1)bzwc0cted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the nfl)ty94q-h hx19/fg n+ icbwcenter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yh9yx b4fn)nq-+lhf9g/c1 wi tears 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 corn5dj 9li u::vdaers of a square 0.50 m on each side. Find the magnituludij:ad5 9:vde and direction 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 k 4m9o r-xvjtnt 4gikb)5y;+edg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienh:vgg7awvup . q5np .*ced by the tip of the 1.5-cm-long sweep second hand on yourq wg p pahu5v..:7n*gv wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weig5 npe2ztt r/8jht around in a circle below you on a 0.25-m piece of fishing line. The weight maktp 82 tejnr5z/es a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwayk bgm: 6z2hg0o is designed so that a car traveling 62 0 :bokgzghmat 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 ca*3z0vy0fsz a a3ppjn +rs 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 friction force needed on a train passenger of mass 75 kg if the track3a*an 0 pvz+f03jzsy p 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.$\approx$    $\times 10^2$