Sometimes people say that water is removed from clothes in a s(dn) c9w)wm u,ny-o .plxcdf /j a8;hspin dryer by centrifugal force throwi(l-/ww o pdfju.),xd9 ); cnmcyhans8ng the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travf:xc)i; t)n d9un chs qoz:))oels around a sharp cur;nx:)i o:)cdnfozc )h 9u s)tqve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constapwk7 *q7 x(86ivb)xdf nffh4jnt speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of* fjp nx (6i87f7xf4kbwqdhv) a hill?

Describe all the forces acting on a child riding a ho9h,ebn p5vniqq /1e bp ux5o/2rse on a merry-go-round. Which of these forces provides the centripetal acceleno/1 / b5iu peqnb,phxq529 evration of the child?

A bucket of water can be whirled in a vertical j,j1 aradhkik9 h.*. acircle without the water spilling out, even at i h ajaar,..h d*kjk19the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you hajb8r5 +su) ts td9)om2fyr8 wcve in your car? There are at least three controls in the car which can be used to cause the caw)sjto5 uc8ysrr 98m2d+tfb)r to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying overj a;19g1 utgrc/1k czh the crest of a small hill, as shown in Fig. rt1z /hc;c1j kaug9g 15–31. 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 Newton’s second law.

Why do bicycle riders lean inward when rounding a cu3on2yp- 6y, y4a-y;ieew dka drve at high speed?

Why do airplanes bank when they turn? How would you comp1t8-; ywgb*csu.hz4 blfpyd 6ute the banking angle given its spwuy4czfb8hy6 ;bp-l*g s dt .1eed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. S 9ct s8.6ggerahe wants to let go at prece sa 9r68t.ggcisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational forq, (0k ,ymcxomce on the Earth? If so, how large a force?yc ,q0xmm(,o k Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouldv8q8u:5; ggvj zeclooji,o:v5jp, v) the Moon’s orbit be different? gl 8,gvjeu5ov:8)c;v, : vjoioz5qjp

Which pulls harder gravitanp5 ee/iuynoq2*na 5(tionally, the Earth on the Moon, or the Moon on the Earth? Which accelerates5 *en i5aqyp/n2on(e u more?

The Sun's gravitational pull j 13*r 3 jj:pb9otb7 2.)fa gvuztbpjkon the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Conside) pbpv tj uo1*fjr7 zj2b3gb.k: j9t3ar the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatorw do-m bjm*.8:jo rpu- or at the poles? What two effects are at work? Do pjdw.om*8- :o bjurm- they oppose each other?

The gravitational force on the Moon due to the Earth is only about ha.wf +8azmn9m . h7mdhplf the force on the Moon due to the Sun. Why is .mh .zd+n9 mhpf8amw7n’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger q-df) j807qavqi si zp(2ka;zor smaller than the centripetal accelerationk 8 vsp)ji0zafq(-d ;qiqa7z 2 of the Earth?

Would it require less speed to launch a sate+pdu 81jwm*q hn7gedo6/rzi/ llite (a) toward the east or (b) toward the west? Consider thep71w*u+ze h /6m8rdqg dnij/o Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in41q25sitqrl6 ya idgez g,e ;2 a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be th g6sq2; qdeg5e,14li ryita 2ze same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lonp:uz2/d hvcv 8g periods 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 objects fall, (b) the force we fee h2 /8upvcz:dvl on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlesc0uq i) j4nip4sness” between)4 jincpq 0ui4 steps.

The Earth moves faster in its orbit around theu9n6me .vxu a;fwxu-3 Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not muw unxuu- me3v.6 a;9xfch 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 it was discovered to have a mo,t jxev-+5oh/ w.sbhq;vn jp+on. Explain how this discovery enabled an estimate of Pluto’shej5b v- s ;+/+thovpjx w.,qn mass.

  The Sun's gravitational pull on the Earth is much larger than the M5tien5u nii hwmpc9s*5d58v - oon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in5inec5 8siwtm*du-p95i 5 vhn 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 travelinzg6 uw .bn5v*ig 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Ear fr:7t8i-vb g us0xm6rth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? gri- :6rsmf bx807 tvuAssume 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 uf*y -3b3ok* b rxrt5ma 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of t3you-f *bmrxrb3 5k*radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ear2uw rxjj,)0 ro rvr)4cth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle incw20)rx uvr) j4rj r,o 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 z7gd +zb2 ff5qof a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the zg+ffd752zbqwheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unifor voo at5tvfw na8t-,7-z(-i jym rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed taw(zittvfj-n-o5, 7 a-o8vy 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 *yn1x,nrzg-cq 3s7b gturn of radius 77 m on a f1z3b ncs- g7ng*rxy,q lat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of statia mtz)gj 6)5kbc friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95kk)5b)z 6gtamjm/h ?   

  A device for training astronauts and jet fighter pilots is designed to /b/ t9l6obxvk1ix qao.)7mt.vmi)e p rotate a trainee ino mltb/xvi)1peqk . av7 6x9 iom)/.bt a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis oan)6t+e7 +g xbv u/gbcf a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntablea n)67g +/tbecgv+ uxb?   

  At what minimum speed must a roller cgibn)/ l,izac9+le (o oaster be traveling when upside down at the top 9) (lgliabio /ecz n+,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 mass 950 kg (including the driver) crosses thig ,:g(e1v.8z-twrgcm 4y 3uj6 yppl ae rounded top of a g v:y 1pj6g(3m,.e4gz-l cyaprti8 wuhill (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 pjp;*4 sdz+omqzzc( l*;m;yyt er minute would a 15-m-diameter Ferris wheel need to make for the pam*mzs; *;pl4 czz( tyy+ ;qjodssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circ(- akfu8fyzm (y9/ cgnle of radius 1.10 m. At the lowest point of its motion the tensionm(kf-zcygf8 a(9/ uyn in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if7xq0,0et:ga8l(n4e d btrsi d a particle 9.00 cm from the axis of rotation is to experience an ac ig(l rdae,:0ed4sq87ttb0 nxceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cw2j e ;fnd /aw/b82jjkarnival, people are rotated in a cylindrically walled "room.bjw//j knje;fd 22wa8" (See 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 a circle on a frictionless air-hockq c2td2 a;kqzak;gq 4,ey tabletop, and is held in thisq kqa g2kqat;z d4c2,; 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 thinfc osp69,oz5s time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find cf6,sp on 95zothe 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 8 7jm nsq95is.wjavl 6for 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 massekhanu-p)v):y (n 4fm7+ njcg xs $ 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 ;jpvcvtrf 5y,w4 *y5m 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 the net fo;fmi,t)x7*j3 s6 cbg q6kjuwv rce exerted on the car (by the ground) i*tjvum;s3qci j 6 fxk7,b)6wgn 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 agkr yk.-8u4ww ccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coeffiw.ry-g wk4k8u cient 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 8yahh5m(sz3d9eh xb0 a horizontal circle of radius 2.90 m . At a particular instan90b3ah(xeshy5dz8hm t, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,/, 7ckdv krf.z800 km (2 Earth radii) above the Earth’s surface if its mass is 1350k/.c,vdfk rz 7 kg.   

  At the surface of a certain planet, the iq0 0zm o+ynpg-5d)hhgravitational acceleration g has a magnitudq p+yn5om-d0h0)zg h ie of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1.7hl;wg5h qq1j*4g *1l q5;qjwhh $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has z:xrixf2x *1( ,t,*j uufiykfa radius 1.5 times that of Earth, but has the same mass. What is thefjxu2t,xr 1z, i*fxki*u( y: f acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,;0r9xaub qh.j3aqed ; but the same radius. What is g near its surfac3b qj .0r;e;a a9hqxdue?   

  Two objects attract each other gravitationally with a force of 2o1svm(*fgs r+e5e9qp .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 (a) 3200zhaoo 7)vmt9(0lk9 zkj*efu w16uk 9 s m 9w jv1 ok(9s f6tkl*kzuuz07e)h9oam   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outt4xq / uau60vj ym(t7kside the Earth where thegravitational acceleration duey6ut0(v kmx7 /4jqua t 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 packed intor 5 13v eu9k9dcy e41blr;xl (atdlr+p a sphere about 10 km in radius. E1(+erlu9rayl 1lpv 34b5 r9dx; ecdkt stimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whjv,juf y85fq /ich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity uyjqf v/,f 5j8on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orb ldwo1y ;w ca fcjd 7:r1pe14q;iga.d.iting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleratil ipw4;ceydgo ;1qarc. fa1.d dj:17won of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners9h.xc vepo /p0 of a square of side 0.60 m. Calculate the magnitude andpo c9vp/. he0x 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 year . 7et8ohqlh9gs most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four phh.7 eqgl8o t9lanets 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 surf s+ )h0mue2sxh* /gsmm cfi,9lace of Mars is 0.38 of what it *l f9husmc0/)2s, m+hmsegxi 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 valuedeo2dvd4 )2; ufwaw0v for the period of the Earth and its distance from the402dwvd;fdawe2o) vu 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 a stable circular orbit abou fossenl8s9:) 9ey3th t the Earth at a height of 3603y essol tns9:8 f)9eh0 km.    $\times 10^3$

  The space shuttle releases a sa-2(,iz x qfngnwo0t-itellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rtxfgw 2zo -(0i-q,nnielative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshipz wf. m /-twbg31edq9u rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your an wm93b.1zwtqdu eg/f-swer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to oo m/7hcdw k+1q :ip7i5k mel:erbit the Earth in 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 radius of the Earth. wo+k klc1:7hd/mi5p:7e eiqm Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top)s/p(neqp1 ik)libg p ,dwgia88 m x87 of Mt. Everest to be place)87g a( pklbim88/ids1 )w ,nxgqeppid in a circular orbit around the Earth?   

  During an Apollo lunar land dn/kqjf. 3,dning mission, the command module continued to orbit the Moon at an altnd.nkqj3 /df,itude of about 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 the pal4snbgu57pyi5x *z1 lanet. The inner radius of t5b x5l*azy inp u471sghe 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 rotambo *6 spagnz6+39frnsw71 fctes once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparefawc1p fs*n7 z3nr so6 6mgb9+nt 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 420,ez:kb1 un*:v/hjvrol db9;cae * 4 ct0 km from the center of the Earth's Moon in a space vehic lc1a/9vo:njkc *deuveb bhzt*, 4 r;:le (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 sx0s- krk(gqhwaiz ljp , 489.system consists of two stars of equal mass. They are obse l89k qw gp0ai4z-j(,.ssxkrh rved to be separated 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 an elevator h .e,b. yzuca3that mov .z3.ybau,heces
(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 tc 9zs.mwxm7 w3he ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acz 3mm ww.xc79sceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with pxt, zdhe1z e+ncu3 n. pswdt4 )s)d;qf8l f)4weriod T , the densi4wzun)d4;lwe) s cdf+t,z8pseh ntqf)x3d1.ty (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 determine the periodfm8d-a; lh;q m/f/ium of an artiflm u-imq/f;8d f;mh /aicial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few khia/jwo(z9woke d8 8g: u8-bhundred meters across, orbits the Sun like the planets. Its period is 410 d. Whaed8wki jk8ooa/h98gw:(-z but is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of /* qtborzl)q9 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 roughfrppldva. clt3 xy 00563q nfr2u)d;kly once every 76 years. It comes very close to the surfaceprqfll0 pt3 r3;nf6v )ddya . 2cukx50 of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: 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 tf/ 5p3ffopt r/he 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, peinmi zi+rj-54r5q+lj k7sf m3riod, and mean distance for the four largest moons of Jupiter (ti zljr5+i7krim+qf ms-53jn4 hose 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 pevsd:)y 541 fs gbmv;crriod and distance of the Moon. 1g:s)c ybrm5 s4vfv ;d   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moodcus r(kdv g0j7,v.+ qns, using Kepler’s third law. Use the d7j.v0 d k, gc(urs+vdqistance 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 Jupitzuk+-me/1 rr :-9uq3wgatthq ,y t d8ser consists of many fragments (which some space scienti9a-y qtzth:1k,3mr dr+ qeu8s-w gtu /sts think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "p1 cn :dm2u,ip; dcs+pelanet" 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 pro1mpu2c de;,dscn:+ ipduce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorg ga e/;g7q,5 ha97jlqcrkg)ldt +nf s:e by swinging in 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, and the vine is 5.5 ;rg /7 aenhlja)9+,5dcqg ltkg7 fq:s m long.   

  How far above the Earth’s surface will the acceleration je ud4*0w sd1u2td(ce yr3.kfof gravity be half what it is on the surfa e4ec.w*tr0f3ju2d (d 1ku sdyce?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in ffu j8e.5rux r4 nmv6;a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long av fu48mn;5 .fjxru6 rend 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 acc/v.r0hz. bse 2 dw+chyeleration of gravity at the equator is slightly less than it would be if the Earth didnv 0he/b cz.dw2.rshy+ ’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eartz+q7m-l2yb toh will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and ol + oy-b2mqzt7pposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you 6.a5c li,xs5+k d.mo gkf8wlostand on a bathroom scale in an elevator, it says your mass.fo.k8i l+sxacgl m do,5k65w is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate a ;iwc(r* bv5tutcc1)fbout its center (like a)5vr;f*c bwciu (t 1ct 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 lsgyb2:m2hq 2 t / kzse/kt -dnx0e4v8goop (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 radiuss (1z n+/kjjnz3hbk*t r, the acceleration due to gravity at its surface and the gravitatb *h+/t(zj zjn3n 1kksional constant G.

A plumb bob (a mass m hangin0kb 6vi .u2suz iez,)umf,k4gg on a string) is deflected from the vertical by an ,.6smfkkubuz e,g4)zii 02uv angle $\theta$ 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 jww84 i-ntkz(design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely hnjk4i8tz(- ww andle the curve?

  How long would a day be if the Earth were rotating so fast that objects 1 ppxk6)ikz yith6t7.at the equator were apparently weighk.zkttx66)p i17i ph ytless?    $\times 10^3$s

  Two equal-mass stars maintain a c+m 1f kqn 8z+oz(mvqtg8o p*1ionstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curvs0awy8ko2 s4nfv1 ajn/x(6wo e of radius 235 m. A lamp suspended from the yxa fwwn0(16/ 8s4vojn ask2oceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times asl c83+ /o) jh9nnnzxg)y oq/lb (ddoe* massive as the Earth. Thus, it has been claimed that a person would be crushed by the fojn)qloohldcyn x*8/+d( n3g)o9b e/zrce 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 for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extrememks knbm + :gyae78z):ly 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 measuz )7sknm8g:ke mby:+aring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill anc gl u.aiid.7(d valley shown in Fig. 5–45. Both the hill and valley hav (a cidug.li7.e 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) uws 4djh8a:)q itilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these sateldai8 hw: )4sqjlites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical 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 2x n5 c*,6 mrtcxgacu28.1 billion km, is meant to orbit the asteroid E mxa,5nu68x*2ctc cgrros 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 6uned4oiel i**8pb4 xrua ) xr0k,i(ishuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. i4 p,dib0ei8(axrnu* )xu64*i k eorl
(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 itsfzyir*r (r;h//m4nfy zus -+e mean distance fromz* rfi-srmu+ze(4ry /h/;fy n 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 zl/c1 nejd)5qrlx /b/ actually "feel" yourself gravitationally attracted to someone near youjbe /lrq nz)/x lc5/1d. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ofnh7wp1 i gv.i: c,.b*q +ru x1kvgmql8 the Milky Way Galaxy (Fig. 5-46) at a distan,.iqpivg8g r v +* 1ckmb7qh1lnx:wu .ce 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 thenk(b2ioih3y 6 corners of a square 0.50 m on each side. Find the magnitude and direction of t6 i3(hbo2yiknhe 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 t)29lpoot*wr vq7ewv1(uwo fg;fz:7x he 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 experie9x oa ano-m69nnced by the tip of the 1.5-cm-long sweep second hamna9 -6n9axoond on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored a4jd qlo-w-ka.nd 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? [Hd a--woq. j4klint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designe8z.s)sp mn5dfdw) l1 fd so that a car traveling at s 5 nsd.fdpwms)1)l8fzpeed $ 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 nppea l owu:)0c, ,ww9fegotiating curves. The angle of tilt is adjusted so that the main force exertfp, wuac)l:,w9 w o0eped 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 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.$\approx$    $\times 10^2$