Sometimes people say that water is removed from clg7 mc)j (ip3ikrery90 3)c uggothes in a spin dryer by centrifugal force throwing the water outwarj7)gp9k 0 uygr3cm ce 3irig)(d. What is wrong with this statement?

Will the acceleration of a car be the same when the c8q2f0gv uq xqg;ug6c1 ar travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the samevgq q2c0fug 6ug 81;xq speed? Explain.

Suppose a car moves at constant sp7 yhi5u)biw7pc-za) aeed 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 bott7 -h 7ucpyaw )b5)iaizom of a hill?

Describe all the forces acting on a child riding a h hnjuxt(5rr x8(5cc+iorse on a merry-go-round. Which of these forces provides the centripetal accele 5(x nix5ujrch(+tc8r ration of the child?

A bucket of water can be whirled in a vertical circle without the water spilli;5*n hf4 0ig 6ij*waq)rhd tw+cy+gq png gar d;qjcyt i6q40*f5in*wp) +h wh+gout, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Thezl om0ku+z -+ore are at least three controls in the car which ca-zko+ l0oz u+mn be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cresp v64.gl2mbypt of a small hill, as shown in Fig. 5–31. His sled does not leave the grounb 6mpg yl42p.vd (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 in ra-tlxu 8m1:nward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking ang1pe2w gw3vo e5le given its speed aw31 e gpe2vo5wnd radius of the turn?

A girl is whirling a ballzy4 .pkip )f+ t,vk9kq on a string around her head 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 of the yard. When should sy k pz+.kf,9 vpk)tq4ihe let go of the string?

Does an apple exert a gravitational force on the Earth? If so hi:z*jy+8j 1eiegncjq4 f:h0, how large a force? Consider an a e04jy 8: ice*+giz1nqhjjfh :pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whatx /1hz29y; mrtl -etn-/fwygu ways would the Moon’s orbit be differe/-ytw n/e rhxyf-m t1l2guz;9nt?

Which pulls harder gravitationally, the Ea -y)id s(dw9kvrth on the Moon, or the Moon on the Earth? Which accelerates k(ysddiv w9-)more?

The Sun's gravitational pull on the Earth is much larger than the Moongq x0vcb32+lu , .uykk1/w hru's. Yet the Moon's is mai3 /c1r+ uug02w k.yqbhvx klu,nly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effectsxz, 2f*t ee/it are at work? Do they oppose,efz*xitt 2 /e each other?

The gravitational force on the Moon due to the Earth is on cdtz:cbi;88 ply about half the force on the Moon due to the dcz8t8c: pi b;Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in 5en.hux-/ xt nits orbit around the Sun larger or smaller than n/nx. htue -5xthe centripetal acceleration of the Earth?

Would it require less speed to launch a sate3jgh5lv q5*( zi rpxq3llite (a) toward the east or (b) toward the west? Considlvgqqi53 3h(xj5zp*r er the Earth’s rotation direction.

When will your apparent weight bgo 4g8owg+va;,( 3xc fsxm l6xe the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are(x6o3;4x aswfcv+ gxggo 8ml, on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adverd f/v 7c wjzpj)kq3e-2sely 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 f3jq2 z-wcjvefp /7 dk)orce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner exper hx*n+,d 5cpgriences “free fall” or “apparent weightlessness” betweenhdcn5r+* p,gx steps.

The Earth moves faster i 6*z o0tkoue.u9 buqx4n its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Expxo96u0bk*u.t zue4o q lain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explaobx0(w tg(s:i yb5yed+w* p, gin how thisytys5wid:e b,g 0gw(x *(+o pb discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth+am nlhbx/ 0u5 is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from t hn+5m0ax/ bulhe 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 3g,p e;-k4jxw49cm vkrbf6zn3ez/g rntqd3 ) 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 sjfp+p; d.v. b* mqx.jy7r(xh0qgt d ,the Earth in its orbit around the Sun, and the net force exerted on the Earth. What7;fpxjh.+d *tmsrd(q,q0gxbv.p .j y exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus*jpu35cll-m2la t 9cf as it rotates uniformly in a horizontal circle (at arm’s lengpu-jclmc3fat 2 95*l lth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earthsb3z kwr)g)0 sr:x/j o's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express yourr)k/ b)3 wx s:srzojg0 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 clay on the edge 9,uii cbtq67frb,a /pof a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diamet,i9q,p/ t6br ifab 7ucer is 32 cm?   

  A ball on the end of a string is revolved at a uniform 4),5miklpivt356s e;l fg okzrate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its ligkisptfm6;k,4 o l3zv 5)5espeed 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(r(/at sai9q2ca w *q-wbk zv2 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 r-(ac9atk/v sz( qr 2bi*wq2 waesult independent of the mass of the car?   

  How large must the coefficient of s g 0eeb awd) p+ 0xvf/var8q/n:4pjy-ftatic friction be between the tires and the road if a car is to round a pf d +fnw//vaqb):-y rje0 gv4ea08x plevel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter rn .x odzs5iip497d9fq; 2dfspilots 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 i99i;q d. i4odsfpzsxnfr25 d7s 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 turntab0m 9ougs37 pbfle 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 coefficieng0upmfs3b9o7 t of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsido,aoe (-gv(c,trr lo-e down at the top of a circle -vcr,a,ol( gor(o -et
(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- - fur7uc1knp the driver) crosses the rounded top of a hill (radius =95uc-pnf 7urk-1 $ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to makok;r*s::ojc 2/ulmvw e for the pasrskom: v:*wlj; 2o /ucsengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circldwf: y1iud zb79ym+-vxf* sf(e of radius 1.10 m. At the lowest point of its motion the t (f1fum:iy9-7 w z+*dysxv dbfension 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 if a particle 9.00 cx 386xj qp i+tizt**nlm from the axis of rotation is to experience an acceleration of 115,i x*pti8*tz3q+n6j x l000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated inr, ,znirc./b 2 ulwjv( a cylindrically walled "room." (See Fig. 5-35..,lj,vnc r2u/wirzb( )
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 fri*/mv 5cjqxri4 ctionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block r4i v*cmqj /5x(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 timp 8wy4n7j ,map bfapy:uxh,d2 i04yf3e, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, fin hx4ym:ap3ayp,df8fb , ji0 u4ynp7w 2d 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 fok*(xe4u ej; kzr 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 masseso .ylj9r -xjz y0.xe2n $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving verticam tj xs-y3,b soj.9u7qlly 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 anda zx6nls9s8x, centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speeds l6a9n szxx8, 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 thabkm tu*c azoyp5 :m8w0j8s tk3 08-iqe 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, whp8:8m kk0tq-imbj*o a5zyc3 u80atws at would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At qrgp2k ,52ua - ;jyelza particular instant, its,pz2g2ekr5u ;ya - qlj 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 1 /nqfqjoq 2rn c-99d5a2,800 km (2 Earth radii) anq9 f5ajqr2q co-d9/ nbove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceler cab.maqw9ms 7k/ox)2 ation g has a magnitude of km s/a)omb2 .q79wx ac12 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 1.7i 9vlo*k0p, 7xarae h+v;w2 zi47v2, hpi +0vexk*;owzaal 9 ri $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiuv6-7zj0o ,fhm;.xs7.z fg q-vl*qnn acobxe *s 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its-o6ozn0 *x,nxq zhf. ca*7j.;v lbfgv-sqm7e surface?   

  A hypothetical planet has a mass 1.66 times that of Envqhgsl 335b0 arth, but the same radius. Whatbs0 5nlgv3h q3 is g near its surface?   

  Two objects attract each other gravitationally with a f/ 1spzxmd:ki*vi/hrwz6 i3 /xorce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (l9tjyma;n-cl 63 5a bz fx(0lja) 3200 m5l ;(m tb3l zfj6aalcj0n9-yx    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the;9*; q8ajvmuhx wc9ptw njr2 3 Earth where thegravitationan9j2*qaw w j8x;hp3t u;rv cm9l acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere 2t5 .p/.1 zh4nap,9qsr(iuwctjk pxt about tn.s,zpap9tp( kc/2rjxuq 4 w t1 .hi510 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun e tta mm-8dj*4but is now in the last stage of its evolution, is the size mjet* dm4t 8a-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 sp nw;g- d0hbku2qg4n-jte8a bk5 vz3t:n(1qwn ace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravityn(1-aq 4bte v tn8:dwg-2kqu j5wzbknhgn 3;0 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lo8 u)a-z2rik+q ek,vgw)jygum 8wk8m,cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total+um,q-wvewiy k8a8k8))mz gg,2ju rk 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 :r)i6 zp q-jxgon the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5xp - jgq:6i)rz-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 wh. h(p+kn6 oermat it is on Earth, and that Mars’ radius is 3400 km, determine the mass of+ne(oph m r.6k Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valu:/7ikstmgqbwk j,(g9pf)l i1k/b+d x e for the period of the Earth and its distance g7 +mwktspdxqi i/f9)bl1j(gkb, k/ : 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 a stable circular gzcbiap-m u(t 3u49gt 2vf2h,orbit about the Earth at a height of 3600 kgu34,2g9- i afv(cb2 m pzutthm.    $\times 10^3$

  The space shuttle releases a satellite into acwk;hv85aae h;agk, 34o sqv0 circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurcka43gk, ;0aswv5qeh8 va oh;s?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are 0n j idpqpe p-ko(dht,bwz11zr:-3ru 3ou1 7 hto experience simulated gravity of 0.60 g? Assume the spaceship’s diameter isn huqij3w:zd ret- (kd 1p3hboupp,7 -11or 0z 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 chz g s;mb3vp w7;gv )d*vx/d /au/s;qsircular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the wsp*bx z/q 3gvavhms) g/ vd/7;u;ds ;surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be l/ d-;4( oz awirqnf5e6cj4ivlaunched from the top of Mt. Everest to be pl c- je/465;v4o wdli iaz(fqnraced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orby (7ps.sxpyx *it the Moon at an s7 *spyxpx.( yaltitude 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 planet. Thte.ax(jju2: apl22 rle inner radius o2aapr2tjuel:xj 2( .l f 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 Fig. 5–9). qq.n) zgol) 74tl, mzyWhat is the ratio of a person’s apparent wei7.zlytlzoq)4,) g nmqght to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of t tsd8ip(fw)- 3sk ky2che Earth's Moon in a spacewp t ci)kf2-k d83yss( 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 consists of two stars ux 14ajhjzgnllw)9-4 of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point mid9g4 uzl1 n j4-ahljx)wway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read fotn4kh xw19t6j r the weight of a 55-kg woman in an elevator tha jx4t w9tkn16ht moves
(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 elevatp3 up4;dfe.tw2x1qz for. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude an4 d qw2fpf.xztpe ;3u1d direction)? a =   

Show that if a satellrj/pyt/gp d 9b28n *+ilam+xhite orbits very near the surface of a planet with period T , the density (mass/volume) of thy/*lr2i9 daxp +/+ mnjbtp8ghe 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 perpacidfq9 ,)z 9j3cih 7iod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth)a9 9ii7j ,3qzdhcpcf ’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun 9)n5 hhl*csb(uh4jbvlike the planets. Its period is 410 )v ch(*54bn sujlhh9bd. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average 94on7 2m sgpekfes -p5distance 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 orbit8vbt o5,t3xiu/n rei6ul c +9qs the Sun roughly once every 76 years. It comes very close to the surfaceiu95et+c,u/3ox 8bv lqinr 6 t 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 7 dsksd:e1oep qfkf5 (ob -tes jt/24*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 largesovn(v4b0vsv4m0 pw0o t moons of Jupit0(v0 bo4v0onm4 svp vwer (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 distanc 9slal3q),c dre of the Moon. 3)qalsd r, c9l   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’sc.xypn 71ra n3r 4 s+36qxubzf moons, using Kepler’s third law. Use the distance of Io and the pericr 6x1z+ xubqnaf.syn7rp 343ods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter con-)cnl cv3okxir 8 s7.nsists of many fragments (which some space scient 3 o8x.k-rin slvc7)ncists 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 tauz(kb8e +e.lu le describes an artificial "planet" 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 distanbu+ l.zeu(ke8ce (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5d, u;1i9m6 k6lmje-jgcmgy: z–41). If his arms are capable of exerting a force of 1400 N on t:e jd1gjiclg,6- 9 umzky6 mm;he 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 the acceleration of gravitg; p06i2o 6mkyipe 1,eg- tcnay be half what it is p;06g2c nt 1iiaek gp6o y-,meon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass v4e8 8e0sq/xcyfq 0kxgrab 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 eqvy08ek qxs8x0f c4 /pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparenireim u2a+)0yx4+qvshyj v+,t acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g ie+ ,yr+yi q2 sjx ah4iuv)v+0ms this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraf.)dq,h7 g xxvmt traveling directly from the Earth to the Moon experience zx v ,)mx.7qgdhero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on ax2:q9ux /(a)2hh sdtpx)ol ya bathroom scale in an elevator, it says your mass )x2 sx y9(h aop2uhqd)a:/lxtis 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 wi (z:xn;ezp)ri ll rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by th(ie:n ;r pz)zxe 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 t;p4 9bqw;s qgx)*kpsy kl3r*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 radiusbe(6 7dc acpy3 r, the acceleration dueec3 ac76yp (bd to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a tifsk18m0 9tu string) is deflected from the vertical by am 1 tkt8fs90uin 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 design sper :sstwm 8 2mnx0hd/jc2k, yg*ed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a carn:j2 w* h/ ,kxdsgmc2y8tm0sr safely handle the curve?

  How long would a day be if the Earth were rotating s:4bu.bl4 1 vgw g9d/vs*yxssko fast that objects at the equator were apb1kywl u g s94 gvds.bs*4v:/xparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant disalex:3 .kdtha q 2ox2l u2n nu0myu-0;tance 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 coe1- ad 4x 1by(zoc 0f;rrc3hkknstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out bry1 h3 k;r czkf4o1-deaxc(0 to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massiv;xzpg3j q, 6qee as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter:g3x p,z;6q jqe 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 Hubblr c.l4w)0*jzquidi+q e 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 e idu. l+jq c)r0iq4*zwscapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trave.ds x7jyh 5br4rses the hill and valley shown in Fig. 5–45. Both the hill and valley have a rax54r. hsy jd7bdius 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 Puz gs1+lw qe-m ,.-,yk)tzlxlositioning System (GPS) utilizes a group of 24 satellites orbiting 1 smu+gltz)l.,ez l-q x, kwy-the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical 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), aftera. ,f+x lm1w*a-c1 nr/- puqqfrlja 7n traveling 2.1 billion km, is meant to orbit the asteroid Erosn./f-a rum pja*c -rwq1,fx +ll1na7q 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 ibz d2ollt8*1 fn the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the safd* 12llz to8btellite (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 ; 2awl;h oz*r rr,l,xyhas a period of 3000 years. (a) What is its mean distance from the Sun?lrwz; arryl,x,o*h;2   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually u 6f9z8tl 83yxrghqx 0lz -*wkw8z9hd"feel" yourself gravitationally wwr*t 8xg96 dykf-hl38uhzxl z9qz 08 attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gama4wmu0. au n61swm2slaxy (Fig. 5-46) at a distance of about 30,000 light-years from th462w masua1s0muwmn .e 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 m on each sidvpq;v66v wpy c.r 3si 0moaq7a,)*rqae. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg maa oiq.v)v*3ay 6sc 76m,0 qvr;pqa wprss placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbaym6eny,6w tkwas4 ,7 its 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 acceleration1ec k7obk8h g: experienced by the tip of the 1.5-cm-long sweep second hand on your wrist watc7 hg c:o8kke1bh?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around /f x,p7xtmji3eb* l3 uin 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 verticf, 7mxi/33*jpbue xtl al? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a newj(q-bnlap-0 e highway is designed so that a car traveling at j--(q lbnp0ae 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 negmnpp er ,ck7k xkitu:s.4/e4(b1o5s xotiating curves. The angle of tilt is adjusted so th emu.r ie14, x7 p:ksc(npsx5otb/k4kat 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 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.$\approx$    $\times 10^2$