Sometimes people say r43mzog3e ,afq)rm/c. kohy9 qcs*5b that water is removed from clothes in a spin dryer by centrifugal force throwing the water outwakq)e,crqb3 mcf.z5m / 4yags *3ohro9 rd. What is wrong with this statement?

Will the acceleration of a car *c+5+h skhts:kxg +bw be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve atsw5x *h:ksbt++ghck + the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the carybl :wz i-r59p exertzl95:rb yi-pw 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 a hill?

Describe all the forces acting on , e.5+gudz ukja child riding a horse on a merry-go-round. Which of these forces provides the centripetal accdugz .5uk+je ,eleration of the child?

A bucket of water can be whirled in a vertical circle without the watej*x,y3+vlgy77 )b*typa piji;j: ntdr spilling out, even;77d jpnt:ix yji plt,v3yg+b*y) aj* at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There arem d j90u+jv sytj/i8n; at least three controls in the car which can be used to cause the car t n j9+u0vjmi8d;t ysj/o accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as sh sy1*o n+n2ftgown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force bet2gof+s ytnn*1 ween 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 i( 4akdw q*c df1/ lgvd)w)fj.enward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking an;n4-o6 l vd 01asvmbozgle gilm0zo 6ad 4n- b;vo1svven its speed and radius of the turn?

A girl is whirling a ball on a string around her head iy:u :n17cfe,moyv zy*.mdh p- n a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the othe*nc vf pm:o .7zy,u1e:myh-ydr side of the yard. When should she let go of the string?

Does an apple exert a gravitational f2tdljbjs0ju5l e7k2: orce on the Earth? If so, how large a force? Considerj2lsjek2l :5jubd 70t an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what itbh pr,x7 bf)bk3r gyupbr; 5as 88q02z is, in what ways would the Moon’s orbit be ),bb bsr ahpr2z0yr 8; k75p3bxqfg8udifferent?

Which pulls harder gravitationally, the Earth:jevw7;5(v 4psd.ey x32*igpu cahqo on the Moon, or the Moon on the Earth? Which accelerates mh wc *4 jux2siyop(e :5q;dv.7apegv 3ore?

The Sun's gravitational pull on thek;q p)n4sax*y7 ymct : Earth is much larger than the Moon's. Yet theyx:tn*yq ps7m4;c)ka 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.]

Will an object weigh more at the equator or at the poles? aiw5rk v4 o(;(avxva/What two effects are ax(r o4/a v(v; ia5vakwt work? Do they oppose each other?

The gravitational foea12aqyu73rn0 3tu jlb6quh/ rce on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled a1 ur62t73y0auuj3qhe q nlb/away from the Earth?

Is the centripetal acceleration of Mahny k*0t as:)cah : v*8wlcq qqm.90mab- -vfbrs in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eartqc-k)s a b v: 8qa .amhwbfm :cv-ln**qt009yhh?

Would it require less speed to launch a satellite (a) tsdjq:je 2)2x7waz x)toward the east or (b) toward the west? Consider th)ad 2:sj)tzxeqx 2wj7 e Earth’s rotation direction.

When will your apparent weight be the greatest, ass- l0z 368s)mhihafku 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 cas3 sh0m kzu-fi68 l)ashe 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 could be adversely affected byxtc z0sk( 1bo:yf0.ac weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gra(yf a0s:t.k zbocx01 cvity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bl 3uxfs(hz;7w c6juc+etween ss(w7x;+3 6clhc fuuz jteps.

The Earth moves faster in its o0taq7p0vgz q9rbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July?9qq zagp07vt 0 Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known u)fo) ah x+m;en54 hwzlhf ux6e(3wa(,yimz;hntil it was discovered to have a moon. Explain how this disch ;wew; yx4ha ia3hln+oz)mm f((feuzh56) x, overy enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull o6oq*3 m6bwbmo n the Earth is much larger than the Moon's. Yet the Moon's is mainl*366 mobw oqbmy 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 the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 (jzi;qyg: grl;6fq5 prw44pu$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerat/ 29j :dubzf3 ldhhlr6ion 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 ohr fh2d lz69j:ldb/u3 rbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unif o+uvpjw23 k7x3*p mopormly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcu kx2uw pppov3+3o *7jmlate the speed of the discus.   

  Suppose the space shuttle is inc) m.ayfmejc*xtw 0+0 orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space tx)0y e 0 mjmcf*cwa+.shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a ;x is 4h:85r 9vdit*.od rawwmpotter’s wheel turning at rmavi:s4idw .x* ;o8r h9tdw545 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved acs4n) y2 l,hqpt a uniform rate in a vertical circle of radius 72.0 cm , asc,4qy)phn ls2 shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with whtqbgu.9 4 q-2rr6 pkhpich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80gk9u h tqr6p42pq.-rb? Is this result independent of the mass of the car?   

  How large must the coe (/*n2cfg osuon 9 wleml)(-t1po4rqvfficient of static friction be between the tires and the road if a car is too( lf*r(o mc -9)4 2wo/1np etsqunlgv round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts anh 5f 4nrl .de1+fhh1wfd jet fighter pilots 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 .l1rf1 5n4hhh+edwff 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 cmec,h*9w: mueb3 :43 lw zrxihl from the axis of a rotating turntable of variable speed. When th3l4: ,bih3c: zmrexle9w hw* ue speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tra*7qzk5zq me.sveling when upside down at the tqe k*z5m.7 qszop 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 k ts. a*)(0erjwav 7o-jgnoy; pg (including the driver) crosses the rounded top t7oo)jg.jps yv ;( r*eaw-0an of 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-v yb4dm7-uxr. m-diameter Ferris wheel need to make for the passengers to feel “wei 7-r 4duxyvbm.ghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cir q8j n8zxrgpu05ui x..cle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is x8np u8. zru.0xigq5j25.0 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 u4 snmj:/sfn 5ymx4laha : 3i8rtgk+)a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration m5i4 jugrf:) s8km 4alnn:/sxaty h3+of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walle970ln,tikypf n,j,jmt tbe pt4df 1:7d "room." (See Fig te 4tjpd fj0yb9,1nimt,,t7fpln7k:. 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 s6e0kc :k*:t / p jekocz78waxjl0k:1kd iu7vrotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) th0: lxe 6cv u7ajpsk1zk kcoi8kk:wt 7*/d:0je rough 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 weighbmtd :m +e qeee gzy;)7:u8re(t of the ball which revolves on a string 0.600 m long. In particular, mu:eeee d; 7(mqgrt 8:e+z )ybfind 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 bankebr*,osux r-2t0dxn 7t d for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses :ht: kckczn j.d1u2 7s$ 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 vertically at 31ne( brkd ga-760 $\mathrm{~m} / \mathrm{s}$ . 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 force exeri2jep7/ j i2agted on the car (by the ground) in Example 5-8 when its speed ispei ig/2j7ja2 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 pi4y)yq t sw(d1l8 ajhd9t 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, assuming1y (t ly8dq4)w9dsaj h constant tangential acceleration. If the curve were flat, what 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 horizontzwdwq 1o s6-+nal circle of radius 2.90 m . At a particular instant, itsd1z +qnw6-osw 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 Eart n 9u90;h0zzk)mj-r ijneb cwzt., wx7+7 shhdh’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Eh+0 z0uze njmk-. x9c,;bz7sr wn 7dt)h9wi jharth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational 6 a:kx6ajhd yoz.k1,xacceleration g has a magnitude of 11d . :hzaykk,ja 66oxx2 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 dps 2y.qek wk .iw*2bl+ue to gravity on the Moon. The Moon's radius is 1.74 eypqk*2 .i.w+bwks l2 $\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 Earthio: 2oicz6 3 yg.jot3ovv,w0 x, but has the same mass. What is the acceleration due to gravity near its surface? vw20zytj:x.vogoc 363oo i,i  

  A hypothetical planet has a mass 1.66 times that of Earth, but joiw59 0ygeg/ the same radius. What is g near its sur i95 oywe0j/ggface?   

  Two objects attract each other gba72hl;yd)tqzg6 d . uravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accelerati4 ,wji;,3br wnffq9nx on of gravity, at (a) 3200 m jr,nb3;4q,fxfn9 ww i    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cenz wck0bel6 j9a2-ez5nter to a point outside the Earth where thegravitational acceleration due toj6enl25 z-0 zwake9cb the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass oc8al3.*adjr8trc8 ur+qx pw(v, i o:sf our Sun packed into a sphere about 10 km incd3:,(au 8 rsrarv+t8w l *.xij 8ocqp radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avmx rt: (+tmke6erage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but tkem6m:x(t+r has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feem.brksg w 5,b,x 4vup0l weightless while orbiting in the space shuttle. Your friends respond that vup4 bm,5kxwrb.,g s 0they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square -.)/wsndhr /lwc eya 3of side 0.60 m. Calculateh yc3s a/wr-.w/nled ) the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Su+*1 mp - at;hd/ 8wkdn6-n+vck hqgbfan. Calculate the total force on the Earth dnp6-w/ch bad-; 1tv8 kmnq+ df hag*+kue 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 is 0.38 of what ie+n-nf6xc r1fqe)w 0rxm7 9ist is on Earix)7xwnfe+ es1nfqc0r 6- rm9th, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun j. ac rb4yyc+7using the known value for the period of the Earth an. yrb4 ccay7+jd its distance 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 stabd;q* pc syotlm17m/2rle circular orbit about the Eartl m/myr*1p2;dt c 7qosh at a height of 3600 km.    $\times 10^3$

  The space shuttle releases xmiv,2 q kpem3 4x9b2va satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when thei3xp q4mvmvx 9,k e2b2 release occurs?    $\times 10^3$

  At what rate must a cylindrical spq 66hiulx fm01aceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed l1u0fxi h q66mfor one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eaqij+ /hhe,1wr,nd 1dfrth in a circular “near-Earth” orbit. A “near-Earth” orbit is o qwh1f1njd,i/e h rd,+ne at a height above the 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 launcnxd f:fw ,wd sg3:kw)6d-5 wivhed from the top of Mt. Everest to be placed in )f:x ws -v5 w36:igkw,ddfndwa circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modts *eh5 lg5l+yule continued to orbit the Moon at antl hl +s*g55ey altitude 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 / o h *;u:/m (v8gmjjpvc.ljquice that orbit the planet. The inner radius of the u/gj mhpm j( vo.c/q8lujv:* ;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 diame:l 3 -5lf(jaxyvzmn/ tter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top5tx(- zf3a:/ ljnyvlm, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centbm ,cp ho- mmwr9:c2)xer of the Earth's Moon in a space vehicmx 2cb omc w:mph,r-9)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 system consists of two stars of equal mashht+j70fp .mvys,p +vs. They are obpmvspht 0h ,+f7 j.y+vserved 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 fo 8lvhacs01y 0lr the weight of a 55-kg woman in an elevator that moy vs8c0l1lh a0ves
(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 fp2m,*k9 w )tb luig,ca cord suspended from the 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 acceleration (mag,pulf k),*i9g2tc mb wnitude and direction)? a =   

Show that if a satellite orbits very near theq .qib-lsgclf ,7 8pp+ surface of a planet with period T , the density (p s-qpilf g .cl7,qb+8mass/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 peri e8/p1 3p tuj+yvgv7nlod of an artificial satellite orbiting v/vp+t7y ln vue8g3 pj1ery near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,/q nvv-dx( to1 orbits the Sun like the planets. Its period is 410 d. Whd n xoqvt(-1/vat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dist2 -s*qdxx4c bepo+z 8r u. hvshxe55d;ance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every s2p fs yebq fwr0 pe4)g,v:o/276 years. It comes very close to the surface of the Sun on its closest appe0yfpegw2qs2 ):so r bf4vp/ ,roach (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 tjkobzcd q4p; sp 1bb 04-dx6j(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, period,s a dsl)tdr-1(4i7zs3adp/rq and mean distance for the four largest moons of Jupiter rdr- /) sd7zisa34(a t1dlspq(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 distfm. gpakq9 alz+p,y f(sadx)q1-+ /ydance of the Moon. q pkz -df)q a++, 9.ax(m1yd/lfgyaps   $\times 10^{24}$

  Determine the mean distdoms.bv: v ov7;o/ 9lrance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tabl9;:do ov7 r/v.obsvl me.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiterx uie vg-2 5+cwa0h*ey consists of many fragments (which some space scientists think came from a planet that once orbiewu y e*v2+0gcx hi-a5ted 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/z.rb,vcd gl39n1wapf h11kv 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 distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's l /p 1ba.1kn hrf3dv,wcg vz91year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hangicjslj:omx n1qn4.(k3e *t j 7kng 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 c3(j4m qkjne*nj olck17.t :sxan 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 ofumkv7z 4 eu+)h gravity be half what it is on the surface? mhz 4e+v7k uu)   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circle2xo5m +g9hdky q 68uyzjsrc*p)da/+2tkxbb 9 once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.+mgh2as28k9 jy td)pkuq /5ycd69 r xbox+*bz0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerati auaaei.1t 60kon of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of iaatk.61eau 0 this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from thg6d )ma.t 3arje Earth to the Moon experience zero net force because the ja gmr) d.a3t6Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bifc)z tv6i wi 96ie;ckb apsfr8/;/8 vathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevato)c tfaf6iri/p8ib/cs 6w9 z8kiv ;;evr, and in which direction?     ----待选择----upwartddown 

  A projected space station consists ocseqd;e uz; 7*6q wr)xf a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle forme uqc7rw6 sqdz*);e;e xd 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 hi xocix8oa51i x h)bk1;+m2:an ohm9zis aircraft 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 radius r, the acceler4dl a+ oedq.k.ation due to gravity at its surface k.4 o d.el+adqand the gravitational constant G.

A plumb bob (a mass m hahko ;; p)jadtv;3 b,odnging on a string) is deflected from the vertical by an; )h 3dpba ,d;k;ojotv 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 desiz3+t -ps q y+ltq;gxw8gn speed of If the coefficient of static friction is 0.30 (wet pavement),yzx38+sqpt tw lq-;g + at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eartt-zmv6 a)k0 j yp:px9s98eq orh were rotating so fast that objects at the equator were apparently weighmr9ka: jo v0xpzy69)p 8q-s tetless?    $\times 10^3$s

  Two equal-mass stars maintain a constant1nn1 *-jb)q bfcx-k ix 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 curve of radius 235 m. A lalacqqqkfv;2m7b 4/6n mp suspended from the ceiling swings out to lv6a4mcnqqq 7bk f;/ 2an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. woxzi k7jz)( ten: ve;w+hl/* hgx;x- Thus, it has been claimed that a per/*:(7ej;t)vxw enlxh;-zh kgxwi o z+son 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: 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 Spacezd7q0q; irpcsyi1. ,v Telescope deduced the presence of an extremely massive core in the ;,s1idc. qvipz0ry7q distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses r yf54) r- kavdjoe+ 8t8hrqq:the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on thea r:r)hk+r8fto4-y8 jqqedv5 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 Positeozv j*vo,5 +s+c;ak nioning 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 ta+sv+5o c n,* kezjvo;he 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 (Ne g:gw4 2wcb042d 3fhuevv+ohr w1vf(EAR), after traveling 2.1 billion km, is meant to orbith+wruecg3f2w(ob2vf h vwg :1de0 v 44 the asteroid Eros 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 shuttl szlx1k2qv 9h- ebo2 ;6ndtru3e pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satelx kusth;16rqzv23ob-l2d n9 elite (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 cz,kxw, , 2u-i9cxkiu .a4svq period of 3000 years. (a) What is its mean distance from the xusk 4zwck9.x i,cu2ia, vq,- 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 wmt7v b. z j f*+.f,pme7p-ilq pw-o1jeould need to be if you could actually "feel" yourself gravitational +m pqwelj.7-t-fv b7,j.e1m zpo if*ply 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 Wj7la; csp dh ed/41tn*ay Galaxy (Fig. 5-46) at a distance of about 30,0s h14d ace*npl/;jt7 d00 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners ofm o 5v(o,4f8 gtsnqyg7j b7/eh a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a ffovom7gy 75tbqjg se 84(nh,/ifth 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 5rhf f:7v*ye 9q/oi9 .a*vtcwq 500 kg 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 experienced byfflx t2ql b4uzq(38h 6 the tip of the 1.5-cm-long sweep second hand on your wrist watch? 8x2 t6(zf 3l4q luqhfb   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aro 03tze1tuu)n6/an pcf und 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 u6znu0c) paen/ttf 13 makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hig0kg rxbp9l7j;k4e+w bhway is designed so that a car travelil brw7+kegb k40jx9;p ng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt oke+wi5rg8j( *r. hrjxf the cars when negotiating curves. The angle of tilt jr.e(r x8kwi5h jrg+* 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 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.$\approx$    $\times 10^2$