Sometimes people say that water is removed from clothes in a spin dryer j i*fl * ntkok)a2p(m:by centrifugal force throwing the water outward. What is wrongn i) tamo(2jfp**kkl: with this statement?

Will the acceleration of a carz2 nlxa7(dn0 j be the same when the car travels around a sharp curve at a constant ldz( nnaj7 x2060 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed ac,7*kstg* eu2h:wnkk6iza *r long 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 a hill 26wtk u*i:heskkzga n*r*c7 ,?

Describe all the forces acting on a ,)e9 zb +owjxhchild riding a horse on a merry-go-round. Which of these forces wxhb jz 9o+),eprovides the centripetal acceleration of the child?

A bucket of water can be whirled in m jq-0yz*ldq3a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explq ql3jm0z d*-yain.

How many “accelerators” do you have in your car? There a r9jp2jccmd46 re at least three controls in the car whijpj24c 9mc d6rch can 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 crest of a smallj 9b)w; l.6dhpyxg1yw hill, as shown in Fig. 5–31. His sled does notp w.)ldxbhwy9yj;g1 6 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 curve at hig;e yaq.o* z9bye:y g3mh speed?

Why do airplanes bank when they turn? How would you comp zj:knn6(v t uz osi4;a9(rh-s2ux*d zute the banking angle given its speed and:nxk-dzr 2z9;s6jaothsui4nz((v * u radius of the turn?

A girl is whirling a ball on a str vk)xphks7fk*xi)z/ 9yn+*l oing 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 yarfv)n)*xy o+xz p/l7*k khsik9d. When should she let go of the string?

Does an apple exert a graub2t g cgs:q/m 80pw yp6da9;avitational force on the Earth? If so, how large a force? Considau9p :gqbcdsy8 m g /t0;w2pa6er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass xs; ubp;)zv8z2 j(93qg5vh nj vo tx-awere double what it is, in what ways would the Moon’s orbit bjx5pvs)bhxuon v92q -a(t;38 gz;zv j e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on tai1r 8*figaumn-6b-dhe Earth? Wh 1b-ua-6 fm*8igdain rich accelerates more?

The Sun's gravitational pull on the E1on odqrs;h8qsh1.l*rw. q9 oarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cd.s rqo91o. q* w1hor hs;q8nlonsider 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 effects are cg wrti ) ,dl7z a+vwvd.+2+o)ysm+efs c-h-aat work? Do --l w+ios7cvthd+s w a+.d+vymc)z)g2f er ,athey oppose each other?

The gravitational force on the Moon due to th ( au 2,p2pr,2szr l90hxd8sv 2hhdeohe Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pullel9srd8shoxeh2 h0upaz vr2,2 (2p hd, d away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lar d*wc rrc*vq6:ger or smaller than the centripetal acceleratio cr6 dwq:*vrc*n of the Earth?

Would it require less speed to launch a satellite (a) toward the east oca xhn. d4m2p0 +4x-j sl-p4ul8txg vcr (b) toward the west? Consider the Earth’su2 j cx8p-a04pvltlxgnx4 c .d-h+m4 s rotation direction.

When will your apparent weiqa9k2,q / nlxcght be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accexka9 2, /lqnqclerates 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 on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lsx dc:pr.e. hvh;po+( ong periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical src.h s:exh(pd op+;v.hell 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 gravity you can think of.

Explain how a runner experiences “free fall” or “appar1s k)j7xgp 7)88ajfnt3ymz3f vpyo1 a:o9mtrent weightlessness” between steps.jt8tf8 7ko 3y3xr)ov91m:py1a m fsj zang p)7

The Earth moves faster in its orbit arozpp 8s m/skqo, p3y36bund the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not musopsb3m,q /z6 pky p38ch 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. Ex .5; frmbvq6puplain how this discovery enaurq.p;fm bv56bled an estimate of Pluto’s mass.

  The Sun's gravitational pull on t b;:h (qsdaz(lmz7mzgx- osb,s;+ *mihe Earth is much larger than the Moon's. Yet the Moon's q*bz-sh7s+o(zm ;; :aigd z,m (lb msxis 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 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 19vh-x, l :dl 0cb6b0klg8uipb;80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eartdhrgv/sf1fkf d -8wyi 13(r c w04.dnzh in its orbit around the Sun, and the net force exerted on the Earth. W swhz/41g d-f v.y08nr ifwddr(kcf 13hat 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 as it rotates unm cs4 qf z0m y;:m71l3y:;ijfv5ifua hiformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of l:s;ji hqvu:m5cfam1;4 i zy yffm307the discus.   

  Suppose the space sh(:l erpkv-c)ji4e )uiuttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the)e-k pluer:i4 i)(cvj gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of jtj.dne5o4 s)llf:, nthe acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute5 ,tf)sj4 dnjllo.n: e) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniforz osi+r ovpkk39go2r /c*)he9 m rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5esoz 2c/giovphk *9ror)+9k3 -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 ys(:q(jkd+ u dwhich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this resul(+sdjd(u :qykt independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and w+r 5po c(: d( dr-qzo(emqwgikb+0f -the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ? r +wm( 0qf-qpkzo:(d+(r i e-5gwdboc   

  A device for training astronauts and jet fighter pilots iy j ,0)ep2wrnpxbxp+, u)nr9 js designed to rotate a trainee in a ,p0nup2e)xwrr +p bjj9 nxy),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 frof)k(wx u0w q/rm the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rwu0r(/xwk)q fate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsideip1 )fy;.jvd0x+ fcpo down at the top off +pox f1.ycv)p0;j di 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 driu6q 6l *uprr,yver) crosses the rounded top of a hill (radirulp,y *6uq 6rus =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter3g)zijw) kf ;4 k/mkt q)tx/* kexuvrh2 i3tq. Ferris wheel need to make for the passengers t*gk)wx/mh/e.rk;3vt )2t3qf uii j) 4t kzq kxo feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At th(n y do sdp-f3/cvc.;he lod.dp;-c3hv n/fys (co west point of its motion the tension 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 cm from the axi- eue02xlkt/ v3 7rymbi) 2zvas of rotation is to experience an acceleratio-ly7ark v2 u3eet)bx0i2v/zm n of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "fxe8t9*-i zjirn)qw4room."q e)jn84*t w frzi9i-x (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-ho4u8hs1-tr l yt6y1dlx tx;b6 pckey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centr4-1;6 6l8ly ds 1rxuptbttyxhal 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 o/ie0 r0/ duakdo0x8utime, by not ignoring the weight of the ball which revolves on a string 0.600 o ox/ia0edu/k rd080 um long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly bankedph)bd3wp( s .5tk6xowg3zyv . 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 massel*47b h*hcux*u k4x iqs $ 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 s v :kky/xbp2 -*bkmm5 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 components3py yk p *zry5h3eeg2g+ uwe9+ of the net force exerted on the car (by the ground) in Example 5-8 when its speed 3r 9epe3hgyuzpyg +*k2e +y5 wis 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going frojy t3 pgqkk/5:m rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be q kpk5:gy3/jtbetween the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particurvk- beu3 (r,ylar instant, its accr yev u,k(br-3eleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth radp r /,wf;t4,.ipt v/njrv/(kvgn 4 eyxii) above the Earth’s surface if its m;rr(n/xyjv i,f/n4wtet,v/ . v4gp kpass is 1350 kg.   

  At the surface of a certain planet lprj5iksgi-c)/-yv* , the gravitational acceleration g has a magnitu)-ji ly-5*vik/ cpgs rde 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 accelerationpf9q0z.e p 9pf0pcwn3ro-m i4 due to gravity on the Moon. The Moon's radius is 1.74 emncp4p-i3rq pow0z.p9f90 f $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same ml7 w u5p8mw/qi0twlc:ass. What is the acceleration due to gravity near its cp 78i/qlwtu:0wmlw5surface?   

  A hypothetical planet has a mass 1.66 tim -/o6mrj+u frees that of Earth, but the same radius. What i ruf m/-+6orjes g near its surface?   

  Two objects attract each other gravitationpn a*mz z4 imob2*:w)tally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravit8plz+bzpy60v dnmdn f2;.w8 v j;st7by, at (a) 3200 m nt;wfd b8b mvs6n2 l0+ ; zpvpj.7yz8d   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point x:ifpc hm,g 8fd,x5h- outside the Earth where thegravitational acceleration due tofp dhx,:fhm g8,-c x5i the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fitso(t: r/c* n x4k;rpqw6go8-hpk t2 ave times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface q;: (aort*rt8 tkn4wpg/k h os2x6-cp gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncegrdsvjq7 +um,k,fwg (9e 7u:x 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 surface7:m,+ g, gqrv fejs(uxkw du97 gravity on this star?    $\times 10^7$

  You are explaining why astronautsyp;sw weg ; tov5r 4:dc).jy*m feel weightless while orbiting 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 cydycw*.4v pw )sr;;tg em:5joalculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of 2 0 eivfher8kf0)l k5pside 0.60 m. Calculate the magnitude and direction of the totalepr0eh)82vlk f 5kf0 i gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of theih h /ycn9l+m7 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 planets are in a line (Fig. 5-+ 79himn yc/hl38). 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 owp,o,f * hrzm8hra 9w9f what it is on Earth, awzom 9h,r*prh a98wf,nd that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eart ha-c*hyho73ch and its distance from the Sun. [Note: Compare your answer t -hcch 7*ahoy3o that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable 8+1fe guunrph i )l6d2circular orbit about the Earth at a hedenur gi2 68h1)pufl +ight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular xte; g4t df04mkl.a1k orbit 650 km above the Earth. How fast fmt;k1 g04dxatke .4lmust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if ott1c-q7 mc tk0g)gr1 xa y3:58xa ckwnccupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.8:xct1gmw10-y rntg3 aq ac 7ck)xt5 k)   

  Determine the time it takes for a ib/ xgm dbf e)990uk:8q6omv+/zcmk esatellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth bbe/f e9ik8qmvu gx:mkc 9z/0)+6o dm” orbit is one 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 launcm+z; i q6 mrh9bopzr/r6+cslu) r/v:ched from the top of Mt. Everest to be placed in a circular orbit arovbh:pm +z6 s9/rcur+i/cz rqm6)ro ;lund the Earth?   

  During an Apollo lunar landing mission, the command module cona79qsf4 5o xjv,lj 9vy4g 3xvttinued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon a j34oglv9fs45 t,xv qv97jyxonce?    s

  The rings of Saturn are composed of chunks ofob;p2k g1-c, 0gxg0h d+tam pj ice that orbit the planet. The inner radius of +xog h2 cb-,jmpdgp1g0tk a;0the 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 rotate5z+wws e9blq.vo 2hp. s once every 15.5 s (see Fig. 5–9). What is t2hw o5 .s+p zewq.bl9vhe ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75 +vopmh ,g9wg,y))wut -kg astronaut 4200 km from the center of the Earth's Moon in a space vehi g,h wypg, )wum+tov)9cle (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 binarcwb/(ita,6 +mtlic 1jy-star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each? it( bw1c/i+,j t6mca l   $\times 10^{29}$

  What will a spring scale reap(tf u)a:h94ydy 7tvkz2c,6 rq0 byyvd for the weight of a 55-kg woman in an elevator that moves0yph(b69az2vf 4rttc7 :qdy ,u yv ky)
(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 ce, kls tt*8jwlqaq t6h3:kzxcz0,n 8l,iling of an elevator. The cord can withstand a tension ,k,h,tsk 8ztqxan3lc qtwl8 :0lzj* 6 of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period z66xv pj mu)wzjvgq )5r.50yczq;- yq T 5xc.u vjyz)q6z6)5 wv rj0q zy q;p-mg, the density (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 determm7mf)jy)u30 yx 2 wrcwine the period of an artificial satellite orbiting very near the Earth’)fy7c y w )ux32wmjmr0s surface.    s

  The asteroid Icarus, though only a few hun31pu 7 kz8jybidred meters across, orbits the Sun like the planets. Its period is 410 d. What is i pu jzk8yb371its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 kd s9ipm(if0 ($\times 10^{9} \mathrm{~km}$ 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 rou-ja;zmx i5,g tghly once every 76 years. It comes very close to the surface of the Sunx gm-;,at5ij z 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 ce 2wh7m; sc*khsnter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the foze96a-lzyzbcp 5 8)mj ur largest moons of Jupiter (those discovered by Galileo e-)mzy5 jlabcp6z 9z8in 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 distzoxd5(( oo) 8fasn*4vmz3z ayance of the Moon. dao3 5( oy(zom4*sf xzv8)azn   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, u *9lcx-nwg/y 2m6rjxt sing Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in m t2w/xc lx6*yjngr-9 the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betwe 36ahk vxvd3o*7m /wxqen Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was dda3w*36 k7vv hxxqmo /estroyed).
(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 artificif-kjfq (.d4*o:dx vp7 96csu gi ;fgbcal "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 ok *pi -gc(vu6oj q; gs4bcd7:xff.d9ff 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 v3kpi-0l2kej)g(c(u u d xiz3in 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 iijgkx)((ip u0k-v 2cu led3z3s 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 oj 0h+v hs0iz edrr:q14g)5jp pf gravity be half what it i5 )g14r0 :h 0vehdprpj+ jsiqzs on the surface?    $\times 10^6$

  On an ice rink, two skateb)d3 795c3g j)opr z2prwfvjwrs of equal mass grab 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 indiv5o wgrj7)r9w3 3 )zvfpbj2dp cidual 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 accels)c ;vou( xpo)eration of gravity at the equator is slightly less than it would be if the Earth didn’t ro) xp(o;vs cou)tate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eacqx7.afxkdgr c a :17/rth will a spacecraft traveling directly from the Earth to the/ gdfxqr1a:c.7xk7c a Moon experience zero 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 a bathroom sca7o /. 5efe64j veua zzo5q+peile in an elevator, it says your mass is 82 koezz 7ip. 4 e+uqa5/feoe 5vj6g. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of ka5;z ;t 2 i,m7e66c+qiomasgiv8agea circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effecva cs ;76gatgiz+q2e k8mi,m5ai ;o6e t 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 aircra5f w0dwo dddy.x t22icv mszf-)qo55 1ft 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/w.rz 8knk*py0 9,bmhi bjfw9 its radius r, the acceleration due to gravity at its surface ./i*0h kmj k8bfby,n wpz9r9wand the gravitational constant G.

A plumb bob (a mass m hanging on a string) ij 3onir,5h ;1 gk/sj6k4eu kqms deflected from the vertical by an an5;jj3 r6/, q4iomhnk gskuk1egle $\theta$ 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 fsh ajom+0 6+ecor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safel c+mjsho0 e6+ay handle the curve?

  How long would a day be if the Earth were rotating so fast that objectb+2 lgqc:ot 72j26cbrb h,fqecdth7 8s at the equator were appareqd2 brto2fbch gq :8hbe67+7 j2c,lc tntly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apg c69 znps4igw*iz u34art 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 l4h2 s;czkodd d ;u(be62j0 ismamp suspended from the ceiling swings o2 e4zud;0 oh (dsjmdskc6;bi2ut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. zextj p4fn+ 31Thus, 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. Uz xj +34ptnef1se 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 theyaflc2m 8jy/+ Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core tycyfa/lj+m 28 o be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown i3tv0 p,+l cifkn Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal fo30, i+cft lkpvrces 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) utilizes a group of 22 zus34qro/by qbc5jdry q )(deo e/9ap,n+c94 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be d 3yjoy5cnra(e/,ezb9b qsqpo 2udq/+94d c)retermined 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), aftnx++e2qm7 s kmpf1(e lp7- wmcer traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 kp7+qme7 em x-mc(w2n1p f k+slm . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repaxd-6niz dg cnf cn0khd0 a7t:;k,8dr8 ir. You are in a circular orbit of the s-c:nad78d 0tkr zhidc;k0n,g86 ndfx ame radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period o fv zq52wi*jljcd:u -6f 3000 years. (a) What is its mean distance from tj-f:z 5lwu *vjqd6 i2che 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+fz4k,16sxtb tw; wdu could actually "feel" yourself gravitationally attracted to someone near you. Ma;tz+b1 u xsdk tf46,wwke reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Ga*egbbc dr-03 hlaxy (Fig. 5-46) at a distance of re3 h-dgb bc*0about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on eqycz5)7 nxudvw3 c63k ach side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom 5 x3ucvnzc76 qdwy3) kside of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 55l mr,/5o2n pwpnnb 6g800 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 acceleration46s(+ f myginj experienced by the tip of the 1.5-cm-long sweep second hand on your wrist s+mg(f 4ni6yj watch?    $\times 10^{-4}$

  While fishing, you get bored and staf rd.2lf9qlc *rt to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a comple fr* lldc9.f2qte circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R sy 8 ii( o*5)( daci/hqvgfp(rin a new highway is designed so that a car traveling at speedysq)*(v(adc i/ii8f(og5r ph $ 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 Acl8e/pqb.p)dg1n 9vbonld*v4ela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less fricd9 8g /bvn1n p*el.qlod )pvb4tion 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.$\approx$    $\times 10^2$