Sometimes people say that water is removed from clothes in a spin dryra w ekskcnf83-,:lf.er by centrifugal force throwing the water outward. What :3 -a8l ffnsc.rek,wkis wrong with this statement?

Will the acceleration of a 2+ uux 2u*pn;70ttsj4szsoyjcar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around auxz0nsjy*s + t2u7p;42s jotu gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car ex8 wc73ciwk ws9ert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two c8ciwwk 7w9s3hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Waw (f,:qqz d25+nsjfa+;xie nhich of these szn;,:nwadfji5f2e qx +aq+ (forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical 8zj2k)3gzgw5eih 4vkn+uca - circle without the water spilling out, even at the top of the circle when the bucket is upsid8w i gnch32k v+ug)-ej5kz4aze down. Explain.

How many “accelerators” do you have in your car? There are at l-mxo:;u b )wc0dbnqjzw+wbu1,f ud .* east three controls in the car which can be used to caus w nmz,f uoq) .b-wdxjb1c +ubu*;w:d0e the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crapnp,7(w* rzp cv.(v f b14-wkh *ztmzest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this dem.,brtkzw(1fp7vn-* avzpcp zh 4*(wcrease using Newton’s second law.

Why do bicycle riders leax5 hieihx;m :(n inward when rounding a curve at high speed?

Why do airplanes bank when they turn? H3 s9 wb8v,odtyow would you compute the banking angle given its speed and radius bo3s y t,8d9wvof the turn?

A girl is whirling a ball on a string around her head in a horizontald4g *lnk59 lepe wk2givi0e) dx.fy5, 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 yav ixy,l*n dl ekfpe5gw5k209 4)i.gderd. When should she let go of the string?

Does an apple exert a gravitational force on the Earx(lel hi. wby2ad6/x0th? If so, how large a force? Consider an ad0yhl6bix.x l 2/aw (epple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways w k ,xqnr.f5jvrje;9 8 elm0mu3ould the Moon’s orbit be difqm,3v8f;u .j lrnj059 xkerme ferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thd fuyjr6vz+r 0ymi*)qt8f( n-e Earth? Which acce (yz0+-r)qtyr djmv6in*fu8f lerates more?

The Sun's gravitational pull on the Earth is much larger than the Mooa *-y/f)avbne n's. Yet the Moon's is mainly responsible for the te *ba )yvan-f/ides. 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 pol2n 3 75xbvj +s5io5r y:uygtcfes? What two effects are at work? Do they oppovryybonif5+xg3 2 ju5s5 :c7tse each other?

The gravitational force on the Moon duejq 32guf88fo .rojo)a to the Earth is only about half the force on th .f3f 88j2ougr oja)oqe Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acce fmj.)a -+(f o/ki(krzmb3kvmleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth(oz3j. m/ik (f)-f rbv+ kammk?

Would it require less speed to launch a sate*) bh 8an(oesbc h/ ;fa n4ymr6hg*6ttllite (a) toward the east or (b) toward the west6g btt;6 n *)8ohc asr4y*nfba(hhme/? Consider the Earth’s rotation direction.

When will your apparenqz/7fav 51:l qswzv(:i6m ppl2cub6b3nbc.h t weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) i(pzvln : c pw u6fh17mic:bvq6.a 2z5bsb ql3/s 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 long h - om47v 3ms,z6nycqcperiods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you -4v hzy3n,ccmsq6 om7 can think of.

Explain how a runner experiences “free .d+ bp +fb(jubfall” or “apparent weightlessness” between s(p .buf+ jdb+bteps.

The Earth moves faster in its orbit around the Sun in xr -yky6(crb1wxsog -, tb:m: January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor :sr,btrxy(-k 6owb:mc-xg 1yis the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until hd18me,ng 3utk(v cu w9k6w(dit was discovered to have a moon. Explain how this discovery gtdk8( h3 cwew9d,nu(m kvu61 enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Ye)hms l(da-9ls t 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 the center of a merry-go-round moves with a speed of 1.2s)-m(sh adll 95 $\mathrm{~m} / \mathrm{s}$ . 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 7+4pf e0kzxt innd9; 1xxf(rhy54y sr$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 w2+67u( fvpmovvt0t lion of the Earth in its orbit around the Sun, and the net force exerted on the Eartm7(v+u6 owvt 0vlp2fth. What 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 ivn8/ vym+o 07o ccuo* 4xw2rwz/6ht fon a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate czwfm *oo02o xt/r/8 4u ychi6+ vv7nwthe speed of the discus.   

  Suppose the space shuttle is in orbisvuml3;fcx hu w2k ko +gu-5zl,6z7r)t 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 lclkfm ; us,z25ok6z-hv)3g 7 u+ux wr, the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of c(si 6l/ dj6.x/znhp phlay on the edge of a potter’s wheel 6j6ds .n (xph//zphliturning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a zhs9 g;sw glres:nnkvk3 9+(. vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4 kw k s:(g;.rzen9g hvn3sl+s9.00 $\mathrm{~m} / \mathrm{s}$ 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 2 -fpcx 5rpldhf;4p ;gspeed with which 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 ;p 4fg2pfrdpxh c5;l-result independent of the mass of the car?   

  How large must the coefficient of static friction be bet34 (axwf(o t*sjej:z zween the tires and the road if a car is to round a le(z(a zj4te wox*s:j3 fvel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is del)6;*r) .e;yen kxdk rwmg*iv signed 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 k;ril)6 e .*keg)my;vr nxw*dher own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the z7*5 -dlklrueaxis of a rotating turntable of variable speed. When the speed of the turntable is slo zk*-u5edr 7llwly 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 traveling when upside down at muh6vps)8e4b1f bzj ;ktld /k -)vr2sthe top of a circle vdesblr8h;k-6kmj4z1up 2b s/tvf) )
(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 (inclj nt b,v 4,:(ok:ndjig :q.xuhuding the driver) crosses the rounded top ox.uih j(:d4 og,qv: ,nnbtjk: f a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to make t;u*ju lj r.kgcro,.; for the passengers to feel “weigh;urlugjt., o;j k*rc .tless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in em2kt;.3x+ o -jeb.-fr el 4krlr.ctj a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in t;-kx.c4j rtekjb m-l rrle . +2eo.3fthe 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 centr;ss7g( etixwd m/-9wyvf zqw)c 7-pw6ifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 7i;97c (gqmsw) -wdpsxyw- /v6 tfzwe115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c.k;2ws b avru;ylindrically walled "room." (Seksbavrwu;2. ; e 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 circlez5 ,x jys*ucuao 21y6c on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5- c,15 ucoj*yzy6u2asx
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, bydgj t z r+2g0bpa(u.7m not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, fgtduz2 .prjg7+(b a0m ind the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car tncok8d4ol- * oraveling 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 massen93a + o;djnrvs $ 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 maneuverambr.88 ar-dux cd ;p3 by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential h ce24q0k bkh(and centripetal components of the net force exerted on the car (by the ground) in Examk24 (c k0qehbhple 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerqwq2-36xkfrb e3ekxd2p- 3w iates uniformly from the pit area, going from rest to 320km/h in a semicircularq-p2 i3x fd2b -3xke ewkqw36r 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 between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a :dukkh af3 /y+horizontal circle of radius 2.90 m . At a particular instant, its ac y:d+ akkh3fu/celeration 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 gz-3dy 6a3zqndhl/ ,hmil7u5 dravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kh ,/d3 q z-h5 6mnily7dudla3zg.   

  At the surface of a certain planet, the gravitv2nrjhi2o*qc- h2 to :ational acceleration g has a magnitu2oiq-vh r2hn2 o jc:*tde of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is ho nn+/v.jht3 1.74 +jo/ hhn3 tn.v$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tim. 1jw xesd;/5qsamnr9es that of Earth, but has the same mass. What is the acceleration due e /xdq9mws j1a;r.ns 5to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the8j0rixwu w r,tjp 5+sd p6)+.klftc;b same radius. What is g near its surfa ;lr6pusbj cpw0+xwtf j)di+ k5 ,.tr8ce?   

  Two objects attract each other gravitationally with a force ofvhje0 i *pak6he86 x8n 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 irms0h5j21 1krmt7m lg , the acceleration of gravity, at (a) 3200 mrlm1 stkm210m5 h7rij    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center 7vglr 8:;nxc0u*+yy bvh tu x q(o6h:dto a point outside the Earth where thegravitational acceleration due to the Earth is x6g(8hq*bd:t h0uv 7;l nx: u +vycory$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pack15yu x+jjr ;+,vc-+gleherd, zq:vz7f3mp j ged into a sphere about 10 km in radius. Estimate the surfamhqf-zg+u;zj +x7 prv 13cel ,d5+ vr:g, yjejce gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wvrigv8 6as53db 6al :das 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 mairald : gv5 sva3b86d6ss 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 spaceoq;7k1uu hqm ;7gpe 9a shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself tkq17age 7up;omu9qh ;hat 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 atnj14 l 52;omvjxi6xzq the corners of a square of side 0.60 m. Calculate 1 jnqz4vml5xi2jo6;xthe 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 year0f bo: bpgkcb)n*/ib 6dz. 4qhs most of the planets line up on the same side of the Sun. Calculate the total force on the Earthqf pc.bdb ogn)*hb04 zb6i: k/ due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of graviid gke54c)( gxty at the surface of Mars is 0.38 of what it is on Earth, and that Marski45(cgd)ex g ’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the p2kfu a7 pm,dv7uhz0h3)kkt: xeriod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s la370km7htazhk ,ku:pvx2)u df ws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed on9*q;fwi0sahj6+gl+ nxxq0 p f a satellite moving in a stable circular orbit about the Earlxsg qq 6+00h *9n;pxfnj+waith at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite inr 8i p1qda9d,rjfl j93to a circular orbit 650 km above the Earth. How fast must the shuttle brpldj, 39aji d91rfq 8e moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyl9p ivg47ntq8 qindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spacevi8qg47nt q9pship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time itpuy4 a 57x, kpystcf(:svman 4ib9m.) takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depen4svk ba)s,cx yu.fm( 57pymit:a9n p 4d on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the t)s/cpbpg 9hm2j r pqz1-t)* rtop of Mt. Evetq)jcgh /p*-bt) 21ppr msr9zrest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing v3/vy uimfg. s5b)n(v mission, the command module continued to orbit th(. 5 unf)v3gmb/vyisve Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn d2am fb0jq46ft d1-* clp tl*dare composed of chunks of ice that orbit the planet. The inner radius of the rings is 7j2q4t6 -dac1 tmlfd0p b*dlf *3,000 $\mathrm{~km}$ , 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 o:w iqdp*.wb *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 top, and (b)dq**wo: w.ibp at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from th6fr 0 0b:chluesxm9h.) *igk ce center of the Earth's Moon in a space vehicle (a) movin: 0eu6x0bf9cgc.s)rhlkh m*i g 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 *8z.h -vxdkposystem 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 poinhvzpd-x*8 k.o t midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read obs6m-7ty:c efor the weight of a 55-kg woman in an elevator that moves :7oem y-6sctb
(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 m+*(j;9mjic w7bgtpw;ynx+i/ v/(pi eg 7gt v 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 (magnitude; +pni//t mc g7b+pjgtje( i*wxv9wmv;( i7 gy and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period Tb*wz,7e-kmmg,4 whf u , t4b kfew-g ,huw7, *mmzhe 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 hefi)m,ag+ln7*j ,.yp -q f fmthe Moon (27.4 d) to determine the period of an artificial satelli pmhyg7m -jnf.la)ifeq*,, +fte orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acros/2a8oq,axy) t yiau5 as, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from tho,i au2aq y)xyaa8 t5/e Sun?    $\times 10^{11}$

  Neptune is an average distance of uhvr.+5 /aw vmgr6at/ 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 76 years. It comes very close tm ojmgpc4pj8z:2oa 9, h:zu 9yo the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of t9jz9oo 8m mch2 :p,j4yupzga:he nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the iskeuk+e r8,;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 largest moons e, u4r- k;sea/ k,qier21l ggvs+u8lj of Jupiter (those discovered by Galileo ilkeg-lv;s 4 i arq k/s2ge8 ,ruj,u+1en 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 disy05/pk;n 0ckr 5o yexttance of the Moon. p5; yk5n kc/etx0o0 yr   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’sux m2nik,q2mke.eh oj+:5k5 b moons, using Kepler’s third law. Use the distance of j 5o2enih ubkm+q5 ,2.kkxme:Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Marsp) qf0(liwu k/ and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed). p/w k(q)u0 fli
(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 d,(632z-;ebdsz ;pput nyax kaescribes an artificial "planet" in the form of a band comple -3aspa y e,n2;bupdkxt6(zz; tely 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 year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging viu1ap vqfmsvw65 (0 xt,ne (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate atfw61a(vpxqts,u0m 5 v the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Eam, mkmwsz;f ld1;s+ -w9o9nhb rth’s surface will the acceleration of gravity be half what it is on the suw 9dn,sz;1-;9ol+ f wmhkbmsm rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mut4,w kmmbl5) qgpma 5)z.d06wkis2roiual circle once every 2 bi l))50z5a.wmk6isdommqwr4g2 kp , .5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of21vv cke;z9 s,ymh .wz gravity at the equator is slightly less than it would be ism 1wv ezkzy9;,2vhc.f the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will8y+5 0+ c6qeap.p8gmhd t7et/rkwyhuawj; * p a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pullehwc/7 y.6hwrjge8 t*; a +dp ppum085k+tyaq with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathr(6 ljevyg f,htwrrg-*i v)15doom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator -)j 5r1 erdt6 ,vghf(l*vwiyg, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatcop 4noem845gp3 1r nxe about its center (like a tubular bic5gx c nrpp4m 84o31noeycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig8yqk6dg7z z;spnc 4 o2. 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, thp/4sje ++u 8xy8zwyxte acceleration due to grayw8z8pye+ tsj xux+4/vity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vert7fvfsu2/ b i7fical by an a7b 7/s 2vffifungle $\theta$ 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 3j:ys bj9f8jmbanked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handlyj:39m b8j fsje the curve?

  How long would a day be if the Earth were rotating so fas1w7fcpek+49 yglpp 8c t that objects at the equator were apparently +4gp e7c9 l8c w1pfpykweightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 p-mhz6t o7x7o0d19tf -ofjhi 5xp 6ub$\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 constar-f7yf:q /ouynt speed rounds a curve of radius 235 m. A lamp suspef: uyoyr/ f7q-nded from the ceiling swings out 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. Thus, it ha032/,)/t dvnwixcl kpcfz .ue s 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 i/z3l2/ec dcwx. u)vft k,np0planet. 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 Hubble5j*zzrt(+dd :r)zyu.( x0uc haf m y4x 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 escap4myczjz5 dxrh(*f:.u0+ yz trda(x u)es). 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 iyyg1 d m1do.8xt traverses 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 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 c1 gyxmd18y .doan the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelliteea a c9pude*qpq;g:-okxd )4r 6 2og8es orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the pe -c92;q ep68)eadax:kpq*rug4oo g dosition of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, ih47mdiqotvlt /)u,a l1 xz, n(s meant to orbit then ,7 tmt4ho/x)qzla(1,v liud 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 shuttle pursuing 1g77n - 9ghndl8. dmzzgfkei8 a satellite in need of repair.edzlgh -ggm 7719ni8nkf.z8 d You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distan*iv;m0rc a e5hce from the Sun?ec avh rmi5*0;   
(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;s;m,k 2aovnz would need to be if you could actually "feel" yourself gravitationally attracted to someone near you.;o kmzv,n2 sa; Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5--h; r4bb hu;gu46) at a distance of about 30,000 light-years from the center-gbh uru4;bh ; $ \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 ofy;b;k4fia+pim d12e r a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg massk;ri1pe ayd 2;4im+bf placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500z zcvscu/g*e m+b6a8. 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 by the tip of the 1.5-cm-long s2c1q,kg 2 zlf k1jog;nweep second hand on your wrist watch1kzc,gl2jg1o 2k;qf n?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a ci1w(zwuftj;8jp 2w8 sb 7,ylbcrcle below you on a 0.25-m piece of fishing line. The weight makes(8j28fwp uw c7 ,bw;1ljsytz b a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway i pg,, ohrd1gpnkc6b3 .s designed so that a car traveling at1pcb, 6hog .rdp3gk, n 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 wr vmard l o.4a:9h)6arhen negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a6:arl rr.hd49)ma ov 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.$\approx$    $\times 10^2$