Sometimes people say5xib(gm,z .;di m c/gd that water is removed from clothes in a spin dryer by centrifugal force throwing the water outw gi.d(gmcmz5d,/ i ;bxard. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels ar xksw4*/r*n2t v*q qljlegj04.owb 1round a sharp curve at a constant 60 km/h as when it travels around vs.jr4/lgqrnle *t1w k*bj*x24 0 qwoa gentle curve at the same speed? Explain.

Suppose a car moves at consz5 as)uj28 w iaz0(fosw jqx-shw+ k28tant speed along a hilly road. Where does the car exer22j sa80axzo ws 5ws-(wz kquhf) +ji8t 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 a child riding a horsejo -4wa.d,rgj96c: x- hvh xta on a merry-go-round. Which of these forces provides jox9ga- r.ch-x4vt a:jhw d6,the centripetal acceleration of the child?

A bucket of water can be whirled in a verticalk7gj0x ua *um. circle without the water spilling out, even at the top of the cj*ux0m g.u 7akircle when the bucket is upside down. Explain.

How many “accelerators” dogcu5r6m m3l3qpafb g:0z vx9* you have in your car? There are at least three controls in the car whichmm g *:6lap3g509 xrqf3zv buc 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 small hill, as shown in Fig. e k xu5.t*5 +st2rhri0mt71d vvfrih -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 h0 r2r7-.shehr i vvk5tt*u1+t 5mx fidill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at (uh1rl8lyi t(high speed?

Why do airplanes bank when they turn? How would you compute the banking angle giftcp n+cgptg2 pk.k26y /1xdojh ;.:ojko2y.g:p. 1ptc/;2p dx 6kgft+honcven its speed and radius of the turn?

A girl is whirling a ball on a string gk 6t.f:) kutid+nb,qaround her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of6.iktdf :,kuq)g+n t b the string?

Does an apple exert a gravitational force on the Earth? If so, ho bt0m;tc pt3 i1xbm-a1w large a force?i0; m3 1tcxat 1bb-mtp Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, inu7cxm lp.4zh0 what ways would the Moon’s orbit bcph lz4.7u mx0e different?

Which pulls harder gravitationally, the Ear:p3b t-iw ofpynw ;9y;th on the Moon, or the Moon on the Earth? Which acc 9t onw3pfbw- ;y;p:yielerates more?

The Sun's gravitational pull on the dx. 3ks6 2blwoEarth is much larger than the Moon's. Yet the Moon's is mainly responsibbs62 d3x .kolwle 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 orcq8dl-ex6qc/ at the poles? What two effects are at work? Do they oppo dcq/x6ql8 ec-se each other?

The gravitational force on the Moon due to the Earth is onvrt f u59cn5a vbp*-j5ly about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the E9- vjt vu*nc p55bf5raarth?

Is the centripetal acceleration of Mars in ib 4mse;3gw;t l +cvk3cts orbit around the Sun larger or smaller than the centripetal acceleration of b ;ktw3 +e 4vcsl3m;cgthe Earth?

Would it require less speed to launch a sampd oecf 5hdq l1*bl3 pk1a5.ys44f2atellite (a) toward the east or (b) toward the west? Consider the Earc*dkqm. fy52pb lfao5p1es4a 3l4dh1 th’s rotation direction.

When will your apparent weight be the gl -4j9xy9hqg;l3on i3xj m g3oreatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it hx;n4j9 ml3jx3lgo -o9iyqg3be 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 cobj7g5n0 (ko* s pvl5cpuld be adversely affected by weightlessness. One way to simulate gravity is ocl50k sb7v( *jpn pg5to 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 can think of.

Explain how a runner experiences “free fall” or “appmf6se tdo36k8 arent weightlessness” betweenem36 fkd6s8o t steps.

The Earth moves faster in its orbit around the Suz pqjl,z2 vgwqt1k1xb.-2ky 2n in 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 is the tilt o tg q pb 2z.kl,2y-v12k1wxzqjf the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have xjg;jf l (, byi:+y*cwa moon. Explain ho,bjg y+(f*l;yjcxwi: w this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet t6uz+ ji- s vjkoak;b)(he Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitaa ; zsjj+u)-kbvi6 (oktional 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 1kcvfifuw; td9e0* kn7jr yp) v g.)g2+980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eart1pp-ti ,oae 8+wzf5skh in its orbit around the Sun, and the net force exerted of,ao+s5w1zpk p8- e itn the Earth. 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 on a 2.0-kg discus as it rotate h -cu-wz2 c(jww58lrv x7rgp:s uniformly in a horizontal circle (at arm’scw -wv 8ugrpx(z:7 wl2crh5j- length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km7s/ vtuxol4*h 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 gravhtx7luv/4 o*sitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of theo8f /4b.(7cgrjzs ltz acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per min8bl.tz(f s 4ojg7rz/cute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratem v f.)n2ej-rc in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. Ifjf v-mc rn2)e. 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 which a 1050- uf2uunc455pn 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 result independent of the 2uu55p nc4uf nmass of the car?   

  How large must the coefficrmi ryvwjx 8,; uit fa7443ac7ient of static friction be between the tires and the road if a car is to8ri ;j7 twx7avm4y ric,uf 3a4 round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fightetkiv 2ch4lb3 6r pilots is designed to rotate a trainee in a horizontal circle of rbcl 2v346tkih adius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotatin(.7j* 2/gzyan6ak odv/izh .a*fhg ehg turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction betweej.2ha.(7y vhihzf oen//a6*dz gk* agn the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at tc z y6,l.bhcwv m24i/cpxno b a/p.+6yhe top of ayl/n opm 2p6vw /+cb4hxia6z,bycc.. circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses th)ixz(8e ;m eboe rounded top of a hill (radius =958 boix(;zm e)e$ \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-diametera ue jp:6onk.xqg6d:0 Ferris wheel need to make for theq0d jnao:pxgk6eu6 .: passengers to 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. l/ik,(li, ep jAt the lowest point of its motion iej,i( p/ kl,lthe 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) musty o.grckc 340z,havs. a centrifuge rotate if a particle 9.00 cm from the axis of rotatico,r.h.c 0gav y34zks on is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyltp:+ b b,m4kxlindrically walled "room."l+ kmt4 xbp:,b (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 hv r107(xlx4zo ;wxz jcircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a vl4x0zj(7x1zh r; xwodangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of theb:81u26sx/ bj lu9.b rf corpy ball which revolves on a string 0.600 m long. In1:u yb9l/p8s6bbj f2r.cxruo 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 banked for a :z:ci3lagf8k s8fk b)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 gebr:vl 1) u 09quxs+-8 dcydd4g16ec2ovbml$ 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 jta,zxn/3 ymt;ddk. - maneuver 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 and centripe:g tgo.a+ed *r -q5qcztal components of the net force exerted on the car (by the ground) in Example 5rt. ez:5gqq*o ac+ dg--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 accelerates uniformly y44xia fk zx 4m.,yqyrq1fo9e,o9 ek2from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acc29r4 ozxfq i fx4 keoyy9.qkm,14a, eyeleration. 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 horizxm)r(dq bk 1nya28y)contal circle of radius 2.90 m . At a particular in 2cky)a(myqxbnr)8d1 stant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 lha 1y1k( ,velkm (2 Earth radii) above the Earth’s surface if its m la(e1 vh,lk1yass is 1350 kg.   

  At the surface of a fhjp,(.4tfo7g ajoj 4certain planet, the gravitational acceleration g has a magnitudfj7jg4of,(ao j4tp h .e 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 dub. i(g.z ,wy(xme. qvhe to gravity on the Moon. The Moon's radius is 1.74vbh..m,w.g( zix(qey $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radijsgs.xdw+3 g -us 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its sudw+-sxj gg s.3rface?   

  A hypothetical planet has a mass 1.66 times that of Eartht+9 g6lb up7xa, but the same radius. What is g near its g9+6 u7l abxtpsurface?   

  Two objects attract each other gravn0m .;hzu4 pmbitationally 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 acc09y5ikdy m6cxeleration of gravity, at (a) 3200 m m5 kd69yixyc0   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earyd3ti;x:i 3 osth where thegravitational acceleration due to the Earthy3 :3 isdx;ito is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five ti5 e)xk6.ixoq,y c.rsnmes the mass of our Sun packed into a sphere about 10 km in radius. E5xe n6 i.q) .scrxy,okstimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avera hl zo2edqz4s7bc 8:nw9+p -jpchi:7age star like our Sun but is now in the lash27 dpnzj9li4h8z:q ce+p o7:wcbas-t stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in t xs9kgh9p 1 )+ 8qzejlg3agls3he space shuttle. Your friends respond that they thought gravity was just a lot weajzle g )3k9psgxh9 3l8g+1sqaker 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 squ bn 7srt*lz1k/are of side 0.60 m. Calculate the magnitude and direction of the total gravitational force ex1tr/bln k7z s*erted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planet, 6z duvt-apul0 ucp:;s line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, p0,pduuucval: 6-z; t 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 wh5n dmjqp m-q2z e(/-n /n,pyeoat it is on Earth, and that Mars’ radius is eq( pz pn//m,d2yej5 -onmq-n3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perioc4 ,c8d(bf kbyd of the Earth and its distance from the Sun. [Note: Compare your answer t8cd4ky ,c( bbfo that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moviojh*u7 gxk )xalo9,mxtb l 8*0ng in a stable circular orbit about the Earth at a heigh*0l j) x,oxkou*bh 7lag9mtx8t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 e c. t0uh8m9. .bz-ckn2msvu mkm above the Earth. How fast must the shuttle be moving (relative to Earth) when the relea8u tnvzu-cbm 29ck.h0 esm.. mse occurs?    $\times 10^3$

  At what rate must a cylio-- dmeyxb99 q l2(ngmndrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diametero-m9-nymxgb29 lqe d( is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit th7u e4mcs2coy /e Earth in a circular “near-Earth” orbit. A /7e2u4ccy osm “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 depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launckqmw00u7y lo3hed from the top of Mt. Everest to be placed in a circular orbit3l0y7w 0uoqk m around the Earth?   

  During an Apollo lunar landing mission, the command modthy 7-m: (hhlic9z(9qizi5 tsule continued to orbit the Moon atthhs y5:(799 zqicti mzl-hi ( an 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 ice that orbit the pl7a0j 0 kzd,cfzanet. The inner radiufz7z0 kcadj0 ,s of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rxl2 xil)uibqbh*ymf* 961f ;lotates 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, an6*)1mi ubl*yxf2bix9f; lhlqd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut -c x 3lup13-g)i* ca e;9ntfkx z(mnnw4200 km from the center of the Earth's Moon in a space vehicle (;nu9aw cpxc-1miekt - )xn*g3 lf3n z(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 ots8 (i)r- virrf equal mass. They are observed to be separate )ir t(rv-8irsd by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator tha (w xt4weq02fxt moves (0xw we2fqt4 x
(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 ceilin zlluj *x-2w/zg of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s 2*j zz/lu-wxl minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet w ku*w6165n ik2okwa1-vf uc4kwnamge0p x7 ,vith period T , the denve5 w iu1*uc,a6-xnv k6n04 a kgk7mo21pwwk fsity (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**m*dzyup4+wck 8(xbb*+ oirveu bw 5 the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very neab+ u*(vi*dx8b uc*yb pwk5+ r*4mw ozer the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik3(x 4;pz(fotmj3 2tt amue7lbe the planets. Its period is 410 d. What is its me32xmol(tfejm7atz; pt3 ( 4uban distance from the Sun?    $\times 10^{11}$

  Neptune is an averagefzz9p9qgx8i rvr* 89llgl l,2mv4ve 9 distance 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 roughlym:lp l)g,w1 r32 ztbcq:k f4cx once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet fromrf ,klc cgtzb:l 2 x1wq3)pm4: 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 of1ewep9mc7euavh 1*n4 hrf: d19:w dnr 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, perij3h:a yqyo n h7py4. 08vf7otsod, and mean distance for the four largest moons of Jupiter (those discovered by Galiles jtyo.hoh:q07y7yf843pn va o 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 pyzzf9o * b0 g9svav+h2eriod and distance of the Moon. yzovgav2b +f0*s9 h 9z   $\times 10^{24}$

  Determine the mean distance from Juprac 3c*js.0e+qk,7got +qaga mf6 e3riter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Ta6arc3qgj+ gke+o3qm t0 ear7*cfs ., able 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter concoeafo28 dw*p (o1 pn:+r-qpqsists of many fragments (which some space scientists think came from a planet that once pqr o12-no8*p wqeocpa :d+(forbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a ba9zlj 70orm5 hm5f 8 wv8hly/brnd completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is alwj8r5h/mhf v8lr 07wl y9zbmo5 ays 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 vin817vvgv r r+xqe (Fig. 5–41). If his arms are capabxv 8 r1qvg+7rvle of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of ;6gbc *+4huekf;1rb-+x d hqdx0 hk vogravity be half what it is on the surfac+ d* -hvoq4xk cbh10u;6rd gehkbx+;fe?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutppx35d;q 4kkkg(f)gh ual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual massespp5k k)gh x(;f4d3gqk are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rot8 ju nzbzp )w(xrqx5uk:j*26cates once per day, the apparent acceleration of gravity at the equator is slightluz) 6w n5x:jzr 2u*qpj(bkx8cy less than it would be if 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 will a spacecraft travelingp7bpo;pdfy67fl4 .hit8d*k zjt +*.i;t n rfg directly from the Earth to the Moon experience zero net force because the Earth*dr;.4pif+jynkhob6d7z*ptf i.lg ;f8p7 tt 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 scale in an elevaw+j 4)k*scbr qtor, it says your masq rk+4j*cs)wb s is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stair- v2a.dbidqg. ;sx-tion consists of a circular tube that will rotate about its center ( i-dgi.xb. 2s-ra vqd;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 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 (Fig.crrs fl2 tizw0:ib3 qw(2 4ay* 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 rixw2wi+ n,ba/jk0nx ti ,nv8u.)e y6 mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the grav)+iun .tyninw 6 k,bx0jx2rev a8,i/ witational constant G.

A plumb bob (a mass m hanging on a string) is deflected from thep/9 pxz4nziu0 vertical by an9i0pp n/zzx 4u 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 rk.cfii -8 h,pm is banked for a design speed of If the coefficient of static friction is 0.30 (wet pi.-fh ickrp ,8avement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Ect.b1 xjq*itl vs *z)7arth were rotating so fast that objects at the equator were appaq *sti*x7)bj.1czvtl rently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a co10gf5,p7j tahv1 qbhinstant 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 la0q2awnkdwe r0zl :ts:c j88 x)( ocfh2mp susp2qwf0l ctj2o w:akr8z8(xh: ce0 ds)nended 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 has bee) bse bl) qkn(4hp9-2imh.op-ms q 3xbn claimed that a person would be crushed by the force of gmpq)23 k m-b.s(i)4xhsnbbqe9ol p -hravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deducedkwj4 5kqp9i v( o(lt8r 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 orbitikrlo9 q(5wp8(iv4jk t ng the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown v;j18jr f+lxbufaz-+tp, y) u 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+x 1yjbfjau) l-8 pv,ztrf;+u. (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 24 satellites or 6xif8 h :v2kr 9o* qno1bwq1eq,8huhzbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the 8u1 oqh,qb:xkh9nf*ev6 q82zrwhoi1 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 traveo99zbnla( lui 1 5ojx*y5p2s6nh3kq h ling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 5a shlpj352hk9 xun69 o(y *z i1qonlb$\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 e 5f;g4gq8c nbspace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radigcgb;8q ne 4f5us 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 per :e : i*e1vs3ot*cfcayiod of 3000 years. (a) What is its mean distance from the Se ::yi3c oves *aft*1cun?   
(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 td1 3p ; tn*r;wp0iaawno be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable ass;pidw nr;*atn 01pa3w umptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Garmuuc,fs cv ,5qxqn:rm4 54b2laxy (Fig. 5-46) at a distance of about 30,000 light-5cn5rm44qqu,s fbx cmu:,r 2vyears 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 0n;bg0v0c6j.k.rge q i .50 m on each side. Find the magnitude and db0envg.g 6q .ik;c j0rirection of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eaw 5hyx 659i i5e n*nnpp:2wltnrth $ \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 sweep secondwr49sxq9 ge+6iuv 7l h)gqexo.+0ktk hand on yorg ks )ivq oeh69.x+9 gt kqw47ux0le+ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circ/ 9iwe m(z+mlole below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the veoe(lm i +9w/mzrtical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travekaoqn c..d9 )xling at speeadokn9xq .).cd $ 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 tiltbj qpmc1t7k1y( s*z 1y 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 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 tr1(yc 1 *7t jqp1ymzskback 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.$\approx$    $\times 10^2$