Sometimes people say that water is removed from clothes in a spin dryer bndb::z u:gc5q2ujl8 my centrifugal force throw l jzm2n:b8:ducgu:5q ing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the ctfe6*+)8rcet; c(r nty8n iypar travels around a sharp curve at a constant 60 km/h as when it travels aroundttct *ey n6+rpf 8yn)8r (cei; a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alongt/;kmx m bn+lwb6i/i. 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 th6 t/i.mlnm+bkxwib /; e bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round sn7rw9 bxb*aw0: *t0y7alroe h3 nxo1. Which ofh*o x0*wsbnraty o3 1n7e:l9 wra07bx these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in aczj4b z;b2ko3 vertical circle without the water spilling out, even at the top of the circle when the bucket is upside dobo;zj kc4zb3 2wn. Explain.

How many “accelerators” do yj0 a *1aco8rldv*kfk wj/ g0d:ou have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are theyrw ja*10l/0:gkj coa *d 8vdkf? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hiajpl;z ap0uid/**6kr ll, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force bep6;au azr/0jklpd* i*tween 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 high spe*2nx7 md )soxved?

Why do airplanes bank when qz,6 fhd0 0hl4g0rzxgtd1 rq4they turn? How would you compute the banking angle given its speed and radius of thr64gzqrxdh qf 0ltg0,z40d 1he turn?

A girl is whirling a ball on a string around her head in a horizontal p9 xyl/m9sws 15qn ibdx 7 tuwn.ki5:(glane. She wants to let go at pw57:./yblxx 9tk1sqn m g5 9 (niudiswrecisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Eartv9n82d1 uhqkn h? If so, how large a force? Cons9vud8 hq2nk1 nider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would them -9w7bsn4so q87wjkhhq0)d v Moon’s orbit be dohn4m0sww bv97qs7qk8) h-jdifferent?

Which pulls harder gravitationally, thqqybew1;kmk 1/(a bj: 73bvgz e Earth on the Moon, or the Moon on the Earth? Which jb7ea ;qw g11/:bkzqvk3 bym(accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's.x;wo+pa0tsyn oo + 3)*mwk3ke Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravmno0 ;o3pw+e)ky3a *kxts ow+ itational pull from one side of the Earth to the other.]

Will an object weigh more at th (c) qkstj r.gh6)p6 :evgq 6duyb.wu6e equator or at the poles? What two effects are at work? Do they oppose each othey.u6 (.)hc6)v6ggqq b ejkr tpdsw: 6ur?

The gravitational force on the Moon due to the Earth is only about half theg)5 vd.toqe54a yy1p j force on the Moon dvo45 j apt1.g d)eqy5yue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accel, o4vp+vjhs7 wqfi0b .6 :x53qakeob heration of Mars in its orbit around the Sun larger or smax+ vjv3h koh0q6p ieobbqw5:7a sf.,4ller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward th4 ncd06vaxm+nzk6s ;x9 .bpjce east or (b) toward the west? Consider thed+.pkcnvznj96x06 c4x;amb s Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a e ch3 +/wcxtz :r*5dppscale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at c/ptc*eh xrcz+: dw35 ponstant 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 b6ge+p sm5l2 8sbvb.c periods 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 (Figvb+eblpc .5s bm26s 8g. 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” owkp:o0ktaacr -w;s /n3(o:g rr “apparent weightlessness” between steps ww/g;0rsno-ap:to3rkc:a (k .

The Earth moves faster in its orbit around the Sun in Januaryde.1n7,n 8nxia up32 x) wpswg 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 prodi.xd7ug,na se82 xw wpn3p)1nucing 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 wasmng+b-0f /el /sg*7 qbzpv4zt discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s masp vmg nb//0 74zbqzl-g es+ft*s.

  The Sun's gravitational pull on the Earth is much larger than the jtd: 0fpz; psz 1s,e0gMoon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational p;j:pzepz 01,g dtsf 0sull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 d 0vsoqsyp:w:1 -4 seq$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earth in itsr+kox+i-iqvllx24 / q orbit around the Sun, and tq o-q/ix rvlx 4++ik2lhe net force exerted on 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 j 8g5u9f3 e6ifvj;eh k+pw8z4 xr0 bjxis exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length)3egi6b9ejx+ 0pw 8ju kvxh8zjrff 4 5; of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbirw vx)53c txg-t 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the ce c3v)w tg-xrx5ntripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of asyr 6;arvpn ,z5i zoky/)um69t7 h p4f potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 ar )6 p4i vr6uohk/s9yzy7z pm;,5nf tcm?   

  A ball on the end of a string is revolved at a unif qd 57p/w8 lgdr0(msrrorm rate in a vertical circle of radius 72.0 cm , as rpd rl 8s5m/d7wg0( qrshown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can ro/ r56h9guj)otz f5jf 6r0o55(mieoijj t p)chund a turn of radius 77 m e 5t6j5/fhz655)jjcjhoo mg ui9t0fro)(rip on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be bet,rx x/wz3.2c pm6mee wween the tires and the road if a car is to round a level curve of radius 85 m at a ser/ze p,xcw362mw.x mpeed of 95km/h ?   

  A device for training astron(27 atdy,fbd6bg9g lgp1u( u nauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the t, gd 27 tg961(duf y(npbblugarainee 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 rotating turntab1h z l-j,.oivh)jp3t-b sr+acle 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 reacj hjh1l+- ,3 a)sbzro.p iv-tched and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a ro.4:/sgwp9uzcq p9n roller coaster be traveling when upside down at the top of a ci9/scpq.ug n:w4r9 oz prcle
(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 (includingf+c/ s nn(cfi9 the driver) crosses the rounded top of a hill (radius+fc n c9f/n(is =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 Fe9y 7cwh3hrqqmvt6) l34)ut c iq,k:bs rris wheel need to make for the passqh)lrchb9qs,67tc iy)4tuk: 33 wmvqengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ve5tbk os8wpm 1: ipy-8nrtical circle of radius 1.10 m. At the lowest point of its motion t5mpb iks8:1tyw8np -ohe 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 cau /wd1+3t hudbhx( u6entrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an6h+duu1 w3dtbu /hxa( acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrk2 huyko)a/ j1ically walled "room." (See Fig. 5-3/1k y2ah)k oju5.)
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-hockey ta.:5cme y dlo4gbletop, and is held in thisyo .l4:5c edmg orbit by a light cord connected to a dangling 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 qwopcj,2hl ., of the ball which revolves on a string 0.600 m long. In pjwq,c .lo2, hparticular, 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 banked0l i/lzvlme sd3-2gr. 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 massesy9tqo sng8q 1e a2/uz.mx8 uq7 $ 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 ia+ vs*o v/gkluqz 8(-;tke v5y+ut-emaneuver 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 cen+)3wfoa1 ut yqgmfk)( tripetal components of the net force exerted on the car (by the gkmg1+ ) au(w yqt3fof)round) in Example 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 50q (b,i3w,k7rfxj wf5i0 accelerates uniformly from 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 acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road tfjk(xf b,q75wiwi3,r o provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 -u;(eq.zprc/r( p( eul;os; kju8 spqm . At a particular instant, ioq-pepru((s/u(sc;je p8 kl.rz;;u qts 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 f havfck1bm(f31n ;-d km (2 Earth radii) above the Earth’s surface if its mass mf1hkvf1;3cd a nbf(-is 1350 kg.   

  At the surface of a certaiu a7jt x)pk6,oa, 2jncn planet, the gravitational acceleration g has a magnitude of 12 m/72)cun,at x koa6j,pjs$^2$ 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 gra;cgsr l7crmw:v 78ivf4:aepkjq 2z( x 7zx(.yvity on the Moon. The Moon's radius is 1.7 j :pmq;72xarrkvsel fci.z y8:z(c7 47g xwv(4 $\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 Earl454f2g ly pauth, but has the same mass. What is the acceleration due to gra5laf l4u42gy pvity near its surface?   

  A hypothetical planet has a mass 1.h c)ont)3pyb+ 66 times that of Earth, but the same radius. W)hy +3cobnp) that is g near its surface?   

  Two objects attract each other gravitationally with a force byq(o1d-/wbknaiosw n nt)-a:h46d3r nn u48 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 gysc6:c0az 5)6 gtfhyv , the acceleration of gravity, at (a) 3200 mc)g60hca fysv y: t65z    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cente2eg)9.(l nptrw,uip4 gbix1 z:b rc,gr to a point outside the Earth where thegravitational acceleration dueb(x ug gwp:, r ,1l z.egi)2cnir4pt9b to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ou9i32g re dsqp7pl:x g5tsc++cw. (vk/le uwa3r Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on3g sw3l w: i5a /cl ruc( eqste+.pg97d+pvxk2 this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is*4mz2 sj.na 2hhtg-cu now in gt.22*hzuj -nah msc4 the last 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 the space s5l;1bcf v1v hrhuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface vvrfb 11h;cl5in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. ai;j hosm 67sh)2g o+.c-jfrqm2a t c4Calculate the mj-o6 )rhsit7hc2oa.;g+q2a4smc fj magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most oh816l8owsom0 tj mab 5f the 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 at05mw6jo8h1 lbao m8s re 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 gravb-h0w0 ;9ogcpdz*qu o ity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radi-ou;pczgod* b0 qw0h9us is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usib3 1p(x3*sg xvmg7i9i8 ac imzng the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawc mixx9pb(s 7i13 gamz 3vg8*is, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stabw 8+hnehwjvfym d--++ le circular orbit about the Eartn8hv+ + fwdehw y+-mj-h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orth6.uru/v(sj/b mtg4g/ shb (d, if:qbit 650 km above the Earth. How fast must the shuttle be movi:rqgd/bu h(,j(mu4 sbsht.i g/6tf v/ng (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylin9b 1ufg(: ti0;2e x:kcde ftlkdrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5due1 ec:tk lb;f92:k(f0igx t –32.)   

  Determine the time iercfq o-u6 i)2t 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 squ)2ir -6of cemall 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 launched from the top3m*rv803ia)9,o0 w/paa mjnpwzq f ld of Mt. Everest to be placed in a circular orbit around the E)3lfmpaazm8,vwj30/inawrd9 q o *p0arth?   

  During an Apollo lunar landing mission, the command mocs1g:-dn enacsw6 : 5pdule continued to orbit the Moon at an altitude of aboc1can -:s:g 56wed psnut 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 orp +v6-zbiki+ gbit the planet. The inner radius of the rings is 7b -iz6vkpg+i +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 onceu:edp-m u 5x8)vr 6,ebfrkup- every 15.5 s (see Fig. 5–9). What is the ratio of a person’s k:pum d -ex8 brp,)-e6 f5vuurapparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fri fv(8u)un*j7 avo3 rw nmn7n. mavt9-om the center of the Earth's Moon in a space *vjv9m tnv(n-u oinfw7rn.am3)7a u8vehicle (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 )h c ui fkpp,+)*nqtg2kp,(vukl ;rp5of equal mass. They are ohip,p2(g*up))clkt+n,r5fvk u kq ;pbserved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an el pxe)f;:--rwov waax/o7 ijh 1evator that moves ia/a-7 o fjw evo)p;xwxr:1h-
(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 susev9-mthc)1xm r14xj mpended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accel x 1h-1cxjmem)vmtr4 9eration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface omdxr 8 ;.ymav+f a planet with period T , the de dary8.x m+;vmnsity (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 determine x6v:y u2q,mc(pvj)z e the period of an artificial satellite orbiting very near the Earth’syz:jmxpe,cv qv u2 6)( surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits x) 3 oyib 2tzqyw,0ja0ir+j(h the Sun like the planets. Its period is 410 d. What is its mean dishyi )0ziwqr o b,jajx0+2t3y(tance from the Sun?    $\times 10^{11}$

  Neptune is an average distand0+-/a i oslb05z*h wm. sliyqce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 yepp 7sfkdcp40xm 3ww7fim*+ i yct)/6zars. It comes very close to 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 the nearest and 6m)if0xz*wkypc47psf m ctp 7/3w+id farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cent e 3hu+ihpegs-2d0hz8er 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, andh56/qu/w imuq1s gpuxy)t lvf ;or51 5 mean distance for the four largest moons of Jupiter (those discovered by Galilltq5qymvog1puu/ ;55s)xf uw6 h/ir 1eo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distancayr fhffmr;9o6ozsti n b ./+9:(h(obe of the Moon. /o+9 f9zbr.t;6 hbh( yion: aoff(sr m   $\times 10^{24}$

  Determine the mean distance hym9 qhgg7m.)nd/ ea8from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the n)ea8q ghdyhm7 gm9./ 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 consists of many frag qbbyg-ye2d0 , 6dd3dpments (which some space scientistsq,be yygd3p dd6db- 20 think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "plan xjkhb7( ns+c0+ :fvecet" 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 ourj+x0 (b:kcsnve 7c+fh 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 7*)69sbq ednf9:- 2vpem,fziw xahci in 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 is the maxi :) w-*z pfebqxeas6mn ,2v fc97hd9iimum 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 gravity be half7 goiwfh;(.eo what it is on the surfhifo( ;o7 ew.gace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and mrxp8( tln 41 nxt8rfgu*90n lspin in a mutual circle once every 2.5 s. If we assume their armp *m(ngxl4x1t8n8t r rf 0u9nls 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 of gravity atswr 4:i ;nj u91m(wjoc the equator is slightly less than it wouldij n1 9s:j wr4;oucwm( 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 spacecraf(9-e gczvvr6 nt traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite foc-g9 6en(vvrz rces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in 0 mj bbtdt q0(t-a6df:an elevator, it says your mass is 82 kg. What is the acceleration t6bj:b -d0q ta0( mfdtof the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate 7s67q/-6mjc 6s uzyaj/im,gpc mi, qq 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 mqcqm6ui/- s, i ,7sq m6zgjjpca /6y7must 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 lo5zu9:mn,/hc q*s xd w,chzk5lop (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 term6na*c;ljze hqz0) ,(mp1 wuefs of its radius r, the acceleratiolp6 (w;emuj n z*qfa hcz0e,1)n due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticy*1fq.zp. *b rlth:nyf j e9:val by an angle 9qne 1: *bzt.j l*yfp:v. fyhr$\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design s/a,z 0pnxtd2rjpq+ m;peed of If the coefficient of static fj+np,z x0ap 2 /m;dtrqriction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotamuw9y5jksy nax 9/ t9wp9 58woting so fast that objects at the equator were apparently9spj9 95owt wam y9xw 5nk8/yu weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance ape h5,est;u ux0az r)t2g*t j1hg,c0 itart 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-g-5c 9k0z yn;ekag jb 235 m. A lamp suspended fr ebcy-a9gng;j0z- 5k kom 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 .5 2p v.kyzhufmassive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter sfz.phuyk.25 v ince 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 ii.2tx .x/6/rixo elq 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 me ixx/. qt/6r2oxi.il easuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the huhx0 g-*.e 9h;o lnk0hsih(:fnt xzy(ill and valley shown in Fig. 5–45. Both the hill and valley hav hxni0k9x l.-( ey zh fhsut(oh*n0;:ge 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 can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utili -.fp(p7vj3 (jnme 1ubuv4 zl,tn1pjhcy; j b/zes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately ;z.b fj-p7(p uv bty4ue( j1l3/1p h cmjjv,nn11,000 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 tr1-azlbe is te 72yf74paveling 2.1 billion km, is meant to orbit the asteroid Eros at ae lats77 z1ef2y-4bi p 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 a satellibz7 e;k:gpno0 3:fp8,n ja ibpte in need of repair. You are in a circular orbit of the same radius as the satellite (400 ,eg8ijp3n : o;7 ppa nfz0bb:kkm 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 meankc1(:e2zdb zo* lx+o n distance from thz:1xk do2 * lceo(bzn+e 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 o:0dxx0/ip s .-ypya(f/hyo raf G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like :xy- r i. xdh//aa(y0 ppyofs0F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (F7zg0-cn,cb s ) r,ovp :70ivyp3rhasjig. 5-46) at a distance of about 30,000 light-yearsp-vby:szi vah 0o)p7, jg3ccr ,n70rs 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 a wc7y7bai10r.gjv3lz .ydqj 2re located at the corners of a square 0.50 m on each side. Find the magnitude an7zb0l1cjad2. ji7gywq r3 .v yd direction 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 Eagp wxek,k; /h)rth $ \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 exper*iyfb 8d0oif,um ,g7oienced by the tip of the 1.5-cm-long sweep second hand on8 bdo*m,0uyif7,go i f your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cg ) f1w5dh(xgcircle below you on a 0.25-m piece of fishing line. The weight makes a complefdw) (ghc x15gte 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 e2ijl6rrius,x1 ic,7/0 p5zegeo+ udis designed so that a car traveling at speedi5207re zuo i1jx6sug pd/,ce,r le i+ $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negk8w-nt(k o5 xqlvvb4fp v(8lfetj* 37otiating curve8 nq kjef-vt owp3l( v5(87ktxl*vfb4 s. 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 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.$\approx$    $\times 10^2$