Sometimes people say u 8ndx4 9z/dqcthat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What8cdz/u 9 dx4qn is wrong with this statement?

Will the acceleration of a c: 3h3, ;04yvo)5ab zcvxr1epbqo lai tar be the same when the car travels around a sharp curve at a constant 60 km/h 3lcqpy)bo1i3a54 r t,; 0:ovvxezha bas when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at consta uag)0wub,7m, nvks2i16rvya8prb d 2nt speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a h2ks mv 6b8nwdvbr aip1,)7uy,20arugill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forcj6k4jan g a3i6s*1phfwe ku87cgrn+1es acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal7*rc6eaks 3i4+pgk wjg1un hj6afn8 1 acceleration of the child?

A bucket of water can be whirled in a vertical cipcvy20 se9m+ y6ngo. y2l,y dg7np7hcrcle without the water spilling out, even at the top of the circle when the bu 2g y 7y+6.sccnm,ppeh97l2vogydy0n cket is upside down. Explain.

How many “accelerators” do you havt:xc;m) u af8pe in your car? There are at least three controls in thet; a:cpx )u8mf car which 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, axytyv1x ,w65 is 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 decrease using Newton’s second lxyv 1,wit6x5yaw.

Why do bicycle riders lean inward when rounding a curve at hn1.f-rl0e5i4t *l-xex4j r hjpmvpe/m u : u)gigh speed?

Why do airplanes bank when they turn? How would you compute the banking angle giz200+m;pnkbna k6)ic.jlqnjz7 7ufq ven its speed and radius of t6nunqk7;fi2 zj0q.)0b mn a+pc z kj7lhe turn?

A girl is whirling a ball on a string around her head in a horizontal pld0d-tpm x. s4bane. Sheb.mp 4 d-0sdtx 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 of the string?

Does an apple exert a gravitational force on the Earth? Iftmf*a/6;z7 u hbfa ,l,glr.as so, how large a force? Consider an apf7mz*a6l,;r fsl gaubtha. , /ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what sv:ix 9-8, ppq vrhpxs+5wo +;-afz boways would the Moon’s orbit be differentvs8ax - xw-hrs;qppzpo+o +fb:95, iv ?

Which pulls harder gravitationally, the E:6ogmyfoj:z q bm9+(n6fmzw6arth on the Moon, or the Moon on the Earth? Which accelerates more:nm q m bzw y(o66fojgmf:6+9z?

The Sun's gravitational pull on the tdols33+()ikzklu/x48b0gd pxse x; Earth is much larger than the Moon's. Yet 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 ot xk de3)u8ob4lgisd( +x/ tkzls;0 x3pher.]

Will an object weigh more at the equator ncq1i6kqk0* 4sjxgjb9 au6 .aor at the poles? What two effects are at work? Do they oppose each other.ix 0n* caj 1q6 quajs69kbk4g?

The gravitational force on the Moon due6oka j093llhf to the Earth is only about half the force on the Moon hj3 ok9l0laf6 due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around thaglg(t2*9a0pn h q kr0xmi9c/ e Sun larger or smaller than the centripnc9g2*mhi9k (a qxp0 l /rtag0etal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) tomxa5mz;9 (g zvward the west? Consavmzx(;z5 9g mider the Earth’s rotation direction.

When will your apparent weighm2ohnp c)) p6ct be the greatest, 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 constap6ohmc) cn2p) nt 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 periods in outer space could be adversel+sqx 0*zk-kmo7hv grtq54i jz)m 11try 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 can think o -xt4i ovrj*+s) h tmm5qk 17zgr0qz1kf.

Explain how a runner experiences “free fall” or “apparent weightlessness” b**pw1(axb m( snhzel7etween s h(7wnxlezamb p*s1( *teps.

The Earth moves faster in its orbit around the Sun in Jan /gllthq+,z -tuary than in July. Is the Earth closer to the Sun in January, or in Julyq hz-, tlg+lt/? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expla0.gwffhd0x u x;za zw 1 )b0zbpiqq.*9in how this discovery enabled an estima1dpw qqfh)*w0zax9 zb0z.gfi.xb 0;u te of Pluto’s mass.

  The Sun's gravitational pull on the Earth is i l(v8zodynog ;wl*q722 ovc( much larger than the Moon's. Yet 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 s2lydnclo*g((8oo v 7;2zqv iwpeed 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 1u8m9qj vxv0 0 3qvn(jp980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Ear ,exnajly*8 5fabtfj ; o+.pv)th in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbi;afe j, 5lt+o*.vayf b8pnx )jt 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 exertedlrd2y7ey4ttdo8,k2 e(y,cfw on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of 4t,2y8det27,d w (cyoy f kelrradius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in of:at33wa5gnk6o 3t-tc x0 q,woajf :zdm i.t6 rbit 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,tdc t:wf3nka6a6 .agt3iq -fxw5z o:3ot0jm in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of;nbhc c ,+yekg;( -ity a speck of clay on the edge of a potter’s wheel turning at 45 rpm (( -cy;ght ki,becn+;yrevolutions 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 vertical civf5w;o 1: 6 rvs,katnxrcle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4, :vnt65;saw k1vx rfo.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 wvzirnskdi6n70y g s (t7* n.xb hj,o.8ith 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 result independent of the mass of. n,xosnv0 nzj*i.(b 77i6tghyskr8 d the car?   

  How large must the coefficient of static friction be between the tires and tbdmn-2 4 4x ip1h.hojlhe road if a car is to round a levp-om4jnhdbl x 412 h.iel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is d a*q9:t4qfe7m+kfb oby i0q1designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 4meob q9f*id q017kfbqt ay+: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.n -l3mwao*m+dz0b4nwx r c9j+0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached andrnmxz+n w4- ml9a3*b + cwjod0 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 upsiw e g9wvjmi-/tn8+;ebx( y;nl40zifs de down at the top of a t+ime4leiy fn g; j(/bx z8s- ;9w0vwncircle
(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 the rouncd9e.rz 2iq :dded top of a e: 9zrdq.dic2 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-diameti+gw (*f6veuq er Ferris wheel need to make f(fgi uq6w* ev+or the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled tl l2 zy08j6py3e .*; : bsiiu:qczpdmin a vertical circle of radius 1.10 m. At the lowest poin :z iqlyuc3p68*l2zity0;s j dpe.:mbt of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a cenu2dy bbn8kuj:n41+ w ktrifuge rotate if a particle 9.00 cm from the axis of rotation is tub j+:y2ku1dn wbn 48ko experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated i g,kmz jyh66;/pyuln5n a cylindrically walled "room." (See Fig. 5-35.)lgj,;hyn5mp/ uzy k66
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 ) i )mr0mfvqb :.ds rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danbr:)vmdq.0 fmgling 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 weig7x o7 0wc9ah 6s2.rpi9j liabwht of the ball which revolves on a string 0.600 m long. In particular, find the magniww9x7aaj6osl0icp79 r 2b .h itude 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 a/7idyb y if q-7r6an,8zlg4hcar 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 masse 5uqzg:x3 b4tt iueavu )0o5v/s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver 8vyi qh7 0rkku1 j0 w1j/xkdl9by 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 centripetal components of the net force exertepz sg9l0g6jfmz q6q /;d on the car (by the ground) in Example 5-8 when its spem/ggl 9zj6 0qzpqf6s ;ed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerat2dwuj- kz+m5h es 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 to provide this acceleration with no slippih+ uz wm52-dkjng or skidding? $\approx$   

  A particle revolves in a horizontal ci;4evwsfv q55v rcle of radius 2.90 m . At a particular instant, its acceleratiewv ;qf5s5vv4 on 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 q,9:7htua rr q9twev7km (2 Earth radii) above the Earth7,h qw etq99:tuvrr7a’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acce3cb:jwvh1dt b vto:s7m+27y y leration g has a magnitude of 12 : 7 hvb+dtb7ocwsy:2m1 v3 tjym/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 Moug yw5i *9x)dc:jjq*jon's radius is 1.74 c)*j 9uygjwj5i*xq d: $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planez92e q213cjwl wi +th:1u ffwst has a radius 1.5 times that of Earth, but has the same mass. What is :w1thz+fe2l i3 w12jsw c uq9fthe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bub7j-n/3 0l/ln y fppznt the same radius. Wh/-nblppn07jfl z/ n y3at is g near its surface?   

  Two objects attract eachy03j j;e+ w2b0zilqv i other gravitationally 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 ocan t 2j9 +ga,bctxq21f g , the acceleration of gravity, at (a) 3200 mq 2bx9ac2gna c, 1+tjt    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where t6 f uye2xfjs s1/7zyl(hegravity s 1/sxzuej7f2f( ly6ational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times rn4.h)ssnd )athe mass of our Sun packed into a sphere about 10 km in radius. Estima snrd.s) 4anh)te the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wasb gm1cb ea 5-d.ywv0l5 an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity oyabvw15.ebgm-05 lcd n this star?    $\times 10^7$

  You are explaining why astronauts f 9mg, hvuojzmu ;k)b94eel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t som;zmh gv4u, 99)j uokb 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 corner/6lphu;/wl3b 4 je7atemfx6 js of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitatio;h/lm 3p6exaj6wt4l ufjb7/enal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side o; yb4ua;lsg +z c*i msw qb)o(v(dxn/3f the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four pl;w luybzb/ so3q+iv*g()(dmcs4n ax;anets 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 ici -47 txep8yu5k 0lols 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the masieo l7kcp-5yu4t l0x8 s of Mars.    $\times 10^{23}$

  Determine the mass of thynd b)epm/,ci,3z wxu/ vi,( le Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepleb,/ pvy )nic,wie/lu3,x z(dmr’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about t*k8l:1/y )nb5uw* c nku mym aohscb7*he Earth at a heig/u kbw5sunaoc:8ny *yml b *7h*k1 cm)ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the 3mxtzowq:ma606. lua Earth. How fast must the shuttle be moving ao:.tq 6u w 6mzxlm03a(relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to e,7 l: .ymrj78mxc kcwqxperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolum,8: wck7ly xc. qjr7mtion. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satelc9ekm z;p*fwg o((av1 lite 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 resultmw1(ape vg*( ozfkc ;9 depend on the mass of the satellite?    s ~    min

  At what horizontal velocity y6 4 kuuvta64/vq dpw)would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit k vy6puv4u ad)/q6t 4waround the Earth?   

  During an Apollo lunar landing aj e2o5+)u v/hjac 5mjmission, the command module continued to orbit the Moon atejm5hc+jvj / 2a5o)au an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of0eya cp9+u u/tb;sum, chunks of ice that orbit the planet. The inner radiusm0,pcuu ;s 9yb+ea t/u 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 rotates oncfu0sb1j9:v,pxnva; d ol 17w;mj6 msbe every 15.5 s (see Fig. 5–9). What is the ratio of a person’s appw ;pl1ud vn0j sa9:f61mbmov jbs,;x7 arent 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 420gdh 0 zke6io.*0 km from the center of the Earth's Moon in a spacod*kzeh g.06ie vehicle (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 two3juo/:n, nl0 : hrxjpt stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betweelxtju:hn,oj:/0 pnr 3 n them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for tg-e:1ymk,a lh,vfn2 a-g 7hzshe weight of a 55-kg woman in an elevator that moves v7al:, h-gg,k y2aez -m1s fnh
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ce +zlfbe yef9fop5ky,9k;( 7oqiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevatf l ,fey+ ekoqkobfpz;y9579(or accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of iz:. aiy9 tk+do2aa/xld p0*fa planet with period T , the density (mass/volume) of th*y :dk0.xa2ptliiadf/aoz9 +e planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the periodf gm/eb;* 9qbg of an artificial satellite orbiting very near the Earth’s surqm *gbfe9; gb/face.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun ljs cc 7 l84jmy:w23w xu3,ypolike the planxo3m37y yu,:lp wc4wc8 s2lj jets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.wzsl+ k 4c0szic4+fkb/ p.pw 95 $\times 10^{9} \mathrm{~km}$ 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 orbit3ux6b/wa hk2vs the Sun roughly 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 from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest dis36 wh/ vaku2xbtance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the o/b)k8 iabs3yb.3f(9a+y m +d3mnrs5 mwecylGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 x1 vx5k5tf0a xlargest moons of Jupiter (those discovered by Gak05f axx vx5t1lileo 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 distance of the Moon. ufcg 9a(bzbm1)k:tw6a )m(9f6 uk1 zbwgc:bt   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Keplf(kz9/b c *zhkm 33grp6*wj kpebjw hk3mk(*z kc z3p9*f6/prgr’s third law. Use the distance of 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 betweens-k fp7cj7 lh: Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun bukcj: 7pf-lhs 7t 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 wuf6 4p(+b + v.lnzx lbp7xkp1of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surfzllx u7bvwp+bf146 +pkpnx. (ace (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 sjr1p lw.z)sfcy0k +)lwinging 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 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. kj.rzc p+0 sf)l)l1yw  

  How far above the Earth’s surface will the accelerhq6prihwk0 .8ation of gravity be half what 6rh qhwpi8 .k0it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equaljvx*ty nx7 :;(tbupss.awp2* mass grab hands and spin in a mutual circle once every x pxsw2ts.(jau:by*v* pt 7;n 2.5 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 of gravitydg9mg61+lv p )* ti ks4udmde( at the equator is slightly less than it would be if the Earth didn’tgdi +4m9 (d l)v6dg*m1tse upk rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wil0q,bl( 6 p rw*b ce3nnbya*v0bl a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppo6 lnc3b baw0 p*yb(b*revq0n,site forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathro hg,,)mc2rmtv om scale in an elevator, it says your mass is 82 kg. What is the accelera)trm,mv hgc, 2tion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo y3t(a5zn0bha ut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to graviyh3(a5 n 0bztaty 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)4:bauzv my-f vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acckeycgdrto-h c u , 79wvtu;-5+eleration due to gravity at its surface and the gr-gy5+ cukort7 dw-t9uc; ,hv eavitational constant G.

A plumb bob (a mass m hanging on a en,3leyt n+0 kstring) is deflected from the vertical by an angln e+el0t,k y3ne $\theta$ 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 speed of If the coeffi 5yjy )wyl d+e0. g:uuc;zno*qcient of static fricti c 0+oyuugq5.nylj zdwy;:e )*on 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 g80/d-xyan b*2ibj9a g c pj6dwere rotating so fast that objects at the equator were apparently weightlexcdb/ 9y* png6aa 8b g0-jdi2jss?    $\times 10^3$s

  Two equal-mass starsc11du0th32o0aun zd x maintain a constant 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 mhqswn9bs9ul,4k6 nm :. A lamp suspended from the ceiling swings out to an anghmslb 9qn,swn :u496kle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mass3x*pw.z en6krc; d- waive 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 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 aw kecp r63.;znx-wd*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 deducnnp 3b61 2;;dgvmky bsed 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). Theypv6bg knbmd s3;; 21ny 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 k h0r.4k lrz*d as it 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?krh.rd *4 k0zl (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 Sys7f7rmz;fs f/o4+ rn-bvmjx za/ n2f3 otem (GPS) utilizes 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 Ear4rafo7 mv/fmf3 + s7n/f;xzz boj2-rnth, 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 travejmvwz 73 ;b:e9a/bkyo ling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eroswz bjyo9bk a7e3m:v;/ 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 satellitky3k7ro r,n 2ae in need of repair. You are in a circular orbit of the sam72, n3 kykrorae 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 h akbw6j0o2jx +as a period of 3000 years. (a) What is its mean distance from the x0a2j+bwoj 6 kSun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel"w6+( sa gzl1jekw7kd+7/g tsx yourself gravitationally attracted to someone near you. Make reasonable assumptions, like +w7x/jk7l6sg (ke1a+ dztswg F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around tdwhbsxpl+ .0 .f3ik9wcesl u/ .+3sedhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-ye9h3fx selw3 ds/i+.k +e..d cups0lbwars 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 kzoia2q m4 lg5(1qii9square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at 5 oq2(4kiimzg1a l i9qthe midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5 ph3,yf*y/efg500 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 sweep sec1leqe02 fhmh9ond hand on your 1ef09e mq2lh hwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkerld:w vl*-5lp ck-+:zak5 rsk7mm7hh u weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete cihkzu -a r:d-sm pkc7l*5:5 vm+kl7whl rcle 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 r jx i;fkm.k*.eadius R in a new highway is designed so that a car traveling at ;k.*x.j fmiek 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 t lgf:3kczwc(8 wu-d.krain, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less 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) Cc ud(k.g 8w zwf3l-k: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.$\approx$    $\times 10^2$