Sometimes people say that wateroln.lafr:8fp qs o2.7 is removed from clothes in a spin dryer by centrifugal force throwing the water out7aql f.8oo2 :frplsn.ward. What is wrong with this statement?

Will the acceleration of a car be the same when i :jn3e,vlf9ek3oef(3g t2hi the car travels around a sharp curvo: nffet(3e3hkl9ji 2,e ig3ve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilo4o mw9-d,b9 yikte k/ly road. Where does the car exert the greate yktd9eo, 9/ikwm-b4o st 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 horse on a merry-go-roh*mm /t,m rplf 1cwpa/l-6u2uund. Which of these fo wl/,l1-c*m6ppa t/2fuhmru mrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without6 /cmwvu n+t:l the water spilling out, even at the top of the ci6/tw vnml:c+urcle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at lm2v 7y1er wff8kf(j. etp18 rzeast three controls in the car which can be used to cae8j fv p1ztk e 87yf(2.wr1mrfuse the car to accelerate. What are they? What accelerations do they produce?

A child on a sled com-1tts/ mjaq ,sxzd7ap)l1( xyes flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this dampl,q x t7(y-1 /s)adxjst1z ecrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hi1u: cgra2ce6 l k+,pxugh speed?

Why do airplanes bank when they turn? How would you compute th wp7u6qonge*92p t:r me banking angle given its speed and radius of the turn?rg:t7q*npe w 62moup 9

A girl is whirling a ball on a string around her bve-v* tg lfrn(7e (*ihead in a horizontal plane. She wants to let go at precisely the right time so that the bal(-*nit re(7vvf * gebll 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? If so, how -5fd,fp)neit daui8 iz-)d.i large a force? Consider an app a tdi id-)pu5.nz) d8-fife,ile
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s o8a q*e43nobuak+er0 hrbit bq3a0*a8erk4o+hbu ene different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thr3 yuj/l ;3umwe Earth? Which accelera juu3wrl/3y m;tes more?

The Sun's gravitational pull on the Ear3cn47 2x z v l)/zvyn,difx-5y2r xqsrth is much larger than the Moon's. Yet the Mooynx-v5q,4c 3/ 2yvrdx7 zfls)2irnxz n's is mainly responsible 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 8xk/hk9nsti/t8iy)*yu u z2zthe equator or at the poles? What two effects are at work? Do the k82znuty)/*k9hx8/iz i yusty oppose each other?

The gravitational force on the Moon due to the Earth is only about half the fs/ 4iu zfx/v cbpma-/.orce on the Moon due to the Sun. Why isn’t the Moon//sbi a u/xpv4f-zm.c pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arou0fi jf8fn33k k5v-s btnd the Sun larger or smaller than the centri t830f k5vs-n3ffbj ikpetal acceleration of the Earth?

Would it require less speed to launcbv 3neei l,+z 1f0e0quh a satellite (a) toward the east or (b) toward the we0z+eqbne 1il0f3 v,uest? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as meascoqmx 8 :r10qvured by a scale in a moving elevator: when the elevator (a) accelvc mo:q0 1rxq8erates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectjd17cg 416l -ixhrt d3:zauv76iq,eqk,e asmed by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical qim1jvg6d7z1t 4 3i,sk d-6:7erxaaqueh l c,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 “apparent weig h7 nx2dvu4k2k,wv9ii htlessness” between stdx4 w9 ii2hu2k,nk 7vveps.

The Earth moves faster in its orbit around the Sun in Jawsud+6g9./)uc9mrdl f y eu(cnuary than in July. Is thyufcgud)6d./(wr9lm c use +9e 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 of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not k2xqk tsz0t0em2 83 wafnown until it was discovered to have a moon. Explain how this discovery enabled an estimats0 fmt2a 3x0tekq8w2ze of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. czr )ayrow562 Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference ir5zc awy o6)r2n gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19806o3on ia qjqw7ggxws:wg) 872 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 E262 ec)9amlxljjs,ni u7jq7 sarth 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 orbit is a 9s7 asu6 ie)7l2ln 2jjqm,xjccircle 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 discz ,g9 vm8mp(h6 cnhst/us as it rotates uniformly in a horizontal circle (at arm’s length) of racz/hv9 ht 6nms 8gp(,mdius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttler tr; .zfk:yf pjh1i.5 is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal.f.i1rhp ytzr5;j kf : 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 s pqbi*gyn6/m.l0svm9-vf(4mfvs y4 :j,gjkv peck of clay on the edge of a potter’s wheel turning p 4bj mgvqv.:vs 9,(6-mkflvsf0ygmjy4n* i/at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at ai l kkou+jy2j *a3z*+l uniform rate in a vertical circle of radius 72.0 cm , as shown in Fazj *u*2yioljkl+3+k ig. 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 r9 cy(j/a-ku9kzz1j28p k ljdwound a turn of radius 77 m on a flat road if the coefjauwy/ld 18 9 z(k2-j 9ckkjpzficient 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 between the (a 8y u05/ ymjo04 x0dlv(ku1vtllbk mtires and the road if a car is td5vu m lbm0(l lky1t4xu8k(ja v 00o/yo round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots isoi(cex,5u1 ia designed to rotate a trainee in a horiz5 uic1,e(a xioontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variabl+ l 3av9cur+4)1 mjw)qi iuwx. fmc8tde 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 coiici wua91))wx+l d3uv mmct4fj+.8rqn slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a df,4+5dhs3miunxi4 msu5/mnd 3v u )troller coaster be traveling when upside down at the top of a circles )+ 5f3u5mdxmduhn,s4iuivdntm/43
(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 rounded topkm az6/mmh 2 attk71 (-qgsma; of a hill (radius 6(ktma-; t az1gh2smkm aqm7/ =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 revolutionsr,wr bcfi2 03.k6oz kn per minute would a 15-m-diameter Ferris wheel need to make forcifk r20n3r.wz o, kb6 the 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. At lza9ei-z*9 s +4kpley the lowest point of its motion the tension in the rope sue 4+-9ek9y*zilpls zapporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate isf4m )9kz v:r xf 3vnkkj91:kgf a particle 9.00 cm from the axis of rot1gjfn)vkkk zsv:x3 9 4:fm9 rkation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated inu* goq aq7.nxd; wl/u- a cylindrically walled "room." *wq-l;7dxugoqu. a/n (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.tug d/qegj *fj5e, ,qi3us9eu; hu, c in a circle on a frictionless air-hockey tabletop, and is held 3hu.ug;ue,i g,5d9*qqj,e fu/cs j tein this 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 thh6,aa4w2uy2v ys h7mm is time, by not ignoring the weight of the ball which yam2,s h w76 uamy4hv2revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a rad :q49ryxnr8exgb;wugf b30-d ius of 88 m is perfectly banked 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 masses r/ eqgu+ 8um ue ;:2zyy8kbtt8$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving verxhs p qn1-fna;3u7l 6itically 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 tangenti2;ngiy7 ndz,xal and centripetal components of the net force exerted on the car (by the ground) in z, g;7 inxy2dnExample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniou)n ak09rko( formly from the pit area, going from rest to 320km/h i ar9o0onk)(kun 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 slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 +7 (m rpjeqrk3.j.yu om . At a particular instant, its accelerati(eukpyom..rr 3q j+ j7on 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,gt.ip jmzx /,1800 km (2 Earth radii) above the Earthzm p./1txg ij,’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratioys;vk4 dkk (.ln g has a magnitude o klvkd.4( ks;yf 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Mooa8wf v sess1x.9t+d 9hn's radius is 1.74 81vw9s e sxf+ d.ta9sh$\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 yum- nqcvst .45jt16lEarth, but has the same mass. What is t s41yut cnlvq.56j t-mhe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times thatlk+i* , eldk-l of Earth, but the same radius. W il,dll+k* k-ehat is g near its surface?   

  Two objects attract each other gravitationally with a fwlt9o cv11vdlcjz *-2 u syw78orce 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 effectivexw42y-cw 4r s;ni.:gn tn)g)z/ di bcx value of g , the acceleration of gravity, at (a) 3200 mn: z24) g-dtwci.n4ry c/ xibxgwn)s;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsidem-64ba3u ka0 ugn79dk-mkkh b the Earth where thegravitational acceleration due to ka- mung9h04 kbbuk6-a3kmd7the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times tekl1dp t:4n2l he mass of our Sun packed into a sphere about 10 km in radius. Estimate t2:t1 epk4lnl dhe surface gravity on this monster.    $\times10^12$

  A typical white-dwar :g)kjfbm7.cl3zhl1z f star, which once was an average star like our Sun but is now in the last stage of its evolution, is the si1m 3ch7 zfg)b: j.zkllze 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 spacma +( 77b/axklybk+ t ,f))ojz2ud olse shuttle. Your friends respond that they thought gravity was just a lot weaker atsozk7x myb+/ df(ao ) +llj,b7k)2uup 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 corners0r )wrxks 0ik9umt*d4q j1:dx of a square of side 0.60 m. Calculate the magnitude and4d ) 9tr d1r*uimk0xksqx0j:w 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 ofujzcx9 v tjp70ze)2a6dsd7 t+ the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus7+)zt e79xdj 2tdp j06vsacuz , Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 oabhqm nr*:7, sf what it is on Earth, and that Mars’ radius is *mh:b n,s7 qra3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known jr aa)f03f) lmu1otegypa s93, nj2-dvalue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s -fujap1joams)l d3gr 02e ,3)yftn9alaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circularb)3 aj5d abs 3tpjo+.g orbit about the Earth at a height of 3600 km.s 5) p3bdja+ atb3ogj.    $\times 10^3$

  The space shuttle releases a satel5 8tn4j8k2kja w:dlymlite into a circular orbit 650 km above the Earth. How fast must the 8kydtna 5k8wj 2j l:4mshuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are ih( n+syajx 8; rsj1:wto experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32;hxaw ys:+s(nijj 81r 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 the Earth in a circah6dj qyh /g yicu. +g,el)-8vular “near-Earth” orbit. A “near-Earth”6gi/hdj,u h8g -eyq+vya.cl ) 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 1ro i6esq) :03azewgtto be launched from the top of Mt. Everest to be zr):w6a sq 0e 13gioteplaced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module conozaz:zmz20e8 gwc +)1ds 7it*oe;lzhtinued to orbit the Moon at an altitude of about 100 km. How long did it take to go aroun ogzzs0) *zeal+8o 1tw iz dch;2:ze7md the Moon once?    s

  The rings of Saturn are comnfg( 7.ucm hpik ;s9r-posed of chunks of ice that orbit the planet. The inner radius of the rings is .k-hcrnm (;ui7pfsg 973,000 $\mathrm{~km}$ , 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 diaft :aijm e+xt ,xw qmdw,5e2)j0f1 4egmeter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weighfmje0,1:ae,gtm w ef)4xjwi+2td 5xq t (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km frys/ )* slzqm5m19 8eea,xrbrhom the center of the Earth's Moon in a space vehicle (a) moviblhey )s q5 a9 /mx8z1rmers,*ng 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 of equal mass. *jl8rf j,4 )afb(b9bk2kt sqt They are observ4)att *fjsb (l2b,r9jk b q8kfed 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 elev 6qy /,4fvlyg 3va 8oqb(4jsjvator that moves o,yj/83 f vygq6 vsj bv4a4lq(
(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 mywfi l et 9cqr+e1.08ceiling of an elevator. The cord can witwe9 ql8y.if e0 c+rm1thstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits v 4* mvwnyo km)v85jen/ery near the surface of a planet with period T , the density (mass/volumev 4e)omm /vjn5nyw k8*) 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 q:4mp3ik( 4eif-egbq determine the period of an artificial satellite orbi-iike4qf(q g b43m :epting very near the Earth’s surface.    s

  The asteroid Icarus, though only ab,akh*4l;x*2nknw /pks 8sur+lg.yvw*ut :a few hundred meters across, orbits the Sun likn.v+* xk,ylslarh*g/8u4usp;nkw * w 2b :ak te the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average diszmqc/7v);hvout-h yo *( zt+ptance 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 yrnk(k0oyj7zc/b47 ,) iuz dt qears. 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 k cji(o y7rz 0z,d /b4tu7k)nqis 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 ceniv0g)k zc: ke9quv5a/ter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four lar)zl . q jka0a4t8y5irugest moons of Jupiter (those discovered8k z54l y)at 0ur.ajiq by Galileo 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 qdvty i(a15 c p*t410j.dxkwqand distance of the Moon. qy*(1cawk4qd5. t x1 p 0itdvj   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Ke/mnqwy117 g ewpler’s third law. Use the distance of Io and the periods given in Table 5–ew1 ygq/1m7wn 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 consists of many fragments s jn9).pwza y*(which some space scientists *wj y9z .spn)athink 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 "planet" in the form of a banozvic+n)gn w9 (.ybd,d completely encircling a sun (Fwgdy()o+z9 nv,cnb .iig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in w8 8rm )z9ansq j+wj9zt+aul-an arc from a hanging vine (Fig. 5–41). If his arms are capable of exertin+waqt8nu+ jszl8ja)z mrw99 -g 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 Earg2m p3- ox)eqwjxml, +th’s surface will the acceleration of gravity be half what it is on the surface? mpx- 2oq wg3 +lmejx,)   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands ann- 8y pe3y umze+ au/p5:lvei0d spin in a mutual circle once every 2.5 s. I e5evm0l 8y p-+zpi3yua :/eunf 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 accelerati54na9rjzxxb8kptsza q .38 :z8)jbwxon of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the ma bn .z a txzx p8zqs5rj:xja3kwb8)849gnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a space.t xmo3d ;abj)/ 1o5,mfwk uhecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite )hjx/m ;ot.1fu,3m o awedb5k forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stants 0ge 5)s*xsspe0;r cd on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevatosp;*ssxs e)gr0tc0e 5r, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thatlo ;0d dh,uw c2ei gxh)ogl749 will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle for2)wc oul7lxi, 4 od0hg;9ghe dmed 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 loopdi08ijni )*d /vl ;utp (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 tcl c6m8lwodf-7c3 j:in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constm7 j8lftc-w6c l3o :dcant G.

A plumb bob (a mass m hanging on a ( c m(w*vfdadgx2(in.string) is deflected from the vertical by an ang ia2nc. x*gmd((vf d(wle $\theta$ 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 Ifkb; uqgzz n g)8mo;q i/xo1;/:dit+ic the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the cu;/ocgbqi zz ogk1di ;m;qn i 8/xu:+)trve?

  How long would a day be if thew :dg a*.epqb) n1x,mz Earth were rotating so fast that objects at the equator werxb *qd1)gpz:ewma .,ne apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distav7negxy ey.6 -nce 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 2-jdyapp:x 1qeul(; 7f35 m. A lamp suspended from the ceiling swings adu;(p:-fy pjql 1xe7 out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times awb+lk4d j3ps 3s massive 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 such a planet. Use the following data for Jupiter: malp3d j4sk+b3w ss =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 deduced the preseq1sp4nxqlfn30 h g 55knce 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 clouq 4 qp05 1gn35fkhnlsxds 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 a 4aq8xujvi3 :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 onqu:a8x iv3j4a 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 Position hj n41f.d de7j+saw,. w ps)niuiwi:5ing System (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 Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an al:75hwii dua1ej )ijw..p,s fs d+ 4nwntitude 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), a:bb0pmg0 n w6cqm64 ncvctq ,3fter traveling 2.1 billion km, is meant to orbit the as qtw0 cvb qn0pc, b66c:m3mn4gteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing arf0q)txz;x u 92jp 70h/(l cbjc9mffc satellite in need of repair. You are in a circular orbit of tr(u9z jlb cch2 f p90 xfxc/f07)t;mqjhe same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its meanb).ipe o95nv(sm 0v1iusjn z8 distance from the Sun? e9vj 0ov1.i n(snsi 8up)zm5b  
(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 wouxvmkx 3sa xp7c g:04a9ld need to be if you could actually "feel" yourself gravitationally attracted to someonxkm0v4c:9 37sg xpx aae near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center 5h, b/+fpotv-h3 c,d(lbji ;bz5bg s 3qcmq8v of the Milky Way Galaxy (Fig. 5-46) at a dista(phj,bb 33 fmo5;l th-gbz/qcc vqb+ idv,s85nce of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.5gcs.p w x3ymu( yazdw 9tl),)/0 m on each side. Find zwxu)w,g9l my (.py tc )d3as/the magnitude and 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 553 f7s6tw khw px+0m1s) pkwg(y00 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 expe 5qaje) /b/qy +1sqa ylso/tly 3-bp:urienced by the tip of the 1.5-cm-long sweep second hand on your wrist watch? oy )l3/q5:s yqb+ 1s //ype-jlbq taua   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cc,tnmo,ey*2if ck9 p.ircle below you on a 0.25-m piece of fishing line. The weight makes.9y*2otk cpfmneic, , a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hgnjf u2+ -0zhkighway is designed so that a car traveli 2kf0jgu+-n zhng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whei*mghfm ,) p2o1m nnx 8agg8v,n 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 track is not banked and the train does not tilt. mfo*g1gn,h,pgn)mm2va x 8 8i $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$