Sometimes people say that watez7/mnbse lksl/7 q o9)r is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemell7)s n/b9qom /k se7znt?

Will the acceleration of a car be theic;cs 4qdn2e7 1z7p:ng6icel same when the car travels around a sharp curve at a constant 60 km/h as when it travels around ng i41c c7d2qn76zece:il;spa gentle curve at the same speed? Explain.

Suppose a car moves at com4d-h:ifd q2 6vshh3 y67g2l txc9dl pnstant speed along a hilly road. Where does the car exert tqipcf sddh3ghm76 y9vxl 22l4-dt :6hhe greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-roundu::p9fcn bg:glko/j ztcv* 1-. Which of these forces provides the centripetal accc -:p:fn1gtu:9/jz vbl g*okceleration of the child?

A bucket of water can be whirled in a vertical circle 47rl6qlll4j x,tbdk0 without the water spilling out, even at th qkb l07r ld,l4xlt4j6e top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in kpxee40,w uj-your car? There are at least three controls in the car which ca- 0wxj,4eku epn be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over th,rht.n5 wz r-5j;vh2goxmsyf wd;t6 6 e crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but w ;vjmt;.,dyf6 r- tr5xg2h h 6wzso5nhe feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle ridersx4f(j-i zq lb4c xge( jhl;7o- lean inward when rounding a curve at high speed?

Why do airplanes bank2mc oz 4cpm5qhtr)6laco.j() when they turn? How would you compute the banking angle given its speed and radius of6 42o5q rm c)cjo z(h.ctal)pm the turn?

A girl is whirling a ball on a string around her head in a horizontvfr d j x jy41d*y:mwg8-xy9s*al plane. She wants to let go at preci*r4j:ywmgdy-1d fx * jy98xsvsely 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 frde(1e lz/7aj.9j8m: wp vbvwet81fxorce on the Earth? If so, how large a force? Consider an appler97v/lz :8 1w8bteej1 .(mvwje ap fxd
(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 orbizvhn-9 1ua +b+cmq,ozt be differentvm9c- azun o,h+1+bz q?

Which pulls harder gravitationally, tz6 ymt;azp 63x y66hfuhe Earth on the Moon, or the Moon on the Earth? Whichma6f 6 ;tyyz3u6phxz 6 accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet vxy gd2b2xf5:ag6*af the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the vbdgf:f 2a xyx 652ag*Earth to the other.]

Will an object weigh more at the equator or at the poles?yik cy-:olv(vi8f l04m q-a*d What two effects are at work? Do -i0yydlf8q l4v-*m ( ak:oicvthey oppose each other?

The gravitational force on the Moon due to the Earv- wgjad+ :ymp.b; ns8th is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the -+bv 8msjy. adw:gp;n Earth?

Is the centripetal acceleration of Mars in its orb u)o*.nxty, sfit around the Sun larger or smaller than the centri*) ,toy.nuxfs petal acceleration of the Earth?

Would it require less speed to launch a s6bvte z5t )q2natellite (a) toward the east or (b) toward the west? Considere6v5zqbtt n)2 the Earth’s rotation direction.

When will your apparent weight be the greatesi r*mtl9ejd,f*nk -)tt, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In w ) ntktl *-,j9irfed*mhich 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 ouh 6n7tqg li2m,ter 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 insi2l hq ,t6gnim7de 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 “( ,qmwwr .;hlj,v z ,psm5.fgwfree fall” or “apparent weightlessness” betweej5 r.f wp(h;wzmvl ,g,ws.m ,qn steps.

The Earth moves faster in its orbit around the Sun in January than in98dd0*bvml vy31go/gc s qxv9 July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main facy8sb1 xlmgcg*ddqv93o vv09 /tor 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 dismflt t,z3;g()l r.e woi4r4 sf3 t7xdicovered to have a moon. Explain how txisl3w3o, r(rm4iflt. 7) e gfd4zt; this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mo(ngd1 ez(*nk pon's. Yet the Moon's is mainly responsible for the tides. Explain. [ (nzngpdk1 *e(Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 1yv v2 )e5x ru9 g1gq:od6m /2sitmgbu6980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 kk/e*bi op72gr-*l-bc1qy * bnt0 iqaEarth 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 circle of radius */rgpikoq n c7 *bbt layek q01b*2-i- 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 1eo 5f nr*vp(qis exerted on a 2.0-kg discus as it rotates uniformly in a fpq n*o(1v5 erhorizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km -be.noj,u i0ztfy: :nggd)y5from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g0)gb j: todyz e.,ufy5ign- n: , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleratio/6/l5 cgyrhpn*ibs2dn of a speck of clay on the edge of a po2/cily db/p56 *sng hrtter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvex 4z* bjecr2y evly7;+fxs*+cd at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33.+lz c*f+*r7;jc y 2s4xvye xbe 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 canl vc*/lo8pf )m round a turn of radius 77 m on a flat road if the co )/cv8l fomlp*efficient 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 frk2(a98q7nxm zll . kjciction be between the tires and the road if a car is to round a level mk q.c(kn2xl8j79lzacurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is dmc*a.c9-5+snb7xd oeddj r4gesigned to rotate a trainee in a hor- dbnse5 ocrxa*d4j7d +mc9.gizontal 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:5gbi*0v z- -rwixhav a rotating turntable of variable speed. i:5iw rg-x0a* vzhvb- When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed i p -mk0cyeqp3cvk+:1n8 yynf c:c+a.gfn 0+d must a roller coaster be traveling when upside down at the topk .:-ny 3paf+cdgyyfnmqi8pnc0 ck :+c+ev 01 of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 . um5t,ylxz4c2km8q2ww* tkj kg (including the driver) crosses the rounded top of a hill (radius =954w tq kjtzm.,x5*22c8wm ykul$ \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 wouvtgd5hkmi 3h4sk;a (1ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the 1aivkt sdh35k(h;mg 4topmost point?    rpm

  A bucket of mass 2.00 kg is ;*0tut w/nrblwhirled in a vertical circle of radius 1.10 m. At the lowest prb0;uw/ n*tl toint 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 m hxcd 3(kzr t*k2kb, v7fy4ajp+-6z na centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,07,+px j 2 bntd(zk4 v6ck-rkha*3yzmf00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peop:emb2v u+g0akvzcm+: k;n a.ple are rotated in a cylindrically walled "room."m0 +2emzauk+n g ;:.ap:kbvvc (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 rota hcx* g7ax fo0m-z;ez9ted in a circle on a frictionless air-hockey tabletop, and is held in t;7e*0axc- xoz 9zmfg hhis 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 ti8qbd6i z,ro- gme, by not ignoring the weight of the ball which revolves on a string 0.600g-zi 6qr8o, bd 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 radius of 88 m is perfectly banke(wvp0+mag w9;3edv gg d 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 massebx7adk j ,ju)(d5f4gcdv 97 mbs $ 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 evasi1j dmimi59 d2cckg4v:7jejv6 ve maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential 7 / xsc .j7sn83nbdbwfand centripetal components of the net force exerted on the car (by the ground) in Exam bb3dcn/s7xsn. jfw78ple 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 uniformly frd3ldist1;w0 r hg 8rz v1a76grg +7otpom 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 slipping or gwrvt7+rts;pr10hi od 67gd 1lz38ag skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m .1 m/-dcp(t-glon/gpx -r:yz o At a particular instant, its lg- rn(/xpy mcd/-: tpz-ogo1 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 km w ;ngm9/ 8uu (oaf6qlq(2 Earth radii) above the Earth’s surface if its mass is 135l8wu9nmo/f g uqqa6 (;0 kg.   

  At the surface of a certain planet, the g0nb q*5tj/ru gravitational acceleration g has a magnitude of 12 m/ brn* 5quj0tg/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is lxl5 c1 -2b l*arvorxi z/0*co1.7l /v zcl -0lrxixr1bc*ao*5o24 $\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 ttzwxc;, k rc*,(pm/p jhat of Earth, but has the same mass. What is the accelew;x( kmj ,*r z,pt/ccpration due to gravity near its surface?   

  A hypothetical planet*0 klrgl-b1dl has a mass 1.66 times that of Earth, but the same radius. What isb0k -lll d1*gr g near its surface?   

  Two objects attract each other gravitatiogi/aer 6u/f:a nally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration (; cynmyfik 4r-qo/.iof gravity, at (a) 3200 my4i r(.-kyq/ mofi;c n    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’su3; jr4ee2aw.oj4ht q center to a point outside the Earth where thegravitational acceleration due to the Eaa;ee3ow juq2 t j4rh.4rth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron sta(5kq a6-xzuz g 7r/k,fem3ka nr has five times the mass of our Sun packed into a sphere about 10 km6m -5aka u7zf(kkg z3,r /qxen in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which / fo zzemma1d;5w)i6n once was 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 ind1meaf;z/)zm5o 6wsurface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitindre)x,*aqof)d8u qar5clcuxv2 5d7,im- a8gg 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 so b,2xduvf*cqx5acro 7e8,da) 5r -qd)g luim 8 ay calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of2ltr1:q(ble;.gbp ij.p xg: l side 0.60 m. Calculate the magnitude and direction of the total gravitational force el:2.(.p;qr1tbb e:gx i jllg pxerted 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 fz85qy7btgk monl+y 2 8c28se of the Sun. Calculate the total force on the Earth due to Venu 5nmyzbyq 2 f+2 e8tgsoc7k8l8s, 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 4+jei wtbsht2s69 dkjg +dhx0xq-4e/w4mzo9of what it is on wth++24diosm sx6-b j/gdhe9zej4t x k09w4q Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earthoebm7.t4h,9 psdq /rl and its distance from the Sun. [Note: Compare y7qepr.9t, dmsohbl4/ our answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circuoc fki: 9f4spm* wl+5zlar orbit about the Earth at a height of 3c f4sw:zm fo 9il5*kp+600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circul trjo z,lbs/e:6rie;73r eub 5ar orbit 650 km above the Earth. How fast must the shuttle be moving (relorue bzst b;57l3j:reer 6i /,ative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrica 83csx:pem txcy9::x bl 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 21sxbpmc:x ec9:tx8 y3:, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth inu9k(d2f+bvvq1d 8i id a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of thd (vd iv1fudq9+8ikb 2e satellite?    s ~    min

  At what horizontal velocity would a satellite have tohvs v+o4 u2vql112h) atb2p wf be launched from the top of Mt. Everest to be placed in a circular orbit aroundhwhtl 2 o1vbv) sf 41+2u2vaqp the Earth?   

  During an Apollo lunar landing mission, thesxs7ayfbeqymh :zbm6:1 s4-; command module continued to orbit the Moon at an altitude of ab fbx z41m67q: ysms;a:hb-yesout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the xqibj ulmo /: ;km0:*iplanet. The inner radius of the rings jq0;i:bok* /mx:uml iis 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 og a crbr47(d5(fep6bg nce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the brdrc(bpgae7(bg6 54fottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fms:ut ok* r3r6rom the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, o rk r6u3tms*:     ----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 twoerjsfrs2ihr:y75/ 5t stars of equal mass. They are observed to be separated by 360 milliofsrrisyh rj5e5/:72t n 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 6yr w5p)b1 -l:5so,lhsd sxdx55-kg woman in an elevator that moves -6dsd xl s5 xh)ol5s1:p,ybwr
(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 co)twsh:qmof p 4z47 d0zrd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevatopws:0qh4tf d4z)z m7or accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with peowgwmo6*sn; )x )qf7 7fd y.frriod T , the density (mass/volume) of the planqffn .6m* ;s7wdf7r )oxy)g owet 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 determinekaxxvmwyi):no3ks, )7b nmd 0:gh/3 v the period of an artificial satellite orbiting very near the Earth’s surface)3: 7vsh yn3xxkk:v gnm 0 o,)d/bmiwa.    s

  The asteroid Icarus, though only a few hundh6/zgar fz-c4 red meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean dist-fch z/4 rzga6ance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4imyb2q 8y;hb xibs; 3 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 76ka . hyvo030jwir;sw; 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 fart;h 0iaw3o.jvyw sk0r ;hest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of2udmt wlc7 a7* 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, perioc/ 5mo vbblrz +32d+cl rae9/zd, and mean distance for the four largest moons of Jupiter (those discovered bcmavlce+dl ro93r/+/z 5b2bz y 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 6absg 8kmzpn: gx,4.bEarth from the known period and distance of the Moon. kgb.4 agm,zbns:68px   $\times 10^{24}$

  Determine the mean distance from Jupiter for eacxi,f1 -pz f-t +hsny(wh of Jupiter’s moons, using Kepler’s third law. Use the disfi fwh 1p+,n-xy-t sz(tance 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 between Mars and J: (: czp 1rn-d lhyrc:n+cg8amupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed). : 8l-a+mp cd: :znr(h1gyncrc
(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).c.mun16bt (9wqve 0e.kge 5yjn enn describes an artificial "planet" 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 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 ne unn e.k1b)qcw0em.t 96 5n.y(vegj as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by w arqe7+ dr9cxl *6vt0d0x/niswinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting d 60 7rdc wne 0xqxirt*9l/av+a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will ,zwxpy/u8.je42q, ig6tttzq the acceleration of gravity be half what it is on the suz g.j4/6 qt ptyzt,quexi,w28rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual 4kwdyqap 2n+gkj 8/s4circle once every 2.5 s. If we assume their arms jwq dpk/ ks24g y84na+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 pe5 28pxoax ;ge3ay.frxr day, the apparent acceleration of gravity at the equator is slightly less than it wopx.aax 5 3rf82x;geyould be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft t0- hh0(c g ufmay a+6ma+dqr 8u(mpi)gr oec-1raveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppm6(mfaad c8og+a0 yuhe 0m--gc r) i(rqu1+hp osite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in 8-.t:xd.njb vywi( pb8dgh( 67 qn lzhan elevator, it says your mass is 82 kg. What is the acceleration of zt8.i-nn dvh hq(b :ydp7( w 6jlg8bx.the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube knfa0n2; fthh q,c//ythat will rotate 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 must be the rotation speed; 0/nnff 2aht/,yqchk (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 aircra +fazl 3:(kcobft in a 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 radiuc mcawh;q,w1h 7-mjt *s r, the acceleration due to gravity at its s-c,awc mmw;ht*q71 hjurface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflech s98z1amvo7koq/a a 0ted from the vertical by an angleq9oas/o71hk aa0m 8vz $\theta$ 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 design8z zt f6wguda,4w 00o pa(cc*k speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car saf 4wcz0 o k(zw,g6aca*08d fuptely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at th/lv;8v,g8g8w. csm4 psb cude e equator were apppmc,/ ; g8v wc8l8gsv4.bsudearently weightless?    $\times 10^3$s

  Two equal-mass stars maintanme 3x3-ursp, xa 6h +vdkk0)rin 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 2pf+4 ed1 oo+)gugpu4d35 m. A lamp suspended from the ceiling swings out toodp4 p1)4+ ugofued g+ an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mass8/l rdq27d,lh3mm/nl y kl1mwive 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 s3dk7/l/2w8r q 1dlh mm ,ylmnlurvive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extr .(vh wkz)eh.zemely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no lig ew.z.kzh )v(hht escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as i5jwwu)e7pe knhpcx4a 358yh.kd -:kbt traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) Hek.hw7cnpy8-hxdej:5b u 53 k4 kwpa)ow 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 Positionin4j y**wrcmij*dtaq)3 g 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 navigation)jy*ji 3qc*4wr*dt maal “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1j :/n m+vlfy/k billion km, is meant to orbit the asteroid Eros at a height of abouy+n /v:k flmj/t 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 tep-rcqrlee: .fk yn s(5q+: ly l,gp(1he space shuttle pursuing a satellite in need of repair. You are in a cielfpq:s: lnp(e1+r.g yrlqyk( ,c-e5rcular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a m62 np 6 c4mv8vnfk)twperiod of 3000 years. (a) What is its mean distance from t6kcw nv t8np2f )46mmvhe 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 of G would ,.:t s,fwcua kneed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make,s:.wf c,autk reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (lt 835):tj i:)czzbjefks -s mj- yf4sFig. 5-46) at a distance of about 30,000 light-y4tszs je-jsffm- :3 :il5 8)kjzyt)bcears 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 9x x5 7ag2huqsk:li(u ppca) k9a:s5c a square 0.50 m on each side. Find 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.gx(:h cs5pk9acq ks5 97: xau ul)2pia    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5 -b8 dnvlanvbb53( j48oc qk1q500 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 acceleratiy1d-exrlw .2 za,kg5 oon experienced by the tip of the 1.5-cm-long sweep second r1wzgk.ox 2e,-l ad5yhand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and starh (2zda -bklv(t to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes wik2bv(-dl(a zh th the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a 6:mll-by:n d gr.2 oky6p2psvcar traveling at speed psmry2gl-l 62:p ynkb6.o v:d $ 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 negotiatjs x4+yn jfjx ua(cu55 (u6kr*ing 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 thatj fjy(un*au c4xx kru(6s5j 5+ 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.$\approx$    $\times 10^2$