Sometimes people say that water is removed from clothes in a spin dryer by bi iqot280i :8hf.mkncentrifugal fon0mtf28okhi .qb 8 :iirce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the sameo ;;9u:lma2xngov 1ll when the car travels around a sharp curve axalv:n ulg19;o2 ml ;ot a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speedsgtqy(1axk ,ak(5zx 7 along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretchq 5 s1x,y(gkt(zxa7ka near the bottom of a hill?

Describe all the forces acting on a chilz0 , iipeack-we/q wvn+x .k,*d riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratioxpc qewe,-k ik.iwz*a +,v/ n0n of the child?

A bucket of water can be whirled in a vertical circle without the 8kmv + 87mgyhgwater spilling out, even at the top of the circle when the bucket is ups g7+h8kmv8mygide down. Explain.

How many “accelerators” do you have in your car? There are at least three convgoe ap2fiz-9 j*xu**trols in the car which can be used to cause the car to accelerate. What are they? What 9pix**auv je2gzo f*-accelerations do they produce?

A child on a sled comes flying over the crest of a small n8,idx c2qh*t hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feelst 8,2inx*dqh c 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 riders lean ;.fcv:*oc qyeinward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking anlvvtd v7n o,n(;h9mj/ni-zj8gle given its speed and radi ;m(vz9/ -ijvhd8nj,oln7tv nus of the turn?

A girl is whirling a ball on1(v/ px pphnx5 a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When x1( x5ppphn/ vshould she let go of the string?

Does an apple exert a gravpizx ve,dngo0q4 (zsu3 )( tw;itational force on the Earth? If so, how large a force? Consider wni4s, zq0utx;)3zv og((edpan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it ii*wtb ,sucl 3,a/-puc s, in what ways would the Moon’s orbit be c upwsa*3b/ ,ctu l-,idifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on qfclwebooa*vp7zp+0m ,2t2 5the Earth? Which accelerates more?a*,0mw 5f2 + 7pvqbc oop2zetl

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th(n wab8(: ip/ tondw8h.km rv8e Moon's is mainly responsible for the vnobrpdh.8(miw: ( 8ta/ w k8ntides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at theydxx-c8h 23m r equator or at the poles? What two effects are at work? Do they oppose each otcx8-3rx dhy2 mher?

The gravitational forzmvz7u0 a fdvr+l*43pb 5gck;ce on the Moon due to the Earth is only about half the force ov dg5k+v 04urzz*3p7f mcbl;an the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration o7i jxa ,mtj)*3evljk7f Mars in its orbit around the Sun larger or smaller thav*kx7j)3m,jal 7ite jn the centripetal acceleration of the Earth?

Would it require less *azt,x 3dqd c+speed to launch a satellite (a) toward the east or (b) toward the westz3 d, xctad*+q? Consider the Earth’s rotation direction.

When will your apparent weighf 61nsm,ba 4mht 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 upwa,bnh6 afm 4s1mrd 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 adverst/m v(luiykf m / tt c:;9)ij:7lgov0nely 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) yu /l:l9t/7mokjv m( nt) 0if:t;gv icthe force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner xirm+:nk*ltgb .x-uwa5l c:5vgh) z( experiences “free fall” or “apparent weightlessness” betweenn+k*l)cx 5-g.ah :iwgm5r t u(vl:zxb steps.

The Earth moves faster in its orbit around the Sun in Janu4vs*xk 3 r0ffvary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of it f3 kfx4*0rsvvs orbit.]

The mass of Pluto was not known until it was disiyy q n/ wa3+gp4 9rxp,ahvj-8covered to have a moon. Explain how this discovery enabled an estimate of y9r-aixjn+pv/4yg 3hwp, 8qaPluto’s mass.

  The Sun's gravitational pull on the Earth is mu*a*ypp4 6 avgbeamk-,9pqg s(ch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference a6qe9k4pa ys (m*vgp-a,pb g* 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 hvbq7 0pu0+ sud .gj,d1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ah4aag ea+2rbx98 gqp)cceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Eara g+a9xg p4)hb28 eqarth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it22n7yvn5 alb a rotates uniformly in a horizontal circle (at arm’s a5l y27nn 2bvalength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, anqd *j e;*;w:nsj klr6sg*8 vfod circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express you; :gef klsown r*sq*vj8*j 6d;r answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude o;jruq*m2 iat+f the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rq j+2rau mt*;ipm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of od pekn8i94r)wo 4 f-ya string is revolved at a uniform rate in a vertical circle of radius 72.048p -)o4 r9efnyoidwk cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 105t/ +px y ,zyb9mja2oc2*tfs 4 ;;wg0cea/sh td0-kg car can round a turn of radius 77 m ontm h;ss2yp9+gc*t;4ajd0a/ zct fo 2,y/w e xb a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficien3kfp)8s-xc8jeo w w 4i+vlef+t of static friction be between the tires and the road if a car is to rou xwef +84wi+pc osfe-j3)k8lvnd a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rot*h: k/h5(vdqjx)ean nate a trainee in a horizontal 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 rota*eajq n d5vh/h:)(xknting?    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**vcdn / dt9hefmq f-;(,qfmc rotating turntable of variable speed. When the spehf,fmced*/* tq m-;f9 dcvnq(ed 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 must ,wwc- lv p8cp,pc82+lx ewir1a roller coaster be traveling when upside down at the top op l81e2cp+,r xwp-i,wcvcl w8f 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 kg (including the d0b+)-4.p;hmjj cijzpkg d pe a4b9b-priver) crosses the rounded top of aph c4ik .;a+4gebpjp- md-bb zj9)p 0j 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 minut ed:kzbc+sxc0q-ohm y6-f0+v o g2xl,e would a 15-m-diameter Ferris wheel need to make for the passengers to feelg,2fc:o0emx6 zbx - o-sdy++vh0lk qc “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cir:nu9sru ,9 ok62y sz )+bzoefzcle of radius 1.10 m. At the lowest point o+zs sue:zn9,br9o2 fz u6) okyf 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 centrifuge rotate if a particleci)r.v; 2jwi o 9.00 cm from the axis of rotation is to experience an acceleration of 115,0; rci )wo.ji2v00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically 9a5f)ek;nt rtwalled "room." (See Fig. 5-35.;tkeft5r 9an ))
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless airf,vxtpdes) rt u82zo;ph(3 c9siip869kxzu3-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown(9 xsk tcf xr9hp2),svo; pte6u3 i8di8u3pzz 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 notgbc, eb c aix)di+ma016m1tq 4 ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude o mqaccat,6xmb)eb0di1i +4g1 f $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 qrct ss*yp1e4 (6j1oeof 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 masselfs(g u,i7 m ) -grq-yyh3 /hqe4pkvi: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 by divc;hxfa u(y522xqw,8b3m chmo :wph o6ing 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 ofck vi5qb(n(xv 1,tvw 5 the net force exerted on the car (by tbv5qxi w5( vc(knt,1v he ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going frobzg dl(a xbm28: un.v a+om4j2 (m/qbfm rest to 320kjmm2b/n bv4 .z+: g(fqo8d2xlab ma(um/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 skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pcx co u o-m/,kfo/3iu*articular instant, its acceleration is c oi umxo*/oc/ k-fu3, 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 gravityvj3 ix iaon2je,*2-.uhur 1f2 h 1nwdr on a spacecraft 12,800 km (2 Earth radii) d.*jvru1 n3rj1eho ixu2fw2i-,n h2 aabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has h.oi 70p19 oz7v ibmzma magnitudi 7hz0m v1.i7mzpobo9 e of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. t84tqce/xn8 fThe Moon's radius is 1.74 48e8cttqn/ fx$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has x mx7j; jm,u yvupu0.w9dx p.-a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near itpujduymxjx wp-xmvu,07; .. 9s surface?   

  A hypothetical planet has a mass z.zini:5j4nohff/(g qpu8s ) 1.66 times that of Earth, but the same radius. What ifi n8p(o.zns4)fug 5zih/:qjs g near its surface?   

  Two objects attract each other gravitationally wity zwtfc f5,0u2uyf+7 bh 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 accele7)xa njnw f))gration of gravity, at (a) 3200 mxn7w))f g ja)n    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wher58y gn zf0qw4ae thegravita5z8wy4ag fq n0tional 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 the mass of our Sunu5se617gtbklo pjd +g( b32of packed into a sphere about 10 km in radius. Estimate the surface gravity on this mot g pj6o(kb+352obefsd 71gl unster.    $\times10^12$

  A typical white-dwarf star, which once w6 +)fq4 js- -wv3 hjxa4gaxqwzas an average star like our Sun but is now in the last stage of its evolution, is thez hxw 4x g fsw6a+j)qa3v-4-jq size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the j (zec5b b02h2qqru 0jspace shuttle. Your friends rhjqjz (q 0 5b2ebcu02respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.ignaz:rckh(- i*89i t 60 m. Calculate the magnitude and direction of the total gravitatr -iik(h na9g tzc8*:iional force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the;tki fva:o1xor p*5 e)56 ztmj planets line up on the same side of the Sun. Calculate the total force on the Earth due to Vekxtj1 aie6m v)55t;*foz ro:p nus, 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 t;raz1rhr0 g8)t pbt y:he surface of Mars is 0.38 of what it is on Erb ry)r1:0aht 8 ;pgztarth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usnzid6v xx, *cl4bp 0-ging the known value for the period of the Earth and in0,p cgi-6lvz x* dbx4ts distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abou **kj pav4d;kr2 uc4eit the Earth at ac*p e2v u4k*kad rj4;i height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above todsscs 20 :;ujh x;yl1he Earth. How fast must ts0:2sldx;yj1u h cos;he shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrp7)h n3amxask)cp - ;ag4rfo.ical spaceship rotate if occupants are to experience simulated grans m3rkp4acagx);) pf 7.-h oavity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eox 6iiq900ycs arth in a circular “near-Earth” orbit. A qy0 x6ioc9 si0“near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hav*) o/jts o8e-z7zr,nx obuq3me to be launched from the top of Mt. Everest to be placed inbt 8zz,muq*jse3 / on) r-o7xo a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command xx(y9.jgr8kc8k3ni +y d;bus 1r/twdmodule continued to orbit the Moon at an altitude of about 100 km. How long did it take to drsx1 9 (nyxu b;. y3/8kdrjc8w g+kitgo around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Tv bc pl(im;s1rj1ah 61he inner radius omiphc(6;b11 sr jva1 lf 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 dz5j8zz zqt*d oclro; 1gz07f (iameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight ; ldzq0gr8f*5 z(t j1zzo7zo c(a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg asf ,9qzkb :h3edlk.+b qtronaut 4200 km from the center of the Earth's Moon in a space vk9+l.e fhq:kbq,3 zdbehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. T4qx h m,aj;qo))ls n,xg(g(jjhey are observed to be separated by 360 million km and take 5.7 Earth yeaajj )ho(sxmx;l gq, qj n4)(g,rs 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 ele bo46k 6meytu2u64 t2l )iwqirvator that 66iwr li6u2y 2m)ebt qu tk4o4moves
(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 ceiling of a/q dt,/ /; uy9y wxn:p*qs7ztnurw iv*n elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magni/x*du / / w y;,tpszyq *r:uwtvn9i7nqtude and direction)? a =   

Show that if a satelqscisc;(,n ,d7f .tz tlite orbits very near the surface of a planet with period T , the density (mass/volume) of the planet iss ntd,ct(;.,7c qzi fs $\rho=m / V=3 \pi / G T^{2}$ .
(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 perv:efv40vqn) k .e4gbjiod of the Moon (27.4 d) to determine the period of an artificial kq0 v 4b:.v4njf)geve satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits th9t-) )q: +qh hnmkzx+pp8a pkie Sun like the planets. Its period is 410 d. What is i ):9n i)pa mq8p hpkt-+k+xzqhts mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4 b(q:psonub2i.6 vs v*.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 years.zoq c/y(e3//h/ et4pwfm m cv* 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 etphz/ m w4/3ceo*qf( my//vc 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 aboutxq(i( io5u0 5iugyt ehy8sqk/l* m5*y the center 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 largest moon+ra/w hwk9c9 ts of Jupiter cwwrh/ak t99+(those discovered 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 and distance of the Moon. xmj; fm4;ptt3 ;fav;k3avtfptfm;4 j; mk;; x   $\times 10^{24}$

  Determine the mean distance from Jupiter for ek:jrh5;3r qj;/b qopgach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in:jop/3 jhrr;k;q q5bg 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 fragmen 8ljvo73gy ;vsts (which some space scientists think came from a planet that once orbited the Sun but was d;8g v3so7 ljvyestroyed).
(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 describei 5b48x(ea6wnmxp ea 7s 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 as on Earth. What will p47bma 8 iwn(5exex6a be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc fw3 3*) 6hfs jrpkkml5oj,mxfs9q o0(qrom a hanging vine (Fig. 5–41). If his 0*q )f k6wjshjmrp,s5 qo(fmox9 3lk3 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.   

  How far above the Earth’s surface will the acceleration, a 7q jr6+dxct4zro8vv;gc i0j/; sth of gravity be half what it is on the surface?tjrsd ;7a vcqt4 jvi/8rgcz;hxo+6,0    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mut;2 i+)krkj5x e-kd-k-lfhht fual circle once every 2.5 s. If we assume their arms are ealhrt k2k )+x j fhkeid-5fk-;-ch 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 d6r7edbiim x/p8wg w5(ay, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude oi/b6e 8dgi(w5wx 7rpm f this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spac3jbt ;1xf86+ haouzhcecraft traveling directly from the Earth to the Moon experience zero net68juh;1 tfzhao3xb+ c force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom :* ana 5junnq3scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, 5aqnjaunn:* 3 and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itscn;p vnf,zhb8hz e()+lb4o j ,1,lq fa center (zlna1pn8v efo,, ) (fcq hzb; 4,jhbl+like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a ver8 fyo 6uwmq2b-.t c+r;3vgegltical 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 acce:tpex 2 f7o/wvleration due to gravity at its surface and the gravitatio:w/pfxe7 2otv nal constant G.

A plumb bob (a mass m hanging on a stringem ier3:0c pk3t6*qkz.bwsj 3) is deflected from the vertical by an angle3 ers*0m:tce.w k3p6bqzik j3 $\theta$ 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 6 okz t+yr(vp5of If the coefficient of static friction is 0.30 (wet pavement), at what rangk5 zty+v(6orp e of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that od.t6ii rh50db bjects at the equator were apparentlytb6 .dh05ridi weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance a.7o,llm cxef( part 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 235z/ ;kvbzbdylfbcna2 jd dp)i;81); h- m. A lamp suspended from the ceiling;az82)l)b f dbn c; vi1/yhzkdpj ;-db swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as d816n ((.ft 9pwveruoi2dxp y 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 c1i986(ywde pf(d u. pont2 xrvan't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Sp2emwir.;j fg +cqa (k4ace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no l4mij+(f;w. e akrgq2 cight 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 it traverses tvuhsnngq,64 )he 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 av,sn 4)hqg6u nt A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satel)g7+ k,bv uhfwlites orbiting the Earth. Using “triangulation”,wgkf )+vu7bh and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 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 Rendezvtkn wd5 *pzl,,oan oa+bl,rwo(4 ;:tqous (NEAR), after traveling 2.1 billion km, is meant tpo,,q :otw;w4 ,+bt* a ( ak5nrolzlndo orbit the asteroid 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 a satellite in need o yfq kp,gj* bt.c*jbe:;ejjgd,/ z-mn /m4)lgf repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km b/,gbbqe/-.:ng zkjl,ype *; )jm4*d j mgc ftjehind 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 ix .7f1ckyozj:ts mean distance from the x ykjcz:. f1o7Sun?   
(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 cosrgqk iz, a9.(uc*2hezi ig3-uld actually "feel" yourself gravitationally attracte3cq.g-rgi* s2(z9h zi iek, uad to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dr( oyye wxgqm306(k kq+5c 4yyistancx yy+r0m 4o6e5y( (ckqygk wq3e 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 locatebn;9sv;.us+n tvghlku- u 6rv;ak7 +1m6oo isd at the corners of 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 miau6 1;o+v76lt .bohunvrg s + ;nk9mk-s;v isudpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 k1-q4sf hnd 7o rn3f1nvg 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 o0nv(s0 f* z-ivi1jjcpmaot., f the 1.5-cm-long sweep second hand on your wrisjjn.*- cavfo m0ii, v(tz10pst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swi qc0buw,54u*6 :az1kobvkwddgl f 7e*ng a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The wei 4 *zkq1wa 7f6blvo0wbeug:cud, kd*5ght makes 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 /izz07 zqzig5isf; l* new highway is designed so that a car travelin z/f g5zqs0i lz*7i;izg 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 trqe judu )k4rkhsq(wu: v2n 4/0ain, 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 cqn uq4kh (uks)e: uvwj0r4/2domfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$