Sometimes people say that water is rr kq.be 9bq4(+ayj d4hemoved from clothes in a spin dryer by centrifugal force throwing the water out kqq(a.9 4yrb 4hde+jbward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around 1o vl5uze-fty *x9q)r w vu2x)a sharp curve at a constant 60 km/h as when it travels around a gentle curve at9yur )xqe15l ftvvu ow-*)z2 x the same speed? Explain.

Suppose a car moves at constant speed ad hzxz081-v 0hp /fhvilong 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 levelv0zxdzf -h 0h phi1/8v stretch near the bottom of a hill?

Describe all the forces acting on:4; ) rn: iu/zxfqcqfh a child riding a horse on a merry-go-round. Which of these forces provides the centripeh:fxnq r)/i:4f u; qcztal acceleration of the child?

A bucket of water canyz*oe:i1prhzj1 a0 b) n.jfw n+vy(q) be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket 1ov 0) hpzz.jqij:yrnab 1+n e*fw(y)is upside down. Explain.

How many “accelerators” do you have in your car? Th7 mrzk;f+ )veqere are at least three controls in the car which can be used to cause the car to acceleratee+q zrvkm;7) f. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hi0g7itp u:k jgnb91inbx6 . yqkr e9/2pll, as shown in Fig. 5–31. His sled does not lxpktry/kb7.e gn92j1: qg p690iuinb eave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when 0gyxlix;jwg)gu o +8, rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle gi wp-ir :ldu.xieb /,tt i*h5l3wihbu t.-tr *p,:xdl3 e5i/liven its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plau/o nbro tmj:vq3(84t ne. She wants to let go at precisely the right time so v3burt :n/ 84ojqtm(o that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? I3+yhu;naeuj3g rx q8o t) t wo.)qv0t9f so, how large a force? Consider an appl tat 8;qug.0q) wr9 hno33xyvej+)out e
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would e.yw;d* psbg+430i5z ssdu eithe Moon’s orbit 0gdwpbsisiy eu + *;se5z3.4 dbe different?

Which pulls harder gravitationally, the Earth on the Moonx3 srzh4xn7n0ma( 6wuv9c+lu, or the Moon on the Earth? Which acc4n w 7h0 6rl9v 3xua+xm(csuznelerates more?

The Sun's gravitational pull on tzdn)bt 5 jn.l:he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravijl:t.)n5d nb ztational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whatj u-trx8h zm.9 two effects are at work? Do th9t hu8x- mz.jrey oppose each other?

The gravitational force on the Moon due to the Earth is only about halfo2 lx w/g1ghof9p,7u f the force on the Moon due to the Sun. Why isn’t th9,o1 g /72xgwpfuho fle Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around g( t: bk y/gk6kui6nl0the Sun larger or smaller thagn ybulkg0 :i6 k6/(ktn the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towardc-k, amzr;ac4p 4 n 0 erslkt6)rzdg,. the east or (b) toward the west? Consider the Earth’s rotation direk4,np6a ge ,z sk4 zrl;tcmcar- )r.0dction.

When will your apparent weight be the greatest, as measured by a scale in a miqu a;l(1 bbis,59wdpxa*ek s x7)y.ooving elevator: when the elevator (a) accelerates 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 1ii ;sq (x usbybpwklaod.),a *9xe75the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in o)wt;8oq* v vyd8m0oi ruter space could be adversely affected by weightlessness. One way to simulate gravity is to shape the iyo; v* o)tvw0 8rmd8qspaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betwe xp.m0/c kqw k,)0dzyp5fidx9pogj-y,ekx;0en sp )ekxj/y,zxm kfo.x k;,0cp 05wi qygdd-p90teps.

The Earth moves faster in its orbit around th(p,oj-mzir *we Sun in January than in July. Is the Earthjw pr ,(z-oim* 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 known unge6wn9+ wxe6y til it was discovered to have a moon. Explain how this discovxg 9y6ww+e6neery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger t)(/zxqi8sul (kvl )5x. xmu * f2vzwy/2gh jjphan the Moon's. Yet the Moon's is mainly respw2 *j uzlku.) qz85fhixxg(j2 )/vxpsymv(l/ onsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 .9 eh rz0gc1tv xn)*da$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 d):d.u ajk fos2ilf8 n: ki(o2Earth 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 orb idfkk).:sj uoi ofan(2dl:8 2it 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 it rosx62 pa2rv6q itates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. a62rs iq6x2 vpCalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cirifx,bp-qne) )b84z ru cles the Earth about o zxfurb))n- 48bqe p,ince every 90 minutes. Find the centripetal 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 acceb8ff5 4lk 3emx bg9w0lleration of a speck of clay on the edge of a potter’s wheel turning at 45 re9 lmbbf gf3x k850lw4pm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate df5, ilzcn.2wet1- t* vqmc0kin a vertical circle of radius 72.0 cm , a, ql cn.5-vwfcz2*0k1 tdtemis 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 1050-kg car can round a turn of ra ygto/+0og n2ndius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepetn/ oygon 20+gndent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the 749j- n16 gaot-u bafepuby3wroad if a car is to round a level curve of radius 85 m at a speed of 9 f3 eo-- 67ypuuagj4tawnb1b95km/h ?   

  A device for training astronauts and jet figwmkt0f a:0 a*lhter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the fora :* wamf0lkt0ce 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 fr;l a3bx dy vm./-kjm3ap6hx 2(xn 0zbgom the axis of a rotating turntable of variable speed. k;0- ybdxmal6z mp/(2n.3 xhagbxv j3When 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 misxl c19i(;om7 jzam. ust a roller coaster be traveling when upside down at the top of a circlmic;(om.91as z7xj i le
(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 thz-t t4e: 7efxae driver) crosses the rounded top of a hill ( f:ez4x7a-et tradius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameterf /vx5;*tspcg Ferris wheel need to make for the passengers to feel “weightless” at the topmo vx tpf;s*/c5gst point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle oth 47owu1kxeqi 2 b- +96ks s3ra6mcdwf radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is eh wk i29m66-txcqw a7urb1sdo3k+4s 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 particle 9.00 cm from the axis *s+vziuddl8 4 )e0q/lu /e/zp0s jvm60zljci of rotation is to experience an acceleration of 115,00+p/ lc00i seu8 v4djl6z)vl i emzjs0/dqu*z/0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindr a)cmjae 6hy2ke0/rlzt.b i56ically walled "room." (See Fig. 5-hcai6r.)aemkylze 0 6 25jbt/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 ) y9() nt8d* lu.xsn aksis rotated in a circle on a frictionless air-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 in Fi9s(naxyu8)dsn .lt* k g. 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 noozvx+/9z x+b tx/s7w bh4j;bir1z7vv t ignoring the weight of the ball which revolves on a string 0.600 mx 7;sz b49/j1v/++txbzvxiw7bv zrh o 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 banked for a car travelf35r sb +v/qa0 rat *l4f5mv1g.hpcul+jt7uhing 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 k1clqwui, m v4h2 /fp4$ 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 verticz(c1)uwiopf :b 4ly .hally 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 componsd4ss.hc o*kq0:/8 mrea ie7aents of the net force exerted on the car (by the ground) in Example 5-8 when its speed q7ae sa4/c0.rk*em si dos8h :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 pio3*.ju l :okipt 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 w.*op3 lkijo:uhen 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 horizonta0 20 wkfmd(ve4pldj c9h56;xy9l yzp ll circle of radius 2.90 m . At a particular inst5p0xv(h0lz9fy4yldlwm e;9j d2 kpc6 ant, its 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 grpn wqj *5r7s9n *e *.gbytuee9avity on a spacecraft 12,800 km (2 Earth radii) above the Earq99. p* nn 57e*gyjtsuebe*rwth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, t:d7icl *k,j1y,us*lyse v sa0+5m g ithe gravitational acceleration g has a magnitude+y 1 dal ,lv*is,c7k*ig e yjms0:tsu5 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. The Mood w)m3c-o9x win's radius is 1.7dwmco9w -xi) 34 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a racasmn9g 7escsww 6; (,dius 1.5 times that of Earth, but has the same mass. What is the 9ms6;c a(secgw7,n ws acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, b6m ;)x)fwq a e3-a7fj7zkfwobp x 3j)uut the same radius. What iswfu6 3f3m xw;7ojf)bqak-epxa ) 7jz) g near its surface?   

  Two objects attract each other gravitati,5cu.wk sg+ 5jqzjpz.onally 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 oabc u/q9alulz2p3mv/am-- i -f g , the acceleration of gravity, at (a) 3200 m3/m 2ua-la -uav/bi9qc-pmlz    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsqtcw lwpj, 13o6-iwo9ide the Earth where thegravitationatlw9c,-op iq3j ww61ol 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 ve/c/(wy sg k0qsd. *)qep 7jcSun packed into a sphere about 10 km in radiusjee7 dw /(.*vkp )scsyqc/ 0gq. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avn6ozql c3m5ggdk:(9p erage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravi p6zc:gn59l(3 gqdo mkty on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting inew* gd zc-e p czul+kjo(39+a- the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Cecz l3- gcdka+ -+*p9 eo(zuwjonvince 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 c -v.tcu3d w;oare located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by ttou.3cc;dw- v he other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pl g84.y:kv3h ih vauu4p,tr2 kianets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The4aty4h38g p2uivr ik.k:, uh v 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 acceler da8; j-g4e -fcpzh42 fohxzt+ation of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deterx 4-gz2-fc+pj8hha t;dz4e ofmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value f.7aa 2h/,yxz5dau 1p s )gtdzfor the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]5)d7 ta2y/ zgx.u , a1dahsfzp    $\times 10^{30}$

  Calculate the speed of a satellite moving ino6hflei)6 m j 2zljlwbeb+ 0kmb4 j(:: a stable circular orbit about the Earth at a height of 3:i)4 6hbwm j:efe(bz+kbml0lj6 jl2 o600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65+qa.gf rx j ./g;56 pahi:cact0 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? xh5..aigag;tcp:fj c +6qa/ r    $\times 10^3$

  At what rate must a cylindricasxkde( n1jcmhh c8(+*l 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 Questiok (x e nhd+s1c(8*mhjcn 21, Fig 5–32.)   

  Determine the time it takes fzk7pe/4v (s xni7t/pc6qwfu/ or a satellite to orbit the Earth in a circular “near-Ear tc/p7i(qvz/pken64sf/w7 x uth” 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 the satellite?    s ~    min

  At what horizontal velocity would u ks jwye7(ng(hx2 ;l-a satellite have to be launched from the top of Mt. ( e jgsx(k-7whyu2n ;lEverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orf1 g;-- i0 xeewewqd(qbit the Moon at an altitude o wgw-1dqieqf;e -0 e(xf about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice t4170:wf nr) q g)(qveelpgh vdhat orbit the planet. The inner radius of the rlvfe4 v pn7q(h1)w:q0 erggd)ings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Wha kh x88).gga9asns)h ht is the rak9 ghha) n .8xhss)a8gtio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the p2*svag ua.ev tb4t:* center of the Earth's Moon in a space vehicle (a) mog*a2.utpe*sa:v4t b vving 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 consist;emu +mpgi l:4s of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point e mm4pl;gu+:imidway 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 c6*3gqu tj pi 24zt0dxin an elevator that 3x t4pit*d qgzuj260c moves
(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 frot7)x dkfeqlif0 9 uv1bi; *d3hm a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N an0vux9b;fkd qild*1)h tife73d breaks as the elevator 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 ple-fl*qlbcym.u41j9iul1kq.e 8 j 7teriod T , the density (mass/volume) of the pla .llqfyu e. 1j-l cmtlqu8jb417iek*9net 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 periob:;o(m; e8ruxl ,wtpx d of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface. el8mx;bp(u t; w,:o rx   s

  The asteroid Icarus, thouz(w +awr0u 3jggh only a few hundred meters across, orbits the Sun like the planets. Its pwu30w zjgr+(aeriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5n3rum b9c v9gqftx9 hw,(r s11 $\times 10^{9} \mathrm{~km}$ 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 yxp3dajbq9a4u p-x ,3 oy/(whe g*p( dxears. 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 fad*u g/e pj(3q9 x4xya p( px-dbwoh3a,rthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cen5i:deh 9 z)k8+n zgoxtter 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, ,qsuw / *brzeb2qqpye 2+ou76 and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 2bu2q,q soub6+7zpye /qr e w*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 a8nacfmc e 1w0+zluza p2psa2; ta;;6qnd distance of the Moon. 2scuzzf 2a l+;1; ew0 cqampa6t8a;p n   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moonxi f.gn0hxcc b y(m15in3qb45s, using Kepler’s third law5gny mb.c4 f5ib30q xn( c1hxi. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betw f 3rkkj n,;8h5l-wanieen Mars and Jupiter consists of many fragments (which some space scientistn-ihn,;f8 3 akrk5wjls think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planeg3*,vath* m1 x irpt7nt" in the form of a band completely encircling a sun (Fig. 5-i n p *v*htga,tx3m7r140). 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 goun4akkyuo 7 p cby.+36rge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a ny+cu7 a46b3. kykuo pforce 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 accewtilt a3(l1 o*leration of gravity be half what it is on the surfo *tl3ial1t w(ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab)4 (;lg(y x +;v7fyycngro r*o9spooc hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses ar4gsf7 )r(roc y+op; lc o9onyv(y*g;xe 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates oncp03 (cg o e3uwhirq8zu3n7oq ;e per day, the apparent acceleration of gravity at the equator is slightly less than it would o;z p3833ou0wqguh 7i n(ceqrbe 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 travel 3 8h/t gpiomy.23iuhping directly from the Earth to them8u 3p yo/i3 p.hight2 Moon experience zero net 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 scale in an elevaxa rx3oah2t )w6c4s03 w zoeb(u)nrf, tor, it says y t3ohx4eou, )cfr2(brwaw)a0 z6s 3 xnour mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of adi c72w5t pb0a circular tube that 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 (revolutions per day) if an effect equal dpb it57wa c20to 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 loo:) ;:*x,xuhqqpas fav p (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 onaq 8hgup ,-n)f its radius r, the acceleration due to gha 8-nn),q upgravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected 7z2m x* i uc0kvo2u7wgfrom the vertical by an ang7uvcmk0wg2 o izu7*2xle $\theta$ 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 +i.9tu sp:9imoqsg-(1is xti If the coefficient of static friction is 0.30 (wet pavement), .qsti +p-m sug(9so9xi i:1 itat what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obofdtma +2 )rn8jects at the equator were apparently weight28a +om)tdnf rless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance a3 (kn.nml.xalq9 g;y 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 23 b: q zg31z1pcno8qvb95 m. A lamp suspended from the ceiling swings out to ancbq zbz8n13v pgo1:9 q angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Eapjw )w)uyc-fn9/ rj 0prth. 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. Calculat-0npuf 9wcjr)/)ypwj e 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 anc) +re2n*mru w 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 clouds orbiting the core to wrn*c urm+2 )ebe 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 s wmc7(snl1pm(peed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, w( (cnm7splm1B, 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/ixm6 /;tkk.oqsj 9oalites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within axk;/6k.sq a t/o9 iojmn 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 Rendezvous (NEAR), after traveling 2.1 billion k nlplx 29qyp k*o+4vh,m, is meant to orbit the asteroid Erx*+khypov n4q l,l2p9os 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 4n8opnr 3 1an+csz;hfspace shuttle pursuing a satellite in need of repair. You a hnpsr oa;c1+4zn3 f8nre in a circular 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 period of 3000 ye- jh4h4u:li.xyo xc h-ars. (a) What is its mean distance from the Sui o.j h-:ch hx4-4xylun?   
(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 16:j2 mr,i/f o aepd*wgx k fmk,mx;n)be if you could actually "feel" yourself gravitatix:enf,oi /1pm j2dfr,6 xa kg m);m*wkonally attracted 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 (Figf 7mz et c(nt7-lb39w v7kqjd9. 5-46) at a distance ote7-(wdj tvmq 9lb7f3z9cnk 7f 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 aa r32qinnjght-8ffi, +z:sp3 square 0.50 m on each side. Find the magnitude and direction of the gravitational for sjg 3,p:rn+tf3nqa8-zhf 2iice on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits t( 6fk /moiahf6)y8zvmp5l a;w he 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 ex:tqdq7 bxg x-k-z wmht4a:w8 (perienced by the tip of the 1.5-cm-long sweep second hand on yokx - -hq:bwtz w :ag7x48qd(mtur wrist watch?    $\times 10^{-4}$

  While fishing, you gemvsgl(-(oal kwpf s6-.p6+rnt bored and start 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 swvgo-f-l6p.lspn( k +a6rm( is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a-n d xt6cm-9p3 jt7skna;uqt; car traveling atjp9xmtnd;3 atqcun76k ts; - - 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, utilizy0t7)u kvl -ye1+yv0)xqbm9n7fg gj m es tilt of the cars when negotiating curves. The angle of tilt is adjusted so that theeq )g-u)+b97gfv v my7kn0y1ylx0 jmt main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$