Sometimes people say that 23cxm1.khp ql water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wronphkm c 3l.x1q2g with this statement?

Will the acceleration of a c4xl.bc,+cg m0h0ffdpar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels04,ffc 0 m dbx.lhcgp+ around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road :pvuno)t*ksj b /--ae. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at avp*j /b):k-ts-auo ne dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a c1+d/lr, dev3 sv- mhfjhild riding a horse on a merry-go-round. Which of these3fhv1m-d e sdvl/j ,r+ forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without*c fhv1sbvt7+hjo65 s the water spilling out, even at the top of the circle when the bucket is upside1c bt h+*j5v h6v7sfso down. Explain.

How many “accelerators” do you have in your car? There are at +n6;cgorgcma;5c z+p least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce? n6+gc ;zc +grm5cao;p

A child on a sled comes flying over the crest of a smal pgu8 h7f usp1*;x:17e swuutll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain tls e;hugp 1tfsw7:*7u1p u8uxhis decrease using Newton’s second law.

Why do bicycle riders lean inward when rod5ph*4u i,kgh1 0u acqunding a curve at high speed?

Why do airplanes bank when they turn? How m: e*b 29tjvl5iyc8h: sely) iwould you compute the banking angle given its speed and radius85 : vibtjeyl 2yh)mi: l9sce* of the turn?

A girl is whirling a ball on a string around her head in a horizorvuf3yt l8y:l8sugy*l,e r+e1n7 4 f antal plane. She wants to let go at precisely the right time so that the ball will hit a ta+lf n8 tl7eu4yarv3l:g sy f8,*1 ueryrget on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational foy0:s wwbp/o 9orce on the Earth? If so, how large a force? Con/wow90pbs: y osider an apple
(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 ou.3y:j 63jvahy3(mmchv3 qsw emf,m2 rbit be .3fqchvsya,6 ujmjvmm3h: ey(2w m33different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon w3;f2x0 tsofp;c b56n +lkdxzon the Earth? no+l 2 zc swfkx0t;b53;pfd6 xWhich accelerates more?

The Sun's gravitational p; mm-.u3dc(4mc 5saqz* te0ek7lao (l2jv pow ull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gre2;koo 0(t lcal3pq*j(uds7 m w-cvm ema.z45avitational pull from one side of the Earth to the other.]

Will an object weigh more at the equany 5 r(/hik mrrc2nu4yn /3o4ltor or at the poles? What two effects are at work? Do they oppose each orcih lruy//5m2( ky3 n no4r4nther?

The gravitational force on the Moon due to the Earth is only about half the forc:i)jst ma8/hwhf0 0rlob x f1;e8hfm)a s1j/:x0wi t 0 ;flrhob on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration (ted wgdx:c 5)of Mars in its orbit around the Sun larger or smaller than d(:ex dtw c)g5the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b)d082eqz g9qts toward the west? Consider the Earth’s rotation direc 829teq0zdgqs tion.

When will your apparent (kdy xmrl v1pz,x128 nweight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the leax, 2z(yr8n kd plv1x1mst? 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 periout;7:*yvssb 3re/d j mds in outer 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 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 aspmv*u :de ;rb3sj tys7/ects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” g 5+ly zav8yz2between steps g8v5+yzl2ay z.

The Earth moves faster in its orbit around the Sun in January than in July.(hnwua,p .vc; Is the E.cwh; vn a(,uparth 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 until it was discovered to hk:yvt kbbxp/ /o+4k uiyl g-**ave a moon. Explain how this discov- ://+bguip xbklvkkoy y4t**ery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth i8 (7rn8lw;mfe,bn qtds much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a 8 dq,7(mtn;e 8lfwrb nmerry-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 1:*a7,sn*hje hy at 6gj980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earth in its orbit aroundh iv.c0fjrc+9ybp0 n 4 the Sun, and the net fjp b.r 0h49ivc+cynf0 orce exerted on the Earth. What exerts this force on the Earth? Assume that the Earth'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 210p))peun vkiedj )6,d4 N is exerted on a 2.0-kg discus as it rotates uniformly in a horii,np 6)p4 uvdke)j )edzontal 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 from the Earth's surface, pi36aw c*tnv:3kpw)dtkxm m73h /c6hand circles the Earth about once every 90 minutes. Find the centripetal aith tc)nx36wv pkdp:h3c36ak m/ *7wmcceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck orm j5*syf vmxy nx; :+,.(wkhqf clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) ifryx+ w5n;qhjs:x y,.vfmm(* k the wheel’s diameter is 32 cm?   

  A ball on the end ofn*85tm 4drk6n fqlbaty m ,0i* a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4*mitt65l4y * 8kmnda0n frbq ,.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 whi6hbe1h2c*9urt k7fdve j*r (- vyb:ajch a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of statv:v672tadkbu( 1* erejr hj* h-9ybc fic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tioya(/g ,j1t;wybv x 0hres and the road if a car is to round x/0 vyw,tbja g;1 o(hya level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate s7xa v38vz5q(tk m:ika trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times ht38mkx5:ziv7(q ksa ver 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 cvyzf8:2j 1ptwfy w 82pm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixedw :j 22ftf8yp 8vyzp1w 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 cm *04r;zji gza roller coaster be traveling when upside down at the top 0zrzg; jic*m4 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 kg (including the driver) crosses the rounded topsb4 nuyf v.u93 of a his93b .u4yvnf ull (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-mnwh8bkjuuotv; 8p6 7 0-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point? p8v;jb8okwu6n 7t0uh    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m7; 8b-zljgv0wh l ;rj a4e2vil uba:/p. At the lowest point of its motion the tensil 0;hljegb;p rv7 w/4:-uvabi j2l8z aon 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 particle 9.00lu+ qa)nd :j25j jdu -agxg:/w cm from the axis of rotation is to experience an accelerationj)lj uqg:a w2/g5d+-aj d xn:u of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatr ro4ge4wv,)n4 xai6ls1og4z 9wp;c jed in a cylindrically walled "room." (See Fig. 5-sexa4 jv c6l4w1, 9gzroi4g4;)pn w or35.)
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 xcz1c45cc5c0d6 rx q rrotated in a circle on a frictionless air-hockey tabletop, and 05 ccrxcq61czd4cxr 5is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisel,eilmlvn 80ve 8uu+9o. 4 gvwiy this time, by not ignoring the weight of the ball which revolves on a string 0.60wo +8 eu. iu9llg0vv,vm8ne 4i0 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 banked for b-0hrcsay-df7 4 +h iga 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 masse(5hg+;g3d quuhrn bjr 1h*pnc m ;uo +h8xwy)3s $ 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 vertically at t+ qs+ x.layz3 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted xbx7o+3rkorl1 2. ky lon the car (x+k .lx3r12o r ykobl7by the 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 pipku m8)8sjj2* *ktrre09 nhnat area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determ0tun p9*srjm* j8nr k8e2)khaine 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 hortyxe3 k :k;pn6izontal circle of radius 2.90 m . At a particular instant, itkn;pxe6 yk 3:ts 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 Eart *:agdt1ebkg 0 :t3dzuh’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 130ged1 *:3 :t dakgtuzb50 kg.   

  At the surface of a certain planet, the gravitational agkabql: 1 b:02nz ufk:xc v1a,wot*x 6cceleration g has a magnitude of 12 m/xozb1g02uqk vkn:*xacabt :1 lf6,w :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 ; 3k xb;odb:xgMoon's radius is 1.74bx3; gox:d;kb $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth,o.,orelw5f,e u z 3ee,igth 7ny3uc2- but has the same mass. What is the accelewoculuz.f retyi een3,o 3, 2,h5eg7-ration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius.b;: zf ++3 +bj uisi)pvj0 eepaagp08z What is g z3eu 0isja;:bpv0a bpejz+i +p+ g)8fnear its surface?   

  Two objects attract each3yhl/v flt4a1io+ce3xq3;u z48 tm mjugn x *7 other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity gibmf-1:ljn0, at (a) 3200 m f-b 0 j:lgn1mi   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance f2e-)n ybtgn(srom the Earth’s center to a point outside the Earth where thegravitationateys bg(2)nn -l 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 oud y) *nj6pwk,hr Sun packed into a sphere about 10 km in radius. Estimate the surface gravith 6)y n,jdpk*wy on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an adz0./ nc*qqt5op voe 0/qyh;z :o+ nneverage star like our Sun but is now in the last stage of its evolution, is the size o n dq/+0e v/z:z0hnoq.q y o5o*necp;tf 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 feellci * 9):yt.m ugrz4zl weightless while orbiting in the space shuttle. Your friends respond that they thoughgzru zy9 cl).:m4tl*it 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 locatedcb v:xtu6et nf4:v0;lnmje-( at the corners of a square of side 0.60 m. Calculate l- bmtvv 4e utnx6f(::cjn;0e the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of qit:n8su1:+ y w8mqfx ii3xl3 the planets line up on the same side of the Sun. Calcula8xq is3 yi qi+l13u wfx:n8:mtte the total force on the Earth due to Venus, 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 p yvk,.9o l8u8ji 3gkhqee ,*rthe surface of Mars is 0.38 of what it is on Eaq3p.ry k, 8v9u*keei 8jhlo,grth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using tff k+u,/glq- ctt8k4-1q wxfthe known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawql1 tc-k 8 tg/ut-f,4q fx+kfws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orrj7 phmk8w rm*e8/fz d6 sw1s+bit about the Earth at a heighs /rm+8 rw68zs*wepdjmhfk 17t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above thiqe-c ox ,f0f0 3m+tzku7tie 1e Earth. How fast must the shuttle be moving (relative to Earth) when the re1t3e + o-tmxeu z 0q7iikc,ff0lease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arj lmdn; 3s /0nlkuk 9w.7( .lw+qeknwre 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 21, Fig 5–32.) k(wr0+w.s ln/ knule k3m;.qlndw7 9j  

  Determine the time it takes for a satellitezvq) r +v2jo7m to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radiu 2mr o)z7+qjvvs of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the tomelaa0 x1kvt6:/g (:utaog,g6u r4 ixp of Mt./k:lta1,rt4e(o x g6maugvi x6g0:ua Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missio2mul 4s-d (;0rjb j q*bfrl;fen, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon;bm0jq2(r4ue b-s l;*fdlrjf once?    s

  The rings of Saturn are composed of chunks of ice than -9zi ajjd6l u*x,tnf::cw 7kt orbit the planet. The inner radius a6k9:-t,n7 * xjc ljuz:dn fiwof the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once 7vvj*uc6mh+qesv5e4 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 j vv5uev+m4qs h*e6 7cthe bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of txf4tfd-2ekz, 1ed / xzcq,u,uhe Earth's f- cddukt ,1xze,4/zfu q,e2xMoon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two9zt3,ed+ymh l stars of equal mass. They are observed to be separated by 360 milliy3h ,dezt +ml9on 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 fs9 vu wj9yvf:7vn ,*bjor the weight of a 55-kg woman in an elevator that moves 7 fvbnvj yu9s*w,j:v9
(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 an elevator. Th. ecorj yovph.a s5;,*e cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude ayj;.,* eh.p ov sa5rcond direction)? a =   

Show that if a satellite orbits very near the surface of hka06lsnvg5e (+s/mnan i6 c 2(rjr+ na planet with period T , the d 0 nanah+65s jvk (cm62snnl/ re(g+irensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to deter/ b u:lbtth.qzunu6: 5mine the period of an artificial satellite orbiting very near the Earth’s 5/tu: bu.n6hqz ultb:surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitsny;3rgm b xwve 9n-82x the Sun like the planets. Its period is 410 d. What is its mean distance yb re-w2 m;xg9nnx 8v3from the Sun?    $\times 10^{11}$

  Neptune is an average cwvea p+9qht9rlp my00+ v,e9distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It c7lb /f0zdb qn6omes 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 0nd f76 /qblzbmean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about thws*gcn ()ez/ne 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 men03a23n k3j* h jj77zfdt wikjan distance for the four largest moons of 2 h dn 3t*7fjkniwja3jk0 jz37Jupiter (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 Eart4 /m 4 ;oadtumj) v)sfj8)weylh from the known period and distance of the Moon. 4jalow/mj) d8ey);tu) vmf s4   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kep;nl*jzszo9 iat.u-s , ler’s third law. Use the;i z,z. *osln-j 9suta 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 between Mars and Jupiter consists of many fragmentsmdxt g7tfq030d- q* fxa:cpm/ (which some space scientists think came from a planet that once orbited the Sun but was destroyema0m t x/ d0xfg dqq3tc7fp:-*d).
(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 descrgz 0a 5iz4c,uirc 2x2nibes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside sxnzu 4c52izr0,i2 cgaurface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in awr ,dvxy 3(g3(voz v/nn arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 gxdzr w/von( 33( ,vvym long.   

  How far above the Earth’s surface will the allo1;; uksl pt1dlw rc4-k;:acceleration of gravity be half what it is on 4uollldk:cw;a -;l;1 rtspk 1the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circle, f9q ,ma*pd fbv g6i*il04dee once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one a0,vd*bg*i edqe6f,4p9lmifanother?    $\times 10^2$

  Because the Earth rotates once per dz(b(g-q, y +(eltteoyoh w*w;ay, the apparent acceleration of gravity at the equator is slightly less than it would be ( tte( +g(hywoyezq- *bw ,l;oif the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance fromzljsriunk;2w 6w v*;f6a4- m b the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force becausezwmk6 fi a;2lu*jnbvr 6-ws;4 the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 0w 5kb+n0b0lgov0j5g c zl4 i t)hf2oz65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, an4 g0ib)cz5v2kt gb low5f no0+ hzj0l0d in which direction?     ----待选择----upwartddown 

  A projected space station c 78h/opl9 mddbonsists of a 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 to gravity at the surface of the Earth (1.0 g) is to /l 7bdm9dhop8be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft a 2hz8v321tcaela 6z/i p v-duwum);din 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 rsqey (heci u 6(f)bu..bqv*6badius r, the acceleration dbc*bqeqvhuy .ei( f66(bs .u)ue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectegh ;7lrhsd oxqfy2:,( d from the vertical by anhqx; r,gsf:(ldyo7 2h angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficientzkaigmbds60xx g8- f94*u-oc7f m-vu of staiv *-xzb 74duk0- af ufc8mo-gg96 xsmtic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth t u.9s*uietq. x)0exb were rotating so fast that objects at the equator were apparently weightleie q)u*tt..0ux9bxesss?    $\times 10^3$s

  Two equal-mass stars maintain a constant distan/d2wgz vwu +lb5cu v82ce 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 constan:k 1kckk-. r9ol-halbt speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17k -1.:ko 9khcklbar-l.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as voj1u0zfdpbp4 z8 ( 9vmassive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gp0f9zvp4(dzjbu 8ov1 ravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: 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 Hubblkphp3u28dq2mkc2 u6 f0,p vin e Space 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 light escapes). They did this by measuring the speed of g8pk 6 f pumv,u3iqhp02d22kncas 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 txsm )(7na2s61 vh5*+qkzcx3jkwwu0w 8 e q wdsraverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the nxcw x8d 6+v (5 ) weujwsqsa*wsk7mk 3zq201hdriver 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) utilx,e7 sq b/1roiizes 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 s1e,7x o/bir qcentimeters. 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),5 rtzrpdkw,q;(i+d*4oaqq i af -3f,e after traveling 2.1 billion km, is meant to or;eqirakzdr , p*+df iq ,fto354qw-a(bit 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 of repa1 tep02 .(6utz6wkmp( e7re ahudeg/cir. You are in a circular orbit of the same radius as the satellite (400 e( 7 e1/eha(e0g6tk.pumdpwc2 6trz ukm above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dix5bp:nogcm qoh,l2yjs,*m : (stance from the Sunx 2o o*b,shn:mpjm(ql :cgy,5 ?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could act n)g1s-(frytg ually "feel" yourself gr( rtg gfsn)y1-avitationally 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 j5 d:iklph;zm:qe+wevp. ) w1(Fig. 5-46) at a distance of about 30,000 light-yea) wm ieq:.wp5v+ek 1ph;djz:l rs from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on ea 3dtt0ein9dr - xd3-6dl joz8mch side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoiid3-rozj80mdtt3dnd-9 x l 6ent of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitwzpr m)eq. 6nf1 74dxzs 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 6mjvup zw 2d87f9nl o+by the tip of the 1.5-cm-long sweep second hanl 6uz9 om2w+v7dn pf8jd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cira)wu - )kvq9qw-snj 9wcle 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 withjnv)u- 9wqkwq -ws)9a the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desigu)1smy:v1g :ilfa z (yned so that a car traveling at us aiy() g1 mlv:zfy1:speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the carmb 7m pt -36wf8ridgypr54*cy s when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is nom8wcy3fpirmbg 56p -*r 4ytd 7t 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.$\approx$    $\times 10^2$