Sometimes people say that water is removed from clothes in a spin dryer by centr1dj-o :t0gk 9kgrl.b xifugal force throwing the water outwardbx.rog0-k9t lk d1 :jg. What is wrong with this statement?

Will the acceleration of a car be the same when foy) f cl3/o:jthe car travels around a sharp curve3 co/j ylff:)o at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constt03lrj 14ku.5ultq owm99x q ita7zn6e s l-;oant speed 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 so6k9 4nxtj01; limza lt9 usreo5q7tl-q u3.wtretch near the bottom of a hill?

Describe all the forces acting on a child riding a ;: lok rwxs9 0mif2*vmhorse on a merry-go-round. Which of these forces provides the centripetal acceleration of to v m;9irxwsml:f20k *he child?

A bucket of water can be whirled in a vertical circzkz 9z,1olp9cle without the water spilling out, even at the top9, pz lz9zoc1k of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your qd+)wv62 o/9 fd*cmxw9iipbh car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produ d/wxi9f*hcv) mq29w6o+pid bce?

A child on a sled comes flying over the crest of a small hill, as shown in Figlon2y-z asqt 2e3 7,-(wukujh . 5–31. His sledweku 2j q3a-so y2nt7u(l,- zh does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders ls j hkm-ks,a40ean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you comfhzkik.-tqd5y.ag94 1zc dduz1zq/t1iug5 )pute the banking angle given its speed and radius of tfz 1u 5/qid.4dk5qtg9 y1hiza g1kc td)u-z.zhe turn?

A girl is whirling a ballvjhd65gj8y6 4i :eu;lami5georl l04 on a string around her head in a horizontal plane. She wants to letjmi5 lugraed; 4 y8o5j64lvig: 0h e6l go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a g2f7 ibdwzoj,0 b)r c;l,vm0g sravitational force on the Earth? If so, how large a force? Consider an7r2)0mcigs,b; f0zv ,w bldoj apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whavl w:dq,lyjkh2)8d 3vt ways would the Moon’s orbit be differdd 8h vy:qlk)lv,w j32ent?

Which pulls harder gravitationally, the Earth on the Moon, or the jpy) 6n21c,3 i4b;wqy r6juxn9nsy zs Moon on the Earth? Which accelers cwb nx6sy1)p2zy964 3n ijjyqr,u; nates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yd :e0pkk0dr ii0r8bt2 q7ps;qet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side pqtkre87:d0bdr 0is0pi;q k2of the Earth to the other.]

Will an object weigh more at (mtz / oe/vr:c0vg3k dthe equator or at the poles? What two effects are at work? Do they oppose each othed :c0 3reo/zm(vg/k tvr?

The gravitational force on the Moon due to the Earth is only about half the fo d2ugix* )uujz 9ea0g+rce on the Moon due )2iag0 eu9+z*ujg uxdto the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in th/g7zw w7d.sx-v y7md0li7 xits orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?sd/.hz ltwmwxg7-x7 id7 y0v7

Would it require less speed to launch a satellite (a;zqz)-jhb t2)po h3 pj) toward the east or (b) toward the west? Consider the Earth’s rotation direction.tobzpj h32pq )h;-)jz

When will your apparent weight be the greatestmh6 tlaw0ol)*, 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 least? When would lo*l h6a) twm0it 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 outbap26kxyp8 +7wypjf 0er 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 f6 8y+y07k ppxf bwapj2all, (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”1p-r1f0h( u3 5luwmemukmrk dw gd )-( between sgr 1l-u w mm dkm-pe)0f 1uhw(d5uk3r(teps.

The Earth moves faster in its; f k1( i6ss9ms9fj ;tyh3pkdw orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Notdyti6sh 9f 9w(j ;;fk ssmk13pe: 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 discoverey 4rjtym op.rem86n t5*p s4o*d to have a moon. Explain how thisr 6* *4t5 .r8popojms ynetm4y discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muco/gx t/ g*z;zq137dg)d.zprq7 lj wmjh 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 merry-go-round moves with a speed of 1.25 jpzgqg* ;/j) m otrzzq gx73.l/ 71ddw$\mathrm{~m} / \mathrm{s}$ . 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 j8yxkpihny -j 1sr 1.- 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 arowlp1 2 m*mf0qbund the Sun, and the net force exerted on the Earth. What exm1*fbwpq 2m 0lerts 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 210 N is exerted on a 2.0-kg discus as it rotates uniftjlg p+*hp 97cormly in a hori l+p j9gh7*cptzontal 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 frr phgvw (8d83fht.wk, om the Earth's surface, and circles the Earth about once every 90 min 88 g3hkw(wt.r, fphvdutes. 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 lk1eb clrcm:gh-00pzw1u: q )the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the g-clpw 0m0hb:) qz1:euk1 l crwheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vht) e+kix f6+bertical circle of radius 72.0 cm , as shown in Fie+b+6fxkti h) g. 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-kg6hgl3kq.jmhx lka2st27am( 0 car can round a turn of radius 77 m on a flat road if the coeff(mskgl2 20 lk3ahht.m6x7jqaicient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frictioq1j3m3l8d( (z +j- xyaqq/ vfq 2bmqton be between the tires and the road if a car is to round a qjdjoq + /1ly(vm qz3bt3-28xqqmf(a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots +) okysdx4u*n is designed to rotate a trainee in a horizontal circly4d un*) so+xke of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rp:02cjq2pk na ahx uwf;(98vtotating turntable of variable speed. When the spea: 9p2u pfhv ; n80xatqwjc(2ked 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 a roller coaster be tr0 q w:ghzty6v: tl+k+paveling when upside down at the top of a l gyzk0tph :t6qv+:w+ 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 rounm2f, ek e2 .k)hbu0owkded top of a e, mo hbkkf2 u0)2.kwehill (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-m-diameter Ferris wheel need to s 65 pf1zwc;qs:w1ey pmake for the passengers to feel “weightless” at sc1yz6pw s5pwqf;: e 1the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticccnow:,f:vazl;8bk r*;mv) t2gq3 n o al circle of radius 1.10 m. At the lowest point of i: l,*o)wn; aczoc vbv8f ;2gkr 3mqt:nts 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 particle 9.00 cm from the axis o9 hised39ahlr ( 7wx7p-mo;bqf rotation is to experience an acc;7b s9 ( mldhxe 9oh7pw3iaqr-eleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot x u i7*nki3a3w98f,v hvt(tbaated in a cylindrically walled "room." (Sevw*h3aftx3(v i7k8ut 9n,iba e Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tabszw( z-fo 1 gfvq +/o;(blr1qwletop, and is held in this orbit by a light cord connected to a dangliqlv1g+ /f- ;w1(fz (zbwqoso rng block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, b8k hps0-(bmkmuf( 5xzy not ignoring the weight of the ball whimkx(s p 0(h-uf8mbzk5 ch revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a ra3m:rj4g*kj ec tz-sb:uhqi -*dius of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massec;:zoangwv ( fo) mv3ugsu51 +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 manepkbqyur q-2kqu4+ff7fp54 :xuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential ahi c 5r*,m:ytq+1ju pcnd centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its,q*5yccp :hr umj+t1i 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 uniformli+;, uak kn7ydy from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleraa7i yk;unkd ,+tion. 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 c+k1vodpy.)vuoivv1p.kw+cxpz 8i* 9m(ul1 horizontal circle of radius 2.90 m . At a particular in+cox 8vkm wvl.(p pc*pk u191v)vd1ou .z i+yistant, 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 g.k+lk :ve/j ),gy/bu3 r6g +kxudopupravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.pubex+k ru g.vl+/pk3yd 6jg:)k,u/ o   

  At the surface of a certain planet, the gravitational acceleration 3l6pkpwy ;ys mg;*/r yg has a magnimlyg3; ywppr6s/*; y ktude 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 accelerab bim+hi ut:5t* k(ea(tion due to gravity on the Moon. The Moon's radius is 1.74 (mthi+b uite *a(5 bk:$\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, but halp (/8:zg ehmbs the same mass. What is the m hl:b e8p(/gzacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same ralakw-.4+v oztdius. What is g near its surface? 4kw- lvo.+taz  

  Two objects attract each other gravitationally witicr5wynd9;t - 35g7qgpo7jz.ifhu 8wh 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 acceleratigts/ lrj:,las3myk 9bg 5nx -7on of gravity, at (a) 3200 mrgss/la9btm k :x nj53 -7yg,l    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from :d:fg-jog z(mbk6 a1sthe Earth’s center to a point outside the Earth where thegravitat(d fbjos z1m:a:6gg k-ional 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 ou erf 6oueyb(5.r Sun packed into a sphere about 10 km 5b(ruf6e eo. yin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which leae(zs 2u8 plc/+k9t once was an average star like our Sun but is now in the last2a(c/ z8k 9p+lulsete stage of its evolution, is the 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 spaco8)cmxng3 p5ym 7d1e:0naalt e shuttle. Your friends respond that they thought gravity was just a lot wa3y:e 8d xmng5an) 1otmc70pl eaker 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 locateos813*y jto 9a wg:uinlx4psmx7bsbo(z+29 kd at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the tlyou:4*b m (213 ast7sxjg+9 inz9o8s bpwoxkotal gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pla8*4 (ynez p .0ixkedof qz(qy)nets 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 zxfn*dpkz(.q)o 0e( 8qi4yeyline (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the:dm-y 5zk kuwc4/f7an surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of M-k5z acm7f n:ydw4/k uars.    $\times 10^{23}$

  Determine the mass of the Sun using the kp0z vhc pfu2q mxtikd( 5 07.dpr9ig88nown value for 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.] i h20 ru (zx7f89t.8p05d pp qcmkdvgi   $\times 10^{30}$

  Calculate the speed of a satellite *doi(m/ q 0phurroj*6moving in a stable circular orbit about the Earth at a height of 3600 km. ur(i0 o djh 6r*moqp*/   $\times 10^3$

  The space shuttle releases a satelko9991lf drtx lite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Ead 99x1of l9rktrth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to exper-j v7mk 0p-xdrf siq-0/w1shaience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer 0iprkfa-1v-s 0m qjxsdhw/7-as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in1 1gk7m zq cognjr0o,pa 6.-3tct y3ou a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very qjray t3z gok 1 6c,o1oc7n0p-mu3gt.small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched frowpw k 71.tw-gcm the top of Mt. Everest to be placed in a circu-7.g1 kptwc wwlar orbit around the Earth?   

  During an Apollo lunar lan 9pci ymjtut31oy-uw6)tx e,5ding mission, the command module continued to orbit the Moon at an altitude tt t 5 y3-peiuc96j)mu w1,yxoof about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chun ),a2puemyiq )ks of ice that orbit the planet. The inner radius of the rings is )uymipqae2 ,) 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 diamete1vb f+sj);szd r rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real ;vs1dzsfb+j ) weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut pay086cgnl t+ kng 1:u llpi,xg+: 5hh4200 km from the center of the Earth's Moon in a space vehicle (a) movi,++5lakg6 plngtc liy 1n:hgu:x80hpng 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. They ac ssri+.4j +ojre observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway bj+.cso rs+i4j etween 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 yvkmsu1 ly6)3 elevator that mo )1y36vylkmu sves
(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 hang mit re4 iu*l:q,d/n 8:tjxwk2bpi b4/s from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eilpk, m /i td42r*4 8i:qje:twnx bbu/levator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very nez32a4 ntav8/h(gap.lpuh6 9 w cyh3fear the surface of a planet with period T , the density (maa2(cl4.6tv9hewg3apya 3nh /8hfp zu ss/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) / m lz.mg2fk2vto determine the period of an 2k/.2m vglzfmartificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the +yqlfr5 czno4 */i9rs92a o)s)u ibf ySun likea so*/+q9or blzui 49yci 2 r))synff5 the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.-;lmvp8 dkpe (vn0x5d5 $\times 10^{9} \mathrm{~km}$ 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 orbitspz 0y9;;kh lii the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is ou0zpk ;ih i;y9lt there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center ofob1o,llqcg)6o 1,cin 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 f+*1a 5vevo j: cihge0eor the four largest moons of Jupiter (those discovered by Galileo ei v o150h jcea:gve*+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 distaa jcs,tc:;+sx nce of the Moon. t,+ :as cc;jxs   $\times 10^{24}$

  Determine the mean distance from Jupiter for -l *zrys(glpgp. a+mlc gyr jkd7 . s9m3t)x2;each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods g.cx;g-3* zmrry l )m+al92.y7ks (ts jpgdg pliven 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 2rwmo f8,xgc; o0vzs5fragments (which some space scientists think came from a plao25z vf,r;sc w8mgxo0 net that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a ban4bz w:yp /ga6gd 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 be thwp4a/yg: gb6z e period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an4i ou.qp0 gfr)j1st )+yek8as arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a for+qu )g .1asr80poy tisjke)4f ce 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 surm,-rjehp6fvqlxw 2h4:k h h35face will the acceleration of gravity be half what it is on tf4re v2hk hp 3,h6:wjh x-q5mlhe surface?    $\times 10^6$

  On an ice rink, two skater;.h/j.:axe hm(by55pvibu / tu+kcsb s of equal mass grab hands and spin in a mutual circle once every 2.5 s. If ujv xckh h sbba iypum5(t.e:.;+//5bwe assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accele 3v gyh 9a6v7akr(afx6o(r.xc ration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. Wh gakrv7ya 69 r(haf( 6xx.3vocat fraction of g is this?    $\times 10^{-1}$

  At what distance fromepvbvn(h9y* * the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? *vp9* y(behnv   $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in axyry ht3:-l og mf:)t5zx(;ohn elevator, it says your mass is 82 kg. Wha y5lgott;:z(3-hr h:mfxyo)x t is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo 2,cug /ggnv2dut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a dia,gug2/nvd gc2meter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 1geuq(-urh8r e g3 12 2oyudbi5–43).
(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, thg5n( t+ikzuq- e acceleration due to gravity at its surface n (-gq5ktzu+i and the gravitational constant G.

A plumb bob (a mass xc 8e.s pzt;-w m hanging on a string) is deflected from the vertical by an;xec.zp w-s 8t 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 f* :hnzswpv3y 6or a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what rs3h v *w:z6pynange of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fakx.f38y; nz / f*yaieeyc w9;jst that objects at the equator were appar. ijwy naekyy8;fz* ce3/9x; fently weightless?    $\times 10^3$s

  Two equal-mass stars ,g8 jf.qg +zct 6ax6stmaintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 2a(0jaih 2z )n,.qfx g4qq qt9g35 m. A lamp suspendedgx4 ig za (qqfqa)htjq 2,n.90 from the ceiling 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 m x t;ysm10m.8qqqrn+ x :fp8ejassive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't s.q+p j1:efyrqxx0q88 stm mn;urvive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an e8, x-g:p,oow8(55jkr. ymzxkn wwhf lxtremely 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 orbit8:klr5 -xk8hojwwf, z mx(o,w ygnp5.ing 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 the hill and valley shown reuc5kbxez4 r, g7 8w)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 driver feel heaviest? Lightest? Explain. (c) Hower4u5kz wbe xrg 8)c,7 fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites o pagqnjh.(24 prbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The sat(a4ppg2 j. hnqellite 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 km, 3vs 8l7ryaod9 a 4al9lrx8d0ris meant to orbit the asteroid Eros at a8r 34lvala8a 97lryo rd s0dx9 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 nee.*vwhy shx92+r i:gb kd of repair. You are in a circular orbit of the same radius as the satellite (400 km above theg2v rhwxih9+ sb.:ky* 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. (aeai (pbo5 -59 jrluny5qc; zt;) What is its mean distance from the ;czr9 ao 5libu(5 5p;-tjyneq Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of fqgx**oelpn: 74* o juun(bo( G would need to be if you could actually "feel" yourself gravitationally att:x nn*4*(ooogu up*q(ble7jfracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center oupp-e/ )z -+ r(wvynyif the Milky Way Galaxy (Fig. 5-46) at a distance o u -wr/y-yze n()+pvipf 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 corner7ircd(j/ rh 9ts 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 midpoint of /d 9i(crhjr7 tthe bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg o5f u6vp lzui77ee;jjjy:8(ckjj4h38lq yf w -rbits 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 of the 1.5-cm-long sweejomr i7mtk :2nomdek3e4i76*p second hand on your wrist watch? or*7i omk3m24ed7t nime j:6k   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ar17mmt* * lgrpuound in a circle below you on a 0.25-m piece of fishin*l p7ur 1gtm*mg line. The weight 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 5jgalp.klt sjluf8uyhn,2e7/ 5 hs1.radius R in a new highway is designed so that a car travelinjshul7/. g atkhs,8l5e yl5p2 nj1.ufg at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utili rkggq-r ,7.zjhc1 qa/zes 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 leszg- agkc. q1 jrr7q,/hs 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.$\approx$    $\times 10^2$