Sometimes people say that water is removed from clothes in a spin dryer b92d i2 6q,h.sst ewhspy centrifugal force throwing t.62 2dhwit,9qs ess hphe water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels aroundu4yd0x y1orn ) a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speedxy d410oun r)y? Explain.

Suppose a car moves at constant speed alom. ea*zef -.mvng a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) mv*az-e.e. fm at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rho:uaycy.,, 32 cgj klound. Which of these forces provides the centripetal acceleration, :c,uc3 .kylh gyj2ao of the child?

A bucket of water can be whirled in a vertical circle without t yglvxo) n4/m(he water spilling out, even at the top of the c lny)oxg/4v(m ircle when the bucket is upside down. Explain.

How many “accelerators” do you 0.kb );pa 3kuu.cam- j3hvwwdlis d,;have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What arj;3m0scub ldu d khiaav)w,3-kp.; w.e they? What accelerations do they produce?

A child on a sled comes flying over the crest7p:j5.smq mxe of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the n xsj.:me5p 7qmormal 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 rounding a curve at b lbp -76c5thpy(a3 ighigh speed?

Why do airplanes bank when they turn? How would you compute the banka89orime (c l p-0bmf- a9pjv9ing angle given its speed and ra8 999jpvr0 amm lcfbp ao(-ei-dius of the turn?

A girl is whirling a ball on a string arou(w jlm*iq- f2jnd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the*ji(w2jm- q fl yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earttgftna0 . 8w6dh? If so, how large a force? Consider an apple 8 6ga0tdfntw.
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whatsuur z5qe**qj0syc6h ; ob(j: it is, in what ways would the Moon’s orbit be ujscy(qjq0 zu res;o* h6*:b5 different?

Which pulls harder gravitation:h:r7l1j 4* n62 yywr jzz(asskeuoi7 ally, the Earth on the Moon, or the Moon on the Earth? Which acce er sy:k*an:1ru4j6w z2jsh(7ioz7yllerates more?

The Sun's gravitational pull on t*1 azuek5cvqxn7wi v2- -ij 9ahe Earth is much larger than the Moon's. Yet the Moon's is mainly r iv-a29k vwx5 -c qnu1ez7iaj*esponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poleb/1,t)zovct :u la y: jbbesdwrnv.**.8v: z rs? What two effects are at work? Do they oppowb.t :: yv zd s ./av8z*1cjorlub)*:rtv n,bese each other?

The gravitational force on the Moon due to the Earth is only aboutvpu)s3w7b4zctt/.v7j es7 ol half the force e7c4t)l jbpsuvvz w7t/7o 3.s on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Se. pljhlztxw7p-(3 .s1g.yckun larger or smaller than the centriht3lejzsp(.yc x 7.lk. 1 -pwgpetal acceleration of the Earth?

Would it require lessj00zs/wf )y z(de 8tuf speed to launch a satellite (a) toward the east or (b) toward th)u8wsfz/ efj d0zy(t0e west? Consider the Earth’s rotation direction.

When will your apparent weight jan j8:+ze3u ussd2v+be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates dvu8sn2jaz s:d j3e u++ownward, (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 the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected by o: ecwpv6, s(-iks nj7weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (F6 - ek7c(njwosvp:is, ig. 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 experien4ui3(8 d.r v gh npib0taa0l:uces “free fall” or “apparent weightlessness” between stb.v pnlu3 uih(ag 0d4tir 0a8:eps.

The Earth moves faster in its orbit around the Sun in January thai-- qms (ylg6o 7rg/lrn in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relativegl7o m/- 6yqi-(lr srg to the plane of its orbit.]

The mass of Pluto was not6nc*eww 7m;l 2 bljw8l known until it was discovered to have a moon. Explain how this diselm w68 2wnwljcb;*7lcovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than vfpay2mf bz- 1/6y3a )xve2t6nnn cb7 the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differ y3p6veny bnx2z/m nb726t)affacv1 -ence 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 cegggt jo)3np9cjp 2;;+ ) whs1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 around th8o33g,hdcx.y4z3:xy wyx m rn;nn5u b e Sun, and 3 nydg3;wmuxyr.b4,z x5ny cn8hxo:3the net force 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 210 N is exerted oni/ j wjw61;n dzd(3yxtv*heo( a 2.0-kg discus as it rotates uniformly in a hoz3 (;ijyv dw/hej* t w1no6xd(rizontal 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, and cir63z8 u+ayqb+ b4zk8u/lb5z hh jd +garcles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its or hy48zjd+5z + u3qb r8 bgaa+hkbz6/lubit. 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 of clay on tsazr/l qc nij 42(*iw*r (fr1the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dia irrf(*l2tizwj(1rq/n 4 a* csmeter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a va:w6,*(c c:hb+g7q 9vmlv* nh lmdu agertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0 nv(w*a:l +ga vhqm*c 6u9mbg,ld: c7h0 $\mathrm{~m} / \mathrm{s}$ 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 15l;so4re z a3gh jz7u3050-kg car can round a turn of radius 77 m on a flat road if t473re oaz;h5jgluz s3he coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static f)suq83cezj7 sds2h;lje +f (ymm7w/h riction be between the tires and the road if a car is to round a level cu+7f z;e)jcs2 equjm(8swh msyd3/l 7hrve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilotsx(z;/ lxe+rhx :l8nm e is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If thee:8l(rm x+h;/xxz n le 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 rk 6abyr.ct3 f45o;g + 7ujjdq deprj32otating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable u;+y j ae75k6b jc dqt3.p32dr4ogrfj 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 coasoa ;jn; u-z6whter be traveling when upside down at the top ah-u;o nzjw; 6of 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 9iar.zoe;fp+ ,gr5 ; wl50 kg (including the driver) crosses the rounded top of a hill (radius =9;;i . f,e+ragpwzorl55$ \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/ dq/jry6a,gy wheel need to make for the passengers to feel “weidrqg y/6ja/, yghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. glq *s6e k5*4j;7qe 1dx jjxgyAt the lowest point of its motion the tension in the rope supporting*d g5qjxje6*lg1 j4 ky;x q7es 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 centrif,7:b /d,f oaonqejf5suge rotate if a particle 9.00 cm from the axis of rotation is to eoq7b/jen f, ,5:ds afoxperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotaep,tnt: 71 ia6xet6jh 2z4srqted in a cylindrically walled "room." a 6rzt e inp7:the2x64s1qt ,j(See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionlessz(-z3guvi2 yo air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a ce- yo3gvzu(z i2ntral 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 , dv l(-a-0yrfv0tw p( m2y iy;nprecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the yt-d i -f 0; avw(0nmy2prylv(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 perfe01at57c88i4uiyik ej vb3cg*l tl8hpctly 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 massev3.hh6ea qruzeh7r /;j4e bg2 s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310 v*-)vzwz)/ e2 4nldz 1txnqlr$\mathrm{~m} / \mathrm{s}$ . 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 th *g dpa l0 opt2pqwi0sm*u,.s)e net force exerted on the car (by the ground) in is0)w p.s*md utla20 op, pg*qExample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit alomro70*5nqb on0 2pirea, 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 0olb507noio2nr p* mqthe 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 hormj(h4lyvlko .ckc, (;izontal circle of radius 2.90 m . At a particular instant, its acceleratiol k.k(l4y;ov,( cmhcjn 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 graviz8drrlty s7.v242qkv9fxe(o ty on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 13504f9vz28dk r2or vlyx 7.qet(s kg.   

  At the surface of a certain planet, the grati ( y ednzqjwth+q2wa3 n62+*vitational acceleration g has a magnit(q22z n+iywj* tt 36qn+dwehaude 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)j9,6o p2hpnskcel3:9z,l tl rg zs0j gravity on the Moon. The Moon's radius is 1.74n gj3ps92 ,jeo,)69 ztzc s :lllprkh0 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiusy(( 26pyd.5yxponlez 2d-tg(h 5ddxu 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface? y(x p(gd25dtn- yd6du z.x yh2p(5o le  

  A hypothetical planet has a mass 1.66 times that of Earth, but thrn24lgl pb8kkpe1*j) e same radius. What p)p2 kllkn r*e4 8jg1bis g near its surface?   

  Two objects attract each other8e,a*zh;4qm p:dot sd:jruf3 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 valueq v5rmsva jvpl,0e68 )oz 25 lhvx anb(-k:p.r of g , the acceleration of gravity, at (a) 3200 m (5 b v j,a)68 -rsqkpvamel5xhpv vn:2r z.0lo   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point oum( w*yuuyz8;+sumy*s tside the Earth where thegravitatium*w; uz +yms y8u*ys(onal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fxr ; tq6c., +-fyaokrnive times the mass of our Sun packed into a sphere about 10 km in radius. Estimq6c - ro.af, yxnkrt;+ate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Suns75so f92;9vdb cyu nze5y3pb but is now in the last stns3 s7d;u zvb2 f99ycp ey55boage 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 w/ 22g+q-akqfkd ctl3dn . s;yjhy astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Cot +dkny;2-qa.l f2jdgq c/s3knvince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the cobncs ))c7yu7qw5vtp8 rners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphn 8pc7)t) bcw75 vysquere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up onxe 5ad 3e *b*mwtah*lowb*6 )z -e:5scia9odc the same side of the Sun. Calculate the total force on the Earth due to Venu*z3ei *o-a)c9h sld:*a tw 6b w*o5eexbadcm5s, 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 bd *.i6 2ejxceat the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the me6x*bdcje i. 2ass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun us 5s :n)(47ruteqs.xjob 45dn ixo zxs-ing the known 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 5s) d unbx.zs ns4j:o iq 5-74ex5(roxt–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circu2 ,ltzsj(9o pxlar orbit about the Earth at a heix9(zp2 ,js tolght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular or h;y8+apa5 hpuevq8c) bit 650 km above the Earth. How fast must the shutt5 e8;hvpp quaachy)8+le be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantz: z we2w9 s:3kx ltw0nlfj8/is are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter90:z:ftwe 83zxnj ik2sw l/lw is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “n)ptkp 2su0h7 near-Earth” orbit. A “neap)shknt 0p 2u7r-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launchedsg9d;x6j j p;q from the top of Mt. Everest to be placed in a cis;q6;g xpd jj9rcular orbit around the Earth?   

  During an Apollo lunar laz9 9j3 *wycolxnding mission, the command module continued to orbit the Moon at an altitude of abol *zc yxo9w9j3ut 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chu7bt:62nfkxo5p 79tei.xjvu ne 7h b5lnks of ice that orbit the planet. The inner radius of thu7 evexttpln 9bb5 x7hji6.o :7kn 25fe 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 every;eue k :u8n.*xxoyb .u 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real wek x. bu8:une;o*.yuxeight (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 center osfhymm x-f65,f the Earth's Moon in a spa- f, 6yxm5hmsfce 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 two stars of eqht(,ep,re+x rk:( z tcual mass. They are observed to be separated by 360 million km and take 5.7c+ tr :xhpze,kret(,( Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring schm/ce2a-c8m/myg 6ot c*t5qw ale read for the weight of a 55-kg woman in an elevator that moveg/ycma c86t*mwo ht5m-/e2c qs
(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 cordwk4 x+6xmz by4 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 elevatk yx6z4bxw4+mor’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet withwm:c* mpy/4 dzuwh03ehxb5kzqx/4o ) period T , the density (mass/volume) ofz*huy0)w kzmcedqb /x4:/xo m4 h35wp 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 determinerawnuin6ei568:egqtd2.9 d e the period of an artificial satellite orbiting very near the Earthe 62.igtu a5n9en dredq:6w8i’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits 2+q nmkx(q:fh*z ook6the Sun like the planets. Its period is 410 d. What is its mean dim* ono(h6qfk2+k:q zxstance from the Sun?    $\times 10^{11}$

  Neptune is an average distance x, 0k4/ p nb-sukd5lrdof 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 comes vzyh+bw8auyu 7 gx w-(,ery 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 nearesty+ ,xway7z - g(h8uubw and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of th 8+ osorlm:vy8e Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest motx 3 o; 2c /liwh0;1qod2rykdhons of Jupiter (those discovered by t xlho2h10o qrdk;;yw /di3c 2Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of thvzqkr5a *s32p vge49j6ohc a6ai0jn.e Moon. je9acikj6r.vavaoq p20sh n*6 g 354z    $\times 10^{24}$

  Determine the mean distance from Jupi(jm1 fu7qiwyv a6 qlw+t7 - 5em/t/ldpter for each of Jupiter’s moons, using Kepler’s thid 5le6q7mmtvw 1uy+ q/l7(/f-wta jpird law. 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 between Mars and Jupiter consists of many fragments p3dgd:rux w3sx7* b8 *b k fh1ab:omh)(which some space scientists think came from1p8b sgx3:bbh3 )mrx : f*w *kouhadd7 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 arti b0i,,xbg0 us,ru b9zhficial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Eai 0,b,bsxb r z09uguh,rth-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 an arc from a hanging vin6m3 hflbl038;d pysvrnty-he rt 40rifn/,9ae (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he ca6, 4nbrhl yl-v;r am8r3nshf /dti3 pte9f0 0yn tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gq86zjs-,*ls ltk wk)*c0loxxravity be half what it is on the su *l,tzkw0lj*)qcokxs-x8 sl6rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands kh)c;ex1 hh 3wyulza-u) 5rp/and spin in a mutual circle once every 2.5 s. If we assume th kecz u/)1r5hwu3xhal)y;-hp eir 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 dniqtyu 2;o*ahhg)s 9 0ay, the apparent acceleration of gravity at the equator is slightly less than it would be if t io ;a h2gyhnq0*stu9)he 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 spac fqdv(a,a2nvho)e 1s+ecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pule(fo va nq,1+)hdsv a2l with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yom auw/ny-z6uq/ed r :4u stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wd nzeamw/4 yru6-/qu :hich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tuk. 1nurc y4.9)ykj d+yhbix*9 li.5b rlha8oibe 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. l h+ydbr)b ykn1.xo *4 k9hiac.rul89ijyi5 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 vertic) a :9hzr7.dviudgt4t al 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 idoa2d9/h3jyv0;n 3 k o:+pjt f3jcqhwts radius r, the acceleration due to gravity at its surfaoqwhj kp d2c3v9;t0fy/ 3n3ad+ joj:hce and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflect1 :r8qqbx wrpv;dz1q:ed5yu,ed from the vertical by an ang5er;qvy:d1, rp8bqd :qw1xuzle $\theta$ 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 baq . 5+zkhfk6t z mx h,6f)x/eohau*)qonked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car sz6ukht *5)eq hax6fqh )m,zofkx. o /+afely handle the curve?

  How long would a day be sb99m,k3nhyy ete0- -if:k xi+qu f*wif the Earth were rotating so fast that objects at the equator90f x w-ubfsihe,:k teqnk -9*yym3i+ were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maint3te+ ricvi i8m8:gxy 8ain 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 constdgb;wsy0tzlx 1yy(2 .ant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swingytbdyl2wg .;xz10 ys( s out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it ha6 *( 3d sn3kvok0sygogs 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. Calculate the number of g 's a person would experience at the equator of such a planet. Us0k63 o* gn dvy(s3oskge 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 th.un u 89tndrt/e Hubble 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 gdt /tnu. 98unras 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 consta ivnnib;mhw(.;.pz9 cnt speed 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, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road .zimn(nwp b;9ihvc .;at A?

  The Navstar Global Positioy 0bmhdr .f;aj5k 6rb4mcw0; wning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately k054f0m.;wj 6cr yabhw;b md r11,000 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 Ren,yf.sa7e5wzmaq 9fxknov7pt* v23/ ldezvous (NEAR), after traveling 2.1 billion km, is meant t. afs97nzv2,p/ wy q7afe3omx vl*5k to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in wp +sodvdv20m:c en-1 need of repair. You are in a circular orbit of the same radius as the satellite (400 km abov0c:+ 1n vv2wd moesd-pe 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 distan 9gcv 3e7d.pjwce frojd .v73pegwc 9m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you cj 1.sjz 0uhncbx92v 3kould actually "feel" yourself gravitationally attracted to someone near you. Make rea0 xjb.s9n1 3uhvzc 2jksonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-4srg gxi93kc4, 2n4vi f6) at a distance of about 30,000 light-years frovii,x f 3k49ggs rn42cm 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 each sewk m k hffaild+:/h*7/dr4y5ide. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at t/:k*/wl i hd5yfha4rd ekm+7 fhe midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ea8su2 e* bzs xgjn(sb)vd( xe98ioh/ d1rth $ \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-h */,)e txbr m32hgseolong sweep second hanhob/x2gs* ee3,mht ) rd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sink 9hb(wpj)pgbunxm *5.er weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every.nb*wg5b(ph xum 9)j p 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travcpm8s) pvo n *jsn,s21eling at speed,s 2n vp*opjsnsc18m) $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatzd vrejs);vu j903ii,ing curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train thivjj;zsr3 )0i ,9d evuat 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.$\approx$    $\times 10^2$