Sometimes people say that water is removed from clothes i )dzk7t/s8( tyethaqyt 40 cm9n a spin dryer by centrifugal force throwing the water outward. Whay9cz0m)e7(ts h/ yt8d qtt k4at is wrong with this statement?

Will the acceleration of a car be the s,;np b64vmc2;fpjkh( 1m duzf ame when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spz;;n,(6m mfu f4 21kjhdbvpcpeed? Explain.

Suppose a car moves at constant speed along a hilly road. Wher60n9y *p i)0,urpe(rodploz a e does the car exert the greatest and least fo lo6or ad( pzpyp*)ier,u0n09rces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting4 t8j,k5xcn) pw4htvp on a child riding a horse on a merry-go-round. Which of these fovj x kptwpt)84chn45 ,rces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wate)ex c v,k;u5 hz1vgt-xr spilling out, even 1xxh,-5t vu;)kcv ze gat the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in you2 8vm0 dkqh kskmv9i2ooj-b,* r car? There are at least three controls in the car which can be used to cause the car to acceleratk*82-om s, bhkk jqi2o dm0vv9e. What are they? What accelerations do they produce?

A child on a sled comes flyiu3t .aejb a3bk qcm/mfbr+10-eun-5t ng over the crest 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 normal force between -ec bfet a5bu.10u3jmq+m nt/k-a rb3his 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 l a)pieaisdv(i5(t ), at high speed?

Why do airplanes bank when they turn? Houiuu( nqwg6 r-eh,7;d w would you compute the banking angle given its speed and radius of nqru ue;,ih7wu(gd - 6the turn?

A girl is whirling a ball on a string around her head in a horizontal pla ebtykn( x((l(ne. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When shoul(klne(t(b(x yd she let go of the string?

Does an apple exert a gravitational force on the Earth? Ifn0n-nax 7)qmf so, how large a force? Considernf-aqnm nx0)7 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 orbitf-xeut oku wy 5x 281/k swzr5*bg+g0d be diffg2krtue 0kuoxf+ b5s5d8xw/wg y-* z1erent?

Which pulls harder gravitationa z*hzkxf-6,/c ic lg9slly, the Earth on the Moon, or the Moon on the Earth? Which accelerates morh6x/z c9*lzi ck ,-gsfe?

The Sun's gravitational pull on the Earth is much larger than thhk1 san 0i;x4le Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull froa0 hkns;il 41xm one side of the Earth to the other.]

Will an object weigh more at the equator or aty -1r) p5nemowh0ue7i the poles? What two effects are at work? Do the5r)p 0 7meni e1wy-ohuy oppose each other?

The gravitational force on the Moon due gi,l co5.m+hvto the Earth is only about half the force on the Moon due to the Sun. Who.c gvm+5lh i,y isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arou1boekuth-i 41 hmro. *nd the Sun larger or smaller than the centripetal acceleration of -11.imto4r*uhb koe hthe Earth?

Would it require less speed to launch a satellite *8 hahmhk0 e v9.*ie+rn9yxbj(a) toward the east or (b) toward the west? Consider the Eartvh n.e9me*9h rihbk0ja+ x8y*h’s rotation direction.

When will your apparent weight be the greatest, as measd q*6d5w0zhyansh -4kxuv3g.ured 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 it be the same as when you are on the gsd6 -hd nw u *kzqghy3a54x0.vround?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in ouypgjh gy9 oz5zsxvvk y.+79 i-x:go4.ter 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. i.j979z:oko - .+psygx4v gvhygyz 5x 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appareg.+bfga0 (j;6l*uevlb z ol 4cnt weightlessness” between steps40lv;zg6ulg ba bjo(fl+e* .c.

The Earth moves faster in )y7r arr(b6q rmyfl1+ its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the s7rq(ryr r bl1)6yfm+aeasons — 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 have a moonafiz/h d0 6n0r. Explain how this discovery enabled an 6h0d0n/z rfia estimate of Pluto’s mass.

  The Sun's gravitational pull on the aek/z7 .spx:kEarth is 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 merry-go-round moves with a speed /k7k.pase:z xof 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 1980c t1a;t+mmkfnv3zj s(12gcic35u cy* $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 aroung,ng4a y zmyf nae7k4b5s9:n* d the Sun, and the net force exerted on the Earth. What exerts tkg4 974nn mbze,*fs:a5ngy ayhis 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-k4adp:muuhk bu 3j2pt.mlqn2: uj,v6 0g discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate 3jmu hpnl6uud2vt0jubqmk :,a2: . 4pthe speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surmnoofo 9w6+h 8mkg. +oface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitation6+hk8n fo m9goo+ m.woal acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of thlt; j d:a-4kndi*/o/2j hdgci e acceleration of a speck of clay on the edge of a potter’s wheel -t/* jl4ic/adnd2kj oi;d: gh turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is rwez*38 iik ay9evolved at a uniform rate in a vertical circle of radius 72.0 cm , as i w3ei9k*a y8zshown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050gungj+y1v )fvz4d0uw),g e; a-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires an,gygnj4+wuadeuv;f )1 0 vg )zd 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 tire :m8utu k,xre17hbu t9s and the road if a car i7u mhru, u 89tkx:bte1s to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is 4v +0jsfaak.z designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 timessa0 4vfkj. +az 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 fromq,d 9sd7ic.s sjw7r u+ the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction bu. is d,cq7srs 9d7+wjetween the coin and the turntable?   

  At what minimum speed must wlcmpnq5 .9o:l24 n9m4zedd ;suta x p,h0k:ya roller coaster be traveling when upside down at the top of a circ oa 95n4dzh .mlu mx;l4p,s:dkqc9te:pny2w 0le
(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 (ag qhs663k;x nincluding the driver) crosses the rounded top of a hill (radius 3k;g 6shxqan6 =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-mo9/l b5ila5nj -diameter Ferris wheel need to make for the passen n55ia/ jl9lbogers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical k ff7n y7:;wznakoersak oy yb4../7k78:no wcircle of radius 1.10 m. At the lowest point of its motion the tefe ay.kkof.nk877 / 7nws :n;orbow4 y7ayk:znsion 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 55vhhcodh *h: +u 1ecbag19f gif a particle 9.00 cm from the axis of rotation is to experiencugb5 +d 9*1oh:vh fehcc5 1aghe an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a car(b(mamq l7x;w nival, people are rotated in a cylindrically walled "room." (b(mw 7(qmx ;laSee 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 a:cjf+be : cd4oir-hockey tabletop, ajo cf4:bd+e:cnd is 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 , precisely this time, by not ignoring the weight of t.bfwljyxd5 ry0au g(j0(-wk:p tk +-whe ball which revolves on a string 0.(j+ :0(x0dlgk-w fkwuwy y.tpb5a-jr 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 radius of 88 m is perfectly banked for a car traveling 75nt5v i,bv1g:e $\mathrm{~km} / \mathrm{h}$ , 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 masseww3;4hqgrh: a7 poz*cma /vv, 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 evasivegpg )b:o:k ausb5/z.yp.ho*l maneuver 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 and centripetal components of the net force / iyrl;8 5eq4utr- zca0iur5* ichrc1exerted on the car (by the ground) in Example 5-8 whcuc c8h5r 1r5ii/ert0iaur q-;l zy4*en its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going fr5wr8fw+kaz8pr vov70om rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential anva7r5o+frwp8 v8k0zwd radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Ajxefj/ .rbrvc;6u7d29*csr ot a particular instant, its acceleration is.j27vcu6/rs;bfrx jc 9 *e rdo 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 gravity on a spacecraft 1j0;-d*f 1i0va98 swbjs fri:jm bz9(dz pp/gc 2,800 km (2 Earth radii) above the Earth’s surface if its mass d: jg /8 zj0zv(910id cpfiawrjfp9bs- b;*smis 1350 kg.   

  At the surface of a certain planet, the gef9htk0mh4qc s; o(hkhprcf.84+3 igravitational acceleration g has a magnitude of f3mhk8fse. 490t ch(qkp oh g4+;ir hc12 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 dvw ncg3rmn: co.fbiw //f81 t6ue to gravity on the Moon. The Moon's radius is 1.74 t3nr fg:/ f8v/owwcn1bmc.6i $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius k0afh;p* 66)uea czsfn a r6g01.5 times that of Earth, but has the same mass. What is;f6usnezka f 0)0h*a6 rgc6ap the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same w+y f/(nz2 vbvradius. What+/ zf2vvy(nwb is g near its surface?   

  Two objects attract each othe 5vgoxa yhkc+1ei0f7* r 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 val2lf +wiiktzq9g9iys8e 88 8pque of g , the acceleration of gravity, at (a) 3200 mizi is+ey88k 99qf tqw8p2lg8    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cente*7rb bejb 3fkbtx05 0x9vo,w qr to a point outside the Earth where thegravitational accel *t95xvbwe3q,x0kbbor f0b j 7eration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fiiaf)/n9 vbe 81,nh:x hkvju6 kve times the mass of our Sun packed into a sphere about 10 km 6 x: j8ieah/ 9nf,)nk kub1vhvin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an av, snqzct/sn18n gdj2,erage star like our Sun but is now in the last stage of its evolutinsjn,d gcz1n8 t ,sq2/on, 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 w80-m4;/7)odzfhecic zsau hyhile orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up ther04z7y/fcis odzm cah8;ue h )-e. 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 le 6b g-qsc)t*bocated at the corners of a square of side 0.60 m. Calcula*)qbe6cstb g -te 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 the planets line up on the same side ofjo;y( b 1q5m7tij4mku the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four qjym t5o; im41ju7kb(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 the su.s)h u hd8co9,mq2sxm rface of Mars is 0.38 of what it usd mcm h9xo28).qhs,is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known vfrtk :m7hs/ 8falue for the period of the Earth and its distahf/ :8r7mtsf knce from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite nj8j)lxx+pesh1h 5*v moving in a stable circular orbit about the Earth at a heigh 1x l p)*+v8hjjnsh5ext of 3600 km.    $\times 10^3$

  The space shuttle releases a j)h*8 evxp,do satellite into a circular orbit 650 km above the Earth. How fast ,p)dev *jxho 8must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience r0 (9gvi-z yossimulated gravity of 0.( zy0srigov9- 60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it take lm*c-d4q 4nces for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface old-m e*4ncc4 qf 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 satyba,wt 6u7xnp)v 4c* gellite have to be launched from the top of Mt. Everest to be placed in a circular orbit a6w)xnp *7b 4tgvuyc,around the Earth?   

  During an Apollo lunar lan lkwc se3bho rf e3+j63c/el*9ding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How lonc/e*k6f9je+3woec l bl s3r3hg did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of 2idr*ncn 5mk8 ice that orbit the planet. The inner radius of the rings is 73,0m*k8d i 2ncrn500 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. km24puz, j6rp jz z/b)5–9). What is the ratio of a person’s apparent weight to her real weight (a) km2z /j6zj)ppbu4,r z at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of nlwx - bb5c/q)a 75-kg astronaut 4200 km from the center of the q /wx5nl b-)bcEarth's Moon 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 two stars ojg+v31k9 rklkf equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midwar+9kklj kg 1v3y between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of g vygsfocytg*9m r.d4 8+ /+kka 55-kg woman in an elevator that move gg mdc*syo+.r ftvg /489kky+s
(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 q ug*62cw2a rsifk)z20wj -ckfrom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minima gfkjq2r2*z 2kw cu0w6-)iscum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with per:g r .n3uq,yzyiod T , the density (mass/volyug rz nq.y3,:ume) 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)lyuq*-xr3h ao n, 4vh4+cgbj- to determine the period of an artific nvax3l *+qhuj4,--y4bgroh cial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundd16 q xy kyj* o)9ks-cc,5cydored meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the )yo6ckx o,dd-j 5y9ky1scc* q Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 4zw accjyzhy g.j4rji3/w:+0 $\times 10^{9} \mathrm{~km}$ 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 7zcp,-mry 4;wes . y wm1d3lyfroughly once every 76 years. It comes very close to the surface of the Sun on its cloy1 cmywe fm, .sz4-dyp37r l;wsest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about tiobjj :)7hjzul( /3m,v2nk 9qgol /fmhe 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, ank3p5y u-mk3 +mcf (;c:m jmidmd mean distance for the four largest moons of Jupiter (thomm-( fu +;mjkkd5my :cpm 33cise discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from-s404:tt xuw qzax.( seyj1 7jjbdr4 h the known period and distance of the Moon. yr: w 10xsz 4j7jj q4dt-btu x4she.(a   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moo.s)5lb+ ,zprjfbr)k b/o dju7ns, using Kepler’s third law. Us/b 7).o 5surj,j bl kfbprd)z+e 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 betwe cpwsb;pfr7t5azf,y +vo89 0ten Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but f;cpvtfz t79 ,so 8b05payr+wwas 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 1/g) gf u5 t+bjx rr7(b5vxkeyof 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+y5b fej/x(7 xt5g r) v1kubrg 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 an arc from a hanging vine (Fig.,sy+-fs7 icz 5kmt)yi 5–41). If his arms are capable of exerting a i7s-yz)m c,k y5ft+s iforce 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 Earthm6:m)5 qwdqw5o ,ro5sb8 nwel’s surface will the acceleration of gravity be half what ,:rmdb)qe55osm wwno6w l58qit is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual c9l ,wf0puf bn+ o2tyv,ircle once every 2.5 s. If we assume their arms l0 ,nyt of fu9wp2,v+bare 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 accelerationqbi mhb-: lqc)v 6h43f of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of tm:v biblcfh-4 3 6qq)hhis effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tqb 1q99 )kywvgih:prm83q a i-raveling directly from the Earth to the Moon experience p bv9 r :w9q ai3hky-q)mgq18izero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom nmr ;3(+bsm6 cwoz3rpi09az.+i u3t4yfxr koscale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevu +z3 b r9smrrkon643;yf+xzp.iim3aw t0 oc(ator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circkutk;dpx 4nagd m,j+ ;n13e)fular 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 d k;nkd ep )j13gm+una; ,x4tfper 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 loopmv):p yx7(2 qd/r yt2cmpkx) v (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 pxtoz4epk ( ( ib3,xf5elanet in terms of its radius r, the acceleration due to gravity at its surface and the grav i4xxtz 5e,b(e3pko( fitational constant G.

A plumb bob (a mass m hanging on a strin 9pyw+1p+puw(a yk x hz3z-cs5g) is deflected from the vertical by aswp+1ua p-ypz3hyw ( 5+9zxkcn 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 coefficioak. )ywmmy::ent of static friction iayko: mm.wy: )s 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eart zuz8o9 n.iwi,h were rotating so fast that objects at the equator were apparently weightlzo9 wzi iu,8n.ess?    $\times 10^3$s

  Two equal-mass stars maintain a constant dik;nuk:wjt )df.zvv 8 5stance 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 spo;i9-x 5adyfreed rounds a curve of radius 235 m. A lamp suspended from the ceiling syxir5 -9a; fodwings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massiv3 fj6h :uts,m *1cmvrqe 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 survive more than a few g 's. Calculate the number of g 's a person would experience at the equat3 ,mvqm6u:1hrtj*c fsor 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 .d0 vz.4y0zfrr8wjwy extremely massive core id0y.w84 0r y rzjfv.wzn the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to 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 val 8bk3ks1wy 4 dqq*ajh dt.b+4wley 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 f8b* ys4qkwa k.bjw 3h+d1qd 4tast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Systq7 gz3pqwu 0y;em (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 orb0wq g ;7ypzqu3it 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 Ren:(vze*b 3:+ xgtr1 un;bpwjpw dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 kmx3nrj;w:z * :tpb(+pe1vgb wu . 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 saten+a*q13xpv p;-da g xellite in need of repair. You are in a circular oe3avp ; adnxgpq-x*+1rbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a pe6f bb.he5(h:6fgs fmfriod of 3000 years. (a) What is its mean distance frommbf.g6b65ffh:ehfs ( 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 could actually "feel" yo 06rp-1+oyrze7ioicz rmc* e( urself gravitatiy 1(e rozoc r*6z7mr iie0cp-+onally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of ths5c8 sxp.vf+cext,e1 e Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lighes txc+fc vsp8,51x.et-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 lof 7(e.:z sv kif6ar6decated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the(6:7z vf dekf6ras. ie gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg im67r4h,sgf e, ruhxx/v tc0( orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of thep0q pz.*aexty tc-4yo a- tt*7 1.5-cm-long sweep second hand on your t* xp y7taetqy*c- ot.4pa0-zwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to ez bt+v,6kn4 l0: jpuq.oicnx*j0j w(swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. Whawv0,0 n4t+e : qjuzc oj(x.n6ibklj*pt 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 bi7k fux.gd;/that a car traveling agf 7iud/kb .x;t 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 d n .;ld3vrvs /(mxmn*4jm7qtof the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approxx7.lqm(mdn jnm tdr4/s*;3vv imately ). (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.$\approx$    $\times 10^2$