Sometimes people say thav-w+om 0zhds, t water is removed from clothes in a spin dryer by centrifugal forc, dz +wm-vohs0e throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the5*-y,5rn cyf or;f swt car travels around a sharp curve at a y *o-c5f5fn ty wr;r,sconstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along d-m3 9wega*ym fuv9b0 a hilly road. Where does the car exert the greatestgu9b9- wamv *3 fmed0y and least forces 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 forc f*-h /ux2z5t ww2zjl1(srmpaes acting on a child riding a horse on a merry-go-round. Which of these forces p1m *zt5lawup x2js/z(fhr 2-wrovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cirqwp qa d6tsx8jma. :u:()r yh.clyp/:cle without the water spilling out, even at the top of th/:rtycypj() 68 q.u asl: dm.:xphwaqe circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at hw6nq4f okfzb8q/6d 3least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerationn h4qdzf6q68k wo3f/ bs do they produce?

A child on a sled comes flying over the crest of a small hill, as shown jhnrp8ph/ideaq .1mi/h 7 1d1in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normalhr 7i1 nh1jd/q8ape.1 idm ph/ 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 3.*c kmuv+iyp3o y sh-ri)l;na curve at high speed?

Why do airplanes bank when they-iro v3ltrrkq 9ly 6(+ turn? How would you compute the banking angle given its speed and radiul9 yrro6l3qikr -v +(ts of the turn?

A girl is whirling a ball on a string around her head in a horizoy4edh-i3lsc5c 3m6q r ntal plane. She wants to 4cesmdqly3 c- 65hi3rlet 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 gravitatb:y,p1b s*;ik eb /rpfional force on the Earth? If so, how large a force? Consider an apple ep:y1 f;i/kb rb* psb,
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is,:aiq-igl+ . ;jkjv sq/ in what ways would the Moon’s orbit b .aj-si:; qki+l/q vjge different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thka8n 0wyznd r(k fi57ch39vb- e Earth? 93nrcy0f( ani 5bhd7zv8-w kkWhich accelerates more?

The Sun's gravitational pull on the Earth is much la parszc 3x6pu)a- 6 8gdvf3s9qrger than the Moon's. Yet the Moon's is mainly responsible for the )dus a36-f6 pps98q zrvxc 3gatides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at trgi1bx 6p**a8wxu 9ttai; qc316j jvnhe equator or at the poles? What two effects are at work? Do they oppose each other1iv8n pg 1 x *3a;ta 96j6*xqwturcijb?

The gravitational force on the Moon due to the Earth is onl9cw/ir j 5qz+2: ydbdsy about half the force on the Moon due to the Sun. Why s:2wc95/ zidqjdyr+b isn’t the Moon pulled away from the Earth?

Is the centripetal accele:khv*8 0m nk0(d ljj.nnmew*aration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration ofnmn0*wkaem :jhk*ld08.vnj( the Earth?

Would it require lesr. r7gp f:1q)wf p3tess speed to launch a satellite (a) toward the east or (b) toward the west? Co)tsw1r .re7qg:3pp ffnsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measurx n7zhm f.qs3 mqw9k32ed by a scale in a moving elevator: when the elevator (a) accelerates dow7whqmm 923sk3znqfx. nward, (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 we/-n5.a 2, em7lkst0 vzov rnby weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the -e vr52tvzm07,.o/ eak snwn lforce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” orer(mp n y9may mz9/hm)bcto(3.y/et2 “apparent weightlessness” between stepsze/y(a3myh)cm9 rtn m9e y(pom b2 t./.

The Earth moves faster in its orbit aryz(ez7644 b th zgw7teound the Sun in January than in July. Is the Earth closer to the Sun in Januatyz(z6ee 7 tz7h44b gwry, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered tr3/-o sq sq.magka w.,2fa49fs uz2 seo have a moon. Explain how this discr uz2k4a2f ,fagoa-/ q9ssq.s3wems .overy enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mq x c rtq. rfn)ll.6y. ty:*iyd9t,o;wuch larger than the Moon's. Yet the Moon's is mainly responsibl. c.;tiy ltt:frl,6x.)nrd*oq 9w yqye for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 0w-x7mrhze sv*x vt95$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 *ro r(( k0l3*ho aagsoin its orbit around the Sun, and the net force exerted on the a0rohl o*(so 3rakg *(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 on a 2.0-kljp 18by/9b24pvn dmxqhw3h6 g discus as it rotates uniformly in a horizontal circle83vxdh 2bb/4 w yml1ppn6hjq9 (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 cibj5b ; qiax.n)yi:2 darcles the Earth about once every 90 minuy nq5d;baxii :)j2.bates. 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;7o gcczi /(yg of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’z(c;y g /ocgi7s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform,/dh4c wbpol - rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed ishc w4/p- ob,ld 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can roundu u4l0dq gjil4/(f g*m a turn of radius 77 m on a flat road if the coefficient of static friction b4g mlfdu(*q0ij g l4u/etween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static6dq7 urda)y( n friction be between the tires and the road if a car is to round a level cur yr7uqad6nd( )ve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desigpaw x2-jdfq- j 38n7uzned 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 times her own weight, how fast i 3jjqz2-af7du8wpn -xs 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 rotating turnh0xks g-7. ye+pu kg+ntable 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 between the 0g +gn-x+eky.7ushpkcoin and the turntable?   

  At what minimum speed must a roller cx52c+jo zte7voaster be traveling when upside down at the jez5otv2x+c7top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosse;wktjya; *); m1xb/f id jkzq,s the rounded top of a hil1k z) qwy*,dj;mfa;i; jx/t bkl (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 minu b8r/(lkbf3sthra9e +te would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmo38 ahf(e +tr bkr/9sblst point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circleb 4w*m d)jmni: of radius 1.10 m. At the lowest point of its motion the tension bmnji)d:w4*m 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 alkx9mwc) 3x t9k4elcn3 m/*plxis of rotation is tk9cl/tc4 *pkemlx 3)mxn9 l3wo experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a ca.kbj v o(ezm uid+cu. j 1ztk93:d(q3hrnival, people are rotated in a cylindrically walled "room." . k:dqm .(h( eu9vj ok3 tibj1zd3u+cz(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 olvsnd4i,/ m,rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangl,n, od4l ism/ving 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 thi.xp1,hnfoz0 kl ao;z +s time, by not ignoring the weight of the ball which revolves on a stringxol1a.nf,+0;k z zph o 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 radius of 88 m is perfectly bmd9p v u vg079amfqz,v1g 4fd6anked 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 masses tca*y fc /8bc2$ 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 divia.b qf4f-srzd8 8ygx5 ng 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 forcek u1fz3wj q5(gm)ukx9 exerted on the car (by the ground) in Example 5-8 when its speed isuf(xgk 5muq )9kw 31zj 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelf1(wc1nr (,8oca cbc8nqt - qderates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determ(cd( tc c8a,11 r8q- nfcnqwboine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radix;/ygii qg4gihwgn 2jo xk0)+ve* (+tus 2.90 m . At a particular instant, its acceleration v;xyk2*ioeg()ixqt 4 0ggwng/ijh++ 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 gravity on a spacecraft 12,800 km (2 Earth radiib:thqya 3ed st3p8k k-a 8j;.k) aes3-:akk q py;btth. 3da8k j8bove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acfbtvgfa1 j ;b8: :npq2celeration g has a magnitudebg:p2afqvfj8; n:1 bt 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 g n5a6c4(j*.p 6uu5ebbuvej sdue to gravity on the Moon. The Moon's radius is 1.7gunjc6(j*45beb5es. au u 6vp4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a ra *en(cp6s +h3hp h0;xnmugz j-dius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?zeg c- +p;p6m0(3hnns*hxh j u   

  A hypothetical planet has a mass 1.66 times that of Eartaig ep90r7 * xttp.ib5v57k6zb,a5vry;nljv h, but the same radius. 7b bk059tzplt nv *yxij;eip5 ,7.v6rva5 ag rWhat is g near its surface?   

  Two objects attract each other gravitationally with a force of wx6 jt 4jy*.km*o o im,9uzwt-2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravir o4*ytqv1 mc2ty, at (a) 3200 m yoqc21rvm* 4t    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the wxmj tq91fr f cz0)jjd3)9o: zEarth’s center to a point outside the Earth where thegra1m 9zrqjd) 3fj0 z:cxft) w9ojvitational 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 e:xj/hnv0*baa ff 5n)our Sun packed into a sphere about 10 km in radius. Estimaf/aj)vn5* x0f: nahebte the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like wreiy t )i+ 6/rpo nnpgsg3.9/our Sun but is now in the lasts)6t.9/ /ogpp3+wr iegi yr nn 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 kqasxqkvwv* 7,c(4 e 5space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by v( a qse,cx7kwv qk*45calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m/ ;h4iqes4g3 udk145q2iitnafl0 i kb. Calculate the magnitude and direction of the total gravitational forck3 ;h /4 nb4 t1lduq0iskf5i2q4ei iage 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 oirzwzq) .;y.qv os) nrd+)i0t -kio ,an the same side of the Sun. Calculate the total force on the Earth due to Ve.r) ;wr-day qo iksqt))i z.vno+0z,inus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of wh3 l2;spq* h vquvrv u2:dwpg31at it is on Earth, 2:rpdu*uh3gl pv svq w2qv;13and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kn *c/z 7ylppca*own value for the period of the Earth and itp/7 *cal*yzc ps distance 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 moving in a stable circulaeju j8 4.v7wpdr orbit about the Earth at a height of4dj .87vjep wu 3600 km.    $\times 10^3$

  The space shuttle releases a satellncpbo 0xc n*67ite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? 7c x0n*n 6ocbp   $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupant-txs y):1s40cqc fwtr ffc swb7:(en(s are to experience simulated gravity of 0.60 g? A(efscs)bqx-7t0fwt:f(cyw1 :s r cn 4ssume 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 takes for 6 olfij.wi )nyc/o16f a satellite to orbit the Earth in a circular “near-Earth” orbit.nw .6fcloo 6 /1y)fiji A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launcheg r2* zla wlpc2cc5n;l8vxk.,d from the top of Mt. Everest to be placed in ac2.zxrl alc8*p n2l;kv,wcg5 circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orw-l :r(clme :8f-gb vybit the Moon at an altitude of about 100 km. How long did it take to go around t:8w lcef(y-l- mbrg :vhe Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The inn6t6xszdl/ s7,pb/s 54f4ugedi9c i m cer radius of the rings is sgd6i/isuc6zc47b le ps5, /9 fd4txm 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 diamete/uxct-wux6w ; r rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottx tuxww;-/6uc om?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 g)kjm;qbba,e(d3 sa*km from the center of the Earth's Moon in a space vehicle (a) movingb j* d (,k)s3aegbamq; 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 systepsk5v v3 er n5*h-9mhsm consists of two stars of equal mass. They are observed to be separaten9vr *km s-hh35pves 5d by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 5x 5nekm2(7edc 5-kg woman in an elevator that mo( 2x cm5ee7kdnves
(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 hangr o+p;d8lv2nrrein,g 7 el ,p(s from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and brr;+(e er2 rpgoidn87ll,, pnveaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the sv95*5:b wpy :2b6jxajx hc npzd7g+l rurface of a planet with period T 2ax: cxp9:6r5pw75hy+* jgzlnjbdbv , the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to y:i 1 r; f7.py8vrty ob+sw;u z/pr-eodetermine the period of an artificiaur+ ;1tpoo.p;zysi- 7/v8ybe wrrfy :l satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though onl g1-oefyi5 k)v:bvk( zy a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from t1 i:ebkvgz )-o5fkvy(he Sun?    $\times 10^{11}$

  Neptune is an average d ek;n5),a vhrwjkc .bs52 jh1distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very ns ui;vo/ pt*1close 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 nea1psut/i ;o*nvrest 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 the centehk9qo1u3j t9 pc1h5m9umt v 5er of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for ypw1kq wqfw8m05-wr + the four largest moons of Jupiter (those discovered by Galileo in 16098p w0q5+ymww -r fw1qk).
(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 frk :i8(iq+)c j+) jdwqblvwam;wu-p 7k om the known period and distance of the Moon. kb8 q i iw wj-+kclvajw):;um )qd7+(p   $\times 10^{24}$

  Determine the mean distance from Jupiter fosg)hu a 0tnt7)kesr,; r each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the pe7)s rugkas0 ) th,ent;riods 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 Juptif5 u3pm.jk16:w vrl q1i pz+iter consists of many fragments (which some space scientists think came from a planet that once orbited iimv :k.6pw 5r t1ujf+ l3pzq1the 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 talem: ) be/lbe+esr0(dbr qe4 w(b describes an artificial "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 su(e)0sbbebl er e:4w/bd m qr(+n is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from fu(lh8a im 1aijpu7p.k 7n+ 2xa hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at th1i7i.h7kpan f( u8x+2jmalup e 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 gravity be half whb3e a kulhs*(n ;1 y-ce:n4wrw(bfvv )at it is ov h nan*yw cr:ve(-s(4k1w;b fl3beu) n the surface?    $\times 10^6$

  On an ice rink, two skaters of equa+fho9..vadrtcr69-u y te 2dj l mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are ddj .a9 +r -.uetf 9hvr6co2tythey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration 4nl c40 sey 7v8cdwi3ug)nhm:p6:zv dof gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. vnn)yh470ledi6 s3vcm u cg:zwd8 :p4What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the bpk2und4 :uh -rm- aybf r(r9pfm8z-;Earth to the Moon experience zero net force because the Earth and- -r9rz(-fu;4k 2ap8mdyb h: punbfrm Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on uu 7sfay shu*)ek 3tqm8ly37 9a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directi 38*3a u tq7yfkhm) y9sseu7luon?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itwf:x -9sugkka:qbk:g:+p/ a o gsdq79s center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.7/go-gbks: +w :fk9 sa:qx9ga:kq du p1 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 aih :g9 22rxuaulrcraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the m+py8exz7 u 0 wx4:rltxass of a planet in terms of its radius r, the accelera x lyr:04twx7exu z+p8tion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by a x*h1g-rl4ne.pk7sb3i -8rkl+cre ann a rbkherpg sn*-r+4xa 7cnie 8 l3.lk1-ngle $\theta$ 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 u4ayzu y2baf5d3w. +; ng qh1r75gahkcoefficient of static friction is 0.30 (wet pavement), at what range of spw hh3dug4ybf1g+rk2q u;a 5naa 5.7zyeeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the /6yb9ni4k ynt equator y /4 ybtki6nn9were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8u i-;)n.c+(n+cnpwdf 6epkkw .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 roundcv17osh *g5oos a curve of radius 235 m. A lamp suspended from the ceiling swings out to anc h oo1s57*ogv angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the5g wg8 rs/uzriz+ul 4- 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 survivez 4u zgrli +8gsru-5w/ 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 the7-s+ kskte,4f9 b sjyz 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 thez,b-sj e kt9s47skf+y 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 asvh.zqp in;7rgf0 *p7a it traverses the hill and valley shown in Fig. 5–45. Both the hill and vallv*g 7 qn70i zppa;.hrfey 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 at A?

  The Navstar Global Positioning System -cj/sfd, 3p tm(GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the positip,c- /sm3ftjdon 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 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 (NEr0as:tr1 z a6p)fo at6AR), after traveling 2.1 billion km, is meant to orb60)apt :rz r6 osa1aftit 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 shuttdj/wxlq2y ( +ble pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km by w(2/+jldxqabove 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.o- 0q6io uzzpt,+y+) c ovfnu its mean distance from the Sun? y ,itv 6zoo.c0nufz)+p- o+uq  
(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 ad9fc xn;5l7rtn1 :ujtctually "feel" yourself gravitationally attracted to someone near you. Make reasonable asjxrtl ;dnc :nt971 fu5sumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) a4: ,;na0ylerjydl yg-t a distance of abolde nja;: ry-4y ,gl0yut 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on m 5i q- 2rxphr9ge u/nmmr)(o)each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg maruo9/rg r2h5)i-m me( qxm)npss placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the-t4 swg 5ww ypmv1fh5g5 3vep: 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 s6: r(xi1jovatg7:yc h weep second har1t6 jicav oh(x7:g:y nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in aq/v s.0zt yo:b circle below you on a 0.25-m piece of fishing lines: qyt. b0z/ov. 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 radius R in ci 8,ofa.zsa7;qd c:ba new highway is designed so that a car traveling at s qo.sb 7a,azcif;cd 8:peed $ 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 trainxd5 a:ggiq)1 w8bch 96y77( nt hovbsa, the Acela, utilizes 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 less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve w tchhav8)b i(x:dw6ab9 q7yn15go7sg ith 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.$\approx$    $\times 10^2$