Sometimes people say that water is removed from cmj q,i5o; x.ielothes in a spin dryer by centrifugal force throwing t,ji. oq5mexi ;he water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a shab fygw.;36boaykav68 wk5ghy3n8 pg 3rp curve at a conb.py83w kgg;6yoa avk6b8 y35nfh3wgstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whshvm;ne v 4+f/ere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between tw4/+ mfv;s venho hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces + o73+4aapwnujh31(0 lnqq,mornp pwacting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chil4wuw1o+mpa7+ o n33na0l( pqjp, rqnhd?

A bucket of water can be whirled in b5peie, bn.1 ua vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explai p,beu. n1bie5n.

How many “accelerators” oxtss+n- r 0joe 9*i+grs:h: ido you have in your car? There are at least three controls in thio- :o e*h09nsx+t:srs g+ ijre car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown; rtfn7.ruji t pey84/ in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrerr;.8/4 ty7et jnif puase using Newton’s second law.

Why do bicycle riders lean inwarmk rl e,qr81q3d when rounding a curve at high speed?

Why do airplanes bank when they turn1 v3d/ye)z/d +4fiq lq4;ofsfx4 bksk? How would you compute the banking angle given it)x/ fl1;boiv/qk fe3 y44qd sfzskd 4+s speed and radius of the turn?

A girl is whirling a ball on a string around her hex w -ge k c3mxqt30tb70l;pz+cad in a horizontal plane. She wants to let go at precisely the right time so that the ball wcg ;tx 3l pb0ewzm 7xq+k0-tc3ill hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gr9ntz4f+ np4p davitational force on the Earth? If so, how large a force? Conpf+p4 t4n9n zdsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wdw h6ckt w. ooa4jezx;f6, s+5ere double what it is, in what ways would the Moon’s orbit be 5; .jf+ ,6cxs tzo6hoakdeww4 different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moo+v6d-aksc/ 1 hwkx 9xuwj q5(cn on the Eartwv ukc 59sxc1qhkajw/d-(x+6 h? Which accelerates more?

The Sun's gravitational pull on the Earth is mu.7ju+ i8yy5o oi, 3m g;vvlxazch larger than the Moon's. Yet the Moon's o7;g yz vyvuil8, 5axomji3 +.is mainly responsible 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 poles? What two ecf+* y t,5wtocyge,n82tz in9ffects are at work? Do they oppose each other8 tcc nz,+9tyni 2ge*w,o5t fy?

The gravitational force on the Moon due to the Earth is only about halvr i3vv6 0. 5bpeq5nhmf the forcmib.p6 re5qv 53 nvhv0e on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration ovrq+rhib(u9a1j+eid0w8 r d.e, uk-uf Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of th w r+vqeuid(iu+r-0d9au. 81j , kehrbe Earth?

Would it require less speed to launch a satellite (a) toward the east h5f+lzzp8r f8yh9*agor (b) toward the w f*zhr gpfa5zl8h89+y est? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measurepxux,f0sw,o2+ gn-ya 5txz )fd 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 sz,x,pafxx+) gw oy5n-u t 2f0your 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 rxqfe7n*7ugn33 ox p 6in outer space could be adversely affected by weightlessness. One way to simru 3g pxex6onfn*q37 7ulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appareng,vad 7ynu hl5c:e6-7p (xywgt weightlessness” between ste:n6cydl5exg77g -yv( a,uhpwps.

The Earth moves faster in its orbit around the Su:jvf ikg 20ny,n in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [No0:k 2f v,igjnyte: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. E8zxdjipri.b k :0y46f xplain how this disb46ir:fk xjp80y z di.covery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larj6av/z+ e4o0c3n wur2ao uu77g 3l:-dyzmeofger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: ue3 dazro7m2z4w7o vocu 3:gy-+uen 6aj0lf/ 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 198c zdu+pw2x+u 80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 qfb:hy60ddd, around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume q,:f b6dd hy0dthat the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unpuu1 277pq.juc9 7:eu b ef.sbcp)a vbiformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed .7)ps7c uqb9:1.uf eb7a v2jecupu bp of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth'sie0cmhkp,eq1h ; dg/- surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the s, ;/i10dqehhepm kcg -pace shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge o 2p37 gscxy/0df+sgmkf a potter’s wheel turning at 45 rpm (revolutions per minute) i7gm3+ 0sdfps x2 ykcg/f the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in mylj5cp;1x:kmn. 4d)j qf6 jm a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spemj)l fj x;:.qpj461mc 5mkdnyed 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 sm:y+3zdz w cb2i;i6wspeed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indb+wmyzdc2w36z s i:i ;ependent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and thezm uxo7x e9.n08dk ct.*cx5eq road if a car is to round a level curve of radius 85 m at a speed xqt 8c*nu70m kc.e x.xdeo 5z9of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate ewh7 s/w6bpd 2y8j)1nuu2 .darkc+zx a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trai21azyj6dp ub+ws nh287 r) udex.k/cwnee 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 rotating turi unv9+)i tat4.+qq dyntable of variable speed. When the speed of th 9.4ntq+qayi )vdiut+ e turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at th7 ke38cgxr4e (ujq9g de top of a cgue9 gq4jked(3r7xc8 ircle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded tjyva s3 qu qk5;rez2:p5ei bqn;ek:65 op of arzk:e6kesu j;yenv253paq qiq :5 b;5 hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferri.)ix0g zw -:d+rx6pjb fgcye: s wheel need to make for the passengers to feel “weightless” ac) + b0wijxg:fpz6y rdg-.xe:t the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At th:hfm xb dn30 uc9tm)x3e lowest point of its motion the tension in the rope supporting tbdx:uctfh9 3mnx03 m) he 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 fro3gb3b:lbzc xa56 /obv jar7-pm the axis of rotation is to experience an accl 7c-xa gbb33pzo v:jba5rb/6 eleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walle;mq.)t-op iuwj * (uzkd "rooukwumz. p ;*i(tq) -ojm." (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 rotal0t* i3b *mv7h dd(razted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block ravd* l70*dt bzi3 h(m(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 u:e* yp0 dq;seignoring the weight of the ball which revolves on a string yep0 ;dseu: q*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 ban /sh45ypzgz*djkg0o;ked 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 rg8p:4ean8y+ ua0ic x$ 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 verticallfk3fo ;w+6dat3s mc 5xy 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 -ageu oi;3ci 9o2pu*i :b;2 agn; 5ydhra-qvland centripetal components of the net force exerted on the car (by the ground) in Evunidbagiqylie2r3 oh9pu-oaa; 5 c*- :2;;gxample 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 ak 1at0ri nx /yj+qlto s7n(3h+ccelerates uniformly from the pit area, going from rest to 320km/h ink1ni+ 3j+ya(/hxr0q7not st l a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential 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 . At a parta0vohoo.ms (: h h3k-dicular instant, its acceleration is 1h:vo s(oh d.h-ak03om.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 .0 no5gbuy78ua h;ukbgravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its u0ugh .oba;y k7ub 5n8mass is 1350 kg.   

  At the surface of a certain planet, thesvor va5x*t-t64es.p gravitational acceleration g has a magnituv- 6 .4tas v5etxops*rde 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 gravity on the Moon. The Moon's radius is c601ecvc6eqn ci oq)f7vq11b1.74v7q0c )1f oc661qvbicceqn1e $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 ti kga0n 4x,aw+jmes that of Earth, but has the same mass. What is4gxj aw,k0an + the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass j9cn6r wu1c(wdy21vz 1.66 times that of Earth, but the same radius. j11y962c wdnw z(rvcu What is g near its surface?   

  Two objects attract each other gravitre),xgbhhj ghk x x;s84j5 j+8ationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , thoz29nfuu o j7.e acceleration of gravity, at (a) 3200 mo29 z7.n uuofj    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the *sz0*z8zg*n4ky4cyeni xl ,5bl/fe lEarth’s center to a point outside the Earth where thegravzcy ken,x* 0b gslil4*8ef4*zz/ yn 5litational 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 mh6mwd9rz,8 ez ass of our Sun packed into a sphere about 10rzz6 98e,dmhw km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whibsz w cdlrq*t esuc1d+8n3k3a64ko8-ch once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mcst1bu - 4a*6 z8+83q3dn rekd kcwlsoass 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 spac uw*7+ p,dasixm7+vp ie shuttle. Your friends respond that they thought gravity was just a lot weaker up theidwmivxu s7ap++7 , *pre. 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 located at the corners o+ ry p9ex:kx(af a square of side 0.60 m. Calculate the magnitude and direcy exrp:(k+x a9tion 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 :upfdh/ n /q qhe1-(vomost of the planets line up on the same side of the Sun. Calculat-q fhuvnqoh: /p1e(/de the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at.y0 kr4im1g re the surface of Mars is 0.38 of what it is on Earth, i41. kgmr0yre and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sj(+ rz1to ajizc7+4 owun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare yourjr1+(t 7 +zoac 4iozjw answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stablj30q gfi:ekliajd 6q/- dw 2e/e circular orbit about the Earth at a heighke/ijwdg: 2qq d0fe ia3l6/ -jt of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into z*uas75(sqy wfci 5hlp2*e7epck83 w a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? fukw*ew* s(sq55hy p3az872lpci7e c    $\times 10^3$

  At what rate must a cylindrical spaceship ua+)vldadd;uf4*ub6rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer av4bad6uafu;ud d*+ l )s the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takk6idpat(rn02 zv.p 3yes 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 of the Earth which is very small compared to the radius of the Earth. Does yo0p 3i6n 2vr(p.akt yzdur result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be li/.7rjduu 9gd aunched from the top of Mt. Everest to be placed in a circular orbit arougdur 9dj.u7i /nd the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit /kz6;: jmrhg hthe Mo;kgh/mzjhr :6 on at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Thy00fp3r64 jz 2r(uw/ku gtqdhe inner radiu 6r /z 0d4wq3uygrutjh2p(0kfs of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once;+/cyqxeqlc(b gxb lyy1 k61 7 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 to;e1+xbq6cyy l/gq7k x ly(cb 1p, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center o9/sh)z hz,pgof the Earth's Moon in a space vehicle (a) moving at const,s/)9o h gpzzhant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal masdi;0cy;; 6kl6mqplrr 99 jtb fs. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the l 6990 jtrmy6kq p;;;fdibcrlmass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator/d et1et:ny,j/ qw6y c that m: tt,ey6ej1/cdyn / wqoves
(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 cojd)71*jt;ir+7imo5bcahpr pb /*mnz rd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accepa*rp5 )ih/ * r1tbn cd7jiz;7j bmom+lerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelli;nero +kw af6z59a*a;mdd+ aste orbits very near the surface of a planet with period T , the density (mass/volume) of the pla5;w9 ;rnamdf+o +aes6a*zd kanet 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 determine toi tkqc;n/m s9(s64 + 6 ygovhyi:v2wkhe period of an artificial satellite orbiting very near the Earth’s surfa4 oi ths2(mvnqgcwk +s v/koyy:;696ice.    s

  The asteroid Icarus,sswzn1yca4 53; ij gd6 though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distancews4; 5zdsj63cgi 1an y from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5/2g1( oy+rqpt0pol c n $\times 10^{9} \mathrm{~km}$ 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 c3t+,k2mgya(mio5hky ymn*u4j6, ba uomes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What pyuhi3mng 2y ,yj (ub56+ok *4tkamam,lanet’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 the center odmbp3;l;y*p u erqj2 2f 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 the four largest 5(yqc o9knsl:.zfthcm qy:87moons of Ju8l9 o:5 nfhyqmtsq ck:.y(cz7 piter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known peri/z x6u3jod3 fy qlp0qd *dza7)od and distance of the Moon. )djz f0*zq qo/ u3x7 d6a3dlyp   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kepl( ohuzy6h g60qtyrn91er’s third law. Use the distance of Io and ther9z(h6h 1yqu y0nt g6o 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 con8m b(dzk8nc cq c3h7pz(eci+s, qt )w7sists of many fragments (which some space scientists think came from a planet that once z n(zktq seq3dm+c(ciw8pc),h b7c87 orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form0jwnz/ o*b.vaa o; d;i ijq-c1 of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine thacq/i* -dvoj1;b 0zoawnia ;. jt this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a 5 r7y/ua,gu pswp*3*ob3oubigorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what iur,* b7p35ou/ay*s uo3pgi wb s the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hal(2u wnwm4ur-vof1m :g f what it unu1 :mr -4vm(wgwo2fis on the surface?    $\times 10^6$

  On an ice rink, two 6chku67p0yusj9bt x2 skaters of equal 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 individuat9p2 6x0ub6s7 ykhjucl 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 acceleration of gravity atopwvp.z8 ys6 2 the equator is slightly less ps wyz28v o.6pthan it would be if the 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 spacecraft traveling directly from th2mk0y :tpto/z7q 4 bra uh(0gye Earth to the Moon experiencezy7 /2t0mkqr:p 0out y(gh b4a zero 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 scale igv;-19p 4jtoxwdgphk)b 5tgf)co5n4 n an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directionpo9 o; p ghbfx41k-j5tt)4vdgn5)cwg?     ----待选择----upwartddown 

  A projected space station consists dh k o6h*kxu24of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an eff h hk2dkuo*46xect 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 ai evo.vrwy28:*+s wmg g0. fanhrcraft 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 mass of a planet in terms of itx/k r mvbr)s2isf5t y: ekm)(kne(9w8s radius r, the acceleration due to gravity at kvk f:br(ky98msr(nw/ex)) s52ietm its surface and the gravitational constant G.

A plumb bob (a mass mbdb2k: i)b07 zq2a4fu rpiav, hanging on a string) is deflected from the vertical by an ang,i2dpau4k0 2b)r 7i v bqfa:zble $\theta$ 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 forn: 1ofy8ayu;/ wn3kbp a design speed of If the coefficient of static friction is 0.30 (wet pavement):ypa ;1o/bk 3nyf8nuw, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fastwktx i/.hz 4j4z(fd;uiz n.6)xf kx h+ that objects at the equator werf i64f )/zk ;zxj +hnzwikhd4. x.x(tue apparently weightless?    $\times 10^3$s

  Two equal-mass stars mq6ce1 gn9 cey18 sxn.laintain 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 constant0 tqczji-0lqf d,i 2y5 speed rounds a curve of radius 235 m. A lamp suspendetfzj c- 0ydi,l05qi2qd from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed tuzte9 30,2k woy8-fbtig:4m ws zo8g nhat 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. Use the following dataft 8 kg2m4b 0 g3tzo:ow y,e9nw-zi8su 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 extremele+gx l;gya /h1 ou: i0lpkzrg tz3,:q;y massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes) gu:l/lr gxzip0o kaeq+ t3,hy;;z:g1. 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 thvsb3v4rp .)j u4m pos6e hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forc). vps44o jmb p6uv3sres 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 (GPS) utilizekoz+m 3s-n :mfs a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of+mon:3fz m-ks 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 (NEAR), after traveling 2.1 billion km, 52zgqsn/tw v *dq 06zsis meant to orbit the asteroid E nq0 ds*2q5s6 gvw/tzzros 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 pursuinyg c/hz20r5oesjqg f;j0o 2 x+g a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above tho sof5e 20qryh0x ;/zgj j2+gce 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. ( f*5gxrtin04ma) What is its mean distance from the if g*r 0xt5m4nSun?   
(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 value0tfwg2; jclb+ ju*8 mf of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reaso20jgjmfb lwc+t;f 8* unable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) zv8rffb am+s (/ m9-l9 *cncjtb 03pduat a distance of abom-jf0ufz/*9tvcs9b 3b la(pn c8rm+dut 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 each sidendzw3 04ktn (hs l:u9z. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.z ku9:std3 nhwnl(z 04    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg / fyug(vw;7ieh-; neh2- teloorbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long s7 v u+z3l1x1 a,daubdaweep second hand on your wrist11z3+dlbax u a7vd,au watch?    $\times 10^{-4}$

  While fishing, you get bored and starxgn *hyolk6d0ip+,+c 7yypp6 t to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circnk6 gcyydy7oip*+0 lp6xh +,ple 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 l0* .yut2sxw(sy ;t4* yhnkgjoy. b.sa new highway is designed so that a car traveling at sl xtwh .(y*02gs.;.sutjy4*boyyknspeed $ 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 cars67.jbl)ahks b when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculata hl).b jbsk67e 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.$\approx$    $\times 10^2$