Sometimes people say that water is removed from clothes in a spiphe5t,k55auf xg (:krn dryer by centrifugal force throwing the water outward. What ke5pra (k5 gfx5u:ht, is wrong with this statement?

Will the acceleration of a car be the samequq66 .a .ipnh 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 speed? Explain6a6. npq. uhqi.

Suppose a car moves at constant speed along a hillyyuo uz6az)i+20hnnq g.u )4je road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two egn2hq ) .j6nu04 oa )uyizuz+hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces 4go3do+mrgk f -orx fj -*k,2iacting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerao-+ odkko,rif4-g3r*f2jgxm tion of the child?

A bucket of water can be whirled in axsqyb)yo (c3) vertical circle without the water spilling out, even at the top of the circle when the bo)qb yxyc3)s(ucket is upside down. Explain.

How many “accelerators” do you hav vwft5gqw 1:6ce in your car? There are at least three controls in the car which can be used to cause thew tvqf6:51wcg car to accelerate. What are they? What accelerations do they produce?

A child on a sled com+ ae70o-o zwz)b.qcrx, scrq1zdkb/) es flying 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 betweesa0./), o z c1bqzrox +7)bdzq-wekcrn his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high ss0d, ul2(glj vpeed?

Why do airplanes banio:shd1 (*rkx4 bai7q:6fa4mwd:y tek when they turn? How would you compute the banking angle given i :e:1ak y4 id dmwhar6(qbs7foix4: *tts speed and radius of the turn?

A girl is whirling a ball on a stri 4-qg3 +jgnz p;dcw+ylxbbk0 /1-w4h9yj fchbng around her head in a horizontal plane. She wants to let go at precisely the ry+; njz4b q+jcxplw1f4-9dggb b c3yk w-h/0hight 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 gravitational force on the Earth? If so, how large a forc9/pdv2bb t gk/e? Consider an apv9/t 2bb /kgpdple
(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 orbitdiqs.l63oo m0c/f e8a be odqlo.m s306fic8ea/ different?

Which pulls harder gravitationally, the Earth on the Moo4bha))6zt tvn2 p9kgvn, or the Moon on the Earth? Whica6tvb2)hgnv)4kpt z9 h accelerates more?

The Sun's gravitational prrrp) / /(u9urln.sp2y t6r9/gyxmql ull on the Earth 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 r.6/r9ylr/(lnpyr2u9 m gx /pt)rsq uside of the Earth to the other.]

Will an object weigh more at tb:e-c akxs10 2nszt ,oqn+ l9lqfq ,9hhe equator or at the poles? What two effects are at work? Do they oppose each blast kl12 q z+c99n:, xnq-q0f,oesh other?

The gravitational force on the Moon due to the E/pftr.1b av,garth is only about half the force on the Moon due a/gptv,1.rb f to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accelera ml7qmaol y4 ).wi)g3:l+rjdytion of Mars in its orbit around the Sun larger or small73:l4.yylmo)rdlm+wqj) ga ier than the centripetal acceleration of the Earth?

Would it require less speed to laj, 0l( t7c *+;snwkdx(oqaoekunch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directio xjqok7t(adw*;kens+,l0oc( n.

When will your apparent weight be the greatest, as measured by a scale in a mos)ai9gv xqp;rb b*(t)ving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In tas b xbp)g)*rv(9i;qwhich 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 qid33l5dbzj ;periods in outer space could be adversely affected by weightlessness. One way to sim 3;jzld53dbiqulate 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 fal8*5z oezzym9 b73pmsrl” or “apparent weightlessness” between step*zz8esm5 b3 roz9p7ym s.

The Earth moves faster in its orbit around the Sun in January tvh08- ;bjo 7v )kq3 mjaa9ss+ 9ngfstfhan in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of itsq 3hf)kssg 87t ;+ -svfabnmoj0j a99v orbit.]

The mass of Pluto was not knownprw*7ws.1cxg+z 2rg i until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mas7rpw wc.1igz g 2*x+rss.

  The Sun's gravitational pull on the Earth is94( u 0ja ndlatk p2;/3wpunfs5d;fog 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.]u;gdja( wd509s4l ;pkp2n t3onfuf a /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 travelingrxx(4so nn , te/xtytp,xy3b30ot2w8 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in itzofy/,peam l0y)7xz 7s orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circlez/pyx0m ),fel77z o ya 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 exerttw2pdbn7febnj4 x4 yn (uro.6l;u6 ( bed on a 2.0-kg discus as it rotates uniformly in a hord7(obn uwn4 jberxbflun4pt ;. 6y(26izontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fro )weg(te7z t)z3qiz 42s .o w.djtan7hy:vgb5m the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space qzy ew(e5)h . b.zt vd)ij:73tns27tzowgga4 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 spec2 . pdc,ll u4ar.5m:dzgdt wbmof.bmcl9t5 03k of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s9cgd:4dat.ul02t d c3.5rm,fblm pzmlb .wo 5 diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertiu4; zipe s25fecal circle of radius 72.0 cm , as shown in Fig. 5-33. Iu z2eei4s;5f pf 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,g 3bptaxnk1(l z z*:3 q/tb (bgsvwcr (csp98 which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static fri/ p(nb1k b(3, (q9czagsvrs83lzpbgtw* t: x cction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of tihacj22o 6tdy y4--j static friction be between the tires and the road if a car is to round a levet2ih-2j c4-yjyod 6ta l curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts opy r q1ww7ea5(zme4.and jet fighter pilots is 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 7.4(qw7e r zo p1a5mwy.e85 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 rotati 3lp2mwhj2/;lz adxp/ ng 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 between the coin and the turnlh;z3l dmx//p2pw aj2 table?   

  At what minimum speed must a roller coaster be traveling when upside down at thj0miv.,lcu( he )s ei(e to,es v(0c)i( humej li.p 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 drv ukd n/xme8jzn(t6,*iver) crosses the rounded top of a hill (radius (j , 6k8 tn/mz*edxvnu=95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to make .tvo gpal0 ;:e*ogb3)sag j0bfor the passel)j.0* b:o3e ags;otgvag b0pngers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical c)ksvi, 3 3(*a wyb1kq*ywye feircle of radius 1.10 m. At the lowest point of its motion thfy 3)i*k abewq3 k yv(*s,w1yee tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centn*6kv; nwom8vi0)canrifuge rotate if a particle 9.00 cm from the axis of rotationv)* m6no ;akn cin08vw is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c31qoylxx*d y*/m (dem ylindrically walled "room." (See Figxm**e xoyq(y3/m dl d1. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hocke7( pnqjv+cw8 cy tabletop, and is held in this orbit by a light cord connectjc q8 n(wvpc7+ed 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 the bww*) dfn6dki +all which revolwdw6ikn*f+d )ves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is per/ary+wiow7poz63g(0(om 0 vxymx xt0 fectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse8sc)(hf yksi6s $ 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 ehil1wq-le6u/en 1k(m vasive 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 forl,kvvh.na xab9 -s*oyqxrh(dl+a *6( ce exerted on the cala (lahkvoys*rx+9-(b n vhax6.*q , dr (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit arefkk( mhu6;z :bn an.)oqx lp4i)3dg8z a, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, whazhn;aup x lkio):kq) 8m3fn dzb4g6(.t 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 o3 zeakd*+9- a8irqne0f+cb e owfm54circle of radius 2.90 m . At a particular instant, it++wz cfan095ie*okd4ebo 3f eraq8m-s acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Ear o dm2v,+6 z1 n/d9fup3wj,po lwwjsw)th’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfww2zv p mu jnw,o pdj)lo9 6sw/,1fd+3ace if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g gv*44 z4 9qwr5.biis .nnz mwbhas a magnitudeniiw..5zwb msv44z r q9ng4b* 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. Th e43kqhi ,v(oh9h6c ewe Moon's radius is 1.74 v4w ci9oh kh,e q6h3(e$\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:k vs1szkan ;a0 )v2 qtvj/u.ames that of Earth, but has the same mass. What is the accelaak2/sv0t vu1jkn;s)z . v a:qeration due to gravity near its surface?   

  A hypothetical planekhs fp xl116i -eg8da+6-gyhwt has a mass 1.66 times that of Earth, but the same radius. What is g1lh-awhkifg g6 eds+8- 1 xpy6 near its surface?   

  Two objects attract each other gravitationally with a forr0yeuh hf96b(yl q5u -ce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 320o,r0:i mg0 xdkiiyf (fyo2x,90 m fr oi9 2xdg iki:0xf,ym0yo(,   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth4 l yk/0kbdio(’s center to a point outside the Earth where thegravitational accek k/(i04boydlleration 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 our Sun packed into a sphere4x (w*kc*xgtvw7dnz5 f u3jr : about 10 km in radiu3z fn45j7krgwvw*: xud*tc(xs. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun butg.m/qfn3 )kp4 hy d*wo is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on thfmh*w d 4k.o p)qy/3ngis star?    $\times 10^7$

  You are explaining why astronauts feel weightless while wo1 tn f-5hih8orbiting in the space shuttle. Your friends respond that fhw8i 5-ot1nh they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of st ckr23w ph67side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other threerk26wshtpc 73.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yejq t yzck03--jars most of the planets line up on the same side of the Sun. Calcuk- t0-jzqj y3clate 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 theqfz3d +t68vjx surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass ofq3 8xt+6z fjdv Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perio cjwom,tf+8vveic, * -d of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s,+ cwetv8o,*-jm cvfi laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular najy m92ze ppv(g ;7em+x.2rdorbit about the Eamrvn.7x 2 p92(+pdy ;egmjaez rth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases osu q7 x+1ztyktsa.8fb1*is (a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Eart(b s.s1 tyz1ikfqxsu7*o a+t8h) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are twmml y sq70+f1foch +7o experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answerhs mff +7 qy0m1lo+7cw as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it ta ,nw.ul1pk o*yh o90gokes 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 your result *h okuo0.olwny9p ,g1depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitey y:t5*0hsmt e have to be launched from the top of Mt. Everest to be placed in a circular ymh5:y0ets *t orbit around the Earth?   

  During an Apollo lunar landing mission, the command )fccn;q z/(l.4 udl acmodule continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the 4fznccad ./;qu( l)lc Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planl/ujb92 jcqb9et. The inner radius c2u99 / jbblqjof 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 dihmg (clg sjmu)d3 571kameter 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) at7h5k1g)sug c3mjl( md the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from ox7bo0ld-xr ; the center of the Earth's Moon in a space vehicle (a) moving at consolox7;rbx0 d -tant 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 z2sy 3ta cxs)7qs0tf* f0k 4veof two stars of equal mass. 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 mskc fxez)s2ts74t03vaqyf0 * ass of each?    $\times 10^{29}$

  What will a spring scale read for the w wbj5k4-)mxqgya9 *v*f3p nhteight of a 55-kg woman in an elevator that moves w9avgjn k3*mph*)b 5yq-t 4fx
(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 from the ceiling of c7w0/yq ;m d4mbj4vkk6 r:k msan elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s / k7k:r bmsq6dmcvjm 4 ;y04wkminimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wu n7 qoz9ugzsyz )0ic ).7a*sfith period T , the density (mass/volume) of zs)cu azf) u 907nogzsqyi*.7the 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 determin gjqwlrglx4 c77fixx(u z /,:8e the period of an artificial satellite orbiting v(ciux8gglq /x jlxfz7wr :4,7ery near the Earth’s surface.    s

  The asteroid Icarus, though onl xyb3o/ ( 7f,piwrdo(ly a few hundred meters across, orbits the Sun like the planets. Its perio3w xd7ooilp( (fy /b,rd is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of2m mm*ock znhp.fj:la s;541l 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 oty29ys ( crlhs-ep3s +nce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from hr 9sp32c y+ -(tselsythe 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 the ce xt m +j-fqf+s+2a5h01 lqljv8uycbp3 nter 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,6xq)5xtap, tkn: 6ti i and mean distance for the four largest moons of Jupiter (thos)tx 6t a inkpqt,x:i56e 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 Ears( gj0;vjh8yd th from the known period and distance of the Moon. 0(dh js8g v;yj   $\times 10^{24}$

  Determine the mean distance from ,dfzxm;,n2 8c( q1xks6f ox eaJupiter for each of Jupiter’s moons, using Keple(foz 12xnfd mc8,k;x, qa6s exr’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which 48-rg2qh cpd:)jy2frks a0 fjsome space scientists think came from a planet that once orbirpj :j8y2 c4 fg2q-sh0rkfda )ted 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 ano blkh szo3okbx;4p9-jy:8 u: 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 sun is exactly like our own;bl-y o:k 8x shz9: 4k3ojubpo, 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 a hanging vine u.t nx2o-cm suep7p4v r9g;j3 (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 the lowest point of his swing? His mass is 80 kg,4c.uotusvgm-xrje pn2379; p and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelhwrh /+d xe 2)*rxzg)wl-7 yiveration of gravity be half what it is on they+2xrww z)de-/*li hrv 7)x hg surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inz y,er+g3+k:uyte g a+ 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 they pulling on one another?+t3 ,e+e +yyr gkz:agu    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravit3 xt9bwc(4udp y0xm1jy at the equator is slightly less than it would be if the Earth didn’t r pj4dm0x3tc1xw bu(9y otate. 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 the Eheaq(l;pi5 -- mb t)c;hni 1t0*ubrsfarth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite 5 *1 u-q-(h r0;ibs hpct;bml)eftainforces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathrlq984be0 uy nl-2ilauoom scale in an elevator, it says y9l4 -uule0i 8aq2 nyblour mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that , qcjpo1 jo:*hwill 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 effect equal to gravity at the surfh: 1*ocqpj, ojace of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43)z ej6*cr s(hq4i;x ir0.
(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 acu*+7am e5coc planet in terms of its radius r, the accelerationu o+c7mc *ace5 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 ve j stzumk+(ekp1/u184ok4zcyrtical by an angle 4mzc /+yj(k tp 8s 1zue4uk1ko $\theta$ 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 coefficient of :p+++vjl ;vvec-t6*ku1r*qybu zlki static friction is 0.30 (wet pavement), at what range of speeds can a car safev++ :zvultqb16 cyjru*+ k;plkev*-i ly handle the curve?

  How long would a day be if the Earth were rotating so fast that object r xw*0x5d9 /)qb:jpnfqstpw3s at the equator were apparently j x p3 fpt:w5s*/xqrqwb n)90dweightless?    $\times 10^3$s

  Two equal-mass stars mainw- 0yk er9k *r,hj4xl+y4gqwstain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve ofi 76t89 qj8enmbru j (a.thqp* radius 235 m. A lamp suspended from the ceiling swings out to7jtm.ti6qn8*bu e(h8ap9qj r an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timesst4joyyhdk 2bg.e4-cl .k-:x as massive as the Earth. Thus, it has been claimed that a person would be crushed4tygdlhcjkbx.-eo2 4-:y s.k 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 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 Hubblqqd4 a0 0/p znko(c.ete Space Telescope deduced the presence of an extremely massive core in the dz0 e0/ ant.pq4qko( cdistant 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 pe- 4:1pegwv m e,f.8bd+a m+n vdsgj9l yd2,dspeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, g jd1 ea,db p:yew,.nfvld s- g49+v m8edp2+mand 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 (G;ne.-c2 km/zdn2xuclPS) 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 “fixesukcn;.n- l2dzc m2/xe.” 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 Asteroidk*k;tayq2 esfzxbud; +q+5p( Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Erot;yb e+qqk f2k*uz5pasx;d+ (s 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 -awf:yy0 um5w bi*(/ mch7yioshuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km ay / mu aimcw-o50(yfbwhi:*y7bove 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 itsuf/e4*(sw+*q p kcw ar mean distance from +w s*cqawk/fe(u p4 *rthe 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 val.pb40v( tgmr hue of G would need to be if you could actually "feel" yourself gravitatio (4rtp gvhmb0.nally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way w14t:bezp a/wl t/vu e8))cqtGalaxy (Fig. 5-46) at a distance of about 30,wa t //w4teql)z8cu p):e vb1t000 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 ofyajt m *er4.0l a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square. .y0* lrtmaj 4e   $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbiyowwcm 0 *9-txts 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 sws:ntmzcm,4v.,v ;cq v: b iao6eep second hand on your wrist az tos,4v;:i6,.cvb q:cn mm vwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkey(i(w41un byw .65jrhoqq(ihp 5rl-ur 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. What is the angle that the fishing line makes with the v jp- brlw4h5qu5iyn(h qoyu (r w1.6(iertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is u -ylerlu+:2ax ib,h7 designed so that a car traveling atyle i, :7h+2lx-bar uu 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 of the cars whehz,b.zt0i)r l 1v;+il/fqp ae n negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accele1+)f e,;hzlr q0 .vtpbazl/iiration, 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) 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.$\approx$    $\times 10^2$