Sometimes people say that watu*pzj q -3ja0ier is removed from clothes in a spin dryer by centrifugal force throwing the water outward. Wup3 qijjz-a*0hat is wrong with this statement?

Will the acceleration of a carj*v8n k .6xzmyeh7g +r be the same when the car travels around a sharp curve at a consvxn6gyr7e 8 j zk*h+m.tant 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. Where does tnge2x* bhk b+fe 8:kg0r iw2u9he car exert the greatest and least forces on the road:i 8exfgbu2 2w+k0 kg:n 9breh* (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting onsff 1b rnn8q1t6ne6f+ a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of te fs nr+ 16t8nbfq1f6nhe child?

A bucket of water can be whirle gglx/wufxcgjh 8,;: :d in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. E/fcgx:8 ghjgulw x, :;xplain.

How many “accelerators” do you have in your cvxlq+r ;bo7v*sg z 3c7ar? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they pro7*+;rvog vxz 3lc7qsb duce?

A child on a sled comes ec7xuq0u hxb /z.c+w9flying over the crest of a small hill, as shown in Fig. 5–31h.c bw7zxexc+ uuq0 /9. 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 decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a c nu6lg -yabxbj; u;/cp) 8tu0vurve at high speed?

Why do airplanes bank when they turn? How wfb(+j:rl u828 rxz esjould you compute the banking angle given its speed and radius of the t8+ l xr8fj2surj (:bzeurn?

A girl is whirling a ball on a string around her head in a a*lfd la37a nb zst u,k-w8y/-horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go3u l* a8ksy/at7zw -b,dln- af of the string?

Does an apple exert a gravitational(zt9q t),kmpwc zibv /)i)wh, force on the Earth? If so, how large a force?)t,/wzivi,bpkmzh 9)qwc ) t( Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways 7 gq 1ph)u4kkpwiqgf8 e7li1-would the Moon’s orbit be871)lqihfp 1kwu 4i7egpk-gq different?

Which pulls harder gravitationally, the Eart*2j.78 dyy.zi blae, vsl 5x(6zxgntgh on the Moon, or the Moon on the Earth? Which. (ti2657sev , gx. nzd*8blgly xjazy accelerates more?

The Sun's gravitational pull on the Earth is -owac dau rp2(o8f4+d he iu21much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from 2 w8dac2urpah1 u4df(+ioeo- one side of the Earth to the other.]

Will an object weigh more at the equator :tm 1luv8em/1k;-q aiu ehbc) or at the poles? What two effects are at work? Do they oa;8e mqkmui)/-:1veu1c bh t lppose each other?

The gravitational force on the Mtv2i/b 1hd)q/tgh 6 floon due to the Earth is only about half the force on the M )vth/f61tdh glbq/2 ioon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun jb ah 0r3h2kh3larger or smaller than the cen2ba3 30jhk hhrtripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) (p cfml7 wz76(z3jj bstoward the mb pjjz(l7cwzf67s3(west? Consider the Earth’s rotation direction.

When will your apparent zzz:gu8 5blwcx6 +) yoweight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on yxzwlu )c6zbo +5z:g8the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outesp.8 ib1lk5fk fe9k4 lr space could be adversely affected by weightless elk pk.94k5 1l8fsifbness. 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 force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall9;81gnvx qwddqun6h 8 h (di ytpp30v,” or “apparent weightlessness” between stepsdwv 8d(38v pnqx;dgyiq p0hh n,16u 9t.

The Earth moves faster in its orbit r9mm9ukw (xf(around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its (f w9m9 (xumkrorbit.]

The mass of Pluto was not known until it :k . o qlnvi.e6(god+hwas discovered to have a moon. Explain how this discoveryvdngq (.e:+i .hok o6l enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ear, v0qs)- pwkxkth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the kp-,q s)xk0vwdifference 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 13vvw2la.wkn ps+ /* pw980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the S)/b:1nup)ij r5y tri:a rx3pdun, and the net force exerted on the Earth. What exerts thi j5)iapp3uy n :1)irr:btd /xrs 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-kg discus as it rotates lominy6u74 */qq shcwn4ph .* uniformly in a horizontal circle (aqc4 *nwi4qs*mhp. un l/7h6yot 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 ciqxfq rv*s) )m 1i6kj6 szv9(fbrcles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Expre)fvqxbj rs1 qi6(f k)96 smz*vss 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 sner-22+5v2u vcea zxd; kid) jp30bic peck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?v25vxe-+k3cu jii 20eb2nc a )dd z;pr   

  A ball on the end of a string is revolved at a uniform rate in a vertical ci:)ou,bp4 :t65e znquug m0vagftmh).rcle ofmvm0.fuu q:hpb46g)z u 5:g t)o naet, radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turnzeii2rdx- h1tk- n6( v of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of-2 vxtn ike1r(zid6 h- the mass of the car?   

  How large must the coefficient of static frictgbn9id5z8f (i;bn0z,cq j8hz ion be between the tires and the road if a car is to round a level curve of radius 85 m at a sh iz9bdz58;ng qbnz0fjc(8, ipeed of 95km/h ?   

  A device for training astronauts and jet figvuegr0 kl 5b/ i;ea8b;hter 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 7.85 ;e/rl; i 50bau8vbgke 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 roq 1y7z(yq sa9ttating 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 qq19 z7ytya( sfriction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at2we3f0wpo m4u theo0wfe p 243uwm top 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 (includa(h 3o*;ennnz ing the driver) crosses the rounded top of a hzan;no(3 n*eh ill (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 Ferris wheerpr3n c85b;g gl need to make for the passengers to feel “weightless” at gr5n p8g;3crbthe topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circg ibnlr3.aigr tf-*.e+v1p/ale of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucke air -nv+l 3fbp1.g*g/te .airt 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 par iwh:/4c zutry*f,ne1 ticle 9.00 cm from the axis of rotation is to experience an acceleration of 115,0ic:t*r4,wzn1/yefu h 00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at al,3 mzemne;u- carnival, people are rotated in a cylindrically walled "room." (See Fim-3e;z ,lu meng. 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 aitv;e 9v7:z oj2h0zjh (z/njzx r-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5- z0hezj jj;z2zn9 t:vo /v7xh(
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , p,ol*mg +re8bk8xg p ;lrecisely this time, by not ignoring the weight of the ball which revolvel;b8r oe+mg*l pkx8,g s 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 nn9fht.) r c/c88 m is perfectly 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 massesd,,vfj: jibom(hs /h * $ 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 manvqqii- k0+ 3qfrnf 6xkn7w7r9euver 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 force36:omyy e9cu e exerted on the car (by thomyuee93 yc6:e 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 tjioz(8p z 3nb9he pit area, 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, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration witop8 bz 9jn(i3zh no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular gj+nm9203hy fqxyjer 4et p68 instant, its p8639em0q 2xrhy +j gn fjye4tacceleration 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 spaou7ttd ,oqim8tf;+ +k cecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 13i fuoto+8t7d; k+,qmt50 kg.   

  At the surface of a certain.nuecqegl 63 :mxgr-vz;* v np:yyd;0 planet, the gravitational acceleration g has a magnitu.zmc0gp6qxv;u y engr:3ld*;yn : e-vde 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 the7: h+t dfcd yc 32mjl 2l/yfbu88bsd7r Moon. The Moon's radius is 1.74 28d 2/ullc8mfyyh:7bt cbd 73+sdj fr$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times thatfrxr3q 4i12ymzev3e+ of Earth, but has the same mass. What is the acceleration due to gravity near its surface? rvrm q2+fz1 4xe33iey  

  A hypothetical planet has wywm/rnuz .( (a mass 1.66 times that of Earth, but the same radius. What is g nea w m/wz(y(.unrr its surface?   

  Two objects attract each otherbj,;a nwe, ,ub gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 320g:jp:7ip5 x;n a zqog+0 m 7g: +zngq:po5;i xpja   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earthrg)t -( cq)zg t xjr6m,-bfd9t’s center to a point outside the Earth where thegravitational acceler)ttf xbm6,rz) d jt -g-gr9(qcation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five:x7ypa. msy )k do9(hm times the mass of our Sun packed into a sphere about 10 km in radixd9) m :pka( .h7yymosus. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star liyxc 0hs-r ;9phke our Sun but is now in the lastc0x9r yph-;s h 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 whil*h sp6.:bje lkse/)mu e orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourselfk/e ) ep*mlhuj:6.bss 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 h:4 pfnknu,nn3* 4elna square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphkln434 pf,*hnn:n uen ere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sun.-zoiu 9 6q:psu Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fouruz6squ p9o :i- 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 h (i 7hyxm:u4tgravity at the surface of Mars is 0.38 of what it is on Earth, and u:4 xt7h(ymhithat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using w1m 3dqwicg pc)7da )-5xjm h,the known value for the period of the Earth and its distance from the Sun. [Note: , pi)7)5dx hc-cjagd wwmm1q3Compare 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 circular orbit about u0l,:;n zq 51gj:yrvm ht-fz fthe Earth atzr:: fvuz0mqtglfy1;n - ,j5h a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a ci+ n hzjsu9ws*e-s9uk xyya:03rcular orbit 650 km above the Earth. How fast must the shu3ay-+0z9wsnj *xyk:heu s s9 uttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to zoc(g;g r*)ev experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time nezggeco) rv(* ;eded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes fq7b5.+7t / p;hkf(kkxixebujor 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 whicpkh;.q7jxx ti +5bekb/fk u7(h 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 launched from the tm : +emws7:fsvop of Mt. Em 7+w:s f:msevverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missionioz q2sq784-,br e kj2mp5pwk.a7l xq, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Mz q. w722 ,iqq r5e8al7bjpmp k-xosk4oon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The;ww 6dvj7yvy0;tvy 7u inner ra y7;t0uv;6dw 7jyvywv dius 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 3 *xz0hu*fwe vonce 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 toxwvze h*3 *0ufp, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a-(k zchv8 syn)s6 vne)n4j* om 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velo-czvs* )vj6 knm)s8y(4 hen nocity,     ----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 (eu m zgstr3l05sii. )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 thesrlezms ti(3. )5 uig0m. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woma+1zq5rnjwckr8(0 ad a n in an elevator that moves5(8wzr a0ndr+aqk1cj
(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 hang wtxr gpy*zku*tko7t:9 h-s/:s from a cord suspended from the ceiling of an elevator. The cord can withstand a tension : kxt sz/*koh:ytuw-pt*rg 97 of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periodmk1do0mnppu ;y) l9 ,i T , the density (mass/volume) of the planet is yud)popkm ,n1l;i 90m$\rho=m / V=3 \pi / G T^{2}$ .
(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 dgj-gss.y g.gl168(0zev onl i) to determine the period of an artificial satellite orbiting veryys.j.ze6 gv8g01 s(i- lngglo near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sux1u *rv2 1-yr(doq gfvn like the planets. Its period is 410 d. Whao1r 2vfr*(g vy- 1duxqt is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dist j5w,ewqab +9g160y (nkxqce zance 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 (j 1:fef2:7lxvalra zthe Sun roughly once 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 the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of e :1j f:zlrf(al2 ax7vthe nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the xbuc2+2 ttrn 6 -(nrqbcenter 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, periodz xbdwn 62q08-t -u2cyocny5e, and mean distance for the four largest moons of Jupiter (those discovnb2 y oy-u czcd6-0e85n2 tqwxered 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 tz7 j9mrsi5t)sb b+pj *he known period and distance of the Moon. jszrj9bm*7 ibpt5) s+   $\times 10^{24}$

  Determine the mean distance from Jupit)w j-ewep;k27 +ue srper for each of Jupiter’s moons, using Kepler’s third law. Use the disw72ewk p-ju)e+r;psetance 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 frahx. y)9m aea5l(t z/6gvkea/qgments (which some space scientists think came from a planet that9 6()g tmaxayeeqh/kz.vla/5 once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an vf *p,u-4cyltz3pt)n3 5o dppartificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the 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. Whatfy)-ct3p,lpptzpo4du*5 n3 v will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in0gg h92iphfn 3(ph4qd an arc from a hanging vine (Fig. 5–41). If his arms are capable df2 4hgp3gh phn(qi09of 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, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of g oi11pj jieg19o v7i qf5o)1anravity be half what it is on thepif1avgoi )5jeonq117 jio1 9 surface?    $\times 10^6$

  On an ice rink, two skatec* s,t36 ndghu//tryw rs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume th6*/uy, nws/td ht3rcg eir arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratiezj78+;q nfu fon of gravity at the equator is slightly less than it would be if the Earth didn’tunz8j; +7ffq e 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 di n,,)tqptq8rurectly from the Earth to the Moon experience zero net force because 8ntqr,, p)q tuthe Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when34lnqx5t/ e qi+q mx9/j .agns you stand on a bathroom scale in an elevatjqqi q+lxmnsn./t4g 3 /59ex aor, it says your 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 circulald8:08pe rdf tr tube that will rotate about its cenpeddl :r088f tter (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 surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical l,nlu t0icmb p, z2j,i7oop (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 its radius r, thej8ovups c w)cxo0/ 1y.(i fw7v acceleration due to gravisvuo/xj.of8pcv w1)i0 y 7wc(ty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical byh7ubrde caknr 94r*;+qh*5 3 apuh +dq ardc4uqq7p+n 9*+5e r3 ahhuak*r b ;dhn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a desom1, 4blx ;o4juid gd6ign speed of If the coefficient of stali d 6umgbx, o4j;14odtic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fs *68 k m 0j1fxhn;hgnli0 d0(;umjqa *hjba-past that objects at the eh;j 1-f0bajxq (hjd is80p0g*kna6m*hmn l; u quator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain an8:fy (q3kii 5iyr: 9pvh(qur 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 of radius 235 m. A lampjex0vg:oa 0b br4 +au8 suspended from the ceiling swings out 0oe ubbj a+8agxvr0:4 to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as ntbzu-ls/n*4 massive as the Earth. Thus, it has been claimed that a person wouln4tzubs/ -* lnd 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 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 ded8i kyv/fpa++t uced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (8tapv k+f iy+/from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed (stb58mzz nut/ ik4pf/ce/s . as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (cp /4/ zi s(.ts/bzn 8fu5mckte) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group ofuia:f-g/u rj lolem/,:0e:hp+jt .f o 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 navigationa, -r+ol:fjafp l :i.gt/:hue/u 0j omel “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 Rendezvou v(hw i;x(wbcie2,d d.glv e:5s (NEAR), after traveling 2.1 billion km, is meant to orlew;cvh:,id vewx (d (gib5.2bit 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 th m4q vj6pw3gz8e space shuttle pursuing a satellite in need of repair. You are jzp3mv6 w8 qg4in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yet3+/nv5/t cj)jk j ottars. (a) What is its mean distance fr/5kj j)jc+tnt /t3 tovom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could aknlf 2vmam/ie* k-x(/ovkgk)- f rl/ 0ctually "feel" yourself gravitationally attracted to someone near you. Make reasonable assum-ik)/v/k */r0mfk( x2f- aekvmnglol ptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wg6bnc3oi h*z)ay Galaxy (Fig. 5-46) at a distance of about 30,000 light-yeab3*)ion 6cg hzrs 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 th v/cu61n yl02l. jv+pwa8qwu xe corners of 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 of8w uy+v x/ 1n.ju20av6qlwclp the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbix kd/qm1x1tqi23) +ytwavf .vts 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 sweep seconsd*n sdeu7.. o* pm;8n+ajwund hand on your wrisoj+u e mn*d;*.nnu8ws 7 spa.dt watch?    $\times 10^{-4}$

  While fishing, you get bored and start togvm)8 a(igecrh 7m8 m0 swing a sinker weight around in a circle below you on am i80geva 7r8 hcmm)(g 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 vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is kmz 5ur8crb99az4nkc)tro oh, 8 k2s2designed so that a car traveling at spee)o rnc2tr8 cbauz5hkrs9 24, m9zkko8d $ 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, uyw j/n0ol1 sbr5vawt-f i(.girm /1i(tilizes 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 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 n1smnifw 5w/lai1(vo/btr j ig.ry- (0ot 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.$\approx$    $\times 10^2$