Sometimes people say that water is removed from clothsruua, j;/-yz xqg3 v;es in a spin dryer by centrifugal force throwing q,uy/jrvax -;;s g3 zuthe water outward. What is wrong with this statement?

Will the acceleration of a car be the same whenf s659vbngrw)ljh k 8m8(ins(ldw j/9 the car travels around a sharp curve at a 9vd98wjbrfwgnsh l j(l)56m(k /i8nsconstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alonruoum -jp( wb6g3d;a 5rbp77 yg a hilly 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 hi6yu(ppo7b3b-r5mug 7 d ;ar wjlls, (c) on a level stretch near the bottom of a hill?

Describe all the forc34fwyq fijl(0es acting on a child riding a horse on a merry-go-round. Which of these forces provides the centrl (fj3yiqf40w ipetal acceleration of the child?

A bucket of water can be whirled in a *i/sps -3p 2)irggyka vertical circle without the water spilling ou skaips-2gir3 /y)pg* t, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you hav)s3f:m20k s )dugrtuj *b.si( kux g/pe in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What gi s(/ xtp3drgssu*.)02kjm )uubfk: are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hie7mab 1+yi l4sll, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this a+41 bs yelmi7decrease using Newton’s second law.

Why do bicycle riders lean inwajn s/+cw;m48w simfat4 h7* yjrd when rounding a curve at high speed?

Why do airplanes bank when tuey gog463edd s 34qs krl+9z/hey turn? How would you compute the banking angle given its speed and radius ofe9z+u3s/ld364 qeg gy o4rskd the turn?

A girl is whirling a ball on a string around her head in a hori0nu4*-c isv)q-zxehp zontal plane. She wants to let go at precisely the right time so that the ball wil 0uhe--4zn* sx v)qpicl hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitu()p dfg75*djoeb9 rb av)q6tational force on the Earth? If so, how large a force? Consider an ) 65d )frj9*uqbpg t7vbae od(apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wagt :jzt5p, ku)bzm +3xys would the Moon’s orbit bz ,tzx)pkmt 5ugb j:3+e different?

Which pulls harder gravitationally, the Earth on the Moon, or the yyg8bv yy6z(5suv ,h5/bqgj2Moon on the Earth/5v2ju by, z (8vyyq bggsy5h6? Which accelerates more?

The Sun's gravitation-p2ys 4zp3z hn))5 nqzn n4gheal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explqnnhz ez )4gypp-5n)s zh2n 43ain. [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 th tl1.o:g 9rbyiggs j5*e poles? What two effects are at work? Do they oppose each otg .gol5ri g*9ys:tj1 bher?

The gravitational force on 4lbynb .yv5,kk -*mg qthe Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled awan4 v .-gky q*ymbk5bl,y from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sz4zjdg-ds )+yun larger or smaller thad z 4)ygjsd-+zn the centripetal acceleration of the Earth?

Would it require less speed to launch a satellitef n4r3 4q-qs .iqzml m)ak. -;aey-lda (a) toward the east or (b) toward the a;.-3qya4e-l.asd -)m 4lfinrqk zqm west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatestv cc8anh:fbr+ at8hjw+)9ab2d;ba *t , 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?ar+8b8h na2whafjt 9 c +acbd;tv :*)b In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodsk-p4v 8ulsu n. in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 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 u8k4sn-up.vl of.

Explain how a runner experiences “free fall” or “apparei+:n on oe4rg3sjrb0 .nt weightlessness” between steps.eojo 4bi+0 rsnrg:.n3

The Earth moves faster in its orbit around the Sun in January thax:+.6* u 3cxxlxwbfv ln 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 seaso+:b.lw xfx3ux*lvxc 6ns — 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. d6rn3 rz+sb(s Explain how this discovery enabl(36nrb s+rs zded an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'sn9o,3hyql w 8u. Yet the Moon's is mainly responsible for the tide3 8lqu9ony,hws. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19 xg3l65y jp8jh(wcp3t(lao7 i80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Sgal9ji-+ epk2 un, and the net force exerted on the Earth. What exerts this force opj 9 a+gkl2ei-n 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 +et.j-3mnfs ly wga8 f.x/+k)wy0n ucexerted on a 2.0-kg discus as it rotates uniformly in a horizontale 8ym ng/s lxnw..ty+-k )afwfjc3u 0+ 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 from the Earth's s 7* -+mc+nksqrjsnw4 surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at th*c wjq+ss+rk-m4ns7 n e Earth's surface. $\approx$    g

  What is the magnitude of the acceleratiof8m x wf;+ovl)5r1xpdn of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the w d;vff 5o+8rp)x1wmlxheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvedj(uv-e 6 axf( ;wsuq8d at a uniform rate in a vertical circle a-8de6xsf;q((wj vuu of 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 4os l9j/7x qahturn of radius 77 m on a flat road if the coefficient of static frictioxso9/4q alhj 7n between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be i q0 )*d6d4+gecpf yogbetween the tires and the road if a car is to round a level curve of radius 85 m at a speed o0o6 +i)g egyfpqd4c*df 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a, ltvr nyv6)i( trainee in a horizontal circle of radius 12.0 m . If the force felt bylt r6,y (i)nvv the trainee 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 turntablen 4xz, fsdbn8. 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 8,xzfd.n4n bsthe coin and the turntable?   

  At what minimum speed must a ko:2spt9y8.ap nqg jqs r.(:kroller coaster be traveling when upside down at the top of a circleg:8s2ko.p q qkpnj(: .ta9sy r
(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 thewz)tq n80f we./mc 1yx rounded top of/m 8w ef)x.nq z10wyct a 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 Ferris wheel needc(y9i, lvgdl 2 to make for the passengers to feel “weightlesgdlv9y,il 2( cs” at the topmost point?    rpm

  A bucket of mass 2.00 kg i):.2 n8d k /4j+,lpniyzx ven)utikzts whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucke / n k8 +luy, v4njtkn)eit:zi.)px2zdt 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 14wjeierxp 21ticle 9.00 cm from the axis of rotation is to experien 2rwe1i 4j1epxce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a nn 3c448rsga qcarnival, people are rotated in a cylindrically walled "rogrn34 s4 nacq8om." (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 rotated in a circle o6d.xvzzz9id* v/;e0 greurzxs2f(7 rn a frictionless air-hockey tabl. r;zv i sg9u6 rz7dv/z (xze0f*rxd2eetop, 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-
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, bymi 7it alh (3 nka;dz+7lv6gw) not ignoring the weight of the ball which revolves on a string 0.600 m lolam7ghtv i3w nz 7 l)6;kai+(dng. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a carq(a f 9hv(ey:d 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 masse87dsf,r zp0r bs $ 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 evasivl 6jb vipc0( al4 +pyxr417is;chij-j e 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 thjacpr6og 7 o/,:p.fps e net force exerted on the car (by the groundoaopp/pr:sf j .,c76g) 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 a)0b z5 l bqten9:ntx+wrea, 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 throubwnnx5b)l9q et + tz:0gh 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 circ( mx7sy t9*hckle of radius 2.90 m . At a particular instant, its accel ch9( *ysmkt7xeration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Ear:z6 ,(tejgfm3fhalr3th radii) above the Earth’s surface if its mass it(ffla,3em zhj 3:6 rgs 1350 kg.   

  At the surface of a certain planet,,j7nbjr;b) bsq qon/* the gravitational acceleration g has a magnitude,jo /b)nnjb7bs*q qr; 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 gra50es6ufnv16 *boyur jvity on the Moon. The Moon's radius is 1.7eys *6n6o01uv r 5fjbu4 $\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 that of Earth, but has the sam(8ni fk2 +hqe3a sci4he mass. What is the accelersqnhh + 4fie a2(8ikc3ation due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 ti+qohu):qb ieeq xkhtb- 6137jmes that of Earth, but the same radius. What is g n6ixqe)3kb :7e tboj+u1- qhqhear its surface?   

  Two objects attract tdq (oige14p y,i(1zscp 4zd 2each other 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 gr7sk320h vzs3g bfs3-4 (ztd hmbcxm c6avity, at (a) 3200 mmz 0m-sthcszb2k6x3( d3h7bsc4 gf3v    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where )tl;amvgu6exxs 5/8a thegravitational aca5 / sm8auxle) ;vxgt6celeration 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 ma.y)gb 3,yc jy ya3oe/8m ezo.lw j:xz0ss of our Sun packed into a sphere about 10 km in radius. Estimate yyw jx.ge0ol)z o 3zby cmja8, ey3/:.the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, wzstrpqk, ph.s7z/ /1chich once was an average star like our Sun but is now in the last stage of its evolution, is the sizpqs./7s/ zktz hp,r1ce of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in t (sq chzoonn1-:l )g*xhe space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in ter: z-xl*goo h(cs qnn1)ms of g.   

  Four 9.5-kg spheres are lo1; stjsxu wrjjn55rz) u7z/a+cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational 7znjuj5s1jw /)xu5 zta +srr;force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most r4b5qw hh2nx8 94tb4 rzan sy.of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming 489a n4w.2s5r hqzxb4hntbry all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the xe-6iom3 u -glsurface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass oxio-ue6g -lm 3f Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for te54 8*sq zc10qsr tauax+z8mhhe period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtai0aecrzx 48ta5u s+m1h qs*q8 zned using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelk7(jwui4u z9klite moving in a stable circular orbit about the Earth at a heighk9u47j ( zkwiut of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a civg( bfll(o) 4e/x uud6rcular orbit 650 km above the Earth. How fast must the shuttle belfo)( db6v(leu/4xug moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupapmrud gus 7 uiy,3b6klg 0u8:6nts are to experience 7ub:ugk3,ip0sd m6ug 86yl ursimulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the px. sn )o-o+eztjl0*yzay. 2oEarth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the)0e zoyap lnso j*..t y-ozx+2 surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launchea /kbt/ih.kp 9 r0dj/vd from the top of Mt.0k9rpj// avkt di h.b/ Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mi0b,vlu ps ez*0t 3ib2vssion, the command module continued to orbit the20it*v,3epbvbu szl 0 Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn arjlw4r+ 4nm7 +stn-h toe composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,000 hswro4n t-+ml7 tnj+4$\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whjp0f x8i8z0f:y ypl ,fat is the ratio of a person’s apparent weight to her real weight (a) at the top, anf80fipj yx08l,fy z p:d (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200nsrg*24dzw 85ka z4, h( ehew,zx:9bp jir,fe km from the center of the Earth's Moon in a space vehicle (a) moving at constant vr h4(*rbwjfz,hgza:4,wnxp8i9 d5k2e ez, seelocity,     ----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 constg 5, ew2ydam,ists of 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 y te5mg2a, d,wpoint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring s .c1koa2c;iaacale read for the weight of a 55-kg woman in an elevator that mia21cco a;ak. oves
(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 ceilg7ra,s: ssoe4ing of an elevator. The cord can w s:og4 ae,sr7sithstand a tension 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 perixdx(jgu,qg e5w-ov3 b) ds u::od T , the density (mass/volume) of the pwx(edgo3qj:- uxb)vd, g5su :lanet 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 perio:hilsh m7u. (qd of the Moon (27.4 d) to determine the period of ahh:.q( um s7lin artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lg/qh. fhgvq8o kuky5,u,o 0 :like the planets. Its perioo 5g,qfl/.h 0: uguh,kqov y8kd is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distagau0tm.xuk o*a,+ojmwl/8 1hu1 hl( b nce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It ckra nq::xj,xwr* -t(-d9xi mity8ss/omes 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? adw ,:ni 9ss j/yxqti-tk-rm :x*8x(r 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 g jm7i* dy+-u)7lmdjonter 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, p6ywsv1db f4. )gaxw *)buea;s eriod, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 160* . swb;)1dgx)aabvy4u e 6swf9).
(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 o b1hogp9y1q-the Earth from the known period and distance of the Moon. 1-o 9 yg1pohbq   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usinqjgs* mn3w9r v-eg-5hg Kepler’s third law. Use the distanjg*nr3g5wem-h -v 9sq ce 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 Jupitc ul k3rtk-e6k+p:n 1;lm:cct er consists of many fragments (which some space scienrn ct3:6lt kec-m ;kp:+u1kcltists think came from a planet that 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 artificial "planet" in hh ke:z- 0p(r(wdmgzfi8*w+ ethe form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inhzh8(zdi(wmr -*+f g:week p0side 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. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a 3c8tp7*mj3cb8 smn +svl g(szgorge 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 is the maximum speed he can tolerate at the lowest point of his swing? His masb *m3c v(+stcn8g38zspj7s mls is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surfacece4k;+li r0u6 mwymq p7u v5n4 will the acceleration of gravity be half what it is on thenu5le;0c k7 +m4p y6u4iqvwmr surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass o v(i)dju1 dp dksw.2:grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 ):djkw ivu. 1p(so 2ddm 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 pb tn3247ijbgday, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractip jb7g3i t24bnon of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacefx; u cu,pe 9d;pakd4,craft traveling directly from the Earth to th;pc4ud df;kpe a,9x, ue Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, g)x+zj naz56vbpn t.(but when you stand on a bathroom scale in an elevator, it says yobpvg5.z jt(6z n) x+anur 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 tu(tndzp)y+kot7bj/l0 be that will rotate about its center (like+dpttz)k(/ n o0bjyl7 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 aircrafv :uddz-c6y/92j sue pt 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 i qegprau .q0r261l-gtts radius r, the acceleration due to gravity at its surface and the gravitational co02guq6qg1r-ltpra . e nstant G.

A plumb bob (a mass m hanging on a string) is deflectsu+t,j2sps-:p 9 wzzm ed from the vertical by an anglw2puzp+ ,s: -tz9sjsme $\theta$ 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 spqg)b, z c2;zbueed of If the coefficient of static friction is 0.30 (wet pag2; ,zb)quz cbvement), at what range of speeds can a car safely handle the curve?

  How long would a day be if rtb) pi 6+g4)bevzrq2the Earth were rotating so fast that objects at the equatv2 ))4pr+gbi tbrq6ze or were apparently weightless?    $\times 10^3$s

  Two equal-mass stars mainjvh3p.,rd/: ll y-tjrtain 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 4 ,h:dduqy/ 6 8yq sblny7hvv9of radius 235 m. A lamp suspended from the ceiling swyn,h89qq: yb6 svlh/d4u d yv7ings 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 claimq ,fn6pmns*e+ed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a plfqse+ p* m,n6nanet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremelhuxfzbf l)b:2 1 ;yshh7. m5yoh:)hhuy massive core 2 1h):)hh mbb:uxs5hzh fh o .f;luyy7in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and vac-cseim1 x5, olley 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?) Expoi- m,xsce 1c5lain. (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) utilizes a groupa5:-v+o 6avkds 1w)v lomvj p: of 24 satellites orbiting thes)a1vm p+ol:va6-w :kdv 5jvo Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites 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)0/cjt ozp3l0kgl3( el85(7 qkgahgi sx pc- z9, after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eroi -ekhz 3pccxtg0(7(l q85lsozgg p3/k aj09ls 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 i6kv-brtw0+ tks( z:xo;7 nt uzn the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but: 6wuz(ork;t 0vzttb7ks-x n+ 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 y46fh6 8yodn8v uuw-lzh8na /zears. (a) What is its mean distance from thw o8vn8hunfya/d4z -6lh8u z6e 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 ac gg;ss)s)*-yf gg tgw , lbv,3 wged9xff,q*-ntually "feel" yourself gravitationally attracted to someone near youe g)-f d,g9-,g3fnsw*vl;fqs*gtw ) y ,ggxsb. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.(g ou 8aahdcrh4;5mi+nrz 7,gm:vs )u 5-46) at a dista, agun47i a5v g(h )dhc+:usro8;mrz mnce of about 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 oz yp.z1z 0/zfln each side. Find the magnitude and direction of the gravitatiol01zzf /.yzz pnal force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits j 8:z ,dls)5n.oijvmd 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-/( dnywmcrhwm,s2;6 * qd e9gtlong sweep second hand on yd, (d9h2/nwcr mmq*;se w6 tgyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sink,l d )ubn7ia g,9sdyp5er weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete cirlgnu9s dy,b) 7,iap5 dcle 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 i35k)fnr9 szpq*fbq* as designed so that a car travelin pq r*53fks9ab) z*fqng at 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, uts/4* fl0hj 3 bs2zmr ,fl9syfjilizes 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 roundsjr4f ,/2mfy szf0*ll sb93h js 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.$\approx$    $\times 10^2$