Sometimes people say that water is rn*qircb3c4m) emoved from clothes in a spin dryer by centrifugal force r3n*)ci4 mcqbthrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp ap8r,0g dsavoli3 /* i6 ruha(j(;zymcurve at a constant 60 km/h as when it travels around a gentle curve at the sa / j 0i s*i(aalo,uma3 y;zg(rhp6v8drme speed? Explain.

Suppose a car moves at constant speed along a h d73 ;c2wpw.g-wuze.zh+wxgl illy road. Where does the car exert the 3g 7+ ux. dl;zw2zpwwhweg.c- greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse onz(mkp 1b5p( s-xphsgr8gb s8: s bb(f) a merry-go-round. Which of these forces provide(ksb8b (g:b-s sb 5pr)x p1m(shzp8fgs the centripetal acceleration of the child?

A bucket of water can be whirled in a vertic(y4-px;fe vetal circle without the water spilling out, even at tf(x v ;4e-peythe top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you hav(wchn(p:8e(yge tlk,spv)* p e in your car? There are at least three controls in the car which cane,he k )(g(*p8ywst(lcppv n: be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig.:+g/bsu+ 52jsg ,wvfo a5gbyc 5–31. His sled does not leave the ground (he does not achie5gg s obcb2/y+5sf,v: wga+juve “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 curve at high sp wu3nzc,s) gg3 n(s3w(hadv:zeed?

Why do airplanes bank when they turn? How would you compute the banking0yj0 rrk, * 2t6hsrjad angle given r,ah6tk2jys r0rjd*0 its speed and radius of the turn?

A girl is whirling a iq 4x: gr);1:a4cq rpdwmc7uhball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so4p): aqcr cr:4w ; qu7dxhgim1 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 gravitw+t+cb7a.. s(dqc j cpational force on the Earth? If so, how large a force? Cw jccb t+7.( +cqs.apdonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dve/:wfuwzg o.) +f* ;r(;o ioegu k;vjouble what it is, in what ways would the Moon’s orbit be diffi /gevfow;egou uwk)v:+(jzf. r;* o; erent?

Which pulls harder gravitationally, the Earth on the 2x.gkaa bpe8px/8,xg9h/ x8s2fds kpMoon, or the Moon on the Earth? Whi2gxxkx 8 8gapk9f sbe/p ,./sd8phxa2ch accelerates more?

The Sun's gravitational pull on the Earth is much larger than the 9 m1-in0idhe2nuco3*zjk .e z Moon's. Yet the Moon's is mainly responsible for the tides. 3 ji9 zn z kcme.0*hn21u-ioedExplain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mwbbfikk ,u95z/jb6jed 0 :lz) ore at the equator or at the poles? What two effects are at work? Do they,b)b kzdjuj bfkwe 09i/z5: 6l oppose each other?

The gravitational force on the Moon due to the Earth is only about half the luud)s(s /dz5force on the Moon due to the Sun. Why isn’t the Moon pulled aw)ud(uzss dl5/ay from the Earth?

Is the centripetal acceleration of Mars in its orbit aroui3 x1fczl4da3phj wl10( h qj/nd the Sun larger or sma3(d3f1 hp 4q/ 1 zca0lljiwjxhller than the centripetal acceleration of the Earth?

Would it require less spe1hxu lnx x.,v,ai7k;o1 anwd9ed to launch a satellite (a) toward the east or (b) toward the west? Consider ondh17 9., xixwxaav,;n 1ulkthe Earth’s rotation direction.

When will your apparent weight be the greates7, tdsp1 9 hf7scylaw3n 0u 8zgzhu9/vt, 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 yh7y1 s/9h3sczp9g zn8ta70w ufuld,v ou are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend z0hczylz. yhwb+ * (3ilong periods 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 asphz*c z0ib. (+y wzlyh3ects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” 6mp*qjdp;f b/wa t.b1between steps q t.b/aj*bf;d1 mp6pw.

The Earth moves faster in its orbit around the Sun in January tha rjgp+ ; cy-4nl s/fhifb8ap+;n 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 facs8cpfj; +p4 ihra;bf +/l-yg ntor 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 ( vf(xlbe)w6b moon. Explain how this discovery enabled anl(v)f 6xebb( w estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thanb ftp mbs,x6:k+7wt;o 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.]A child sittin:oxt7pbs+m6,bk ;w tfg 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 198 .rsv2*6ngg qo6bn4cw0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eart(3/g v ol.w:deqjgx3i1zno-xh in its 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 circle of radius xw :qogijgd1 xe.z-vo n3/ 3l(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 rota*pa0ijwmci p +1p sz:;tes uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate tha+p*0mp c z1 s:iijwp;e speed of the discus.   

  Suppose the space shuttl* whk/) 2dk95j nhmmtce is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answedc)m wk9nkth* hj/5m2 r in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on r+k2 8u c/*w*lwe dqgaftc4. lthe edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32* cckqwr+d*g42l/ w tflau8 e. cm?   

  A ball on the end of a string is revolvey6w o0n)zlmz( d at a uniform rate in a vertical circle of radius 72.mln )z60(zwy o0 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 turn:p 2a*hrjz 6v cp:nkd03r:fja of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is trdh0zakp: :ap cj:nvj6 * f2r3his result independent of the mass of the car?   

  How large must the coefficient of static frmc m s ,pqc3rxxcc- k7ziy+ 0,--li(cwiction be between the tires and the road if a car is to round a level curve of radius 85 - ccqxswyc7 lm( zki,imxrc0p3+--c ,m at a speed of 95km/h ?   

  A device for training astrot 7t :l0;tbpbcnauts and jet fighter pilots is designed to rotate a trainee in tb;lt0 7:tbcpa horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast 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 turntable of,hp b7 h +:n9b5t(azcnw8bni iea.8zg variable speed. When the speed of the turntable is slowly increased, the coabn h7(,bp 589z za.iighcw8tn :be n+in remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coas-jxvp-m)u 5n jw (dj ,pz2-e2ro( jqtpter be traveling when upside down at the top o)j( x p2n--u dw(jerv2p tzqo-j m,p5jf 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 masz(jn al-8q9* no( g4g(kziflf s 950 kg (including the driver) crosses the rounded top of a hill (ri*- nalg9lgzo( 8k (nff(4q zjadius =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-diad+iyg6r1,bj8k:t 3 5vnol u ypmeter Ferris wheel need to make for the passengers to,u381:+ioryb v 6l p5ydtgjnk feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle offtq2a 3e,/5 d;bwyaj :p73bda uhf4ta radius 1.10 m. At the lowest pointyqaw at35/; 74abj 2a:bf ,3tdp fheud of its motion the 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 centrifuge rotate if a 2b8. x yn 5qluub/,fhvparticle 9.00 cm from the axis of rotation is to experience an au82q hfu, yvn.x /lb5bcceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in riarp-x bm4 rz3b: +3/ fk,udla cylindrically walled "room." (See Fig. 5-35a-/ mbiukd4l r zfx:,r+rbp33.)
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-hockey tar5* za xf79; mioklx(zbletop, and is held in this orbit by a light cord connec( liz9*zkmr a ;f57xoxted 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 thel0p* lk7lpp. d f gw00q2g/nxa ball which revolves on a string 0.600 m long. In particular, find the m*kal0g q.pldpw07/02g lfnxpagnitude 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 perfersow *qp/wl+6kcw l 4qgd:9i42z ad s6ctly 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 massecf4god kc6a zs1db j/w7g(j(6s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at hgnxx5 t3v q vso,u1jjtud;, 1,mi:h4 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 tangenq :zkxwnv wrj; 239p:jtial and centripetal components of the net force exerted on the z 3 rnkpw:jqw9vx j;2:car (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 accelere 66cxe2/z rqdates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radi xce qz26ed/r6us of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular in9;ehf g +j7osustao fg7u9js+;ehnt, its 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 Earth’s gravity on a spacecraft 12,800 kmqa8( jvbea x(gn h:12p (2 Earth radii) above the Earth’s sujqh 8g:nx b(2eaav (1prface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceler2zits8c533) syv fvm8w /r phjation g has a magnitu83/s2j tc vziw)v5 8ys h3fmprde of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moond/y(*qyoq ;wdhl: ,l n's radius is 1.7y,l q ynd(wlqohd *:;/4 $\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 hasq7 ez8oe0il y- the same mass. What is the acceleration due-l80oy7qez i e to gravity near its surface?   

  A hypothetical planet hkni hw2;ujvj/n if6 n u97a4o4as a mass 1.66 times that of Earth, but the same radius. What is g near its su ijn 7n6u f42a4ok/ iwnvhju;9rface?   

  Two objects attract each)io +6u- nhf-yvrz9(e2om :qo;gb13wfxe jjc 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 gexjpc:a6q l 75 , the acceleration of gravity, at (a) 3200 m ec67x pal:5qj   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earj3ds 241ht mjmth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is mmt124 3dj jsh$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fiv4a8pfs 31c csxe times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the scs4xafp1c3 8s urface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once ro7:sc enq:u gdu.,xvu7i0 y :was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface g .cusq7uuevy:i xgnor,d7 ::0ravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting iza.:nklg 1bn 0.t 3eyyn the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it nnay31.eyzg: .btk0l 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 si0n+gt+r nw kzz; w:ov7de 0.60 m. Calculate thv;kw +z:+rt7 0gnnwoze magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Su(l5dx1du l vw:upo1 (zn. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The mavuuwldpl (xz: 511(dosses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of1fosl,0d. s)l wp(,fa * odtpg what it is 0 flpfo a d*,1p.dslst)o,wg(on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ear,/ boz7o u* uqn4yis0ath and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example q*ob /o4 uusznyia0,75–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circux7/dj, us 8 (qexezh+xlar orbit about the Earth at a height of 3 j7se e ,xhzux(dxq8/+600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular or.-y, lifxef)t hge)0dpp;q ,p bit 650 km above the Earth. How fast fp.),0 ;xqe h-dpi)lft epgy,must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to c q/lo*y( 6yfati0q)0v r4rya experience simulated gravt v0f0/y) (rc4 l airqqayy6o*ity 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 Earth in 3 4)j l-jeb3cd g8khbaa 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 thecah k -8l)e3bd4b3gjj radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal ve69bpu 6y n4tlmlocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular 9m 6 y4np6btulorbit around the Earth?   

  During an Apollo lunar landing mission, the comua* qpfo22n*j wn)9r hmand module continued to orbit the Moon at an altitude of about 100 km. How long jpun9 nrw2)f*oh2 q*a did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks ohtvh7,93 16cg zwlaa0x4yw(vp k:q ezf ice that orbit the planet. The inner radius of th v0x htkwwgey aa 1pl:7q4h(,c9z36zv e 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 dii0d7q(p kd;q qameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) q 7qpk0;(iqdd at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fro0 w+vewub4st8 .xayvke0a 4:um the center of the Earth'sb40 auvv ae.w suy:4kx+0w8et Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two staltko d q 2gf5q)/ auqs/wc;-j0rs 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. Whau0qfajqlgt/kwo d2) s-5c/q;t is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevato af 9jm r51z *p(mmg+(wtjs6fzr that moves r5 p(1fza9fj+zm6 m m sj*tg(w
(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 fr9e bm 4tpvw, w*n,uf0pom the ceiling of an elevator. The cord can withstand a tension of 220 N and brpw 9,fwn0m*b,e vu tp4eaks 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 period3a+s(mewt2je cv+ f1ija.4xh T , the density (mass/volume) of the planet is +wih+t c31av sa24jfee m.jx($\rho=m / V=3 \pi / G T^{2}$ .
(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 the6l v3m4*g 6afh.seesp period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfag6l.s e a634f vehs*mpce.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the S j;d pmisc--,lun like the planets. Its period is 410m sd,;-c-jipl d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of h(xk0le2rh; pl(/;cvc -)ash al* eji4.5 $\times 10^{9} \mathrm{~km}$ 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 rs9a qd dk1v3-noughly 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 wv a9s3k1q-n ddhen it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of ;1yd0 *i5mwwkxxczx6:o4t oe the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four larr w87j1fhnwtf 19g7y vgest moons of Jupiter (those disf nwwy77h1r1 98gjft vcovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Mo82pv 2bh8i2v3fdnrt*9izm m; rt cb j6on. c 82r zmhrti2pvmtb39fn8di6* ; jb2v   $\times 10^{24}$

  Determine the mean distancejdi 5k7p4ss02 al.5;dms adz+ 6 ukbkf from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tableiz a f 4k sku6b.j7apl+d5; ds50skm2d.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars ae9*bgr.q)v 3ahylol 0ogbp /.nd Jupiter consists of many fragments (which some space scientists think came from a planet that once or 9 ll.h0g/)ap*y obe3grv.qobbited 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 u 6d-guyosp )+hp--xi describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this 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 peisp pux-o+ -yu-g d6h)riod of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vinea sf6akw6qnlk9 +)v l) (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 swinlnsq+9 k wa)6lafk)6vg? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the nwl/i43t6lw hrv3d8 nacceleration of gravity be half what it is on the surface?ld 83nw/ v3tn6hr4wi l    $\times 10^6$

  On an ice rink, two skategpr6 htfs(h9s( bc)/mrs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they p gc h(t9rf)/h6smp (sbulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acce1ce xzc;a/7qc leration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate t zcec1ac;/xq7 he magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eartadrq(d0olg *5 i:j+ joh will a spacecraft traveling directly from the Earth to the Moon experience zero doo:a0i5*lrj gd(+j qnet force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathro2 8nl,2l e e-dhopg 1nc/hmcg+om scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator,n ,l n hh 228gc-+do/e1pelcgm and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about its j7g;6st*p7 ee)v3ts2c dq ouv 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 uv7t dv g3*7eqc;o2t6 ejp)ss 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 hisu8cq ab64y x)c aircraft 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 its radius r, the acceleri hva f:k5x0)wation due to gravity at its surface and the gravitational cons0 waih)5fx:vk tant G.

A plumb bob (a mass m hanging on a strixs9 p2+ zw6wdbng) is deflected from the vertical by an ws2dz6b9 +xwp 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 design speedr itp o ,i(jc szw7k95.(*xhy;t6s uxy of If the coefficient of static friction is 0.30 (wet pavement). ;,*tps x7x(6yc5z ki9oihru ywt( js, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were roti8s4 dt4qt712vl fgj cating so fast that objects at the equator were apparentl g8 qlv4ficsj 41ttd27y weightless?    $\times 10^3$s

  Two equal-mass stars ma3.y21v tb-xygtjby,6,u2 w oj, jl jreintain 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 curvess3t1s g7gjnip-)e 0 v of radius 235 m. A lamp suspended from the ceiling swings out to an anglg-tine10 vsj) ssgp73 e 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 bee.(o jt iga t. dok/7vnf,gju*:n claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive mj,7t dv o( uagj*t/.:gkf.inoore than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of yd9/4d 0gbce tan extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring tb0/ gtyd49edche 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 valley shz3kfn5beg5m3 own 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?) Exp5nfeb5zm kg3 3lain. (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 Sg+zm7 lv u 7egdcfr67v:e;e6to9* sqmystem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals t e 6o+7gqtc f9drmsmeulg:ze;vv 6 7*7ransmitted 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 (NEAR06h tt(dsp(xyb7 ik+ o), after traveling 2.1 billion km, is meant to orbit the aster0h b(6t sp+(xotdyik 7oid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need d;ppg;tgg8jdq ka8 2.of repair. You are in a circu.d;tdp; 8q8ggjapgk2 lar 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 3q0m0 s 3+gtnutt.q(t.+ong ts000 years. (a) What is its mean distance from the Sun? s +tnmo t.s0 (tnq.tgug3tq +0  
(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 actually 5sd/jtpa.: sl "feel" yourself gravitationally attracted to someone neats5dj . l:/apsr you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkytj7+7krn teics3/**cl.3 w xoz v*gsc Way Galaxy (Fig. 5-46) at a distance of about .nle3co*wtcgj*/ss i7ck xz vrt3*7+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 o( tzwtd+ 91 z)ftym*cbp5gzg8n each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpointzz8)f* gzcy dm twg(bt p91t+5 of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg od-i3j88w yyje 3vi*qvh9cx8 x y7r8mprbits 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 sw1(iz/ gpykn 1n6awb ,jg) v5rweep second hand on your wrist watch6z,5/11 i(ap ) vrnkjynwgg bw?    $\times 10^{-4}$

  While fishing, you get bor a- r 9bh 0ak8*0qgytfrn1;jgqed and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes wikrbr n 1q a9;y8tg*a0f -jqhg0th the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that f1uqk: k lkwn*z; i(fqdf 681ta car traveldwzf;q * :t(8 1kk6klfqui1fning 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,w/2v/om.;nzi nmhq/19jh cas the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comforto.nns/hqizjw/ m1c v/9;2h maable. 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.$\approx$    $\times 10^2$