Sometimes people say that water is removed from clothes in a1mufs39mupl ;w 5 ;jk(1m oixu spin dryer by centrifugal fo1ow1(93 xl m;u uu5jfm;ikspm rce throwing the water outward. What is wrong with this statement?

Will the acceleration of m o zg9t*1u5dna car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curv*9d gm5z ou1nte at the same speed? Explain.

Suppose a car moves at cnqrbo:j 45)l0 ns q.fb02w obaonstant speed along 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 0abqoo )r .4 j0lnn 5b2wq:bfstwo hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse 9s7(kn*voxjp on a merry-go-round. Which of these forces provides the centripevsp on9(xk*7 jtal acceleration of the child?

A bucket of water can be whirled in a vertical circle wi,. c,xfyj (letthout the water spilling out, even at the top of the cir, exl(f,t.jy ccle when the bucket is upside down. Explain.

How many “accelerators” ( ixe ghvn:p2.do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? W.i(2 :p xehvgnhat accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as showjvzh(i7 *row7 9mbut( n 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 (( u*morizwb tj7v 79hsled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve6jvsp m61:;k)wi h -e lziu1ew at high speed?

Why do airplanes bank when they turn? How would you compute the banking anglev3 vxwe -gu *.wc(kkk0pl 7rm4 given its speed and radiux 0ur7wke*4kpvlw 3 (.cv g-mks of the turn?

A girl is whirling a ball on a string around h.5 hvlc)as6 xxer head in a horizontal plane. She wants to let go at s6alx)h .cxv 5precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so,1pfd f, exu hz lt/l)4ig)og*, how large a force? Consider a*4)o1f/l,pltghed,ux) fzi gn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit.l)mctg*(asg am 3pf/ be (at3)cf s* mm ag/pl.gdifferent?

Which pulls harder gravitationally, the Eaj6 lfc si.3jx:rth on the Moon, or the Moon on the Earth? Whijc s6j3f:.xlich accelerates more?

The Sun's gravitational pull on the Earth is much larger thy.jb.vmi ,*jzk4*qr);(e;w gsbbeog) er;rf an the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationaq ),kb;(; * jyr e.eoiez 4)g*b.b;rsjgwrvmfl pull from one side of the Earth to the other.]

Will an object weigh more at the equator ot5 m:- y q.doy4a7ubntr at the poles? What two effects are at workbdot7y u-:y4 n5atm .q? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the.9+jo jsbv; tj force on the Moon due to the Sun. Whyj;9tbjs+ o.vj isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larget1sq2.y y.x,j9ns go )8nxshvr or smaller thasxn)n.sx,2y9hys gq j.tv18on the centripetal acceleration of the Earth?

Would it require less speed to launw7p bb3+ v)8 p uq wwiif*kyd/bdg,)p*ch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s ,3uwv/8 diybb*g ))d7wq+ *ppiw kfpbrotation direction.

When will your apparent weight be the greatest, as measurkhjn7:wd6 ;w pu yo25 b3qint3ed by a scale in a moving elevator33hbnn i6y d:ko2uwt w;pqj57: 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 the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely adl4ptc (epzi6kl:6(bg i4bc m3nie7js/ 1t9mffected 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 z97eg b4mem (icciktbj3 pt 16 (pd:64lns/li(c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “a x;v9pnb j xp*0)amq0ipparent weightlessness” between stepspq9am* p; 0)ixvn bxj0.

The Earth moves faster in its orbit around the Sun in Januarawt6t h(0nfc (y than in July. Is the Earth closer to the Sa f ntct06(wh(un 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 orbit.]

The mass of Pluto was not known until it nbn*+av jr94dm ;64b;miagpl was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s ;m d4 g ljnr+;6vnbm* 9iap4bamass.

  The Sun's gravitational pull on the Earth is much larger than;nb-xr1k v go( the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consob; rk v1ng(x-ider 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 1 i k(wk n18byn1y8d l+e8aj,lp980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerati5/uf55nytt8 msj* pvlon of the Earth in its orbit around the Sun, and the netu y/tflv 5m85*j5ps tn force exerted on the Earth. What exerts this 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 pcd4 /e0u.tog as it rotates uniformly in a horizontal circle (at arm0 tp/eg.uo c4d’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 zm0,pfcxe- jn/ a3mf5circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answerx3fmec/ 5p am0jf, -nz in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a4l.lo4a05nu 9 z5 yhchh3/4 yanb vzdb potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dal3b9oh lnhbh zya 0454/ny5cd.4zvu iameter is 32 cm?   

  A ball on the end of a string is revolved at a unifbmx/dmm p r697orm rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spe7b6xr/m m 9pdmed 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 1d 6p h67jkvg8cer1he -050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction bet8kh6 rep-6 h7decv1 gjween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficien zvo jyw:1k1 pk+n3)mwt of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a sz pnyk :)+m1 1k3owwvjpeed of 95km/h ?   

  A device for training astronauts and x lw:sm vpe;d 5o7-cg7jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 wm 7g:eos vxp5cld-;7times 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 turntrape y;*4qwl 7xl6se td.wwq0)0b7s m able of variable speed. When e.pbew ay7w074;d* xlm6s qwql r0) stthe speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller cbok4-y 6, wbl-d4kxjlp/cvk2oaster be traveling when upside down at the top of a circle,4j-l c dkvb opl2-64xkyb/k w
(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 95/45gsqfmtgl1y2 ps5 i0 kg (including the driver) crosses the rounded top of a hill (r qggt5/lp54im s2yf1 sadius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to ma,3ygjrhbx )azjl w5y8u ,ot69ke for the passxo85 wry,yzt 6bj3g9j a,ul)hengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whir: e9gmyg4tby-j 6 6qnuled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tensi69tu6-nmqybgj 4ye :gon 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 aeva-f89:tj nj*)hvg 9fyx 2n a particle 9.00 cm from the axis of rotation y:98gn-) jehanjaxftfv 2v9 * is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peooo6p;v ln2w2 nple are rotated in a cylindrically walled "room." lw;2nnovo62 p (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 c +m h,ysa,r6siircle on a frictionless air-hockey tabletop, and is held in this orbit by,,yrshm 6asi+ 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 , pro5z,y. 6 ghhqmecisely this time, by not ignoring the weight of the ball which6z.o,m5hqh y g revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelia3 n dh2( 3f0zkkmxbwche 23d3ng 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 massep5 kwbzg e 4fy)e2s71sjw wo;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 jyvvsdn l6l cb+qe n-5r7:2u+ 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 .fjk7v x3ab+aynj 2t f (yekd845*iqucomponents of the net force exerted on the car (by the ground) in Example 5-8 when its spe*7dik3axb2f y+5 f un4kjeaqtv.(y8 jed 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/6dw o2l q(e39dfofy9rm2b au the 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 with no slipping 6(9yd ufw el2ad ro2oqbm9/ f3or skidding? $\approx$   

  A particle revolves in a horizontal circle ofrh ki7s1 a/ gkot2z:q( radius 2.90 m . At a particular instant, its accelerati gro2t iks(/ :z7qkah1on 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 grfj 8(;dk3iih ravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 dri3;(fkjih 8kg.   

  At the surface of a certain planet, the gravitationas8wqpips.0zhwf53 e t:)9e yhl acceleration g has a magnitude of 12 m/y s8he:wfip9z3. 5ehwtsq) p0s$^2$ 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 t8ja5:gpv;tx;etg w-w o gravity on the Moon. The Moon's radius is 1.7eg x;jat-w ;5:gt8v wp4 $\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 Ea br3-w;vqe e ;h1/hneaeb.x,wk8x2 hzrth, but has the same mass. ;e.en r- z8vb bw/2xe 3qkexwha; ,1hhWhat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 i7e ebp*nu9-h.3fooq 4wla7 nprgt /d*a 3ph1times that of Earth, but the same radius. What is g near iti- a/4tpn. hbfp317lg*e9ahqer*w 7 n upood3s surface?   

  Two objects attract each other gravitationally with a 1gw) d-. *4wdu(aztl;dukd-hp bhsf) 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) 3200 7hdbkv t bdc,y2i(q*+ *2seah m +e dybi722t,h ( dq** hbakvcs   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to q5d qn1( v0+oqd 7 .qmxw1ruiza point outside the Earth where thegravitational acceloiqq uq15qndz.v7+w m1 (rxd0eration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times z,0n4o e3ztu9 krun)q the mass of our Sun packed into a sphere abouu 0tkeoz9z3q)n,nur4 t 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is xl:gzvz luly rr0: cd;;+. i3snow in the last stage ofl :l;yzlr +0 r3g:.icv;zdxsu 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 while orbiting in the spa cn1)ufb6p3om ce 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 incf)1 mnb3o6up terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 2qk4slj i,k :rtvy5kjd/b 7x/ m. Calculate the magnitude and direction of 4j:kvbdykqt//ixrjk5s 7,2 l 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-k c/ze*6tdt je1+c6,eaedu e planets line up on the same side of the Sun. Calculate the total force on the Earth dueuda/ 1cc ,eetzj+ket6 *e6de- to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleratioezm :ft9vw fan w:k)0(n of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radiezkf0:n :9fw(wtamv)us is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th5sy;w ,7mtu/l /1i2x guthva te period of the Earth and ivat,us7 yt m1itxw5h/ 2l/;g uts distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of ao8c y8;u lq2gnv +5.bjg n3yge satellite moving in a stable circular orbit about the Earth at a height o;8vcq y8 eyb.ng5ul2o jg+3ng f 3600 km.    $\times 10^3$

  The space shuttle releases a satqvicbd5(8 jj/)wz0 (;hus0otwp rxy:ellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rezwuy:jc00rib; hjvxs ) tqod/p w(58 (lative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindr1q uekjc,+p14 zuh w.wical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spacuec1.,1 zw+4qpuh wjkeship’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 tr1 gy.ri)pe t6he Earth in a circular “ney)p 6r1r ie.tgar-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satecg;djxzdp 3y2df *1j/llite have to be launched from the top of Mt. Everest to be plac1 d*/zpfddjjyx3g2c ;ed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the commandki s m-rii 27cyl)p4+b module continued to orbit the Moon at an altitude of about 100 km. b m)i4spr-c2k7 +i lyiHow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks9s mmi4avbjo,t3 t.a; of ice that orbit the planet. The inn.34imaavbj s;t9m to,er radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once eve s/u p 0pwrwl;x6w zs.jbh-q,:ry 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) at t-px;lusz:w srj q,p6h.ww b0/ he bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 2 qa1c i2m+g/a3oqqokvjs/+6b da* rmkm from the center of the Earth's Moon in a spacs q1 mbajrq*d2+gac62oi//v3okma+ q e 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 star s63f 6op9i2h5fd kxqbs of equal mass. They are observed to be separated by 360 million km and take q 626ds3ioffhxp95kb 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 5i7rq i3zf+ v:t5-kg woman in an elevator that movef3 i+vi7q:rz ts
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling o7 hhyj)/rdcekp ra +5+f an elevator. The cord can withstand a tension of 220 N and breaks +depr+/yh 7ck5)hraj 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 perih44(rg ujalx )od T , the density (mass/volume) of xagj)u4(h 4rlthe planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period ofzy( -pv w9ul dt8ojjfsax8a* s2:pd 62 an artificial s da2w-8pv8:f9 t*s x(jjzy2 dou p6aslatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metersmyob, 9a)e8nm across, orbits the Sun like8n9o ymeb,am) the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis;ijr t ly8on,,tance 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. r ::y(,utrau iIt comes very close to the surfac(t:u :u,a yrrie 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 the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cente24f ks2qc0rzqn, gkmt88 k+abr of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mea8 fw(/flhh* my;y2xde n distance for the four largest moons of Jupiter (those discovered byl/fhdxh; 8e *(wyfy2m 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 zb,26pgye 8 xnthe Earth from the known period and distance of the Moon. ze ,8b pnx62yg   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, ud6ua7p v dqxnwy.6 sets6.u.5sing Kepler’s third law. Us66 v6s q.xepws7anud yu.t.5de the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frahwex2wu/y l65 5afn +agments (which some space scientists think came froyufxaah/l52wew +56 nm 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 "ppu/)ou ias-/ 4v7 teo(2 gvxexlanet" 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 /2atgoi/x exp)-vu e(7svo4uown, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by)gyi3t e, bee7 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 tolbe7tye i) e3,gerate 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 accelerat9 sabgh0;nzy ;qtpd70b5g/7o;bif cmion of gravity be half what it is ong05; fygm ;qdh ;b0bip7/cotns 7zba9 the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circvw appu8sd(u63 v8vh d 9oaakco7 0h53le once every 2.5 s. If we as o vav(uc3a0o d hw8v7d593u8sp6hkapsume their 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 onqmccj2su2 1w/+ iv 0zsce per day, 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 thz cjcuwq0 ms2+is21/vis effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tql jzrv2s16(e;x feq 7 1jg8rgraveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal erqqejj 7 8svf;2(gx1z rlg61 and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an )wwfc) 2b v5qh3 td+oi1 rm(wxelevator, it says your mass is 82 kg. What is the acceleration oq ch+ )dwbwovit1(3 m) 2wr5xff the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about its33o3np aopi.5wu dgf( center (li fgi3uo5 3pnd(a ow3.pke 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 log9vb4wpux u-1 bm v-; rs;mo:oe6c gts)sr:g2op (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 termsm 4hgxc0eh7 79lkhncii8i0p1 of its radius r, the acceleration due to gravity at its surface and the gravitational constant mi08nh70k 7xe9pc hlci1 hg4i G.

A plumb bob (a mass m hanging on a string) is defl6 y.clygiit/ 9ected from the vertical by any/iylti9 gc6. 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 bana bdesm/9cr /k0h;n;hrc.z e4ked for a design speed of If the coefficient of static friction is 0.30 (wet pavemera;0m. nhkr 4 ;/c9/zdbeehc snt), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast thac gmg84wsii.aidf;,* t objects at the equator wemggf;w c4*isi,a.i8d re apparently weightless?    $\times 10^3$s

  Two equal-mass stars mainta xa a.ve nufzz-(nryp21;2x v:dap u)hr-;g,sin 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 rounqzn t-hx fjzf(:x 97y:ds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an anglf(z:hft:z9q yxxj 7n- e of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Ey8f/nh+rllk ) arth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive mol8rh+k l)n/y fre 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 an exwg ekw 0h+45f tv5; kljvp,mq)tremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They divl gwtef ; 455wp) 0kjh,+vkmqd 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 valle 4gkwv:-zd9i)jyo9 k tfksux w4 .k3r.y 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. (c) How fast can the car go without losing contact with the rok4j.k3xgfkr.9)iu4t owz 9v s : -dywkad at A?

  The Navstar Global Positioning System (GPS) u/ m0qzm1 x:cvrtb58z etilizes a group of 24 satellites orbiting the Earth. Using “triangutc/0 mmzv1zq8x e5br:lation” 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), after traveling 2.1 ktx*.;kbke n0emz2. kzf k,i;billion km, is meant to orbit the asteroid Eros at a height of about 15 km . E kxzek2 .kz;k,. mi;0tnkfbe*ros 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 s-wfv f a 5/-aim*fbuvvl*4jv 0:2qx oqhuttle 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 25 km -q4q *v: 2boijuflvwv vaxf *-m /a5f0behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Wa vaq8 .:;vb.mv4ho jkq54azbhat is its mean distance from z qkaa5 a. hbovvq44.b:8jv ;mthe 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 y/1j) ksd(w/ pgeua fn:ou could actually "feel" yourself gravitatikg sud/en p):/a f(w1jonally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. qz +eycoi +sk1mf4/k. 5-46) at a distance of about 30,000 ligc/4 eoqi+k.zk1 +fmys ht-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 a1/gu.l(f98niq u7vs4 jog7lz5wgm dwt the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth v qu iowj71zu 87 lnm4f9(g sl./5wgdg1.0-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 j :dkx0q: 6r)ykhez+z kg orbits 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 sdmxwq h(6uh /4econd hand qh(x 64/mudhwon your wrist watch?    $\times 10^{-4}$

  While fishing, you get boredn6 vukt0/dl gr)*/c se 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 fishi/6*cd /tnsegkrv 0lu)ng line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a no44mocjf e-bp3aw :6v9mq 1xq ew highway is designed so that a car traveling at s 6 4ecm1wv:xfpbao4moq q3j9 -peed $ 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 Ar b s7jn( b(vqbz158lgc;(s ygcela, 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 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 ysc7vgj5;(brb1qz(8 s(l bng 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.$\approx$    $\times 10^2$