Sometimes people say that water is removed from clothes in a spin dryer by cen w::pqoji vv:n5r 9ii)p) xo4ttrifugal force throwing the water outward. What is wrong with this stq:i5 4ivrp :jno )) w:pxotvi9atement?

Will the acceleration of a car be the same when the car tra *vcdu nf:b8k5vels around a sharp curve at a constan f:* b5nkd8vcut 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where do qam u.iy 8gtwq jo8op(+:p8f8es the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip betw8w au 88ofppqy:(j .gti+om 8qeen two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridin-n5 c z6)btlx-if jxt0g a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chill 5j0bc xin) --6tzfxtd?

A bucket of water can be whirled in a vertical circle without the6e u bfbvra*a*at;(:9 *s pgtc water spilling out, even at the top of the circle when the bucket is upsiusfa t:bg(br;ta9*e*c6 pv *a de down. Explain.

How many “accelerators” do you have 2kx 8 n8)ze qg4f j nyxolalk)4mbl-31in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelera3fnl4nakx2b lx8m1go4) )yez k jql8-tions do they produce?

A child on a sled comes 7 ste(ryuegm,f893*2 6qe bbb ghngx4flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newu g8nybm ge3t*7,(9sexqb b2 4ref6ghton’s second law.

Why do bicycle riders lean inward when rounding a 6hb39mn 4rl akcurve at high speed?

Why do airplanes bank when they turn? How would you compute the banking an 1y(7xnur h5kigle given its speed and radius of the tun1khx5 iryu(7rn?

A girl is whirling a0 uq c7q(+j6xgr5oh1 lak(qye ball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of thuq7qg01rxe a5h j6c(k(olq +ye string?

Does an apple exert a gravitational force on the Earth? If so, how large a forc/;f3og8j8betji/ a oje? Consider b38j8e jgaooj/; t/fi an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wer q+c m1e0nd-qee double what it is, in what ways would the Moon’s orbit be + 0q ceqe-nm1ddifferent?

Which pulls harder gravitationally, ycznq-u yy)* y*fr f600ca4ehdm9aw+the Earth on the Moon, or the Moon on the Earth? Which accedcfyzy6-0* c qwh nar+y*4a e)f09 umylerates more?

The Sun's gravitational pull on the Earth is,k/ lz4ag e-/mws xd h9usar5ovfz 98; much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from zx4/vh z-r9u,/fsmoe swk ;85lag9 adone side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are ,tw . inb sa;vxaul(r ;s.p.1bat work? D..x v bsua;b.wtna ,(p irl;1so they oppose each other?

The gravitational force on the Moon due to the Earth is only about hag1ksa y,4c v5-9 pxdyolf the force on the Moon due to the Sun. Why isn’t the Moon pulled away y, g - 5p19csakyvxo4dfrom the Earth?

Is the centripetal acceleration of Mars in its orbit aroum *dh ov ;ubjkeag41utea2v,g,. 1r8ond the Sun larger or smallee1j ;u*kvrm uo.ag1e gt, d,h4boav28r than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellxx2:r ;df.0r6cszy imite (a) toward the east or (b) toward tsfyxzirc.02d 6;m x :rhe west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, a vp /dgpmux/3+3r;cm rs 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 leas/c;g mrvux d+p3/3rmpt? 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 yyg01 npal)0;dfwsq fq 28p/gaffected 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 1)0yn0g;p lf28/fpdswgqqy(a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experda1me 4 jn9yz8l n8w4d 7xq2eiiences “free fall” or “apparent weightlessness” between step4je7e8y8 m dwxnl q4n2 zd9a1is.

The Earth moves faster in its orbit arounk69.68jdz6kisinuj sa/ w h; gd the Sun in January than in July. Is the Earth closer to the Sun in January, or in Julks9 ;n6 haijs6k 8/wzj6.gudiy? 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 k ,/f 2res6zmul w x8d(li0wl1nnown until it was discovered to have a moon. Explain how this discovery enabled an estimat86xilm l2n 0/d(eswuwflz r1, e of Pluto’s mass.

  The Sun's gravitational pull oog )6bs,u2xgw n the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-rou6 gsouw)2,x gbnd 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 travelingmg 7-mprmi p;5 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arou:./7xh8exitr ksowb* r-5uuu nd the Sun, and the net force exerted on the Earth. What exerts this force on the Eu/.rx *b8u-us:rte75 xiokwh arth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it roa is irbqb o;l7j831-otates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the l r;jqas7o18ob i3b-idiscus.   

  Suppose the space shuttle is in orbit 400 km from the/o6 rl p+6,*3 ygjsj5mg9u3stf rr pys Earth's surface, and circles the Earth about once every 90 minuttj 3 rg jyp gslr3s9+sr ,6p65yuom*f/es. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the exst4bmu0(y t6s,nk 4sdge of a potter’s wheel turning sy b(0x u st644snmkt,at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stringyh a 1s22oi aimbdx0q(56qds: is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If i ii(s 6ambd :xyhdqo0a215s2qts 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-ki5-.blgbz xy sp84dnig ):/veg car can round a turn of radius 77 m on a flat road if the coefficient of static frictioln /4-s e.gzdbi 5yxb)p8g vi:n 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 bmjeertb 189j. e between the tires and the road if a car is to bmejj19.8rte round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighte) uw mmcz7m./nr-xu knap-8zk 2e 6j(f mup)6er pilots is designed to rotate a trainee in a horizontal cir-k7-nume 6( pprkmzua)mc6xw2 j/fzu n)m.e8 cle 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 rotatiniotyy- t(kb(vn:*c6bmqg gs5wq. y. :g turntable of variable speed. Wh bt-6:gvi 5gwy(k :.y*myoq( ntqbcs.en the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed muecd:cu-x7rqke r q8nsi9 v6uv+wh1.. st a roller coaster be traveling when upside down at the top oic qsuh8new6+xkq 9evc.:1- r.ur7 dvf a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the r k69zcehgw2/e ounded top of a zwce9k2e g/6hhill (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 /,j3e(zkd fjj*dou7 kneed to make ojfuezkj(k73dj*,/ dfor the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kgui* z0 cic(cw- is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.i0- z uc*c(ciw0 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 particle 9.00 cm from the aot kdphsts089 .3i- (kxg:j(zrpolp :xis of rotation is to experieno: .p(rkh8 gdk03t9xspj tloz -(s:pice an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in kyaj8:kz400d 6 cupo 3rxc)b ea cylindrically walled "room." (3zkb r0y dx :0c p48o)6kajuceSee 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 inizh(jg .xv;dt/a 3 3esd-jrq7 a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as ar/v iq t;z- .(jegj7hdx3ds3shown 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 isx-c2;zk ;pwdgnoring the weight of the ball which revolves on a string 0.600 m longszdpwc- kx;2;. 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)8ihb(oj 8iofq 2 m+rcr ;fp)r6cere( is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massex 8n;+oc3lneuq lr2m3v:d3 vo3/ijiys $ 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 ji0 e2k6u ws0pio,b4m 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 centripyh)(97zzum w uetal components of the net force exerted on the car (by the ground) in Example 5-8 when itzh(9 )w muyzu7s speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500b 965evi7 0iddgjpxu sqx)5t/ accelerates uniformly from 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 accelerat07e6 dbis vg95d/)5jiutp xx qion with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radplrjm fn45 evfv10-g 8ius 2.90 m . At a particular instant, its acceleratf 0jl54erf 1pvn m8g-vion 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 al 5exmm2wo1d5 spacecraft 12,800 km (2 Earth radii)m5oe5wd ml 12x above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, tcwr rpv 1bw-7.he gravitational acceleration g has a magnitudp7-w1 v.b wrrce 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 Moon's radius5 r)uk4k1hh j:ktlgs,:m wc6zyxck;8 is 1.7h w6:hg z5,cyju8k:x41kcm ksk;tlr)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 z0:nm5csb4s.ij c ,(yni.k 4j cgl3ysEarth, but has the same mass. What is the acceleration due to gravik( 5.jlnyg:c43n.y jc4ssii,0bzmcsty near its surface?   

  A hypothetical planet has a masss-()bonhcw.y1v7 zgz6 k .jtvgfec /, 1.66 times that of Earth, but the same radius. What is g neahongzcky.e/6 vtsz()bw1f -,7. vgjcr its surface?   

  Two objects attract each othenh(wv 0 dn82xor gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at93oh) uxc(lc h (a) 3200 mhh(9 x)3uocc l    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fromec ;5(p4:tqipfu 6p+c ,jvesu the Earth’s center to a point outside the Earth where thegravitationq:5(ecu pt i cs;,64uve+fppjal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five t2-e h,pn-zymbimes the mass of our Sun packed into a sphere about 10 km in radius. Es2 b-mep- ynzh,timate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf s .1ng0-:f2v p3zkulz boh3 zb7qk :axdtar, which once was an average star like our Sun but is now in the last stage of its evolution, is nvd1bzzf. : q o: u7k3x3kg-za lpbh20the 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 +lua :h17tsn;ww-9si:swvqr l-g q 6nz7lw0v feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Cosrizlsnh7q 1 sn7--:vv0;:qlw wa+ t lu 9g6wwnvince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners o.*pyd)ol-g;xrd kd. j f a square of side 0.60 m. Calculate the magnitude and direction of the total kgr)o;x-p.d.ly jdd* 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 planet ns5.hj)zmg3vs line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). 5 shmngz v.3j)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 surface of Mars is rap7c.2z9s j e0.38 of what it is on Earth, and that Mars’ radius is 3400ap7szr e29 j.c km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the k-u8e7 5wi-5b -xo 7;bbyaibacdx:p bunown value for the period of the Earth and its distance from the Sun. [Noic58wu: xibda -op-7ubby57 b- b ;axete: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stablp ej fdsms*4,-e circular orbit about the Earthse4 md- fs,p*j at a height of 3600 km.    $\times 10^3$

  The space shuttle relj8*pmy d qu o8r5b0z*beases a satellite into a circular orbit 650 km above the Earth. How *mr u*8 8od y5bzpjb0qfast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spamzg 7fho-4*)ndcpn3 s ceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolutio-sf gzondn p m37c*)4hn. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellidmn.c bo ) cm:v5l2+7bko2 xrmte to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is 2b)+ov cmbck:mx od7 .lnrm 25very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top oh5 5 p -7u 2hr8i:msywnscy+brf Mt. Evere8yu nrwcrhsb7:2 sp-5y+5hi mst to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module conti pk/8a70vsw ip0(0l eom 92ogkc ck:ifnued to orbit the Moon at an altii9 w0s kc7cmkpa(2:if/ e8o0lop vk0g tude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The in4 0zsis89 ;xtwyi dl:uner radius of the ringsid yx8u90;l4 switz:s 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 rotatesfigz:w.-m;wnu9 u h*o+3du rz once every 15.5 s (see Fig. 5–9). What infoz3 r z*dg9 ih;wu+uu-m:w.s the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the ,/8zzobjcp;c center of the Earth's Moon in a spa ;,zc/oj8cbzp ce 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 eys gmnhf.06,s of equal mass. They are observed to be separated by 360 million km and take 5. yh0.,mfe sng67 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 55-kg woman in an elevator tk acy( (kwp .iju+wcy;w1f0/xhat mpjyy.(wc ukfkwi1/w(c 0+x;a 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 it*w7 vn77o s u0q50uqr3kys mceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s miniq*m ssk oitu5 wu7y00n7r73q vmum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a(r9j l 5qbthi(k56 0x oe6jntv planet with period T , the density (maso nt( l56bxi0qjt5(k6rh 9evjs/volume) of the 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 pv x04r i+a+iz7f,lybneriod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s sbna 7yzvxi f40+, lri+urface.    s

  The asteroid Icarus, thoumrx*+tj71je4r p4 hhf gh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean disr4hxfj41pe+rmt* j h 7tance from the Sun?    $\times 10^{11}$

  Neptune is an average dis7r3xzwa4 iq:gtance 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 bt2)r 2 kc/jdr+z 9hjlevery 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 Sy z )b9r2 2jl/hctkd+jrstem? 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 center of the Galaxy /3fmserg4f vdhk9brg oh*6 )v3u(+xz$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 m66f av1 c5eedaass, period, and mean distance for the four largest moons of Jupiter (those discovered vea6fecd 6a15by 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 ouq+,kt5cwc7hw,e0w period and distance of the Moon. ec ou 7,cwtqwk0h5,w+    $\times 10^{24}$

  Determine the mean distance from Jupiter for j8qeb s g fhhl1pw :10k*,5vhq:hjg)eeach of Jupiter’s moons, using Kepler’s third law. Use j8b1f:hhkhqe)l j0hqgpv:e 1sgw,* 5the 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 f8d+asv 1(houmz+f, )bpaw tr2(jknx: ragments (which some space scientists think came from a planet that once orbited the rxt 8p +hav1u nf(wojb,m zd2)ak(+:sSun 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 b7d gww3y92 b gbn/ -u7wfsj:edescribes 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 that3b7:72g udwfwygeb s wn/j9b - the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in j,z,hc1a+:-: xd ddcqe did.t hc. m4xan arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N :c,j4 i.1-mx d,z.ch:etqddchd ad x+ on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whazzv20w k vg1a9gy 53tqng+9yzt z5yv 92g tykgngzvwa93q +z10it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spisx0* z6hicz4h tz;ij ydw 31z6n in a mutual circle once every 2.5 s. If we assumeijt;zi6zz 0 1 dc4hhz*w3x s6y 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 1 5 qb*2h0yfc0qlgd1a qls 3kqhk. pu,m+0pu honce per day, the apparent acceleration of gravity at the equator is slightly less than it woq.bskhh, f+ u*qc30p 2l 15qagqhlpk1umd0 0yuld be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling k obcmw-)h.,rdirectly from the Earth to the Moon experience zero net force because the Earth and Moon pull r-ob w)hk. ,mcwith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stando s:/yvc zlh.fi3r)3f on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction? hcszfil33. :ryv f/) o    ----待选择----upwartddown 

  A projected space stationj r;7qekkiy3 iy m)4tm;)xe/d*4s*b 1 inpewg consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) 7k3/ *brei; w ;n1*isetqxkmpmyyi 4j4) eg)dif an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical l 4vxbzv cbm-p5ay2( e2oop (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 ggmwp;-ik2f8vn37 u b radius r, the acceleration due to gravity at its surface and the gravitatig v8g7fu w- kn;2p3bmional constant G.

A plumb bob (a mass m hanging oi-.0msspda 3.h79g3tr c,ve+hzrd nkn a string) is deflected from the vertical by an angle 9- dz 73mak pvehhcs tgr+0,s..idnr3 $\theta$ 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 de, vox wom7fsh/qxp157sign speed of If the coefficient of static friction is 0.30 (wet pavement), at whs 5f1 7xw7o m/pvoxq,hat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objectsezgg :ixgg* /5ch.j *b at the equ ih.j:z gx*gegg/bc5 *ator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance c0t7n0 h m/rykapart 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 ro9zx1tb1sypkx7gbz1jif 7/x:k q1r,-p h0g o tunds a curve of radius 235 m. A lamp suspended from the ceiling swing th11jz1zk x-oxbxt07i/kpf1s,rb9q : pgg y7 s 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 claimedp*dy: 72hgdy1(xt skp 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 gp(xd y*dh2yt 7:kps 1a 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 Telescoq:u (-34bno9u*p pfvo:yzzz nip0ci9 pe deduced the presence of an 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 the speed of gas clouds orbitingzi::poc 9yupif* u43vpbq (o -znzn90 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 valle5j w0w3be wszj4w: of5y 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 3sbf5jj5zw w0:4w we othe car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) uticrl c()c:d7yulizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 1(lyucc ):d7r c1,000 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.cv,z(3 jos3da 1 billion km, is meant to orbit the asteroid Eros at(av3 3zcs jod, 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 pursu c9+ ,i6xv)fophst(*7 xoyqsning a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the6y7oo xxhn9*f+p,(sqi t c) vs Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 y/*ks gi ylr2w5i5 zjv1ears. (a) What is its mean distance from the Sul*wv2 ry15/k siz 5igjn?   
(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 "feeju:i(zm d4gm ,xz(uk 4l" yourself gravitationally attracted to someone near you. Make reasonable assumption:(4idm4 kxz,umzgu j(s, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the l. nqg* fqw.ia+tuj6v3q:ue+) ptb4 pMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center u.tuvint+3f: bj wq*pg 4a+6q . lpq)e$ \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)0g au87fxla x.50 m on each side. Find the magni)xlua 8x70agf tude and direction of the gravitational 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 orbitv1oa5e 2af2sg-9 mq8* z8vgnt)je vu is 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 hkbzs52u4d.(k9 jsb0a 5dne r of the 1.5-cm-long sweep second hand on your wrist watchb sdzn 4shd9k5ae 5r jub(0k2.?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker w o0omk)bb 64cheight 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 fishinom6ch)o b kb40g line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R qda9vn pq5-4fin a new highway is designed so that a car travelf4 dqqna5-9pving 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, utilizes tilt pk)bxu*wdin wf28f ; vwyufg:w ; :y04of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on t ;pw4g 8y)fwdu :*f2b uvknw0:fwiyx;he passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is 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.$\approx$    $\times 10^2$