Sometimes people say that water is removed from clothes in a spin c*.d0)oo lh n)0y bhusdryer by centrifugal force throwing the water outward. What is wrong with h0o)o0.ncbds * y) uhlthis statement?

Will the acceleration of a car be the same when ; 50y(ykx3zvmu8ns -w-dmj mxthe car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle c3xnsjv(w8 m k0xd z; my5-umy-urve at the same speed? Explain.

Suppose a car moves atj5hptci ds0yk w q8:51 constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a)p 5d:h q05jks1wci 8yt 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 on a merry-go-huhl g +8kdzo 2l,hs97round. Which of td,h k2g9sz h7l8o+ulh hese forces provides the centripetal acceleration of the child?

A bucket of water can be w.gudg0 h67 ggwhirled in a vertical circle without the water spilling out, even at .7hdgwgugg0 6the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Ther:ul s106 mo2yoegt3mq e are at least three controls in the car which can bogl 2qeou3ym 61tm :0se 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 sheb+b5 yjd-(9j-n j3 rhany8u xown 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 dee59y-xrndu(a3 yhnb- 8j + jbjcrease using Newton’s second law.

Why do bicycle riders lean inward when roundcezs f8ux/ iagq8-0hdo .7 lb7ing a curve at high speed?

Why do airplanes bank when t45 r wej0e87jccgcn-jhey turn? How would you compute the banking angle given its speed and radius of the ture8j-j cg0rej57 4nc cwn?

A girl is whirling a ball on a string around her head in a h8p aekkiq d;l*pf3n4 rf)zx7 0orizontal plane. She wants to let go at precisely the right time so that the bal*3)id8n p;k4lf07zfx qeka prl 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 o-e wgf c 5l*l(dqwmkv4hx3i(2 n the Earth? If so, how large a force? Consider3h-i(lvlm4f *wqd xew 5c( gk2 an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what illw-7yor4om o ((un rm+6u 3tjt is, in what ways would the Moon’s orbit byumor3 6 uw-t4(rojo ( 7n+llme different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E04 (xeh0psf qx 0ma(orarth? Which accelerates mormo0 h(xasp0( 4exfq0re?

The Sun's gravitational p6w.uol/ dqaj *5zw ry6ull on 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 Ela j65r y*/w qduzo.w6arth to the other.]

Will an object weigh more at the equator or at the poles? What two f;mdhrla(w ,2ei6 .wm 5c-pugeffects are at work? Di h;,gefmu5 c6wral( 2d-pwm. o they oppose each other?

The gravitational force on thega 44.t pvecn+ Moon due to the Earth is only about half the force on the Moon due t4atgep.ncv +4o the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around t k8:*/mz- ma (zsnkshfhe Sun larger or smaller than the centripetal acceleration of the Earnfa(mkszz/8 m:h *ks-th?

Would it require lessz*)7 * mg1slqudzcwj- speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direcg -wd1zm*7s*u lcj z)qtion.

When will your apparent weight be the greatest, as measured by a scl98q1jgjw ,:wvjc sfl ib/24jale 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 whic:bg1 swq8fj9 l/vlc, wi24jjjh 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 couldp* em1p9 x4. izyc*h( yboxt)c 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. Consib (p 4cym.oxzpyh*9)ci tx e1*der (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 experi/23tu*hrtat(dp )v rpences “free fall” or “apparent weightlessness” between ster)tu 3apdt( tv* /2phrps.

The Earth moves faster in its o0ebu eb5k9b:a rbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Notekb09:5b e ueba: 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 was discovered to have a moon. Explainho)an7sf.ac5 p/vnlr, p a/z : m)-fyf how this ) my :lfa7.fvch) -nns/ rozpp,f a5a/discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth ilmezl-7qmn h)ykro5.3r ; (fzs 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-round moves with a s-myrm)7. nlhlqz3e ok5r;zf(peed 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 198hropo02n5 rkm r5ys(1 0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Egz+4g6cn*s jbarth 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 radng4 cszj6g*b+ius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unifo -+wn 2a7- jl7piynvlqrmly in a horizontal circle (at arm’s length) of radius 0.90 m. C wv7 pa7ljy +--ni2qnlalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from t z97uzm g.wjn0he 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 answer in terms of g , the gravitational acceleration at the Earth's surfacegzu0z nm9.7jw . $\approx$    g

  What is the magnitude of the acceleration of a spe7 m;k9fcy 0feq5lv, ipck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per milmc0 if7e y;,fpvk95 qnute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vehdshl kn*j td48+va-8rtical circle of radi 8a*d+-jns8hlvt4 hkdus 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turnpvyoo1 2i(30 n8 wy 9fe5wterm of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepo 2iypmef8oyr(w5n0w3 et1 9v endent of the mass of the car?   

  How large must the coxh k +x li4g+.ifa9f9oefficient 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 sif4 xlghafx9oik+9 +. peed of 95km/h ?   

  A device for training astronauts andso + ./x c)rtj,dji,ut jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainej t od/,)s+.r cjix,ute 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 turn/hoqm (, 9bg fhxgh*)ltable of variable speed. /hgoh 9xhm (bql* f)g,When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling whei,n*w 6:hz(r8p/btjcngb 4 ukn upside down at the top of a cir/u6 4b tb: nk8z wnc*r(jghip,cle
(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 (includi/nv-f/bwsvst hw 95etknv.f; zr, y;*ng the driver) crosses the rounded top of a hill (radius =95.9b fnsefwnzv; hk5 yvvt;s -,rw t//*$ \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 g3g8 mq+,n6l 9ksqyu eneed to make for the passengers to feel “wek+mu98sge3ny6 gq,q l ightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is d xk5, edgm3+;;eyj ntoc8cz046 nuqdwhirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportingdk ,txdcdye8e z q;5g4m6o0j 3u+;nnc 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 par5hk*mven* w( /v4hp azticle 9.00 cm from the axis of rotation is to experience an acceler/pa4enw *kv*vhzh 5(mation of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "r rw)yk:+q)yu qjj5z zb7o+n8 wl7md4poom." jo y75kpmb:+duqzwn7+ )w8rj4y q z)l(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 rotatelgxb1 7jdo c p4xfg i0)dc3i09d in a circle on a frictionless air-hockey tabletop, and iol)dibc0ig j37p xfg9dx10c4s held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by fac.ys-jmc.(1 x 14 vyord-nuaqv34 nnot ignoring the weight of the ball which reynf1dy.o3q c4c xvsju( ma v41- nar-.volves 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 travelingllg+x io9w,5 :yeum i707k)1uijtekh 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 masses vuvu :po(73tk n/j7jbfcps27 b :o-ck$ 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 q2cps17f)wem qt3o7c 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force io9.*lnpolwae ;(dg/exerted on the ca.l9 pgoi ne(/owla* ;dr (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 accek5v;wol ff7tpd,p7 qna8x)o +lerates uniformly from the pit area, going from rest to 320km/h in a se+ta) p7qfnp8fo 7 v ,dw;5koxlmicircular 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 or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particuqc3s-)bwfxvj2ni pv9m((szs 0v 4:*i* xke dl lar instant, its acceleration is 1q()le92 ix-p(jb 3*nsfm ivcvw* ksz0v xd:4s.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 k* rcc5v z/7tdkm (2 Earth radii) above the Ea7kvz c/ tc*rd5rth’s surface if its mass is 1350 kg.   

  At the surface of a certaiw - .l-g1n8ct g*cl6we ozasj.n planet, the gravitational acceleration g has a magnitude of 12- lgecnwsz.* lw-8gac6 .1t jo 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 thzy8b/y 8lkwkc2l+ .ghe Moon. The Moon's radius is 1.74 8ykg lkc w+b/y.82lzh $\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 Eart-j(tn;;tqfj 2yv;q wbh, but has the same mass. What is the acceleration dvwj(bjq; qty;2n;ft-ue to gravity near its surface?   

  A hypothetical planet has a massadcsg+voj n 10q +8y..ul(fetihh ./w 1.66 times that of Earth, but the same radius. What is g near ind(. +uj gi+8sa/eof. v0tqly1 h. hwcts surface?   

  Two objects attract each other grav4 /vo dcr3gktf)3h jv:itationally 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,r9 y2u 2knqytky0t)q, at (a) 3200 m qkr uy , 29yn0tk2tqy)   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the so+3j 8qezzc*Earth where thegravitational acceleratze3ocz+ sj*8qion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed iqtb ffs 8r*aw jm3*)gr:36buq nto a sphere about 10 km in radius. Estimate the surface gravity om8a3t :qw uqrb6 g* frf)b3s*jn this monster.    $\times10^12$

  A typical white-dwarf star, which oncqe.1+ -2b4c5c7xuu gn mno npee 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 su1+x nucgp e42oqebc.- n7 un5mrface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless wipm96qjz-uql s yh/3 0hile orbiting in the space shuttle. Your friends respond that they thought gl96 imj us/ qy0qz3-hpravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of si- xsom(l f.jy6de 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere- mjo6sfx.ly ( by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line 6lx rv 5b2dig37 5yxoava)4a aup 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). The mas xxvadagor4va)7ayil2 56 53bses 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 ggk 8l9sic1:rct 6-e awravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass61e:g 8 sli-9k ctacwr of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the psjua 21m(o0egcn mm1kj6o0/reriod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtainm m10 kg0(jm1 cao6nu/ jrse2oed using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable c1ax ,fz :y+*l3blxdys 8f4sbjircular orbit about the Earth at a heighba1, zxjsfdlb +fs3 4xy: l8y*t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite ihrkz.- 4p /pmsk qu9(*pxec8 unto a circular orbit 650 km above the Earth. How fast mu eu*pp4kqpm89 .h/zsuk(cxr- st the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occu h;9enjdi3y d p/h0pu4pants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, a3 ypun4/p 0 dj;ehih9dnd 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 oda3,dwx v2qv. a/mi83aw k;ksrbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the ,svx .d3a2qia;d/ 8k v3mk wwaEarth 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 veloc1xddjx 4(eh h loap;z;)wr(e5ity would a satellite have to be launched from the top of Mt. Everest to be placed in a circuh(4( 5odh;p1 xjewz la); rxdelar orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to o+ oqjnywjrzsex;8 /1dk 1f0 n,k *1bpqrbit the Moon at an altitude of about 10e8qfdj b s nj; k*1xrz1+nqokp/1w0y, 0 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed .bav *0p ms;nos3 /xsmo/av7 w2h iv/zof chunks of ice that orbit the planet. The inner radius of the rings is 73,073v xm*oa;bv /sv 0wpni2/ao s/.zmsh 00 $\mathrm{~km}$ , 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 onmhbabf 2bwa m9)vfil.87 9 sx)ce every 15.5 s (see Fig. 5–9). What9wm 9)b72fishxlb bf.m8v)a a is 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 astro yb6u9 kxvqu*2p +gibpoia3 :,naut 4200 km from the center of the Eayibk o2v,*g+bp iuxq: a9p 63urth's 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 c)fp u ,33f/zgbru,qpstars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth ye,bpc3),u zf g 3rpfuq/ars 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)m9cx on14 y+eos.uej weight of a 55-kg woman in an elevator that movesou) xs4.ey +oc9mjn 1e
(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 cdt86a 0p h 5iu9duaj,weiling of an elevator. The cord cana8wdputui06 jh 9,a5 d withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a plane odcu fnp7a 5gxx-/uh+oll852t with period T , the density (d l 2phx+5x/lafoocg8 u7n-5umass/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 p:o7i o glr,kpg;wd ;p)qxk0-period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’) 7k;,-ogqkp;i :d og l0rxppws surface.    s

  The asteroid Icarus, though only a few hundreca)5obv za/ p9p )h55ma-yrkod meters across, orbits the Sun like the planets. Its period is 410 d. What is its 5a) /ko om9b 5 zaapp5yrcv)h-mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average div-n585qedgep7 q sm- q,8pn fsstance 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. 1aip,8 jkslczfyc. *:It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate thsp8*lcz yk1:c. i,jafe 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 center of the Galaxy/1 :8 pt) t8 ynoi2h;swt/ jydhl4z ixx*ckaf: $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 meaniw.j.im 3m 9xtq6( jfi distance for the four largest moons of Jupiter (those discovered by Galileo in 160 fjm.tjmq6i (xi3i.9w 9).
(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 kno8glak4z je:+ +wlhqo+ wn period and distance of the Moon. oelgq++84 l +k jazw:h   $\times 10^{24}$

  Determine the mean distance from Jupiter i0fbb2mf;1uzm ny3) s for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given bf i0 ) f23m1zyb;usmnin 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 cw-/huw.nm4i j zuj. 3rt*d rj4onsists of many fragments (which some space scientists think came from a planet that on4rhz/udt nu*.mjwj 3- wj4.irce 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 "planez m2ix( u, :,ap vyzapqib1s+-t" 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 period of revolution, this planet's yp (uv aa1-xpbzy,2i qm:iz s,+ear, in Earth days?   

  Tarzan plans to cross a )x1ndqry) mlcigkd;s9e:-8 s*z*hpkgorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? g)n yksr 1zek *dqs;- mxd 9lp8c):ih*His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravityq1l.j d5(znt m be half what it is on tht5q1mzjl.dn( e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hgq gi0ink+el*6: tlfk)n,mt i eh3f9-ands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and theie60n g9f3k ,t+m)*klqfl ge niihi:-tr individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once ea3e0zj5 b f*0-a,mj *-mrxovc9 yua+trm6lr per day, the apparent acceleration of gravity at the equator is slightly less than it wou*xf9-r*j,aaa0l3c6tjr ey m e50zv+ m murb-old 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.a-i 6ywwjit/h 7ds7vuc2j06hu 6xs x ioi/7k will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppositsykxuhox60i/ / wv .2hit cs-67iiw6jad u7j7 e forces?    $\times 10^8$

  You know your mass is 65 kg, b)n7gh a3q gda50dnzo*ut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, ad3gd*h0oqn)z7 gan a5nd in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cswxm oc*0gvz;,(y ,h0xe fry 6ircular tube that will rotate about its center (l;y , cv,mwz0r(xef*oy sgxh06ike 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 in2r0w jz(qq er *;q7xrswfud53 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 mass7 m9h9serdqmc x4:we- of a planet in terms of its radius r, the acceleration due to gravity: 7 mxe99sdwqem-hcr4 at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the v4 kejvj7d-5 +p.zce yiklp2) eertical by an a kvl.z+k jc-ey54j2e)ed pp 7ingle $\theta$ 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 desigl vh *6d*a/ ne64:hlf)o askucn speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely hanh:*akvh6e*ll nsoa6 d4f / cu)dle the curve?

  How long would a day be if the Earth were rotating s(ydylz *cuir imjdwz2/xos;q-;w:6 um 6 j8/n o fast that objects at the equator were apparently ry i/*cmx q6i uyl2 sw6u-z/j ;:mzo8;wndd( jweightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di )vysm1q7r e9gs 7ib)astance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m.u-j+g f)7 l(j dgg)tax A lamp suspended from the ceiling swings out to an adg-)g j)u x+(fj ag7tlngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as te v9lv9svyo92 he Earth. 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 more than a few g 's. Calculate the number of g 's a person would experience at the equator of such v2 999ev syvloa 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 pnhelef1 f *v -w2q2ol bt;n:7qresence of an extremely massive core in the disqlvt : fno-n1w 2*l2 ;qeh7febtant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constzhjs++1r r 1 ;ehfs7baant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go wit fhs;j7rz rh11s+ae +bhout losing contact with the road at A?

  The Navstar Global Positioning Systemi)olvs2 n wf3v sa41.g (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth .nss w2 vv)1lg 3ioa4fcan 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 billion km, isoe1.cl 14tbdgo 0xz +i meant to orbit the asteroid Eros at a height of about 15 k bxoego4+ci1.d ztl 10m . 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 ** pk abwwgd w-*zq.k2r+v+*fnmq 3 qusatellite in need of repair. Yo**kfz*kub q 3 aqwrnqwm.v2pw +*+d -gu are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distanz7 io,z66(ugxor-k lkce from the krl zz76 kx(o ,6i-ugoSun?   
(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 "feel" tzy. d0s(xxst):cc -qxi( gr xf:;y+oyourself gravgicxx.sdcz0yf - +(s(::xr q ;t)otyxitationally 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. 5-46) at a distsipl*c82:wvs8 begs( ance of about 30,scs(lwv s8b*28i:ge p 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 cornu 6 744dsgdoxtl-pch 2ers of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a f g6 d4 odx-72slhuc4ptifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eadf1sdqj7(*j 0hlf(ktl a zz31rth $ \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 s5q* ,d .zjrscg,ot 7pof the 1.5-cm-long sweep second hand on your wris zd*5r7t cs ogj,.qps,t watch?    $\times 10^{-4}$

  While fishing, you get b pb 4q2wz f b/r:vy0b8exh4)diored 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 circr :w 8/bh2xfy )z4bib0e4vdp qle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travel3 laok a4(;kzsing at spe3 alo kz;ksa(4ed $ 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 of the c( (:x.hmx3e;vrtccjpw5gt 9vars 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 f(.g(5h j3: ;rpce9txtv mwvxc eeling 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.$\approx$    $\times 10^2$