Sometimes people say that water is removed from clothes in a spin dryer by cerf 2 q,j zu5(9j/s4tr8msujmbntrifugal force throwing the water outward. What is wrong withj j tu /sr8j(u9mb5m2z,sfq4r this statement?

Will the acceleration of a car be the same when the car travels around a l;;unt/ rx:o psharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sppn ;;x lo:u/rteed? Explain.

Suppose a car moves at constant speed along a hie to-;3h6u qsvlly road. Where does the car exert the greatest and least fos3h-6v;qtoeu rces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child rut6hd/ /htednr2z o 6dk9o0y8 iding a horse on a merry-go-round. Which ort 8tu 6h/oe60 nod/khz2yd9d f these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled dc.; 30q7vsua xv5cluin a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. x 5dv7 quvcula3s.0c;Explain.

How many “accelerators” do you have in your car? There nzh2ldeim+ dh l/3 h(,r*wk)k are at least three controls in the car which can be used to cause the car to accelerate. What are they? Whak * wemlk2r+hddz in/,h lh3)(t accelerations do they produce?

A child on a sled comes fly4x4n pc*h:7:n9bz p7ygj p2ovmnw9z hing 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 ox4n:pv*74 zhnp hn7c w99ygbp2j z:mthe sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lea5 ok/u se)qvjy 64oh:dca99izn inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankfas *+abs/ fih l8ikx ,soblo. 84s0.ting angle given itsih b*xl.sb4,+fs o k/0t8sis8aafol. speed and radius of the turn?

A girl is whirling a ball oqj9+ p3hna:u jn 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 sid:aqunj9p j+ h3e of the yard. When should she let go of the string?

Does an apple exert a gravitatiolg3zmb- 8caf2vf1 7qanal force on the Earth? If so, how large a force? Cons8lf2 fqz3 cvmgb-7 1aaider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dor-xr jvm ni,9j)( p1wv4ygn6fuble what it is, in what ways would the Moon’s orbit be diffev(r6g 4p1 f-vix y)rw,j9 nmjnrent?

Which pulls harder gravitationally, the Earth on the Moon, or th+5jmi3igh,id y-cx u 2e Moon on the Earth? Which ayi -cidj+iu3, h5 gxm2ccelerates more?

The Sun's gravitational pull ony6enr.8 sx/oyw*xmy/7 tc ir : 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 fromx w6ys miy 8t:. n/o*r/er7cyx one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What twwhw c(1: 1oh;x*rwsbe ;jto-po effects are at work? Do they oppose each ot 1rto j h;(x-eb1wwso:c;*w phher?

The gravitational force on the Moon due to the Earth is ohf1 o 2 7r3 vy)rd.wy)yd(jwuvnly about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away rdy 7v ohw3f1u.ry2d(vj yw ))from the Earth?

Is the centripetal acceleration of M h-mjo7a9pm8.h1 2w :nhkyigh ars in its orbit around the Sun larger or smaller than the centripetal acceleration op 7o 2 mn9a:.1yhwk -h8jhmhigf the Earth?

Would it require less speed to launch a satellitebv3w p1a sb0apablh/6h qs2)0 (a) toward the east or (b) toward thlshhsa36b)qw2a / pa0bbpv1 0 e west? Consider the Earth’s rotation direction.

When will your apparent weight bezz etfc6c,h:p5zjn4 z yov:,7 the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be thejco4: ynz6zc:z ,z,fpve t5h7 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 affected asyc;z9 gn ez)5-s6 rfby weightlessness. One way to simulate gravity is to shape the spa6-;zrsn) cya 5ezs9 gfceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “app ksqe7 kk*k58m-n0nqvarent weightlessness” between stqk-v mennq0*7s5k kk8eps.

The Earth moves faster in its orbit around the Sun in Januptv 0/ 127v*litivbfyary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in prot/pf1 bit2vvi*lv7 0yducing 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 mooi3nwdvgq7 5d7n. Explain how thiw5i 3dqg7 7nvds discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tgd;-g4/xdpt5 eqx /iu he Moon's is mainly responsible for the tides. Expla/g-/4ieddguq tp5; xxin. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelinta0pq9 +ram*d g 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 inmajyu 0-9 (1yfmo 7eoo its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on toyaum-ymjoo19 e7(0f he 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 l vr.v,4/ d: rh8fjsrla 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculasr.8r/d lf4:v hvj r,lte the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's gt q0y thgh8ay ew3auny2 +4*4surface, 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 yatgahg4n43h e w2 0y8*yu+q t, the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the ,qjzjn )v k964a2yuudacceleration of a speck of clay on the edge of a potter’sq 94d ,)nuav kyj26jzu wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical w3 mw 59u8l-g3i49xqdqunre scircle of radius 72.0 cm , as shown in Fig. 5-33. uiedn54w3q q -gmsru9 x893lw 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/d0tsb/d f,pydkuhi 26 pn )6t a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of thy /d2/s6p0d bfdui6 k)nttp,he car?   

  How large must the coefficient of static frictir*xkv;rm6cmxk9vz6/ o6b 4(fq a ob/ton be between the tires and the road if a car is to round a level curve oofr a6vmz ;rxo* bvm6(9b 6/qxtk/ k4cf radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilotlx3c0y.g 7 6c-dn ;tsrfkj8ris is designed to rotate a trainee in a horizontal circle of radius 12.0 m . gnr jcd;t76y-.c f s8xilk 0r3If 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 osws cw8/6xz:qs c -hq7sahr;+0f1fto f a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate o ot :s1hwsr8/7;0zasc wcq+ qxfsfh -6f 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 wheqn sh0-qj6 nf +.) ac3r wbbjzlp-6edrro/e)6n upside down at the top)q0 n- c6peas on 6)rf-h/djrr bqz6w.l b3+ej of 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 js-cg c +fmqy+xh2k6: dr(aq( the rounded top of a hill (radiusmc ++( q d j-(6cqaxg:h2ksryf =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)nrb4xux cg8zi 6* .oi Ferris wheel need to make for the passengers to feel “weightless” ac i) 4 gbirz.xuxn68o*t the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ve rodh.7o1 mlhd 0p0wi.rtical circle of radius 1.10 m. At the lowest podimw0oh.o1 l7rdh .p 0int of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifugr bx4acuy8-whfsy 747e rotate if a particle 9.00 cm from the axis of rotation is 47 8afyw 7xc4usyrh b-to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricalp6 o-zt 8cxd *l j.oy(aw,x1cmly walled "room." (See Figmzpcwcl t - xy68*(.o,1dx oaj. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionle *- gz/s*qq4sl beqt5sss air-hockey tabletop, and is held in ttqs e q-zs/sl q45b**ghis 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 not ignoring the weight ofz qecj;b: ;cpw9 hb3/j the ball which revolves on a string 0.600 m lo:cbwb;3q j;zhe9jp /cng. 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 radi5nd-d6f*k b1+a kkg hjus of 88 m 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 masses 6 vjp4 0ywoj1a$ 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 3 suh p:qf4p,x ew1;u *q9f6ait10 $\mathrm{~m} / \mathrm{s}$ . 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 nejw 6x5;g5hfzs lse08q t force exerted on the car (by f6 s8ezw;55sjl 0gqhx 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 50m,(rzh +u uc/i0 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 weumrchz+ /i,u(re 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 horizv y9325azam m0 qo)imqontal circle of radius 2.90 m . At a particular inst205mq9viq 3z ymamoa)ant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km ( i0 aqac. axil23hw6f02 Earth radii) above the Earth’s surface if its maaih2x0 0 6.ql3 ifwacass is 1350 kg.   

  At the surface of a certain planet, the gravitaticexa2e u t6 d89*+ua1hlb; vxaonal acceleration g has a magnitud12ebcu98* ;6uax+dealh xa tve 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 radius i1d+rld,n*g2p 57t9zx)zs yqosimy- fs 1.74 ld5t+g,ns)x i1 ry7s*o-qyzm 2zpf9 d$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but 8+0l alkfy7nf has the same mass. What is the acceleration due to gravity ka ln08 yf7f+lnear its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same 0zu8 xkkkmtx:-s- c zvjz;+q)zs,: zgradius. What is ,cvkx;q-zzjzx-gm:szzt 0 : k)k 8+usg near its surface?   

  Two objects attract each other gravitationally wit-ct.9fbkc mn m +hp4 1ebma/2yh 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 am:: 8fs dmau3lcceleration of gravity, at (a) 3200 m fs:lmud :a8 3m   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the x y)2zera; t2hwlof2k+ 2y ht*Earth where thegravitational acceleration due to th2t2kyo2yaze *w +f;htx )l2rh e Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of 3/tw;hay wqw3v .u1cuour Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster.yw wv3acu.3 h;1w qu/t    $\times10^12$

  A typical white-dwarf star, which once was anc hnw))g5d 4xa5ya z*h 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 su) cy *dnaha)55whgz4xrface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in 8arn afkm((59d4(: aju nhaz*cou8ynthe space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of dcuar((a9k: 8*8n mnn4aj(h fa 5yo uzg.   

  Four 9.5-kg spheres are located at the corners of a squacs we;*d l,gkfix- z++re of side 0.60 m. Calculate t-ic;gx w, e+z*l+fdks he magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the wpudq 3*uema )2*nt fs;xz6bxi94zd9planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming2)d 3*qpt x mdx 6 4;bzau9wfiesn9zu* all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface m0segh f- in949xgf x1of Mars is 0.38 of what it is on Earth, and that Marm19 n-h9x0gg xfefs4i s’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periszhidmf (o0q5n/ v;1c 6htt 1vod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kevt/cvi5nt zms6;h1q1 0 fho d(pler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular oroq xyqa/ 0zp+vxi2: 5wbit about the Earth at a height of 360wq ap5xo i0:v2/q yxz+0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abx;.axqfk5tg56.c2gv(zv hj-ax2nobove the Earth. How fast must the shuttle be moving (rela 6c52q5gvxzgxhx;. 2aft.v okj-nb(ative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spacez *qmhjzmrn5( 31jspv0m ,: pkship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 mz5n:1pj jvkmh(3sr0z p*m q, m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular c;z6xy :rt t:b“near-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 ;:zbrt: tcy6x your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from thz (ndz1+)3zq-tjede dy q4yq1e top of Mt. Everest to be placed in a circular orb1 1qzeyjdd()4zet+nyqqz3d-it around the Earth?   

  During an Apollo lunar landing mission, the command mo jo d dq/5wri3r5sz;2mshj;gt:q,d9 adule continued to orbit the Moon at an altitude of about 100 km. How long did it take to g2 35i;djdw ,mo zqs/ar ;jdq:r9sgt h5o around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit t)+ti zhp/ma0e.(b5enkz yo ,xhe planet. The inner radius of the rings i .0nmitbpx(,h+y5)zeoz/aek s 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 every 15.5 s (see Fi;pgx5*gl1tn w g. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, alg5w* 1g ;pxtnnd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 420yyv- o8nh8sgwj/ lc.30 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocitys-ly8vygj 3hnw o/c8.,     ----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 consistjr /b1u 2ojcmp4m b8a3s of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orb m3u4aomrbc21/pj8jbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weig*p x/ttirr1g0 ht of a 55-kg woman in an elevator that moves i*ttxgp1r/0r
(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 of an e -jz n:l.yx:db(/se nnlevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitud ne:-/ y:nbln sjxz(d.e and direction)? a =   

Show that if a satellite orbits very near the surfa2am2ty3b hwl -ce of a planet with period T , the y23 awmlbt h-2density (mass/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 period ofuy+fj1 7dym2w msh2g 6 the Moon (27.4 d) to determine the period of an artificy 612w 2d7jmuy+m hsgfial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundredb9 ug9 dgo6rv* meters across, orbits the Sun like the planets. Its period is 410 d. Whatvb6u*g odgr99 is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc;jg/ q3 .mipf/ syi;exe 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 everyupxvj 02q: rg; 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distpjg 20;vr:qxuance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga kp/p3ac5,j eflaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons k5v.-t:oridpz u;(59diqca r of Jupiter (those da: o9d 5uc;r itq vdzk-i5p(.riscovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Ea ;pp1-ef2f)erayr wc1/ asrz*rth from the known period and distance of the Moon. 1 sf )re*wzap-rec1pa2y ;f/r   $\times 10^{24}$

  Determine the mean distance fr pfbrqjx,1 *u-bfk/m1om Jupiter for each of Jupiter’s moons, using Kepler’s third law1 mur-1,fkfb/pqj xb*. Use 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 fragm1av n8yq1wr,w*qvs(:f n y gp7ents (which some space scientists think came from a planet that once og(f1vqp78qnw v ,w1r n ay:sy*rbited 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 e;j b3u;1 apji"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 ja ;jb1ui e;3pto 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 swinging in an arc from a hanging vine (F0talc 3n d+y3 0rp2woiig. 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 atw y0r cda0o23tipn 3l+ 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 whatahtz5 *6yz)i(q(r xo t it is on the surface* z(x r56(oiha)tzyq t?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands anddm ;.6ig:4qf v9 efnyt ;kg-gg spin in a mutual circle oq9ggfygmetf i-n4d.: ;g6;vk nce every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravicw j 4ax3( (cc11vkp*mhky+ udty at the equator is slightly less thapjc4 *x3dvk(huk+ 1( mcw 1cyan it would 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 directlymidf6-u31xp b from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite force-dfb 3im1ux 6ps?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in,s myovb998 m e5booh kma/.qb.z4b-e an elevator, b9 o 5 -sab.qo,v.m9bykbe4omhm/8e zit says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station cqc dpy5wiv; 9m,h yf:;onsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed :w 5i;;yq, 9mdhfyv cpby 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;g3 k/ xde9vp(/sujvn vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet wgw23sxj /d v7 6o/ya fsp2amjrc+24t in terms of its radius r, the acceleration due to gravi4 mo76y 2sftwr2wjjd2p gs3+/vc /aaxty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertv ;h6lw a. *1njbb-wvjical by an bvl1j ;nh-jw6w*.a bvangle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If w*ldt7 +job0q lggop6k6m;g 64tb7 mithe coefficient of static friction is 0.30 (wet pavement), at what r7gm w6blkg4*o0;jb6 dm6go ttqlip +7ange of speeds can a car safely handle the curve?

  How long would a day be if the *xqo:m5l le bn(g/rf,Earth were rotating so fast that objects at the equator were apparently weightlessox*me lbr, q/f5g(:nl?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ofjuj)g2hw:kna 1nip5 ) 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 constaauuj:o ydc65xa ewp o5aw z5g1xl6/78nt speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swuua58jzw:x5paw oda1oe c5l/6y6g x 7 ings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massi 0q2sox2z)l8ar h4ktpu3. mp fve as the Earth. Thus, it has been claimed that a person would be crushed by the forcea p mxk2ruftpz2 sl8 q0).h34o of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a 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 Telescxr *do:2:cnnw6fw* i/cmoja*ope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from f:w: r**2w6caic*mdox / nojnwhich no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traversesv/ axb2m6z7lizo l8( x the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How x76ob xl8zvmzi/(a 2ldo 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 road at A?

  The Navstar Global Positioning Syste7isj)gxlvep 60qo8 q7f i b2s-m (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulati2ox lgib 7v6 j0pqssq)e78f-ion” 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 billte -;bv j3z2idion km, is meant tovjt3 ezid-b2; orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite r(a 7bhis1us1in need of repair. You are in a circular orbit of the same radius as the satellitesuib(a1 rsh71 (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. (; klpq i9 i-lyg/avv;5a) What is its mean distance from thqy-;aipgkil;lv9 5 v/e Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could a /+:,yed;c ynh6m 0m bs(*bcoabt2l ;j5u busictually "feel" yourself gravitationally attracted to s5b*mmbnicyy; 0us;2bc :e+sjd /lht6ao (bu , omeone 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 distghn+ +ylda 2w+4m;nvt ance of about 30,000 light-years from the centemv + nh;t+2ldya4wgn+r $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on4 q5fuu3zx 9tr each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom si 9u4rxtz53 uqfde of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth lq 11xtx9 ih0v1v+ xmx(a3xbd $ \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 ofy iam3e hi 9p(qz-(3df the 1.5-cm-long sweep second ha9pm fd (hq3 3-(izeiyand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroul* i;be5sg yv1nd in a circle below you on a 5vg1lb*ie ys; 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thatzrfcz93(f. qy7c7 njj a car traveling j77czr.y cq(fn 9f zj3at 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 of the cars when negotiatinnp, wk8.,d c3l 4.6azvp*c wb2mzfbapg curves. The angle of tilt is adjusted so that the main force pk ,bw lc6,*bwz8fpz.4n.3 amdav2pc 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 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.$\approx$    $\times 10^2$