Sometimes people say that wxr+eoa6+ 4qfd.(xtjeb h.v 8 zater is removed from clothes in a spin dryer by centrifugal fo+eqvobr e a.h.8x+f( jzxd4 6trce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when t 6h58dll9m ;bhgxclogdxmc:f *;j/) qhe car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the jh85xhm ogc*b;d69;l)fmc gq:x /dll same speed? Explain.

Suppose a car moves aj.tjtfpvx h/1l/0h q)t constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hijv/xhfjlt tp)/q. 10 hll?

Describe all the forces acting on a ck)s ddxt;1lo; hild riding a horse on a merry-go-round. Which of these t; dd)oxls;1kforces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wa fiygd d39o*hyw9./zster spilling out, zdf9sygod.3/iy* h 9w even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in ynrjn- j- yvbs /5+n 7yb)w4)dce9gkh mour car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they )y7) srgcn b-k4-m bnn jve/ h9j5+dwyproduce?

A child on a sled comes flying over the crest of a small tzt zlif./p57 hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he z/ 5 tlifz.pt7feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lea//w+ )v n ,v,tnlz6fev 7llhsjn inward when rounding a curve at high speed?

Why do airplanes bank w zp; 4mzrpdhdn ro(a:0.r8e5xhen they turn? How would you compute the banking angle given its speed and radius of the a mp05.d zn hp8:4edrozr;rx(turn?

A girl is whirling a ball on a string around her head in a horizontal ) dnbp7l( )hqeplane. 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 the string?l)qp(b e7d)h n

Does an apple exert a gravitational:vbzg;m 1/laq7w -qo7r; gryx force on the Earth? If so, how large a force? Cogqobawg 77 r-l 1vq:ym/xz;;rnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wer p 9tzqkras+-x9t2 /ga f(bq-be double what it is, in what ways would the Moon’s orbit be diffep s2+t(axfq9 -/gqb-rz a ktb9rent?

Which pulls harder gravitationally, the Earth on the Moo.a -d2hge6nc9:a zivi n, or the Moon on the Earth? Which accelerates .e-zd9 a:2 iah ncvi6gmore?

The Sun's gravitational pull on the Earth totge. 7y b)rf0 80tvgis much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint:et80 y7rot t bvf).gg0 Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equato whzc*twoi /-ehj8v jky:*9he7b 8 ,wcr or at the poles? What two effects are at work? Do they oj*hwh9 w oke8 :hw-7y8ijcc b/tvze ,*ppose each other?

The gravitational force on the Moon due to thjnv8 )oo4f;ehe Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from efv4nj; o)oh 8the Earth?

Is the centripetal acceleration of Mars in its orb.c+sinq +e(b j)nuzoomw37 brg1p7u:it around the Sun larger or smaller than t7:nqunw mc b3ip.or )+1 jbeuo+(sgz7he centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) 1izv o9rngk/9toward the east or (b) toward the west? Consider the Earth’s rotation direction. /i91krgvzn9 o

When will your apparent weight be the yz53msg6o4 bp q+yh ,lgreatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward4l3m6 o5pq+y bhs ,zyg, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outexl so.(pp7-t p,jx qoae3ze*,r space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how thi3-xeao ,7,ptzeqj xp*p.sl o(s 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 “ap2je+sm7 *lj )ofzg4zvq d+z* l2w.bauparent weightlessness” betweenz.wa f2jd*+q2zsgm l) ozbj4*eu+vl7 steps.

The Earth moves faster in its orbit around the Sun in January than in6 ctd *x- fnvaf39 pt+nqqk .::n5zptx July. Is the Earth closer to the Sun in January, or-t x dqv+3n9n.a5q:tckf 6pn:p tx*fz in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovegx v6tw:y q4 22c0cmgered to have a moon. Explain how this digw:4tycm26qe g2v0 c xscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tvnj a )0: ,egbr3jm(vjhe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in grava(j:gb vj ) ejnmr3v,0itational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980proy2mh 2we-4 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eao8e6 up.qgc+l/i x u9wrth in its orbit around the Sun, and the 8c96ex golu.+ /p uiqwnet force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force o4pql5yi3 h9cqf 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90yqcip h5lq39 4 m. Calculate the speed of the discus.   

  Suppose the space shuttle is i*/wcrl 2 yh,min orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the 2 m* /ihr,clwyspace 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 acceler. 82v9goykwsjfb 4)b xation of a speck of clay on the edge of a potter’s wheel turning at 45 rpm .s)w f94xgo8vbby2 kj (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 4mr -r )gqfu4utv/zy90g0 w-k/t dnu hcircle of radius 72.0 cm , as shown in Fig.44 rqu mvg y-k f/d0tnthzwug90r-u) / 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-c*k()m03xits7vk9n kkuik4 ekg car can round 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 mai)7cvm*0kk 394u k kni( xetksss of the car?   

  How large must the coefficient of static friction be between the tires a;3 .i5vds whaja(dbw)nd the road if a car is to round a level curve of radius 85 m at a speed of 95km/w;. as)w i(d53adjvhbh ?   

  A device for training astronauts and jet fighteg gt)u3v :1fepr pilots is designed to rotate a trainee in a hor1pv:)3egfgt uizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable spe d q 60co-enwbv-a:rr.ed. 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 or:.v0qwe-n-ab ro6dcff. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mdx puh4j -w2q3ust a roller coaster be traveling when upside down at the top of a cx j h-2pdq3wu4ircle
(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 95wlqw6y )0tsf 60 kg (including the driver) crosses the rounded top of a hill (radius t)wqlf6sw 06y =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-diamesd s)am.w7-toi( .vda ter Ferris wheel need to make for the passengers to ssm.. d7(a woa)t i-dvfeel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 clpq y.0c0- pjk+2( ngg(ggtf kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of f cc g.(plggpgk+2qy(j0-t0nits motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 c y3ya lcn 2x(u.yca7brbtf5t(yr9 1/jkgm,)l m from the axis of rotation is to experience an acceleration of 115,000l(xltbrr(y,ja/.95g2bkcyf m1 ) 7tyun cya 3 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are ros8vo:dh/6k3f g n9li 5n rb+jstated in a cylindrically walled "room." (See Fig. 5-35khsob3 vgf/s95d 8 ni6 ln:+jr.)
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 rotatet (f.fpngv c+kz// d/pd in a circle on a frictionless air-hockey tabletop, and fk gcp v.pz//n +t(/fdis 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 not in x ssn1l3ukolvq63z;2+)jc ggnoring the weight of the ball which revolves on a string 0.600 m log xs2un3ln6l ;kz)j+s c 1voq3ng. 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 traveli cj5 eh/1laf;e egklg(k6)f)ang 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 xg jhk6*(pll-$ 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 vertical,vsh, wsz e aaskxj;hy 55**:oly 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 centripetal component4sopq z b hf1h810xma:s of the net force exerted on the car (by the ground) in hq:fbmoxs0 p1184h az 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 accelerates uniformly from+.3ycg c3 lob;iabp,;8gb buy 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 fricti .8o babb,lcy;3gb+ ;iuycp3g on 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 h 869-qnvx1zmy*f u jyof radius 2.90 m . At a particular instant, its acceleration is 1.zmh 6fv-1u9 *y xn8jqy05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 (2 Eartho(.4eent 7ifke7wv 3a radii) above the Earth’s surface if its wafe4 k(t3 n7oe7ve.imass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerau 41/ g jlmt v alug2qfn)8dw+)7j2ohbtion g has a magnitude ofj2tqgwj dlhun + fo8b 1ual)/472 mgv) 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 rx b:e5c5)wp/z5r 1e2rqzsv,x jyeiwu -qj 4+uadius is 1.7 p cr:e42biqrw ,1 v5xxj-y sejez55uqw+u)z/4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, buxi,t v x v+vjdra9z( 6g4t0an0t has the same mass+0jxvat9rd6xvt n vi, 4azg 0(. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same raw2 e.0jcg,adi dius. What is g nwa2d. ,i0gejc ear its surface?   

  Two objects attract each othevu6 r93a uas rudf/:c zu3ue:2r 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, at rkd i/)/l-kcduz, 1ql(a) 3200 m -kiulr, k)1/ lcdd/qz    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the 24lz:96 hgaw (yi/tzqwql;omEarth’s center to a point outside the Earth where thegravitational acceleration due to the Earth o wa /tm(9ql2;giyh :6z4qlzw 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 into a sp c*3b dry-u+yly jbn6:here about 10 km in radius. Estimate the surface gravity o6:j y -*+cydrnbyu3lb n this monster.    $\times10^12$

  A typical white-dwarf star, which once was abrv fvo.,e*sui ;rjk33sqb 7my/ge9fp s9 ;d*n average star like our Sun but is now in the last stage of its evs 9vspi7 rgd*/b3vb e,ue f;r jf;my*.39kqsoolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless qsqobx 8 1aype;wr.+o hn p;sq/ef;1 5while orbiting in the 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 acceleratia e ;e;q h5w+ nqsq/ofp.;11pb8xroyson 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 sid4m cnk691:24mlrkxld s .pcbwe 0.60 m. Calculate the magnitude andbmkmc9rc l26 d4lws4. 1: pxnk direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side oqwh8dqp*( e*l gd3un0 f the Sun. Calculate the total force on the Earth dueq w8hqn(p*d0d*g u l3e to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfaczq i q7sc8kcy.je/f /;e of Mars is 0.38 of what it /cfks;iqjz./e 78ycqis on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kno+ dtb0x89vk)oglyn:f wn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Keplnl9boxg)t80 f:y+kv der’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sak-vd3o;y+o7vx:plc+ p k5 s+b.7/vuup ridwrtellite moving in a stable circular orbit about the E+ o- dkwkv 3r7c+:dyv5 iu+upvs /;prxp.o7l barth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abov3swo+81btp (- d aomaetj t,e4e the Earth. m o,ot1ajt(t eaw 34+ep s8db-How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experienqy-tcf,k ab2 k e*bp,.ce simulated kk*p. yqct2f aeb,- b,gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time ibmk*822rmc h vt takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “neamvh82 r2bc *kmr-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would af/kh;qg0 ax ix mi :;vi /ugh4c2t8g.t satellite have to be launched from the top of Mt. Everest to be placed ft.im:g/ k8hixg qg4a0;tv 2/x;chiuin a circular orbit around the Earth?   

  During an Apollo lunar landing mission,)bv 99.mffzu a/id z8f(j6s8zu+ zrlk the command module continued to orbit the Moon at an altitude of about 100 kmklsvz9a8m+ 6ufzzb8i zr/ .d )u9 (fjf. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice -lh49)eyw1hvm6b v c fthat orbit the planet. The inner radius ob) 9mf-h1lwchve4y 6vf the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (ynz9a4l v :*ypuy1di: 5 p2xbgsee Fig. 5–9). What is the ratio of a p:piadvuly15zg9*b pn:x2 4y yerson’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 ygijhrz-7 w .xz 99:iccenter of the Earth's Moon in a space vehicle h.9x i-wy gc7jz:9zri(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 sys2n -m6 7o0sa-tmdbnj3tepov 0tem consists of two stars of equal mass. They are observed to be separated by 360 million km and t mam6 on-pn7v3 j-tob02 ts0edake 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of xxu5ls brb 4m8h8 + vz40hsq:fa 55-kg woman in an elevator that move u08sx+mh5qh: bv4fl 4brzxs8 s
(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 suspeq/pyn ii +pc,k0j*x.bnded from the ceiling of an elevator. The cord can withstand a tension of 220 N a pn/+i ,pik qbjyx0.*cnd 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 4ljpzdk4z9yfx1h+ocu u +jl+ f (t9*ma planet with period T , the density (mass/volume) of the planet is f9 z1 +pj+u*ld4 oftmcukj9xlh y(+ 4z $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine th5m pu)z0oi93i luy n4je period of an artificial satellite orbiting very n9 zi) l5p o0m4ui3nyujear the Earth’s surface.    s

  The asteroid Icarus, thoujq)4; w;ii73k mwkmaggh only a few hundred meters across, orbits the Sun like the planets. Its period iw)mkwaijkqi m7; g; 34s 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancptio 0hj 8a:r2ht+nxzlvt8(3 e 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. It comes veryr -/y653uhmvp l bdgr) 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 dis6 lrmd5v h/b)r3py-gutance 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 t 1b-7a 0eujtikhe Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moo o ,ynbc5kpsmsoyo0.1u7z9 * lns of Jupiter (those discovered by sno7yo1 0lc5mo yzsp uk9b.,*Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period asegt f+zofouin fh 606r96t 47nd distance of the Moon. ztsfoo4 n6fegi69706t+ fhur   $\times 10^{24}$

  Determine the mean dinerq9e.;i,ei na3/qli a1 0 owstance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance o ;0iaeweeo9.3 in nrila1qq /,f 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 co1xio- nprv42p3 um.ayo j1lq 4nsists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed).aj21r1n34ppo-lxuim.y4vq o
(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 "planet" in the form owyyx2*7r8 , 7;zw2v xc/uyzmet wvz t;f 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 gw v ty* zc,u m2wt7vy/7x8; wryz2;exzravity 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 (moq+30 -glsbaiqwork952kc ) Fig. 5–41). If his arms are capable of exerting a force qgi 2wl3 mar5+k9- c0qo ksob)of 1400 N 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 grav/p.jnsitqj3 i,s7 k/ef:az 0city be half what it i:pc.i7q a, s izk0fnst/ e3/jjs on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutu cz w8*;;+moxx 7hylmdal circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anoth+8* hcxxw7mdzo y m;;ler?    $\times 10^2$

  Because the Earth rotates once p 36v g zu 8zscq:9e2u3fh mjf2y(wlvq5er day, the apparent acceleration of gravity at the equator is slightly less than it would be if th5zgm9uj2ve(6q sqvl3fhc f8uz2:w3y e 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 spacecra4ct.n gdj ;n obizq6,9 4dwh4pft traveling directly from the Earth to the Moon exphdt4,wcd4qgn j.i6z9b o 4n;perience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathfo:4 jrs8a6s mroom scale in an elevator, it says your mass is 82 kg. What sorf 4s j86:mais the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about6vdk7( o /. dekkfn5oe4isgn) 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) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be fedn.ksivdenk46ok7(f eo / 5g) lt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical cd/1r il tj1b+8zu mnn/yiy59loop (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 +3/-(jq z)fa v5iavxbiczp4htij) c ;terms of its radius r, the acceleration due to g 3jq/ acibzvv pc ;jhz(5i)t)x+i4- faravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve:6,21sxg op op2 kmmcfrtical by an anglgo2cs1:mk ,m2o p px6fe $\theta$ 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 the coefficientm(*7kx o c*dy stkx30o of static friction isx(k7 *cx o *30ostdkmy 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fasm aqak 8zt,g1)t that objects at the equatoz,m aag t1k8q)r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance q5v-yw /)wk gcvzz(o;h)*xep 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 s+vnxne, p+xy,*2it xupeed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out +etpn, xni +xvx2,yu*to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive ac0yl,7j qu ob(e v+xuf e-5v-ms the 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 canlmev-y b(7fvj5 q0x+o euc- ,u'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 Te( wipa;p/sq p.lescope 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 measspp;p i.qa/w (uring 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 0 mcxf gk9ei./speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius o fx90.mi/ kegcf curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utili( tqml+whz9n;e gpzh /s p1*d*mhq46i0(q dsk zes a group of 24 satellites orbiting t(m9gtqs k z/q4q d*0 dn;w phemphs*1i+lh 6(zhe 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 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 travelkk.n5c9 -l w,sjw4jluing 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros wj-,lw9 jks. 4nl uk5cis 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 shy8l 6 gm,sd5yhuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 d,m5h8ygl 6 sykm 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 di xykmk.ukl 050stance froklu k5m0 kx.0ym the 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 actually "feel" youqzz t-db f..9aw h*pj,rself gravitationally attracted to someone near yo9azh jdwp.*,btz q. f-u. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the9ti/ hv(i) d7rpwjsvq .s:i 71f6 wfsj,4walz Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years frod6q7z7(ss,a h j .i/jrwt fl:fip9wv)w i1 sv4m the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each si1qdovo/-mo:0t fi.) c racb0ide. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the v:10/cfm0tiocoi.b a )o- qrdbottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 k(yk84/ agkr xzl*qh jgj*5p 4dg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of t08v af;n ayrx1g;3jqj he 1.5-cm-long sweep second hand on your wr ;;gj3 vax0qynj af1r8ist watch?    $\times 10^{-4}$

  While fishing, you get bored and start t7o7 e(c kws( .zp (0bxvkbs2qn gw)r4wo swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line ma w0bo g)7wn(ck7rv4.kxs(pz2eqws(bkes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designez43sjto d)lu,d so that a car traveling at spes3 ),jolduz4ted $ 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 when39kxig3al,wx r 3vn(f negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal3k3xx ,ilang(3fr v 9w 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.$\approx$    $\times 10^2$