Sometimes people say that water is removed from clothes in a spin dryer by p wqb s)5pl+. o06rkiccentrifugal force throwing the wwbcslp.+ 5 0 )ro6piqkater outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travenoz8 f6( :exyow2aw3 wgkw:0gls around a sharp curve at a constant 60 km/h as when it travels around a gentle curve a3e w8o:w 2fgn6y(a :0ogw xzwkt the same speed? Explain.

Suppose a car moves at constant speo gw dp1 a6) .,f*mt2wwi/aadjed 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 awdp*,ji)m.wd2 aof/aw ta6g 1 level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. W7s)jnhsti8czgdd6qib7j;2zt 1,f0 m hich of these fo6ti7jzzssc7 )d21d ,ijf0hg8btqn ; mrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cir fstkt0a d, xyk:+dg)9cle without the water spilling out, even at the to)d:tt0k+ 9a,s gyxdkfp of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least thr200eg3 p (xtpovcd2prao hd)hpo7t:- ee controls in the car which can be used to cause the car to accelerate. Wha0tc0h :xppg2v eor htd 72d -(po3oap)t are they? What accelerations do they produce?

A child on a sled comes flying overacx3p:f4)o7bs lzz z+ the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decreas4+fop:caz z 3z)l b7xse using Newton’s second law.

Why do bicycle riders leanqe2 2tusxz(l-kxk .n5 inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How9(8mbwuh01bifszoygk +s6v; would you compute the banking angle given its speed and rad wkiszu1gy(fv b9o6bs80m h+;ius of the turn?

A girl is whirling a ball on a string around her head in a hor(/xik/1,u qhapl5z upyu-q c;izontal plane. She wants to let go at precisely the rp ,a1(ql pyih5zq/ k-ux/u; ucight time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force8v yppj 6dy mwq;a/n7uc1x- )x fuzl)5 on the Earth? If so, how large a force?)yy-x1 u8u7jamq5/nzfxp)pcld w6;v Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wayhll0ad 5 mb;2 ) qznex xhhr5n65.;wgus would the Moon’s orbit be differe r.hua2g5 5 wqlzl;mx6nn 0h );be5dhxnt?

Which pulls harder gravitational zst9hln+c- 5kly, the Earth on the Moon, or the Moon on the Earth? Whinl-zts 5 c+k9hch accelerates more?

The Sun's gravitational pull on the/67knyweve;(y 8x-qmdax py * Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. *-ekxpy a7w68/dm;xqy( neyv Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles?2gppd5 3b)eza What two effects are at wor532dpba)zp ge k? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the arw au.q+ ;s/nuyul-) jaid.e; u+um(force on the Moon due to the Sun. Why isn’t theel/- a.au +sj; uuqu+y;rai w.mu()nd Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or( n7ovqk4al5u smu olq7v5a( k4naller than the centripetal acceleration of the Earth?

Would it require less spe*dez)nq1n:ed 1b.w/ lw*ob 8vsv* plred to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rodw8/lo)1r* vn*vle.q1w*b znb e ds:ptation direction.

When will your apparent weight be the greasn0z1 o )97 tjb9cmj2 e8eqecatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates u9oten9q )aezcjc1 2smje0b87 pward, (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 xqxkjpi7 e- .rquqf6tav181 4 outer 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 this simulates gravity. Consider (a) how objects fall, (b) the force we fe1 .fpvxaxr kt671-i 4ujqeq8 qel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiencen rnt2-ynim09wh+s p7s “free fall” or “apparent weightlessness” between sm-hy t+ 90n7nrpnw si2teps.

The Earth moves faster in its orbi p;ozh f:i3e)st around the Sun in January 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 producing the seasons — the main factor is the t:hzsieof 3;) pilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was notkn8na (2cb/n x known until it was discovered to have a moon. Explain how this discovery enab(nna 28knb/c xled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is go 0 w6dc6y8gfcd9ci h, x;-mamuch 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 am0dw 98gg;6cfo6 xyhc a,idc- 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 1980o ltd8cs ud499 rxt(5x $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centrixm8f45ns meo7x)e f0;vlb3 zc petal acceleration of the Earth in its orbit around the Sun, and the xb5v l0mm) fz8c4xnf ee7s;3 onet force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 Npg )2fji( a*do s x+;w4kw9ind is exerted on a 2.0-kg discus as it rotates uniformly ipxf* i9n)iwds 2kd(4jog+a;w n a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, :s lyw )k2: *3ye+1l-o(mltcp zb gfuhand circles the Earth about once every 90 minutes. Find the centripetal accelerat1l+elc 3y-s pg:uhtw * (:m)ozb lyf2kion of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a poyi 4*;lubi nv8s*8t wowe mr88tter’s wheel turning at 45 rpm (revob mi w*t*u8v8wi8eoylsrn 48;lutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revoax **r up 3/j8gaf8qfh)(sfltlved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig.srfhxgj(aq*u *3fp) 8 / 8lfat 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 rouw/jn ac33pm22nh mcyw *yej 92nd a turn of radius 77 m on a flat road if the coefficient of static friction between tiwp 9y m32hwc ajnmy*2/njec23 res and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between thz3l mxd) t*rc.e tires and the rr. t)*czx 3dmload if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotl+1ase 3fti ;cld4wtv9n,m o*ate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 ti,;9tstcae vf*d431i+mwn ll omes 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 axir/pumg5gg6u. 9ja:.id q jd .os of 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 of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable? orddj g..gu9gmq/6i :.u ajp5  

  At what minimum speed must a roller coaster u- ,barci .qttrm.hc:36 z2jqbe traveling when upside down at the toqt6q.:m-b uaz,ci2. ht3 r crjp 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 druhx2c-j9 tjl ms.; b9*hiq xr,iver) crosses the rounded top of a hill (radius =9.h;xj c-i9rsh2u jlxt,9m* qb5$ \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 k-7; *.pfauk fqm;m ucneed to make for the passengerk mf p;;f.mk*auquc7 -s to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.16tuj:-aqg; e c0 m. At the lowest point of its motion the tension in the rope supporting the bucket i-tec6 uqag ;:js 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 parttv juvi6 /ymsf 2(;oj)dc2lk4icle 9.00 cm from the axis of rotati y/v)vftl62j ;okuj4ds 2c mi(on is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people arho43 v t0k: fov.aceh.e rotated in a cylindrically walled "room." (See o veh k.a0. :hvot3f4cFig. 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 frictionless air-hockey 8ak:dtnf8do 4/h mg3/17ao dufcjgkv ,0ix2ytabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole t 0aggjm7183vcdakynf,8o/ huk xof 2d :/i4d 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 , precisedhz 959y)pzyet-b 6nnly this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitu -)hz65b9ep t9 yzndynde 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 bankedcqqjd5c zcs*uufgh h m: /n 74.gl,k is1/1cb6 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 k+i(kle36 k2q- qzrdi$ 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 divin:f)t5 z n6r+ nfg t:/ahwkow1dg vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal compond;9 hio8gcg t9ents of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 1h8gc9o d;gti9 5$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapo+pqr +jjmnj*, lis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide ,n+qr p+j*j jmthis acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle o1)33 f1 sdkax/ q uw kql48cbk6wgmpj+f radius 2.90 m . At a particular instant, its acceleration is 1.05 csf 1g3/1 +q8bkxlqdm 3jw) kap4u6kw $\mathrm{~m} / \mathrm{s}^{2}$ , 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 Earmw4(z96tp k7 xho0pk tth radii) above the Earth’s surfpmk6z7kt (t 0px49 owhace if its mass is 1350 kg.   

  At the surface of a certain planet,4*x dez:u7xv nxwy10z the gravitational acceleration g has a magnitu:x1nz4 wx*d70z euv xyde 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 graviquc*06v9 opf 8v1id vnt 3i8xtty on the Moon. The Moon's radius is 1.7d8 91v * xut0t8in6p3i vcqovf4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 jjq/gw7;9,gdqgoh 6c times that of Earth, but has the same mass. What is the acceleration due to gravity near its h/c9gj7;dqgjqgo6 , w surface?   

  A hypothetical planet has +o*4-yc o z (usjkkyd8a mass 1.66 times that of Earth, but the same radius. What is g necysojk*odkz y-48 ( u+ar its surface?   

  Two objects attract each other gravitationally with a fob)cfmm/ublr lml x 2,k* )n63wrce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 *el38(+j r ajyh7gn* f;ny r(.wcf hqhm lwn8;hj( (3 qhya* f+e7fynr.h*cjgr    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside th+8zbwend 0*zh e Earth where thegrbde0*+hz z 8nwavitational acceleration 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 in* :u3ztajwf:dd jy(*jqosl4 1 to a sphere about 10 km in radius. Estimate the surface grw ofj:q*u 1*dj4(sy z a:3tjldavity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star evibsf(ft7 a: (6nl0o 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 is7 vlotf(0si(ab: f6ne the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weig)h 4b9mso 6wr b+p9on4 +qxiwehtless while 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 acceleration of gravit bw hi4nmw9o+ q)sbo4p+xe r69y 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located /a6ivga3 ng; ow4,f fvat the corners of a square of side 0.60 m. Calculate the magnitude and direg,6fnvgw/iaa;43ov f ction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yea8/jj7e utn7e s+ught3 rs most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The massje3 t7/sj7gu+ 8uh tnees are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of r x,rx(54b4munok 1wpwhat it is on Earth, and that Mars’ radius is upw kb5r4,xmo(4n x r13400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knohslh0 kj50a8v1k7n1krh7ibt jt1x 6 swn value for the period of the Earth and its distance frnk l10x1h1 b itj76 ak5t0hhrs87kj svom the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the8lr7 hmn; bu)y Earth at a8h7by; nu)mlr height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into awkmn))g h-.jhod30ei .f b n1i circular orbit 650 km above the Earth. How fast must the shuttle be moving (relati .b-o.whnfdj1i) ihnemgk 3) 0ve to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are tk-an,-iz-bwtj s l9)pc; cix1o experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolu-;1t-,inlasij bx9z kc -)wpction. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbi fert+y.:4j1wu5deln t the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above th:. n4d rt+1yw5lj feuee surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitr kf-unct :)-6 kvfee5e have to be launched from the top of Mt. Everest to be placed in e-t:-5nef f6 v)rkcku a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit thjah,zl y q65a/bzk1tne7l2 t8e Moon at an altitude of about 100 km. ,ja2q75bh8 yz/61 tzenalt lkHow long did it take to go around the Moon once?    s

  The rings of Saturn arexqvm0l)e* j :i composed of chunks of ice that orbit the planet. The inner radius of the rings 0 xiqe:*lv )mjis 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 Fig. 5–9). ,3npsw )88 ,xsuw vh1.d fvxdvWhat is the ratio of a person’s apparent weight to her re1v8s) udfwxxv3,d,h8vpw .s nal 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 thel:;a.zk zzy:x center of the Earth's Moon in a space vehicle (a) movl;zxzy .: :akzing 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 binaryzzm vu,+c;zp,-star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midwc+mv,,z u;zp zay between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elet: +ga g0k by;h0m-vqfvator that moves -b:vyghf 0kg mt;0+aq
(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 elevator. opliht( fg88 )zm d5s3qp4: hfThe cord can withstand a tension ofo:sdh ghm) 8qpfi853(pz l 4tf 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 pl phjsztej rss(n8y3w(05-82 wpl5esn f p8um9anet with period T , the densitp ez rp3jwulhne2ms8tj85 y0f( 8sps -5n(s9w y (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 th6v rx *4 apap;pp*jy,ce period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s survpaa;4*cj*px, y6rpp face.    s

  The asteroid Icarus, thougt7w 6wwz p1v(i)f-kq ah only a few hundred meters across, orbits the Sun like the planets. Its periokqz)7f vwp( 1-wt ai6wd is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average disyss*j9htg z -0tance 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 oyzz(+,bcia *ie wpp*lai+5a4 nce every 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 whe*i za+ebc+ *zi p4 ly(pi,waa5n 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 o srd;dh-mohp -j/2to(f the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons o ei+8cqv)ak1:ddfs ,f g89a- vh ahv;mf Jupiter (those dis+av vc8 a 8)-m:dqfsgfkhv,dae1 i;9 hcovered 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 Earth frog2 jrdo /p3uynu 6zmk79xz39qm the known period and distance of the Moon. 9n67/zu9ujq 2dyk3o przxg 3m   $\times 10^{24}$

  Determine the mean di4by2ce yvax o 2l05m) nk9ar2estance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods eymx52rkvy 9n0la ) a22cbo 4egiven 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 fragments (which luk+6lsaxnd;7 2 s uo38fh/m jsome space scientists think came from a planet that once orbited the 2mon;jauds l/x+s3fuk6 hl78Sun 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 deohsywfp4 e*(uqx :+szv;1 zr( scribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabi(os4;(fequpr:zw 1yvh +xs* ztants 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 year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an;2rmiw :9occ ui ze17w 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 toiz9oe:2mru 1 7wicw ;clerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity bg.p 6c i7dgov0-o 2wgr jhe1+i,yydd+e half what it is d.i 1gj pr7h+gd0dycvei,-g 6o+y2w oon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal k;olki**dsbe ( 1a+qd mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individuadslide*kkob *1q;+( al 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 gravitycy r:amjb;l+nj *6(ey at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. 6 bj+jay *( mrn:cey;lWhat fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraf74vl,. nfktq ct traveling directly from the Earth to the Moon experience zero net force becausktv4f 7, .qclne the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kr/ pwyid9yg; 9g, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elev9d ;i9gw/p yyrator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will r:c 2ia 4i.xi: gb1-iit pixj*kotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has ai.k:b*xt- ai pi 2ixj41gi ic: 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 ii w9*2)ddoj-gv p74/affygwd n 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 mass of a planet in teri6 ztvcbz b-fvy2bzqot5 fcrb:7av 7i 43)4x3ms of its radius r, the acceleration due to gravity at its surface and tz6rbv yx7f2bt3:)44 ai3c qoz-7v5tfbv z ibche gravitational constant G.

A plumb bob (a mass m hanging ol.f mle)47dy7; bih9ar)i s zkn a string) is deflected from the vertical by an)f)r;l4h lae 7kmz 9d b.syi7i angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m i6p43 x 2t3hph /bhz xkfc.fkp,s banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what ran3k2xbxc ,.34pzt fk6/ hhp pfhge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the. tqfpj6c j2ly 9;gn fbw-.fj: equator were apparently weight lj .jt2j9-n;.yff:6pfcbgw qless?    $\times 10^3$s

  Two equal-mass stars maintain a const4dklz96;6dr x g h yrin6(v.oqant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant sp 8itogb8rxq r7*-egsqk6 p1, ceed rounds a curve of radius 235 m. A lamp suspended from the ceic qrkg 16r7p8ob *sqg,- 8xiteling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as/.2nsnni jy mj lr.vf 2z2 :zug/s;g+p massive as 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 can't survive more .j2 z:n zg/ /up+r.2mnvj2sfgsl iy;nthan a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced ai ft h67*d8cb: r7jpcthe presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gaatf78db*p: hc c7i6jrs 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 sppg*pfsx cmovw42 -v3 9tls65aeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (ao 5pltm2p-4 9sfwx6s3 ga cv*v) 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 (z0d1m8s 8sz; nbyrog)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 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 a; zzbd)s 8m 081oyrnsgpproximately 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, is m;c5 f6a u*rwx6 *e l3gm.7/rsgovzck aeant to vka ef5uc*;/6c7gxlgs a w o63r*m.zrorbit 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 p,b(jr cjjokt7: p, tn1ursuing a satellite in need of repair. You are in a circular orbit of the(, k1,ort jnjj:7bpct 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 nf 8+mje r4-st),atyeyears. (a) What is its mean distance fromt-+snfaymr4ej) 8 te, 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 ti ir96 dcy7hz/o be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reas9 cy 7h6rid/izonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. ds)lr3p )sxy0 5-46) at a distance of about 30,000 light-years from thr ))lypx0sd 3se 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 si e5axdi 37s.m8q7b czade. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint o zx8a7b3i.7cq m eas5df the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits -m+:9z*ryousbzw+d r 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 experien)m*usd38 kaaeno 3dz-zdoatz 77c.,z ced by the tip of the 1.5-cm-long sweep second hu a*d, .-dza3)oz ckt8ezm 7 ansd3zo7and on your wrist watch?    $\times 10^{-4}$

  While fishing, you ge;a;hzyslla+jh+rc(z 4 t 2 sb3t bored 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 circs 4b+a3+(h z y2;l;caszjlhtr le 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 ak(r9f33r 0vedc hx)ry new highway is designed so that a car traveling at sp)ref hrck9vy d03rx3( eed $ 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 s3y66:bwme -h z,kqir, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accelerationzh6iq r:w,6y3s be k-m, 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.$\approx$    $\times 10^2$