Sometimes people say that water is removed from clothes in a spin dryer by cent 0itj0*4qn fskrifugal snjtq*0f0 k 4iforce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same whe;gk e/4s3czpp2lgcie p13 :azn the car travels around a sharp curve at a constant 60 km/h as when 34szgpl2 cep3;: ziega/ p1kcit travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car e77 l kg7h8jg0kcccbtu g4*9tuxert the greatest and least forceglb g4tucu 9jk7kc870c7h*gts 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 (y(hke c116p2m 1n)evjexl p91i(edpcv:wte child riding a horse on a merry-go-round. Which of these forces provides the centripetal avn:l(2c)ph eic pwe1 vm(e6dx(jte1 1 ye1p9 kcceleration of the child?

A bucket of water can be whirled in a vu(po xvfz a. s0dmra 9m:p0l.zkf:(5dertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. :arumsfz5xp0 (vlopz:dd0a9k fm..( Explain.

How many “accelerators” do you have 18g jgr kf1za.in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accajkgz1g8 r1. felerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shd),8ecr(y b4b0l a.: ibwldh fown in Fig. 5–31.cry ,bl:e(i df 4dahwb8bl)0. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean it*s ma)v4n9je m)vmp;.,uhl s/*itsfnward when rounding a curve at high speed?

Why do airplanes bankl*7nmw-kxv jk k8wi ) 97e8qtv when they turn? How would you compute the banking angle given its speed and radi*w7kxw7l) ekv 8q-j9ivm t kn8us of the turn?

A girl is whirling a ball on a string around her head inkybnf:a, r r*7 a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the otheb yar 7,*f:knrr side of the yard. When should she let go of the string?

Does an apple exert a gravitati ):k l;az6nybbkwax* /,k.x.r,vabn qonal force on the Earth? If so, how large a force? Consider an ap6 . wz,,b )vba alxk qry.n:*kx/an;kbple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit (l,x4bdcf /z ;fwsiw w5w9y*q1 ucdx.be dqd1 x(bx*9/dw wf;w4fz ,iuyc.5l c swifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on t 29czo)hevrqk*,7 gofhe Earth? Which accelerat)rhfoqvc,7ke o*gz 92es more?

The Sun's gravitational pull on the Earth is much larger than the M+1( ecte m3dlfoon's. Yet the Moon's is mainly responsible for tht+meed1f3(c l e tides. 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? What two effebzb /m7f;1ldqcts are at work? Do they oppose zld7 /b1 ;qmfbeach other?

The gravitational force on the M o0rar, ( bqan2.w9d9qklt 3haoon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from (wkarq.tbh3ol 029a 9n q dar,the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or, /qikn0au-9fop(mv , slmj8q smaller than the centripetal acceleration of the0u 8m pivnk /js-fq,oa lqm,9( Earth?

Would it require less speed to launch a sate 0are*ef180ud0yrzvvxa6j n,qkk3o9 dg o(b4llite (a) toward the east or (b) towarnv 8 0fo v xkgaoe 040u k36qe*rjda1r9,y(zbdd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale iph ,pnu7g-hde f /im4fduzqkj8pe24tlf -) ;2n 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 leaszdf4g2 hikje8lppu ) h2d;4 tqf,umfp7e n--/t? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affe;pcqh9)gq;ai0 c f l8vcted 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 feel on our feet, and (c) any iv;l g;)9cqf8hc0pa qother aspects of gravity you can think of.

Explain how a runner experiyj u1xe3 8rfh3ences “free fall” or “apparent weightlessness” betweeuf 3h13xeryj 8n steps.

The Earth moves faster in its orbit around t;t yiu2p ulb84he 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 tilt of the Earth’s axis rebul82i4 y ptu;lative to the plane of its orbit.]

The mass of Pluto was not known untcl.,ei u; hy0awwp s93jf5s( fil it was discovered to have a moon. Explain how this discovery enap9.uw(cya3elsf;5 jf,0ihs w bled an estimate of Pluto’s mass.

  The Sun's gravitational pul-dc /) nioynj0g t+sa6l on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side nt6+ djog-)0a/i n ycsof 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 travelin+lf wt)zwm s/;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 in 28lpbgmuti; d 3vh;c3its orbit around the Sun, and the net force exertemuhvt2 ;i 3;gc8dl 3pbd 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 N is exerted on a 2.0-kg discus as it rotates un0 b*6b4bg6t. xx9i) c(*c robdmgamcdiformly in a horizoc0x g49bt)a*b*6cibmd ( .xcbmrodg6ntal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 40/zt9z /q52bd yta qpyp grw3lh(17,sn0 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle 7gs(qw 1/tt93lndqb y ,apy2hz5p/ zrin 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 oflhq 5yk:xkce2w2i**t clay on the edge of a potter’s wheel turning ai2wht5c :*kekylx *2qt 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 unifortyy8mbbfu0n+mtvhk ,gpe ) :(/jtq08m rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3yj(y/8,tp gb+m0):hn mtv t 8bf0uqke3. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turl )nil;m2-spl n of radius 77 m on a flat road if the coefficient of static friction )2-plsmn ;lilbetween tires 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 ttl,/m, f*nlox jfei1l 8*q9qthe tires and the road if a car is to round a level curv tlx i1,,ljtq* o*e fqn8l9fm/e of radius 85 m at a speed of 95km/h ?   

  A device for training astrdqmug2 hg cya 4nr y6d07wndt:ot4q/ c (//mr8onauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 timeqc4dnydr n/mh u8om:w ct y7a r6/4q/tg02d(gs 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 bt+9lvorx 2al7hzr.o slq2r87hfo(h: jbr1: the axis 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. Whaolr(brv77+zhoaq :r2o x :t91fl 8lbs2h j.rht is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must,rz.t59 vv ed8qxst2j a roller coaster be traveling when upside down at the top of a.tvjdx r z5et ,8q92sv 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 thz5npt9d eh/r, z(*fes e rounded top of aen dr /sze*(5,9ftzph hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel g:nn -jyao0yq3* k0 k.btp6csbdjzq3 ..u;w gneed to make for the passengers to feel “weighpqj .*3aw6t0 bnqon 0sb u.ykyzj;:.g-3gckdtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radi wv 2/2ucs2l tthn:hz4us 1.10 m. At the lowest point hh4wlv u/s:tn 22ctz2 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 centrifuge rotate if a particle 9.00/ pjyyn 0+y+rn cm from the axis opy+r0jn yyn+/ f rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricall8wj/.-:y vhjn3k eps ,uyh61w t6jc ryot5 po5y walled "roo8n1,tjp-6.5u v:wc esk5 r6yhy p3ot/j hjoy wm." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotx5dto4xz9+ d8m ve p:gated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (ma4+ e:g8opdvdtxz9m5xss 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 of the ballxbi2/06nc jvi otd 46w whichd/j b i2tv0 noxcwi646 revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a cay,a5+r od8aj 9 2uaivbr 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 massesnmfcsi.s1s0 (,,j k+x j- pwqwxia5*s $ 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 vertically4w4, ms 5h7y8cm;ewi0 lq mtdz 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 components offfxp5wkp:4 e1 the net force exerted on the car (by the ground) in Example 5-8 when iwp5ex kpf4:f1ts 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 uniforo2gs,dde:d 3g7l va0umly 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 andavo3gus, 72g0de:d l d the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radzlcu4s*ne)n 7mcit6m k4u(ps7u hp6 -ius 2.90 m . At a particular instant, its accelerationku htczms e4c6lus* 7i) m6pp-n(un47 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 spa rr bozfv5nein:5f++z;r1,gxcecraft 12,800 km (2 Earth radii) above thenr+g:;,fzi1 5rbevx+z ro5nf Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, ovt9*q4cq3lp geq+p8 pxw/n. the gravitational acceleration g has a magnitudw+l*pt93/ epcv4xq 8p qnq og.e 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+ ip+zgj:gm0+c uky8w on the Moon. The Moon's radius is 1.74 8m0kg+p :uz+yj +wgc i$\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 thatcrv /:8sh;c 5nlq h./ekuzv )f of Earth, but has the same mass. Whlv fe/csrk/z)vq; 5n:cu 8.h hat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a m7q-t31 yzcx phq+h1tiass 1.66 times that of Earth, but the same radius. What is g near its hx3c z+p71tyt -q1hq isurface?   

  Two objects attract each other gravitationaltl a2w7 v+* drc)yu9nily 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 g4t5o.ux toziqq-b2 q:-ai8 ovravity, at (a) 3200 m b.zqx uai4 :ivq o-o8 2to-q5t   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where ue k(+ep,l krdt405rdm+hauoo7x q+5 thegravitational acceleration due to r5kuumo5th4x(p a+d 0k++erde7olq , 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 Suz7; oraoc3oy) n packed into a sphere about 10 km in radius. Estimate the surooyzao);r 3 c7face gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a ymgru1ixj(s a*9q b41n 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 surface*b(x4ysqaj1u1rgi m9 gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitindo) -1n zebx,9c:djskg 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 gravity 250 km above the Earth’s surfacd ),k sn o:b91zcjed-xe in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Ca; rdg/6wwm*zdp l 3*palculate the magnitude and direction of the total gravitational force exerted on one sphere by the other threedl rgz6wmwda; /p* p3*.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of t lam,eyr 3e q6pmq)8w0he planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, ass68l eqw)a0emqy ,r3m puming 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 of Mars is 0.38 of whattm1.;gg:zltr,whit /i 3a bf0 it is on Earth, anrt. iawit1 g30 ; htb:m,fgl/zd that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the k( ;qh)1hkyc gn /1uzdjnown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to t /z)d 1cu;qhhkg1 nj(yhat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite/3bi9uynmud 6.y/*ehcp u k4hk,c . gv moving in a stable circular orbit about the Earth at a 69,*d yhvumuc u ei kk.3 gynpb4/c/h.height of 3600 km.    $\times 10^3$

  The space shuttle releases a satr*d *f-gwv inp18ufifl jn,: m2d9h3s ellite into a circular orbit 650 km above the Earth. How f1dn9 fs 8*i 2mjh -d* rifgpn,uv3lfw:ast 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 e ed6h*o vzgg*9xperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (Se*eovd*6zggh9 e Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite tzyos gjxb i.l(ads+;2c6-wv 2o orbit the Earth in a circular “near-Earth” jv l+.6awc soxd-i;bsy22z(gorbit. 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 your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be lafq :7 a..hdicni l;stx) c6*ncunched from the top of Mt. Evere:x *adf) i6 .cchtn7nlcq.si; st to be placed in a circular orbit around the Earth?   

  During an Apollo lunar l6n wi mi7ysoy.g d:q23anding mission, the command module continued to orbit the Moon at agq3i26.ioy w7y :nms dn altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ibd: 9al/ ;f2fw4n zclnce that orbit the planet. The inner radius of the rinl: 94wfabn nfc2 /d;lzgs 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 rota/elw*b 6o;fdttes once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s appar ;/o*f6tld bewent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of ptxb fdqn2k0b9 bf,j)cs 36t ;a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant 6fbkbn tf3dxqc,2);psjt 9b0 velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of i1xcgdfr0 l-3 two stars of equal mass. They are observed to be separated by 360 -rd 1iglxf0 c3million km and take 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 a 55-kg woman in an e13z vnozy(ax0nfj z,1 levator that mon(z j3nfa0y1xv 1oz,zves
(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 cory)wxh(6xr: bub 0xb;r d suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elx( u:0;wb6hxxb by )rrevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very neaiij q0 2m2b *f8(xmyimr the surface of a planet with period T , the density (mass/volm x0 q(b8fm* myi2ii2jume) 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 th zm*k5z. vresf(,*wgg e period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’sm(zw*eg.gfz, v r*5sk surface.    s

  The asteroid Icarus, though only a few hundred meters across,/v 4jgmb zh8)k orbits the Sun like the planets. Its period is 410 d. W)b j8zmg k4/hvhat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average /ata .ep: my+u jm7j)fdistance 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 Suf qiy, yemjwrh5a,j(-k-u .y(:gic m *n roughly once 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 when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and f e(c-a,yqr5hiu,fgy*i wykj.- m( j:m arthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxn- ik sk*z-n;:8kknt qy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 mos:v2i*crgjnxa 35)ik ons of Jupiter (those ki5*i2x s ga:jr vnc)3discovered 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 thek0x/+mxlw z2s /pm.a q Earth from the known period and distance of the Moon. pm aqx+x.0k/2z/sw lm   $\times 10^{24}$

  Determine the mean distance from Jupiter4-cign n6 pud3 ymll5, for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the pigm ny5l ,pnl4 -uc36deriods 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 atl p+a ko3bg/s5pq/:z nd Jupiter consists of many fragments (which some space scientists think came from a planet that once/ pl /z+st35a o:kgqbp orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of* lqy1,n;v+ ./bggyfhlaj z7vc(z v6z f)bxh4 a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What wilv l*hhflx c za(y+g)6gb/yqn.74fz;vv 1bz j,l be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an aomj+ t ec40ny9rc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the v4 emcj+0nyot9 ine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity- hrmznz +r-0:,smute be half what it is on the sr- z,hzsr +0:uemn t-murface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and d6el )c+gqra 7spin in a mutual circle once every 2.5 s. If we assume their arms are eacad e 67+clg)rqh 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 gravity 5o(qc 8)) jkp xkoc*ur 4pvbb)at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What frrxb*cjcpq()bk)k8 o)o 4u5vp action of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Eal r*u*j2th, -kpkld 8trth to the Moon experience zero net force because the Earth and Moon pulllj*dk t2*-klr u th8p, with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scallx8j4*gcvm8qmw+ h m21g r*am e in an elevator, it says your mass is 82 kg. What is the accel+2m8 c4v*gmqhwxgra ml*18 jm eration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat ain). ;xwiv-q mb sei:)*v*ote about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formedm* binxe iwitosv q).:v)*-a ; by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. +br7u 0dysg ,k5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accelse,(wbd 6,cef eration due to gravity at its surface and the gravitational cons,cfe ds(b,6e wtant G.

A plumb bob (a mass m hanging on a string) jc8drhtv1y 1:is deflected from the vertical by an anyvj t1dr18c:hgle $\theta$ 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 .u;wnn-e128h*ls al2g ak5i patvb9fdesign speed of If the coefficient of static friction is 0.30 (wet pavement), at w ;8 nusf* ibaa25-kte gw29v1lnp.lhahat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that 8, th/w4xjtfr2aax 0 umih/4zobjects at the equator were apparently weightless? hu zfh/a8jt4w2a r0m,xi/xt4    $\times 10^3$s

  Two equal-mass stars maintain a constg 1u5lwsmq v5-lwq2fd3 s;r2aant 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 conyrg2 c 2dj8wr/stant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 1r /8wjy2gd2 rc7.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth ,a e8q oduu(f-p-lq/n. Thus, it has been claimed that a person would be crushed by the force of gravita, n(uq8pu/ --eoflqdy 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 Telescope deduced the presrqbq 6t2ml40m x0(6z4n tkosx ence 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 qm6r2ok s0q xx b4tt0(n64mzlof 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 traverses th.x nzg, jld/eyjiid j:w25u (-e hill and valley shown in Fig. 5–45. Bxid (2uy/ w5 idjg:,lz. ejj-noth the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positio;x n*+ 3wrvxor: ,ywjmr-r8yc 6+o1nvxypcm1 ning System (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;jncyyn3o x+x:* -vm+x1p v6o8rrrw w r,1myc 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(o 9(5frix pjevta. 1w traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eroxvpriaw( (t 9 j.1o5efs 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 pur4u3akbe )n yvhai97b .suing a satellite in need of repair. Yoh ev a)3 ib4u9kba7.ynu are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3b.,y1/5nf jp6iopjwq 6eu3vt 000 years. (a) What is its mean distance from the Su3qteuj6nyob6 jw v1.,/f 5i ppn?   
(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 o:qad e u)mvna4h;cq)jp (o*0e f G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Mak0d*ehqapjqe :cn;4mo ) uav( )e reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gal +zub 1mwb75)oj hb/guq. 5 (4kjsbxwkaxy (Fig. 5-46) at a distance of a4 u(+w7bmkb 51)gj j u.kbwsq/5 zbhxobout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located a2gvozr4 .prkr j i4-5:t+jpe at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed 2+pzjr te:a44roj5v g- pik.r at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the 1vh4g z7xuxnqup9jwj x4:; s8Earth $ \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 the 1.5-cm-long sweeme)aw+ ,+vxp rp second hand on your w rav,)mp+exw+rist watch?    $\times 10^{-4}$

  While fishing, you get bored and s r0m sx9cm6f o.gun+n3;0fvegqp)o2 xtart 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 circle every 0.50 s. What is the angle that the fi m;xpogugn3vrx es60mfq.02f nc9) +o shing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a ng l6sbs j894 nqq:7tiiew highway is designed so that a car traveling at speed gis 4sq8l6qti9: 7bjn $ 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, tkn 8wfbgy -1.jhe Acela, 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 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 jw8gnb1k f.y- 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.$\approx$    $\times 10^2$