Sometimes people say that water is removed nz05i4k m6 mrq 5k1pyjfrom clothes in a spin dryer by centrifuga ijm4rknqm5 015p zyk6l force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the ajh+ 4r*j9iubsame when the car travels around a sharp curve at a constant 60 km/h as when it t jai 9hru*j+4bravels around a gentle curve at the same speed? Explain.

Suppose a car moves at conh91,l6ei 9rn11doaudz f b aajjq* 32rstant 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 levqeh o1u 6r931 df2*ain lja1bjazdr9 ,el stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. d *b cq6b ac4* *8hqrwlk5eu0eWhich of theseb *cqwrh8 e4d*e5uq *c6ak0lb forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci2 amfz kv:4gc:rcle without the water spilling out, even at the top of the ci:zfa2cm 4v:gkrcle when the bucket is upside down. Explain.

How many “accelerators” ,2.s 2rtyj1i7gnnh6f(wr3 bjytn s ,bdo you have 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 acceleratjnr h,71ifb6,. 2ngyrs(ttsw jn2b3 yions do they produce?

A child on a sled comes flying over the +t ./at)ab19hdl.uah dtb: ypcrest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but +bl.aty9.a:h/ 1pt ) adbtdhuhe 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 iu9e.kfz f6i6lean inward when rounding a curve at high speed?

Why do airplanes bank when 8ad(x k4q) p) cwv4j6afkv.9ea2wjnj they turn? How would you compute the banking angle given its speed and radius of th 4akn jj8vfcw42(w. )6jekqap x9dva)e turn?

A girl is whirling a ball on a string around her head iea 5 +8oi*u3iay;velfn a horizontal plane. 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;fi+3eue*l5vy8 aaoi should she let go of the string?

Does an apple exert a gravitational force on the( +vgyn )dqn 6.yhn(hvj *c,rr Earth? If so, how large a force? Con hy,yn6h (vr q.rv(+*jd cn)gnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, ins3 vff*0e 0v+jvxo x3,fr, vylvnnw*( what ways would the Moon’s orbit be diffenov0 v x,sev 3rw+y*n 3*f vfjf(,xvl0rent?

Which pulls harder ghiw,:.(zeeq( rdbq e7ravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelere zqi.:ew(7b,hqde r(ates more?

The Sun's gravitational pull on the Earth is much largmuu )-60v8zitebvog 7er than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hu-7vbu)igm t0 ov ez68int: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the e)a hs,:im ,c jbf pkgm3jub/33quator or at the poles? What two effects are at work? Do they oppose eaa h,sk3c j3f/m :bm)u,ijg3bpch other?

The gravitational force on the Moon due to the Earthlod;vn1zfwhd f)0tm u*+2:eh is only about half the force on the Moon d1v fh)*+n;:zwe ohtd2f0dlumue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun (xa k)f15ke yzlarger or smaller1k5e(xf )z yak than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a)z*c 0dq .v fgkpw-/o;z toward the east or (b) toward the west? Consider the Earth’s rotation v0*dc; w fg q-zok./zpdirection.

When will your apparenth,oz os27 6,fnckb) ) ligiv;s weight be the greatest, as measured by a scale in a moving elevatoroc f7sk h,g2novb)zl6 is,); i: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be 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 ad5gn+ ov bom3gvyt5-t .versely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astrono+5t3vbn -gt.vg my5oauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experienf+, o/dks 0;q5gofu+r e csgh4ces “free fall” or “apparent weightlessness” between step o r+0u/fk45hogf; seqs+c,gds.

The Earth moves faster in its oey vevb0-v2/n rbit 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 tilt of the Earth’s axis relative to ty0e b2n-e/vvvhe plane of its orbit.]

The mass of Pluto was not knol m-+uh okz-v5wn until it was discovered to have a moon. Explain how this discovery enabledu5mho --kvz l+ an estimate of Pluto’s mass.

  The Sun's gravitational p-dn fyub;mo3 485ez m zvoqh.d4r*) dgull on the Earth is much larger than the Moon's. Yet the M eru;zomf5 4og3h q zdv)84.db *dyn-moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a 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 3fuujz y jd)n(6kz+ (ir :cx,z1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 its orbit ar4ndg0a+ mb) voound the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circlv0d+ag4m o)n be 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 un9 :,tu l+v01buoyrv tdiformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the dist: t+yl0udv1b v,o 9rucus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and r( c b4h kdn+aewu m6 ziyqdg34i49((rcircles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its odz(ga34mk y(r n64i+d r4qhi(u9 bcw erbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration uhfm32 o:u7dv *+grn/nzb 2sf ;u/ailof a speck of clay on the edge of a potter’s wheel turni23sh/ rd ff2n ;z+ li m*abn7/ouugu:vng at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical cf oj hki4mw)-va f9n:7ircle of radius 72.0 cm n 7omh)fk 9:-awifvj4 , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a.eao: k9qf9b q 1050-kg 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 indepenbq:9ekf q.9 aodent of the mass of the car?   

  How large must the coefficient of stat;(wa*a.d-two7:p q m5 suix,wiyio3 uic friction be between the tires and the road if a car is to round pi xow yaiu: tqw,5d-s;o.*3i uma7w(a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed toiy:btz) xz7taf.9 +tz 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 times fz)byz xa+tt .97zti: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 boy6s-m:6 k0p.hj flsa 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 belkms.f: sj p6y 0-6ohbtween the coin and the turntable?   

  At what minimum speed m w25j ou(lf4szust a roller coaster be traveling when upside down at the top u5lj4s(zwo 2fof 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 95g4fmww 1.t.5pe xj8ez0 kg (including the driver) crosses the rounded top of a hie j4fe. wtpxgz8 m1w.5ll (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 nea idm 7f5*;(kdyngy-r 6:vhzqed to make foryzhqf5 nyk(-ra* 6dv; :idm7g the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ofp,cnqmx.u 3gz.l,:sb radius 1.10 m. At the lowest pq u .z. ,,s3pxl:mbncgoint 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.m d/30u;d 1wz sj/p1bgpv/nnx 00 cm from the axis of rotation is to experience an ac3vpm1dbg 1dsn/j n /w uzpx/;0celeration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carni:r4e 6 dt 8zeq*6kj5wuj *uqscval, people are rotated in a cylindrically walled "room*t64u8 js ec*w 6q je5urd:kzq." (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 rotated in a circle on a fricti1d-,idz0bzwy advu9k : kd 3;oonless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blozdod9k vzd :3u0 i ;,kw1a-ydbck (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 , precici0u.g,dv8yv sely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of uvi.d ,c0yg8v $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 traveling sr dhv10a nm9u lj591w 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 massezc3n/ u(3p hlt (qgm6js $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310 g3m/lpsx 6n5 czi+ge4$\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted on f2wbp--dr)t;pc 7zokthe car (by the ground) in Example 5-8 w-zp7 ;dobk p-wrc t)f2hen 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 unzt- (iw3blg (e1nqs(x a6,rr ziformly from the pit area, going from rest to 320km/h in a semicircuw6 i1( asb(qern xzgt3r-(z,llar arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radi-vw9zmq+sbvt5)h rh1us 2.90 m . At a particular instant, its aq 9hsrw1+ vv-mth z5b)cceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (99,a duxylpbx us62y,p8,h3g c dx;xm2 Earth radii) above th 8mb g6u,d9dx;9, xh2,cx a ypply3sxue Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gra- 16wpwchq,szvitational acceleration g has a magnitude of 12 m,p1 qc6 hs-zww/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 th8ki hqy*g6 gw3e Moon. The Moon's radius is 1.74yk6 wgg83qh* 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 timew f 1gvr f0dck)(h5mc.s that of Earth, but has the same mass. What is the acceleratio cwrv(kmh51d.f 0fcg)n due to gravity near its surface?   

  A hypothetical planet has a mass 1.6ktw*8w ,c6 xs s46u1e9le ubon6 times that of Earth, but the same radius. What is g nea6x,sc swuto9 4 *ek1nwlbeu68r its surface?   

  Two objects attract each other gravitati ol;5 ko60 3zxlcvenujk ;s0k-onally 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 gravp6 ;4oxcqmp( hity, at (a) 3200 m pxp hom6c4;(q    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eart5ewem:l; 8rmz8)( 4vlcwl cyzh where thegevcl c5(;m4el 8wr8z: ymwz)lravitational 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 tsxjvk. 4475hhl zd gr :(,rzvthe mass of our Sun packed into a sphere about 10 km :vrjx h,(k5 zlr. 4vghzds47tin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which f-w 6mcw) z8mmonce was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. W6 mmf8wc -zw)mhat is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orb;aar vhriv5-pzwwx68r /t cx2x3;5v1/trmvq iting 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 am5v-xriq;r rtxv/286 xrta vz1h/vpa; 3c w5wcceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locfm, vuu8x(sjvi)i 9 (zs(ivt9ated at the corners of a square of side 0.60 m. Calculate the magnitude and s8i)i 9vm9 (,jvf(izvst uxu(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 yearsvmr.3pyw; n9ztgqqoof s: m;e84x 3:m most of the planets line up on the same side of the Sun. Calculate the total force on the Earth duvewsqzmo9yn :o;m m3r t:p. 8x q43;gfe 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 surface of Mar yv 4,-fw;wkzjqy1gsg)( 0gp9hak) do s is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determi )1hdy k)ypj s 9q(g-wz0wof;av4g,kgne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of thekb2-n2a/ lz rk Earth and its bn-kk lr2a/z2distance from 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 me4hj;4w q;f ugoving in a stable circular orbit about the E ehqwuj44f ;;garth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite ltec2*d ik:+hpa9:pminto a circular orbit 650 km above the Earth. How fastma pec+ p:klti2*dh:9 must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cx4r th()lz 9ujylindrical spaceship rotate if occupants are to 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 revolution. (See Question 9j()z luhr4xt 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit 7thrx,k5 p)0ylw7bafthe Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is ,w0plhyta ) k757bxfr 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 launched from the top o75ip nom4t1ph( ap n3kf Mt. Everest to be placed in a nkm41 3t5o hpp7 inp(acircular orbit around the Earth?   

  During an Apollo lunar landing mission, the commd)+jkrhpefh-j5w* s: ,/ys:a ve 1wxtand module continued to orbit the Moon at an altitude of about 100 km. How long did it takesd:p/:-*)vhjaetke hw5x, jr+y1 wsf to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.eenemda)e s; rc-qal7uvj a:3vj v/e3x(6)) q The inner radius of the rings is q- qs ua)dvml3c;ve )an3exj:r /e 7(j6e va)e73,000 $\mathrm{~km}$ , 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 1kh)/9unae k(z 5.5 s (see Fig. 5–9). What i9k(h/ueaz k )ns the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kp 1cb.bokdz1xj0 r,) qg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant v,1 0o1 zqxr) jb.bdkpcelocity,     ----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 -vn,gg o7z9od 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 midway between them. What is the mass of eachogzg, 7d-v no9?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-ki ut20f45pbi 3nags3 d elh67vg woman in an elevator that e n a432g us35iplbf7vhti0d6 moves
(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 zuo 5qnd3::4q /quyo:b hp w:icj6dj ,cord 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 elevator’s minimum acceleration (magnitude and direcq4z,5j3j/owu::i yq q:6dopn :ubdhc tion)? a =   

Show that if a satellite orbits very near the surface of a planet with periodr9(qfca 94o moq-fe8h T , the densit- fao 9ho4erqm cqf(98y (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to deter6*12iamep mv. jh/jbwg+)o(yafb4w. z vv +cimine the period of an artifici i +jbci.6m4 *1v z2vo(apg.e)/hww yb +vjfmaal satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thouhj:m-8kizk d 5gh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its 5kdjmz :h- k8imean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 0i esji.(b m60tp(z,zk )k1sliq +7nj q+jubm4.5 $\times 10^{9} \mathrm{~km}$ 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 eve)wd.l3q- ab hlpd low9vces1 ,jah *+ha57l8mry 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest dissplw57 lvd.la h h*eq 9+jb8, la)awdomc-31htance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centercnr0j0je4cxybf m*8,z2 b p8 d of 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.08x2l mlhbi hpr3uln qrlvabk9 9)7a9pt ;(q for the four largest moons of Jupiter (those discovered by Galileo in 1609).8 9nmaka2rbph b.i llpl07;)q qx (ht39u9 rlv
(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 and distance of the aw*eou bpl0s/7 c +aa*Moon. a 7*obap +sluaw0/e*c    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,eaj29a mxafn1d-a 9 sg414h kk using Kepler’s third law. Use the distance of Io and the periods giv nhdj-ae2 411 g9ksfaamkax94 en 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 ma+z3n 5vcds 3:+greugj5e5hbqny fragments (which some space scientists think came from bnh 3j u5c5d 3eqgvsg+z:er+5 a planet that once 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 talepmrt47xx.axz)d j + ovt v6:r: describes an artificial "planet" in the form of a band completely encircling a sun (Fig .tv:pzv7m4a6) rx :o jxdtx+r. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hangiuvp 3 h6pzeh-*ng vine (Fig. 5–41). If his arms are capa6pve-z pu3h* hble of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the aknzv:6ua biz*:)9 g mrcceleration of gravity be half what it is on the smi: b)n96zr* zak:u vgurface?    $\times 10^6$

  On an ice rink, two skaters of equal 4ar5-6/ gh tguo/g wiqmass 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 individual masses are 60.0 kg, h 6g5oqt/ h iuw/4ag-grow hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates on)cpyi:px0sn.,uem 9hbhyrql-*8m6 wce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotatey:uiqm p0rh )m8.xl wchn9ys,p*6 eb- . Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directlyxf csw8(skoeqt+56 - p from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposi5w(cqsf+ sk-oe p 8x6tte forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elev:o3;on ysx/h iy n/,ulator, it says your mass is 82 kg. What is the acceleration of the elevator,n ooh/s3yxy:l/ i u;n, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cicxq k1wj 0wf5aijj;tq+f2ag ;w/ : hg5rcular tube that will rotate about its center (like a tubular bicycle tire) 05jjh 1;c;w:f qx5qgaw itj2/wa g+kf (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). 2qzm/mlr 1u s*
(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 planeg;hd b1rf s hcp7- v)e.e;bwy-t in terms of its radius r, the acceleration due to gravity at its surface .dvsr; -17 bwgcphhb)y;e-fe and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verti0y2 wh 0sq4 m;6kmsn +a+pd6caj-e jvjcal by an anm02ce4hymj j6; +wa 0knqadjsp6 vs-+gle $\theta$ 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 coefficient oluq j.aos 8j31f static friction is 0.30 (wet pavement), at what range of speeds can a car safel3.a8jsjq1o u ly handle the curve?

  How long would a day be if the Earth were rotating so fast that objh zi3()crjtdn* 5vy5lects at the equator were itc*5 )hjzr5v ndy(l3 apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 - ra7/i+ 9kg7bf5skuatq zz+t $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of rn, qto*m8u bj46lju;uadius 235 m. A lamp suspended from the ceiling swings out to an ;ljo48un6 umjb ,u*q tangle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the z j ve2t(w6: 5pfzm6,3y-eb vsipe6mxEarth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few gf6e eybwm, i(v :mzvxj3-65 z6p2 tpse '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 Hubblezstllp7w47; x Space Telescope 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 escapesx7p l4 7zt;wsl). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant sp6y 9l hvzbxwa.o;1 o(wez8z4 seed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest?61; lz.w8(xv4z w zhoaosyb 9e Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes i.dr o k:n/i 83uhrr0gf8pe)ka group of 24 satellites orbiting the Earth. Using “triangulation/.o0:kii ) f ud g8rrke8p3nhr” 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 trave2ij3u3ax/i vq ling 2.1 billion km, is mea2vqi/ixuj3 a3nt to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need o,h4 wx a7crueyl8,sz;f repair. You are in a circular orbit of the same radius as the satellite (400 km abov us;xr7cy8 za 4,ehlw,e 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 gf, si;sxthf2i1+x0s3000 years. (a) What is its mean distance from thfx gsf 10;2s,sx tih+ie 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 " sue0p ,8u1d: 8atjqztfeel" yourself gravitationallyst ,: e t1p0j8q8uazdu attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at v 7 1gdnf92 pldq.9rbba distance of about 30,000 bg l7bpr19dq.9v df2nlight-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a ne zbtbq,w ;-6)us 0stsquare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the squarest 0u)ews 6-;,zbtbqn .    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits th uaqwltb5 f7+;e 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 tadf3 +dl,xck +he 1.5-cm-long sweep second hand on your wr+laf,+c3dxd kist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight 4vtbcn:fg yn;35 1ekkj81wnparound in a circle below you on a 0b31 kkg4wevnn5 t y:f p;8jn1c.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius oso:k j *i wf58klc7 f4oheg0ao) h6z1 R in a new highway is designed so that a car travelineo5o6osf8i j7hf*l4kzwo ):g0ah c1kg at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, thu1 ih.i2lu8g gp)mze/ e 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 speed of (e2.giump) 8h 1zu/l igapproximately ). (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.$\approx$    $\times 10^2$