Sometimes people say that water is removed from clothes in a spin dryer b 58q vslfxq4h*/i7 clcy centrifugal force throwing the water outward. hcx5sl7f*q qc/ i8v l4What is wrong with this statement?

Will the acceleration of a car be the same when the car travels aroun:he ;mf1( acaid a sharp curve at a constant 60 km/h (e:1fmc ah;a ias when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whet.7o 1axf v+)oyynrcry (8/f1 budn.bre does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretchofny(yx1d r)yn .bvac /1t7u8 obr f.+ near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round.smv:2f 1o p- o8ekqqn3 Whicvfq3 ep k q1o-:som8n2h of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a verticah3fr m 8:zij+3 ni5axml circle without the water spilling out, even at the top of the circle when the buckix8n5fzmmj3ha+ ir: 3 et is upside down. Explain.

How many “accelerators3ilssu d.tfid x8tk9;(3tl n ,” do you have in your car? There are at least three controls in the car which c 3, l.; d3ut(kn9t8sxtidlisfan be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a sm ;mvk.og6ms 4av9m- kjall hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal fo;sv- gmj6mk.9kvo am4rce 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 lye i,wr d/)kpgkab8a+ qw-8 x(ean inward when rounding a curve at high speed?

Why do airplanes bank 1nue+ o 6mdkmj4kc;m2when they turn? How would you compute the banking angle given its speed and radius of the turn?nm1ed+2km jc;4 ok6mu

A girl is whirling a ball on a strigq0w.w9ryg1u ng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the otheqwr1 g9w.ygu 0r side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Eetf9qk-u nz vn bk,.+tvx 8r/2arth? If so, how large a force? Co urq, t8.k+t /nx- vnzefbvk29nsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double wqps-jiqk 0z; -hat it is, in what ways would the Moon’s orbit be differe pqj-qk; s-zi0nt?

Which pulls harder gravitationally, the Earth on the Moonkt:uqeu0nbju l: 5uc,jtwf-1e1o /i- zf1p o8, or the Moon on the Earth? Whnulk :fe/ue j-qf 5wttp 8ub0,z-o:11jociu 1ich accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Mo(wma/h3 jli :mon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenlmijm h w/3:a(ce 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 effects ar/or)j()i5ucoz+f22 0asqfadfvik p5 e at work? Do tr ) afc j/25fzuk5(o qpd+v ao)0f2isihey oppose each other?

The gravitational force on the Moon due to the Earth is only about half ca35 qcrl(//sr 4 shwlthe force on the Moon due to the Sun./srs l cw/ qa4(3rchl5 Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleev)0if 1u;rtvr0 xw-r0 cno,xn(mt;x ration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the vrtn0rixc-;xerv t( u; 0fw x,)o0n1mEarth?

Would it require less speed to launch a satellite tzn5l. 7:t wrwh6 k8of1u hjk)(a) toward the east or (b) toward the west? Con h :8t kk1 z6wht)ru75flnjow.sider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a mz r(d fjd gsl-/:h1g)voving elevator: when the elevator (a) accelerates downward, v fj d )/1s(:dglrzhg-(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 be4n2sj)* xek bb 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)2* k4bns exjb (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “app8smnvsdlo ,l8 ha) 40parent weightlessness” between stossla88 ,0hp)m4nlv d eps.

The Earth moves faster in it3j q5nbo7-rw ws orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, oo7bwnw jq 3r-5r in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to h.g*ww.z 5t0dssk+ m ceave a moon. Explain how this discovc*.ks g dms0t.ww+e5zery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is 6:wup2tk *wachzr 6z0much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diffpw6rchz0z2 wkt:u6 a*erence 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 e+le 7grz v 5 uhmc+7n,yjfg)71980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acytvg1p+ 2qo.kceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Asygtqop . v12k+sume 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 isq j ur:xyz6 : .sxspu6f;ngb)2 exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of g zf y u:s)2u sjrb6p;:.n6qxxradius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surt(b4 lib +ei3nface, and circles the Earth about once every 90 minutes. Find the centripetl4tib i(3eb+nal acceleration 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 osh1acicnxb n)agpt7zx57fo( ,( ;en+f the acceleration of a speck of clay on the edge of a potter’s wheel nb;z7no 5)sxei(+ch,x7ct g na (fp a1turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revoxu6hzz 1 h s btd1c.u: cmh6q6tfe1qho k9-39elved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fibheect. h1zs :qz u9d -co 1khhmf619xq366t ug. 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 round a tupez+ 3ws kbm )ar;a/;irn of radius 77 m on a flat road if the ;)ik + abm;/3wzaprsecoefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static audk+nweli96 )xor,*friction be between the tires and the road if a car is to round a level curve of radius 85 m at a sieauxow*d , 6kr+ 9ln)peed of 95km/h ?   

  A device for training ast29wg 9tlyt/,b d/ gyjbronauts 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 times her own we/y/ yb2gbjd,99t ltw gight, 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 l0tk up.dly)+mox 5 q2cm from 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 re)lu l5xm.k 2y p0doqt+ached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed71; :jpx rmfrr must a roller coaster be traveling when upside down at the:1fjrx rrm7;p top 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 9:pm a*/xyo,ku 50 kg (including the driver) crosses the rounded top of a hill (radiu :m, kp/*uayoxs =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 need todbbgcpx9) h4 d3)/ ygk make for the passengers to fe3ybg)4 h gcxp) bkd/d9el “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vert9pwp3s- o4 kswical circle of radius 1.10 m. At the lowest point of its motion the tens4 wpk9w-ss op3ion 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 cm from the a4sstfl qh;06h xis of rotation is to experience an acceleration ;0st46 fshhqlof 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "r;6mosn0 pc h lanbr/69oom." (s0/lopn mc66r;h ban9See 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 g)l2qt: q:uf dfrictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blo q)gu:qdl2t f:ck (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 , precises0g-cg ko4u7gq1xt;5rx qb2 fly this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitud-oqrkfb0;s2 x utqcgg4xg175e 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 ra7 h(da86njxr1wxxr :ddius of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses lquzr6k(ml/ie 1pge b q0*n(6$ 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 evasu9rxnp/3v6 he.hzx + sive maneuver by diving 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 comp+(d3 iyjirr q0onents of the net force exerted on the car (by the ground) in Example 5-8 when its speed is rr3q0d+ jiyi( 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500560uq ,s.skrs quxds5s:w u j, 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 tssr u,565 :w. sjdxk,suuqs0q ires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal v-) -oiplex 72tjuv4uh*o2ez circle of radius 2.90 m . At a particular instant, its acv4 eh*-z2ji-)vole27 touupxceleration 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 grav.hzmuaqpov 5.sas l sy,1x750ity on a spacecraft 12,800 km (2 Earth radii) as5 .s0hypz5u71a,avsmx q .lobove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a c ,gl cdt zt*/6b8act0zertain planet, the gravitational acceleration g has a magnitude z tz t60dta,8/c*lbgc of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on edq0+rni xq6y 1 i(3bgthe Moon. The Moon's radius is 1.73gbq+iq d0 16ry(xein4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 103 tfxc:v f58h i/ 38mtlv7zlrs uxb/r.5 times that of Earth, but has the same mass. What is the acceleration 8x:c 3i v3/7l5r8zhxmt0u vr t s/fflbdue to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. rkj *cb 2p.n/eWhat is g near its surfenbp .2ck /j*race?   

  Two objects attract each other gravitatiob jzy0 ie2l3*znally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a)yt7t; r:8 fjy: jyp0gf 3200 mj t:y7 pj0fry ;8y:tfg    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earh(f0jh83 p kvokf7 *o) fkh-ygth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is h vp kgjkhh 0k-f( 87ffy)o3o*$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times twz*lw1aex 5clbci 2,.he mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity onz 5w2a. l,cilewc1* xb this monster.    $\times10^12$

  A typical white-dwarf star, which once was an amg*faylps3+; verage star like our Sun but is now in the last stage of its evolution, is the size of ou3 fls yg+pa;*mr Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the sp;18wytvs vh+ uace 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 calculati8;t 1vu+ws yvhng the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side /r zucxf0ur2 50.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the o5u2zxu0cr r /fther three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the34elo:- wvvlfdo8 7wt Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planetewl8odwt:vf4 7- olv3 s 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 acceleratirf3 k uqg/)-ftk/yg +uon of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’q+r/ ) ufutyk-gfk g3/ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun ir+(gsb n58ln using the known value for the period of the Earth and its distance from the Sun. 8 (brg nl5nsi+[Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelliqcnv md; h-i8;te moving in a stable circular orbit about the Earth at a height -8;;ivnd qmchof 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a kg* ngjt+* ,;qvci5x ocircular orbit 650 km above the Earth. How fast must the shuttle be moving (relat ;t*xg,5jgvncq i+*koive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotzb3z2i4l0,c /;11xlv kmjwr2kk(vszj bm1 ltate 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 21, F /jvk1vjslt m 0mi21;3bwbxkk(zc 4l,lzz21r ig 5–32.)   

  Determine the time it takes for a satellh)d+;l) gmkv.ei*jbd yp 0t.eite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth*ee)l..t ik+vbj)hg md0p; dy 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-n- /d kcf9q*yu ncwz42u ddb4 from the top of Mt. Everest to be placed i f/4kud2wdy 9un*n q-bzdc-c4n a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module a,yqf ov: q,:scontinued to orbit the Moon at an altitude of about 100 km. How long did it take to g:,qy osv:fq,a o around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planeth(vc8- ,es5xvar d/yt. The inner radiusv dhxec (,5/-sy8artv of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whatz4 q:yl/cwuzc +wsb)l. o6, zp is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bo,wlocs:zpzuqcbz /4w+l y )6.ttom?
(a)    (b)   

  What is the apparent weight offx2s38tbm *alrcql*q0hbq 03-u xms , a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movm8q0blhsx* u 02 c*q,blasx3rt3 qf -ming at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-o+ mt3 xdu..jqstar 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 midway between them. What d+t3jqxmou.. is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator tha 9rtr;69b-sml;f itkj t mbk ttjfr-s;9 9i6rlm ;oves
(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 elevatorqo/g8vp; z2 ek. The cord can withstand a tension;vegzq k p/28o of 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 planet with pndty :nbu, ;1uo;q,e heriod T , the density (mass/volume) of the plb du,qhen,uno;y1t : ;anet 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 thi 1vr7 rx-qrv/e period of the Moon (27.4 d) to determine the period of an artific7vq-/ rvxrr 1iial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though q:v+m/ h2 0a,jwbss*srncy m(only a few hundred meters across, orbits the Sun like the plane0vwycr mh2q* b,s:anm ss (+/jts. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of ;f tldkv09:c2fhi0ic1 6 pmp x 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 roughlu9 d6x,i n-dhny 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 oud-n 69 hd,ixnf 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 distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy( 8n - :2pazoj01hox6ww hilj1v uxf,f $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 larges cc;oj1l k7; ;ded:veet moons of Jupitedl kdeoec ;ec; 7:v1;jr (those discovered 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 from the kns)x ve;gyv4747en: gkyav 6hvown period and distance of the Moon. vka7egg;4)xyns6y4 7:vhvv e   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jm*l:j9gzuiit x 7bz5pbg8q2;upiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. 5bi; 8gjqlt*9g7ubzz2ipm :xCompare 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 e qw2.-:ra jsasome space scientists thwarsq:jae -2.ink came from 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 tale describes an artificiah5 k0j4ip czd3l "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to thz3hc pk0d5j i4e 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 hangin(nn1n ; - 8xomqw-klx r.9gsw7kqmbs+ g vine (Fig. 5–41). If his arms are capable of exerting a force of 1(89nwq n+w- kxbqomsxkm; 1 -sl.rng7400 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 acceleratioj9 j la*f .mms6 g:p )r/-s2zij23cvl+lcuku jn of gravity be half what it is on the surfacsfrl2a ).-si+zcg/:lvmjj3 m *l ucjpj9k 6u2 e?    $\times 10^6$

  On an ice rink, two skaters of j4 me* u5jxdfz*-r b,nequal 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 individual masses z*n4e-mfb5 xdjj u*r,are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates9x(+v:enxff 92gz nolla 85ni once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if ofi2ex zn 859lxn(9 f +l:avgnthe Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trl)n k-u/ndozo/siz 1/aveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite f-z/o nz/olnsid1 )k/uorces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathro+ky5 gsxp9n x2om scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directi+x2 9xk pynsg5on?     ----待选择----upwartddown 

  A projected space station conqpfsrg2 qa;5r2 0. hynsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). Thr0qg5pf 22 rqns ahy.;e 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 ifa/i rp kr;ip:)b h2;on 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 fp3fuqc6t*at * 3f2 zjthe mass of a planet in terms of its radius r, the acceleration due to gravity at its surface andtjz6 *q2c3pt f*ffa 3u the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deff 6sndm b5,d2flected from the vertical by an afd2,s db m5nf6ngle $\theta$ 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 ttc5rnok am 3fm:p 3j/p/,x*bi he coefficient of static frnx/pfm ,3/om :pkj* icb5r3 taiction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if t*n8 lx v42rak1 yotai*he Earth were rotating so fast that objects at the equator were appaykt 8 iovrl an4x*1a*2rently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a con7 -8hoh kdvj-d*yfx*dstant 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 speed rounds a curve of radius 20s34flt )3tpx k2+hestr dr4;*z blhj35 m. A lamp suspended from the ceiling swings out to an a4lr3js3e;t4)lhxk2 b d0 tr z+psth*fngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has bet9ry*a l/)u .rmnc;y3 of.zw rtkf 05fen 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 g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the folf5y f 0wf t39/ .zm )ayl;to*u.krcrrnlowing 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 Teldei,x*3 idk -/ sgz1 fm7tp- 3xivjlj2escope 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 escapeig /i3etmi xvk2dfxp 1sz l*d-3-7,jjs). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the his hf0k,ev mlr3-m +r(bll 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? Lig-+3,(lker b0hrmmfsv htest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 6fcg a+a5t; )dm4d xkdsatellites 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 approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellga dt)k45;a6d xd m+fcite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvpcr 6fos q 77g9:egqob:va 72vous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 7 s:2p ofrqo6ev:g9avbcg7q 7 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 gdrg .)kza q7*in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellitq .)rgg adk*z7e (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Wn1a3w9 y4 rkdehat is its mean distance from the Sn1d49ykra 3ew un?   
(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 "feeyr 5z*8a+zbzof(e+*gnr 2qk al" yourself (+ 52 r*kzo+*rybazq azng8fegravitationally 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 (Fi0f.xpx k+/ v;uqcq(t1zdd ;.tiha 7hkg. 5-46) at a distance of about 30,000 light-yearphix.dk1;tfd zkqvc.q7u0+ h txa (/; s 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 - za-5y to dq6hsz67salocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of6z5t-q 7shza 6o yad-s the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thevnsb4d .;4jqh dd 4nr;q8:my:auu l4a 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 acceleratio*m f-rfqisq3g0 9mh c(n experienced by the tip of the 1.5-cm-long sweep second hand on yf *g i(sq -q9r3mm0fhcour wrist watch?    $\times 10^{-4}$

  While fishing, you g5 tonlb*4 -bzn9kyat7y*h ;wl86 t4bgng (n bbet 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 circle every 0.50 s. What is the angle that the fishing;yzwbn*ybkt4t96bh74n o tll8g(ng5a bn*- b line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a caxv +j sqf5ln.dh+*fit24a0vnr traveling at sps2 av t4n+d5f+ vl0h.jq*n fixeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tis4dgsdsm 7 y+/lt 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 passe4ss+yg dd7m/sngers 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.$\approx$    $\times 10^2$