Sometimes people say that water is removed from clothes in a spin dry..6-zopq/o8 fkkl4d;n: ds jynwy (swer by centrifugal force throwing the water outwardfzqjo .ndy -lk6 o.pn4k ws/;:( dwys8. What is wrong with this statement?

Will the acceleration of a car be the same when the car travee ar. 7a0l2qw0r qvq,ils around a sharp curve at a constant 60 km/h as when it travels around ar,eavi00q2 a .r qql7w gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a 5awmycc:j.vf**tjs81 9 mr ichilly road. Where does the car exert tjct*f*yir:19vaw jm.85 scmche greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on zq(nfzw qn8(;op :0sm a merry-go-round. Which of these forces provides the centripetal acmz0q :qzfnw (8p;n(so celeration of the child?

A bucket of water can be whirled in a vertical circle without the water z-5e;ehj jnh2spilling out-ne5 jh2zjh;e , even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cottfd2pth5wp5 4p7g- i5zjc b(yvz5 1entrols in the car which can be used to cause the car to accelerate. What izptfwythp7 ct5j 5 4dz2 (p -e51gv5bare they? What accelerations do they produce?

A child on a sled comes flying over the crest of . vot dtc sd3q+juhb4mw6:7 )ya small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hiltw 3.j7udbhdv o4 m:6q )styc+l. Explain this decrease using Newton’s second law.

Why do bicycle riders lean *hl-:v m(qcxb luo asv.kr9 /2inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking a t)x :z -m:jm.u3hg2fl omn9rungle given its speed and rgmxo:2 9)uhm r.n m:z3f-lutjadius of the turn?

A girl is whirling a ball on a string a;.xkyu( :ju fhround 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 other side of :ju.x;(f uk yhthe yard. When should she let go of the string?

Does an apple exert a gravitational force b;qnxb:38l3dg 6qkidk n y69f on the Earth? If so, how large a force? Conside qdqb6ni3n ;l36b 9kx y:f8kgdr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wa ap g,8)6usleq 6mhv5kys would the Moon’s orbit be diff6 ,epgm8su)ak6lq h5v erent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moonxvyk7wc . ok hz4x92)j on the Earth? Which acceleratex ) kx4 jz2y9.7ohcwvks more?

The Sun's gravitational pull on the Ear:t2vb nqyp -)-2kuvqlth 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 of - 22tu qkb)l-:npv yqvthe Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are ttorr ;. v1h /opa7m:pat work? Dovt1 r m.rp:ht7pao; o/ they oppose each other?

The gravitational force on the Moon due t(-luu y ziq (x0zl(fv,o the Earth is only about half the force on the Moon due (0qy (,fzu-llu ( zxvito the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratd pvnhwx;*qs/8y n 3w fe7rec20.om9lion of Mars in its orbit around the Sun larger or smaller than the centripetal a0cn9x s ed*np/l.h woreyqv 7283wf; mcceleration of the Earth?

Would it require less speed to launch a satellite (a) toitls 9cuuyoj jq o5-j2.0e/y)ward the east or (b) toward the west?9o0ujyc5/ jq ly) toj.i2s eu- Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured zi+ yg5j5*+,eifukyf by a scale in 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 least? When would it be the same as when you are zue i*fyf5g, k5y++ jion the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space coiiz/ p847qk jdhgv-. d yhy;be (+1fppuld be adversely affected by weightlessness. One way to simulatd ;bhgh1yf zpkq4(+i7 jv- y .eipp8d/e 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 other aspects of gravity you can think of.

Explain how a runner experiences t )h2,k *sm qrffct4h4“free fall” or “apparent weightlessness” betweekh4qs,hf 42) tmtcf*rn steps.

The Earth moves faster in its orbit around the Sun)xik-ou711ul)etb h y 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 the plane of its or)ou- 1bu1x)i7telh y kbit.]

The mass of Pluto was not known until it was discovered to have a moon. Exsl*y/wjts0 y4 plain how this discovery enabled an estima s/40stywy jl*te of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thanjflf 2/cu5wabfd3mx cih; .s. i.o /z0 the Moon's. Yet the Moon's is mainly responsible for the tides. Explain.h/; 05fjiuf.d./ ax2zfm locwcsi b3. [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 1k(t 7e ej scv0g(()2 jm9gwblj980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 aroundjjv+l w -/e,m ca)w*6zkfmf6u the Sun, and the net force exerted on the Earth. What exertjlv c,*maw6 6-kf m z/wue+f)js 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 v/ab16mo,s ceexerted on a 2.0-kg discus as it rotates uniforml1mcs ve6 /b,aoy in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shutt4f-o wgz*yp2u+znw3hle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleratuzww-4n 2p 3 f+gyzho*ion of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the e2 hyankx ol( 1u0yg46odge of a poku a2 0 61ny4o(oygxlhtter’s wheel turning 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 v/g2hkn j/x1i certical circleikn1 x2/g/j ch of radius 72.0 cm , 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 1 t+)ve3p 1tcdrz42oi7jt 2kd2d1k yju050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between t7 )jkotetk4ut2d2dj+ 1 2idz3yrp1vc ires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient o zmr 8xz34yfvmdzn*00 f static friction be between the tires and the road inm0x0zm * 84dfzvz3yrf a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is bmlf pd7 vgc1gexf229q9z fx734 wx2ddesigned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt b74 zp3mffg7c2lf2x b1ve x9w9gd2 qdx y the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntab3xd wlq /jwced 9qm+(/le of variable speed. Whedqcx +jww3 mq/edl(/ 9n the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at7n;ibuorgghdv-/0i9kk vr *;g pd 1(n the top dgi7 krpndbv-rhk*(; /g;91gu ovin 0of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the r)snj1k i9ysp, ounded top n,)p1s9skj iyof a 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 wsstr .le*53n need to make for the passengers to feel “wet* sr.5swl3enightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad 7i w /g4be0)rzwnxnr.ius 1.10 m. At the lowest poinr4g/rnew x.0bzn )w7i t 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 cm from the aqxdflo*yg)aw q/r-q /ca :9a.xis of rotation is to experience an accelerati:/ ar9-gxac owl */dyq f.qaq)on of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rop/4 dw rhe,+0n ai.hqftated in a cylindrically walled "room." (See Fig.a4i+/ed nh.,0 fwrpqh 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,qyuacjs:* hg-c0(i y in a circle on a frictionless air-hockey tabletop, and icgay0: sih(cuy, j*-qs held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring thee.wictjpt.m9 e01wq - iqs(f ) weight of the ball which revolves ocp 0tfi.m.q(jw9iq tw1 ese) -n 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 i 5d7k om pc:s8t7 ;r5aks5flras 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 masse q8nn azku66f24 c/87btgse fzs $ 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 -/)f-l yi7dhrwf :z2 m/(.qseovvm /pg2 lxkc 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 componet: )am92z)d whpq*i xfnts of the net force exerted on the car (by the ground) in Example 5-8 when its spdix*)w am 9 2qt:zp)hfeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit arv)-gk 6bn xql;ea, 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 t; n-gq6lbk)v xhrough 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 inl.wlfihk:941q g n;00 imnlkz a horizontal circle of radius 2.90 m . At a particular instant, its accfhni00z9:gmk1kl .i q;l n 4wleleration 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 (u1 bet*2uby it4r4xm(vs- n*vn ch -/q2 Earth radii) above the Earth’s surface if its masst b(tb v1msh*-* nru /-2xqu4cniv4ye is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a m)(4l1p, n bwka6vl sxu plv-7pagnitude of 12lkbnplw a 1)s4xv l- (,upp6v7 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moonq-: pp(ux upgpi3vzs0v9+re 7. The Moon's radius is 1.7zipu r9vqs0uv p:p(+7epg-3 x4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of ze14nev;q8y mEarth, but has the same mass. Whmez8yen ; q41vat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same raqg(*nvy 7tfd 3dius. What is g neafn yq*(t3dg v7r its surface?   

  Two objects attract each other gravitationayqq-rgu8o a76 lly 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 (aqcu6.pa3 dq/a ) 3200 mqp3aa /.du 6qc    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’1nhf7oiik ,gu t2e- 8xnia0 z/s center to a point outside the Earth where thegravita7/kite, 128na igiu ozhf0 -xntional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hb3h5,/iz vjcv pv27nxas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity p5v n/xv73,ijz2v hbcon this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is+j b djb1j08v t zn.ali4jgx).re yk)4 now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What isb))xjryjla.jj8bnez+4d . ik gv0t1 4 the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts ek8f2r7zxp*u8mgwe 0d ndg7 5bkc04 pfeel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km abgpg w7fm nxe5 4d8*kcpe8kr0zud b207 ove the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square ofcrhy9 p4uczku43 2: yb side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by thchp 3r49zu2yb:c4 yuke other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same 8/v7-cf: : nrq4euawq d+ce -iveu v:mside of the Sun. Calculate the total force on the Earth due to Venus, Jupitac4q/:r iudm: vef vwu -8e7nev+q-c:er, 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 Mars is 0.38 of what iy yg a2e 0se4zc11bu8ft is on E0 1ge1y yua4sezb2c8f arth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the fg;j (/p*-.uwcrrk5 pxfuc4f Earth and its distance from the Sun. [Note: Compare y(5xfcp;fwu. *k/u rg4 cp fr-jour answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of 40 lt*3uw i tstbkvjp(72br; a8lsw:s a satellite moving in a stable circular orbit about the Earth at a height of 36 (wuv28jb:tas;l r 4iptwls*s7k3t0 b 00 km.    $\times 10^3$

  The space shuttle releases a satellite into a circularqb/99 1 tcwvmi orbit 650 km above the Earth. How fast must the shuttle be movi mqi1 t9v9c/bwng (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyn;u 0g f7wo 3gb-kl7n)s4nh eklindrical 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 Quest3w ;esl bnu)0o7k k7fnn-hg4gion 21, Fig 5–32.)   

  Determine the time it hwbrm*z)1s3: k)w+tto ):dyk k zm4wwtakes for a satellite 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 which is very small compared to the radius of ymo3m): *wt 4)dk whkb+sw1w r)z :ktzthe Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wouv9uw6w za;(gdld a satellite have to be launched from the top of Mt. Everest to be placed in a circu6du z9wgav(; wlar orbit around the Earth?   

  During an Apollo lunar landing mission q14ix; zu;uro, the command module continued to orbit the Moon at ;ro; uqi4xuz1 an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn sl:jm3 yvd68- gc:e-z/np.gh jxxi8e are composed of chunks of ice that orbit the planet. The inner radius olgzx8sed i6n:3 -j vc.h:/ gm8epy- jxf 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 g ci l9q//dbt;(see Fig. 5–9). What is the ratio of a person’s apparent weight to ctd/ ;g/bq il9her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wz1z:jfcf 9a9jhv b 73height of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (ab z 3j1 vfj:a997hfhzc) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equ;0/zwv4e,tg4mhjewc al mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbiwe0wcg4h;/ evz t4jm,t 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-//l-k izejh s+/ng c8ckg woman in an elevator that movn/shjeig +//8cl kc- zes
(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 suspc/ag nt(emns2p qgxb8k1v62/m 2 t (dbended 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 ancd m1 tgb/gx2(8(2bknv 2s6qpm ae/ tnd direction)? a =   

Show that if a satellite orbits very near 3gik qhfftu1;0)y)2u1 ce rr jthe surface of a planet with period T , the density (m3f; )u20u)jhic ey k11fg rtrqass/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 determine the peri v7cgtuu/*w i-od of an artificial satellite orb/t-uvu c7gwi*iting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few e9w-z) va6 (8cv tkazuhundred meters across, orbits the Sun like the planets. Its period is 410 d. What iz8(t6ca- u vew9akz v)s its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc;q 9rh ledv/tck 7af)3e of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very clotw7z,nw-853r+gy .uib ufoty)ly ns9 se to the surface of the Sun on its closest approach (Fig. 5 -lno9yu yt) 5n . w7urtw,b3z8yf+gis–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 distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of th) n n3ws -l/syhft*tih;bsm8ba2 4-cce 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 l4udl: sdimzll7 -)5f for the four largest moons of Jupiter (those discovered by Ga4dsl7ld ) 5-:limlz fulileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the4 l58 yd: 8cdneqjo x+c(ake3t Moon. 4e8l8 aytd+e3q 5(oxcn j: dck   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using K5yg0 gvx,pzx, epler’s third law. Use the z0 ,g5 xpygx,vdistance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consin:quyb z0p (1asts of many fragments (which some space scientists think came from a pla1 :za(nqu b0ypnet 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 artificial "2laaw5(4 ; zsvora,uwplanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always nor 4,wlzva( w2;5 aasuoon). 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 nm:9jriod 8cd5/k ;w phanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he c5d :kj;m pn8io /9wdrcan 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 be halfk6 dkl+ m5a:+r -cuehu what it is on tu5 a k+r l6ecuhm:dk-+he surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mu zk sjj ji/8ish 8,s-97+z9pgnz qzy1gtual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60si,g/zzjs h nk8s-gjj 1zq i8y9+pz9 7.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparen + awxxb82e5or qcyt w5cz,0:c 5m pm+,iwj*ljt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude w: x*ay5 2jxol+,cm+m q ji5z0 wccw8tbe5pr,of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraf;o 6w3tjf l9qy65-yxotw *lk ft traveling directly from the Earth to the Moon experyxl *39 ;o- l 5ftqjwtwof66ykience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on as(pg (.kkm,ju bathroom scale in an elevator, it says yourm gk., spj(ku( mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboutsd( )fwkb ;ecsd1y btq(p2d3 n76e kc: its center (like a tubular bicycle tire) (Fig. sf ctw:eb()2 q3e (pddkyb;d7k61nsc5–42). 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 lootq)*m:mmt9gk*19va z gzwy,fp (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 ir+ xd3k3nr7egr -i8qthe mass of a planet in terms of its radius r, the acceleration due to gravx-r3g e+qinrk7 ird83 ity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging ykggq5+qwqi de3d(3:t z2d2r 7 npd9ton a string) is deflected from the vertical by an angl5e d+y qdt d zqd:(ni933q2 2kgrtpwg7e $\theta$ 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 cnw, v)3ink(tioefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the cu3i(n, wn)itkvrve?

  How long would a day be if the Earth were rotating so fast that objectse) q)zi6:wha g:sj ) -pv+tvxw at the equator were apparently weightlesjqxhes :):a6 +v ww-)) pgtzvis?    $\times 10^3$s

  Two equal-mass stars maintain a constant dist:sx( d)ll2ro np:/c 6vx1psd6s ,abkbance 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 r 0-7hsnh k:(ku 6yylajadius 235 m. A lamp suspended from the ceilinjh7 y: h -yl(0nkusa6kg swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it h paszo3jpy7 bj/ 97*gs9 )j8jfaiiri;as 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 g 's. Calcbaf7 yiaj/z8sj *99io j7jpi;p 3s gr)ulate 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 presence of an b; ,pnpdh agf+ q82kj;extremely massive core in thegfp;;ph +2a kqdn8 ,bj distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of 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 hill and valley shown .e n-u1t lt: hi p lovci38zvs1n(77zhin 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? :i-cuvz3 v(1h 1l 77it8nzshnlp.o te Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) ut9qy9pakz)o,vep + vk5ilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite. q9a)+ez 5vp 9kk,oyv p   $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, ist6ze8; ,skcrz meant to orbit the asteroid Eros at a height of about 15 km . Erost8;rcs,z z6ke 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 vi/pgrz29 j41f3j8y nn/c 38 ffs5uprz u f7yathe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the cfn u 42 ru3yngy3fj i z79r8p18fp/azvs5 f/jsame radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance 5ju,s /cjf+yp 07rrpz 3u*gzddn7na2from then rcsz5d *z7uy02,7r +jdgaf/pu 3pnj 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 k1te5o clcoymq)9c5;c8cu) x be if you could actually "feel" yourself gravitationally att cc 9koqyuxc5 )m;l8c51)oc etracted 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 Gsgox9 ti-* 9)j1)cgpp,fi vcnalaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centerg)91ivotxg c9p,f cj *)snp-i $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side.o3,ye bmq n :.ipx5fd5a*ge u2 Find the magnitude ay 5o2x.fuapn*e eb5 qgi3:m, dnd direction of 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 the i q- x8e4oxsc rz59v3zEarth $ \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 bh0lm /7)4 cxdwg;g0pc*cabqthe tip of the 1.5-cm-long sweep second hand on your/apw4b0qgml*0x;h) 7g dcccb wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroundsv4 (n:7qtzux 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 thau 4s(n vqx:t7zt the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwaypyw18a3lwvn or a*5k. is designed so that a car traveling at.a83na o5l 1k ywpwrv* 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, the Acela, utilize-mz+d lhkoezr-922tp1 ty : xbs tilt of the cars when negotiating curves. The angle o ylek rbmt-912hozdp -z x+2t:f 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 (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.$\approx$    $\times 10^2$