Sometimes people say tvqb+9rgtb 8:g hat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is v br:+9bq8tgg wrong with this statement?

Will the acceleration of a car be therrs iv/rf0ir:kxy 6bg38kw,oy654t i same when the car travels around a sharp curve at a constant ivo/5 r:i0tfw,i ks6xy34r gr k8ry6b 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a ;r, 5 hxtn,wy9j* axmwhilly 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 level stretch ne;mn9xjyt w a wxhr5,*,ar the bottom of a hill?

Describe all the forces acting on a child riding a horsrm )7r9pq7x dme on a merry-go-round. Which of thxdrrqpm7) 9m 7ese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci zj+f++ud6e wurcle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaidje6uu++wzf + n.

How many “accelerators” do you have dn8q.l1n* 0x7 wphmpo in your car? There are at least three controls in the car which can be used to cause twp.xd1m0nhp*lqn o 78 he car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Figk sf2am1*li+ y. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest kas 2m+ fi1l*yand the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding 1h j: 3a4gj/ruyto:l )m7ethw a curve at high speed?

Why do airplanes bank when they turn? How would you compute the rm* ;qo8lf(uuj)(oia gnu8(dbanking angle given its speed and radius of the turn?m ino((8l(q*)gufurao ud ;j8

A girl is whirling a ball on a stri :ci5.nouy drlz0g00vng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a targety0 u:d5 ong0rz 0cli.v on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Eartfhowhe6 aj37)t(s iab r16m7 gh? If so, how large a force? Consider an apm(wf67s7oigb ha)1 tj e6ra3hple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would7 -rd,kg og +3ku8njuz the Moon’s orbit be differentk j 7rdzgn+o3kg- ,8uu?

Which pulls harder gravitationally, the chyb/evo p onk1z123fr q6e/,Earth on the Moon, or the Moon on the Earth? Which a q/b1v2nyerz kc1o6/p3e,f ho ccelerates more?

The Sun's gravitational p**y+hj zno7 ahyp:8z iull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consid:z8yaipjho*7+zh y*n er the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects8 oyc p5p/y+nj are at work? Do they oppose each othe8cj/ yo +nppy5r?

The gravitational force on the Moon due to the Earth is only s 6fewn,d3t ojzlx.((o-e3 tw about half the force on the Moon due to the Sun. Why isn’t the do w sx6w.(-jz,tneleft3o(3 Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sunuic-e,8vjya,q +ka t: larger or smaller than the centripetal acceleration of -8tvj:au a+k,yi ,qecthe Earth?

Would it require less speed to launch a satellite (a) toward the eashv /(b6-i umnp(k)bj mt or (b) toward the west? Consider thhm n )vmk-(6jbbui(/ pe Earth’s rotation direction.

When will your apparent weight be ) az +.wthaqr +,vjn)cthe greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward jh anw)v,)azc+.qt +rat 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 adversely af/vee g-q) pac4fected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32ep 4e /cvaq-g)). 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 “apparent weighxh0h;00/vv pbvvl2 bw tlessness” betwee/vv; hv wh2vlpb b0x00n steps.

The Earth moves fast- nzy-zdcj z)y8ag5r )er in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain.8 zzzyj-gd- r) 5yan)c [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 have a moon. E4 -ffx4kc+ylj xplain how this discovery enabled an estimate of Pluto’s mask4-+fyj cxlf 4s.

  The Sun's gravitational pull on the Earth is much lar.f a25rdgc x + rcp7) f+cwiqjb5lx)h2ger than the Moon's. Yet the Moon's is mainly responsiblex5.7dricaxlqgc wfr )+ h)c2j2 +b5pf 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 1980vr u) .dn m+7a1an/:wsxnf ma( $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ivzbs l;6c3yf9cie-d * n its orbit around the Sun, y fec*9c d;-s6v il3zband the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unifom-p c(vv.; huzre*s2cc)owwi35 l dl.rmly in a horizontal circle (at arm’s length) of rachoe;i z(. ws*m2rcv5pdlw.l3ucv) -dius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eart,af 3-8tm 6smqyr.eihe1ztc l(p * pn(h's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answe m 3 .,zpe6(rtmay1sq*lp8tcnih( - efr in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of 1m 1a a nq/zoz 9,tr7pwjrfn*.the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revo9 t. */j nzarpw amr,n7oq1fz1lutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a sb+yth(nl +5hutw)qn 9tring is revolved at a uniform rate in a vertical circle of radius 72.0 cm ,+n5twth+yu qlhn b9)( 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 1050-kg car canf5ptk ouah 50prou g40d7g; :p round a turn of radius 77 m on a flat road if the coefficient o :krpp fou o4t0 h57;au5gpdg0f 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 friction be ,bt21 vmir-dt between the tires and the road if a car is to round a level curve of radius 85 it-vdtb1rm,2 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotale8k7qg 65jach zis,ze5o/+ate a trainee in a horizonta6aasiq5 jzg hc ,e z7k+oe/l85l circle of radius 12.0 m . If the force felt by 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 r;jhu o25 : inlm:,vux q-h(xxootating 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(hl :oq5m:ux nxxojuv-h2i; , 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)vgx6dc bpk*. when upside down at the topv x*dgpcb)k6. of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) h+s 7 ntpyof2 ek:44xncrosses the rounded top 4ey2: tkxnpn4s+7fh o of 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 need toa1z dgc- 63jom make for the passengers to feel “weicj36 1 gmzao-dghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circlzj k2v2pwrnczsx9 3 24e of radius 1.10 m. At the lowest point of itz2z vcw3n2js p2rkx49s 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 rota*oyha s/ rx3 s-s4i4xnte if a particle 9.00 cm from the axis of rotation is to experience an accis4*x/so4 syh xr3-a neleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnv,wqpbun*1g9 ks m5)qb7rs* yival, people are rotated in a cylindrically walled "rb9spry m,wbns )7 5*uqq1kg*v oom." (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 rotaht-jfuak- (y/jj5we3m9i8k kted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cor- em twji/y53khu8(a kjfkj -9d 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, bn bx;za4p;,ig:-h jc iy not ignoring the weight of the ball which revolves on a string 0.600 m long. In ph-z; x;,4bciangi: j particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car trave my ne mnx/bx10n+i4;kling 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,2dhuhl+e8jk.n mq;o s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver b mv)2id,cik3 py 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 icvt4jh 97s mic;,p+ iand centripetal components of the net force exerted on the car (by the ground) in Example 5hcii7;m t ,+9v4icps j-8 when 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 accel4r-l/jwhy6 evsg )u)yerates 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 yr)s-/gyu )jwv 64e lhthe 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 radius 2.90 m . At a partvuco 7k 46y)leicular instant, its accelerc)vy6ekul 7o 4ation 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 12,800dqt )h u,8ysa.f 0nr+,9rkbewjbg: m. km (2 Earth radii) above the Earth’s surfa0ueabnbkf:.jm9hq dt .)y,+g r8s wr,ce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationa +6ofw7sgc 2xk0ys5y hl acceleration g has a magnitude of 12 m/f go7 ckxh6+yyss w205s$^2$ 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 dueh yqryjzp k.j 8).*1cg to gravity on the Moon. The Moon's radius is 1.7ycy).rjkp1z j hg8*. q4 $\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 Earth, but has the samk rsh fpj2rsk4ctg ;(((kss5; 74c uese mass. What is the acceleration due to gra2su 5th; kr(cs(fr7j4 kscs(s;ek 4pgvity near its surface?   

  A hypothetical planet hap6q;i8 f4eab)(aebd 8h4wkee s a mass 1.66 times that of Earth, but the same radius. What is g near it8k ad)eiw6pa44 hq;ef 8bb( ees surface?   

  Two objects attract each other gravit-bl z nef87d0jfy :e7bationally 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 gra.zzzpr)v5kjc0 bg,p 9:kau2 bvity, at (a) 3200 m 9 5)bpczvkpr,bz 2 zj0: ua.gk   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s ce rcf60yn:6 halhwz-4w e o+v4anter to a point outside the Earth where they n06 v6h:+fw ecl z-4rwaoa4hgravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mbvatvxpor6bey - hz,n/36(c 6 ass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monstrv6 /t -yn,p3b6xoz c(ve ahb6er.    $\times10^12$

  A typical white-dwarf sh*memgy. ptdkyq,1lx)3 *m f jfoe0 ,7tar, which once 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. What is the surface gravit0qh)3kxf*mf mg yedy 17j e,p*o tm,.ly on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in/m dbw-2wq,lw 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 twbdq l2/ wwm-,he 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 0. xn/ m,-l,n d+ff)4tgqd+pd9dx m t:rh60 m. Calculate the magnitude and direction of the total gravitational force exerted f drhx)9l/:d nddtm4tq+pfxn,- + ,gmon one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the s:am r5o +a-+lv;lyvf lame side of the Sun. Calculate the total force on the Earth due ma-v:o 5llyr;++af lvto 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 surfacem+6e4ssed gl0c) 1pi eeiud383b xa,j of Mars is 0.38 of what it is on Earth, and that 3a gems3,+ je0c1s6 pldi x8ie )ub4deMars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valm ldo9:rvms4*ue for the period of the Earth and its distance from the Sun. [Notl4sm9r *m :dove: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moviniy-d)kq/c y0pg in a stable circular orbit about the Earth a-dy qi0k)y/c pt a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite m ( z)f1d2o8o lcft.s94hurrb into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release o f tbr4loz. fm2ho8)1d(9rcus ccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if v imh0m);qgm6kf+nm l5tk35dzn5i e 9occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 3mi ngvkt) nme+ 6zhd5lqi5k5mm; 09f m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth ion -evqyuq ) lc9c-fs2/(7r ynn 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 radiuq/-vy2nyfcn ru(7c)qleso - 9s of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite heju42kc7f+r xre +gr;(m2lx w 8eq aoap5q(:nave to be launched from the top of Mt. Everest to be placed in a circular orbeq k lj2u 8c;xargn r4fe57(p2w(:+e qrax+omit around the Earth?   

  During an Apollo lunar landing mission, the command mo8cfecnxz qrgnht d--v3x91h6- - fr*wdule continued to orbit the Mfn8nf t-rd*eg-9 - 1 3vxx q-hcczrw6hoon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planexyxs zj1n;,m .sri*q6+ h:qmkt. The inner radius of th*x:zmn +,6 krxshm q.s;yqij1e 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). Whaa0ycj 8+q 6 8exj-pjqo:he l+p/kxir,t is the ratio of a person’s apparent weight to her real weight (a) at the top, /kq peaqh0+p c+ -oje88rjlx:,x j6yi and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cet7jbi5u l+w p5k;vcr0nter of the Earth's Moon in a space vehicle (a) moving at constant velock 0w55vjl piubt+ cr7;ity,     ----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 opkch,l8.wa39a c9i n+swpfe 0f 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 masshi e csn0awpp8klw3ca99 + .,f of each?    $\times 10^{29}$

  What will a spring scale r e;)5 b2yd/kk qd866t wzcsif8en4rg zead for the weight of a 55-kg woman in an elevator that mk)s i wc fzz8e 6q26ten4 gbd;y/dkr58oves
(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 etd qel) el-*-xlevator. The cord can withstand a tension of 220 N and breaks as the -ee) q lxldt*-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 p+v wb .ba kx3hnb6k45 8zynni0lanet with period T , the density (mass/volume) of the planet is b6nxbz +5i.n akkwny83b40hv $\rho=m / V=3 \pi / G T^{2}$ .
(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 Moo0 x , rq7odc1tj0tzhv/n (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s sur x70hjct,d 0/qvzto1rface.    s

  The asteroid Icarus, though only a few hundred meters a+0 1r*ecvipc3 r0ljq jcross, orbits the Sun like the planets. Its period is 410 d. Whael0irjqrpc3 *0 jcv+1t is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of , *pf; if)yu dwzb 7cc7ecr04pkua)q5 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 -.+7 gslj-x)jibhb oavery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distanceha7)b -.+jgb-jil sxo 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 cen9zmph9 fo5xt f ;ai/3dbiv 92jter 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 m w su2pr8bq3ea v(y t(9)nux6for the four largest moons of Jupiter (those discovere a wq2byt3emxuv(n)69rs8p(u d 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 known period and dis lx2.xw/cvrhd ns1:+ .mario 6n4zhr 0tance of the Moon. v: ha nrzx4r /c01nrsh+wi6. lxm d2.o   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moonsrd3t43vnw 1t k2zk4 dh, using Kepler’s third law. Use31t3ztwd h4n4vkrd 2k the distance 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 ci s.d v9atsu*fsed6iw v/42 u* ;)osnwonsists of many fragments (which some space scien4/vtss**2ivn9du6; f u ei.aowdws)s tists think 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 artificial "planet" in the form of a butd 2ghfd: n60and completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent2dg tn:dh06 uf 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 hanging vine (Ftvc54ji (5pr ublf;+s/ ,ddsjig. 5–41). If his arms are capable of exerting a force45u, djf cd5s(l;jv ri/sbp t+ 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 acceleration of u;g*xa9vd swz;;)hhggravity be half what it is on ;wsggz*;hx)h dv;9u athe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands awm x1ioa ;yyw-nelp;(,04icsn(a xe8nd spin in a mutual circle ,(mii18wx; al;4ys(a coxep y w-0ennonce every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotax)rmrfvu 6r fi(2ei0/cza..y tes once per day, the apparent acceleration of gravity at te.vc6z2fiy r/x ar)0f .iumr(he equator is slightly less than it would be if the 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 spacecrafd(afz ibsug,04 : x6lmt traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppositem6:adsg4u ifbz(l 0,x forces?    $\times 10^8$

  You know your mass is 65 kg, but w(ejo(r: f2 ec0nlu(gshen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is t gu (e l:one((sfr2c0jhe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rota) :h*ptcda;)rh1v(4qomb fad te about its center (like a tubular bicycle tire) (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 tph1 4t:a(dr v;c)db*o fmhqa)he 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. e8ljk0le ol y: f+tf;ii*0je+5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet 6h)eg uwjuvx7 e;*ay 9in terms of its radius r, the acceleration due to gravity at its surface and the gravitej; )vyu*7wx hua 9g6eational constant G.

A plumb bob (a mass m hanging on a string) is deflh8lwg50 uc5xz5ylp4 ;rw2uszected from the vertical by an angsc5r l 8hu2wl5xzz0upy;4w 5gle $\theta$ 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 banx .,n w w7izoes1wg7o0ked for a design speed of If the coefficient of static friction zw ,nwoeo17.g0x s 7iwis 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth rc(z1sfnzwlr :yfc*nr 3(j. 1o.t6cawere rotating so fast that objects at the equator wer(nsl *.c 3. azrn6zc( or1j frwct:1fye apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart c o32i s.;yurh3 wsx9lqecqfz; ,v x 8gtu1.w*of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant sp*ni z9o3a 0brjeed rounds a curve of radius 235 m. A lamp suspended from the ceiling swing janibzor9*30s 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 has been cln2d+u 7 ujeh6bkay *ccv,q.8laimed 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 en8. *q+6jy vc,h2duc7ua l bkperson 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) ad)mvrgy x7+ Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be aa )y)dxr +gmv7 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 t1.i r */ndvrl2hfhrc3 raverses 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 fcnvr2r*lh1 3hird /. the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orfc7v l v8*kr zq7.mot,biting 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 ]. (aqlv7 mfr,.z v7ockt 8*) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), afta -qpgm4 8znf pw -/5.el9etieer traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 ki8gl n z9-/pt4m-.pewa f5qe em . 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 shrve.ay/9cxwf r/( *erer im7* uttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abor.y9v 7crr/ eri/aex** w( mfeve 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 zwx.kydp4b ( 110jifu 3000 years. (a) What is its mean distance from the u 41k(w f1byxz id.0jpSun?   
(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 vaaj/w 9/cx5)x/.nn qkz 87bpp 2nvlgaw lue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make rea j/.2xg)ax8 7nlwqv 5kwp9z nac /nbp/sonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around epx xqa,+7w 0exd ylg01.nb*o the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yp.nwb*o 70 +eq0xx1,d yxlg eaears 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 square 0.50 m on each gzpzstrv1x )my: 6(e3side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass pme)1px z(sv:z gr3t6 ylaced 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 E9seys; yd wg2-f36rxqarth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long swec9m7b5ey w4xh jc e/woxf1* 0bep second hand on your9j/mbbocw5h ee xfyw7x* 0c14 wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a h0ay3+n. w0 3 vd, v)fzqxbpzlcircle belop+ nb zqlhd0).x0vfvw3,zy 3aw 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 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 car trav8t49bhjf z: zbelbh8z4 jfbz:t 9ing 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, the Acela, utilizes tilt of the cars when nev0nu- * n-u0 gi :eoqh+j56gohtz( tbtgotiating 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* b-h-0tgin(go6jqzt0euh+tvo :n u5 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.$\approx$    $\times 10^2$