Sometimes people say that wat*a75sf5km( w:1pmykyf ro a+qkq)ol j9cz) u3er is removed from clothes in a spin dryer by centrifugal for )y:y*us f5m(wm9cj rolkqq)a75ko1z+3p akfce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sn ua7ar tyf8bs*e q3.-harp curve at a constant 60 km/h as when it travels around a gentle curve at the sa-fy a3s 8a.ru7 qb*etnme speed? Explain.

Suppose a car moves at constant speed as wllm*vr5)v7 long a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the botlvv)7 5mwr*ls tom of a hill?

Describe all the forces acting on a child rid:f gskz t7a :)fzum47ding a horse on a merry-go-round. Which of these forces provides the 7f)tsz7zamu d::k f 4gcentripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillingxm u /bh v,v/g53*2w(* qhbxsobgin i *p-qxm( out, even at the top ofw*v*hqg(*x q/ -p/nxmvb5 sg hb ii2,(ox mu3b the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? oz:8)d fw tqf8There are at least three controls in the car which can be used to cause the car to accelerate. What are they?w :8z8q )tdoff What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown e3xy 7bp;ntqf huz2 5n (c/-kzin Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feefpz /kx tb;-qc (nuez5y 73h2nls the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding av/(bb c o xa.v(t do)3kr2bn weeill,+;b0 -gi curve at high speed?

Why do airplanes bank when they turn? How would7yybq/6cji qoc 1kk 7 iyx+2/w you compute the banking angle given /2w1+ kyi7icq/ycb qyx76o jkits speed and radius of the turn?

A girl is whirling a ball on a string around her heq qo h3wiz okn5k+e)pa z+ ,+-zoro,s+ad 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 the yard. When shouldnk,5e+ o, a+rz-zw+q )q3hzskoio o +p she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, xixubsie2 6nn,z9k,0 how large a force? Cons,kxs, z 09x6iuein nb2ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dv5mso4 doya8;wosq4 * i)1 l3zz7ot0 ufyy/ncouble what it is, in what ways would the Moon’s orbit be d o /;)zy0y5ctood*uslo71 s nv4za 4yw38mif qifferent?

Which pulls harder gf ,k- a/+xxghtkr ybjzj) /14jravitationally, the Earth on the Moon, or the Moon on the Eart1kh4 xj/g)yr/jxfa jt kz ,-b+h? Which accelerates more?

The Sun's gravitational pull on the Earth is mu (uuy6x eq*-jw(k, :e1w g jc3qcy-povch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differencee-u*3cj (vwc- jyeg6, kx (1 yu:pqqow 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+y7f*qc 1ikfj6ki.moedui /. effects are at work? Do they oppose each oth6o kcj .qy +uf1f*.imid7iek /er?

The gravitational force on the Moon due to the Earth is only about half tj*6jv.f-vzml+g4e nmj eh: m2he force on the Moon due to the 4ev g:6zj*+m -mm vejlfnh j2.Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal a0 podg (15be4 qdfvt8t (uf *i1yvyp9icceleration of Mars in its orbit around the Sun larger or smaller t8(p 01vtify9b*q detpd5 1( oy4gviufhan the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towa0,at9 *ndj74smmwh m/q88cyy lx8 phwrd the east or (b) toward the west? Consider the Earth’s rotati cdysm *p q,07 j4w8lmxmw/han8t h8y9on direction.

When will your appare0ol1 qv rk;ho1ex)f1*9 rqwwqnt weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acc)q hfwxv wr;q19*1oo1lkr0e qelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be aae*k*9doa v y/pt j8v4dversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walk4/vje p*k8 voay9td*a ing 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 “free fall” or “appare-qz4fb md.jvpl s2,, i bu6yrs4a*w;rnt weightlessness” between stepw6, bvbiq.u d-, ajz4m*sr2;r ysf4lp s.

The Earth moves faster in its orbit around the Sun in Januar)jit:j,m q0y cy than in July. Is the Earth closer to the Sun in Jjyi :j m)c,tq0anuary, 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 orbit.]

The mass of Pluto was not known untib)uh hjezuw w7+pf 5zlj/3w *m( r1.eml it was discovered to have a moon. Explain how this discovery enabled an estim*)bjluzf e3r/hjew7mu w1w z5m+ ph(.ate of Pluto’s mass.

  The Sun's gravitational pull on)u lce, vz+kk6 q3b fgz2ad 7*anqg3x. the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a spe+7*,zvezqg63f2 g3ad). nkbkx qcua led 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 travelinggzl; lw5:c ij 0sm*xl3 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in 1jjs88*aej :ib yd (x3lp d*ylasc4; jits orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orb byej48(asyjds 1d j3x*;lcij*lp:8a it 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 itz0 r( ea4hzds4qr-0nh rotates uniformly in a horizontal circle (at arm’s a(zrzeq4 hn- dr4hs00length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and lrd99 wss+d 76q,giy , gspc*e7ryl:i circlesd *,sirrqlig7sy p ye9l :sgw7,d+c69 the Earth about once every 90 minutes. Find the centripetal 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 magnitud.l a2hc g)zi*ve of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolution2 igzl c*h).vas per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unifop g78 7,jjm -6cobkdwmrm rate in a vertical circle of radius 72.0 cm , p-c wmj m 8jdg7bko76,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-;8 zerj ym*,f;dj) fjskg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the cafdj8s);yz, emf*;jr jr?   

  How large must the coefficient of static friction be between the tires and8 vn2h.d r6nbv the road if a car is to round ad vn6r.h 2bvn8 level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designem1 26 1bxcy (tr1ahxztd 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 cb1ma1 zht(t 1x 2x6yrown 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 turntable1k/ee dzv(q+sv cn t-. 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 kq+zv vtns./1- eed(creached 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 downsscd ai tocm uc:+vzo2k:g)n cc5/;49 at the top of a cig2c)act so/:4v c;zukd95 s cco:+ nmircle
(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 k* dh1huxq5vk2 g (including the driver) crosses the rounded top of a hilu *k5h2qd 1hxvl (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 to mz r7+ic4ftx7f nj8 (mxake for the passengers to feem( xcjffzr78 t 4n+x7il “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At t 3mduzl3r4c 1ohe lowest point of its motion the tension in the rope supporting the buck13rud3colm4 zet 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) musoa(ul , mo/0 vlgs4ewca3lh8; t a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experienc(3e glmh;4a cl,vawu s/ l8o0oe an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated56(jzz0s kfjj in a cylindrically walled "room5 z6jskj f0j(z." (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 rotat.+b *oxcs (.io6k.mq eqgwi)red in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected t6meq+cx. (k qroo* .wbgis i).o 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 toxs sqr, l:dqwlrf-;v8l/j:- he weight of the ball which revolves on a string 0.600 m long. In particular, find:/: wlrd,sl8j-;qrv fl- x soq 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 ra3m en,qcwi x/2. (b5uwxu5ggkdius 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 si/pk;sz73 0eb vpl/ 4q umv :x,ezgmf*;mgo7$ 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 vertica 917zkxaeajg 2lly 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 componfm99o a7yiez5 ents of the net force exerted on the car (by the ground) in Example 5-8 5a ze97yoi9 fmwhen its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area 1zfld /k wvilw.7kx+8, going from rest to l lvdz+/xk7wf8w.ki 1320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires 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 partr7cy/*o7 9el wiq0a8 qdtij6cicular instant, 7i/jqt0*a9cod8 li7e rc6qywits acceleration 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 g *: goi:91 ;enp*rto z (dpeqguu/yvx(ravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if ip ru ne uoped:1;:/otiyqx 9gg *(vz(*ts mass is 1350 kg.   

  At the surface of a certain planet, the gravitation/96dw5t+ rt 0ce uuogkal acceleration g has a magnitude of 12 metgd wr65o/ u +9cku0t/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 Moon. The Moon's radius is 1.74a4qvmf5yw 0u u5y0mw4 f4avq4 $\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 hapdr18y oie0a) 6oa;e c)c2b(+g waxsy s the same mass. What is the acceleration due tod oweicb28 (ay0))+ as 1ap;cyreo xg6 gravity near its surface?   

  A hypothetical planet has a mass 1.66 time8l pi,7s,ne3ydof ( ujs that of Earth, but the same radius. What is g (,y7fn,eijlsdu8 o3 pnear its surface?   

  Two objects attract each other gravitationally with jkmfv3g((4 l jb.5neh 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 accelewv-yyy 18+ ds+t,7oo:obkxburation of gravity, at (a) 3200 m k oxu,b1w+:s-8t +yvydb 7oyo   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to ken8xki cjae2 *.bl* .0djxc0a point outside the Earth where thegravitational acceleration due t*xcxkaic8 .j e0d.e n*2b kj0lo the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the masswkdufd 59 50fw of our Sun packed into a sphere about 10 km in uf 9dkw5 fd0w5radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a, ju mem9h5rf44.qmqz g;o(r on 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 gra z9hfur e4m., o5jq(mo;r4qgm vity on this star?    $\times 10^7$

  You are explaining why astronauts feel wei xz at(b79e4ufghtless 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 gravieubz479f xat( ty 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locatehcp wv(.a+ft* yb xb:(d at the corners of a square of side 0.60 m. Calculatyt(vx:p*wc+(.ahf bb e the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same si0w9cstwez1 j s:ygjbh /jqi)e*5,s1tde of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four:sej q/yg0w stt,z)wi1 jejb91c h *5s 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 9ebh 2us6z)au/v+lhshmd2 9iis 0.38 of what it is on Esz mvhi29s 9lea2hbu6h)+du /arth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the s -izu mlom0 b/6r-em*Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare yom ui60- z/mmbsl -eo*rur answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movinc/j :x 3) b:vr1s mw+ew5fbe,u iref3gg in a stable circular orbit about the Earth at a height g)ebrwve+cwr3fx,:isj 1 fbm e:/5u3of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular or3/zve hdq, ywq *;hddk4 ccz23bit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release4kc2 q3d cd/wqzzdh* hye,;3 v occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occu7,tge-z-wt 2t 7vmy blpants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and 2,g7mz--t lv7 tb wteygive 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 in a c)-ioqn zf1 6mey dozfv-j)r (/ircular “near-Eznq-io f/)y fvd-)omzr e1( 6jarth” 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 the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from xsp:5s ./mrskthe top of Mt. Everest to be placed i.ss5r:p/m sxk n a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orb 59-o 20rtape9 +obcauhlg+fhre9q j+it the Moon at an altitudqhju-f 2he9 +gcbre+a5 otp0o+rl9a 9e of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunib8t )9 a z5cy8:buzvwks of ice that orbit the planet. The inner radius of the rings is 73,000utb )89:awy z8i zvc5b $\mathrm{~km}$ , 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 o3pzwf6hq u* 90 b tybon kg9i068:gdiunce every 15.5 s (see Fig. 5–9). What is thegb03 9 py60 kw:zqhuiob f6i n*dug8t9 ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 7n* mp;ci 7jbyesix //55-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocitypmbce7 * nix/5j/syi; ,     ----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 equa+g/n2 ,rb5o.3m w+f,x qn nl hfa/yvcil mass. They are observed to be separated by 360 million km and take 5.fafwm /3inyb ln,q+o.g ,h2 xrv/ 5n+c7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for-hsgta4l0j ) zu*nq.92 yrncg the weight of a 55-kg woman in an elevator that motsa-)qhnz9jl.n gc r g4y* 2u0ves
(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 elevator. tfj( fypz c+mqf.3.w ,The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum+3f ,jzqm fyt c.(pwf. acceleration (magnitude and direction)? a =   

Show that if a satellite orbitq7b 7+9wcnwq js very near the surface of a planet with period T , the density (mass/volume) of t7nc7q9j+b w qwhe 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 Moonh yw ,4qzix/.o (27.4 d) to determine the period of an,xyiq/w h4.zo artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundr-4*gn bxxee (eed meters across, orbits the Sun like the planets. Its period is 410 d. What is its mx -ee( gn4*xebean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc j/r l jjz,wwgi6kfq2/ s1pr6fjt2 5/se 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 Su)a :v7);blgbwke t.ro1; fzgx n roughly once every 76 years. It comes very close to the surface of the Sun on its closest ax;. 7:z1 tve bwf;)ogrbakl )gpproach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of tx , +rds7b*kb-cz/cvohe 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, p 3vc2g 4eykzh3:bj4lyeriod, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 3b 3vy2zck: gej4lh y41609).
(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 u8 i*eb*:mxj irk2)u5q-p rmuthe Moon. 8-m5jxk )i:qupr*e u r2u*bim    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mol2vma/qfxl4uf/l7x y/a ul. ;ons, using Kepler’s third law. Use the distance of Io and the periods x /7l/;qaa /l2 mfvuy.ful4 lxgiven 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 betm a;dtj tcs. pc7thfel39ndjem0/( 12ween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was dest 3 1.fj7 d m h9ec/daepttnt2l(;mj0scroyed).
(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 pe8u4 mtbsz 7i+6q 8la"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, t4zb u8 q7e6plat+sm8 ihat 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 cros0jvevpjoo)exs: 04 2pnw43p nl.l3i ms a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exert3 eexpl4njl4j3v npo)v:o2 p0 m. s0iwing a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s sur7rrs-3 rh vgi2face will the acceleration of gravity be half what it is on the ssv 23i7hrr g-rurface?    $\times 10^6$

  On an ice rink, two skaters of ln *4h 8z.d-u:p vgiqhv4g np1equal 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 are 60.0 kg, how hard are they pulling on one an* g updh:q-41 phgi.zn 8vvl4nother?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerationd fjar;b*)m-,xi) zk u of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g j*z-db k,)ux;)fa imris this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directln9zz ,y h3ouz,5y)vha y from the Earth to the Moon experience zero net forn,oz ua5zz),h39 vh yyce because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you5les+xl-fmheyni )m) 43i )vz/a1dmxi 2md6y stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelerde lmv5 hm) 14+ x/6snmidfm))23yzae l-yixiation of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that w fy05dm0l ib1i vui*1fill rotate 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 5vdib 1fi01lf*0uyim (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 l g5wkisk 2 3 bz4w9kllyiba//:oop (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 the mass of a planet in ter*igd1hk1 gv3 fb:5b vrms of its radius r, the acceleration due to gravity at its surface and the gravitational bbr:v1vh1d 5g*fgi3kconstant G.

A plumb bob (a mass m hanging on a string) is deflected iul8 tu+jkqbed-3 /)usx4p 0hg1 io/vfrom the vertical by an anglusbdiuu-3 pge t 0oi8hkl+jqv/)4x/1e $\theta$ 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 desi(i+in07yq uq iwev7dr0vtc1no /;0zp l 5wg/dgn speed of If the coefficient of static friction is 0.3dug7+vt; iil/0p qwv0z(0 w1n/n7 ie qrdy co50 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fastyr bf6l tx-o lsznx u8q0s(f 5(og-.;i that objects at the equator were apparently weightl-bgs8xni5yf (l-.f s(zurt; ooql 06xess?    $\times 10^3$s

  Two equal-mass stars ddi 77lrayav ; u3it;(n2*a/tmxc*j u maintain a constant 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 r)-juq+n piwpeo* 1g:badius 235 m. A lamp suspended from )up bewpn-1qg:i o+j* the ceiling 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 massivb pa+a3r61o; y3t u30wbmxrc8dffc( v e as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person w ox8c3w+3fv rytfbra6udmp;(0c1 b3a ould 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 prese:0u av vzqav6lb7j4qc4o (yx4 nce of an extremelvc vjx u(vq4:44y 7ob60lza aqy massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed 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 val) 4qe6kzuf0ju: t7 lueley shown in Fig. 5–45. Both the hill and valley have a r07le4 uk 6:fuejt)qz uadius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sqx2.: jjpkg (afhx9c0ystem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approx9qgh 2:.apxcxfk(0j j imately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.(za grtd8x - 5dhz /,bh68yh4ybb5 gqn1 billion km, is meant to orbit the asteb6gz b8gqz/ha( dr8yb 5,-ynh 4 hxt5droid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuy2b 1g f1d.klwing a satellite in need of repair. You are in a circul1gyk f2 dblw1.ar orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is nr3h:r:bop jfwf g26-; pu8 gbits mean distance from the Suh3nu: b :rgbo2g8pj6fw ;p-f rn?   
(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 of0pax r7 abtp-: G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make xp a7-p0at: brreasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wakee8--44zn u1qu w / cyky:qg hor:6qry Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from- nhy r8e 4q4/qgucuq6 :kwekz-ry:1o 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 locatebz/0e; )iftd ar:5f tp0y:d hmd at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at tt d t0)ye:;50rp:zhiad fbmf/he midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500kd2hw8qk 2dbl in.plo7dh 21( kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration exy q9: -fdyc9ghperienced by the tip of the 1.5-cm-long sweep second hand on your wrishyg 9q:ycf9 d-t watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aro. pvb oq(fwy35jpm9l) /qnoi a+8r9kkund in a circle below yojwomi.+ fq9)a(pr ql/bk 83knp9yv 5o u 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 l4 * quy47 4(fohcqjebdesigned so that a car traveling at speed q4fo 7ly4*(cb ujheq4 $ 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, utilizeqet0f/:xofr ) s tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed tff0oq x: r/)eof (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.$\approx$    $\times 10^2$