Sometimes people say that water is removed from clothes in a spin o;k0v d6gf*yl l5*k bvdryer by centrifugal force lkl6f* y0bo ;vdvk5*g throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car 1rb/-r l- lrf --fovletravels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explavb-eorlrf l-1l-- rf /in.

Suppose a car moves at constant speed along a hilly road) fagy 9osgp0ez 6 2vm21t0gbp. 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 levelmp9ptva20 eb 0f2)ysg gzg1o6 stretch near the bottom of a hill?

Describe all the forces acting9cd * aksl*b3 4tljkb/ on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratio3b94t/as lclb*j* d kkn of the child?

A bucket of water can be whirled in a vez)1n:- y nkh/pv vfn8vrtical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Ex1:ykvvz pv /n)8fn-hnplain.

How many “accelerators” do you have in your car? There are an evpx;6j*dg 4( u 2n;a2ycstlt least three controls in the car which can be used to cause the carn6en;*x2jv4(sg2a ul cy;pd t 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 Fi u+vp *xmz7s.mg. 5–31. His sled does not leav p. +um7*mxszve 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 hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounpn*rls* +zd- m0u f9v1n,v clhding a curve at high speed?

Why do airplanes bank when they turn? How wouljy1z. cwg0-4u 2 m:6umkvbplbd you compute the banking angle given its speed anm06 g uyu-jzcwpb24:mv kb1l.d radius of the turn?

A girl is whirling a ball on a string around her head in bhv-xf ;zqe6ep*3; uda 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 should she let go of th pb6-e;u*hqdefzx ;v3e string?

Does an apple exert a gravitational force on th7ef;8ad 2z;jlu18hfj yay3 lye Earth? If so, how large a force? Consider anj2uaye8yf 8h7ajf1;d y3;l zl apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what waysdua7gbolc9 :-i* x7y n would the Moon’s orbit bexo97 cng:ibld*-ua 7y different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon +x- +vyr30 h q9uuiition the Earth? Which acceleratesi39ui0rhqu- x v+i+ty more?

The Sun's gravitational pull on the Earth is much larger than t +zdf0hpo/pm2he Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hpoz dm/2 hfp+0int: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more aa:: pc d87t2llkuxx,st the equator or at the poles? What two effects are at work? Do they oppose eacdt2xl7:,ap:ck luxs8 h other?

The gravitational force o ),pueh1ga0u/fsn pb+ n the Moon due to the Earth is only about half the force hpf0pe+/unagsb )u, 1 on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger orqfs:ef;v.2n 04bmdktq4 (cnv7p a 4g d smaller tqct;d s.mv4 nf7vk fgq04n( p:da4e2bhan the centripetal acceleration of the Earth?

Would it require less speed to la de,b0gqe*0;)6 al ltt jz;u8 actp;tqunch a satellite (a) toward the east or (b) toward )a6;8pdtz, l;lt t0gb;ta *qecju0 eqthe west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale i*f7end9zrb.zw94 b h./fe aorrp2 ud+n a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at coe+ .b4 d/rzapnf hrufo9rb2d.*ze97 wnstant 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 adversre *po4*6y(ddm. h6s gvdczp6ely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how thdh * depdcrzmvy 6*op.(s6 4g6is 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 experiencesxh,rruka+d.sr( y+b- “free fall” or “apparent weightlessness” between shdyur, kbsr+-x .(a+rteps.

The Earth moves faster in its orbit around the Sun in0)sf uvq;g4 +v(weg qj 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 Eart )v0w4f;+gg(suqjvqe h’s axis relative to the plane of its orbit.]

The mass of Pluto was not jyq 5ig,03* okggqqs ;known until it was discovered to have a moon. Explain how this di qkqsgyo5g*0g3 , iqj;scovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull-7 0s kbcdj1; zb/ygs*n dd4go on 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/-y047k*d jd ds;n1 gszbcbog.]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 rwp:gg .oofxn 5v15a, 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 a86 ao8)p b26yfbjyrs qcceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts thioqf6ay 2r8ys p )b6b8js 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 exerj//cf7chzk x9 u6nw 1oted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate/7zof1j9x k6 uh/wccn the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circl )9 3co1oulvkkes the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express l 9o)oc1u kkv3your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spec, 61 igiwvlat;*r0fqwk of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 326 gwv f,wa10lr *qiti; cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical cdewhclmx69)ha- ;h-i mr-*k *p sr isnq6e q+)ircle of radius 72.0 cm , as shown in Fig. 5-33. If itremh ld-)-hxq a9 * i)-6sp;eswnm 6ir+k*cqhs 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 wb 7e4u3 r r teu+l,5r5g8: dbr5kvekythich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of staticrylebev5ugru+4tbr :k r t,8355e d7k 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 hil:ivj:dusm b6 g19c9)1 hyi be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of9h lbiiiv:16:1sdgjy cum)9h 95km/h ?   

  A device for training astronauts and jet fighter 43bhqwycn 7 +d.a 5abnpilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . acn5hbnb4y+q ad 3w. 7If 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 rotating turntabl 4h7tl*t/qqa ve of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntabl4t7/*t vaqhq le 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 mustg. d8xa h qad)ck2w;-p a roller coaster be traveling when upside down at the to.w)d8ghad q2;x -akc pp 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) crosses v6*,unp3(/dwe4h2zfhh sjivh) r i.kthe rounded top of a hill (ra kiwirhvs6d)h 4 f( h2ep* 3.,v/juznhdius =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 Fetcii+f8 0g4aq -qm 6aarris wheel need to make for the passengers0g4at6qm i +a8afic-q to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad+g3cgieo)2 ,haz 7l.ftvr q(dius 1.10 m. At the lowest point of its motion the tension in the rope su eh)3q+avf (2ig .,rdz7ogtlcpporting 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 rotatwxg*akm-w8i* g97jzgf u/u/ue if a particle 9.00 cm from the axis of rotation is to experience an accelerax*uwf wk8imzu-9u g*/ag 7j/g tion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically w8unc,i3ie:d9f;9xwdf nf r5 yalled "room." (Se cnx;eu, 9rffw3fd i:5d yn9i8e 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 rotated7hf a9rh ox5g cv6tu a4ds-*k;st99 ov in a circle on a frictionless air-hockey tabletop, and is held in this orbit -oo*g99 kah s f;ttr u c5964xav7hsvdby 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 the weight of the *k( 00f srajnso1l ,r1dce+oyball which(lsac r0 o f o0s1d,r*1eyn+jk revolves on 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 is perfectly banked for a car traveling 37jn ,idg0uce(hi f4t 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 1a;)oyz-w dveaww-a 9e1ie4v $ 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 maneu0pmv vw*mm;u 2.djx7g ver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of u2kjqkhtq 0ea7l3. v 7yk0p.pthe net force exerted on the car (by the ground) in Example 5-8 7hyv0.u7tp kq.qealk3 2p0 kj 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 accelerates uniformlyvyw+wi1 ;am;3d7u aq/tkk:zh. bmb /o from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires an / /t;ud:+ba;m 1b mqwkyko7wh3.azvid the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a (b ta5nw+i3) :frcc5yvuu x0h horizontal circle of radius 2.90 m . At a particular instant,:3bcr50(5 wyn ua)vthci +u xf its 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 grab 88s sel ouhzk5o59y7qod2 2tvity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its l 5 byso8s9ko u8zdteq 722o5hmass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g h;j1:h c ga6aawas a magnituacj 1w6a;ha:gde of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity cu7 r; y2ec b8meu*d;fon the Moon. The Moon's radius is 1.74 er7;u*bd2mf u;8e ccy$\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 th ,l qddff,fe0.wwy*s .j3cv z+e same mass. What is the acceleration due to gravityeldwf,* . .j s cfw0v+q,fz3dy near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, be/ndbi)-cm yx7oae coe2h kx+68 hb 28ut the same radius. What i e/k+72heb6ad2 e o xcob88hc-xmn)yis g near its surface?   

  Two objects attract each other gravitationally with a forc7,venm+9moiu pm4 0ps e of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3+z +7z rim yinl+c7u;k200 m nizu+k77yi+ +r clmz;   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frj8(jy f:qj7ypl91 seu om the Earth’s center to a point outside the Earth where thegravitational accellq7 jpyf su18j9j:ye(eration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five+wb t1:yp jmpkemic0x ,21( uzyv6 q-a times the mass of our Sun packed into a sphere about 10 km in radius. Estimate c w+t( 2ku0-ma:j,y ie p1ypqmx6z vb1the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like 6:,ahw1x*w8yxvgbpt entu .e2s qared;8*l(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 th .ql 1:etn(2abwv6,dph8y;sgwa*u8 *er xe txe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlesq,u*ish k1 /n9tnc0aks 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 above theu0anc9sni* 1,hqk /kt Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of d5mj wvc*.rht c:u)xz u5:qn( side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerthn qt(x *wuj.dc )r:5 mvu5cz:ed on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line upa1 :m sfq5g .wh5un. 4ma0wjrk on the same side of the Sun. Calcaskm0n qfm hwuw.a4r.g 55:j1ulate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity ankcp xp9,ev -cz1;mc(ol3i1ut the surface of Mars is 0.38 of what it is on Earth, and that Mars’ i1lc-9e3 ,nu( ppck;m1xvzocradius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for:/uf9da+sg m e the period of the Earth aufed+/9:am s gnd its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abow0 xkm*. cjih hs8f0w)ut the Earth at a height of 3600 km. w.0*ckxfm h hijw8s0)    $\times 10^3$

  The space shuttle releases a satellitfj+-j/gg nrl :e into a circular orbit 650 km above the Earth. How fastnlj fg-j/g +:r must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylind+7/ v)t;l (;mb/x nzmiehk *)rgjldf mrical 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 tir;fhz 7+em; kmtd j/)ll)binx/v( *g mme needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit4 y75m2zw8txk:yp m1; at9dj (f/ qv reh8cfdb 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 the Earth. Does your result depend on the mass of j h m1 8k 48(d5a2q:bxmyfcytwt;9e7 fpr dvz/the satellite?    s ~    min

  At what horizontal velocity would a satellite have to b g7p7br4p3:azi( h0*gkr(ylm q-c myze launched from the top of Mt. Everest to be placed in a circular orbit around thp(*i 7 yzzq:43k0c7h mbamryr gp(-lge Earth?   

  During an Apollo lunar landing mission, the command modull*e- gnwlmk0h;6e 19fh g*jjje continued to orbit the Moon at a h9 hflmgkj60*nej 1glw*e- ;jn 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 orbse2zl7oi b9lijd t)68it the planet. The inner radiusedo6zjl 29ls7it b8i ) of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9).q2 mz3 9dd82c8uh*mc q;p myly What is the ratio of a person’s apparent weight to her real weight (a) at the top, and l9dcm3py28; *hqmyq8 c2 u mzd(b) at the bottom?
(a)    (b)   

  What is the apparentth )o1wa. (tyy:+ em9sz2q cs;mk)irb weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at b;himqt2(akeocr ))mw1 .z9 t+yss:yconstant 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 equiui e k.p5n0*fal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orb. pn*ufi5ki 0eit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weigd8nmf e b.7g(- ictmy ix6-rf-ht of a 55-kg woman in an elevator thatb 7 i-fn. -e8mtrm-cf 6i(ydgx moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspe1pwc+rmt8gqf 5pa2 ntgmn hs 6bln)(+0g/ 5ry nded from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks5sn lmqn (c ypwbpn2m6 +g+frr1 0h5/tat8)gg as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with s(vwjbyzj,,.+i q) ru period T , the density (mass/volurbu.,v j(js z,)+qwiyme) 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 th7cgt 0jlnj1yb/9ir+ v e Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’ g+ vn10cy jrj/79bltis surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits fr76e :0po nx ch0ht6lthe Sun like the planets.6c x0: h e6l0nh7oftrp Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average di*kp. hl;fheenywy784r 7t1tr stance 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 vj l4ggj/f*kvnsu26 j8lv: jc1ery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.] j8: 2 *jnvcl jg16u kj/sfgvl4    $\times 10^6$

  Our Sun rotates about the center of the. r wux4n6(pdyz8vmm 1 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, peqkh vj e 90((;n/fd5lz z+zoejriod, and mean distance for the four largest moons of Jupiter (those d;o(jzlve zzj9h ef (/nq5kd 0+iscovered 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 5i: wz)wpt de7:oh z)n.5yxvn known period and distance of the Moon. x5.)d7v zp5e:n woy)h:wz nti   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usin(dt 99ff)+a fns 9kotpg Kepler’s third law. Use the distance of Io and the periods given in Tao99(k)fnttasp+ 9d ff ble 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 betweetvy+v 6x 5dvpz bp9r3*uxu d5:n Mars and Jupiter consists of many fragments (which some space scientists think came from a vp b y+6vp v5*d5tuz3dx:u9xr 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 fo;n-l+4o+tqwa4 qt vio6qhbzc 5jg 4l2rm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quic4bait5c+ qqg+4hl;4n jolvto 2w z-6qkly 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 arcw4/3qqbzt g8x from a hanging vine (Fig. 5–41). If his arms are capa8/qw x3qtz4b gble of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be5bcybe , m p4q8dg).hl half what it is on the shp45.cbl8 b,eyq gm )durface?    $\times 10^6$

  On an ice rink, two skaters of equal mass g-*prkky s (yx7rab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each *-yry7pxsk (k 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 rotate,op . yn4g 7q6sfurma-s once per day, the apparent acceleration 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 is th7pmo ysarg uq 46,f-n.is?    $\times 10^{-1}$

  At what distance from the Earth97 g0v17slkmtnrgz1c vad1het/i c;ik(j , 4b will a spacecraft traveling directly from the Earth to the Moon experience zlnvzk17 b1;m ccv4ki/0igtjed g7s,9 rt1 (haero 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 stana 2 -s0xjw9d ;lyedsr,d on a bathroom scale in an elevator, it says your ss2x-j ;yl ,9rdaedw0mass 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 willt;s tvl; jkj/;lwk* m- rotate about its center (like a tubular bicycle tire) (Fig. 5–ls;j t;kvjtl;kw *m/-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 verti h:gojqfvd3 hw9+ wmgwd+;;p,cal loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a pl /g7u1u x*lybpx. qk2ranet in terms of its radius r, the acceleration due to gravix .ur ubk1l* ypx/q2g7ty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical b m, *q1zyyd5nrrpst* ,iw* .vpy an angle .p1intd*, y vpw*m5sq *zr,ry $\theta$ 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 coefficieb0dw0) p:t*ieq0+, e qg9bknzrc,w ygnt of static friction is 0.30 (wet pavement), atn0cq9 wt *:,b be yreip+qgd)00, gwzk what range of speeds can a car safely handle the curve?

  How long would a day hb9-o*hl z5heyk,j3 z,t klf8 be if the Earth were rotating so fast that objects at the eqh 9o kh-3zhb,f*ez8 tl,k5ylj uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dist ) :01jqb8a6.ranbd c 3rfhmsrance 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 curvespi1o33tx4i+ w haw i7 of radius 235 m. A lamp suspended from the ceili+4wsp1xii 3w ta7h3 oing 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. Thfz*lshqv ( - uzyp6cm7m+9y:8qi6dvqus, it has been claimed that a person would be crushed by the force of gravity osl-6 mc* 7 q: 6vy pmhuzv(+diz9yqf8qn a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the 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 presn;m: .r;gyyjxence of an extremely massive core in the distant galaxy M87, so dense th;n:; .gy mxryjat 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 andfwyu*,c7 6z 29 pcaubh valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car gzh *u 9yucw2,b6afc p7o without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of:c9 m9:kks97b(vsxv1bw0iq w uqycs - 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 k:( qsbkw c-m w79 vv9c 90sixy1qs:buaccuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroidsc6mni/3s ,b d Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Erosds3 , b/isn6cm 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 s-t8f a8.umh ud fe6b)gpace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 k fbh86tf8gu-. m)aue dm 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 yeav*st uf.vvh; + ice(3brs. (a) What is its mean distance from the ;vic(s.hu3 v* ve t+fbSun?   
(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 t:7t mk: yfe3ho:x*mzvo be if you could actually "feel" yourself gravitf7vzy*:mxo 3me:k t :hationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the c scw. 57frc 6guqo*kc.6 y6kpzenter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fgcz67k5.wp 6uk*q fr y.s cco6rom 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 76nwr b/v. c * hllibm8e:ai2gm on each side. Find the magnitude and dib/wmea*cnbvhi 7 86 2l:.rg ilrection 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 orbif1k 05pp(ge lats 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 experienced by the tip of tg/mh yan1yc,4t)s e/x1pftr*he 1.5-cm-long sweep second hamns c,/ tref/a th*1)g41pyxy nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get y73 vzpg ha 8yq-k0ep8kyq4nc, 0,laxbored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that kze,hay3x-7l0y qgv0c8 p ,4 8nkypqa the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a vg r uq1;c9))x(+kh:xyqxm einew highway is designed so that a car travelin);h q)+ icvq u1(:xrkex9mx gyg 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 t3o -x:3srw3ic3sbi;nxavh6sq 6j j1the 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 66:rw;ixvq-j sjbao c3n33tsh 1xis3experience 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.$\approx$    $\times 10^2$