Sometimes people say that water is removed from clothes in a spin dryer by centrt25vjpdt.io.tu s, fwd g7, r,ifugal force throwinp,,.d 2i 5twst.d ,v ugfr7tojg the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travel)dykus ia+.r a,h,wu0zhbvk4( jy, 5ts around a sharp curve at a constant 60 km/h as when it t)iu , 0ad .y (ha kvthsz4y5k,b,r+ujwravels around a gentle curve at the same speed? Explain.

Suppose a car moves gz1 .w p 4w-t(c rm:6nxq1bqe+cx+t ybat constant speed along a hilly road. Where does the car exert the greatest and least forces .ycz-c+txt:q p1qbnx+14w 6wre bg(mon the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces aph7logd3do8cd, zd8; z-,4k uix+tjacting on a child riding a horse on a merry-go-round. Which ooc 8gulkz4 3 -p8dz, jdo,t+hxda ;i7df these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without3mftdw(4 j j, *(ff(vf,zzulm the water spilling out, even at the top of the circle when the bucket is upsid,fd( (, 4 mjvjmwfz( *3uzlftfe down. Explain.

How many “accelerators” do you have in your car?synq u8 /62v ;x9eqmk g/qv+n aav.0oh There are at least three controls in the car which can be used to cause the ca; h/vanayv0sux+/oq g.em9n28qq kv6 r to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying ov-u q1v(k(wl y qwt4g6kq*c yj6er the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his c- vy (cqtyq*wkq1g6u kj6l4w(hest 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 a curve at high speepfed/gzsmp c -go0 7nv5):ou 3d?

Why do airplanes bank when they turn? How would you compute the banking angle92+fl,e; d9z6zmdwsomyhf( l(*/t ohatpk7u given its speed o;f l a,9yhz+(otl(*mtw9 zk2fd p6du7esmh/ and radius of the turn?

A girl is whirling a ball on a string am *p6iy1s 1ldess3 cac h.f98zround her head in a horizontal plane. She wants to6i .lpy9s*3z f1a81dhm sces c 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 the string?

Does an apple exert apv35p x +4ildmr9+q9xyo.h vu gravitational force on the Earth? If so, how large a force? Consider an mqlxi3r+ 4o. dphpxvv+yu959 apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wafazh.4/z :n*u,r1kae1 hoi iays would the Moon’s orbit ir* h zh,uk4iznoa/a1f1e: a.be different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on th ddf)pq0vthz6s 8 jenw- 8r0i9e Earth6wq-jvpt 0)di90rfzdens 8 h8 ? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger thanv plbfcf-8 jo2; +g)vk the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consvfocg); v82k- bf+ lpjider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equfh;ac,w1e0c hator or at the poles? What two effects are at workh0 ccf1h,we; a? Do they oppose each other?

The gravitational force on the Moon due to the Earth is onl62y, ;h3vqbgwiu;q a4neu oq .y about half the force on the Moon due to the Sun. Why isn6,b g .;;wq4o3vueqy2anuh qi ’t the Moon pulled away from the Earth?

Is the centripetal accelerati4* rxnkyko4pkrtejs9 .m r3; 2on of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Ea;k *r4yrokmp 2.kjr9 4 xs3netrth?

Would it require less speo:h id9 ipcu;h2l /hi8p- ,fzoed to launch a satellite (a) toward the east or (b) towa- od,2l; ihic9o zi:/h pfuh8prd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greate f-.w7p +dretkst, as measured by a scale in a moving elevator: when the elevator (a) accelerates d twe.f-+pr k7downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods inz5paw4 zy- 6 1i5rflgc j7s)eh outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindricala45)-p 1zeysjzgi 657wh lf rc shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free -bgid692 ni 4p gglvq9fall” or “apparent weightlessness” between9vi lgd2 6i9gn b-gq4p steps.

The Earth moves faster in its orbit around the Sunp;9tw;mov8e , jd6uuh in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is pj;mhvu9we;uo6 d 8t,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 untwm: ttkmv6q) (dq4r k,il it was discovered to have a moon. Explain how this discovery e m6r( qv d4:qt)wk,kmtnabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth iodmeam8/ ph y be-6o+0s much larger than the Moon's. Yet thedeo0e m+/hy6 -b8m oap 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 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 19i6w9c hqxvgx1fy(r t) o 0wi;*80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratio8zd+if9p*zz ;ye7 ld yn of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? z8+79 ;yplfzdzdye * iAssume 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 exerted9mf04kjtww;4t g k1xf on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcula 9wj4k0 4ftkgxtm;f1wte the speed of the discus.   

  Suppose the space shuttle is in orbit 400fj4: dc87l(j efssaj)w jk))g km from the Earth's surface, and circles the Earth about once every 90 mink :dc(jl)e4gj) ajw)j ssf7 8futes. 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 magnitude of the acc(sbgo x : ,s+fyyxvj--eleration of a speck of clay on the edge of a po, o-f yj+( xsyv-:xgbstter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rtqg /zs-2yb(pate in a vertical circle of radius 72.0 cm , as sq2(bgp z/-sty hown 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 ch8sr 5y tgwr 2vq+9/en7nh*: vit m.guan round a turn of radius 77 m on a flat road i q vts/eythg+9i8vnngr r h:7.2w*u5mf the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tireshtul .vj 3bsojdswtc(,8707n3; ovnq and the road if a car is to round a len tjjq3n;uv c07.sh,7od( w 3ov8ls tbvel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is d3ji;urg6 mp9designed 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 tim ui6 93jpd;grmes 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..o +l.zgc hk7n0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What nz+lhc7. k. gois the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be trdw6;+k s5a7hs0fljoqaveling when upside down at the top o;j+do5a 0skq7sf 6whlf 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 d-/jx *jm4 xrg950 kg (including the driver) crosses the rounded top of 4-/x gx*rjd mja 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 to makvt skhmo 8 4h-e98n/joh(+slklf61vx e for the passengers to feel “weightless” at the topmoov1l -+o6sjx4ef h9 hvtnm8l ks8 /h(kst point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical ci 98sxumrvwa c 02:7k vh5xyg8ircle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 ic 7 k8xmawv8r5ux9yvhg :s 20N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from thwfej,g802t hpjpv, o-e axis oj o0,2f,h wpgjv 8-tepf rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated i1 vs 9lo7xuf7in a cylindrically walled "room." (See Fig.1ul s9foi77xv 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-s1www41 9inq3 . nn u.v;dqygzhockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a z9wwys g;uqdinq.431. nw1n v 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, bx 4 27e8arq)99wbvlutvfivc; 3fn8vw y not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, fi;u8w9avvvve fn8q7f234) rictb w9 lxnd 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 pz ) 7ozi jazx5q(:c8e75 $\mathrm{~km} / \mathrm{h}$ , 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 massexd l3-l2 :qsrfxg*a .ls $ 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 vertically at r cfsf5lm; x*0310 $\mathrm{~m} / \mathrm{s}$ . 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 the net fo/clbn3)nqh6-5.3c f icum 6ks jayxmlp 7;b5lrce exerted on the car (by the ground) in Example lh; 7acnxucfj.b5-6np m3m/q i clkl)sy 53b6 5-8 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 accelerates uniformly from yq;jn ++ e blfbq g/.kcr/w5p7the 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, /ynlk/p bqgwb7 e.++;q5rjfc 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 cirf eg 3b+gdb0f7cle of radius 2.90 m . At a particular instant, its a07bfe fb +ggd3cceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii)aj.v(8 emvcg*jdpg yl0+d- *wyj 7 aw( above the Earth’s surface if its mass is adlg*j*+mj8 ey(7 wdpjwvcv0gy(- . a1350 kg.   

  At the surface of a certain planet, the gravit0lu:auvqyml b8kk5-:ff+ qc 6ational acceleration g has a magnitude of 12 l5q y qkf+:-8ub:vfma60luk c 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 grav x 8-hey+olw;qity on the Moon. The Moon's radius is 1.74 xowl;+qh e- y8$\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 same jwu kv p18tdc4 yhk+8. :oldktg9ugo)kf2p5 4mass. What is t kvuk4oddg9+8k5:4g1hw )otf8cu j ptp k.y l2he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 tic u5,u(ekxn h4:zqg /dr0 2rekmes that of Earth, but the same radius. What u xz02k5e:nudhe/r, 4kgqc(r is g near its surface?   

  Two objects attract each other gravitationally with a force of 2. s6 o2taresw-65$ \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 wi*1m ; t8k+ gs3fl:oat yaonkyh (w04g , the acceleration of gravity, at (a) 3200 mhw8k ytl;k+1 a4(:ysi o3w0m ofat gn*    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cente;zt/y,+z e u;2/ow6otbwpl tlr to a point outside the Earth where thegravitationalz2; buol 6z;yt+p/e ,wtlo /tw 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 mass of olro*z9qbo7q wfal(q + g m/3r,ur Sun packed into a sphere about 10 km i9 q(* mlrlqo,gw q7b zor+/f3an radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sunwf7me ixgtnbb; /0r dlwh6) z 7,pb17y but is now in the last stage 7 /bw 7ym pwt)lrenbbidhg07 z,61fx;of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the rnvb 77sef p7o 02y)sespace 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 the Earth’s surface inofyb)pe77 s er7nv0s2 terms of g.   

  Four 9.5-kg spheres are locaxjm6g7kclre5-de.n(. lz o. m ted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the otlj .d.x r7m5co(.6nl zm e-gkeher three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets -burlx ix.3z41ihz1 nline up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four p3-izrl 4.bi1 z 1huxxnlanets 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 surfa.smz;x i qwv75ce of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass o7qsx ;.vm5izw f Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period- xt-:q 7d(oq tosb2balu1ol8 of the Earth and its distance from the Sun. [Note: Compare:ol2oatd7t (18lubq--xqb os your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in gs3hvf -1c-u. *wx,t te8wm5zk kk.oga stable circular orbit about the Earth at a height of 3sgg.kz. -mtwufk- vh,58wkxoc* te3 1600 km.    $\times 10^3$

  The space shuttle releases a satellite intom0zv) 3po)bi e a circular orbit 650 km above the Earth. How fast must mb3 iopez0)v) the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cy5co3ksr/2*7 j7 vvfcjyj6bg tlindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answv j7ojt*fcy/7k6 c5s r 2vjg3ber 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 circulazf zh; 210cw6j +s ;sxjprrtd1r “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surfs jz;f txj+rcd;602zw 11prshace 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 laun nu u82hpp.3p*o5t3 qxds5qhpla. n(zched from the top of Mt. Everestpuql2 z(ph* q op.5hn3p 3sa8txund5. to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, thel yjgwvb4w46(yd k)jm),mn4 l command module continued to orbit the Moon at an altitude6d m jnybm4kj)yvgwll)w(4 4, of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of cq, h 5fna7rcrco m l25o*snf39hunks of ice that orbit the planet. The inner radius of the*35o 2ro nfcfh7l 5 san9qrcm, 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 dijh h+tk;(iyn) ameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s appare)n i(hykj+;ht nt weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronai,if( o-qnmb1ut 4200 km from the center of the Earth's Moon in a space vehicnq1 ifim(ob, -le (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. Tynsi k80:mea, c z lhk- j:*pyhj76rh9hey are observed to be separated by 360 million km and take 5.7 Earth years to orbrh j n*h,y il 68pz-k:a9chs:keyj7m 0it about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for t+axer 58za/xgmnk ,q57k y8l tqo/3zthe weight of a 55-kg woman in an elevator that moves ay , l8argtxk 5/mq+z5qe tz78n3 kx/o
(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 /hd1n ab.ag.dceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accel hbddn.a1g./a eration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period 3e , ymtq7ixi:j-a3lr yphmv -5qs: i+T , the density (mass/volume) of the planet isvqpj7 xa5y3:mhlei-m 3i s:-,y+ irqt $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the p 8vw odr+yv1x0eriod of an artificial satellite orbiting very near thr1do w+xvvy8 0e Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, o.bd x +0n+vmdjrbits the Sun like the planets. Its period is 0bdjm dvx.+n+ 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagestsk ) mhcc7cu(8w)2u distance 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 Suq-rm-if) dp u9n roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What -q-p)9 murdfi planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galacv+ekpuihjjs.d y,yi/f nq z4)) b5ze,(3j +qxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons oj x5pb+hwyye601 bt.m2h:lhag j 69f of Jupiter (those discovered y b :htmbge.9 h+hjpwa5xj f1y6l26 o0by 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 Eae +pt10 /vnpqprth from the known period and distance of the Moon. p+ /p10np etvq   $\times 10^{24}$

  Determine the mean distance from Jupiter for each ct1sqj qvf9e3+ x5jh) of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in jq3+)qf tc 1v9sxj5ehTable 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 consists / hgsxh /06 k/sb p/2k1) ,t(ykjtbg2eqmkqe cof many fragments (which some space scientists think came from a planet that once orbited the Sun 1sgkee0q/k )q jt/bm2py/bh6t k(c/xh 2g, ksbut 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 tagnd7kq w paf 5*t6c6ds t77)aale describes an artificial "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,7stdd k77n6f5a aatqwp gc6* ) that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging v7 v*nt9ndhhrur2.b7.eyu l w 2ine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can toleratlr7dut..e7 nbhw u yh9n rv*22e 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 sqzbu6o6dh1o vocg(6v ;xke i2:w2i) wurface will the acceleration of gravity be half what it is quki(co1w2vb2e6 gd;vz i6o6x:)hw o on the surface?    $\times 10^6$

  On an ice rink, two skaters of eq5 x7jx,vw.caj ual 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 another? 5j x. jc,x7avw   $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration ofp;.xx7mf-kohp9yyo t8uc3/ f gravity at the equat3 ffxyou89c-xpy . p;k7ho tm/or 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 willf)zhe+ +x6nx rjlg2lp:ky5 h - a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth 2ph) zg r6+hny-:+elxxlfj 5kand Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is m s31+qilk ys(qk7hzk/ip y26xs/+dy65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in w+ l yz+q6s /ks7s23iy 1k(pikdq/xmyh hich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube th--3 bgpk .l1w5tps cgyat will 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 (revolutions per day) if an effect equal to gravitypg5l1 k3sbcp.gyt w-- 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 loop (Fig. 5–4t7 v 59g+*v-ynb + gqq13brmi ccy,xmo3).
(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 terms of its radius r, the ff.3tob()kf p acceleration due to gravity at its surface k(f3p.) ffbo tand the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflz /v*bj/i(tn uected from the vertical by an angle (* /u/nzivbtj $\theta$ 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 desigqpw45 vqvfr ):n speed of If the coefficient of static v4pq f)q5vr:wfriction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day 1( vnevp)b5lpneunqx. 71 r8sbe if the Earth were rotating so fast that objects at the equator wer.x1pn l5nue8)(nq7sp rbe v1ve apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 80tz q8f. b-85ctd-k c6 ipvvpz j0kb(p.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 roundsnbqd/8ws+y2gbdk 0(d a curve of radius 235 m. A lamp suspended from the ceiling swings out to an wqg2 b( 0/+dbysnk8d dangle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Tqtxby5 uv3i5ac*aw+/ f0ox 3z hus, 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 3+/cqtiuza5xb a * vwo0x3y5fwould experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence oyqi6tg*o9vz 0lwh 4j,f an extremely 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 measwi04y6z oj q*v ,9thgluring 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*r icj -pf(q1jley 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 dr f*1iqr jcj-(piver 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 ofce tm4zl3:n4s/ * xsha 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 s4ns* 3l:/m s4ah tzexcatellites 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 Asteroid Rendezvozqt::o +z w/flus (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroil/:fq:o+tz wz d 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 sp0svbj*5orp 4race shuttle pursuing a satellite in need of repair. You are in a circulpr5v bjs4o*r0 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 its mean distance frmo.urde aqb 3. k)a4s*o oqd4rm s)*ue3a.k.abm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of 5).g qa2gfhwy G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like F fq.g5wahy2 g) $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky0f0 sob e)ghp3 Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cent0 3behp0og s)fer $ \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 oft f0(p )hcq(ee a square 0.50 m on each side. Find the magnitude and direction of the gravitational force (pqtee f0) (chon 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 kuc)7 jbxm 7 +ar6k8r5ja7flvb g 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 experienced by t2c(+6yohwxc d ef :tj9 afl1*the tip of the 1.5-cm-long sweep second hand on your wrist watcfxe+a2 :clo fdtt96wj*hyc(1 h?    $\times 10^{-4}$

  While fishing, you get bored and start to sw -php o(muayr; 88 d--w;eqsioing 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 anglospo hu-p ;8qa-m -8;we yr(die that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of rccux )kn)8b3rkm nw +1adius R in a new highway is designed so that a car travelin nn8cwkb 3m)rkx+ u1)cg 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,ewwg5l sh 78 *ab:xh(m the Acela, utilizes 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 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 doe (g8w 7hmhl:exa*5 wsbs 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.$\approx$    $\times 10^2$