Sometimes people say that water is removed from clothes in a spin dryer m;h5gr:rau ) r ajv:+ g6tt+pyby centrifugal formay 5ar6:+g )t; j :rphvutgr+ce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels scgcbm4gan-) 2z)fhu04zsj;4i2dgc around a sharp curve at a constant 60 km/h as when it travels acuai-hs0s2zgb;g )2g jc )4dm f4czn4round a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where dofh/ 18iylb y/8foluxjv ar5pou8::,zes the car exert the gra8 u5vy,x8llfo: hfry1 /8u: pozi/jbeatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridin: o yl: 2m69qcxjf)orw 07rjdgg a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the 7roy0:cj g d2m:x6)lwfo 9jqrchild?

A bucket of water can be whirled in a vertical circle without the wate593tswuz n ssfcij(:fp nwl534 xj)c+r spilling out, even at th3ujn9)x pnjztc fwl: c545+wi3fsss (e top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least/pu;;82crh l xp b bwy3c qhe5dy3+:oc three controls in the car which can be used to cause the car to accelerate. Whap3c2+;pduhweblc o3by y8 c/qhr: x5;t are they? What accelerations do they produce?

A child on a sled comes flying over the crest oolqjg+ 5z*yk6cz7w5 v f 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 normal7z5k5 q+cjzv6gw lo* y 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 rodg5 h0bf chdap-4d6s q3u;,agad4l 4runding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bv0gaa 4zjbhln2,( /e ranking angle given its spehba/nae jlrg(v4,0z2ed and radius of the turn?

A girl is whirling a ball on 9whc bsix)y7/y8i 7ac a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of t7 w8cbys)a7 hy9 xic/ihe string?

Does an apple exert a gravitational force on the Earth? If so, how large a forcess 3o *-uqp/phn-e1rd? Consider an apple ue3hdq /*srs1op- np -
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what thv hkc;l88u4wn: 82 wb-dgvf it is, in what ways would the Moon’s orbit be dif-:f 8td2 unh g4l;vwh8wbkc8vferent?

Which pulls harder gravitationally, the Efnn)n76o+vwd78vtmpnwtdu4z r,5 ( x arth on the Moon, or the Moon on the Earmrvnwd5f,x8 u(n ptz ot7n+ 7n6dv w4)th? Which accelerates more?

The Sun's gravitational ;(e2 y4u yazkipull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides.a(y2ek4 uz;yi Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two mg;q 9:/fjoab-mh4wo 4qnj p: effects are at work? Do they oppose each other?oha o;:4mq f m qwjj-9:gn4bp/

The gravitational force on the Moon due to the Earth ip)y)b d +wl*-(c cd+zbdiv,xob-0rcm uvf- d*s only about half the force on the Moon due to thecf)cz-d0bd,)m(bu- dpb y*vl+doriv wx *+-c Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratio5ti hi9x/ )rbzow+ /ain of Mars in its orbit around the Sun larger or smaller than the centripetal hwbt a)5+/9o iirz/xiacceleration of the Earth?

Would it require less speed to launch a fs2g(+ *l -eg*5hgt kd 4amffysatellite (a) toward the east or (b) toward the west? Consider thds*t42 f gal k+5(mgf-yghe*fe Earth’s rotation direction.

When will your apparent weight be the greatest, s1xdjj aa2po 3quvn 2ofs/* :.as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When 22:xa . *asn/j du3sqfpojo1vwould it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely muw* zlk58 m2xaffected 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 this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our fee8 x*zul5mwm2kt, and (c) any other aspects of gravity you can think of.

Explain how a runner v8eq/x,0r1hticp4 wt7h7 vs t experiences “free fall” or “apparent weightlessness” betweenvh,te t0iq 17wpx8t vsh7c/4r steps.

The Earth moves faster in its orbit around the vy:*f 37kstl:a tgn t-Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not: tn7stk yf- *vagl:3t 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 know-+3 .zfo.ar5,dcgdym w tuzd5 h5c)a sn until it was discovered to have a moon. Explain how this ddasw 5drmc+5 5tu3c )d.,.h f-yzgaoziscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muchkr s7lt4ybb u ml4n.09 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 yt .79sbubn4r4m0llk.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 19s91s/. a5. e.o5k/bzx1jztcf vo /fme lix2pb 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 ac1 +v e0y48a rd wshv9bv1 c-6/wjzuspxceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's or a x80pj cwsv-64rz/yd+9v1v1 eubwhsbit 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 271b;qi*nuy b m10 N is exerted on a 2.0-kg discus as it rotates uniformly ;nb mbq7u 1yi*in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's me0ad :oo-qesj 0es; 6surface, and circles 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 gravia6em0d;je0:oe -ss oqtational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerath+m ef fvid4 /:4a.mzzion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revoev44:/zhi+ dmaf.m zflutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string gev; ah8bjqb-p7d t /.is revolved at a uniform rate in a vertical circle of - d/b a7bqehpgv;t.8jradius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with whic sc6f +*44+tl9vc rci szmsxzoi s909jh a 1050-kg car can round a turn of radius 77 m fs ix+49*mzo 6 9sctcz+rcss j940vilon 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 car?   

  How large must the coefficient of static friction be between the tires aonddpca49zf 2un i.(,pcsz92 nd the road if a car is to round a level curve of radiacd929i 2(zdpunof pn. 4zsc ,us 85 m at a speed of 95km/h ?   

  A device for training astronauts andf:v c ny l2yi 66u-rv1foc(w-b jet fighter pilots is designed to rotate a trainee in a horizontal circle of radiusyf l6 21 vuf-:b-nryoiwvc(6c 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of vswnihev 893;p x .eqv)ariable speed. When the speed of the turntaxn;ie3 eq8 9.)wvphsvble is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a ro:u*e 56zwj d 5iru5delller coaster be traveling when upside down at the top of a circll:i*wjr 5deud 5z65u ee
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded 8)ooeyvue1uvcb80r j7* 4dr stop of o1)oe0rrb4u8vd8vc *jsu 7 eya 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 mi kb zt: fh)8: kb7edz2pup8;hxnute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlbkfkhb:;z u 7hzx2ep8:d8 p)tess” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10p kmwg+6zd6 y1ra74z o m. At the lowest point of its motion the tension in the rope support+ 7z4gpkz a6oym wd16ring 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 rotate2g4hx:zyu fr 3 if a particle 9.00 cm from the axis of rotation is to experienceh:gyxr3u 2f 4z an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people,;j+ agj1vpm q are rotated in a cylindrically walled "room." (See F m+j,pav1qgj; ig. 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 frictionleqnq3o-/khuok*+n vt *i0rfi8x m)- - vrp*zgmss air-hockey tabletop, and is held in this orbit by a light cord connected to a da*i- ntri +x-v/*0km)u pfmqr8q g*3oz h knov-ngling 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 thezj: l8o1v cvcxrf5w11 weight of the ball which revolves on a string 0.600 m long. In particocr zcvw:1xf1158jv l ular, 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 o pw ym*c3r 6 sx,d0il8fao65rpf 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 masses1lj+,zxa l* n2k9 dcls $ 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 vesq (,om uy0e6rrtically 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 the net force exerted o janugrk0* o0zb4saq)u. - d5an the car (by the ground) in Example a r0ujk q-bdano*).zau5g4 s0 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 the pit area c usx4*+:wbwp, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangentia*+ cx4bs:uw wpl 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 particular 5ppbk0gf rf jmv f-m.;5-g 1fcinstpvfp g .m-fg5fj1cm0kb r5f-; ant, 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 gravity on a spacecraft 12,800 km (2 Earth radoday: viel 43 rov+39nnz 88ahii) above the Earth’s surface +vdh8n i :v893n4oa3o zaelryif its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationm77 +.tjm qileal acceleration g has a magnitude of .m7j i7mte+lq12 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 ti 8 q3nwz-y cnf /z-ixkx6p28fo gravity on the Moon. The Moon's radius is 1.74 8f zpy36z-cqxn x2 w8- k/infi$\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 Earui5;2gknmvt)n+hg5h th, but has the same mass. What is the acceleration due to gravity near its s)2h5thkgmivg ;+n nu5urface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same ra/zkv(.1v;mw krp3h (wy q if2-hjhu,hdius. What is g w1fvh(- (ip2hmu . qkk/r,hvjw3;yhz near its surface?   

  Two objects attract each other gravitationally with a forcerpsqy-i )gum( ,(l, gb 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 accele*s *hl5ybzm)yqz8dk+ ration of gravity, at (a) 3200 mdy5zmks+ ** lhq y)zb8    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to aa o,-y-k 1/nnxinapw8sw 0g,t point outside the Earth where thowy t0ank1i pn8g,ax-n /,sw- egravitational 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 our Sun packed into a sphered26v xxv +yl0c about 10 km in radius. Estimate the surface gravlxd xvv+6cy02 ity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average s u2nbura.jv9 ;.kp 1idtar like our Sun but is now in the last stage of rp 1 na9kiu.2vj;bd. uits 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 space smk 8msul/v *(;7 cghqmhuttle. Your friends respond that they thought gravity was just a llq8*/m;hsgm vuc( km 7ot 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 in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.6e80 29um5csrd obl5d;wu qsz;0 m. Calculate the magnitude s95e qu 5os8rz bwd l0;;mu2cdand 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 side of th0 )h1gbqpis7w e Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming allwb10i)q hps 7g 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 accelerat .ftr,j pmstaj,+t,( gcm7z p,ion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars. mpz,p(s. mr t,, tg7fj,ja+tc   $\times 10^{23}$

  Determine the mass of the Sun using e3mn whpg6:b3e jvg;0the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that m:3g;6nwbegep0 hvj 3obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving /2 (pna/efd/u3cabggc je07gin a stable circular orbit about the Earth at a height of 360e2da jc/a 7ggubpge3n//( fc00 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650ozqa0 ffra-5 : km above the Earth. How fast must the shuttle be moving (relative 5aqf:0az or-f to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate*(8hx n /at2(mx evljp2 vk4ck if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, xkhc2v*jnt2mvk e 4/8aplx ((and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cir+xl: aamx31i ke3d/x zcular “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 t:a/l1zdmi+ek3 3a xxx he mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite havec7ne1hd8.t)s + wepv+xiws0kjbe67 g to be launched from the top of Mt. Everee c)x67sihk1.+tw8d s0pjn+ v b7ewgest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuedpx*n+lg2*; lo,n sqemskh k; 73sgo q+ to orbit the Moon at an altitude of abonhl+g **so,7 3n2+q osp kkesq;;gmlx ut 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn ar5g -txdhsuqgj/q +r r/c rh/n.o 6g;)ve composed of chunks of ice that orbit the planet. The inn+- rg/ cu/;xo.5qn /6g gjdrsv)rthq her radius 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 in6zdn+cmj 34cb diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a4n+b zcm6d j3c) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weigh,:zr,b2bk vw ct of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space wz:b2k rcbv, ,vehicle (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 opzao0 zh; u+y(11tzx vhwa,r7 f two stars of equal mass. They are observed to be separated by 360 million km andx7y h1h;wza0, tvp+zauz 1ro( take 5.7 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 the weightnver2ua . h8or,b slv tk,/q36 of a 55-kg woman in an elevator that 2,v 8utn.s6oe/ah ,3qbkvrrl 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 suspended from the ceiling of an elevator* bsk2a;5nx87megcq l . The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s 2 ns*5 emg7;b x8alqkcminimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near t(vq yd4 (-yasblv;hj9he surface of a planet with period T ,lbhay vy(9(j4ds; v-q the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the perio xi3n4o: zdbb,d of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s sur i:bzdo4xbn,3face.    s

  The asteroid Icarus, though only a few hundred meters r c, ,uqp4v0 9gvn)zh+i-nehh across, orbits the Sun like the hr-v)n,+icuph v h90g4q,zneplanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.;vn62f nr)zulr32z3in8ddi ro1( bu g 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 roa3 j()awkpec. ma.sopq-s- j9 ughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distancec a3.( a)ksoajeps-mp- wj 9q. 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 9wjn0 cl(xzfox ohd-*;ehi 5 8the 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, x8a630 f wxbi;hjpgr0period, and mean distance for the four largest moons of Jupite0 f60x wh;rxija3 bgp8r (those discovered 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 Eirz7r (t -4xriarth from the known period and distance of the Moon. r(r7it -4zrxi   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moox nzd-t0 (xcc)ns, using Kepler’s third law. Use the di n cdc-z(t)x0xstance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (w(r1((lrjdi k jhich some space scientists l r(d1(i(jjrk think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form482w gh oy4dy-xzto b+ 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 quickly enough to produce an apparent gravity of g as on Earth. W y+z4 tdx-h 4y82bwogohat 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 hangind5e hpzfdc-/1q(fgssv(*s q .g vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what iq(cdsqd1zv ( 5se.gs *f-f hp/s 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 acceleo 8+xcxrz43tuj 4ou:f ration of gravity be half what iotx38+r 4xo ufcj:uz4 t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hand01vo4uq elnf 9s 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 are0f9ol1n4 eqvu 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration q14zj 9nr difo5w ec46of 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 t1o6c rnq ji zf4d59ew4his?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft ty8okbe2 , 0cuoraveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and 2bo0ocye8u k,opposite forces?    $\times 10^8$

  You know your mass is 65 k:uv7m0j rxdmgs we 6,. e*r(w*k6i msog, 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 which direction? 0jw:(*os *v r7,wr id.mm mkese66x gu    ----待选择----upwartddown 

  A projected space sta4kxqk3 6ezqsz3uu p9, tion consists of a circular tube that 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 3uz, u4eqzq 6kps9k3x (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 ver4 axcnhy(x:b0a ,.tssc0h)yuq +3m eh tical 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 planet inv-)gf3ftr4r *wj.a6lft56 7fuf yc mz terms of its radius r, the acceleration due to gravity at its surfacz6 f47uy5fw* t ftj -gaf6vcl)r3fmr.e and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is def-(b0rx(x djx448bjdfllzs 3 z 16 ir tnl)d;qolected from the vertical by adt(; -nx( 4rzxq)0 dosi ldf8bxlj46b1 r3zljn angle $\theta$ 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 27 on/a eh ff*n5ei3lw If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle*n3oi/h2e flfw5a en 7 the curve?

  How long would a day be if the Earth were rotating so fast that objects at bvpo5 r qall,/4 4gge6the equator were apparently weiaqrl/,g4pgov 4 5e6b lghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dista-mntp0uxt(n7 .k/ agfnce 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 radius 235 m. A labph82s1k8 i q wmbz*c/mp suspended from the ceiling swings out *8 qkp2h s/wzbbic 18mto an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus e5q4dfr1t1nx5q rg-rhh y3 ehmz*d.*0zm5f c, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since peop*1d c t5rd3*ghmhqq r zne.fx5yf h5mz0e 1-r4le 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 presence of ne0rs3 * +rnwqan extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from 0nqw ns*r3 r+ewhich 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 valleys8dfa7rfno pjzg 3jxj 04(v2/ 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?( / g2jso3fna8d0p 4xzfjv r7j Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utz6)jc3u6jm1 vw zup6g4be 9 nzx/wtv5ilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine t 4vcj 1 5u b)w3tvpz9wz juxg666nme/zhe speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after trab n; 0zz,m1xa / b6piijxe9db:4*bk raveling 2.1 billion km, is meant to orbit the asterorbxnk iaib*0bb pzja1 x;d/, 4 6em:z9id 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 pursuing a satellite in need od;zm2 76shakgz1xr.i z /o2msf repair. You are in/; ao2z.z 1 xmsirmzk27dgs6h a circular 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 dist+4bfdriafb 7j a2)wo n 82nsb9ance from the Suna89)42a rbo2+ jw7snff ni bdb?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" y t9ebn9xz/odt qt/ne/6f;x p8ourself gravitationally attracted to t d/eexq9 9xp6 8 otn/nz;/ftbsomeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milbl i/ufrhw+a-*-;b acky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ce+aic- blf u/b -;ha*rwnter $ \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 yv25n 5vj )n.ivkx+ bxqkiftqamhvc *4h/60 ,square 0.50 m on each side. Find the magnitude and direhj6vnh.a+i0cxi5v 2 ,k/mt *vbk qf v5x4y)qnction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eap4 oufu d w:ofdg0y(*4 p/6bsfrth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep mktwqby xfjh0g8;;4 2+qpwcu as u 6k-7(/cujsecond hand on your wrist watch? (6a -qx/wub4m0yspkkuj 8qh c 7gc; jf;w +2tu   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around neu wza6f 4y76in 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 the fishing line makes with the vertical? [uw nz4ya66fe 7Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so yl)pylx2k y8suecwl0: +a*zq3nj z0 2that a car traveling at sp3wy2l0slpjx z ua:*l eyz0n2cyq)8k +eed $ 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, utiliz6bdwk(,7h vra( ax4j5qd 9 ja71ixqzges 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 passeng k( 7jj,vbdda6rxq i (x1wz5q4ha9ag7ers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$