Sometimes people say that water is removed from clothes in us,giv5 3g h3 r *xg*7ydec;rfa spin dryer by centrifugal force throwing the watershiuv ; f, 3gyegc*r7d3r5*xg outward. What is wrong with this statement?

Will the acceleration of a car be the sk.ru6eiuih y dearft10q8,;; ame when the car travels around a sharp cur1uqf.eur yt;i6h i0kde8,; arve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car erugfnrec6ey ) *8e g.(e76vvexert the greate6rrfc6y 7g).geee evvu(8ne*st 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 riding a horse ok/yp r oyp8w*mt f:wu:a6ia90 n a merry-go-round. Which of these forces provp:k frwyauypao69w 0 i8m*:/ tides the centripetal acceleration of the child?

A bucket of water can be whirled in 9pjguoawj ib26 oi6;x5b5zp9 a vertical circle without the water spilling out, even at theu9 ij gb;ji6pw56b2oazx95op top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three c uj rpj 5p6zcasml+.sw,hj/++ontrols in the car which can be used to cause the car to accelerate. What are they? What accelerations do theyr/psa +5+jchw. +jzusm6,l pj produce?

A child on a sled cokvp xzky e/f:.w/3jc;fl4 b5pmes flying over 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 chest and the sled decrease as he gkz.j 3yv/4pc:flpf;/e wb 5kxoes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cur37baf5qh3jziy4g ubw;o c *7wve at high speed?

Why do airplanes bank wmygg5z 0n2;yi hen they turn? How would you compute the banking angle given its speed and radius of the tg0y m;g 5zy2inurn?

A girl is whirling a ball on )b oy,/nt)eqircn 9rh ;a a677sy1tmb-qz.l sa string around her head in a horizontal plane. She wants to let go at precisely the right time so that tariyl7cr tqq7/)n nbhe. ot1,)mzbs sy 9;6a-he ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational forc)n,d tj1.6mrydzn h- cun l6o5e on the Earth? If so, how large a force? Consi,ntycdd nr u6.6z-5)onlj m1hder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is06m- rv/ e2jsyq- lrf z9vz-ad, in what ways would the Moon’s orbit yr rj2z --zd/9-vs e0vfmlaq6 be different?

Which pulls harder gr0mrrlrr 9 ak9q4p2 idscn7m.1avitationally, the Earth on the Moon, or the Moon on the Ead ar107 k9smcpr nrm.4r29lqirth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Mooyum+s mqk;v13n's. Yet the Moon's is mainly responsible for the tides. Explaiqmm+kv 1;3usy n. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatorp c wfv0*vg/ *w 9g9c.izq2hxt or at the poles? What two effects are at work? Do t w *v9pq2g*vcwh/tcfxi0. g9zhey oppose each other?

The gravitational force on the Moon due to the Earth is only abouta7gvrvtho gb(d2:zd ;d; oj/) half the force on the Moon due to the Sun. Why isn’/d;bt (gh 7:v;go dovdjz)2rat the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lauokd) bjegb69e, w *dq.x um46)f8tdtrger or smqt xu8*mdd4obw g ,bejud6ef )6)t.k9aller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or ()y -dnvq m(f+du u;tu/b) toward the west? Consider the E - vu+tmfuqu(n/yd d);arth’s rotation direction.

When will your apparent weightrt(i bljkzzz3 4x,(sa .o cv87 be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight ks3 4v 7( tjzx8o clzb(ir,az.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 x5m:nxg4,ecg cyb 15a periods in outer space could be adversely 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 this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, andnceyx b ,a515gmc 4x:g (c) any other aspects of gravity you can think of.

Explain how a runner experience dd,ke pl:a e2ig0st :r8j9az+mmyq;0 s “free fall” or “apparent weightlessness” between stepd:rmit 2y0:ma9sl+ 8,z0eka; gqjd pes.

The Earth moves faster in .gfges v h/6u0its orbit around the Sun in 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 Earth’s axis relative to thge usg./vh60f e plane of its orbit.]

The mass of Pluto was ng d o2s:)jg 9s5mv-tfeot known until it was discovered to have a moon. Explain how this discovery enabled am g5g9sejtds:2) v f-on estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. m uqxj qop uvi;-p.j7-2mh4 *rYet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationj mi2mo*qup; .7phr xu-vqj4- al 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 travelingt27+ p/1cayyed npjlpx da ,2: 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 accelewp47u)nwnrv),p8hzxk0cl , b ration 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 )nw4vknxplc0brh,u ,z 8 pw 7)that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as i:brf sne l6h5/t rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of 5r lb:sh6n/ efthe discus.   

  Suppose the space shuttle is in orbit 400 yoxk6 ivw7(c8g5 6xrs,/ ndco km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express8y, xg5vi ncx6(do 7/so6 wkcr your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of 8,b)r.kl wgvva potter’s wheel turninggrbk ,l8.)vv w 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 rz jrof 1h 2y0d2v)al48rpc zw(ate in a vertical circle of radius 72.0 cm rvwfc0pz2ldy(82r)jz1o4 ah , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can r6fu6gx8juyy o+sx5 g 4) c1jbfound a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of txj6fbu ugoj gs c65)y4 +f1x8yhe mass of the car?   

  How large must the coefficient of zkb .utyaqolau;o640em 9jg,/c+6qry sit5 * static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speeoq ziey myl; 6u+*4 0 aba,qt.9 t65uskcr/ogjd of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designe*/v kw jga4u 1y2ccc(cd 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 times1ck/vcg4yajwu* (2 cc 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 fromgc. w.tvm-ur*g/ n7yaitywcm* /ni +0 the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed vat wun-*+/gcni/mcry. y*gt 7w0m .i 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 roller coaster b8(4jzazt8 6e syv ;amqe traveling when upside down at the mysqz(z 6ea8;jv4a8t top 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 db/e;lpxhq;fr .xmda t -a(1)oriver) crosses the rounded top of a hill (radius bh/dl ma1;toe.xqf(r)a;p x- =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-iux6 mrt75 )ndwt; bh-m-diameter Ferris wheel need to make for the passengers to feel “wew-6tu7b x5nid); h tmrightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a h*v5m3yws:pde y;.at vertical circle of radius 1.10 m. At the lowest point of its motion vt p:a3dywe.5m s;y*hthe tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuv*+idjhgj( sh8 f,pg4 ge rotate if a particle 9.00 cm from the axis of rotation is i hjd, j8p+ gfgh*v(4sto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatks fos)x cd;j.gt7 wg- n:8(pbed in a cylindrically walled "room." (See Fijfn skds7-8p;g(ctxg wb:o). g. 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-hocke 53ayckqssvt- u7c76 fy tabletop, and is held in this orbit by a l3 7s sk-c75q6uvtcyfa ight 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 ig4evl0xt bev): ,hu7ad noring the weight of the ball 4bht ,d) e7e0uv:xal vwhich 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 raqcj *s/ 5:e2mp,gdpk tdius of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masseh:es/up 3 4n74mvaq rt(-bixjs $ 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 3ixp) . zbc+v5c10 $\mathrm{~m} / \mathrm{s}$ . 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 an +8o1 f7iuhcsuob(r6nd centripetal components of the net force exerted on the car (by the ground) in Example 5-8 f 7oi sbu+ 6r(hn1co8u 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 d zufy/v7z m27 i72mzbpit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tang2 myz/z7bv7ui2 zmf7 dential 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 hor m/ dhtnnr82sv88h)mf2it k rdsx;41ii3 3evqizontal circle of radius 2.90 m . At a particular instant, its accelermshfeh3 t83);iri kd2rnx8 1 ti8qvsm/d24n vation 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 pd74q l3 ff 3wbfk8/ig(2 Earth radii) a7kwdl/3fibq3pf f8 4g bove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the g a0*b2uxdo 4-qca,tuvravitational acceleration g has a magnitude of a q,0ubd2atux4 -*oc v12 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 gravityob r)mu9e44ldy39 3mplj * wre on the Moon. The Moon's radius is 1.74 4j3y 9ldp wr *e e493lbu)morm$\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 .- rte 4id i;+r oq cfzo76rv-q:kmkj8c47bdeEarth, but has the same mass. What is the acceleration due to gravity near its surf7rqcok ib6v.-+je7i :ekt;c4rfrd4zod m 8-qace?   

  A hypothetical planet has a mass 1.66 times that of Earth, bu9)wsqmt,yj3 zo .l *qjt the same radius. Whaqsj *,).3 lqyz omw9tjt is g near its surface?   

  Two objects attract each other gravitationally wit mona6)roqcl0z,- 6 euh a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accelera*mpy a4 g9cs6t,+fidw+gzmwe8 n o:a. tion of gravity, at (a) 3200 m* oam9t.w,ws fc8 dpmn+4gz6iy+ eg:a    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to qhrzj vv)6 ecukg ;8,z7ek3c3 a point outside the Earth where thegravitational acceleration due to the 6u7eg3h v,c kqvr z3zekj8c) ;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 s;mma/g*iscrb vf9/z;* u xeb7 );gtzpacked into a sphere about 10 km in radius. Estimate the surface gravity on this monstev/ xzcm ug*ig/etbr 7s)f ;b*zs9a; m;r.    $\times10^12$

  A typical white-dwarf star, which once was an .qsf+v(hilr , average star like our Sun but is now in the last stage of its evolution, is the size qr (f+vl.ihs,of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining wh9okiqe x4m2o;n(be-t eif.- cpc bn.4y astronauts feel weightless 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.o;nbe cx--(qn 4 f4 9 bceem2koit.pi 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 squep xn3913v6eqad2 wah are of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other t6n3dwaxp2hqa91e 3ve hree.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the uk,l. tsx.bp)8 q jg3fsame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, agfx8bu. tl3).pjkqs , nd Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at tqs,; ui9odir9 kr wk2,q. jvd+he surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 340iokv;d wrdiu2 9k,r s,q.j+9q0 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using thk)9j( gqfdd5 xfsq8s: e known value for the period of the Earth and its distance from the Sun. [Note: Comparex59k:fsqq d 8 f)(dgjs 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 2k*e3 o4oseltj1)k-cv 9zfad circular orbit about the Earth9 d ajl12ef -o cs)v4kt3*okez at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite inxnc*vp-aua i j5 h18i8u,x.gmto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whena gvj hicx1in-5u 8x.m,a*8 up the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshiyibijo.z,4( k4t1rl v wuh8b* p rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your a84uj.,i tiw4 bo(rv*1h bzy lknswer 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 circular “h80j5xcrzpu jp)/zg+near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which +zjrzjxcp/u0) 8pg5h 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 lau6tw7eka 7uf8*xu. bx1f1or j *r;qi rsnched from the top of Mt. Everest to be placed in abxr; oxui8fj.wsu* ra76r *1kqe1 tf7 circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command mo1cgbznc6 pyq04x q+5 tdule continued to orbit the Moon at an altitude of about 100 km. How long did it tak0tqq1+5c6zgc ny bxp4e to go around the Moon once?    s

  The rings of Saturn arjy 1inhz9gdf ;dz*-;wx6i is0e composed of chunks of ice that orbit the planet. The inner radius of zhi9 y6w;xjf*i 0-zi;sgd1ndthe 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 ono;.(,:xje g,ek sh2 8nizw tvace every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the (e 2i w8vxts kn. eh,j,;zg:oatop, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of-62i)r+ mhhz(ab/ s+s1 peol5e iarqk a 75-kg astronaut 4200 km from the center of the Earth's Moone +o)(ami2i /5arse- qrk hpl+szh6b1 in a space 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 of two stars of equal ma,dr5zwxzdg tmxzp, ,q/j x:23ss. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them.z xmdg z 32jd,xq:5ztrxpw,/, What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for tfe7)bm ( 7bb*fjum9rq p0dbw9 he weight of a 55-kg woman in an elevator that mov f7j*)b (dr9mmqebufbb 0 wp79es
(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 elevatoh 3vow1 lk3i4or. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directiow4oo lk i3h13vn)? a =   

Show that if a satellite orbits very near the surface of abdj8b:9 8mcpu planet with period T , tj98 pb8md: buche 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 period of the Moon (27.4 d) to determine the per2vtf u zypzhfs73h/ 70iod of an artificial satellite orbit 3s27zfpzhfv0/yt u h7ing very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,ri5fr0-dn ddg0 la v,244g ldk orbits the Sun like the planets. I-4d2dlrkf gd,gi0avd r 5n4l0 ts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagezn+: tjh) )zom 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 Sun roughly once every 76 years. 83fpp-mmppq er;2 6sxIt 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 planet’s orbit is nearest when it is out there? [Hint: The mean distance;3mqf-m2ppe p8rsp6 x 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 cente;mj +owk7w t.fr of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the tfn0,ws2wy- m wko*0tfour largest moons of Jupiter (those discovered by Galileo00mwsfo y *w,tt wn-k2 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 th io+;.u*xybg ze Earth from the known period and distance of the Moon. oyuzg;.* bi+ x   $\times 10^{24}$

  Determine the mean distance from Jupiter for eaa ed:za8 mn7c7ch of Jupiter’s moons, using Kepler’s third law. Use the distance n8aa7:d me7cz 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 befuyt5mjda t r, m,+0p wcq54w1tween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet tha+ t pa 01dtqymwwcujfr55m4, ,t once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band c zlg -53wta6s0k/mj uoompletely 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 5/lkmtj 60uo-s a3gw zon Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorgec;vtz 3x lj0y3bw3 dw1 :d+llr by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of erllx1c;t:y33d j w3 zldbwv0+xerting 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 surfaclwog,:hv)t-mm0hcp* kufx i j* (w*k 6e will the acceleration of gravity be half what it ml(o-:wht6kujhk i fx*cv*pwm )g0* ,is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual 80y7uv; .ubbqti (mr;xzmn7 scircle 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 th7uu 0mn bb(rv8;i;xyt.s qm7z ey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per d2gh utyk45odw 7) 77k+16ingnxsuyiwi0ryi6 ay, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didgirk72 oyiy7dik0u6n 1 xuh4sg+ wwny t)7i 56n’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly fromytazlic.i6o y1 /7 z fz5-ah3x the Earth to the Moon experience zero net force because the Earth and Moon puzzaly3-.fh/xiz tc 6o7 5a 1iyll with equal and opposite forces?    $\times 10^8$

  You know your mass i,uyw ,1.c yhcqis :j;qs 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass c.jcqq i;1 sywhy:,,u is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consist4uu0+5puzvx6 a yf0i ts 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 (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felta +4f zyuui5xv0 pu60t?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical+lu( t;b dpv hfhm14l1 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 in terms of it2nuqw r:1w5: inqe1kxs radius r, the acceleration due to gravity at its surface and the gr5:2re qin n1u:w1q kxwavitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from ;e fxhz7k*e2y the vertical by an angl e k2*xe;hzyf7e $\theta$ 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 tc(7oj ryo:/xmhe coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safelyjom( r7 yoc:x/ handle the curve?

  How long would a day be if the Earth were rotating so fast tlc79m 09*iexk8mr qxihat objects at the equator 7il9ie90k m*8rc xqxm were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanceb).+eqvf n 1ac ig6u:x 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 sehi irf//:i4i+/ux ykn7 hd.i9d a5m. A lamp suspended from the ceiling hiei4h9/+ di sdki aimn/ /:yxuf75r.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. Thus, it has been claimep(: )-vnyxutzd 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 uyz-n(v)pt: xwould 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 an extremodpbu c2h37:1 tj- byiely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did thisj7h y-ipb13 uodtb :c2 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 a;*/1 pq*5jrk,lj m qqmur5cf vnd 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 go without losing contact witcml*mvrjqqu/;krj 5fq, 51*p h the road at A?

  The Navstar Global Positioning System (GPS) utilizes a pf+y,xx4 h:qn2izsv) 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 Ear:fnz+ yx 42ixv)q ,pshth, 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 Asteroid Rendezvous (NEAR), u s7wehs t, 637xp3hfvn4td.jafter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about w,hus6sp3hdxt4 7v .fnj3 et715 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 jtcrb*y3x5,j 4 aoru)pace 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 E r4ut*r,ajcoy3)j5 xbarth), 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, swy4lr m.x0p of 3000 years. (a) What is its mean distance from the Sun? 4 ,ym.0xprswl  
(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 woul*;y/rv *qud dx 8 :o5rd(zt pxjbk(1ztd need to be if you could actually "feel" yourself gravitationally attx y*j:*t;z8q ( k/z(vodudxtd1rbp5 rracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Figg(s-nj ua/, o*elqv* samdh v,2.vgq6. 5-46) at a distance of about 30,000 light-years from the cengds vq6a.lq ,a *gem,2s-hn(vv/u*o jter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each sh :aj;*ie nzx*xa2z6t. mboqaj) xp1 +ide. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed *j+h t* 1z2xanjb 6 p:ia;zexxaqm. )oat the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg,v q tf3cmtd.spzw y4g; y,lzf4q /-*m 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 etl u:kg3):sgm xperienced by the tip of the 1.5-cm-long sweep second hand 3tl:: kmu gg)son your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around iy likno5ut2b 60-d*pln 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 wo -byn6ll05uid t*k p2ith the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiuc*73*ikuzv3hz n, rb92fki2hf f :lg fs R in a new highway is designed so that a car travelingfvi *bnic 29:kf,kgrz lhf*f33 u2z7 h 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,r ea99yd5,q5c kt4ipb 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 q5ay ir 99,peb tdkc45of 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.$\approx$    $\times 10^2$