Sometimes people say that water is removed f- +.,g,obvgn(o dmiwvrom clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with , +dwgnom.i, g(o-vbvthis statement?

Will the acceleration of a car be the same when the car travels around a snft,/-k z ea+:154hblgthskz : l; lotharp curve at a constant 60 km/h as when it travels around a gentle curve a,l fnzge4/ z:ahkb:1 t-5t l+s thlko;t the same speed? Explain.

Suppose a car moves )k6hsycpnl +dmu / jvso28*9pat constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between twuod c pyn8l/9ksjp+*ms2)6 hvo hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hz. sfov c 7n44f83ujqxorse on a merry-go-round. Which of these forces provides the centripetal acceleration of theu.f x jn34v q78fscoz4 child?

A bucket of water can 7 hdo-ljcwe+ucy3,2vh f d -0mbe whirled in a vertical circle without the water spilling out, even at the top of the circle when the buc0d+udm 2ehhfwlcjc oy,3 7-v-ket is upside down. Explain.

How many “accelerators” do you have in your car? There are pgodlk0+ c4 yaz0hv2en) j**jat least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations dplj yc24*oa v*he j 0)+ndgzk0o they produce?

A child on a sled comes flying over the crest of a small 1( :g utfvbfn0zz*,kswu32 m thill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normaf*( z,1zvfbtntmu kg2 0uw:s3l force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curvex 2fi1apyr/ecq.b: (w at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle g31ge/s x(f vd 03h.yaub,twotiven its speed and radius of the turn?t3x0 y/d,fego uhat3s.vwb(1

A girl is whirling a ba3 fas :tj+0*v ;dcolxgll on 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 o;a +gxfj t3v*dolc:s 0n the other side of the yard. When should she let go of the string?

Does an apple exert a wl ej6dsmj.j0 .zn * *qg:l1sugravitational force on the Earth? If so, how large a force? Consider an .*j.u:gl*swjjqn60edl1 smz apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were )sxf (by kwx5cvu;cp l;+y prrc9(m.9double what it is, in what ways would the Moon’s orbit be different?.;fxwrc5p(sxp (c)yr ml+k; b uy9cv 9

Which pulls harder gravitationally, the Earth on the Moon, or the Moon ls l,n01dk6hkon the Earth? Which acceleratesls1h 6k0k, ldn more?

The Sun's gravitational pu fepk;k(y qm9i2/vdvs0wu4 l;ll on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsiblef;ip9k( 0k;sq me4vdly2uw / v for the tides. 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 effect(y kt1x/7mx4tfnwo 1 qs are at work? Do they oppose each ot7xn1mttk(x wf/ 4 yqo1her?

The gravitational force oytk)v wnd:n0;hy+vlx b-+a(x n the Moon due to the Earth is only about half the force on the Moon due toanldvyh 0()+ :b; k+tvyxwx-n the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acc l t4/;.vkculveleration of Mars in its orbit around the Sun larger or smaller thal/ kc.ltu;4 vvn the centripetal acceleration of the Earth?

Would it require less speed to launch a satelf r) ow2p od,kthz/0:* ads5ulfu3u*nlite (a) toward the east or (b) toward the west? Consider the),f2/o0*ualdr n :ok3tph*wfu z s5ud Earth’s rotation direction.

When will your apparent weight be the greates6m.qf6p,nng et, 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 would it be the6mn e,.pngf6q 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 affectedhj unu om wapg8h).8:* by weightlessness. One way to simulate gravity is to hj8uapwhomn*u: g).8 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, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appa3l28 10 acmgzefecc:v3r qw1d rent weightlessness” between gz v1dee0c1:fr 3lcm2caqw 38steps.

The Earth moves faster in its orbit around the Sun in January than in July. Is .(wp/y eg wr* -(rfncsthe Earth closer to the Sun in January, or in July? Explain. [Note.(wrf rge(/ ws p-ny*c: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was disqx l8/gq9;c (hskkni ;t,hri. covered to have a moon. Explain how this discovery enabled kl8.rhg h9iqnt;ki,q/( ;csxan estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tr; n eb75bd7+asjb2xh he Moon's is mainly responsible for the tides. bhb77jx2dr;+en5ab s 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 1980b3 4mznv9s:lk83(s 5hl tt hwo $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 g-kqqasp9,- aflgl2)k+b u/ b l njg8.acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth ggb/ ku)9ls.q8 , qaljfnk+2a- -lbgp? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exejwbpv+. y3 10kbc1grhrted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length).cj0h r1kgwbpb3 y1v+ of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's,li- cg6bmq*(el :farol 0(j s surface, and circles the Earth about once every 90 minut-,e:0slrjmca(llg 6*oi q(bfes. 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 acceleration of a specy-wbki juu* c,bmv. p0 9zq8p)k of clay on the edge of a potter’s wupj8bw9b,p)i mkqczyu-* v0 .heel 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 rate in a ver,+d(kb+d kehvfds +8a5p u7xxtical circle of radius 72.0 cm , as shown idhx87s u,kp d+eb +vad5x(fk+n 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 witbe .x/9grsbtr ko w57+h which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient oft9w/ +k5osr7b r xbg.e static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the co9 * * loxfi::.6 i dj2hqrt*nevy+jwksefficient of static friction be between the tires and the road if a car is to round djvoi:+qes2.t6kr9 xn j:wl fy*hi** a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronau4jre(qouo 35mqr :2kh ts and jet fighter pilots is designed to rotate a trainee in a horizonj :m 5o3ehr4q2roqku(tal circle of radius 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 46 qzhp:5xlbethe axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin re5b 4q6xzlph :emains 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 roller coaster q0t ik-w.b1zy/+ rzu1 j/nkjzbe traveling when upside down at the top of a cir/j- ubnkyz+ 1 j1iqzr wkz0t./cle
(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 1ec73(n n 8f nf0tm:qbizfh6x the driver) crosses the rounded top of a hill (radius =9c0bxf1etq768 ni:ff 3n(nh mz5$ \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 w3je c37rc5yl n m0wa*pould a 15-m-diameter Ferris wheel need to make for thl3cnre7w c0j*5 p m3aye passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad.ve) h1i hr+ebius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buck.ibvhhe 1r+ e)et 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 rotate if a particle 9.00x3; k a;tou7sd m9z*my cm from the axis of rotation is to experience an acceleration oy dt;9kma3*;u ms7xo zf 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindri ip*k q4nju:1ycally walled "room." (See Fig. 5-35.jk1 :qpun4iy*)
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 ) 1,dt kdry8;j6bmep7 h 00qtqz is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit 0 h t7meyjz r0;,6kb 1dqptq8dby a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this tkj26s vs.jy:dime, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the m2ydjs: sjvk6.agnitude 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 rad0cw;qs lgefbdg x ;j*8id /l95ius 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 massesxrnxif)6ok 8 zr wlv:)x2;12evww 1j m/2bkfc $ 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 maneokhz 5 15xpsw,uver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and 5(6zcspbsv,tp:3fbx centripetal components of the net force exerted on thbstz,pbcx:p65vf 3(se car (by the ground) in Example 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 areakm am/6027t vo)zin(ywu1uj7 zzfg )a9wk a9x, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of9to9kz zjy17iz mfu7w a/mu2n vx(gaw ak) 0)6 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 horizon8kpu qxye- 84ital circle of radius 2.90 m . At a particular instant, its acce84eu8-k qx piyleration 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+ay sf;w w:m0t:lmiajbx i):*’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mmw0balf:i w) s+a ;m:x:jy ti*ass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hasoknub0v 7y-(vls(4ll a magnitude v0(lolbkus7-4 yn(v lof 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radiu19 c/f3nvwhfpf ynq l 3lsj809s is 1.748pn93w1chj0 vlnsfy3 9fl/fq $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 ti7warg rpm (, p4ehvfokz6rl8k* h*iy2v/ot+ /mes that of Earth, but has the same mass. What is the acceleratiohl,8*f vrrh26/kg 7itrva4pp wo(y+ekz*/mo n due to gravity near its surface?   

  A hypothetical planet has x.)b ricpl, n8a mass 1.66 times that of Earth, but the same radius. What is g near its surface,ibl.8pcr) xn?   

  Two objects attract each other gravitationally with a fo k 4dmv9tg7-yarce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration euzx9a6d8d /o8s nh0cof gravity, at (a) 3200 m/xzd6 sda8 809ueonch    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center0tn*jb;ko3or7u p vgoqv7q7 j1lp*1r to a point outside the Earth where thegravitational acceleration due to the Earto07;7 q 1vo qlv r p1tojrk*pj3bu*gn7h 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 sphud;u.9nuruaqnc/7y+n1/v b t5ojfk 7ere abo o7jdau9yub1rn7kqu.u;5c t /n +nvf/ut 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star xevm pm12t23gtk)z1 yr,emj/ like our Sun but is now in /xj2ttrmp)y 13mgzv1ke m,2ethe last stage 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 orb1uq wfx2b;a h:s35;udpdoi c souk1m4qsb 69 9iting in the space shuttle. Your friends respond that they t ;1uux iwmb p sfd65u99dh;basqoc 3 qo42k:1shought 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 in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squareep)d- : 9a n0imvznh 6plj7se+ of side 0.60 m. Calculate the magnitude and direction7 inved):pme+0hs9- j azp l6n 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 upe01a:r mmnd9 r on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). Tr0:d9nmm 1raehe 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 ah z/zuag625 mw m::0rz0iraih3juo z7t the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the uir r0zz/3zg60j :m2ma : wa hiz57houmass of Mars.    $\times 10^{23}$

  Determine the mass of the Suy2x fsk tww.;41s8g7 gd6 zqxnn using the known value for the period of the Earth and its distance from the Sun. [Note: k.2zw;gqf 4s18s7xnwx y6tgd Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mexrelubd*/ dg2upv( 5y : /mn)oving in a stable circular orbit about the Earth at a he2 p:*m(/nl 5/rgxveydued) buight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite iiue9f3rr o:6b nto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the re:u9 e6bo rfir3lease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expe;zjrlmo2.eh pw9a,su4eo ut2*-b+ yvrience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your ans voe.rlm2- y9sb*awuj zh otuep4+;2,wer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orh*i. nawj+i2 ubit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of thn.wj* 2+iahiu e Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top 0bfib,ivr .n4 bt;l/ hof Mt. Everest 0 ,i4fhnr ./it;b vlbbto be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing miss 39tj(f45feb ntp6f hbion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take 6j3ffbh n(tt4e 5bf9 pto go around the Moon once?    s

  The rings of Saturn are composed of chunks 2z526o zxrlw zxjz * ygkvnn(c/-6 ;iaof ice that orbit the planet. The inner rzyzraxxv6gn/ (6 ;-n 2jkzolz5c*2wi adius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter r52 (fta u0)/rrcc 1 a7axdm:trem iv*totates once 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 top, and (b) c dc(ru:amr5t2 / a1*ve7t f)txram i0at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cen t;ygg9(f)z9 vka:t h6q;ly siter of the Earth's Moon in a space vehicle (a) moving )kt9is yaf: qgh(9yl 6gz vt;;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 stars37 rkaefgp1 wo/nqe.b2,0 ifw of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a pqbe 1 wna7,o ./k 2riw0efgp3foint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale91 e 33gh2j1lv*l8,g2eh wk hibgq ahh read for the weight of a 55-kg woman in an elevator thahew2gg3 129,gvh3*lhja b1 hl8q e khit 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 hangsv 5 rrkfl(rmnkz0*vs( . bt(x. from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitudemr t..b lfksr(zr x*0v5n(kv( and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wb24 +rad vzlg ,c;/xxvyll,6zith period T , the l64crgv v+z b,az,x yll2d/;x 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)n ah 867b442krw 4wywfeszf0 m to determine the period of an artificial satellite orbitibmfw a y ehn4fs6rz0wwk2 7484ng very near the Earth’s surface.    s

  The asteroid Icarus, though only .) .ginh7bqd z5e8zxq( oqen; a few hundred meters across, orbits the Sun like the planets. Its per z qebx.(75hq)ind8n g; qezo.iod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average a0 x 5jwu2-mjadistance 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. I(nizi u4q uo3:t comes very close to the suuzi4: 3n q(iourface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about thek4, ;igxv) of es6x-tt center 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 four largest moons op w6e*:halpx+ l*.ib+j t ,8ci yfu-vjfj*ap:6ilivlb. 8 u*yjc +w+,peh xft- Jupiter (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 Earth from the known period and distance of dtauf .68yya 1.h;fgdmb6 j6o the Moon. goym1fdj ha.dtbfa y6.6 u6;8   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’f q7juf/;p4+fu 8i /fe yzuqh2s moons, using Kepler’s third law. Use the distance of Io and the pefe/;uq pu i47yff/+ q82j uzhfriods 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 consistx t) 11dbkb-jrs of many fragments (which some space scientists think came from a planet that once 1xt-b1br)kj d 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 codbi uc qm dkh1;9 yp;q1;-ifnz0 q2 -f/hc;xxvmpletely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Ima ;ixpn;-ki;/qfvuz 9-hhdd qxmf;2 c011bqycgine 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. 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 vine (Fig. 5b+jwxfu 1blb9ahy , e np563*e–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.53be, bh1j9 pbewy56 fnu*xal+ m long.   

  How far above the Earth’s s7+eq enan p(i*oupvcoj*hb eo6799* z urface will the acceleration of gravity be half what it is on the surfop (+npu*h97ie b76*nee zaovqo c*9jace?    $\times 10^6$

  On an ice rink, two skaters of equal nf kj6* .v e9bwe y+4q,pm kbev8ymu1:x:cy u;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 60.0xecfm1.u:y; w 8:6p b 9+jm qyv4 v,bknyeuk*e kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparr xyme:, yb+ mu*dbnx/+vj-q;;)n u oment acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of thu ;yxu- :boqe,+d v;r)b/x*+m mnnyjmis effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecs4fwsg++r z(ygxwa 3) raft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull) fsr4y3+a +g s(xwwzg with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but i:xiip quu1 0/when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the q1:ipx iui u0/acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station cons5tq*q )au mn7 ;yetyq9ists 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 beqy; tqqu5n*7 )9ta mye felt?$\approx$    $\times 10^3$

  A jet pilot takes his /4rby ix5+,g0s;nziipy) wtn dmv ,,yaircraft in a vertical 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 term b*xu* :w8njcg,+ u(vsjgau q)u p8vn/s of its radius r, the acceleration due to gravity at its surface and snngj ubqawuv:pu(,88*+vj */x)cu gthe gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the4tmvjze ;vo.)11oscaco zfp7 1a+tm; vertical by an ang+) 1ajozac1mcp zm;o.;v tt 7f4e1vosle $\theta$ 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 fxtongqk41v+c//vq z* +uew3 hor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of ne/z3gc4w /vt*v+q1+uxhko q speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at ti-8cx- yqfm (bhe equator were apparently weightlessbcmx8(qyi - f-?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart exa w2v)fm(8 p 2wsjg9yjwl6xuse)99of 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 spee 46r5/x 4imkdngg( oj dc ctgluf; o5n6;1:rejd rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle;nog;6g4 i e g5(klrtn o14uxcr ddcmfj :/j65 of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timexu-sk ,354ksgdk 80ginfuz1ks as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate thedk ,5s4ukn gugiz8 k3x sf0-k1 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 Tyr *.; zqtnfw0elescope deduced the presence of 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 measuring the szftn; *y.w qr0peed 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 va 4u uk5q3h sy9qbg,n0hlley 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? Smallests3yh5uh0 9n ,4 uqbqgk?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gg*n fr ofli4q l0(cq1,roup 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 withgi0*lfr,q f1 4 oncq(lin 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 the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NE-fn vewl/ ,1j.d)zblzAR), after traveling 2.1 billion km, is meant to orbit the asterw/fbl1je,vn.l z)- dz oid 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 t6;d.l(l l zj 0jzisng io 91wdluk7j/8he space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above tlkd ;lj06j lzo d9ls7i. wng(j 1iz/8uhe 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 hasyx+to(sbfjma / 3 ww o./g;r*p a period of 3000 years. (a) What is its mean distance from the Sun? ;rsoyx (ft3w b//.j*ow+ gpma   
(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 acb,d, cw0/yq auc ;qz,xtually "feel" yourself gravitationaw/,zd,cay,q cqub;x 0lly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around t *e1dni49b wm:r /klrfhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ldnmkf:wil 9r/r *be14ight-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each sidehnivb zh(7 :b.. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of z . vbhb:7i(hnthe square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg o+vu* wk vta kgx0*+1gcrbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long 2cs 1g9be,ceizeka5 8 nymx;/ sweep second hand on your wrist watign5e8c9 cx aszee /2m;bk,y1 ch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a3d11gy4uk245u x4z vnyhx fty1t(she circle below you on a 0.25-m piece of fishing line. The weight makes a complete cht34v(5 yxn4uy 1 4th ze1s2x1ykufdgircle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is des8frg rwq 4e/pu/7gd9 figned so that a car traveling at sp7/edr r gg4 uq/wffp98eed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes ti7kp:0aei 7yxui(z ku- 3dif 5r: vja6clt of the cars when negotiating curves. The angle of tilt is adjusted so thacpair7k:ev06k:y x u a-ziu 3f5(7dj it 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 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.$\approx$    $\times 10^2$