Sometimes people say that water is rwsg-s23kw 5 odemoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statement?5 wdk-osw23sg

Will the acceleration of a car be the same oy4i(wm(jzrq5 ge k(:vwo: jxgo: l1/when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the samew/e(:4(iq mkojjx:vo lw( gry o1:5zg speed? Explain.

Suppose a car moves at constant speed along a hilly ro bcmwm)jtl.a-x57q * wcw 3vv7ad. Where does the car exert mcwlwqj-cv xa5 )77 vbt.*3wmthe greatest 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 m k*o/;;ftoes horse on a merry-go-round. Which of these forces provides the centripetal acceler;oom ;/sekt* fation of the child?

A bucket of water can bc58hzm4 8 q snel6ne) 2xbizy/e whirled in a vertical circle without the water spilling out, even at the top of the circle whee42 xemc5z6y) hnlnzb/ s88i qn the bucket is upside down. Explain.

How many “accelerators” do you have ikc .d+/yd)hgyba/nj79 p wqa+n your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they pro.dk )++ja9a7p/nh w bycd /gqyduce?

A child on a sled comes flyic p*x;fbei6m-hg,re l 4o +(oyz2m 6le:l:fjkng over the crest of a small hill, as shown in Fig. 5–31. His ze or m-2 4ce(f6 liolmbx:yh l6+*; epkj,fg: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 goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high5 ugz6 9n)hacp speed?

Why do airplanes bank when they turn? How would yo1x6xul3r s1f yu compute the banking angle givenlyxfrx3116us its speed and radius of the turn?

A girl is whirling a ball on .1:sm eexa 4lig;vwe. 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 e v:41i me. .;saelgwxon the other side of the yard. When should she let go of the string?

Does an apple exert a gravitat 3pg+ lkc w1(y0u iroz8x)oswna8 tt4vds.y) 5ional force on the Earth? If so, how large a force? Conside1l5rz tnidkyus (o.a3 0)p 8 v xyc)sgtwo+w84r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would b3p emlg ky6o1dl95,ie )ke*kthe Moon’s orbit be m6)eo9eklygl b i15,d*3ek pk different?

Which pulls harder gravitationally,d*x bw:;hwp lz.q*y 0w the Earth on the Moon, or the Moon on the Earth? Which acceleratesp ;ybxlhz. qww 0d*w:* more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tz1: vouzq1;/tf2 eamg he Moon's is mainly responsible for the tides. Explain. [Hint: Coq;2uvf1 mz/oga:te1z nsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at wb p zj6xv8ouy9*;qm l75+mxv the poles? What two effects are at work? Do they oppose each otv 8m 5x oumjwl;yz769pqbv x*+her?

The gravitational force on the Moon due tp hhlwybol:.14dws c-yk(:zpu0m 2v8 o the Earth is only about half the force on the Moon due to the Sun. Why is:.k 21wz4 yb8o -cyh:ulv (m0pdswl hpn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around t 0ns,r 8ooox5yhe Sun larger or smaller than the centripetal accele5o0xrons8o,y ration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) towr(;ah f,,kkv5 ftdpq-ard the west? Consider the Eqadf(kr,ft ,k hvp;-5arth’s rotation direction.

When will your apparent fci1x ) 0je+iuweight 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 caei1+0j)cxi fuse would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adrhar rp/:gi*qo7 6d/z versely 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). r7az hr*o/6i: dpqr/ gExplain 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 “freyr.3c(b 3gpneyz+ fzg /t7z 96w3ocqee fall” or “apparent weightlessness” between step9rgz 3n/cfp3 qw3y 7z.z(te +6ecobgys.

The Earth moves faster in its orbit around the:q ri) p6a8nik 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 6 8rnki:aqp i)factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not k.ras-ezy7, q v, bk,hknown until it was discovered to have a moon. Explain how this discovery enabled an estimate kvhz a ,-r,yq.e,kbs7of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than ther.gt.h8 l v5rh 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 1.10 mgtr8rl.v.h5 h 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 1980 jt3yotj-vxrywc * om9. nn*-xh(ks ,1$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleration of the Earth in its orbit around-+s 4crht q 0mom1p,bp the Sun, and the net force exerted on the Earth. What exerts this force on the 4r-pm, os1qb0+tchpm Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotahax 3i,d;9a mc8 ,hutetes uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of tum3,hd 9 aac8, htx;iehe discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ci1pdn dyq+dr/q:1g g,+ew6 n obrcles 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 , th :gq16 +ng ye dqwpdd+rn,/ob1e gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude ow-+5lc hso*q9)kdi yt f the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel i-k+hwcy9o q5t )*lds’s diameter is 32 cm?   

  A ball on the end of3d7n(h va ak0a a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speea hvad(na37k0 d 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 car7- g uw4jrc1mi5zn g)o can round a turn of radius 77 m on a 14cz7in m- jgr)ugow5flat 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 co e3o;e3n7 x:d2uu cm08xw gpg6hngv n0efficient of static friction be between the tires and the road if ahv8w 7n gu0 ;nemnpe3 d6c:23oxggu0 x car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter p nim-f52h u03fdn1vsi ilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee o f s03mhi dv-i1un2f5nn 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 rof9l7pcbb)lfl gd 1152m nca *htating turntable of variable speed. When the speed of the turntable is slowly increased)9pl hl cfn g7*fl5c1m1b2adb , 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 roller coaster be travelin lo.onq71b3 uafwsi. cq48 y(bg when upside down at the tooq8wc b( 4i.sn1f qaoby7u3.lp of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses (w8ies iy;bf)) er d2mthe rounded top of a hill (radius y2iew)emb8(ifrs) ; d =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to m9.8kt)pr 7 qxuffadj )ake for the passengers to feel “weightless” at the 8jxf)u)d rkp a .ft79qtopmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius ozcty::im8i1 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2o i m8:yz:1ict5.0 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 v ;gh(dmay,/fhbuqi (.b86u xcentrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,00(., v mhd8u/xb(ayg; ihbuqf6 0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotate:m z:s)e ngqk3d in a cylindrically walled "room." (Sekzgnq:m s3:)e e Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tabw+r -hk*ezqzs ( x3qkft+*e f2letop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central holx (fhe -*rweqq+tzfs2 +3z*kke as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the wlbgxla o9 1sx 5igcnr e*;i0:+eight of the ball which revolves on a string 0.600 m long. In particular, find the 5x 9 li+1xlg0sa* ngc:eobr;imagnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a c f(0r. y1)ubf4vryygdbah 6sr4r 6.hrar 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 massesdw19 uw: 4bsc447xlad fvo d5z $ 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 evasiv(xy vp*;p vpur.a3k) fe maneuver 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 centripk2axa 1 p6 yqb 0n)1ca mftrsrv*.vi53etal components of the net force exerted on the car (by the ground0aq1* ibt ksp26v1vran)ayrcf5x m . 3) 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 accelerate e8ujdpr-cfd;7/ w 3xhs uniformly from the pit area, going from h; pxdf/w8 7de -ju3crrest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires 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 ate*hznsz) 33hy1k fi8n gi- k; particular instant, itsf83n ;h 1zks y-in3it)k*ze gh 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 Ear:8 ba(0efixl k,auug;th radii) above the Earth’s surfaceu8u:i e, fk(ag0xlb; a if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratu3j(0clq mh9g 5fmp6u;s8ut u ion g has a magnitude uhsu l 89tpq5;j m6(u3g0cfmuof 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 themufz 55 us796:pvdihyk+q k* d Moon. The Moon's radius is 1.74 qk55pfi*u6z hy k9+7dsvmd u:$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a f4w h;7kbnr0lqmic 6 q72iv w5radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity n6v0 n2cwf;li4q i7 5w7qhr bkmear its surface?   

  A hypothetical planet has a mass 1.6 qe ,x. 2iwfswadl/;z86 times that of Earth, but the same radius. What is g near its surfa ,sw xwead q/.z28if;lce?   

  Two objects attract each other gravitationally wi64jx7 u wrety,th 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 acceleration of gravity, at (,dq /rsd-dakm m 4n(d.a) 3200 mkmd4ra. / d qmn-sd(,d    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ou5;2:pvzd k l ymo -8r74 nuwoilocg8(ktside the Earth where thegravitational acceleratyc ok;i7w(vln85o8:zod rglp k -um24ion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timesvi tf-)mmj 91lst((vhy s2-ts the mass of our Sun packed into a sphere abv- s s(t2l(j h ims)tvfm-1y9tout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average s4n/yc4- vp6ab 8dpbuytar like our Sun but is now in the last stappu cyn8b4- d6yav/4bge 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 whywdexr( v5 l9d *pvz27ile orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 25dxwyv 7*l2v dprze 9(50 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located c+:gl5 0s b v-ii 0ot(kxfdyx4at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational forct0(v ixco 4ky0gb:5i+-x slfde 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 rrhg5qmz 2(q3s*wl( wgpai:*of the Sun. Calculate the total force on the Earth due to Venus, Jupiterga5 wr(*l3h(qqzpims g*2:w r, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at qa0d v7+iuj *ithe surface of Mars is 0.38 of what it is on Earth, and that Mai u+adiq7vj*0 rs’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th wfpkv5qh;v;l +v,u;u5 tcda6e period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examplevk;cph al65d;v vt,w q+uu 5f; 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular s u/(wm89cg)vcg;gch orbit about the Earth at a heighggmg9;)c(u v h8 wc/cst of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65k6et.fpuey k(.;5 ank0 km above the Earth. How fast must the shuttle be movingek (pkefy.6k; 5ta.un (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spq/dnsz jpj 2gra db9zc2;*,8waceship rotate if occupants are to experience simulated gravity ofdrzga ;cs2 j/b9pwdq2j nz ,*8 0.60 g? Assume the spaceship’s diameter is 32 m, 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 Earthmzfz3v-w r 0;s+pc gz+ in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whigsz 3;w-v p+m0zfzcr+ch 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 wouldry(kv;ih8 ks* a satellite have to be launched from the top of Mt. Everest to be placed in a circvy ;k8(rsh*i kular orbit around the Earth?   

  During an Apollo lunar lan*b) q9 dle- djq.ofo ;vl9+axcding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take tq)x9o ;-vclf* +lbe 9q o.jaddo go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit z)z *3rwt5 ,mcwvx4ac8d/ m rjthe planet. The inner radius5w) ,8 zcma xm3rcd z4j*rtv/w of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 1.bz-g sv8 txfp 5*nx8zxcgp3s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her rpp1zf8 g 8s-xxt 3 xnvzc.g5b*eal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of th6xqsyp tin t3eeqvaga0:)4/iy )fd29 e Earth's Moon in a space vehicle (a) moving at constant veloci)0/nvy q6ea tyi te q392x4igp:dfas)ty,     ----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 g /s7ex4hdn 7kr/*lyvorno3t f+7 zu7of two stars of equal mass. They are obse77eu +nvtkolo ns rr/*7/ yd fzxgh347rved to be separated by 360 million km and 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 weight of a 55-kg woman in an el/ 4cq:lbz;dih e-zh dt3f z o32umv.e7evator that c7elio; mzh. d -ubzq4d2:ztvf 3 e3h/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. Thse (t:jd,s-jq dzw( .fe cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? asst- ez fwjd(j,( .dq: =   

Show that if a satellite orbits very near the surface of a planet wbbm16v27 tqme*vvjsz gx)b9.(,p yd i ith period T , the density (mass/volume) of bb9my v7qg *(2vjv, sez6xi.pdtm1b)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 detee .esq(jq0t/injr9e9 y; s,8js vzf.ormine the period of an artificial satellite orbiting very near the Earth’s surface. ye v (z8tj/e e.9oqjs0n .,r fjqi;ss9   s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik*gw a 5pur36 gxp7,puie the planets. Its period is 410 d.ia5g 7g x*r3wuu6pp,p What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average d 8wyy/8wea(muistance 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 orbit5*y *+huf wupo4y1b/ g7ohreps the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest a15b4*uh*fyru+pe7p/wh y go opproach (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 the center omws r1c2mk1 , o6c,linbype.6d23 rghf 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 u /6k ek-mm1m.c*w,sw mo;rwuthe four largest moons of Jupiter (those discovered by Go. 1w,m6s mmwe/;kr* kwuu-cmalileo 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 f5he(4d5b+nm z+ cwwj prom the known period and distance of the Moon. 5ph wd+bne54cm(z+ wj    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using pr sj,5 rni+vfb+c,(qg )aer3Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table. fq g,p+erjcb+(5s,i)anrr3v
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of manyi-r *ma)r0gan-m*b pq7 1tc oz fragments (which some space scientists think came from a planet that once 71at- mmnc)i*-q r0*rbzg ao porbited 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 artii :je; 4c6d tdsrjfqj,(0t jg )nhb,0nficial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the i ,ed0i j)qh 0; 4fr6jt(sjt gjbdnn:c,nside 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. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an w);9o (gackjiarc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest p i)jok9a(;g wcoint of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’m1b p p)(pcq dg0hj/5;sfko 8ys surface will the acceleration of gravity be half what it is on the surfcs q)f pb kym;dop8h(10/pg5j ace?    $\times 10^6$

  On an ice rink, two spl)tv)auw; h jsvmc 9qr21n 3sfh/xg+/i x/:v katers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg3 j )hs a/ vq9v2ix:vcmlhrn)ptfs+/uw/ xg;1, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once p:;.n i 1; nv/dgt( m2kaacuruyer day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn;a;cn.mavyutin / 2 :d(1 grku’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 travel8gcv2x mv6 fm4 )jlz4ming directly from the Earth to t486 m4 fm2xg vvjz)lmche Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in ;;w kaitp:t1hxr1 8 zman elevator, it says your mass is 82 kg. What is the :hp; wzx18kai trm; t1acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abycpi)ue4f sok 9ri5 +q9c/7tfout 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 surface9y c 7pt4 q) /ii5+fcufoskr9e of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertjpu +8 f/ot-w2aav mf7ical 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 planvh.+ s2p6m,*uqif k ddet in terms of its radius r, the acceleration due to gravity psh2v6 +mk. dud*,f iqat its surface and the gravitational constant G.

A plumb bob (a mass m h;biv cww,x,5r(wdq 1x anging on a string) is deflected from the vertical by anv(1,qwwr c,xb ;dwx 5i 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 If the 8i 0kedz;)+ndc -z lt0 lcpp3ycoefficient of static friction is 0.30 (wet pavement), at what range of speeds8i0 0e)cz-; +pylnzpdc3td kl can a car safely handle the curve?

  How long would a day be i h,x)/. yt xi(b)r: q5v w-zfypkwmuv6f the Earth were rotating so fast that objects at the equator 5,6xk/q- y)muwt (vz.rfihx)b y p:vw were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aparc x9bz)0.uldvuj;d pk8y)o v4 t 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 4rgkm07fe a1ccurve of radius 235 m. A lamp suspegr 14emfk7 a0cnded from the ceiling 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 c8p +cg8s;mos6hp 0(9 1epbuyrevt 5 hilaimed 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. Calc65er;msv( pp9c8pot hs yguh+0be1i8ulate 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 kiyfwk4q* .5qSpace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a kkqqwy.5f*i4 black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it tra rl67j6p0kv wgverses the hill and 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?)rlp70w6 gk6vj 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 group g7de2:ded,i 0 ig ra)eof 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.7 d0g dd)erei2ag:,ei 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 (NEAR), q ;94 kv0ynew 2qf+1vuajm9vj after traveling 2.1 billion km, is meant to orbf4mvvywqnj+9 v 91uk02eja; qit the asteroid 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 shut+ :tpo4+zmh.n lvjlfj *jzli*4b7* ootle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km +*jjzh vmln j*:o74tl*o.+ lo 4izbpfabove 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 .ur;pl-qd4brbx* bn5kr9z+ f years. (a) What is its mean distance from the Sun?9;q nbrrxz*5k p-du. bf4brl+   
(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 yo nbhks-a hq 16ttu/4;eu could actually "feel" yourself gravitationally attracq; th16-bukst 4ehan /ted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around lpue758 4sxg:woxkre74 x8xjthe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years froo 4gr8x l7 uxe:esxk75j8p x4wm 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 l78 sewr. (os5wk (yakcl5cp0hocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpo5.0lc7k s are(howpc(s 5 w8ykint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits t7n1jmy9bge ;.k tnqeue; b: hk+n1u,ahe 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 acceleratioz c7/o+a+)ke, xfwaxbn experienced by the tip of the 1.5-cm-long sweep second haao+,w+x/eax bk)7 f zcnd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circl) ci;bs5 ui2ss8rr;k wi*dr( (9c7eh1ud eno le below you on a 0.25-m prde(kc7 ubnr5 s*8o;1h l2i s()i w u9s;idrceiece 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? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desig;ml* l- m dk+6tsibdr.ned so that a car traveling at spe.rdd*t6; mkbi ml-+lsed $ 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 tlkv3 -zzf,//dxa3(d,ilzcbt rain, 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 norkza,tvl,bzxdl/3z/(-d3 f ic mal 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.$\approx$    $\times 10^2$