Sometimes people say that water i k qyy.1j (thpb.aw69ps removed from clothes in a spin dryer by centrifugal force throwing the water outward. Whwp ya.p(hq jk1tb6.y9 at is wrong with this statement?

Will the acceleration of a car be the same when the car travels aroun3htoh 6db -kk6d a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explaikt h6-b3hkod6 n.

Suppose a car moves at constant speed0,c 0wza2ow drjnc 4q+bsv;n3,zcvo. 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 two hills, (c) on a level stretch near the bottodnc cvzz,c n o04ja0b ,2w3vswq;+. orm of a hill?

Describe all the forces acting on agg0vcm fol2-tq 3 -3wl child riding a horse on a merry-go-round. Which of these forces provides the centvq--clt2gw3go0 lmf3 ripetal acceleration of the child?

A bucket of water can be whirled kw1j;o :ufqk-( qn;pr)ir2 ws in a vertical circle without the water spilling out, even at the top of the circle when the bucket is up;s1iqqn o)wr(rk;fkj u -2:w pside down. Explain.

How many “accelerators” do you have in your car? There are at 4lt38c ;6blmfyf,r u dleast three controls in the car which cancrlut;,8dlf 6b 3fym4 be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comeytu3 5kh*xvw5h)hb6u8 sx /bvs flying over the crest of a small hill, as shown in Fig. 5–31. His sled does nb x*6b58 5hv3 )/twxukhh yvsuot 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 high spee b+ 4yshb m;;8*.na uamz/p:avtaj h7h xhad)9d?

Why do airplanes bank when they turn? How wbra/-qubjbq9e;jf6 /yt8+ gl ould you compute the banking angle given its speed and radib/ 9 fb6tqu jal;jr -8e/+gqybus of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shey wr80o iag4n1i0g8kc wants to let go at precisely 0 8ya80rgo 4cni kgi1wthe right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If2ms1o .sqx5nf so, how large a force? Consider an applxq foms12n 5s.e
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what waysubc(8of04 j:09o 5tdkl od xpn4oxyl5 would the Moon’s orbit be dy l: oo0lp x (ko jdc9nfx85odb44ut05ifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the g) jjfvmh zm-5a )++hnEarth? Which accelerates mor5h +agmmj+nzv)f)-hj e?

The Sun's gravitational pull on hz1*po hk.q/tthe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Eahzk./t hq*1po rth to the other.]

Will an object weigh more at the equator or at the poles? Wh 4dj, f*p 39qzxfjxm7:6gif juat two effects are at work? Do they oppose each other?4j9jz xg imuqxff :j3,67 *pfd

The gravitational force on the Moon due to the Earth is only about half t7a 3x+f nio4 2-er t7jz9ps,n7y enomlhe forcepf+enr-n l7x3e,y7o4zj inso2m 97t a on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal a5e( 1btay:tc: knkcx4 +w wo-vcceleration of Mars in its orbit around the Sun larger or smaller than the centripetal c4 xcy-t(:k kbot+:vn1ea w5wacceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eak x.p. s47ptdist or (b) toward the west? Consider the Earth’p4 .kx7.sdtp is rotation direction.

When will your apparentm2 skhcpxn 823 weight be the greatest, as measured by a scale in a movin2m823x spnckh g 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 the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods c 7 d(u hdf)pxgg3.xqc0k fb(1in 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, (bfhd1 x(p fuccqd) 73gkg.(x b0) 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” op;g/q o4eenf 4 64bjdgr “apparent weightlessness” between steob6eendj/ g;q4f4pg 4ps.

The Earth moves faster in its orbit around the Sun in J -xoroxqk:l w sg:4o*5anuary than in July. Is the Earth closer to the Sun in Jx*:-qooxkl :gr4so w 5anuary, 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 the plane of its orbit.]

The mass of Pluto was not known bbyvrex80 u5 5until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s u be5b0 8rv5yxmass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Ye*)6u1osto:a bsc5g4ce f2gay t the Moon's is mai)6o gcgeu s5ob*sa4 c:1ayt2fnly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling f lb9pus1 nq*;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 acceg,,p 1m 8kjkw;dm5nv ileration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle8 nivd,51mkpwj gm,; k 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 discx7x 1tw53lxly h1 92q wj4jzjcus as it rotates uniformly in qjtj7w hxyc12lx4l wzx9j 531a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from thex 5rcm9q6l1t l Earth's surface, and circles the Earth about once every 90 mrt56lq 1xmc 9linutes. 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 speck of clay mb1wp fc 7vgw25:p(52 j rvhimon the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if wv 12 rh5pg w:57m pjb(vmcf2ithe wheel’s diameter is 32 cm?   

  A ball on the end of a strmeq(x-d(j 1o uing is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If j1x domq-( eu(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 spr5 lputl1e 5r mkl/7-keed with which a 1050-kg car can round a turn of radius 77 m on a flatk7l lk-5r/pue t 5l1mr road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tiresqf+-wb ncjgns( p2 f25 and the road if a 2 pf gqw(j5f+b 2n-csncar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed gyuwju4*6 6t eto rotate a trainee in a horizontal circle of radius 1yw*ujeutg4 66 2.0 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 11.4ij/l 3 ma*llgm5*p jg0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turnj lmg/ ga* j4lmpl53i*table 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 travelinikv,u g9 ;d:iawc4ym 6g when upside down at the to, y9mu iic:6wg a;v4kdp 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 (incion67h1cw : v(i 5csdcluding the driver) crosses the rounded top of a hill (radius (n6:7s oi1vcidwc5ch =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 Ferrisi7z*5v wez2cz wheel need to make for the passengers to feel “wez i5z*zcv ew27ightless” at the topmost point?    rpm

  A bucket of mass 2.00 *k1dj6 z 0y0gw6mx0 mf1cg. xaxknr; 6czki8okg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope su0o mwjifcry1 6 6gx1 zx.ka x8c0 06dgkn;*zmkpporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotat /98+q3c+bwc.cv d s( dosecehe if a particle 9.00 cm from the axis of rotation .csv w39chq(oedc+b c8+/dse is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated(ajyc:pui7j . in a cylindrically walled "room." (See Fij(j7aciy .p u: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 frictionevan l0ss5af:948efmless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) thrfm9svne:a0s4 l af58eough a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of th xbay0*fspb1t i2fs(0e ball which revolves on a string 0.600 m long. In a(0 bfx 2ts01ip*fy sbparticular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is pnm ovjunn t4g/(.b-fthbp fl *:u.d+1erfectly 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 masse+ kz kok1i3es8ywb 69-hkut.ss $ 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 divinbwj k8m ;7; txph)zp;cg 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 centripetal components of the net force exertecafj ic,f6m9:h+glg+pu/ urc4c -nk 7d on the car (by the ground) in Example 5-8 wh: mfn hukg7ju 6l+cfi9+-ar4c,/cc gpen 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 thlro *z/is y1 d6(n ;gdy-rvd:ue pit area, going from rest to 320km/h in a z*; yug1o: nsyidv-l(dd/r6r 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 horizp)(madp 9l g:* ejl)w/e8eaptontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.me e (ajlgw9/)l :)ped*pt8 ap05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 12,80vq587bds.z ue 0 km (2 Earth radii) above the Earth’s su 5.zqd7b eu8vsrface if its mass is 1350 kg.   

  At the surface of a certain planet, ;d7 9si+it8cqtpc lv1the gravitational acceleration g has a magnitude of 12 l7cc+9d8 iqt1s vti; pm/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 gravpf: -6omqne+ dity on the Moon. The Moon's radius is 1.74qd p6-o +nme:f $\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 Eakywu5x-i* t*ga qc-)o2v ue8hrth, but has the same mass. What is the acceleration due to gravity near ck2* )x avhyeugq-i8u-*to5 wits surface?   

  A hypothetical planet has a mass 1.66 times that of Ea6c.cqcaqgp 9k4sqn aq gdnj1u /yse27p7(;b3 rth, but the same radius. What is g ne(c7gnnsaq.3eqbgqk 6/cds1ca7q 2yp4pju 9; ar its surface?   

  Two objects attract each other gvq9ceznkos.xc 766dshc; 4f8:wdrx *ravitationally with 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 valuej pf8z,7m -ypo:2wjl t5kws7 y of g , the acceleration of gravity, at (a) 3200 m mjppy,kw-z28 o77st wljfy: 5   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the3t y/wywkbahg7e*1 *z2 uqxxnfnn:q.t8+h 4n Earth where thegravitational acceleratiof17 2yn *w :nga*8ktq eh3+4bnun. /ywxtxqhzn due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun 9 6p)bigyc t:rpacked into a sphere about 10 km in radius. Estimate the surface gravity on thistp:cb6y )ri 9g monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun 8xbrz)c hk0hq(95 coz9)rk1k2fgciwbut is nowhc) c9z z2 frx0kiw)ko b89ck51h rgq( in the 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 astrow7e+ p(xk p-m*y0 enahnauts 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 acce+ewxayph (m*ke 0 7n-pleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are loca r qp5j6ca)q ht- agfb5: kv07b;f8xputed at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphe rpbqu7vjq5aa p6 hc )-5fb0k;xt:f8gre by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lio0 rn fyl;4l);gnchs- ne up on the same side of the Sun. )ll yrnh4;f-gon0cs;Calculate the total force on the Earth due to Venus, Jupiter, 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 the surface of Mars is 4 4;tthx8yb8.baoakgn oe .9g0.38 of what it is on Earth, and that Mars’ radius is 3400gnx;8hb8o4ao a .t4.9 eybgkt km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usinx43pg/5a 9di;eepfuf x7m7w m g the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s 3u fm4ig 5 p;axfexd/ 9e7p7mwlaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit +8ljeyg2ns1oba 7q 6cabout the Ea+on q2ba8y7 6g el1jcsrth at a height of 3600 km.    $\times 10^3$

  The space shuttle releashs7d fg y keisb2vs p5(u/((q0es a satellite into a circular orbit 650 km above the Earth. How fast m(sb0yh (7q e 5gdvi2s(/pfskuust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindu9*hh 35wzlzy rical spaceship rotate if occupants are to experience simulated ylu 95z3*whzh gravity of 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 g lxg9sie7m l7./izv1takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of th9 l.7x/gzms 7vglei1i e 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 o) gb t5orw2dqs /*y jpi.+j0qef Mt. Everest to be plwj ybj.ge/* o5 di0s+ p2qtq)raced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit tcd5g, m4k usg5i;hj ctb- 1fz ewd;7p.he Moon a pt;f ,c5m;u 5dbg.dkh4gw7c1e ijsz- t an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunksv4om49trt13ud )tr tg of ice that orbit the planet. The inner radius of the rings ) 344rt dt1tru t9vmogis 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 s (see F 0( jqwfsrd5e2ig. 5–9). What is the ratio of a person’s s0j5(rfd2 ewqapparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaus1134b bldqp po1jc3+ z5gju30ncgqbt 4200 km from the center of the Earth's Moon in a space vehicle (a) moving atgj111qn35pb pc d0+zog3bblj sq4 cu3 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 star 89 8 oeq .8z5vtj4a1w-zntdz wqoc g6ylwyi6;s of equal mass. They are observed to be separated by 360 million km and tzcqo8j9zy;wq gt6ae4.o- wt 6ivd8 ny 15w8z lake 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 i rq)r 5q14mopkn an elevator that movo5k p m)4rrqq1es
(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 elv/t,s9/h yt yhevator. The cord can withstand a tension of 220 N a yy/hst/ th,v9nd breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface oghz06o (p.gkx * )ibeof a planet with period T , the denoi hx.b0zp ek)*g(og6 sity (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 periovy:y*v.iw hkpw-s * )qd of an artifici ypqkvys*:h.*- vw i)wal satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hunxjfa o hpn* yjp)3+6y/dred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fna+3) /6phx*jypf oyjrom the Sun?    $\times 10^{11}$

  Neptune is an average distance oalxei - 2 tf7ks-goh/-yejw68f 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 oniip 16yji np7/ce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest p y1ini6pj7/ idistance 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 asjg1l5bag fc e9. (-2tkfg 2z9k6mxhcenter 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 distan)86p n :xoeipuocgzm5 0z0u2j ce for the four largest moons of Jupiter (th68jz0op p5u0gzionxu) :2 m ecose 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 tqp2 3 :ya/k 2 ybolu7zm/j9mouhe Earth from the known period and distance of the Moon. upu 9ykob3zmma:y2oj/7/ql 2    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kya-zy167wmnr9qc 9nlq 6s pv0 epler’s third law. Use the 619 carn-w9zq7svpymyq0n6ldistance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter cons w8 k hrzyid *1;x:d5f)l8q uudyrd1j.ists of many fragments (which some space scientists think came 1uqifh81.8; jlx:u*rzyrk5d d yd)wd from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes anh imcj1 fgwq :/5d*1pj artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exmwqip/1 jd1j fgh5 :c*actly 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 swingi8h44 ulbcoilcx ; 7v3xng in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, wh;vcil4o cl 7u8x3h4 xbat 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 Earthjo/d21ey y ,nc’s surface will the acceleration of gravity be half what it is on the surfa1nycd,j /2oye ce?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in 3+gjnt8p8q nza mutual circle once every 2.5 s. If we assume their armstn388 +zqg jpn are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appare2z4nx 4z0ewmx nsth0 .nt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotat4z0zxeh t4x0n .2s wmne. 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 dir*b h;qoj-)c(azgjbo a-o(3c puf+ 6ftectly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite j) *z t3+(ap;u(-bfocahjf6goqo-c b forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sc n )4+st 6k5fob.ncsvnale in an elevator, it says your mas5b o 4 )ns6ckfvsnt+.ns is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulaonk wnwv;1. ;tts)8q or 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 grav;o.)qno;nvwt1s t8k w ity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his qdi ( jt40psh;p01olw aircraft 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 p(sk4 efwrw5 9alanet in terms of its radius r, the acceleration due to gravity wf4ek(w5ras 9 at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string)cvjxqy(v/k/e76 eeik4 z9xv 2 is deflected from the vertical by an a4ky ve7zc(v 6kv / xxqi/ee9j2ngle $\theta$ 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 )s;2iamyw w+namy(6 .f+q s ybtld+0wbanked for a design speed of If the coefficient of static friction nq ).a;+mw tfw w0ymyb s+2si(l6+yadis 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast .nz.ayn/;:z ibcis3 b,x5 gsothat objects at the equato, 3/.sso.cbyzginbx : i;azn5r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain ap. prypuoi(s j5j;u ): constant distance 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 z q;d.v9j 6xdoa curve of radius 235 m. A lamp suspj .xod q6d;v9zended 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. Thusvdjaryf8) s6w-qinh/t)ae8 8 , it has been claimed that a person would be crushed by the force of gravity di8 na)er8yaswf8t)j h/v-q6 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 would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presea+b2kgtx s*2 o5myb ,vnce of an extremely massive core in the distant galaxy M87, so dense that it could be atkovx +,2bbm* 5 as2gy 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 7h sc d8: : ;rrrm-(ozffux:f5lj8mw v-dl mi; as it traverses 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 dvol-w chrr:ffu-im: lfs7:m; z(xd88 rjm;5 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 with the road at A?

  The Navstar Global Pw4xw;piq8v/(zi bsgqs s88ct55ayh 3 ositioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters ps 4t;a8 isy(b8vw35x8g z/c qiswq5h. 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 .4of2(6bagp m3mhvnk(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid E3b6 p(hamf.kv2o nm 4gros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in nea25fq*5ffnjzs 4g h( xed of repair. You are in a circular orbit of the same radius as the satelnh5fgjq sa2(5*4 zxfflite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 umg(gzs+ rz k5xa8/2qz-rvr3 years. (a) What is its mean distance frguzm r2s(x +z5gzv8q ra3-k/r om the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if yo+i// nw(6 zliscip0w0x -akpy .lrcr9u could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, lcxs w 00an+k-p/wi ir iy6(l z.pcr9l/ike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.rizrkwj+ :6 /z7z ayt929g gba 5-46) at a dista9rr/ jkigz zta92a+ y7gwb z6:nce of about 30,000 light-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 xqn))f qj;i)ay;fp3/*wq0 qx+se4 mhveaq c 9 square 0.50 m on each side. Find the magnitude and direction of the gravitation*aqm4 9/p cvxfy)w;ahjq;e+iq)q)0q3 xs fneal force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 j ;vz*dc6oig1h:jnw y(i z-v 6kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-lo*fy x crx7(g.jng sweep second hand on your wrist watch?g7c* x(fj y.xr    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aro k v5y3hh3abb2*k-e tkund in a circle below you on a 0.25-m piece of fishing line. The weig5kva bh* k3kt2ey3 hb-ht 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 designed so that a car 6 eu dfb:(hv 5iexjtt-95mvvj. a-h5otraveling at spe:h5(ouvajtvbemd.6i v9jxh--f 5t5 e ed $ 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 Ac bpwx9gm m 7zg6,xq4h8ela, 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 no hx8gp79 bz6w4,m xqgmrmal 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.$\approx$    $\times 10^2$