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Ch19_Sec3-4_Ex-43-45-48

Ch19_Sec3-4_Ex-43-45-48 - r 1 19-43 The pendulunj consists...

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Unformatted text preview: r 1 19-43. The pendulunj consists of a 5-lb slender rod AB and a lO-lb wooden bl ck. A projectile weighing 0.2 lb is ﬁred into the center of hei:lock with a velocity of 1000 ft/s. If the pendulum is i iti embeds itself into t e ’lly at rest, and the projectile lock, determine the angular velocity of the pendul‘ m just after the impact. lax: Moment of Inertia :9 The mass moment inertia of the pendulum and 1c embeded bullet about point/l is ’5 1 s (I 1 =_. — 2 ___. 2 ‘)- 12(32.2)(2 ) + 32.2“1 ) +€a(%)< = 2.239 slug . nﬂ l() 0.2 2 z 2 3 1+1)+3—23(2.5)+322(2.5) Lutnservarian of AngularaMamemum : Since force F due to the impact ’ Internal to the system consiéting of the pendulum and the bullet. it will cancel “1- Thus. angular momentum is conserved about pointA. Applying @1947. we have (HA). =05): (mbvarb = (IA)2 Q): E 0.2 ( )(1000)(2.5) = 2.23912)z a;a = 15.94 rad/s Ans 19.45. A thin ring having a mass of 15 kg strikes the 20-mm-high step. Determine the largest angular velocity €01 the ring can have so that it will not rebound off the step at A when it strikes it. The weigh: is non - impulsive. (H4 )V‘ =‘ (Ht); 15(4)(o.18xo.13 —o.02)+[15(o. 1101]“). ) = [15(0. 18)' + 15(0.18)1]aa m; =3 0.9444m +\z‘r, = mag»; (15)(9.81)cos O—N‘ = l5m}(0.18) When hoop is about to rebound. NA - 0. Also. cose= %' and so (01 A 6. 9602 rad/s 6.9602 ~__.= ,7 l Dhaoﬁ 73 rad: *19-48. The d It has a mass of 15 kg. If it is released from rest when ‘5 30“, determine the maximum angle 0 of rebound afte ilt collides with the wall.The coefﬁcient of restitution tteen the disk and the wall is e = 0.6. When 9 = 0°,t e isk hangs such that it just touches the wall. Neglect frqetion at the pin C. i l Damm atlowct posihoh of G. L 1 H+K=n+u f‘ / ‘ w 1 0+(15)(9.81)(o. 1%)(i—cos30“) = %[%(l5)(0.15)1]a} +0 } 0= 3.418 rad/s ;) = =;‘-(-o.15ai) ( ) ° 0'6 *3.318(0.lS)-’0 a: = 2.0st lad/s T2 1’ ‘6 = T3 + K 1 3 1 5[5(15)(0.15)‘]l2.bsoze)z +0 = 0+15(9.81)(o.15)(1-coso) 9= l7.9° Am! ...
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