Question

PROBLEM 17.127 Member ABC has a mass of 2.4 kg and is attached to a pin support at B. An 800-g sphere D strikes the end of member ABC with a vertical velocity v of 3 m/s. Knowing that L = 750 mm and that the coefficient of restitution between the sphere and member ABC is 0.5, determine immediately after the impact (a) the angular velocity of member ABC, (b) the velocity of the sphere A С

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Answer 1

Solution :-

Solution to this problem is based on the concept of collision principles and conservation of angular momentum (L). we used the difinition of coefficient of restitution (e) which is defined for point of collision along common normal. And we write conservation of angular momentum (L) about point B, because about point B the contribution of impulsive torque due to hinge becomes zero. Please read solution carefully and feel free to ask any doubt you face while understanding my solution. I would be happy to help.

= 0.8 of 키 O . 3 L = ML2 Sel: (m) mass of ABC = 2.4 kg mass of ephere D (mg) = 800g. 0.8 kg Length of ABC (L) = 150mm = 0.150 m . Let o be the centre mass of ABC. - Sog moment of Inertia of ABC about centre of mass o of A B C, be to 1. just after collision of mass (m.) with point A on ABC, Impulsive force due to hinge at B will act. so We can't apply conservation of angular momentum about o, because of impulsive torque of force at hinge B. Instead we apply conservation of angular momentum about point B. So that the contribution of hinge force becomes Zero (or torque better to say). so just after collision Let w' be the angular velocity acquired. and to be velocity of separation of sphose mv om A B at Impulse C Angular

centre ABC. V - L 4 0.45 = & and to be the velocity of of mass of A from Figure Iwi and VA = { w Applying consecution of angular momentum about B. Linitial - &final moll L + 0 = mul + [50+ mile) Two 0.15 W,' [0.1125+ 0.084315)W! 0.45-0.1500 + 0.196875' Definition of coefficient of restitution. It is defined for point of collision : + Let va be the velocity of Point A before collision. vol be the velocity of Aphere & after collision. A be the relocity of point A after collision. (Coefficient of restitution) e = velocity of reparation velocity of approach point of contact. V VA - - elv-VA) along the common normal the VA=0 before collision point A was at rest. vo - w - - (0.5) x(3) 1 -0.18750 -1.5

9 on loving equation ② and ③ We get a W = 3 rad I see cante clockwise) ( velocity of sphere) u = -0.9375 m/s (upwards) after collision