A gate is free to rotate without friction about its hinges at H. The gate is ini

Question

A gate is free to rotate without friction about its hinges at H. The gate is initially at rest. A 4.00 kg ball of mud is thrown at 18.0 m/s towards the center of the gate and the path of the mud is perpendicular to the plane of the gate. A) Compute the magnitude of the mud's angular momentum about H. B) If the gate has a rotational inertia of 2.00 kg-m^2, compute the angular velocity of the system after the mud hits and sticks to the gate. C) How much kinetic energy is lost (converted to other forms) in this collision?

Explanation / Answer

NOTE-since dimention of gate is not given

let distance of hinge H from centre of gate is 'd'

a)angular momentum=mv*d=18*4d=72d

b)angular momentum=72d=I*omega

omega=36d rad

c)assume inelastic collision

loss of eneggy=1/2*2*18^2-1/2*2*36d^2=648-1296d^2

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