You have a ballistic pendulum. However, in the case of this pendulum, the mass o

Question

You have a ballistic pendulum. However, in the case of this pendulum, the mass of the rod (which is of length L) cannot be neglected and is given as Mr. The mass of the projectile is mp, and the mass of the pendulum bob is Mb. During the experiment the projectile strikes the bob and becomes stuck within. After the collision the pendulum undergoes simple harmonic motion with an amplitude of theta. The projectile may be treated as a point particles for purposes of calculating the moment of Inertia. The pendulum bob should be treated as a hollow sphere of radius r and with Icm=(2/3)Mb(r^2) a) Find the angular frequency and the period of oscillation. b) Find the initial speed vo of the projectile.

Explanation / Answer

this can be solved using principle of Conservation of angular momentum about the axis of rotation of the pendulum. w = angular velocity of system after collision. mp * v0 * L = [mp * L^2 + (2/3)Mb(r^2)+Mb(L^2) + Mr*(L^2)/3] w thus we get w as w= [mp * v0 * L]/[mp * L^2 + (2/3)Mb(r^2)+Mb(L^2) + Mr*(L^2)/3]

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