Question

3. A 75 g , 33-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10 g ball of clay traveling horizontally at 2.2 m/s hits and sticks to the very bottom tip of the rod.

To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?

Answer 1

Given that:

Mass of the rod, M = 75 g = 0.075 kg

Length of the rod, L = 33 cm = 0.33 m

Mass of ball, m = 10 g = 0.01 kg

Initial speed of the ball, V = 2.2 m/s

Moment of inertia of the rod-ball system is given by:

Apply law of conservation of angular momentum to determine angular speed of the rod+mass system:

Apply law of conservation of mechanical energy:

Initial rotational kinetic energy = Gravitational potential energy

That is Maximum angle the rod rotate is 25.9^o