申論題

1.A uniform rectangular wooden board of mass M is pivoted horizontally along its top edge without friction. The vertical edge of the board has length L. (a) Show that the moment of inertia of the board is ML²/3. A bullet of mass m and horizontal velocity u strikes the board at the center and is embedded in the board. (b) Calculate the angular velocity of the board right after the impact and express it in terms of m, M, u and L. (c) If M = 0.900 kg, m = 0.0100 kg, and L = 0.500 m, what is the minimum u needed to swing the board over? (15%) (g = 9.80 m/s²)