An open door of mass 5m and width L is at rest when it is struck...

An open door of mass 5m and width L is at rest when it is struck by a thrown ball of clay of mass m. The ball is moving at a constant velocity ? ⃗ = −??̂ and hits the door a distance L/2 from the rotation axis through the hinges. The clay ball strikes perpendicular to the door face and sticks after it hits. Neglect the thickness of the hinges. All calculations must be carried with good, consistent vector notation. Simplify all results and write in terms of known quantities.

(a) Calculate the initial angular momentum vector of the door+clay system and state any assumptions you make.

(b) Calculate the final rotational inertia of the door + clay system.

(c) Starting from first principles, calculate the final angular velocity vector of the door+clay system and explain whether this result is reasonable.

(d) Calculate the percentage change in kinetic energy of the door+clay system as a result of the collision, then use the result to explain what percentage of the total mechanical energy was dissipated in the collision.

Expert Solution

genius_generous answered 2 years ago

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