Because of your physics background, you have been asked to be a stunt consultant

Question

Because of your physics background, you have been asked to be a stunt consultant for a motion picture about a genetically synthesized prehistoric creature that escapes from captivity and terrorizes the city. The scene you are asked to review has the three main characters of the movie being chased by the creature through an old warehouse. At the exit of the warehouse is a thick steel fire door 10 feet high and L=7.0 feet wide weighing about W=2950 lbs . In the scene, the three actors are to flee from the building and close the fire door (initially at rest), thus sealing the creature inside the building. With the creature running at v=30 mph, they have only 5.0 seconds to shut the door. You are asked to determine if they can do it by calculating how long it would take them to actually close the door. You estimate that each actor can each push on the door with a force of F=50 lbs. When they push together , each actor needs a space of about d=1.5 feet between them and the next actor. The door, which has a moment of inertia of 1/3 as much as if all its mass were concentrated at the far end from the hinge, needs to rotate =120 degrees for it to close completely.

Explanation / Answer

Net torque about the hinge, T = I

=> (50 * 32.2) * (4 + 5.5 + 7) = (2950 * 72 / 3)

=> = 0.55 rad/s2

= t2/2 = 120 * / 180

=> t = [2 * 120 * / (180 * 0.55)]1/2 = 2.8 s

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