You are working as a consultant for a movie about an alien creature to determine

Question

You are working as a consultant for a movie about an alien creature to determine whether a scene is physically plausible. In one scene, the creature chases 3 actors through a building who run into a room with a 8000-pound steel fire door that is 10 ft high, 6.5  ft wide, and 3.0 inches thick. The actors need to close the door to save themselves from the creature, who runs at 30 mph, giving them 5.0 seconds. Each actor pushes with 59  pounds of force and they need 1.5 feet of space between them to all push together. The door rotates 120 degrees to close and has a moment of inertia of 1/3 as much as if all its mass were concentrated at the edge furthest from the hinge.

How long will it take the actors to close the steel door?  This will determine if the creature escapes!

Explanation / Answer

Ans:- A steel fire door 8000 Pound. door closed time 30 mph. each actor phuse the doors distane 1.5 feet for space & applied 59 pound force in 5 sec.

door rotating 120 degrees to closed moment of inertia 1/3 the mass concentrated as a edge from the hinge.

so we are very cleared no need the dimension of the door. we should find the momentum of inertia for the distance in  pushes force applied. now we are using the equation

I=r2dA  

r is denoted as vertical distance to the hinge, is denoted as the surface density of the steel fire door,                   dA = is denoted as height of the door into the area differential.

    r = 6.5 feet

    = 3,4 lb/cu.ft      (Suppose the fire steel door are insulated doors for polyisocyanurate sheet core

dA = 10 feet

I =(6.5)2 X3.4 x10 = 1436.7  lb. ft2

as per equation the moment of inertia 1/3 the mass concentrated as a edge from the hinge. it means 478.83 lb. ft2.

if I= (mass*((width^2)+(thickness^2)))/12

I = (8000 * ((6.5)2 +( 0.25)2)))/12 =20208.3                             ( thickness 3 inch = 0.25 feet)

Total moment of inertia = 20208.3 in fore steel doors.

time taken for the door to closed = 20208.3/ 478.83 = 42.2

when force applied in 1.5 feet in distance of each. a door rotation 30 mph, it mean in 1 sec 0.0083 mps. so as given 5 sec , 0.0083 x 5 = 0.042 mps.

we know 1 feet/sec is equal to 0.6818 mile/hour .so we are getting 28.8 mile/hour. 0.008 mps

so it not possible to close the doors in 5 sec . because of it only move 0.008 mps after force applied the door .it means doors will not closed at a time .

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