A trapdoor on a stage has a mass of 16.9 kg and a width of 1.58 m (hinge side to

Question

A trapdoor on a stage has a mass of 16.9 kg and a width of 1.58 m (hinge side to handle side). The door can be treated as having uniform thickness and density. A small handle on the door is 1.41 m away from the hinge side. A rope is tied to the handle and used to raise the door. At one instant, the rope is horizontal, and the trapdoor has been partly opened so that the handle is 1.13 m above the floor. What is the tension, T, in the rope at this time?

can someone please help me with the procedure and work through this...

Explanation / Answer

The rope is tied to the handle of the trap door, is horizontal, and crosses the "y" axis at y = 1.13

The trap door passes through the origin (0, 0) and the handle at (x, 1.13) forming a right triangle with the length of the hypotenuse = 1.41 and the length of the vertical leg = 1.13

The horizontal leg of the triangle equals the sqrt(1.41^2 - 1.13^2) or 0.8433

The center of gravity of the trap door is 1.58 / 2 =0.79 meters along the hypotenuse since it has uniform density and thickness

At the instant the rope is horizontal

The rope exerts a clockwise torque around the hinge of (1.41m)(xkg) which balances the weight of the trap door which is exerting a counterclockwise torque of (0.79m)(16.9kg).

Actually, the force on the rope is a little higher since it was only in the specified position for an instant as it was being raised.
So, at the reference instant, (1.41)(x) = (0.79m)(16.9kg); and the rope tension (x) = (0.79m)(16.9kg) / 1.41 = 9.47kgor 92.88N

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