Calculating Torque on a Trap Door: Question and Equations

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To calculate the torque on a trap door held at a 65° angle, the relevant equation is T = rFsin(x). The trap door, measuring 1.65 m and weighing 11.8 kg, experiences torque from both the tension in the rope and the gravitational force acting at its center of mass. The system is in equilibrium, meaning the sum of the torques must equal zero, leading to the relationship Tc = Tg. By analyzing the forces and drawing a free body diagram, one can determine the effective radius and force needed for the torque calculation. Understanding these principles is essential for solving the problem accurately.
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Homework Statement



A trap door, of length and width 1.65 m, is held open at an angle of 65.0° with respect to the floor. A rope is attached to the raised edge of the door and fastened to the wall behind the door in such a position that the rope pulls perpendicularly to the trap door. If the mass of the trap door is 11.8 kg, what is the torque exerted on the trap door by the rope?


Homework Equations



T=rFsin(x)

The Attempt at a Solution


I can't seem to figure this out. I am not sure how to get exact values for the radius and Force.. any help would be great, thanks
 
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Draw the door as a bar (no z dimension). Make a free body diagram. Use the hinge as a pivot.
 
I don't think you need the length of the string.

This system is in equilibrium, which means that the sum of the torque must be equal to 0.
The things that cause torque are the tension in the string and the force of gravity. The tension is applied at the end of the rope and gravity pulls from its center of mass. I assume this is a uniform body which means the center of the trapdoor is its center of mass.

ƩT=Tc-Tg
0=Tc-Tg
Tg=Tc

Now break down the torque of gravity into its definition.
 

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