Torque exerted on trap door by rope

[streeter]

Homework Statement

A trap door, of length and width 1.55 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 14.6 kg, what is the torque exerted on the trap door by the rope?

Homework Equations

Torque=F(r)

The Attempt at a Solution

Honestly I have no clue.

 

[Astronuc]

This is a statics problem, so the sum of the moments/torques must equal zero. Find each of the moments about the pivot. One of the moments (torques) is due to the rope which is acting perpendicular to the plane (and moment arm) of the trapdoor. The other is the weight, which must be resolved into normal and parallel components with respect to the plane of the trapdoor.

Think about center of mass.

 

[ogb p]

I am not familiar with the specific problem and I am not sure what the variables represent. In order to accurately calculate the torque exerted on the trap door by the rope, we would need more information such as the force applied by the rope and the distance from the pivot point (hinge) to where the force is applied. Additionally, the angle at which the force is applied would also affect the torque calculation. Without this information, it is not possible to provide a specific answer. However, we can use the given information to make some general observations and assumptions.

Firstly, since the rope is attached to the raised edge of the door and pulls perpendicularly to the door, we can assume that the distance from the pivot point to where the rope is attached is equal to the length of the door, 1.55 m. This would make the distance (r) in the torque equation equal to 1.55 m.

Secondly, since the door is being held open at an angle of 65.0°, we can assume that the force applied by the rope is acting at a perpendicular distance of 1.55 m from the pivot point. This means that the force (F) in the torque equation is equal to the weight of the door, which can be calculated using the mass and acceleration due to gravity (9.8 m/s^2).

With these assumptions, we can now calculate the torque exerted on the trap door by the rope using the equation Torque = F(r). Plugging in the values, we get Torque = (14.6 kg * 9.8 m/s^2) * 1.55 m = 226.12 Nm. This means that the rope is exerting a torque of 226.12 Nm on the trap door. However, please keep in mind that these calculations are based on assumptions and may not be completely accurate without more information. In order to provide a more precise answer, we would need to know the exact force applied by the rope and the distance from the pivot point to where the force is applied.