A trap door, of length and width 1.95 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 18.0 kg, what is the torque exerted on the trap door about the hinge by the rope? Enter a positive value if the torque is in counterclockwise direction and enter a negative value if the torque is in clockwise direction. Note: Give your answer in units of N-m. Do not explicitly include units in your answer, however (include number only). Including units (like cm) will result in the question being scored wrong. 65.0° The following image may help think this one through. 65.0° 65.0°

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A trap door, of length and width 1.95 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 18.0 kg, what is the torque exerted on the trap door about the hinge by the rope? Enter a positive value if the torque is in counterclockwise direction and enter a negative value if the torque is in clockwise direction. **Note:** Give your answer in units of N·m. Do not explicitly include units in your answer, however (include number only). Including units (like cm) will result in the question being scored wrong.

The following image may help think this one through.

### Diagrams:

**Top Diagram:**
- The diagram shows a side view of the trap door held open at an angle of 65.0° with a wall and a hinge pivot at the bottom.
- The rope is shown pulling perpendicularly towards the wall from the raised edge of the door.

**Bottom Diagram:**
- This diagram offers a more detailed look at the trap door, illustrating forces and angles.
- The length of the trap door is marked as \( L \), and the gravitational force \( mg \) is shown acting downwards from the center of the door.
- Both the angle between the door and the wall and the downward direction of gravity are marked as 65.0°.
Transcribed Image Text:A trap door, of length and width 1.95 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 18.0 kg, what is the torque exerted on the trap door about the hinge by the rope? Enter a positive value if the torque is in counterclockwise direction and enter a negative value if the torque is in clockwise direction. **Note:** Give your answer in units of N·m. Do not explicitly include units in your answer, however (include number only). Including units (like cm) will result in the question being scored wrong. The following image may help think this one through. ### Diagrams: **Top Diagram:** - The diagram shows a side view of the trap door held open at an angle of 65.0° with a wall and a hinge pivot at the bottom. - The rope is shown pulling perpendicularly towards the wall from the raised edge of the door. **Bottom Diagram:** - This diagram offers a more detailed look at the trap door, illustrating forces and angles. - The length of the trap door is marked as \( L \), and the gravitational force \( mg \) is shown acting downwards from the center of the door. - Both the angle between the door and the wall and the downward direction of gravity are marked as 65.0°.
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