trap door of length and width 1.65 m is held open at an angle of 65.0 degree 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 16.8 kg, what is the torque exerted on the trap door by the rope?

The torque applied by the rope must equal the torque applied by the weight. Compute it at the hinge, to make the problem simpler. The center of mass of the door, where the weight acts, is in the middle of the door.

Torque = M*g*(width/2)*cos65
= 57.4 N-m

To find the torque exerted on the trap door by the rope, we need to use the equation:

Torque = Force x Distance x sin(θ)

Here's how you can find the torque step by step:

1. Determine the force exerted by the rope. Since the rope pulls perpendicularly to the trap door, the force will be equal to the weight of the trap door. Use the equation:

Force = Mass x Gravity

Given that the mass of the trap door is 16.8 kg and the acceleration due to gravity is approximately 9.8 m/s^2, calculate the force:

Force = 16.8 kg x 9.8 m/s^2

2. Calculate the distance from the point where the force is applied (raised edge of the door) to the pivot point (hinge). In this case, the length of the trap door (1.65 m) is the distance.

Distance = 1.65 m

3. Determine the angle between the force vector and the perpendicular line from the pivot point to the line of action of the force. In this case, the angle is given as 65 degrees.

θ = 65 degrees

4. Convert the angle from degrees to radians since the sine function in the torque equation uses radians:

θ (radians) = θ (degrees) x π/180

θ (radians) = 65 degrees x π/180

5. Calculate the torque using the equation:

Torque = Force x Distance x sin(θ)

Plug in the values:

Torque = Force x Distance x sin(θ)

Torque = (16.8 kg x 9.8 m/s^2) x 1.65 m x sin(65 degrees x π/180)

6. Calculate the final result:

Torque = (16.8 kg x 9.8 m/s^2) x 1.65 m x sin(1.134 radians)

Once you calculate this expression, you will find the torque exerted on the trap door by the rope.