A trapdoor on a stage has a mass of 16.3 kg and a width of 1.51 m (hinge side to
ID: 1374655 • Letter: A
Question
A trapdoor on a stage has a mass of 16.3 kg and a width of 1.51 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?
A trapdoor on a stage has a mass of 16.3 kg and a width of 1.51 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 timeExplanation / Answer
The angle here is
theta = Arcsin(1.13/1.41)
theta = 53.266 degrees
Thus, summing torques, as the weight is at the middle, r = 0.755 m,
T (1.41)(sin 53.266 degrees) - (16.3)(9.8)(0.755)sin(90 - 53.266) = 0
Solving for T,
T = 63.8 N [ANSWER]
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