A trapdoor on a stage has a mass of 19.3 kg and a width of 1.53 m (hinge side to
ID: 2264327 • Letter: A
Question
A trapdoor on a stage has a mass of 19.3kg and a width of 1.53m (hinge side to handle side). The door can be treated as having uniform thickness and density. A small handle on the door is 1.41m 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 1.13m above the floor. What is the tension, T , in the rope at this time?
A trapdoor on a stage has a mass of 19.3kg and a width of 1.53m (hinge side to handle side). The door can be treated as having uniform thickness and density. A small handle on the door is 1.41m 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 1.13m above the floor. What is the tension, T , in the rope at this time?Explanation / Answer
sin(theta)=1.13/1.41
=> theta=53.26 degrees
by moment balance about the hinged point
T*1.13=mg*L*cos(theta)/2
==> T= 19.3*9.8*1.53*cos(53.26 degrees)/(2*1.13)=76.59 N
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