While exploring a castle, Exena the Exterminator is spotted by a dragon who chas

Question

While exploring a castle, Exena the Exterminator is spotted by a dragon who chases her down a hallway. Exena runs into a room and attempts to swing the heavy door shut before the dragon gets her. The door is initially perpendicular to the wall, so it must be turned through to close. The door has a height of 2.90 and a width of 1.15 , and its weight is 800 . You can ignore the friction at the hinges. If Exena applies a force of 280 at the edge of the door and perpendicular to it, how much time does it take her to close the door? Use 9.80 for the acceleration due to gravity.

Explanation / Answer

torque T= F * moment arm = 280*1.15 = 322 N-m......... I = (m*r^2 / 3 = (800/9.8)*1.15^2 / 3 = 36 kg.m^2 T = I * alfa ====> alfa ====> alfa = T/I = 8.94 rad/s^2. angular displacement = (1/2)*alfa*t^2 ==> t = sqrt ( 2*(pi/2) / alfa) = 0.59 sec

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