While exploring a castle, Exena the Exterminator is spotted by a dragon that 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 90° to close. The door is 3.00 m tall and 1.25 m wide and it weighs 750 N. You can ignore the friction at the hinges. If Exena applies a force of 220 N at the edge of the door and perpendicular to it, how much time does it take her to close the door?
Solution 64P Step 1: Consider the door performs a rotational motion,accelerated by torque exerts on edge is given by J. = F.w = F.w/J Where J moment of inertia angular acceleration w width of the door F length of the lever arm of force Step 2: Moment of inertia of plane rectangular object,rotating around axis through on edge J = 1/3 m w * * Since mass equals W = m/g J = 1/3*(W/g) * 2 Angular acceleration of door is = F 3 g/(W w) * * * = (220 N)* *(9.81 m/s )/(750 N * 1.25 m) = 6.860 s2