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 to her. The door is initially perpendicular to the wall, so it must be turned through 90 degrees to close it. 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?

Explanation / Answer

torque = I*alpha = LF

torque = LF = 220*1.25 = 275 N-m

I for rod = (ML^2)/3

I = 750*1.25^/(3*9.81) = 39.9 Kg-m^2

alpha =torque/I = 275/39.9

alpha = 6.89 rad-sec^2

wi = 0

theta = 90 deg = pi/2 rad

theta = wi*t + 0.5*alpha*t^2

t = sqrt(2*theta/alpha)

t = sqrt(2*pi/(2*6.89)) = 0.675 sec

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