You go to push a 1m door open but you realize you push form the wrong edge of th

Question

You go to push a 1m door open but you realize you push form the wrong edge of the door. If youre pushing with a force of 110 N what is the torque you are applying if you push 10 cm from the hinges? What is the doors acceleration? You then realize your mistake and push on the other end of the door, pushing 10 cm from the outer edge of the door with the same force. What is the applied torque and the doors acceleration? Where on the door must you push to apply a 75 Mn torque? Assume you are pushing perpendicular to the door in all cases.

Explanation / Answer

torque acting on the door

T = r F = (0.1 m) ( 110 N) = 11 N m

Angular accleration of the door

T = I alpha

alpha = T/I = 11 Nm/ ( 1/3) m d^2 = 11 Nm / ( 1/3) m ( 1m)^2 = 33/m rad/s^2

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T = r F = ( 1m - 10cm) 110 N = 99 Nm

alpha = T/I = 99 Nm/ ( 1/3) m d^2 = 99Nm / ( 1/3) m ( 1m)^2 = 297/m rad/s^2

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