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Doors and Torque



A few days ago, my sister and I were leaving school.  As our hands were both full, she used her body weight in order to push on the main door in order to exit the building.  However, the door would not budge.  I quickly realized that my sister, in her attempt to open the door, was not applying torque to her favor in this situation.  Torque, which is the rotational equivalent of linear force, is dependent on three factors: the angle at which the force is applied, the magnitude of the force, and the radius at which the force is being applied.  To simplify my sister's exiting scenario, however, we will only consider force magnitude and radius, because she applied her force at a direction perpendicular to the door, hence applying the whole component of her force.  When my sister went to open the door, the force she applied using her body was concentrated at a location that was somewhere in between the midpoint of the door and the hinge.  Hence the radius at which my sister applied her force to was about 1/4 the length of the door, causing her torque to be of a significantly less magnitude and the door to not move.  All she needed to do was to apply that same force to the end of the door opposite the hinge, which would produce a radius four times bigger than originally, and hence a torque of equally greater magnitude as well.  After this quick switch, the door did indeed open, and we were on our way into the brisk cold.


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