Torque in the Library

On Sunday I was in the library and tried to push open the door. However, it didn't open. I realized I was pushing too close to the hinge. As I moved to push farther away from the hinge, I thought about torque. I realized the reason the door wouldn't open is because the radius, or the distance from the lever arm at which I was exerting force, was not long enough to result in torque to open the door. Even if I pushed harder, the small radius would not be large enough to create torque that opened the door. This is explained by the equation T = rFsinϴ.