The iron door of a building is 3m broad. It can be opened by applying a force of 100N normally at the middle of the door. Calculate (a) the torque needed to open the door, (b) the least force and its point of application to open the door.

The iron door of a building is 3m broad. It can be opened by applying

1.	The iron door of a building is 3m broad. It can be opened by applying a force of 100N normally at the middle of the door. Calculate (a) the torque needed to open the door, (b) the least force and its point of application to open the door.
Answer» Solution :(a) Given F=100N distance of point of application of force `r=1/2 times` BREADTH of door `=1/2 times 3m=1.5 m` Moment of force (torque) NEEDED to open the door `= F times r=100N times 1.5 m=150 Nm`…….(i) (b) The force required will be least if it is applied at the farthest point from the HINGES. Therefore the force should be applied at the FREE end of the door i.e at a distance of 3m from the hinges. Let the force required be F. newton , then Moment of force =`F. times 3N m` From eqns. (i) and (ii) `F. times 3=150` `therefore F.=150/3=50N`