The door of a room is 1 m wide. The door opens when a force of 10 N is applied at the end perpendicular to the door. What should be the force, if it is applied 50 cm from the hinge and is at 60 degrees to the door.
The width of the door is 1 meter. It opens when a force of 10 N is applied perpendicular to the door at the end. Whether the door opens or not depends on the magnitude of torque due to the applied force.
A force (F) applied a point that lies at a distance D from the pivot point and if the angle between the force and the line joining the point of application and the pivot is theta, the resulting torque is T = F*D*sin theta. Here, the torque required to open the door is 10*1*sin 90 = 10 N*m
Let the magnitude of force applied 50 cm from the hinge and at in a direction making an angle 60 degrees to the plane of the door that can open the door be F.
F*0.5*sin 30 = 10
=> F = 10*2*2 = 40
A force of magnitude 40 N is required to open the door when it is applied at a distance 50 cm from the hinge at an angle of 60 degrees to the plane of the door.