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.

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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.

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