# Yvonne is pulling on the doorknob of her door to keep it closed while Joyce is pulling from the other side to try to get into the room. The doorknob is 0.7 m from the hinge of the door.  If Yvonne is using a force of 75 N exerted at 75 degrees to the door and Joyce is exerting a force at 80 degrees to the door.  What force does Joyce need to open the door? Yvonne is pulling on the doorknob of her door to keep it closed while Joyce is pulling from the other side to try to get into the room.

The distance of the doorknob is 0.7 m from the hinge of the door.

The force used by Yvonne is 75 N exerted at 75 degrees to the door. This creates a torque about the hinge that is equal to 75*0.7*sin 75.

Joyce exerts a force at 80 degrees to the door. To get in, the torque due to the force should be more than the torque created due to the force exerted by Yvonne.

Let the force Joyce exerts be F. The torque due to this is F*0.7* sin 80.

Equating the two torques:

F*0.7* sin 80 = 75*0.7*sin 75

=> F = 75*0.7*sin 75 / 0.7 * sin 80

=> F = 75 * sin 75/ sin 80

=> F = 73.56 N

The force exerted by Joyce should be greater than 73.56 N.