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...

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.