Horizontal Force on a Gate Hinge?

AI Thread Summary
The discussion focuses on calculating the horizontal force exerted by the top hinge on a door in equilibrium. The door's weight and hinge configuration are established, with a mass of 10.5 kg and hinges spaced 0.7 m apart. The vertical forces are balanced, but the participants express confusion about deriving the horizontal forces. Emphasis is placed on considering the torque at the bottom hinge to understand the horizontal component. The conversation highlights the need for a thorough analysis of forces and torques to solve the problem effectively.
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A door is attached to a frame by two hinges and is at equilibrium. All forces and torques are therefore balanced.

The door has a mass of 10.5kg, a width of 1.1m, and the two hinges are 0.7m apart.
Find the direction and magnitude of the horizontal force applied to the door by the top hinge?

I think I've got the vertical component of the forces sorted. The downward gravitational force on the door must be equal to the upward force provided by the hinges, with each hinge presumably supplying equal force. As for the horizontal forces, I'm at a loss.

I'd appreciate a detailed response so I can answer variations on this question in the future. Thanks for your time!
 
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Think about where the centre of mass of the door is, and think why they wrote "All forces and torques are therefore balanced."
 
I'm afraid I've already factored the center of mass into an extended free-body diagram and am still left scratching my head.
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I'm just not sure how to derive horizontal component forces from the system.
I understand that upwards force must equal downwards force:

m.g = V1 + V2 where V is the upwards force supplied by each hinge.

But when it comes to the horizontal aspect, I'm at a loss...
 
Think about the torque on the bottom hinge.
 
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