# A uniform rectangular trapdoor of mass #m=4.0kg# is hinged at one end. It is held open, making an angle #theta=60^@# to the horizontal, with a force magnitude #F# at the open end acting perpendicular to the trapdoor. Find the force on the trapdoor?

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This diagram was given as a hint. I was working based on #phi=theta=60^@# (not sure if this is right). I'm not too sure what causes the force N. By taking moments about the hinge, I got #F=19.62N# , but this apparently is not the correct answer.

Thank you very much in advance!

This diagram was given as a hint. I was working based on

Thank you very much in advance!

##### 1 Answer

You are almost got it !! See below.

#### Explanation:

The trap door is

So the center of mass is at

The inclination of the door is

This acts at distance

So you have a moment relation like this:

or