# Calculating mass of object by lifting edge

Assuming a solid rectangular plate, hinged along one edge. How does one calculate the mass of the plate if the force necessary to lift the opposite edge is known?

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Something's missing in your problem... – Pygmalion May 10 '12 at 12:35
@Pygmalion What are you thinking of? It is ok to make generic assumptions regarding mass and dimensons. – ARF May 10 '12 at 13:48
As described, plate is the vertical position at the start. If you wish to lift it, you have exert some force. What is the direction of the force? And don't forget that after applying force, the plate will start accelerating... Problem is hugely underdefined. – Pygmalion May 10 '12 at 13:55
Have you ever heard of a Free Body Diagram ? – ja72 May 10 '12 at 18:35
Does the problem assume slow (static) lifting, or a sudden lift with appreciable vertical acceleration? The answer is different for those two cases. – ja72 May 10 '12 at 19:29

You know the force $F$ that you're using to lift the end of the plate, and you want to know the force $mg$, where $m$ is the mass of the plate and $g$ is the acceleration due to gravity.
You find $mg$ by taking moments about the hinge. The distance from the hinge to the end of the plater where you're applying the force is $l$, and if the plate is a rectangle the force $mg$ acts from the centre of mass, which is $l/2$ away from the hinge.