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If actually weighing the plates is impractical, you could try hanging the plates from a spring, and testing to find the spring's k value, and recording the displacement of the object while hanging from the spring, and use that to calculate the force on the plate, which equals mg.

if the density is known, you could immerse the plates in something to find their volume and then calculate their weight from that.

or, you could try and pull them with a force meter, taking two data points so that you can solve for the both the friction coefficient and weight.

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Q: How can we calculate the weight of iron plates?
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