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I was recently watching someone weighing the grind of an espresso in a portafilter. Baristas have to measure the weight of the grind in order to know if the grinder is outputting the correct amount of coffee by the gram.

We use a pretty simple scale which measures by the gram and we can tare the initial weight to actually measure what we are weighing.

Because the portafilter is pretty big, a lot of people have the handle on the table with the main portion of the portafilter (the metal part) on the scale. For reference here is a picture and you can imagine the scale being only under the metal part.

enter image description here

Someone called out to me recently that because the handle is on the table, it wouldn't be good measure because the table is "supporting" the weight of whatever you add on the other side since the weight would get distributed. I see a lot of baristas do this so was curious how much of an impact is this really? My initial thought was that because we are taring the initial amount, that weight is accounted for? Also the support from the table happens on both sides I would think?

I imagine since most of the weight is on the portafilter side, perhaps it's negligible? Maybe I misunderstand the physics entirely.

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This seems legit to me. When you apply a vertical downward force to a beam that is supported at both ends (which this could be modeled as), the effect on the reaction forces from the two supports depends on the position of the applied load relative to the supports. If the applied load is halfway between them, then it will be shared equally between the supports. However, as you move the applied load towards one of the supports, the proportion of the load that is reacted by that support increases. Once the applied load is directly above one of the support points, then all of the load will be reacted by that support and none by the other support that is further away.

This can be shown by equating moments around the support that the load is directly above: in this case, the reaction force on the other support must be the same as it was without the applied load.

So, given the load applied by the ground coffee is very close to the reaction force that is being measured by the scale, the tared scale should give a good indication of the mass of the grind. Seems like your barista has a good handle on their Physics :-)

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  • $\begingroup$ Ahh okay that's what I suspected. To clarify for my sake, does center of mass matter at all in this problem? $\endgroup$
    – aug
    Aug 22, 2018 at 22:11
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    $\begingroup$ @aug the center of mass of the portafilter would determine the values of the reaction forces at the two supports, before the ground coffee is added. However, it is taken into account in the taring of the scale, so it won't affect the resulting measurement. $\endgroup$
    – Time4Tea
    Aug 23, 2018 at 14:17
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    $\begingroup$ @aug this relates to a branch of Structural Mechanics called Beam Theory. This case is an example of (three-point bending)[en.wikipedia.org/wiki/Beam_theory#Three-point_bending] $\endgroup$
    – Time4Tea
    Aug 23, 2018 at 14:19

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